Program
Speaker List
All plenary, minisymposia and contributed talks are now posted.
PLEN - plenary talk, MS - minisymposium talk, CT - contributed talk
| CTC1a | Abbas, Fazal | |
|---|---|---|
| University of Guelph | ||
| Biofilm Model in Soil Fractured Media | ||
| biofilms growing in the soil pores lead to a reduction of hydraulic conductivity (bioclogging), which in return leads to a decrease in the supply of nutrients and thus reduced biofilm growth and -- in the context of bioremidiation -- possibly a reduction in purification performance. We introduce a macroscopic model for biofilm formation in porous media, such as soil, starting with the classic mesoscopic one-dimensional biofilm model extended by a recently introduced model for shear induced biomass detachment that explicitly relates biomass loss to the local hydrodynamics. For this purpose we couple the biofilm model with the stokes equations. Homogenization technique is used to upscale the model. We also introduce a new detachment rate expression. The resulting bioclogging model is qualitatively studied with elementary techniques. | ||
| MSE5a | Abedi, Ali | |
| University of Houston, Downtown | ||
| Multivariate Data Analysis: Relationship between Environmental Factors and Vector Frequencies Affecting the Spread of Pierce’s Disease across Texas | ||
| [Jointly presented by Ali Abedi and Audrey Gonzales.] Pierce’s disease (PD) is caused by Xylella fastidiosa (Xf), a plant pathogen that infects grapevines. Sharpshooter insects transfer the bacterium, which multiplies in the xylem (water-conducting vessels), causing plant death. The objective of this study is to analyze the relationship between environmental factors and sharpshooter frequencies. The multivariate data set includes a sample of (n>30) insect frequencies and environmental variables (i.e. elevation, precipitation, cold hardiness) at different vineyard sites. The insect counts were yielded from vineyards which had traps set out over a period of one year. For the statistical analysis of the project, we chose a canonical analysis method, Canonical Correspondence Analysis (CCA), which is developed by the Eigen-analysis technique. This method will be utilized to represent the significance of the vector-environmental variable relationships. The statistical analysis will be completed with the aid of the XLSTAT software package. | ||
| CTF6a | Adams, Ben | |
| University of Bath, UK | ||
| Man Bites Mosquito: Understanding the Contribution of Human Movement to Vector-borne Disease Dynamics | ||
| In metropolitan areas people travel frequently and extensively but often in highly structured commuting patterns. We investigate the role of this type of human movement in the epidemiology of vector-borne pathogens such as dengue. Analysis is based on a metapopulation model where mobile humans connect static mosquito subpopulations. We show that hubs and reservoirs of infection can be places people visit frequently but briefly. The relative importance of human and mosquito populations in maintaining the pathogen depends on the distribution of the mosquito population and the variability in human travel patterns. We conclude that successful public health intervention may require identifying areas with large mosquito populations together with a form of contact tracing that maps recent movements of infected people to pinpoint the mosquito subpopulation from which they acquired the infection and others to which they may have transmitted it. | ||
| Coauthor(s): Durrell D Kapan, University of Hawaii at Manoa | ||
| MSC3a | Alberts, Jon | |
| University of Washington | ||
| Agent-based simulations of filaments, crosslinkers, and motor proteins | ||
| Complicated cellular behaviors emerge from networks of simple molecular and/or force-based interactions, and they underlie all of biology. Our failure to understand such "emergent phenomena” limits progress today in many areas of research. We therefore urgently need new methods for dealing with such complexity. One very promising tool is so-called agent-based computer modeling, which involves the explicit simulation of small-scale local interactions, following the trajectory through time of thousands to millions of states. The construction and application of these models integrates classical mechanics with biophysics and computer science, and it requires a great deal of data from experimental cell biology. Detailed agent-based simulations give us a way to explore, through a blizzard of arithmetic on fast memory-laden computers, the complex emergent behaviors that characterize all interesting cellular behaviors. This mimicking of biological systems in silico does not generate an elegant mathematical encapsulation of a system. But it has the great advantage of avoiding any need to intuit the outcome of myriad biochemical and force feedback loops, a task at which human intelligence is demonstrably frail. I will demonstrate features of a 3-dimensional agent-based modeling framework, describe biophysically realistic actin filament and myosin motor representations, and present results from the modeling of networks of filaments, crosslinkers, and motors. | ||
| CTF7a | Alexander, Helen | |
| Queen's University | ||
| Regulatory T cells in autoimmune disease: dose dependence arises in a stochastic approach | ||
| Regulatory T cells have been identified as playing a key role in preventing autoimmune disease. We present an ordinary differential equation (ODE) model of their action within a system also including self antigen, professional antigen presenting cells, and autoreactive effector T cells. Deterministically, qualitative long-term behaviour is predicted by the basic reproductive ratio (R0): when R0<1, solutions converge to the trivial equilibrium (interpreted as self tolerance), while when R0>1, solutions converge to a non-trivial equilibrium (interpreted as chronic autoimmunity); bistability does not occur. However, a stochastic treatment of the model demonstrates, through Monte Carlo simulation and a branching process approximation, that either long-term tolerance or chronic autoimmunity may arise from the same initial conditions, and that the probability of mounting a chronic repsonse depends on the initial "dose" of self antigen or autoreactive effector T cells. This result parallels observations of dose dependence reported in the biological literature, suggesting that stochastic effects may provide a straightforward explanation for experimental results, in lieu of a more complex ODE model exhibiting deterministic bistability. | ||
| Coauthor(s): Lindi Wahl | ||
| MSG4a | Allard, Jun | |
| University of British Columbia | ||
| Force generation by a dynamic Z-ring in bacterial cell division | ||
| FtsZ, a bacterial homologue of tubulin, plays a central role in bacterial cell division. It is the first of many proteins recruited to the division site to form the Z-ring, a dynamic structure that recycles on the time scale of seconds and is required for division to proceed. FtsZ has been recently shown to form rings inside tubular liposomes and to constrict the liposome membrane without the presence of other proteins, particularly molecular motors that appear to be absent from the bacterial proteome. Here, we propose a mathematical model for the dynamic turnover of the Z-ring and for its ability to generate a constriction force. Force generation is assumed to derive from GTP hydrolysis, which is believed to induce intrinsic curvature in FtsZ filaments. We find that this transition to a curved state is capable of generating a sufficient force to drive cell-wall invagination in vivo and can also explain the constriction seen in the in vitro liposome experiments. Our observations resolve the question of how FtsZ might accomplish cell division despite the highly dynamic nature of the Z-ring and the lack of molecular motors. | ||
| CTA6a | Anazawa, Masahiro | |
| Tohoku Institute of Technology | ||
| Relationships between population models in terms of resource partitioning and spatial aggregation | ||
| The population dynamics of single species with seasonal reproduction are often modeled using difference equations. The aim of this study is to present a unified view to understand the mechanistic basis of discrete-time population models from the viewpoints of resource partitioning and spatial aggregation of individuals. We present a first-principles derivation of a new population model which incorporates both scramble and contest competition by explicitly considering partitioning of resource between individuals in the framework of a site-based model. The derived model has two parameters relating with the type of competition and with the degree of spatial aggregation of individuals respectively. In various limits in these parameters, the derived model incorporates various classical population models. In this sense, this model provides a unified view about relationships between various population models. Furthermore, extending the above argument, we also demonstrate that population models exhibiting the Allee effect can be derived from first principles if assuming a population consisting of females and males. | ||
| CTB6a | Andasari, Vivi | |
| University of Dundee | ||
| Modelling the Cell-Matrix Adhesion Pathway for Cancer Cell Invasion of Tissue | ||
| When invading tissue, malignant tumour cells (i.e. cancer cells) need to detach from neighbouring cells, degrade the basement membrane, and migrate through the extracellular matrix (ECM). These processes require loss of cell-cell adhesion and enhancement of cell-matrix adhesion. We model the cell-matrix adhesion pathway describing interactions between the matrix glycoprotein fibronectin, integrins (cell surface receptors) and actin filaments in the cytoskeleton. Binding of fibronectin with integrins triggers a clustering of protein complexes, which then activates and phosphorylates regulatory proteins that are involved in actin reorganisation causing actin polymerization and stress fibre assembly. Rearrangement of actin filaments with integrin/fibronectin complexes near adhesion sites and interaction with fibrillar fibronectin produces the force necessary for cell migration, accounting for cell-matrix adhesion. The results are used in a continuum model of cancer cell invasion of tissue, along with results from previous research on cell-cell adhesion. | ||
| Coauthor(s): Mark Chaplain | ||
| CTF2a | Andersson, Tom | |
| Stockholm University, Stanford University School of Medicine | ||
| Evaluating competing models of nociceptive neurons with sensitivity analysis | ||
| Peripheral nociceptive neurons have electrophysiological properties that differ from the behavior of other sensory neurons. In particular, slower kinetics, larger overshoots and hyperpolarization. Furthermore, they show characteristic responses to dynamic stimulation, characteristic patterns of oscillation. A number of conductances (ion channels) have been proposed to mediate the behavior. Here we present the method of sensitivity analysis applied to an extended Hodgkin-Huxley model, evaluating the effects of a number of parameter variations. In particular, we compare the relative effects of ion channel type, density, and modulation on nociceptive neuronal output, during both deterministic and stochastic stimulation. We estimate the likelihood of competing models within a multivariate parameter space. Finally, we discuss the implications for neuronal information processing, considering the relations between sensitivty analysis and information theory. | ||
| MSB1d | Andrews, Steven | |
| Lawrence Berkeley National Laboratory | ||
| New particle-based simulation algorithms for molecule-membrane interactions enable a yeast signaling model | ||
| Particle-based simulation is a method for computationally modeling biochemical reaction networks with both spatial and stochastic detail. In it, a simulator represents molecules of interest with individual point-like particles that diffuse, react, and interact with surfaces, all in continuous space. I will present several molecule-surface interaction algorithms. These simulate adsorption, desorption, and transmission through permeable membranes. While technically inexact, these algorithms are nevertheless quite accurate; they are exact in the limit of short simulation time steps, yield correct concentrations at steady-state, are simple to implement, and are computationally efficient. The adsorption algorithm uses a fixed adsorption probability for molecules that diffuse into a surface, the desorption algorithm uses an error-function distributed initial separation between the surface and the desorbed molecules, and the partial transmission algorithm combines these approaches. I implemented and verified these algorithms in the Smoldyn simulator. These new algorithms, along with others, enable a simple model of signal transmission between yeast cells. By investigating the distribution of pheromone molecules that bind to yeast cell receptors, it shows that cells are best able to find the direction to potential mates when approximately half of the receptors are bound to pheromone. It also shows, somewhat paradoxically, that this direction sensing improves substantially when yeast cells secrete a pheromone-degrading protease which destroys some of the pheromone signal before it can be received. This occurs because the protease amplifies the local pheromone concentration gradient. | ||
| MSE4a | Andrews, Steven | |
| Molecular Sciences Institute | ||
| Mechanics can explain coiled shapes of bacterial cytoskeletal polymers | ||
| mages of several cytoskeletal protein polymers in E. coli, B. subtilis, C. crescentus and other bacteria show that they form coils or rings on the inside of the cell membrane. Some of these structures extend the whole length of the cell (e.g. the proteins MreB, Mbl, and TubZ), some are localized primarily to a pole (e.g. MinD), and some form rings (e.g. FtsZ). Using stochastic mechanical simulations, I found that these shapes can arise from the combination of inherent protein polymer mechanics and the constraints that the curved cell membrane imposes. Five polymer morphologies are possible on rod-shaped cells: rings, lines, helices, loops, and polar-targeted circles, where the particular one that arises depends on the polymer’s bending stiffnesses. Each morphology has been observed experimentally. This mechanical explanation is sufficient to explain a wide variety of observed structures. It also provides a simple explanation for the dynamics of the Z-ring in a sporulating B. subtilis: the polymer transforms from a ring to a coil, to 2 rings, and finally constricts. In addition, the theory enables cytoskeletal polymer mechanical parameters to be estimated from fluorescence microscope images. | ||
| CTG7a | Arciero, Julia | |
| University of Pittsburgh | ||
| Predicting migration of the intestinal epithelial cell layer using a continuum mechanical model | ||
| The rapid migration of intestinal epithelial cells at a wound edge is an important initial step in tissue repair. Mathematical modeling of this process may provide insight into the mechanisms that govern cell migration under normal and disease conditions. Here, a two-dimensional continuum mechanical model is used to simulate the motion of the epithelial layer in response to a wound. The model incorporates the effects of the forces acting on the wound edge and induced by lamellipod formation, the adhesion forces between the cell layer and the substrate, and the elastic stress of the cell layer due to the deformation. The model is solved numerically using a level set method, which tracks the moving boundary on a fixed grid. Initial coordinates for the simulated wound are defined using data from experimental cell migration images. Time to wound closure is shown to depend on initial wound shape. The location and velocity of the wound edge predicted by the model is compared with the position and velocity of the recorded wound edge. These comparisons show good qualitative agreement between model results and experimental observations. | ||
| Coauthor(s): Qi Mi, Kristen Pueschel, Maria Branca, David Hackam, David Swigon | ||
| MSD1d | Arino, Julien | |
| University of Manitoba | ||
| A metapopulation model for malaria - Efficacy of control strategies | ||
| I will present a metapopulation model for malaria dynamics. In each patch, mosquito and human populations are put in contact. The humans are described by an SIR model with the property that recovered individuals are only partially immune to the disease. Humans move from patch to patch, while mosquitoes remain in the same patch their entire life. The classical methods of analysis of such systems can be applied, and a basic reproduction number is obtained that governs the local stability of the system. In the case where control is applied, we use type reproduction numbers, in order to evaluate the effect of control policies on the various patches. Finally, the existence of a backward bifurcation, with subthreshold endemic equilibria, is investigated. | ||
| MSG5a | Arino, Julien | |
| Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada | ||
| Metapopulation models - Applications to the spread of infectious diseases | ||
| Metapopulation models describe the spatio-temporal evolution of the number of individuals of various species in a set of spatial locations called patches. In each patch, a system of differential equations (ordinary, delayed or partial) or a stochastic process (Markov chain, branching process) describes the interactions between species. The patches are then connected to one another to account for the movement of individuals between them. I will present some general theory and results about this type of systems in the ordinary differential equations case. I will then discuss the use of such systems in the description of the spatio-temporal spread of infectious pathogens, giving examples of applications in the ordinary differential equations and in the stochastic cases. | ||
| CTA7b | Atkins, Katie | |
| University of Edinburgh | ||
| Marek’s Disease Virus: Defining Virulence And Understanding The Drivers Of Evolution | ||
| Marek’s disease is an oncogenic poultry disease affecting chickens and is estimated to cost the worldwide industry $1-2 billion annually. The causative agent of Marek’s Disease (MD), MDV, provides a well-documented example of virulence evolution occurring over the period of half a century. The reason behind this evolution is unknown, although certain untested hypotheses have been suggested. These include vaccination (with increasingly potent vaccines) and other aspects of industrialisation, including the decreased cohort time of successive generations. Disease control is mainly via vaccination, indeed MDV vaccination was the first such vaccine offering protection against an oncogenic virus. There have been pathotyping studies which serve to define ‘virulence rank’ as the percentage of vaccinated birds dying or displaying gross clinical signs. To be able to understand the cause of past virulence evolution and develop future strategies for controlling the disease, addressing this problem is of prime importance. In this study, two sections of work are undertaken. First, estimation of epidemiological parameters is tackled: virulence of MDV is quantified by looking at mortality and virus shedding rates in vaccinated and unvaccinated birds. Both of these are achieved via Maximum Likelihood Estimation and Bayesian McMC techniques. Second, viral fitness is quantified by defining a lifetime fitness function using the parameters previously estimated and fitness landscapes are calculated to understand the direction and force of selection and the optimum fitness for different cohort times and vaccination strategies. Parameter estimation results show that the time to death for an infected bird decreases and its virus shedding rate increases with virulence rank. Model results suggest that both decreasing an individual’s lifespan and increasing the potency of vaccination of the bird serve to increase the virulence corresponding to a fitness peak. This illustrates that both decreasing the broiler lifespan and introducing, and increasing the potency of, vaccination may serve to drive evolution of MDV to a higher virulence. By estimating key epidemiological parameters and using simple mathematical models to understand the virus life history, it is anticipated that a better understanding of how MDV affects poultry flocks will emerge. This work not only explains past trends, but serves as a predictive tool for the future impact of current decisions taken by the farming industry. | ||
| MSC2a | Aukema, Brian | |
| Pacific Forestry Centre, Canadian Forest Service & University of Northern British Columbia | ||
| Spatial-Temporal Statistical Modeling of Outbreaks of Mountain Pine Beetle | ||
| The mountain pine beetle is forest insect that undergoes intermittent population eruptions. At epidemic levels, it must kill its host tree to reproduce. Currently, an outbreak in British Columbia and Alberta, Canada covers over 14 million hectares of mature pine forests, exerting landscape-level mortality and carbon impacts on the order of megatonnes. We consider two different ways of modeling mountain pine beetle outbreaks across space and over time in British Columbia, Canada. One approach is a spatial-temporal autologistic regression model in the framework of Markov random fields. The other approach is a generalized linear mixed model with spatial-temporal random effects. We devise computationally feasible algorithms for Bayesian inference in both approaches. An example using real data of a mountain pine beetle outbreak is provided for illustration. | ||
| MSD4b | Bachar, Mostafa | |
| Department of Mathematics, King Saud University | ||
| Sensitivity analysis of a cardiovascular control system model | ||
| This talk presents a sensitivity analysis of a mathematical model of the cardiovascular control system. The model incorporates sufficient structure and complexity to allow for examining the action of control mechanisms to respond to cardiovascular stresses. The model includes 10 vascular compartments and baroreflex controls to alter resistance, unstressed volume, and heart rate. Total potential number of parameters are 86. The complexity of the model allows for the representation of a variety of modes and sites for control action but at the same time the number of parameters renders the validation with accessible data problematic. Sensitivity identifiability techniques are employed to examine which parameters are mostly likely identifiable for a variety of potential sources of data on the state of the system as well as various testing protocols. The information provided by this analysis allows for a reasonable reduction in parameters to be estimated and can be used to consider which experimental tests might best allow for study of the control response patterns. | ||
| CTB6b | Badoual, Mathilde | |
| Paris 7 University | ||
| A "go or grow" model based on cell interactions in brain tumours | ||
| Glioblastomas are malignant brain tumours associated with poor prognosis, due to the capacity of glioma cells to invade normal brain tissue.
During their migration, cancerous astrocytes interact with other cancerous cells (homotype interactions) as well as with normal motionless astrocytes (heterotype interactions), in particular through gap junctions. These interactions appear to strongly influence the migration of glioma cells. We have developped a cellular automaton where the strength of each type of interaction is ajustable, in order to describe the migration of glioma cells [1,2,3]. From this automaton, we were able to derive a macroscopic diffusion equation, where the diffusion coefficient is original compared to other classical models [4]. First, the diffusion coefficient is nonlinear as it depends on the cell density. Second, it depends on the two parameters measuring the strength of homotype and heterotype interactions, as well as on the number of normal astrocytes coupled to a cancerous astrocyte, through heterotype gap junctions.
We show that the inhibition of homotype gap junctions leads to the increase of cell migration, whereas when both homotype and heterotype gap junctions are involved, their inhibition leads to a reduction of migration. This result is in agreement with experimental data [5]. Our model also accounts for the variability of the expression of connexin 43 (the major junctional protein in astrocytes) through different tumours. We suggest that the various migrating behaviours observed among cells in a tumour correspond to different expressions of connexin 43 and we propose a model for the "go or grow" hypothesis, based on a differential connexin 43 expression.
[1] Aubert M, Badoual M, Fereol S, Christov C and Grammaticos B, 2006, A cellular automaton model for the migration of glioma cells, Phys. Biol., 3, 93. [2] Aubert M, Badoual M, Christov C and Grammaticos B, 2008, A model for glioma cell migration on collagen and astrocytes, J. R. Soc. Interface, 5, 75. [3] Deroulers C, Aubert M, Badoual M, Grammaticos B., Modeling tumor cell migration: From microscopic to macroscopic models, 2009, Phys Rev E Stat Nonlin Soft Matter Phys. 79, 031917. [4] Tracqui P, Cruywagen GC, Woodward DE, Bartoo GT, Murray JD and Alvord EC Jr, A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth, Cell Prolif, 1995, 28, 17-31. [5] Oliveira R, Christov C, Guillamo J S, de Bouard S, Palfi S, Venance L, Tardy M and Peschanski M, 2005, Contribution of gap junctional communication between tumor cells and astroglia to the invasion of the brain parenchyma by human glioblastomas BMC Cell Biol., 6, 7. | ||
| Coauthor(s): Christophe Deroulers, Marine Aubert and Basile Grammaticos | ||
| MSA2d | Baker, Ruth | |
| Centre for Mathematical Biology, University of Oxford | ||
| Comparing deterministic and stochastic models for cell motility and domain growth | ||
| Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this talk, individual-based models describing cell movement and domain growth are outlined, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs. | ||
| MSH1d | Band, Leah | |
| Centre for Plant Integrative Biology, University of Nottingham, UK | ||
| Modelling GA-regulated growth in the root elongation zone | ||
| GA is a hormone that is thought to regulate cell growth by affecting the cell-wall remodelling enzymes. In this talk, I will present a multiscale model that describes the role of GA in the root elongation zone. The model includes: (i) diffusion and dilution of GA, (ii) a genetic regulatory network that details how GA affects the DELLA proteins, (iii) a description of how the DELLA proteins influence the cell-wall remodelling enzymes, which in turn affect the cell-wall material properties, and finally (iv) a cell growth model derived by Rosemary Dyson (presented earlier in the minisymposium). Using the model, we can understand how these processes may interact to produce the growth patterns seen in wild type and mutant plants. I will also discuss the work of my experimental collaborators, who are currently collecting data to test the model's predictions. | ||
| CTA7a | Basanta, David | |
| Moffitt Cancer Center | ||
| Games that tumour cells play: using game theory to study the different paths of tumour progression | ||
| Cancer is often viewed, not as a single disease, but as collection of diseases with more differences than similarities. One unifying theme in all cancers is that it is subject to evolutionary dynamics that determine, among other things, whether it will progress towards malignancy. The root of this evolution is the heterogeneity of cellular and microenvironmental elements in and around a tumour. Cells, tumourous or otherwise, interact which other in different ways, altering the adaptative landscape and selecting for and against specific cellular traits and phenotypes. Thus, the emergence of a new cell phenotype, a common event during tumour progression, impacts the fitness of each of the preexisting phenotypes as well as the overall fitness of the tumour. The complexity of these interactions, their impact on phenotypic evolution and the fitness of the tumour cell population can be characterised and studied using evolutionary game theory. In this talk, the role of cancer as a complex system and the idea that tumour cells are part of a larger tumour ecosystem that also includes non-tumour cells, will be discussed. I will also show a few models in which evolutionary game theory is used to explain the emergence of phenotypes as a result of comensalism, the influence of space in explaining that behaviour and how these model can be leveraged to improve current anti-cancer therapies. | ||
| MSG3c | Basanta, David | |
| H. Lee Moffitt Cancer Center & Research Institute | ||
| An integrative study of the role of TGF-β mediated tumour-stroma interactions in prostate cancer progression. A computational view | ||
| There is a concerted effort to provide a predictive morphological distinction between relatively indolent and lethal forms of prostate cancer. Data from patient biopsies suggest that both the tumour cell phenotypes and the composition of the stromal compartment can be predictive of the clinical significance of prostate tumors even if the biological mechanisms relating phenotype to function are still unclear. We have implemented a mathematical model, using hybrid cellular automata (HCA), that recapitulates key interactions in nascent tumor foci between prostate tumor cells and stroma. The computer simulations demonstrate how stochastic interactions between tumor cells and tumor stroma may lead to a structural suppression of tumor growth, modest proliferation, or unopposed tumor growth. The model incorporates key aspects of prostate tumor progression including net pleiotropic growth factor activity, net matrix degrading enzyme (MDE) activity, and stromal activation. As a result of this computatinal work, cancer biologists at Vanderbilt University and Pathologists at Baylor College of Medicine have carried out experiments in vivo and tissue culture that corroborate some of the main findings from the simulations. The implications of the model underscore the need for quantitative experimental measurements and integration with computational modelling that could eventually lead to more accurate diagnoses and treatments of prostate cancer. | ||
| MSG3d | Basanta, David | |
| H. Lee Moffitt Cancer Center & Research Institute | ||
| An integrative study of the role of TGF-β mediated tumour-stroma interactions in prostate cancer progression. An experimental view | ||
| David Basanta will continue his previous presentation, allowing time for extended discussion. | ||
| CTD7b | Bearon, Rachel | |
| University of Liverpool | ||
| Understanding the NF-κB cell pathway: a paradigm for systems biology | ||
| A systems biology approach is required to make a step change in understanding how cells function, whereby state-of-the-art experimental methods are combined with novel modelling and theoretical analysis. Such scientific progress is currently being undertaken using the Nuclear Factor kappa B (NF-κB) pathway as a model system. This important transcription factor regulates cellular stress responses and the immune response to infection. Real-time fluorescence imaging of single cells and mathematical modelling have shown that the activity of the NF-κB system can be oscillatory (1). Furthermore, deterministic and stochastic mathematical models predicted how negative feedback loops regulate both the resetting of the system and cellular heterogeneity (2). We demonstrate that integrated interdisciplinary research results in significant jumps in scientific understanding, and improved training opportunities for early career scientists. 1. D. E. Nelson et al., Science 306, 704 (2004). 2. L. Ashall et al., Science 324, 242 (2009). | ||
| Coauthor(s): L. Ashall, P. Paszek, M.R.H. White. | ||
| CTC1b | Bearon, Rachel | |
| University of Liverpool | ||
| Individual to population models of swimming micro-organisms in fluid flow | ||
| Swimming micro-organisms in fluid environments are ubiquitous and diverse. Such micro-organisms frequently undergo movement patterns which can be modelled as random walks. The presence of external cues such as light, chemical gradients, or gravity can modify individual-level behaviour resulting in the random walk being biased towards a preferred direction. In still fluid, at the population level, this can mathematically described as a diffusion process with drift. In many natural environments, swimming occurs in fluid environments undergoing motion. The fluid flow will interact with the swimming behaviour in several ways and alter the spatial distribution of a population, leading to such phenomena as bioconvection and gyrotactic focussing. Here I present the derivation of a population-level advection-diffusion model for gyrotactic algae which is based on extensive experimental observations of individual swimming cells in still fluid. I will then present theoretical predictions and experimental data describing the behaviour of gyrotactic micro-organisms in 3D flow. Finally I will discuss the effect of flow on the population-level spatial distribution. | ||
| MSE3c | Beheshti, Afshin | |
| Tufts University School of Medicine | ||
| The induction of DNA double-strand breaks in bystander stromal cells by cancer cells, a biological perspective | ||
| We investigate in vitro and in vivo influences of tumor cells on neighboring stromal cells, as one aspect of multicellular effects during carcinogenesis. We study the constitutive level of DNA damage/repair, as indicated by standard g-H2AX and 53BP1 repair damage protein foci assays, in cells from tumors and neighboring stroma. We found that conditioned media from tumor cells produced an increase in genes related to DNA double-strand breaks (DSBs) in the stromal cells. In vivo studies also demonstrated a diffusive pattern of DNA DSBs in the stroma of the tumor. We demonstrate that cancer cells induce DSB and activate repair proteins in neighboring cells analogous to the radiation bystander effect, indicating that DNA damage is communicated among cells. This effect could indicate tumor subversion of the microenvironment to facilitate the breakdown of host barriers to tumor expansion and thus tumor progression. We develop a hybrid discrete continuous mathematical model of tumor growth within a stromal tissue environment. We show that certain tissue architectures can maintain the tumor in a space-restrained dormant stage. We simulate diffusion of stress-signals from the tumor to its microenvironment and induction of DNA DSBs in adjacent cells, which can with a certain frequency trigger cell death. We present simulation results that show how tumor-induced cell death can enable tumor progression and invasion. | ||
| MSD4c | Ben-Tal, Alona | |
| Institute of Information and Mathematical Sciences, Massey University | ||
| Circulatory Delay Vs. Neural Feedback Dynamics | ||
| We used a recently developed mathematical model of the control of breathing to study numerically how circulatory time delay and the dynamics of neural feedback affect the response of the respiratory system to hypercapnia and hypoxia as well as the appearance of periodic breathing. The model we used integrates a reduced representation of the neural controller with peripheral gas exchange and transport mechanisms. The neural controller consists of two compartments - one representing the brainstem respiratory oscillator in the pre-Bötzinger complex and another representing the rostral VRG, which transmits the rhythmic inspiratory drive to spinal motor neurons. The neural model was coupled to simplified models of the lungs incorporating oxygen and carbon dioxide transport. The model regulates both frequency and amplitude of breathing in response to partial pressures of oxygen and carbon dioxide in the blood using proportional (P) and proportional plus integral (PI) controllers, which provide chemosensory drives to the neural elements. Heart rate and heart volume are input parameters in the model. We compared the dynamic responses of P- and PI- controllers to several stimuli. We show that a PI-controller, representing the dynamics of the neural feedback processes, fits published experimental data reported in the literature better with or without additional circulatory delay. Additional delay affected the length of apnea following the system responses to hypoxia and introduced periodic breathing in some cases. The source of the delay (blood velocity vs. distance from the lungs to chemoreceptors) is found to be important. We show that a PI-controller is associated with a shortening of the length of the ventilatory “afterdischarge” (slow recovery of ventilation) after a brief perturbation of CO2. We also show that there could be two possible mechanisms for the appearance of periodic breathing and that circulatory delay is not a necessary condition for this to happen in certain cases. | ||
| CTH3a | Besse, Ian | |
| University of Iowa | ||
| A model of cardiac action potential that incorporates stochastic caveolar dynamics | ||
| Recent investigations into the structure and function of cardiac caveolae, small invaginations of a cardiomyocyte’s plasma membrane, reveal that treatment of a myocyte with a beta-agonist opens caveolar necks and presents the sarcolemma with additional sodium ion channels. As such, caveolae constitute a substantial and previously unrecognized source of sodium current that can significantly influence cardiac action potential morphology and the conduction velocity of the excitatory wave front. In this work, we formulate a model of cardiac action potential that incorporates stochastic caveolar dynamics and simulate the effects of caveolar sodium current on the action potential. In particular, we use this model to suggest that in pathological cases, caveolae may play a role the development of the late persistent sodium current known to cause the cardiac arrhythmia called long Q-T syndrome. | ||
| CTB7a | Bhattacharyya, Samit | |
| Mathematics and Statistics, University of Guelph, Canada | ||
| Imitation dynamics, delaying strategies, and vaccination in an age-structured population | ||
| While overall vaccination coverage level is reasonably high at present for most of the vaccine-preventable paediatric infectious diseases, vaccination does not always take place at the recommended age. A number of field studies (for Measles-Mumps-Rubella vaccine for example) report that many parents delay the age at which their child is vaccinated due to a perception of higher vaccine risk at the recommended age of vaccination. At the same time, because of herd immunity, there is also a strategic interaction between individuals when they are deciding whether or not to vaccinate their child, since the probability that an individual becomes infected depends upon how many other individuals are vaccinated. So, dynamics of age-appropriate vaccination uptake is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. As a first step toward exploring this issue, we have constructed an age structured game dynamic model, where individuals adopt strategies according to an imitation dynamic (a learning process), and base vaccination decisions on disease prevalence and perceived risks of vaccines and disease. The perceived vaccine and infection risks are age-dependent, with higher risks from both vaccine and infection at younger ages. We present here some early findings with this model. For instance, at certain parameter regimes, the model shows that populations can switch between a strategy of vaccinating at a young age and a strategy of vaccination at an older age at a certain timescale, and that this switching is coupled with the inherent oscillatory tendency of infectious disease incidence. We also discuss possible future directions for analysis. | ||
| CTD7a | Birol, Inanc | |
| British Columbia Genome Sciences Centre | ||
| De novo assembly of transcriptomes with ABySS | ||
| Second generation sequencing technologies are being used routinely to investigate the genomes and transcriptomes of a wide variety of species. Although the increasing read lengths and protocols for paired end reads with various insert sizes enabled de novo assemblies of genomes, so far analysis of whole transcriptome shotgun data was carried out through alignment of reads to a reference. As powerful as alignment-based analysis methods are, they would be obtuse when it comes to detecting novel events. In this study, we present a de novo assembly approach for the analysis of transcriptomes, using the ABySS assembler tool, to address such shortcomings. The problem of transcriptome assembly is substantially different from the problem of genome assembly. For example, whereas changes in coverage levels in a genome assembly may be indicative of the repeat structures or otherwise be distributed randomly; in a transcriptome assembly, we would expect them to have wide swings, as they would be affected by different expression levels of various transcripts. Similarly, whereas contig growth ambiguities in a genome assembly would represent unresolved repeat structures; in a transcriptome assembly, they would correspond to isoform, gene family or allelic variations, thus would harbor useful and important information. Due to these variations, as well as to abundant small products, the contiguity of a transcriptome assembly will be low, and again unlike a genome assembly, this would not be an indication on the quality of the assembly. On the other hand, a capability to assemble transcriptomes opens up many opportunities, including the identification of novel transcripts and retained introns, and resolution of isoforms, gene families and allelic differences and their relative expressions, which would elude detection by alignment-based analyses. The ABySS algorithm is based on a de Bruijn di-graph representation of sequence neighborhoods, where a sequence read is decomposed into tiled sub-reads (k-mers) and sequences sharing k-1 bases are connected through directed edges. This approach is amenable for distributed representation, and our parallel implementation relaxes the memory and computation time restrictions present in other available de novo assemblers. ABySS reports three levels of output: (1) the assembled contigs, (2) information on allelic differences, collapsed near-repeats and read errors, and (3) contig adjacencies through overlaps and connecting read pairs, if available. In this work, we also report on our assembly visualization tool, ABySSexplorer, which uses the output from ABySS and enables manual inspection and refinement of assemblies. Furthermore, it aids incorporation of additional data and guide high throughput assembly finishing work. | ||
| Coauthor(s): Shaun Jackman, Cydney Nielsen, Jenny Qian, Marco Marra, Steven JM Jones | ||
| CTH7a | Borowski, Peter | |
| Dept.of Math., UBC | ||
| Predictions from a stochastic polymer model for the MinDE dynamics in E.c oli | ||
| In the bacterium E.coli, a group of proteins - the Min proteins - play an important role in reliable cell division. The proteins show a complex spatio-temporal oscillation pattern and have attracted a lot of attention from theoreticians in search for the underlying mechanisms. Most of the models proposed so far are based on variants of reaction diffusion systems. Here, we will analyse the stochastic version of a different kind of model for this oscillation - a simple model where the Min proteins are assumed to be organised in polymers. The dynamics can be described in the framework of a stochastic hybrid system which we solve analytically in the biologically relevant limit. We provide distribution functions for quantities that can easily be obtained experimentally and can serve as a testing ground for the model. | ||
| MSE1b | Bowman, Christopher | |
| National Research Council of Canada, Institute for Biodiagnostics | ||
| Optimal Control for an Influenza Pandemic | ||
| The control of an emergent influenza pandemic is a major public health challenge. Since pandemic influenza will likely be a novel strain, it is unlikely that a vaccine will be available until quite late in the pandemic. While non-pharmaceutical measures can be effective in curtailing the spread of the disease, the pandemic response plan will likely also include the use of anti-viral drugs. Unfortunately, the widespread use of these anti-virals will generate selective pressure for the emergence and transmission of drug-resistant strains. Furthermore, it is possible that drug stockpiles will be limited, leading to potential run-out and drug shortages. I will present a mathematical model for the spread of pandemic influenza which includes the effects of anti-viral treatment, including the transmission of an anti-viral resistant strain of the virus. Principals of control theory will be applied to search for optimal strategies to control the pandemic, using several cost functions and taking into account the effects of limited anti-viral supply. | ||
| MSE5f | Bradshaw, Catherine | |
| REBMI Claremont Colleges: Student's perspective | ||
| Our project involved evaluating and improving the use of visualization and navigation software in the operating room. We worked with two orthopaedic surgeons, Dr. Mohammad Diab and Dr. Shane Burch, from the University of California, San Francisco. A deep understanding of mathematics and computer science was required in order to integrate preoperative surgical plans with the intra-operative navigation system. Strong interpersonal skills were vital for working with people of varying levels of technical knowledge, including surgeons, engineers, radiologists, technical consultants from biomedical device firms, and hospital staff. | ||
| Coauthor(s): John Milton (UBM PI), Christine Abraham | ||
| MSG5b | Brown, Richard | |
| Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand | ||
| Dispersal, fragmentation, and space: Determining the importance of spatial structure in different models of plant dispersal | ||
| There are a multitude of different mathematical models used to model plant spread and dispersal, from the simple Levin\'s model, through reaction-diffusion equations, through to integro-difference equations and stochastic individual-based models. These models account for spatial structure in different ways (or not at all) and it can be difficult to understand which model is most appropriate for a given scenario. We look at a simple 1D stochastic process for plant dispersal and study the conditions under which the various continuous deterministic models are or are not good approximations to this process. This helps in understanding when it is important to build spatial structure into mathematical models, and to what degree. We then investigate the differences that arise when fragmentation, or random habitat destruction, is introduced into the models. | ||
| CTH3b | Bungay, Sharene | |
| Memorial University | ||
| A 2D Model of Calcium Activation in Cardiac Purkinje Cells to explain the source of lethal arrhythmias in post-MI heart | ||
| Purkinje cells (Pcells) are specialized cardiac cells whose role is to carry electrical signals from the pacemaker nodes to the ventricular myocytes. Thus responsible for the initiation and synchronisation of the cardiac beats, Pcells have been involved recently in the generation of spontaneous action potentials underlying lethal arrhythmias (VTs) in patients with myocardial infarction (MI). Although experimental evidences clearly support the idea that the arrhythmogenic electrical activity originates in abnormal spontaneous oscillations of intracellular Ca2+ concentration, the mechanism of Ca2+ handling in normal Pcells remains still unestablished. A 2-dimensional spatio-temporal mathematical model of calcium dynamics within Purkinje cells is presented. The model includes calcium release, uptake, diffusion functions and integrates various ligand interactions. As an extension of the previous model of Stuyvers et al (Circ. Res.2005), the current simulation algorithm includes in particular three types of recently identified intracellular sites of calcium release in canine and swine Pcells (IP3R, RyR2, and RyR3). The constant synergy between computational and experimental data obtained from fast confocal Ca2+ imaging faithfully support the physiological relevance of the model. The final version of the model represents the starting point for the construction of a 3-dimensional model of calcium activation in Purkinje cells, which we anticipate will be instrumental in the identification of molecular abnormalities responsible for post-MI VTs. | ||
| Coauthor(s): Kazi Haq, Bruno Stuyvers | ||
| MSG5c | Burie, Jean-Baptiste | |
| Institut Mathematiques de Bordeaux, Universite Victor Segalen Bordeaux2, France | ||
| Modelling of a powdery mildew epidemic over a vineyard | ||
| In this talk, we consider several models for the propagation of a plant pathogen over a canopy. We focus on a fungal epidemic of powdery mildew over a vineyard. The vector of contamination is the spores that stem from the lesions at the surface of the leaves. We introduce a model at the vinestock scale. It is a variant of a SEIR model and is based on a system of five ODEs. We use data from a mechanistic model to identify the parameters of our model and perfom a sensitivity analysis. One of the specific features of this epidemic that will be discussed is that the host growth cannot be neglected during the development of the disease, and moreover, the leaves cannot be infected once they become too old (ontogenic resistance). Next we investigate the propagation of the epidemy at the vineyard scale. So the previous model is extended by adding two PDEs to describe the short (intra-cep) and long (inter-cep) range dispersal of the spores. The spatial structure of the vineyard is periodic. Again we study the influence of the parameters of the model and of the periodic spatial structure on the epidemic. Eventually we give a result on the existence and unicity of travelling wave solutions, that is solutions of the form U(x-ct) where x is the 1D space variable, t is time and c the constant wave speed, for a variant of the previous spatial model. The proof uses a re-formulation in the form of an integral equation with measure kernel convolutions. As we are concerned with the long term behavior of the solutions, in this part of the talk we do not take into account the host growth. | ||
| CTH4e | Burrow, Jenny | |
| University of York | ||
| Linking plankton dynamics and stochastic fish recruitment models | ||
| Fish larvae live in an extremely variable environment. They are small relative to the spatial scales of prey heterogeneity and to the turbulent fluid flow at these spatial scales; they have only a local knowledge of their immediate environment, limited by a visual perceptive distance of around one body length; and they are subject to massive mortality, with a newly hatched individual’s probability of survival to metamorphosis being O(1%) or less, driven by typical mortality rates of 10% per day in the larval stage. Because the key natural phenomena are inherently stochastic, deterministic models are likely to be inappropriate for quantifying recruitment. However, the usual stochastic modelling approach, which assumes that individual-based variability can be captured at the population level by a diffusion equation, may not be universally suitable. In particular, diffusion-based models cannot necessarily capture sudden jumps in growth caused by rare encounters with favourable patches of prey, or turbulent effects. Lévy process based models provide the necessary mathematical extensions to capture these jumps. Initial work has extended simple diffusion-based models of larval growth to Lévy jump-diffusion models, and has examined the consequences for recruitment probabilities [1]. Here we develop an explicit coupled stochastic model of larval-zooplankton-phytoplankton interactions, with the aim of exploring the roles of temporal matching of spawning and prey abundance, and prey heterogeneity and foraging strategies on the relationship between stock and recruitment. [1] J. F. Burrow, P.D. Baxter and J.W. Pitchford (2008): Lévy processes, saltatory foraging, and superdiffusion. Math. Mod. Nat. Phenom., 3(3):115-130. | ||
| Coauthor(s): Jon Pitchford, Paul Baxter, Alex James, Mike Plank, Joe Horwood | ||
| MSE4b | Cabeen, Matthew | |
| Yale University | ||
| Mechanical Control of Bacterial Cell Curvature | ||
| The cytoskeleton is a key regulator of cell morphogenesis in bacteria, as in eukaryotes. Eukaryotic intermediate filament proteins are notable for their ability to resist strain, or stretching forces. Crescentin, a bacterial intermediate filament-like protein, is required for the curved shape of Caulobacter crescentus and localizes along the inner cell curvature, but how crescentin governs cell curvature has been unclear. Here, we show that crescentin forms a single filamentous structure that collapses into a helical configuration when detached from the cell membrane by drug treatment, suggesting that the crescentin structure is normally maintained in a less favorable stretched configuration. As the peptidoglycan cell wall is the only bacterial structure with the requisite size and strength to maintain the crescentin structure in a stretched configuration, the crescentin structure must in turn apply a compressive force to the cell wall. We demonstrate that the presence of the crescentin structure along one side of the cell generates curvature by producing a gradient in cell wall elongation rate around the circumference of the sidewall, creating a longitudinal cell length differential. Consistent with a compressive force from the crescentin structure setting up an elongation rate gradient to produce cell curvature, physical force alone can produce curvature when straight, crescentin-null C. crescentus cells are grown in circular microchambers. We show that production of crescentin in the evolutionarily distant bacterium Escherichia coli causes this straight rod-shaped organism to adopt striking curved and helical morphology, arguing that crescentin does not require species-specific factors for its function in cell curvature. However, the function of the bacterial actin homolog MreB is important for crescentin function in C. crescentus, and crescentin is able to pull down MreB in both C. crescentus and E .coli. Our data argue for a model in which the crescentin structure, which is highly static and elongates from its ends only, is stretched as the cell elongates. The stretched crescentin structure applies a compressive force to the cell wall to which it is connected, locally lowering the strain borne by the cell wall and thereby reducing the kinetics of cell wall insertion to produce an elongation rate gradient and hence curved growth. Our study implies that bacteria may use the cytoskeleton for mechanical control of growth to alter morphology. | ||
| MSA1d | Cairo, Christopher | |
| University of Alberta | ||
| Diffusion of adhesion molecules in the T cell membrane and the role of lateral mobility in signaling mechanisms | ||
| The plasma membrane is a complex and heterogeneous system, and critical biological processes take place in this environment. Microscopy methods are able to provide direct observations of membrane components in live cells. While microscopy is limited by its resolution, nanometer-scale interactions can still be observed either directly or indirectly. The diffusion of membrane components can be a useful parameter for determining the microscopic environment of specific objects. For example, different lipid compositions may have altered viscosity or large protein complexes may experience retarded diffusion. Our group is interested in the observation of T cell membrane proteins using single particle tracking (SPT). We have used this method to observe changes in cytoskeletal contacts of the T cell adhesion proteins LFA-1, CD2, and CD45. In each of these systems, SPT is able to reveal changes in cytoskeletal interactions of the proteins as a result of cellular activation or other perturbations. Our current labeling strategies and developments in methods of data analysis for these systems will be presented. | ||
| CTE6a | Calmelet, Colette | |
| California State Univ. Chico | ||
| Mathematical Modeling of Cellular Intercalation during Zebrafish Gastrulation | ||
| In this paper we analyze a model of zebrafish embryo notochord development. We are interested in studying factors contributing to the mediolateral intercalation of mesodermal cells, particularly adhesion and cortical tension, which is a part of a more general problem: how the mechanical properties of cells at the boundaries, contribute to intercalation or large scale remodeling of tissues seen during embryonic development. Our consideration is based on Cellular Potts Model that describes the dynamics of cell intercalation. We calculate the total energy of the system of cells at different time intervals at the cell-to-cell and cell-to-wall contacts. We use experimental data of cell outlines obtained from time-lapse images of cell movements in vivo during zebrafish embryonic development and show the decrease of the total energy with time in both 2-D and 3-D cases. We discuss the effect of cell adhesion and cortical tension at cell-to-cell and cell-to-wall contacts using a variational analysis and examine whether anisotropic adhesion and contraction can serve as the main driving mechanism for intercalation in zebrafish gastrulation. | ||
| Coauthor(s): Diane Sepich | ||
| MSH2c | Chakraborty, Gargi | |
| Department of Pathology, University of Washington | ||
| Bridging from Anatomic Imaging to Molecular Imaging through Multi-scale Models for Brain Tumor Growth and Invasion | ||
| Gliomas are diffuse and invasive primary brain tumors that are notoriously difficult to treat and uniformly fatal. Much of the difficulty in improving the outcomes of patients with gliomas lies with the extensive invasive potential of these tumors. To help quantify the effect of tumor cell dispersal on the overall growth of gliomas, over the last several years, we have explored a spatio-temporal bio-mathematical model of gliomas based primarily on two key elements, net rates of proliferation (ρ) and dispersal/invasion (D) of glioma cells - aka proliferation-invasion (PI) model. We have already shown that these two key rates, characteristic of biological aggressiveness, are obtainable from routinely available serial clinical MRIs and, somewhat surprisingly, seem to remain fixed over extended periods of time in individual patients (Harpold et al, 2007). Overall, this model has successfully defined many of the behavioral features of low- and high-grade gliomas, specifically the orderliness of their over-all imageable growth, and predictable durations of survival if not treated or if treated by surgical resection of various extents (Swanson et al, 2002; Mandonnet et al, 2003; Harpold et al, 2007; Swanson et al, 2008). Despite many successes, the PI model is limited in its ability to differentiate between low and high- grade gliomas and the related imaging and histologic changes that occur during progression between theses extremes thought to be linked by the angiogenic cascade. These successes have emboldened us to enhance the mechanistic detail of the model in order to now explore quantitatively the histologic characteristics underlying the biological heterogeneity seen amongst gliomas, effectively linking immunohistochemistry, imaging and individual patients, in vivo. I will discuss how such a multi-scale model can be used to integrate data provided on anatomical imaging (MRI) and functional information provided by molecular imaging (PET) in individual glioma patients. This integrative framework provides novel insight into cancer biology and allows for improved predictions of treatment responsiveness in individual patients. References: 1) Harpold et.al (2007) The evolution of mathematical modeling of glioma proliferation and invasion. J Neuropathol Exp Neurol 66: 1-9 2) Swanson and Alvord (2002) Serial imaging observations and postmortem examination of an untreated glioblastoma: A traveling wave of glioma growth and invasion. Neuro-Oncol 4: 340 3) Mandonnet et.al (2003) Continuous growth of mean tumor diameter in a subset of grade II gliomas. Ann Neurol 53: 524-528 4) Swanson et.al(2008) Predicting Survival of Patients with Glioblastoma by Combining a Mathematical Model and Pre-operative MR imaging Characteristics: A Proof of Principle, British J Cancer 98:113-9 | ||
| MSC6c | Chakraborty, Arup | |
| Massachusetts Institute of Technology | ||
| How T cells see antigen | ||
| Complex organisms, like humans, have an adaptive immune system that enables us to do battle with diverse pathogens. This flexible system can also go awry, and many diseases are the direct consequence of the adaptive immune system failing to discriminate between markers of self and non-self. The orchestrators of adaptive immunity are a class of cells called T lymphocytes (T cells). T cells recognize minute numbers of molecular signatures of pathogens, and T cell recognition of these molecular markers of non-self is both specific and degenerate. It is specific because if a T cell recognizes a particular molecular marker as “foreign”, point mutations to this marker abrogate recognition. But, at the same time, a given T cell can recognize many different pathogenic markers. The specific (yet, cross-reactive), diverse, and self-tolerant T cell repertoire is designed in the thymus. I will describe how an approach that brings together theoretical and computational studies (rooted in statistical physics) with experiments (carried out by key collaborators) has allowed us to shed light on the mechanistic principles underlying how T cells respond to pathogens in a digital fashion (“on” or “off”), and how this molecular machinery coupled with frustration plays a key role in designing a T cell repertoire (during development in the thymus) that recognizes antigen in a specific/degenerate fashion. | ||
| MSB5a | Chan, David | |
| Virginia Commonwealth University | ||
| Gene Dispersal in an Insect-Mediated Tree Species | ||
| For many plants pollen, and thus genes, is dispersed by the wind or by animals. Plants have evolved to develop special strategies to move their pollen from one plant to another. We have developed a model that examines the differences between these two types of pollen dispersal measuring some important biological statistics. We discuss the differences as well as the impact of the differences. | ||
| CTB6c | Chaplain, Mark | |
| University of Dundee | ||
| Multiscale modelling of vascular tumour growth | ||
| In this talk we will present a new multiscale mathematical model for solid tumour growth which couples a model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the multi-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression. Consistent with clinical observations, the hydrostatic stress generated by tumour cell proliferation shuts down large portions of the vascular network, dramatically affecting the flow, the subsequent network remodeling, the delivery of nutrients to the tumour and the subsequent tumour progression. In addition, extracellular matrix degradation by tumour cells is seen to have a dramatic affect on both the development of the vascular network and the growth response of the tumour. In particular, the newly developing vessels tend to encapsulate, rather than penetrate, the tumour and are thus less effective in delivering nutrients. Implications for chemotherapy treatment of solid tumours are discussed. Co-authors: P. Macklin, S. McDougall, A. Anderson, V. Cristini, J. Lowengrub | ||
| MSA2b | Chauviere, Arnaud | |
| Technische Universität Dresden | ||
| Cell migration features in glioma tumor invasion | ||
| Gliomas are very aggressive brain tumors, in which tumor cells gain the ability to invade the surrounding normal tissue. This type of brain tumor comprises an extremely interesting paradigm of invasive tumor, where its dynamics and mechanisms are not yet fully understood. Our work is motivated by the migration/proliferation dichotomy (so-called “Go-or-Grow”) hypothesis, which might play a central role in the biology of these tumors. We propose first a “Go-or-Rest” model and describe cell migration as a velocity-jump process including resting phases. By using scaling arguments we derive a continuum (macroscopic) model that provides anomalous diffusion, which is further analyzed. In particular, we show that sub- and super-diffusion regimes can be obtained, and are governed by a parameter describing intrinsic migratory properties of cells. We demonstrate the potential of the model to explain some in vitro data of glioma tumor expansion. When proliferation is included, the framework previously used is again the base of our extended model. In particular, we developed a lattice-gas cellular automaton, which provides a discrete, stochastic description of the afore-mentioned mesoscopic framework. Our goal is to test hypotheses of cellular mechanisms involved in glioma tumor invasion. To this end, we use again data of in vitro glioma cell cultures that allow for the analysis of the invasive behavior of gliomas. The main observations of these experiments are: (i) different core and invasive radii speeds and (ii) a high radial persistency of cell motion nearby to the core. Our analysis shows that the migration/proliferation dichotomy assumption plays a central role in the expansion of glioma tumor. Morever, we find that a cell-cell repulsion is required to explain the observed radial persistency of glioma cells near to dense areas. The combination of these two mechanisms is a sufficient and necessary condition for the faithful reproduction of the experimentally observed behavior. | ||
| MSH1c | Chavarría-Krauser, Andrés | |
| University of Heidelberg, Germany | ||
| A mathematical model of primary root growth | ||
| In young plants, primary roots need to be able to grow with high rates to ensure delivery of water and nutrients. In the elongation zone relative elemental growth rates of up to 50 %/h are common. It stands to reason that coordination of proliferation and elongation is essential to keep these high expansion rates. A simple 1-D model of a primary root, which assumes that the root is composed essentially of three regions: meristem, elongation zone and mature zone, will be presented. Transition between the zones, and hence, coordination of growth is achieved by introduction of two hypothetical hormones. One is produced in the root tip itself, while the other is assumed to be transported polarly from the plant shoot towards the root tip. Cell expansion is described by the Lockhart equation and coupled to the hormone concentrations. Hence, the description used is semi-discrete. The approach chosen allowed to examine how the growth zone of primary roots might be regulated and how regulation copes with a physical model of cell expansion. In a near future, quantitative models of root growth will be needed. Therefore, to achieve this, it is a must to couple physical models of cell wall expansion with signal transduction (hormone transport) and regulatory networks. The model which will be presented can be seen as a small step into this direction. | ||
| MSH1a | Cobb, Alex | |
| Singapore MIT Alliance for Research and Technology, Singapore | ||
| Growth analysis of twisting roots in arabidopsis | ||
| Several cytoskeleton mutants of arabidopsis have roots that twist as they grow. Cortical microtubule arrays in these mutants adopt a consistent helical handedness opposite to that of the root. A kinematic description of growth in these roots is presented, incorporating axial elongation, radial expansion, and twisting. Then, using data on the orientation of cellulose microfibrils in root cell walls, the biomechanics of twisting growth in roots is explored to determine how the presumed tendency of individual cells to twist relates to a twist manifested at the whole-root level. | ||
| CTF5a | Cobbold, Christina | |
| University of Glasgow | ||
| The evolution of parasitoid developmental timing | ||
| Parasitoids derive all their resources for development from a single host individual and it is this that makes them a particularly ideal model for studying the evolution of predator life histories. In this talk we will explore the evolution of parasitoid development time and the timing and efficiency of attack. In particular, we explore the conditions that might select for rapid parasitoid development at the expense of reduced parasitoid growth and attack efficiency. Host parasitoid systems often exhibit non-equilibrium population dynamics (cycles or chaos) and such variability on population abundance can change the evolutionary behaviour and promote evolutionary branching. Thus using adaptive dynamics we consider parasitoid evolution within the framework of a modified Nicholson-Bailey model and explore the conditions under which parasitoid variation may evolve. | ||
| Coauthor(s): Emily Hackett-Jones, Andrew White | ||
| CTF1a | Conrad, Matthias | |
| Emory University | ||
| Homeostasis by interacting positive and negative feedback: insights from the in the HPA system | ||
| The hypothalamus-pituitary-adrenal (HPA) system is closely related to stress and the restoration of homeostasis. In this talk we derive and discuss a novel mathematical model for the HPA system. It is based on three simple rules which constitute a principle of homeostasis and include only substantial physiological elements. In contrast to other models, its main components include, apart from the conventional negative feedback ingredient, a positive feedback loop. To validate the model, we present a parameter estimation procedure which enables one to adapt the model to clinical observations. Furthermore the dynamics of the system is investigated. Finally, the computed parameters may be interpreted from a physiological point of view and thereby gaining connoting insights in diseases like depression, obesity, or diabetes. | ||
| CTE7b | Conway, Jessica | |
| University of British Columbia | ||
| Latently infected cells and viral load in HIV patients on antiretroviral treatment | ||
| While on antiretroviral treatment (ART) for HIV, an infected individual's viral load remains non-zero, though it is very low and undetectable using standard equipment. Occasionally, regular blood tests show viral blips: very short periods of detectable viral load. Interestingly these viral blips have been shown not to be associated with patient or demographic variables, and to be only marginally associated with reported episodes of nonadherence to treatment. Further, there is evidence that the virus is closely related to the pre-treatment virus, suggesting that the low viral load is not due to ongoing viral replication, since HIV replication is a highly error-prone process. We will present a stochastic model that shows that this very low viral load can be explained principally by the activation of cells in the latent reservoir, seeded before the initiation of treatment, and that viral blips represent deviations from the mean. The model is calibrated using patient data. We will discuss the implications that a central role of the latent reservoir would have on the emergence of drug resistance. Our results reinforce the notion that the latent reservoir is an important factor to be considered in the design of therapies for HIV. | ||
| Coauthor(s): Daniel Coombs | ||
| MSC2b | Cooke, Barry | |
| Northern Forestry Centre, Canadian Forest Service | ||
| Climate change and the emergence and spread of forest insect 'superspecies' | ||
| MSC6a | Coombs, Dan | |
| University of British Columbia | ||
| Serial engagement in T cell activation | ||
| T cells of the immune system are activated by interactions with antigen-presenting cells (APC). T cell receptors (TCR) on the T cell surface transiently bind to defined signatures of infection (antigens) on the APC. Productive TCR-antigen binding leads to biochemical signals within the T cell and an immune response. T cell responses occur even when the antigen is present at very low concentrations. It has been suggested that during the T cell-APC interaction, over the course of minutes to hours, each antigen can bind to a series of TCR and that such "serial engagement" plays an important role in determining the T cell response. In this talk I will describe the biological questions in detail and show how mathematical tools can be used to better understand the experimental data. | ||
| MSA1b | Cooper, Jonathan | |
| Fred Hutchinson Cancer Research Center | ||
| A mechanism for transmembrane signal transduction by Src kinases | ||
| There are many situations in which cells respond to extracellular ligands whose receptors lack intrinsic or constitutively-associated catalytic functions. Well-studied examples include the antigen receptors on B and T lymphocytes and antibody receptors on myeloid cells. Less studied examples include lipoprotein receptors that are activated by Reelin, a secreted molecule important for brain development, Ephrins, which are activated by Eph receptors on other cells, and C-type lectins. All these receptors have intracellular regions containing phosphorylation sites for Src family kinases (SFKs) that become phosphorylated when the receptors are activated by dimerization/oligomerization by ligand. Current models to explain signal regulation generally either invoke weak prior association of the receptors with SFKs, conformation changes in the receptor intracellular receptor regions that expose SFK binding sites, movement of clustered receptors to membrane domains with altered lipid composition, or various SFK-regulating enzymes. We use two known properties of SFKs - their ability to trans-activate by intermolecular autophosphorylation and the ability of active SFKs to bind to phosphorylated receptors - combined with rate constants and concentrations gleaned from the literature - to explain how transmembrane signaling can occur. No changes in receptor conformation and no other enzymes apart from a constitutive phosphatase are required. This core signal transduction mechanism may be fine-tuned by other molecules within the cell. | ||
| MSB3d | Craciun, Gheorghe | |
| Department of Mathematics and Department of Biomolecular Chemistry University of Wisconsin-Madison | ||
| Dynamical system models of neurofilament transport in axons | ||
| We analyze reaction-hyperbolic equations that arise in the transport of neurofilaments in the axon of a nerve cell. These particles are moving alternately by processive motion along microtubules with the aid of motor proteins, and by diffusion. We describe a maximum principle and establish existence and behavior of a unique solution. Numerical simulations show that the predictions of our model agree with pulse-labeling experiments from different nerve cell types, and also agree with stochastic simulation results. | ||
| MSG2b | Craciun, Gheorghe | |
| Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison | ||
| Graph-theoretic criteria for injectivity and unique equilibria in biochemical reaction networks | ||
| Biochemical reaction network models give rise to dynamical systems that are usually high dimensional, nonlinear, and have many unknown parameters. Due to the presence of unknown parameters (such as reaction rate constants) and to the wide diversity of kinetic laws (such as mass-action, Michaelis-Menten, or Hill law) direct numerical simulation of the chemical dynamics is practically impossible. On the other hand, we will show that important properties of these systems are often determined only by the network structure, and do not depend on the unknown parameters. For example, some reaction networks may give rise to multiple positive equilibria (i.e., they may function as a "biochemical switch") while others cannot exhibit multiple equilibria for any values of the reaction rate parameters and any type of kinetics. We will point out connections between the capacity of a reaction network to function as a biochemical switch, and properties of signed graphs and digraphs that encode the combinatorics of matrix sign patterns of the associated dynamical system. This is a joint work with Murad Banaji. | ||
| SI2 | Daniell, Ellen | |
| Author of Every Other Thursday | ||
| Opportunities for leadership | ||
| This workshop is geared to the development of women faculty in bio-mathematics, to foster both tangible and "intangible" qualities that are the makeup of leaders. Participants will also have the opportunity to share perspectives and lessons learned pertaining to tenure and industrial aspects. The participants will have the opportunity to expand their network of colleagues and peer-mentors. Ellen Daniell, author of Every Other Thursday is scheduled to present insights into her experiences. Participants are encouraged to read the book prior to the workshop. An added benefit will be a discussion on negotiation skills and time for lunch together. Lunch will be provided for up to 40 participants. For over 30 years, Ellen Daniell, author of Every Other Thursday: Stories and Strategies from Successful Women Scientists has been part of a professional problem-solving group of women (and some men) who have attained extraordinary distinction in various scientific fields. The group meets every other week to help one another with the professional and personal challenges of managing highly competitive careers and fulfilling lives. In her talk, Dr. Daniell will describe how the group works and some specific experiences of its members in the course of their careers. She will share some of the strategies the group has devised for combating the competition, isolation and inequity of academic science. The talk highlights the importance of cooperation and of not going it alone in a competitive world. This session is sponsored by SIAM, the Society for Industrial and Applied Mathematics. Thanks to their generous support, refreshments will be provided. Schedule 12:30 P.M. - 1:00 P.M. Lunch 1:00P.M. - 2:00 P.M. Ellen Daniell's talk, Stories and Strategies from a Professional Problem-Solving Group 2:00 P.M. - 2:10 P.M. Break 2:10 P.M - 2:40 P.M. Small group discussion about leadership issues 2:40 P.M. - 3:15 P.M. Panel Discussion about negotiation skills, organization skills, family management, etc. with Ellen Daniell, Gerda deVries, Zhilan Feng, Renee Fister, Mary Ann Horn and Holly Gaff  | ||
| Coauthor(s): Holly Gaff (Old Dominion University) K. Renee Fister (Murray State University) Rebecca Segal (Virginia Commonwealth University) | ||
| MSB1a | Das, Raibatak | |
| University of British Columbia | ||
| Imaging and modeling the recruitment of cytosolic signaling proteins to the plasma membrane | ||
| The recruitment of cytosolic signaling proteins to the plasma membrane is a key step in a variety of intracellular signaling cascades initiated by the activation of membrane-associated receptors. The translocation of a cytosolic protein is frequently observed within seconds to minutes following receptor activation. The in vivo dynamics of this process are typically difficult to quantify accurately. As a prototypical example for such a system, we study the recruitment of the adaptor protein Gab-1 to the plasma membrane of B lymphocytes upon B cell receptor crosslinking. We use a combination of confocal fluorescence microscopy to observe this process in individual cells under physiological conditions, and image processing tools to quantify the recruitment dynamics. In this talk I will present the details of our methodology and the efforts to model and parametrize this phenomenon. | ||
| CTH4b | Davoudi-Dehaghi, Bahman | |
| BCCDC | ||
| Early Real-time Estimation of Infectious Disease Reproduction Number | ||
| When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a reliable estimate for the basic reproduction number, $R_{0}$, from the limited information available. We present a novel method that enables us to make a reliable real-time estimate of the reproduction number at a much earlier stage compared to other available methods. Our method takes into account the possibility that a disease has a wide distribution of infectious period and that the degree distribution of the contact network is heterogeneous. We validate our analytical framework with numerical simulations. | ||
| MSD3a | Dawes, Adriana | |
| University of Alberta | ||
| Cytoskeletal reorganization in the early C. elegans embryo | ||
| Shortly after fertilization, single cell embryos of the nematode worm C.elegans have a symmetric protein distribution on the cortex, a thin, actin rich layer below the cell membrane. In response to some currently unknown cue, the cell begins a reorganization of proteins and cellular structures, including the cortex, transforming the cell to a highly polarized configuration with distinct biochemical domains at the anterior and posterior poles. In this talk, I will present a model of interactions between the actin cortex and Par proteins, which are asymmetrically localized in the polarized embryo. Small perturbations in the Par protein distribution in one area of the cell may be sufficient for symmetry breaking and the initiation of polarization in the embryo. I will discuss possible biological mechanisms that could give rise to these perturbations, and their significance for the initiation of polarization and cytoskeletal reorganization at the single cell stage. | ||
| MSD3c | de Vries, Gerda | |
| University of Alberta | ||
| Quantitative Analysis of Single Particle Tracking Experiments | ||
| A commonly used experimental technique to study the movement of biomolecules is Single Particle Tracking (SPT). SPT involves tagging biomolecules (such as proteins) with a fluorescent label and observing and recording their trajectories over time. A diffusion coefficient describing the movement of the biomolecules then can be extracted from the data from mean square displacement calculations. The method of data collection from individual biomolecules is analogous to that from individual animals. Ecologists regularly quantify movement from observation of animals moving in the field, using the concepts of net squared displacement and residence index. We (1) explore the quantitative methods used in ecology to characterize the movement of animals from tracking data, and (2) investigate the possibility of adapting these methods to characterize the movement of biomolecules. | ||
| CTC1c | Deroulers, Christophe | |
| University Paris Diderot-Paris 7 | ||
| The phase diagram of elongated migrating cells: aggregation without attraction | ||
| Many migrating cells have an elongated shape, e.g. cancerous astrocytes diffusing out of a spheroid [1] or myxobacteria [2], and they tend to migrate in a preferred directions, with changes of direction, or even complete reversal [2], from time to time. It is well known from simple models that a population of point-like migrating cells behaves, at large time scales, in a diffusive manner [3], unless the cells exert some kind of attraction on their neighbours. Here, we investigate the collective behaviour in two dimensions of elongated cells with preferred migration in the direction of elongation, random rotations at a fixed rate, and hard-core repulsion (to prevent cells from penetrating one another). We find, on the basis of numerical simulations on a regular lattice, that the cells may spontaneously form aggregates if the random rotations occur not frequently enough and if the density of cells is high enough. This happens even though there is no attraction between cells, and even for cells that do not migrate always in the forward direction, but are allowed to make random backward steps. The parameter space is divided into two regions with nontrivial boundaries, one where cells form aggregates, and the other one where their population behaves in a simple diffusive way. The change of behaviour is abrupt when the boundaries are crossed. Finally, we establish approximate equations for the density of cells. They enable us to give an analytical model of this phenomenon. [1] M. Aubert, M. Badoual, S. Féréol, C. Christov, and B. Grammaticos, Phys. Biol. 3, 93 (2006); C. Deroulers, M. Aubert, M. Badoual, and B. Grammaticos, Phys. Rev. E 79, 031917 (2009) [2] Y. Wu, A. Dale Kaiser, Y. Jiang, and M. S. Alber, PNAS 106, 1222 (2009) [3] H. G. Othmer, S. R. Dunbar, and W. Alt, J. Math. Biol. 26, 263 (1988) | ||
| Coauthor(s): Mathilde Badoual, Basil Grammaticos | ||
| MSD6b | Di Rosa, Francesca | |
| Institute of Molecular Biology and Pathology, Consiglio Nazionale delle Ricerche, Rome, Italy | ||
| Kinetics of in vivo proliferation and death of memory and naive CD8 T cells: parameter estimation based on BromodeoxyUridine (BrdU) incorporation in spleen, lymph nodes and bone marrow | ||
| To study naive and memory CD8 T cell turn-over, we performed BrdU incorporation experiments in adult thymectomized C57BL/6 mice and analyzed data in a mathematical framework. The following aspects were novel: i) we examined the bone marrow, in addition to spleen and lymph nodes, and took into account the sum of cells contained in the three organs; ii) to describe both BrdU-labeling and -delabeling phase, we designed a general mathematical model, in which cell populations were distinguished based on the number of divisions; iii) to find parameters, we used the experimentally determined numbers of total and BrdU+ cells and the BrdU-labeling coefficient. We treated mice with BrdU continuously via drinking water for up to 42 days, measured by flow cytometry BrdU incorporation at different times and calculated the numbers of BrdU+ naive (CD44int/low) and memory (CD44high) CD8 T cells. By fitting the model to data, we determined proliferation and death rates of both subsets. Rates were confirmed using independent sets of data, including the numbers of BrdU+ cells at different times after BrdU withdrawal. We found that both doubling time and half-life of the memory population were about 9 weeks, whereas for the naive subset the doubling time was almost one year and the half-life roughly 7 weeks. Our findings suggest that the higher turn-over of memory CD8 T cells as compared with naive CD8 T cells is mostly attributable to a higher proliferation rate. Our results have implications for interpreting physiological and abnormal T cell kinetics in humans. | ||
| PLEN2 | Dieckmann, Ulf | |
| International Institute for Applied Systems Analysis, Laxenburg, Austria | ||
| Dynamics at the interface of ecology and evolution | ||
| Adaptive evolution is ecology in action (Krebs 1985). Selection pressures in natural systems cannot be understood without accounting for the often complex demography, ecology, and ecosystem embedding of populations. Conversely, predicting changes in natural systems exposed to strong anthropogenic impacts requires accounting for the prospect of rapid contemporary evolution. This presentation provides an overview of modeling approaches linking ecological and evolutionary dynamics, ranging from evolutionary games, adaptive dynamics, and reaction-diffusion systems to individual-based multi-locus genetics and eco-genetic modeling. Particular attention will be given to the role of ecology in speciation processes and to describing rapid evolution induced by harvesting. Different research questions are best addressed by different modeling approaches, underscoring the need for methodological pluralism in ecology and evolution. | ||
| MSA5b | Diekman, Casey | |
| University of Michigan | ||
| Clustering and Temporal Silencing of Electrical Activity in the Suprachiasmatic Nucleus | ||
| Neurons in the suprachiasmatic nucleus (SCN) of the hypothalamus are thought to communicate time of day information through circadian variation of their firing frequency, with low rates during the night and higher rates during the day. Based on simulations using a detailed model of the ionic currents within SCN neurons, we predict that the neural code of the SCN is more complex and that throughout the day clock-containing SCN neurons can transition between firing and quiescent states, including an unusual depolarized rest state. We also simulate networks of 10,000 SCN neurons at a set circadian phase with GABAergic coupling, and observe the formation of clusters of neurons with near synchronous firing. We find that the clustering depends on network properties such as synaptic strength and density. Experimental data supporting these modeling results will also be discussed. | ||
| CTH4a | Dimitrov, Dobromir | |
| Fred Hutchinson Cancer Research Center | ||
| Modeling the Gender-Specific Benefits of Wide-Scale Microbicide Interventions | ||
| Vaginal microbicides (VMB) are currently among the few promising biomedical interventions candidates for preventing heterosexual transmission of HIV. More than 40 products have been tested in clinical trials and some of them have already produced encouraging results in reducing susceptibility of their users. However, there are concerns that the next generation of microbicide containing ARV (ARV-VMB) may lead to the development of antiretroviral resistance and could paradoxically become more beneficial to men at the population-level. We develop and analyze deterministic models of HIV transmission to study the public health impact of a VMB intervention in a sexually heterogeneous population. We formulate indicators to evaluate population-level benefits and to quantify the likelihood of male or female advantage in the benefits of a intervention under a wide array of utilization. We investigate the influence of different factors such as VMB efficacy, transmission probabilities, and rates of development of resistance on benefit distribution between sexes. Our analysis shows that VMB is very much a female prevention tool. The likelihood of male advantage in benefits is substantial only if the risk of systemic absorption of the product is high and the HIV-positive women remain on VMB indefinitely. Successful control measures that restrict VMB-usage by HIV-positive women reduce the risk of resistance development and further increase the likelihood of female advantage in prevented infections. | ||
| Coauthor(s): Ben Masse, Marie-Claude Boily | ||
| MSC4d | Duffin, James | |
| Departments of Anaesthesia & Physiology, University of Toronto | ||
| Modeling interactions between the control of cerebral blood flow and the chemoreflex control of breathing: implications for stability | ||
| The regulation of brain (central) hydrogen ion concentration involves both the control of blood gas carbon dioxide tensions by altering pulmonary ventilation, as well as the control of cerebral blood flow by altering cerebrovascular resistance. Cerebral blood flow is sensitive to changes in arterial blood gas tensions and particularly to carbon dioxide, while pulmonary ventilation is sensitive to the hydrogen ion concentrations at both peripheral and central respiratory chemoreceptors. The central respiratory chemoreceptor stimulus is determined partly by cerebral blood flow; increases in cerebral blood flow wash out central carbon dioxide to lower the central hydrogen ion concentration, and this cerebrovascular reactivity thus helps regulate and maintain central hydrogen ion concentration. These two control systems therefore interact. Modeling this interaction requires measurement of the respiratory chemoreflex characteristics independent of the effects of cerebrovascular reactivity. This goal can be accomplished by using a rebreathing method that controls the peripheral and central respiratory chemoreceptor stimuli, in terms of carbon dioxide and oxygen gas tensions, independent of both pulmonary gas exchange and cerebral blood flow. Combining the results from a large number of rebreathing tests to produce the response characteristics of an average subject has yielded parameter estimates for a chemoreflex control model. This model has been applied to interpret the changes in respiratory chemoreflex regulation observed in several experimental conditions including sleep, the acute response to hypoxia incorporating hypoxic ventilatory decline, and the facilitation of ventilation by intermittent hypoxia and long-term hypoxic facilitation. Extension of this model to include the relations between the partial pressure of carbon dioxide controlled by pulmonary ventilation and the hydrogen ion concentrations sensed by the peripheral and central chemoreceptors has allowed the model to reproduce the influence of acid-base changes on the control of breathing, including the adaptation to altitude. The physiology of cerebrovascular control is not yet fully understood, and measurement techniques are still in development. Nevertheless, recent experiments have provided the basis of a model of cerebrovascular reactivity. When combined with the chemoreflex model, a steady state model of respiratory control is produced that is capable of predicting the changes in respiratory stability that matches recent experimental findings using pharmacologically-induced changes in cerebrovascular reactivity. A dynamic model with these features offers further insights into the interactions between the chemoreflex control of breathing and the control of cerebral blood flow. | ||
| CTF6b | Dumont, Yves | |
| CIRAD - UMR AMAP | ||
| Some results about vector control for the Chikungunya disease | ||
| The aim of this talk is to present recent investigations on the Chikungunya Disease that hitted Reunion Island and other countries in 2005-2006. In a previous work, we proposed and studied a deterministic model developed to explain the outbreak of 2005 and possible links with the explosive epidemic of 2006. Here, we study various possibilities to contain or to stop the epidemic of 2006 through appropriate mosquito control tools. Based on new results on the Chikungunya virus and several experiments done by health authorities, we study several types of control tools used in 2006 to contain the Chikungunya epidemic. After a short analysis of the model, we present several simulations with and without mosquito control. In particular, we show that an early use of a combination of massive spraying and mechanical control (like the destruction of breeding sites) can be efficient to stop or to contain the propagation of Chikungunya infection. | ||
| Coauthor(s): Frédéric Chiroleu | ||
| MSA1a | Dushek, Omer | |
| Sir William Dunn School of Pathology, Oxford University | ||
| A role for localized rebinding in rapid and reliable T cell responses | ||
| In this talk I will first attempt to provide context for the symposium talks by providing a brief overview of membrane reactions, focusing on the regulation of the T cell antigen receptor (TCR) which is expressed on the surface of T cells. I will then discuss the role of TCR-antigen rebinding upon chemical dissociation in antigen discrimination by T cells. Antigen discrimination is the process by which T cells rapidly and specifically discriminate between potential stimuli based on the kinetic parameters of the T cell receptor – antigen bond. These antigenic molecules are presented among thousands of chemically similar endogenous peptides that may also bind TCR, raising the question of how T cells can accurately and rapidly make the decision to respond to certain antigens but not others. Using mathematical modeling and simulation tools we investigate the role of immediate T cell receptor – antigen rebinding in the rapid and reliable decision-making process. We show that including a signal persistence state in kinetic proofreading models allows individual receptors to integrate the duration of multiple binding events. Discrimination is achieved via an effective threshold in the sum of binding durations, a quantity that is sensitive not only to the off-rate but also to the on-rate. We conclude by discussing existing data that supports the notion that receptor/ligands undergo immediate rebinding at membrane interfaces and provide evidence that rebinding increases the potency of antigens. | ||
| MSC2c | Dwyer, Greg | |
| Department of Ecology & Evolution, University of Chicago | ||
| Models of pathogen-driven outbreaks that are motivated by experiments | ||
| Many insects undergo outbreaks, in which their densities rise from levels that are undetectable, to levels at which massive defoliation occurs. Mathematical models have played a key role in identifying the mechanisms that drive outbreak cycles, but most models are constructed only to explain observational data. Testing models with experimental data as well can often reveal the importance of mechanisms that are not immediately apparent in observational data. Work in my lab therefore attempts to use experimental data to motivate the construction of models, which are then tested with observational data. We have used this approach to show that population structure has a strong effect on interactions between the gypsy moth (Lymantria dispar) and its nucleopolyhedrovirus. The nucleopolyhedrovirus is a fatal pathogen that is transmitted as host larvae feed on leaves, and it often causes intense epidemics in outbreaking populations. By allowing larvae to feed on virus-contaminated leaves in the field, we are able to directly test for factors that affect viral transmission rates. Our preliminary experiments showed that heterogeneity in susceptibility among individuals plays a key role in transmission, but inserting our estimates of this heterogeneity into models of pathogen-driven outbreaks leads to a stable point equilibrium in the models. This type of behavior is inconsistent with the cyclic outbreaks observed in gypsy moth populations. Further experiments, however, showed that susceptibility is heritable and appears to evolve, whereas standard models assume that average susceptibility is constant over time. We therefore extended existing models to allow natural selection to drive fluctuations in average susceptibility. In these evolutionary models, susceptibility declines immediately after outbreaks because of selection for resistance, but it rises during inter-outbreak periods because of a fecundity cost of resistance. The resulting models allow for realistic outbreaks even if heterogeneity in susceptibility is constant, and accurately predicts changes in susceptibility observed in the field. In ongoing work, we are further extending our models to allow for mechanisms that underlie susceptibility. In our current models, susceptibility is expressed as a per-capita risk of infection, but relating infection risk to variability among individuals is difficult. We are therefore developing models that relate individual host behaviors to a host's risk of infection, and thus to disease dynamics. In addition, we are developing models that incorporate the evolution of viral virulence, by keeping track of individual virus strains. Our ultimate goal is to combine these separate models into a combined model that relates coevolution at the level of individual hosts and pathogen particles to the long-term dynamics of insect outbreaks. | ||
| MSG1b | Dyson, Rosemary | |
| Centre for Plant Integrative Biology, University of Nottingham, UK | ||
| Mathematical modelling of anisotropic plant root cell growth | ||
| We consider the root elongation zone of the model plant Arabidopsis thaliana, in which cells undergo rapid anisotropic growth: the radius remains approximately constant whilst the length increases 30 fold or more. Plant cells differ from animal cells by the presence of a tough cell wall, containing oriented cellulose microfibrils, which maintains a high turgor pressure within the cell. Growth has been traditionally modelled using the 'Lockhart equation' which relates the growth rate of the cell length to the internal pressure but takes no account of the mechanical anisotropy caused by the microfibrils; growth is assumed to only occur axially. We employ a fibre-reinforced fluid model for a pressurised hollow viscous cylinder, exploiting the small aspect ratio of the walls, to represent a growing cell. By taking an appropriate limit of the various viscosity functions we give a solution in which the microfibrils maintain the cell radius whilst allowing growth axially. We find an expression for the growth rate of the cell length, which reduces to the 'Lockhart equation' upon appropriate simplification. The model therefore provides insights into the geometric and biomechanical parameters underlying bulk quantities such as 'extensibility', and shows how fibre reorientation may influence growth. | ||
| CTH5a | Edwards, Andrew | |
| Pacific Biological Station, Fisheries and Oceans Canada | ||
| How a lack of statistical analysis led to claims that many animals forage using similar random walks described by power-law distributions | ||
| What do the following foragers have in common: fishermen, grey seals, microzooplankton, wandering albatrosses, bumblebees, deer, reindeer, jackals and human hunter gatherers? Through a series of papers, it has been claimed they exhibit similar movement patterns, namely Levy flights (which are scale-free random walks with step lengths from probability distributions that have heavy power-law tails). However, the power law distributions were concluded by fitting straight lines to log-log histograms of data. I show that such methods are misleading - for simulated data they give the wrong answer. They also implicitly assume that the data are well described by a power law, without allowing for an alternative. Using likelihood methods and Akaike weights (to test simple alternative hypotheses), re-analysis of the data sets finds that Levy flights are far from a universal foraging strategy. Some of this work is published in Nature, 449:1044 and J. Anim. Ecol., 77:1212, yet many new results are also presented. | ||
| MSG2c | Eiswirth, Markus | |
| Fritz-Haber-Institut | ||
| Application of quotient rings for stability analysis in chemical systems | ||
| Concepts from linear algebra and algebraic geometry (polynomial rings) can be used to determine analytically the stationary solutions in systems of ordinary differential equations of polynomial form. The stability analysis via the Jacobian matrix often leads to complicated expressions which can hardly be analyzed. It is shown that these expressions can be simplified using elimination theory, i.e. forming quotient rings of the corresponding polynomial ring. The normal forms obtained by generating the quotient rings are representatives of the coefficients of the characteristic equation so that their sign changes in dependence of a parameter and hence the stability and local bifurcations can be determined. The procedure is illustrated using a simple surface reaction. This is a joint work with Sonja Sauerbrei. | ||
| MSE3d | Enderling, Heiko | |
| Tufts University School of Medicine | ||
| The induction of DNA double-strand breaks in bystander stromal cells by cancer cells, a computational perspective | ||
| We investigate in vitro and in vivo influences of tumor cells on neighboring stromal cells, as one aspect of multicellular effects during carcinogenesis. We study the constitutive level of DNA damage/repair, as indicated by standard g-H2AX and 53BP1 repair damage protein foci assays, in cells from tumors and neighboring stroma. We found that conditioned media from tumor cells produced an increase in genes related to DNA double-strand breaks (DSBs) in the stromal cells. In vivo studies also demonstrated a diffusive pattern of DNA DSBs in the stroma of the tumor. We demonstrate that cancer cells induce DSB and activate repair proteins in neighboring cells analogous to the radiation bystander effect, indicating that DNA damage is communicated among cells. This effect could indicate tumor subversion of the microenvironment to facilitate the breakdown of host barriers to tumor expansion and thus tumor progression. We develop a hybrid discrete continuous mathematical model of tumor growth within a stromal tissue environment. We show that certain tissue architectures can maintain the tumor in a space-restrained dormant stage. We simulate diffusion of stress-signals from the tumor to its microenvironment and induction of DNA DSBs in adjacent cells, which can with a certain frequency trigger cell death. We present simulation results that show how tumor-induced cell death can enable tumor progression and invasion. | ||
| MSG4d | Erickson, Harold | |
| Duke University | ||
| FtsZ bending membranes inside and outside liposomes | ||
| We have created FtsZ-YFP-mts, where an amphipathic helix on the C-terminus tethers FtsZ to the membrane. When incorporated inside multilamellar tubular liposomes, FtsZ-YFP-mts can assemble Z rings that generate a constriction force. When added to the outside of liposomes, FtsZ-YFP-mts bound and produced concave depressions, bending the membrane in the same direction as the Z ring inside liposomes. Prominent membrane tubules were then extruded at the intersections of concave depressions. We tested the effect of moving the mts from the C terminus to the N terminus, which is approximately 180 degrees from the C-terminal tether. When mts-FtsZ-YFP was applied to the outside of liposomes it generated convex bulges, bending the membrane in the opposite direction to the concave depressions. We conclude that FtsZ protofilaments have a fixed direction of curvature, and the direction of membrane bending depends on which side of the bent protofilament the mts is attached to. This supports models in which the FtsZ constriction force is generated by protofilament bending. Coauthors: Masaki Osawa and David E. Anderson | ||
| PLEN5 | Fagan, Bill | |
| Department of Biology, University of Maryland | ||
| Riverine Landscapes: Exploring Connectivity, Extinction Risk, and Biogeography in an Alternative Geometry | ||
| Riverine landscapes differ in fundamental ways from terrestrial ones. Of particular note is that the dendritic patch geometry and downstream flow of river networks leads to inherently asymmetrical opportunities for connections among parts of a landscape. My colleagues and I have been exploring what happens when spatial ecological processes such as dispersal play out in riverine systems, with a particular emphasis on understanding how these processes influence species' biogeography and extinction risks. Here I will discuss how critical spatial features, such as branching hierarchical geometry, upstream-downstream sequencing of habitat units, and habitat fragmentation, are important to species ecology and conservation in riverine landscapes. To illustrate these points, I will discuss recent research drawing upon detailed empirical datasets for the biogeography of fishes in the Colorado and Mississippi-Missouri River systems. Taken together these research projects illustrate the important contributions that riverine geometry makes to our understanding of interspecific variation in extinction risks and the potentially broad relevance of the neutral theory of biodiversity. | ||
| MSE1a | Feng, Zhilan | |
| Purdue University | ||
| Control and Prevention Strategies for the Spread of Influenza | ||
| Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However, the benefit of antiviral use can be compromised if drug-resistant strains arise, leading to an increase in epidemic size with a higher level of treatment. Using a mathematical model we explore the impact of the vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes both drug-sensitive and -resistant strains. Analytical and numerical results of the model show that the the conventional quantity for the control reproduction number is not appropriate to use for gaining insights into the disease dynamics. We derive a new reproduction number by considering multiple infection generations, and demonstrate that this new reproduction number provides a more reasonable measure for evaluating control programs and identifying optimal control strategies. | ||
| MSC5a | Fitzpatrick, Ben | |
| Loyola Marymount University | ||
| Undergraduate Training in Mathematical Biology at LMU | ||
| Loyola Marymount University is a liberal arts school with a student-centered focus. Except for Master of Arts in Teaching degrees in Mathematics and Natural Sciences, LMU has no science graduate program. Preparing undergraduates for graduate and professional school, as well as non-academic careers, is the goal of our science and mathematics departments. In the third year of an NSF-supported Interdisciplinary Training for Undergraduates in Biology and Mathematics (UBM) program, we have developed strong collaborations between Biology and Mathematics faculty, and we are actively working towards the implementation of an undergraduate degree program. This talk will describe some of our experiences (both positive and negative) in recruiting students, building bridges, and improving course content and offerings. | ||
| CTC1d | Flach, Edward | |
| Technical University Dresden | ||
| Motility and the CPM | ||
| The differential adhesion hypothesis suggests that a mixture of cells will sort by type due to the difference in their adhesiveness. The cellular Potts model was proposed to simulate this behaviour. This model has gained popularity due to its extensibility: the model reproduces many complex biological systems successfully. However, the basic dynamics of the system have gone untested. Cell sorting presupposes motility, and so we remove sorting from the simulation to examine movement by itself. Within a framework of experiments, we test the model response to each parameter. We find that the model is essentially well behaved, although some aspects are unintuitive. We review our findings in the context of biological systems: do the parameters have physical meaning? does the model simulate reality? | ||
| CTE7a | Forde, Jonathan | |
| Hobart and William Smith Colleges | ||
| Dynamics of hepatitis B virus infection: what causes viral clearance? | ||
| Hepatitis B is a virus that infects liver cells and leads to either acute or chronic liver disease. The mechanisms responsible for the infection outcome are not well understood, with immune responses being involved in both curing and killing of cells. The formation of cured cells and their role in the infection outcome is studied analytically and validated numerically. Mathematical models for the hepatitis B viral dynamics are developed, and local and global stability analysis of their long term behavior is performed. The models are then fitted to patient data of viral decay following the peak of infection. The results show that viral clearance is only dependent on the strength of the combined killing and curing and independent of the characteristics of the cured cells. | ||
| MSC4b | Francis, Darrel | |
| Imperial College London | ||
| Dynamic therapy of periodic breathing with exogenous carbon dioxide delivered as an inspired gas or endogenously using a cardiac pacemaker: the theoretical potential and the practical challenges. | ||
| For a disease state characterized by oscillatory ventilation, an ideal dynamic therapy would apply a counteracting oscillation in ventilatory stimuli. In my talk I will discuss how this goal might be achieved by either: (a) Dynamically fluctuating FICO2; (b) Modulating respiratory gas transport through the circulation by repetitive alternations in the heart rate, using a cardiac pacemaker, to elicit oscillations in respiratory variables. I will list some challenges involved in dynamic exogenous CO2 therapy (case a.) and discuss how they might be overcome. This will include examples of simulations of periodic breathing and periodic breathing with automated dynamic interventions. I will provide details of the equipment we are developing which is designed to facilitate this kind of a therapy. I will then discuss the potential of using pacemaker manipulation to dynamically alter ventilation (case b.). By including acute cardiac output manipulations into an integrated mathematical model of respiratory control, we can see that a rise in cardiac output should yield a gradual rise in end-tidal CO2 and subsequently ventilation. An alternating pattern of cardiac output variation might therefore create oscillations in arterial CO2 and consequently in ventilatory stimuli. I will present clinical data indicating that well timed alteration in cardiac output might really be achievable. I will then discuss the difficulties in converting this kind of intervention into a practical therapy for periodic breathing in heart failure. | ||
| MSB1b | Freeman, Spencer | |
| University of British Columbia | ||
| Regulation of tumor cell adhesion dynamics in 2- and 3-D matrices | ||
| Once cancer cells dissociate from a primary tumor, metastatic progression depends on their ability to adhere to extracellular matrix (ECM) components and become motile cells that enter the circulation, invade distant organs, and establish secondary tumors. Much focus on the metastatic cascade has been in determining genetic and proteomic signatures of invasive tumor cells, however, how force-dependent molecular switches and cell tension affect invasiveness are less well understood. Here we describe the Rap1 GTPase as a molecular switch activated in response to changes in extracellular force. Activated Rap1-GTP binds a number of proteins that control integrin activation and actin dynamics at the cell membrane, thereby serving as a rheostat to balance intracellular tension to extracellular compliance and cues. I will discuss this role for Rap1 activation in the context of tumor cell motility and cell morphology at the single cell level. This will be related to how Rap1 activation and intracellular tension affect adhesion dynamics at the focal adhesion level in both 2 and 3-dimensional microenvironments. | ||
| MSB2b | Fricks, John | |
| Penn State University | ||
| The Role of Neck Linker Modification in Kinesin Stepping. | ||
| Kinesin is a molecular motor which processes along a microtubule by hand over hand steps. In recent experiments, the motors have been modified with the insertion of amino acids to increase the length of the neck linker connecting the heads of the motor. These modifications can have profound effects on the velocity and number of steps taken by the motor. In this talk, we will compare three different stochastic models which incorporate these modifications and discuss their relationship to the experimental results. This is joint work with Matt Kutys, Venkatesh Hariharan, and William Hancock. | ||
| MSD2d | Friedenberg, Nicholas | |
| Applied Biomathematics | ||
| Some ideas about climate and the future of forest insect pests | ||
| Abstract: Insect phenology defines the nexus of climate and population dynamics. Thermal effects on development are generally non-linear and stage-specific, creating bottlenecks in the developmental program that determine not only the timing but the synchrony of cohort emergence. In turn, synchrony affects realized spatiotemporal density, providing a mechanistic link between climate and density-dependence and a means for approaching problems associated with species range limits or outbreaks. These ideas are explored in two mass-attacking species, the southern pine beetle and the mountain pine beetle using a stochastic differential equation approach to ecophysiological modeling that captures basic demographic rates as well threshold attack densities. While the two species have similar requirements for success at the scale of a single host, their phonological differences lead to an interesting divergence in the role of climate in population dynamics. | ||
| CTC7a | Fuhrman, Kseniya | |
| Milwaukee School of Engineering | ||
| Modeling Nutrient Flow in Virus-Host Interactions in Aquatic Systems | ||
| In this talk, we will examine the development and analysis of a mathematical model for describing the dynamics of infection by a virus of a host population in a freshwater environment. This interaction is part of the microbial loop, as it incorporates microorganisms as an integral component of the aquatic food chain. Our approach illustrates a new type of theoretical models that link population dynamics with nutrient cycling. We provide a biological description of the processes involved and discuss the mathematical analysis of the resulting system including the existence and uniqueness of solutions, equilibria, asymptotic, and persistence analysis. The biological relevance of the proposed model will be addressed, as we validate the model by solving an inverse problem with use of laboratory data. | ||
| Coauthor(s): Gabriella Pinter | ||
| MSB5b | Gaff, Holly | |
| Old Dominion University | ||
| Effects of migration on tick-borne disease risk | ||
| Human monocytic ehrlichiosis (Ehrlichia chaffeensis), HME, is a tick-transmitted, rickettsial disease that has recently increased substantially in the USA in recent years. The ticks that spread this disease have white-tailed deer as a major host species. The increase in deer populations in recent years has led to changes in their dispersal patterns. The impact of this change on the areas of risk for humans is explored using a mathematical model. | ||
| MSC6d | Ganusov, Vitaly | |
| Los Alamos National Laboratory | ||
| The contribution of cell-intrinsic vs. extrinsic factors in determining magnitude of expansion of CD4 T cell populations | ||
| It is generally accepted in immunology that after initial activation CD8 and CD4 T cells undergo programmed proliferation and differentiation into effectors. What controls expansion of T cell populations and what constitutes the “program” of the T cell response remains poorly understood. Broadly speaking, proliferation of T cells after initial triggering could be controlled by extra-cellular (e.g., level of antigen, cytokines, other cells, etc.) or intra-cellular (e.g., number of cell division) factors. Using a system of in vitro stimulated CD4 T cells, we investigated how the concentration of interleukin 2 (IL-2), a known “growth” factor of T cells, controls the magnitude of expansion of T cells in vitro. Specifically, we analyze data on the dynamics of CFSE-labeled polyclonal CD4+ T lymphocytes in vitro after anti-CD3 stimulation at different concentrations of exogenous IL-2. We find that to adequately describe the dynamics of T cells at low concentrations of exogenous IL-2, the death rate of divided cells has to increase with the number of divisions, cells have undergone. IL-2 hardly affects the average interdivision time. At low IL-2 concentrations 1) fewer cells are recruited into the response and successfully complete their first division; 2) the stochasticity of cell division is increased; and 3) the rate, at which the death rate increases with the division number, increases. In contrast, the model in which division and death rates of T cells depend on the IL-2 concentration, failed to adequately describe these data and also generated predictions that were inconsistent with additional measurements. In summary, our results suggest that expansion of CD4 T cell populations, at least in vitro, could be controlled by cell intrinsic factors. | ||
| MSG1c | Geitmann, Anja | |
| Institut de recherche en biologie végétale, Université de Montréal, Canada | ||
| Coordination of material supply and growth - vesicle delivery in pollen tubes | ||
| Tip growing plant cells generate a cylindrical cell by surface expansion at the apical end. In pollen tubes this spatially confined, rapid growth activity requires enormous amounts of pectic cell material to be delivered to the growth site at high rates and with precise targeting. The spatio-temporal movement patterns of exocytotic vesicles in growing pollen tubes are controlled by the actin cytoskeleton. Remarkably, the target region at the apical pole of the cell does not contain much filamentous actin. We model the vesicular trafficking using as boundary conditions the expanding cell wall and the actin array forming the apical actin fringe. Dynamic advancement of the fringe was obtained by imposing a steady shape and constant polymerization rate of the actin filaments. Letting vesicle flux into and out of the apical region be determined by the orientation of the actin microfilaments and by exocytosis was sufficient to generate a flow that corresponds in magnitude and orientation to that observed experimentally. This model explains how the cytoplasmic streaming pattern in the apical region of the pollen tube can be generated without the presence of actin microfilaments. (Joint work with Jens Kroeger and Firas Bou Daher) | ||
| CTB7b | Gerberry, David | |
| Purdue University | ||
| A data-based model for tuberculosis: Who should be vaccinating? | ||
| One of the first lines of defense against tuberculosis is the bacille Calmette-Guérin (BCG) vaccine. Although BCG is an old vaccine, studies of its protective efficacy have had widely divergent results. In addition, the vaccine can interfere with the diagnosis of latent TB infection. Due to these qualities, the international community has adopted varying policies on the vaccine's use. We introduce a dynamical system model for tuberculosis dynamics at the population level in order to examine the conditions which justify discontinuing BCG vaccination. Whenever possible, model parameters are defined in terms of control indicators estimated by the World Health Organization. The model is fit to TB data for eight countries with varying TB burdens and analyzed via numerical experiments, sensitivity analysis and dynamical systems theory. | ||
| Coauthor(s): Fabio Milner | ||
| CTB6d | Gevertz, Jana | |
| Princeton University | ||
| Multi-scale Mathematical Modeling of Brain Tumor Growth | ||
| Mathematical modeling of tumor growth has been an active area of research for the past several decades. One of the holy grails of the field is to develop a simulation tool that can be utilized in the clinic to predict tumor progression and propose individualized treatment strategies. In this talk, I will discuss the work we have done with this long-term goal in mind. In particular, I will focus on both the implementation of, and the results drawn from, several of the models we have developed. Questions we have addressed through our modeling efforts include: 1. How do the geometry and topology of the environment in which a tumor grows impact the shape, size and spread of a tumor? What are the consequences for patient prognosis? 2. Under what conditions can a tumor overcome its limited blood supply and grow to a macroscopic size? 3. What is the likelihood that advantageous or deleterious genetic mutations arise within a tumor and how do these mutations impact growth dynamics? After looking at a set of model variants that allows each of these questions to be addressed, I talk about recent efforts to merge these models into one comprehensive cancer simulation tool. I use the merged model to highlight biological features that must be considered in a clinically-relevant tumor growth algorithm, and to test the impact of vascular-targeting treatment strategies. | ||
| CTA6b | Ghosh, Suma | |
| Mathematics and Statistics, York University | ||
| Spatial Distribution of Pathogen in Pest Control: Traveling Wave Solution | ||
| Spatial pattern of pathogen distribution in site of control in an agricultural ecosystem has a major role to play in strategic planning of control the pest population. As the spatial spread of disease depends on horizontal transmission of disease agents, there are numerous factors like pathogen susceptibility, host movement, abiotic components such as climate one, which influence the overall effectiveness of the control policy. Insects exhibit a variety of physiological, morphological and behavioral responses to infection, which can affect both pathogen and host fitness. Behavioral modifications caused by NPV might have some inevitable effect on virus transmission and dispersal as well as on the predation in the system. Infection makes the insects more vulnerable to predators to some extents. On contrary, predators do not take more deadly insects. Thus there always exist some trade off between infection strength (such as virulence, etc) and predation for successful spread of infection in the site of control. This also contributes to the risk assessment of biopesticides, particularly the genetically modified baculoviruses. As initiation of new infection cycle in the system depends on the number of infected inoculums in the site, so spatial movement of infected hosts during the course of infection (i.e., latency period) influence the dynamics. Moreover, infection develops some behavioral changes inthe host, which makes them more vulnerable to the natural enemies. Thus, overall infection process in the system depends on such interrelated factors. We derive a delayed reaction-diffusion system in one spatial dimension using Von-Foerster equation and compute the minimum traveling speed at which infection spreads for successful transmission. We show that the minimum speed depends on the various system parameters, such as diffusivity of infectives, force of infection, incubation period, etc. | ||
| MSC5b | Goins, Gregory | |
| North Carolina A&T State University | ||
| Forming A Biomathematical Learning Alliance Across Traditional Academic Departments | ||
| Minorities are significantly under-represented as advanced degree holders in the biosciences and mathematics. A formal cross-departmental alliance at our University has connected a learning and research community among biology and mathematics students and faculty. BLEND was specifically formed to enable both faculty and undergraduates greater access to biomathematics learning and teaching. This new synergistic alliance of biology and mathematics faculty members became known as the Biomathematics Learning Enhancement Network for Diversity (BLEND). The BLEND alliance has significantly expanded and connected our small existing efforts across campus to promote collaborative biomathematics research and training. BLEND also has served as a forum for students and faculty to express their creativity, and ultimately succeed in careers at the intersection of math and biology. We believe BLEND will help lead to future re-shaping of our math and biology undergraduate training infrastructure at North Carolina A&T State University (NCATSU), a historically minority campus. This paper describes a comprehensive process of how early-adopting BLEND faculty at our campus bound together and built a critical mass of collaborations and partnerships. As a consequence of BLEND activity from 2005-2009, there is a significant increase in faculty pursuing research and shared discovery at the interface of math and biology. Particularly noteworthy, more underrepresented students, as undergraduates, are actively conducting research related to biomathematics. Because BLEND harnessed more meaningful integration among the Mathematics and Biology Departments, biomathematics research is highly promoted at NCATSU. As an immediate outcome, an increasing number of undergraduates are actively engaged in biomathematics, and many more students from our campus are motivated to continue graduate research in this area. | ||
| MSC6b | Goldstein, Byron | |
| Los Alamos National Laboratory | ||
| The Role of Serial Engagement in Mast Cell Signaling | ||
| The terms serial triggering and serial engagement entered the immunological lexicon when Valitutti et al. (1) reported that within the contact area between an antigen presenting cell and a T cell a few antigenic peptides bound to major histocompatibility complex mediated the internalization of hundreds of TCR receptors (TCRs). Although there has been a considerable effort to unravel the role of serial engagement of TCRs in activating T cells, the role of serial engagement of other multi-chain immune recognition receptors in cell activation has been ignored. I will review the roles that valence and receptor density play in determining the mean time for dissociation of multivalent ligands from cell surfaces and then present new results that allow us to estimate the number of receptors a single multivalent ligand can serial engage and the rate at which this engagement occurs. Finally, I will present results that use a detailed model of the early events triggered by bivalent ligands that aggregate receptors (FceRI) on mast cells (2). By simulating signaling induced by bivalent ligands that serial engage receptors at different rates while undergoing the same degree of kinetic proofreading, we can assess the role of serial engagement in mast cell signaling. 1. Valitutti, S., S. Muller, M.Cella, E. Padovan, and A. Lanzavecchia. Serial triggering on many T-cell receptors by a few peptide-MHC complexes. 1995. Nature, 275:148-151. 2.Faeder, J. R., W. S. Hlavacek, I. Reischl, M. L. Blinov, H. Metzger, A. Redondo, C. Wofsy and B. Goldstein. 2003. Investigation of early events in FceRI-mediated signaling using a detailed mathematical model. J. Immunol. 170:3769-2781. | ||
| MSE5b | Gonzalez, Tania | |
| University of California, Davis | ||
| The Spread of Avian Influenza Across Heterogeneous Farmscapes: | ||
| [This is work of Tania Gonzalez, Andy Huang, Mary Jacklin, Michelle Jensen, Christopher Mosser, Tushar Rawat, Matthew Reed, and Ying Wu.] Highly Pathogenic Avian Influenza (HPAI) is a virulent disease with many documented outbreaks across Europe and Asia. HPAI is endemic in Southeast Asia, but has the potential to jeopardize both human health and the poultry industry worldwide. Existing research on HPAI outbreaks has not examined the influence of poultry farm size and spatial distribution despite evidence suggesting these factors may play an important role in the spread of the disease. We developed and analyzed a multiscale model to represent HPAI disease dynamics. We used a spatially coupled stochastic SIR model to portray disease spread through a heterogeneous network of farms. The model was used to determine control strategies that minimize the number of poultry lost to infection or depopulation. We found that patterns of disease dynamics depend in a non-intuitive way on farm size and spatial patterns of farm location. These patterns also affect the combination of culling radius and response time that minimizes loss of chickens. Specifically, for some spatial patterns, an intermediate culling distance is optimal. | ||
| MSG2d | Goryachev, Andrew | |
| Centre for Systems Biology, The University of Edinburgh | ||
| Intracellular pattern formation with small GTPases | ||
| Recent experimental analysis of cytoskeleton regulation, membrane trafficking and other manifestations of membrane dynamics demonstrated that small GTPases of Ras superfamily play a fundamental role in these phenomena. However it remains unclear what makes small GTPases such a ubiquitous and almost indispensable element of the underlying molecular networks. Recently we demonstrated (FEBS Lett., 582: 1437, 2008) that the biochemical processes in the emerging bud of yeast S. cerevisiae comprise a Turing-type mechanism. The roles of the prototypical activator and substrate are played by GTPase Cdc42 in its active and inactive states, respectively. Analysis of the instability that results in the formation of the pattern, a cluster of the activated Cdc42 that marks the position of the bud morphogenesis, was performed by a complementary set of analytical and computational approaches. Among these, a graph-theoretic method developed by Mincheva and Roussel for spatially-distributed systems (J. Chem. Phys., 125: 204102, 2006) has been particularly insightful as it allowed us to identify in the complete reaction mechanism a critical feedback loop that undermines the stability of the spatially homogeneous state. In this presentation we will further develop the concept of the GTPase-based mechanism of pattern formation and address issues of stability and uniqueness of such patterns in biologically realistic models of intracellular pattern formation. This is a joint work with Natasha S. Savage. | ||
| CTH7b | Green, Edward | |
| Ohio State University | ||
| Non-local models for the formation of hepatocyte - stellate cell aggregates | ||
| Liver cell aggregates may be grown in vitro by co-culturing hepatocytes with stellate cells. This method results in more rapid aggregation than hepatocyte-only culture, and appears to enhance cell viability and the expression of markers of liver-specific functions. We consider the early stages of aggregate formation, and present a new mathematical model to investigate two alternative hypotheses (based on evidence in the experimental literature) concerning how stellate cells promote aggregate formation. The first hypothesis is that each population produces a chemical signal which affects the other, and enhanced aggregation is due to chemotaxis. The second hypothesis asserts that direct physical contact between the different cell types is the dominant mechanism: the stellates extend long cellular processes which pull the hepatocytes into the aggregates). We formulate nonlocal (integro-partial differential) equations to describe the densities of cells, which are coupled to reaction-diffusion equations for the chemical concentrations. The behaviour of the model under each hypothesis is studied using a combination of linear stability analysis and numerical simulations. The results are compared with experimental observations and suggest that the hepatocyte-stellate attraction is strongest in practice. Based on this, we predict the optimal seeding ratio of hepatocytes to stellates for promoting rapid aggregate formation. We also suggest experiments which could be performed to discriminate between the two hypotheses. | ||
| CTC7c | Greenman, Jonathan | |
| University of Stirling | ||
| Invasion, Resonance, Control | ||
| One of the most pressing problems with continuing climate change and natural habitat erosion is the invasion of undesirable plant and animal species and virulent pathogens. To study the conditions whereby such invasions can occur it is important to take into account the major impact that environmental forcing can have, especially when the ecological system is overcompensating and therefore vulnerable to resonance. The underlying theory, developed both algebraically and numerically, is presented and applied to eco-epidemiological systems and their subcomponents. It is clear from the analysis that the response of the system to forcing is highly sensitive both to the pathways taken by the disturbance through the system and to the configuration of the external forcing components, in particular the strengths and periods of and the lags between these components. The analysis addresses the key issues of (i) whether forcing helps or hinders invasion and (ii) whether the interaction between multiple forcing components leads to reinforcement or destructive interference. The theory can be used to solve the problem of how to design control strategies to prevent or (with biodiversity) allow invasion using anthropogenically managed countercyclical measures, exploiting the lag structure and the positive or negative reinforcement. The interference effect can also be used to address the biodiversity problem of how to reduce the risk of species exclusion when large amplitude oscillations force a population to dangerously low levels. The general point that ill-informed intervention can worsen the situation is well illustrated by the analysis. | ||
| PLEN7 | Grieneisen, Veronica | |
| Bioinformatics group, Utrecht University | ||
| A Reflux Loop Between Experiments and Modelling: Plant Development, Morphogen Gradients and Cell Polarity | ||
| During this talk I will illustrate the strength of connecting modelling concepts to novel experiments in the field of Plant Development, emphasising how both can and should develop side-by-side. I will show how such an alliance has been important to shed light on problems of (i) Morphogen gradients, through the example of Arabidopsis root growth; (ii) Patterning of new organs, through the example of rhyzotaxy; and (iii) Cell Polarity, through the example of pavement cells -- jigsaw-shaped cells of leaves. We use multi-level modelling, which combines processes occurring at different space and time scales, and apply obtained modelling concepts to instruct and design experiments. I will illustrate that the three topics are actually connected: we found that macroscopic organ properties (the Arabidopsis root), cellular geometries, internal gradients and cell-polarity dynamics are intimately intertwined, and only together can account for plant morphogenesis on the correct spatial and temporal time scales. All these studies yield generalising concepts that I will discuss in the light of animal systems as well. | ||
| CTH5b | Gurarie, Eliezer | |
| University of Helsinki | ||
| Modeling of encounter rates for randomly moving individuals: Mathematical predictions and ecological consequences | ||
| Encounters between organisms are universal prerequisites for many fundamental ecological processes: Feeding depends on the ability to encounter food items or prey, survival can depend on avoiding encounters with predators, and reproduction depends on mate encounters. The most widely applied null-models of encounter rates are variations of ideal-free gas models. These models, developed in the 19th century by Clausius and Maxwell, assume linearly moving particles with a heterogeneous distribution of velocities. Models of diffusion and dispersal in ecology, on the other hand, often assume homogeneous populations of randomly moving individuals. Actual movements of organisms are best approximated by some mixture of deterministic and autocorrelated random movements, while movement processes within populations or individuals are often heterogeneous. We present mathematical predictions and simulation results of the effect of random movement models and population-level heterogeneity on encounter rates in one and two dimensions. We discuss potential ecological consequences of the results on survival and foraging success, explaining, for example, some properties of observed rates of survival in migrating juvenile salmon. | ||
| Coauthor(s): James J. Anderson | ||
| CTC1e | Gurarie, Eliezer | |
| University of Helsinki | ||
| Characterizing three-dimensional helical movements of microorganisms from two-dimensional microvideographic tracking data | ||
| Helical swimming is among the most common movement behaviors in a wide range of microorganisms. Helical characteristics affect long-term migrations, short-term taxes, transmission and detection of hydrodynamic signals, predator-prey encounter rates, swimming energetics and other critical elements of microorganism ecology. However, microscopy data to characterize helical swimming in microorganisms is usually two-dimensional. We present a versatile, continuous, stochastic model of individual movement that can reflect helical swimming and a variety of other three-dimensional trajectories, but that can be efficiently parameterized from two-dimensional velocity autocorrelation data. The model separates the instantaneous velocity into a slowly varying, advective component and a perpendicularly oriented rotation. These deterministic movements, together with randomness and scales of autocorrelation in each of the components, can be interpreted in terms of the mechanics of movement and environmental stochasticity. As a case study, we estimate three-dimensional swimming parameters for hundreds of videotaped trajectories of a biflaggelate unicellular alga, Heterosigma akashiwo. On the basis of these parameters, we quantify cell-level and strain-level differences algal cells, and demonstrate how microscopic observations can be "scaled up" with data-driven simulations to much larger ecological time and space scales. | ||
| Coauthor(s): Mike Nishizaki, Danny Grünbaum | ||
| MSA4d | Gurarie, David | |
| Case Western Reserve University, Cleveland | ||
| In-host dynamics of mixed malaria infection with adaptive immunity | ||
| Multiple pathogen species or strains interact within host environment by competing for available resources, and by stimulating cross-reactive immune responses. Such "competition" plays important role for understanding the dynamics of infections, both on individual and community levels. It allows among other to study such evolutionary adaptations, as drug resistance or virulence. We shall outline some basic principles and mathematical approaches to modeling host-parasite interactions with adaptive immunity. Those will be applied to study in-host competition of multi-strain malaria (or malaria-type) pathogens, and its effect on evolution of virulence. | ||
| CTF1b | Haber, Eldad | |
| Emory University | ||
| Inverse problems in mathematical biology: energy metabolism and glucose models | ||
| Modern biology and medicine deal with a wide variety of control and inverse problems. These issues are mostly computational intensive and in general ill-posed inverse problems. We like to showcase solutions and algorithms targeting these ill-posed problems. In this talk we will present a general framework on ordinary differential equations dealing with parameter estimation, numerical control, and design issues in mathematical biology. To illustrate our work we will investigate the glucose metabolism. The glucose metabolism is a tight regulated system providing energy in humans. Dysfunctions of this system may lead to pathologies like diabetes. Establishing mathematical control algorithms is therefore essential in imbalanced glucose metabolisms. Along with the classical Minimal Model we will present a novel glucose model incorporating new findings in the Selfish Brain Theory centering the brain as the main control element. We will demonstrate the potentialitiesof our inverse algorithms on clinical data of a IVGTT (intravenous glucose tolerance test). | ||
| Coauthor(s): Matthias Conrad | ||
| MSE1c | Hansen, Elsa | |
| Queen's University | ||
| Characterizing the Effect of Emerging Resistance on the Optimal Treatment Strategy | ||
| Mathematical models are playing an increasingly important role in understanding the dynamics of epidemics and determining the best strategies for public health interventions. One of the numerous issues that should be considered when deciding how best to treat an infectious disease, is how the threat of emerging resistance affects the optimal treatment strategy. Using optimal control theory, we address this question for a deterministic SIR type model with mass action contact rates and characterize the treatment strategy that minimizes the total outbreak size. We show that the presence of resistance can, but does not always, change the optimal treatment strategy. We discuss the importance of accurately assessing the threat of resistance emergence and how the level of this threat changes the character of the optimal treatment strategy. We also detail how the basic reproduction numbers of the regular and resistant strains play a crucial role in determining the form of the optimal treatment policy. | ||
| CTH3c | Hartman, Jana | |
| The College of William and Mary | ||
| Calcium sparks and calcium homeostasis in a hybrid model of local and global calcium responses | ||
| Intracellular free calcium signaling in cardiac myocytes has been studied extensively through both experiments and modeling. Of particular interest are the changes in bulk calcium concentration in the cytosol and endoplasmic reticulum and the dynamics of localized calcium elevations due to calcium release from clusters of calcium-regulated ion channels. This paper develops a hybrid whole cell model that accounts for both of these spatial scales of calcium signaling and examines the effect of stochastic calcium release (i.e. calcium sparks) on whole cell calcium homeostasis. When used to simulate experimental studies that examined the effects of tetracaine and flecainide on local and global calcium signaling, the model behaves consistently with experiments and supports the qualitative explanations of experimental results that appeared in Zima et al. Biophys. J. 94(5): 1867, 2008. [Supported by The College of William and Mary's NSF-funded Undergraduates in Biological and Mathematical Sciences (UBM) program and NSF Grant No. 0443843 to GDS.] | ||
| Coauthor(s): Gregory D. Smith | ||
| MSE5e | Hayes, David | |
| Truman State University | ||
| Measuring the Structure of Vascular Networks | ||
| In cancer, the metabolic support of both the primary tumor and the metastatic cells is generally thought to require the growth of either new blood vessels from existing blood vessels (angiogenesis) or the growth of entirely new blood vessels from precursor cells (vasculogenesis). If a pharmaceutical agent can suppress new vascular network growth, one has a powerful adjunct therapy for cancer treatment. Common methods for measuring the effects of treatment on networks involve comparing control and treated networks on the basis of counts of branchpoints, network area, and thickness and lengths of vessels. We propose new measurements based on algebraic graph theory that are motivatived by the biology of the networks. We also describe the Vascular Network Toolkit (an ImageJ-based system) that automates the process of analyzing digital images of the vascular networks we study. | ||
| Coauthor(s): Bo Forrester | ||
| MSH6b | Heffernan, Jane | |
| York University | ||
| Immuno-Epidemiology: Bridging the gap between within-host and between-host dynamics for measles | ||
| Immuno-Epidemiological models combine individual (in-host) and population (epidemiology) level approaches to create an overall perspective of pathogen spread. We have developed a within-host model for the dynamics of measles, whose resultant dynamics can be used to drive an epidemiological model. Under the assumption of life-long immunity the population-level dynamics of the typical SEIR model of measles spread and our immuno-epidemiological model are identical. However, if immunity wanes over time, as evidence suggests, the effects of waning immunity can only be mechanistically captured by an immuno-epidemiological model. We find that, prior to vaccination, waning of immunity is epidemiologically irrelevant since repeated exposure to measles leads to multiple boosting events. However, with high levels of vaccination immunity can wane to such an extent that large-scale epidemics can ensue. We discuss the implications of this observation and the insights that immuno-epidemiology can bring to infection control. | ||
| MSA3a | Herrmann, Harald | |
| Functional Architecture of the Cell Lab, DKFZ, Heidelberg, Germany | ||
| Molecular mechanisms underlying intermediate filament organization: The impact of inherited human disease mutations | ||
| Intermediate filaments constitute, in addition to microtubules and microfilaments, the third principal filament system of the cytoskeleton that determines the architecture of metazoan cells. They are fibrous, coiled-coil forming proteins, which in man are coded for by more than 70 genes. Through interaction with various junctional complexes they integrate cells with the extracellular matrix and neighboring cells, and hence are the main determinants of cellular plasticity. The investigation of the in vitro assembly mechanism of cytoplasmic intermediate filament proteins such as vimentin has revealed that filament formation is characterized by a very rapid lateral association of soluble tetrameric subunits into 60 nm long, full-width “unit-length” filaments (ULFs). We have demonstrated for this proto-type intermediate filament protein that filament elongation occurs by the longitudinal annealing of ULFs into short, regular filaments. These filaments further longitudinally anneal and thus constitute a progressively elongating population of filaments that overtime become several microns long. Previously, we have provided a mathematical model for the kinetics of the assembly process based on the average length distribution of filaments as determined by time-lapse electron and atomic force microscopy. Thereby, we were able to substantiate the concept that end-to-end-annealing of both ULFs and short filaments is obligatory for the formation of long intermediate filaments (R. Kirmse et al., 2007, J. Biol. Chem. 282, 18563-18572). In a next step of our investigations into intermediate filament function, we have characterized the impact of previously identified disease mutants of the muscle-specific protein desmin on its assembly properties. Thereby we have gained further deep insight into the mechanics of intermediate filament assembly and higher order network formation as well as into their role as central element of cellular mechanical stress buffering systems. (in collaboration with , Dorothee Möller1, Norbert Mücke1, Harald Bär1,2, Hugo A. Katus2, and Ueli Aebi3 (1) German Cancer Research Center (DKFZ), Heidelberg, Germany; (2) Internal Medicine III, University Clinics Heidelberg, Germany; (3) M. E. Müller Institute for Structural Biology, Biozentrum, University of Basel, Basel, Switzerland) | ||
| CTC7d | Hilker, Frank M. | |
| University of Bath | ||
| Complex wildlife disease transmission dynamics in populations with demographic Allee effect | ||
| A general epidemiological model is considered, in which the host population is variable and subject to a strong Allee effect (population decline at small densities). The interaction between disease transmission, virulence and positive density-dependence due to the Allee effect can generate complex dynamics in a simple two-dimensional model of SI (susceptible - infected) type, including tri-stability, limit cycle oscillations and homoclinic loops. The various dynamical regimes can be understood mathematically in relation to a Bogdanov-Takens bifurcation. The system appears to be very sensitive to perturbations and control methods, which may have profound implications for biological conservation as well as pest management. Threshold quantities are derived that provide biological insight. The results highlight the importance of demographic processes in infectious disease models. | ||
| CTE6b | Hirashima, Tsuyoshi | |
| Department of Biology, Kyushu University | ||
| Mechanisms for Split Localization of Fgf10 Observed in Lung Bud Branching | ||
| In early lung development, endodermal epithelial tubes (lung buds) intrude into mesodermal mesenchyme covered with pleural cells, and form complex tree-like networks, via repeated use of morphogenetic processes: “elongation”, “terminal bifurcation” and “lateral budding”. When a bud is elongating, a peak concentration of Fgf10 is formed in the mesenchyme near the tip; whilst when a bud is bifurcating, two separate peaks of Fgf10 are formed instead. We develop a mathematical model to explain the spatial pattern of Fgf10 in the mesenchyme. Mesenchymal cells produce Fgf10 in response to SHH from the tip, with the highest concentration for an intermediate level of SHH. Fgf10 distribution has a single peak when the distance between the tip of the bud and the lung border (L) is long, but has two peaks when L is short. We also examine the orientation of two peaks and the condition for lateral budding. | ||
| Coauthor(s): Yoh Iwasa, Yoshihiro Morishita | ||
| CTH7c | Holloway, David | |
| British Columbia Institute of Technology | ||
| Chemical Dynamics and the Development of Plant Shape | ||
| How plants and animals achieve their forms has been an enduring question in the history of biology, from early descriptions to modern genetic manipulations. Plant shapes are especially challenging, since spatial chemical patterns determine cell type, but also drive (and respond to) tissue growth, a major determinant of overall plant architecture. Increasingly, physical and mathematical scientists are becoming involved in the unique problems of mechanics, transport, and pattern formation in plants. My work uses Turing-type reaction-diffusion models to drive localized surface growth, in 3D. I have been able to generate many of the shapes seen in plants, fitting results to data from single-celled algae and more recently to conifer embryos. These shapes can be understood in terms of transitions between solutions to the reaction-diffusion equations in response to domain change. I will describe some of the computational challenges to achieving stable, accurate model solutions with large domain growth and arbitrary shape change, and some of the directions we are taking experimentally and analytically to further characterize the chemical control of plant shape. | ||
| PLEN8 | Hosoi, Anette | |
| Hatsopoulos Microfluids Laboratory, Massachusetts Institute of Technology | ||
| Optimizing Locomotion: From Biology to Robotics | ||
| In this talk I will discuss various projects in which we take inspiration from nature to advance technology. The driving force behind bio-inspired design is the idea that, thanks to natural selection, if a structure exists in nature that performs a desired function, it is tough for engineers to dramatically improve upon the natural design. Yet, historically, the countless failures in biomimetics have been more notorious than its successes (e.g. airplanes with flapping wings). There are many reasons for these failures - impractical energy requirements and complexity of controls, among others. To avoid these pitfalls, our bio-inspired studies focus on simple biological systems (preferably organisms with primitive or, better yet, non-existant central nervous systems) in which the energy requirements are low and the biological solutions to challenging questions are grounded in mechanics rather than in neurological controls. | ||
| CTF5b | Hsieh, Ying-Hen | |
| China Medical University, Taiwan | ||
| Predator–prey model with disease infection in both populations | ||
| A predator–prey model with disease infection in both populations is proposed to account for the possibility of a contagious disease crossing species barrier from prey to predator. We obtain several threshold parameters from local analysis of various equilibria of the proposed system as well as coupled conditions on these threshold parameters which determine the stability of these equilibria. One of the coupled conditions, in the form of an ecological threshold number for the predator–prey ecosystem, always determines the coexistence of predators and prey. The other condition, in the form of a disease basic reproduction number, dictates whether the disease will become endemic in the ecosystem. Under one combination of these coupled conditions, a highly infectious disease could drive the predators to extinction when predators and prey would have coexisted without the disease. For another combination of the conditions, the predation of the more vulnerable infected prey could cause the disease to be eradicated in the ecosystem, in some case even approaching a disease-free periodic solution, when the disease would have otherwise remained endemic in the prey population in the absence of predation. This indicates that the presence of disease in both predators and prey could either promote or impair coexistence, and its precise impact needs to be explored specifically in each particular situation. By considering disease infection in both populations, our model also yields more complex dynamics, allowing for the possibility of bistability and periodic oscillation, in either disease-free or endemic states, in the ecosystem for which the conditions are obtained analytically and with the help of numerical simulations. | ||
| Coauthor(s): Chi-Kuei Hsiao | ||
| CTA7c | Hurford, Amy | |
| Queen's University | ||
| Selection for incomplete mimicry in parasites | ||
| The duration and severity of an infection depends jointly on the traits of the infecting parasite and the immunological response of the host. Parasitic molecular mimics are characterized by a high degree of similarity to naturally occurring host peptides. Infection with a molecular mimic can result in various autoimmune diseases in the host; for example, Campylobacter jejuni infections have been linked to Guillain-Barre syndrome. Host selection against autoimmune disease may cause the immune system receptors that destroy molecular mimics to be eliminated from the immune repertoire. This motivates the question, why are all parasites not molecular mimics? We formulate an infection-autoimmunity model to determine how molecular mimicry affects the fitness of parasite strains when the total reactivity of the parasite in the space of possible immune receptors is constrained. We determined that selection favors parasites with epitopes that react strongly with a subset of host receptors and not at all with other receptors. Selection for incomplete mimicry occurs when hosts with autoimmune diseases generate relatively few secondary infections. As the number of secondary infections from autoimmune diseases increases, higher degrees of molecular mimicry are selected. Depending on the prevalence of self-reactive receptors this may result in a higher prevalence of autoimmunity, chronic infections or both. Medical interventions to prevent some autoimmune diseases are currently under development. We discuss how such therapies may effect parasite selection for molecular mimicry. | ||
| Coauthor(s): Troy Day | ||
| MSE2d | Ingalls, Brian | |
| Department of Applied Mathematics, University of Waterloo | ||
| Overactuated systems and Metabolic Control Analysis | ||
| In this work the main results of Metabolic Control Analysis (MCA) are reinterpreted from the point of view of engineering control theory. The standard model of metabolic systems is identified as redundant in both state dynamics and input effects. The key feature of these systems is that while the dynamics are typically nonlinear, these redundancies appear linearly -- through the stoichiometry matrix. This means that the effect of the input can be linearly decomposed into a component driving the state and a component driving the output. A statement of this separation principle is shown to be equivalent to the main Theorems of MCA. | ||
| MSB1c | Isaacson, Samuel | |
| Boston University | ||
| Effects of cellular substructure on the dynamics of gene regulation and expression | ||
| We will give an overview of our recent work investigating the influence of incorporating cellular substructure into stochastic reaction-diffusion models of gene regulation and expression. Extensions to the reaction-diffusion master equation and Smoluchowski diffusion limited reaction models that incorporate effects due to the chromatin fiber matrix are introduced. These new mathematical models are then used to study the role of nuclear substructure on the motion of individual proteins and mRNAs within nuclei. | ||
| MSB3c | Janmey, Paul | |
| Departments of Physiology, Physics, Bioengineering, University of Pennsylviana | ||
| Assembly and mechanics of intermediate filaments | ||
| One cellular function of intermediate filaments is to provide cells with compliance to small deformations while strengthening them when large stresses are applied. IFs accomplish this mechanical role because of the unusual non-linear elasticity of the gels they form and the very large strains that single IFs can accommodate without breaking. These filaments have persistence lengths less than one micron and form networks with mesh sizes on the same order. Therefore much of the elasticity can be accounted for by entropic models that predict the forces needed to extend the filaments' end-to-end distance. IFs are unique among cytoskeletal filaments in withstanding large deformations. Single filaments can stretch to more than 3 times their initial length before breaking, and gels of IF withstand strains greater than 100% without damage. Even after mechanical disruption of gels formed by crosslinked neuronal IFs, for example, the elastic modulus of these gels rapidly recovers under conditions where gels formed by other cytoskeletal filaments are irreversibly ruptured. Assembly of individual IFs into crosslinked networks occurs in large part due to electrostatic interactions between these highly anionic polyelectrolytes and polycationic ligands The strength and reversibility of these labile crosslinks contributes to network elasticity in a manner that has yet to be thoroughly modeled. Recent studies of IF network rheology and self-assembly by multivalent counterions reveals some of the unique properties of these cytoskeletal elements. These experimental data can help distinguish among different theoretical models for network elasticity of crosslinked semiflexible polymers. | ||
| MSD4d | Javaheri, Shahrokh | |
| University of Cincinnati College of Medicine | ||
| Consequences of obstructive sleep apnea | ||
| One of the major advances in clinical medicine has been the understanding that obstructive sleep apnea (OSA) is a cause or contribute to progression, morbidity and mortality of various cardiovascular diseases. OSA is characterized by recurrent complete (apnea) or partial (hypopnea) upper airway occlusion. Apnea-recovery cycles result in recurrent episodes of hypoxemia / reoxygenation, increases and decreases in PCO2, arousals and large negative swings in intrathoracic pressure. These acute consequences result in poor sleep, excessive daytime sleepiness, falling asleep at work and while driving and a variety of cardiovascular disorders such as hypertension, heart disease and stroke, all of which may contribute to mortality. Effective treatment has been shown to decrease mortality associated with OSA. | ||
| MSE5d | Jensen, Ethan | |
| University of Nebraska, Lincoln | ||
| Using coupled systems of differential equations to model competition for light within a New Zealand forest stand | ||
| Light is a limiting resource for trees within the understory of a forest because of the extensive shading produced by the crowns of the overtopping canopy. Thus, access to light is a critical determinant of growth for understory trees. The effect of the understory light gradient on tree growth has been modeled by a differential equation describing diameter growth rate of a target tree as a function of its neighborhood, which is the sum of the basal areas of the trees within a given radius that overtop it. However, current application of the neighborhood function fails to adjust the growth rates of overtopping trees for their own light environment. To create a more realistic model, we developed a system of coupled differential equations that simultaneously adjusts the growths rates of all the trees within a forest stand for light availability using neighborhood estimates. We will present analyses of our model, using data on 26 years of tree growth from forest dynamics plots in New Zealand, and compare its ability to predict growth rates with simpler models. | ||
| CTH7d | Jilkine, Alexandra | |
| University of British Columbia | ||
| Bifurcation analysis of a wave-pinning mechanism in a model of cell polarization | ||
| The ability of eukaryotic cells to polarize is essential for their division, differentiation into distinct tissues, and migration. During polarization various polarity proteins segregate to form a distinct front and rear. To understand a mechanism for polarization we consider a simplified PDE model describing the interchange of a polarity protein, such as Rho or Rap family GTPase, between an active membrane-bound form and an inactive cytosolic form. An initial transient signal results in a traveling front of activation that stops at some point in the domain, representing segregation of the cell into front and back. Using phase plane methods and numerical continuation we analyze the transition from a spatially heterogeneous (pinned wave) to a spatially homogeneous steady state as the ratio of the diffusion coefficients of the two forms and the total amount of material in the domain is varied. We discover a second spatially heterogeneous solution that acts as a threshold for polarity establishment, and give biological interpretation for this phenomenon. | ||
| Coauthor(s): Yoichiro Mori, Leah Edelstein-Keshet | ||
| CTA6c | Jin, Yu | |
| Department of Mathematical and Statistical Sciences, University of Alberta | ||
| Population dispersal in a periodic environment | ||
| Integro-differential equations have been presented to study phenomenon of biological invasions, for example, population invasions in stream environments and disease spread in some space. Such a model takes into account the long-distance dispersal and describes the dispersion via a dispersal kernel, which specifies the probability that an individual moves from one location to another in a certain time interval as a function. In view of the effects of time-varying environments (e.g. due to seasonal variation) on population dynamics, we consider a class of periodic integro-differential equations and study their spatial dynamics. By appealing to the theory of asymptotic speeds of spread and traveling waves for monotonic periodic semiflows, we establish the existence and formula of the spreading speed and show the coincidence of the spreading speed with the minimal wave speed of periodic traveling waves. | ||
| CTH5c | Johnson, Leah R. | |
| University of California Santa Barbara | ||
| Optimal Foraging Strategies in Albatrosses. | ||
| All animals must successfully gather food in order to survive and reproduce. Therefore, understanding foraging behavior and resource allocation strategies is a major goal of behavioral ecology. Various types of mathematical models have been used to understand foraging behavior. Here we present a dynamic state variable model to explore the factors shaping the foraging strategies of Albatrosses (family Diomedeidae). This approach allows one to incorporate a wide variety of biological constraints, such as spatio-temporal variation in prey availability, body condition, and reproductive stage, within a single framework. We focus here on the factors that shape foraging behavior during the postbrood stage in black browed albatrosses. In particular we compare model predictions with observed patterns of foraging patch selection, trip length, and chick feeding. We also explore how changes in the external environment, such as prey abundance and variability, influence behavioral patterns and fitness. | ||
| Coauthor(s): Richard Phillips, Mervyn Freeman, and Joshua Abramson | ||
| MSA5d | Joshi, Badal | |
| Ohio State University/Mathematical Biosciences Institute | ||
| Dynamics of Sleep-Wake Cycles: Insights from Development | ||
| Brief awakenings in humans and other mammalian species have been observed to follow a power law distribution, while intervening sleep episodes have an exponential distribution of durations. Such observations of the dynamics of sleep-wake regulation provide clues to the nature of the processes underlying sleep-wake cycles and the neuronal circuitry involved. Recent experiments reveal that the characteristic distributions of sleep and wake episode durations typically are not present at birth, instead developing during infancy in parallel with the development of neuronal circuits known to modulate sleep-wake cycles. I will discuss a mathematical model for sleep across postnatal development, combining approaches from stochastic processes and geometric dynamical systems theory to address questions concerning how these circuits generate and maintain sleep states. | ||
| CTE6c | Jupp, Charlotte | |
| Centre for Mathematical Biology, University of Oxford | ||
| A cell chemotaxis chemical source model for feather bud formation on a growing domain. | ||
| Pattern formation describes the mechanism by which an initially equivalent field of cells differentiates to form different structures in developing tissue. We propose a chemical source model to study the patterning involved in the development of feather germs in chicken skin. Cells respond chemotactically to chemical concentration, with more sources added as the domain grows and concentration dips below a threshold value. We shall explain the biological background behind the model, and reproduce the five main experimental results involving the determination of size and number of germs, the interprimordial spacing between buds, as well as the simultaneous and sequential formations that occur in vitro and in vivo, respectively. | ||
| Coauthor(s): Ruth Baker, Philip Maini | ||
| MSC4c | Kappel, Franz | |
| Institute for Mathematics and Scientific Computing, University of Graz | ||
| Parameter Estimation and Experimental Design for a Cardiovascular Model | ||
| Using a model for the reactions of the cardiovascular system to an ergometric workload we discuss the use of sensitivity functions and generalized sensitivity functions in order to predict the performance of parameter estimation techniques. In particular we show when generalized sensitivity functions indicate non-identifiability of parameter sets. Our considerations concerning experimental design are based on a generalization of measurement procedures which incorporate discrete and continuous measurements. A central role is played by the corresponding generalization of the Fisher information matrix. References: [1] H. T. Banks, Sava Dediu, Stacey L. Ernstberger, and Franz Kappel, Generalized sensitivities and optimal experimental design, submitted. [2] J. J. Batzel, F. Kappel, D. Schneditz, and H.T. Tran: Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control, Frontiers in Applied Mathematics Vol. 34, SIAM, Philadelphia 2007. [3] Franz Kappel and Mohammad Muni, A new approach to optimal design problems, Proc. International Conf. on Nonlinear Analysis and Optimization Problems, Budva (Montenegro), October 6 – 10, 2008, to appear. [2] K. Thomaseth and C. Cobelli, Generalized sensitivity functions in physiological system identification, Ann. Biomedical Eng. 27 (1999), 607 – 616. | ||
| MSD5a | Kepler, Grace | |
| North Carolina State University | ||
| Application of mathematical modeling and simulation to within-host viral pathogenesis | ||
| Patient health outcome could be improved with suitable mathematical models that could predict the disease course in individuals and ones that could suggest optimized treatment strategies. This talk will focus on the application of mathematical modeling and simulation to viral diseases, with these goals in mind. Modeling of within-host viral pathogenesis is illustrated with applications to Human Immunodefciency Virus (HIV) and Cytomegalovirus (CMV), which is a signifcant health threat to immunosuppressed patients. Ongoing work and results from application of HIV models to clinical patient data are presented. We then present a model for CMV infection in healthy and immunosuppressed patients and present some results of the application of the model to transplant patient data. | ||
| MSB4a | Khadra, Anmar | |
| Laboratory of Biological Modeling -NIDDK/NIH | ||
| Investigating the role of IGRP-specific low avidity T cells in the protection against T1D | ||
| Recent experimental observations have revealed that during the onset of autoimmune Type 1 Diabetes (T1D), different clones of T cells with various T cell avidities and protein specificities are naturally generated in diabetic animal models. One particular protein IGRP, the most dominant autoantigen, is responsible for activating low and high avidity IGRP-specific T cells via APCs. Although high avidity T cells destroy ~90% of beta cell repertoire, leading to the abolishment of insulin secretion crucial for glucose metabolism, low avidity T cells appear to play a protective role. Several hypotheses concerning the kinetics of these low avidity T cells and the effects of certain drug treatments on this populations have been suggested. We present here series of mathematical models that investigate these hypotheses and the outcome of certain drug treatments. We also examine the various features exhibited by the T cell clones. | ||
| CTE6d | Kheibarshekan Asl, Leila | |
| Ghent University | ||
| A Stomatal Lineage Model for Arabidopsis Leaf Development | ||
| The lower leaf epidermis of the plant Arabidopsis thaliana consists of two cell types, stomatal guard cells and pavement cells. Stomata are small pores on the surface of leaves whose aperture is controlled by two guard cells. Here we concentrate on the initiation and regulation of precursor cells that form guard cells and pavement cells. We build a mathematical model for the stomatal lineage. The cell cycle duration (L) and the growth rates of pavement and guard cells (gPC and gGC) are involved in this model as parameters, as well as two thresholds (TPC and TGC) for the area of pavement and guard cells. Two other parameters are p1, the fraction of pavement cells with area below TPC that are in the process of dividing into pavement cells and p2, the fraction of pavement cells with area below TPC and 2TGC that will divide into guard cells. The model is based on a map from the density functions of pavement and guard cells on a given day to the density functions on the next day. We use optimization methods to estimate the parameters. An important and rather unexpected result is that the cell cycle duration is nearly constant during leaf development. Another unexpected result is that there is no evidence for the existence of a threshold TPC, hence the cell size in itself does not determine whether the cell is in the endocycle phase. | ||
| Coauthor(s): Stijn Dhondt, Véronique Boudolf, Gerrit Beemster, Lieven Deveylder and Willy Govaerts | ||
| MSH2b | Kim, Yangjin | |
| Mathematical Biosciences Institute, Ohio State U | ||
| A hybrid model of interaction between tumor cells and microenviroment | ||
| Fibroblasts and myofibroblasts near the tumor microenvironment are important players in tumor growth and metastasis because of their unique ability to coordinate events which increase cell proliferation especially in breast cancer. It has been experimentally shown that fibroblasts play an important role in promoting tumor growth. A multiscale model of this interaction between stroma and transformed epithelial cells in vivo will be presented. | ||
| MSD6a | Kleinstein, Steven | |
| Yale University, USA | ||
| Transcriptional cascades during anti-viral responses in human dendritic cells | ||
| Dendritic cells (DCs) play a key role in the early immune response to viral infections, especially in the production of Type I interferons. These molecules signal through the Jak-Stat pathway and activate genes containing ISRE elements in their promoters, ultimately leading to the up-regulation of many potent anti-viral factors. Pathogenic viruses express interferon antagonists (e.g., the NS1 protein of influenza) that subvert the normal interferon response. To better understand uninhibited human DC function we are studying the human DC response to infection by an avian Newcastle Disease Virus (NDV), which lacks the ability to evade the human interferon response. We have attempted to systematically define the genome-wide gene expression changes that occur in human DCs during the first 18 hours post-infection. Using a model-based analysis method, we estimated the up-regulation time of critical genes from time-series microarray experiments in different human donors. We found that this timing was highly correlated across donors. The high level of conservation we observed over so many hours was unexpected, and we thus sought to determine the mechanisms underlying this temporally-ordered cascade. Through a computational promoter analysis, we found that the specific base-composition and location of ISRE elements in the promoter region of each gene was one driving force that was especially important during the first ~12 hours of the response. However, this mechanism provided a reasonable explanation for only a subset of up-regulated genes. To investigate the extent to which the timing of gene expression could be driven by a transcriptional cascade, we performed a statistically rigorous enrichment analysis that examined combined patterns of gene expression and cis-regulatory element detection. This approach identified a single transcriptional cascade that spanned the experimental time-series and could account for observed expression changes in ~60% of all up-regulated genes. The predicted cascade includes many transcription factors that are already known to be involved in anti-viral responses including NFkB along with various IRFs and STATs. Several novel transcription factors were also identified as having important roles. | ||
| MSG3a | Kohandel, Mohammad | |
| University of Waterloo | ||
| Examining the implications of the cancer stem cell hypothesis in solid tumours | ||
| The emerging cancer stem cell hypothesis indicates that only a (typically small) sub-population of so-called "cancer stem cells" has the capacity to drive and maintain tumor growth. Cancer stem cells have been putatively identified in leukemias and, more recently, in a variety of solid tumors including those of the breast and brain. This hypothesis helps to explain certain clinically observed phenomena, such as the apparent inability of conventional anti-cancer therapies to eradicate the disease despite (transient) reduction of overall tumor bulk. We begin with an introduction to the biology of cancer stem cells, and proceed to discuss mathematical models of tumor growth based on the cancer stem cell hypothesis. These models are applied to discussions of the treatment of glioblastoma multiforme, a common type of brain cancer believed to be maintained by cancer stem cells, and to the phenomenon of the epithelial-mesenchymal transition, a process recently implicated in generating cancer cells capable of metastasis. | ||
| MSB3b | Kreplak, Laurent | |
| Structural nanomechanics lab, Department of Physics and Atmospheric Science, Dalhousie University | ||
| Nanomechanics of self-assembled protein filaments | ||
| Over the past twenty years, several experimental tools have been developed to measure the mechanical properties of single biopolymers such as DNA. Atomic force microscopy (AFM) or optical tweezers provide direct measurements of the force versus extension curve. So far all the single biopolymer pulling experiments can be described using either the worm like chain (WLC) model or various two-states polymer models. I will present mechanical studies of a more complex class of biopolymers, i.e. self-assembled protein filaments. This group encompasses proteins such as myosin, collagen, fibrinogen and intermediate filament (IF) proteins. All these proteins have in common the ability to self-assemble into rope-like or rod-like structures 10 to 100 nm in diameter. Another common characteristic is the shape of the building-blocks which are 50 to 500 nm long coiled coils with diameters around 2-3 nm. The mechanical properties of these systems are much more complex than the ones of single biopolymers and necessitate different experimental approaches. For example they can exhibit, high extensibility (above 100% extension), strain stiffening effects, and anisotropic elastic properties. I will present experimental evidence of these behaviors and our first attempts to interpret our data in terms of molecular deformations. | ||
| MSD1c | Kribs-Zaleta, Christopher | |
| The University of Texas at Arlington | ||
| Multi-patch sylvatic transmission of Trypanosoma cruzi | ||
| Trypanosoma cruzi, the parasite that causes Chagas' disease, is endemic throughout the Americas (except Canada) in a sylvatic cycle involving hosts such as raccoons and woodrats. In Texas, two transmission cycles overlap, with distinct hosts, vectors, and distinct strains of the parasite. One strain, known to cause Chagas' disease in humans, extends into Mexico; the other, which extends east to Georgia, may be less virulent but is adapted to vertical transmission and provides cross-immunity against other strains. A multi-patch model measures the capacity of the latter strain to resist, through cross-immunity, "invasion" by the first strain. | ||
| MSE2c | Leite, Maria | |
| Department of Mathematics, The University of Oklahoma | ||
| Bifurcations from Quotient Coupled Cell Systems | ||
| A coupled cell system can be seen as a set of individual dynamical systems (the cells) with interactions between them. Therefore, every coupled cell system is a network, which are widely used by biologists to model dynamical behaviour of multicomponent systems. We discuss that every network, when restricted to a flow invariant subspace defined by equality of certain cell coordinates, is associated with a quotient network. Also, we describe a general method to construct coupled cell networks admitting a given a (quotient) network. We furher investigate the impact of a generic codimension-one synchrony-breaking bifurcation from a synchronous equilibrium, occurring in the quotient network, for the different networks having it as a quotient. | ||
| MSE1d | Lenhart, Suzanne | |
| University of Tennessee | ||
| Optimal Control in Epidemic Models of Rabies in Raccoons | ||
| We discuss a framework to analyze temporal/spatial controls for vaccine distribution as it impacts the spread of rabies among raccoons. The control gives amount and location of the food packets containing vaccine. In this epidemic model, the goal is to minimize the number of infected raccoons and the cost of distributing the packets. We discuss models with discrete and continuous features. | ||
| CTE7c | Leviyang, Sivan | |
| Georgetown University | ||
| The Impact of Stochastic Effects on the Population Dynamics of Within Host Viral-Immune System Interaction | ||
| Within host viral-immune system population dynamics are often studied through a deterministic dynamical systems approach. However, viral and immune system evolution involves many underlying stochastic processes, and it is a subject of debate whether one needs to model viral-immune system population dynamics with a stochastic dynamical system. An important aspect of this debate is the difficulty of analyzing stochastic predator-prey systems, and indeed such systems are not well understood. Within host viral dynamics often occurs on a faster time scale than immune system dynamics. An important example of such time scale separation is HIV, which evolves on a time scale of hours to days while being targeted by a CTL population that evolves on a time scale of days to weeks. In this talk we consider a stochastic dynamical system model of HIV-CTL interaction assuming such scale separation. The scale separation allows us to employ asymptotic techniques to analyze a stochastic predator-prey system. We consider a case in which two viral types are competing. In the deterministic case, the viral types coexist, but we show that in the stochastic setting either one of the viral types may be lost with a significant probability and on a time scale that would affect within host viral dynamics. | ||
| MSA4c | Li, Jia | |
| Department of Mathematical Sciences; University of Alabama in Huntsville | ||
| Modeling of the Impact of Climate Change and Mosquito Transgenes on Malaria Transmission | ||
| We use a simple SEIR model for malaria transmission dynamics, based on a system of ordinary differential equations, as our baseline model. We derive a formula for the reproductive number and investigate the existence of endemic equilibria. We then introduce a simple two-stage-structured mosquito population model where the mosquito population is divided into two classes. After a brief investigation on this simple stage-structured mosquito model, we incorporate it into the simple SEIR malaria model. We present basic analysis for the combined model and discuss how this combined model can help us study the impact of climate change on the transmission of malaria and other mosquito-borne diseases. We show that, using the reproductive number as a bifurcation parameter, the simple malaria model and the mosquito-stage-structured model can have a backward bifurcation. We also talk about the interaction between wild and transgenic mosquitoes and its impact on the malaria transmission. | ||
| MSH6c | Li, Jing | |
| The University of Ottawa | ||
| Modeling spatial spread of infectious diseases with a fixed latent period in a spatially continuous domain | ||
| With the assumptions that an infectious disease in a poulation has a fixed latent period and the latent individuals of the population may diffuse, we formulate an SIR model with a simple demographical structure for the population living in a spatially continuous environment. The model is given by a system of reaction-diffusion equations with a discrete delay accounting for the latency and a spatially non-local term caused by the mobility of the individuals during the latent period. We address the existence, uniqueness and positivity of solution to the initial-value problem for this type of system. Moreover, we investigate the traveling wave fronts of the system and obtain a critical value c* which is a lower bound for the wave speed of the traveling wave fronts. Furthermore, the simulations on the PDE model also suggest that the spread speed of the disease indeed coincides with c*. We also discuss how the model parameters affect c*. | ||
| CTF7b | Lipsmeier, Florian | |
| Bielefeld University | ||
| Probabilistic T cell activation and negative selection | ||
| The mature T cell repertoire proves to be quite capable to discriminate foreign antigens from a background of many of the body own's molecules (self antigens). Despite considerable research, the mechanisms involved in this foreign-self discrimination process are still not well understood. This is especially true for negative selection. Generally speaking, this process depletes the immature T cell repertoire of self-reactive T cells and should thereby have a considerable impact on the discrimination capability of the mature T cell repertoire. However, next to some estimates on the number of killed and surviving T cells, deeper insights into this mechanism and how it helps to optimize foreign-self discrimination are lacking. Of particular interest are recent findings such as the promiscuous expression of tissue restricted antigens by medullary epithelial cells in the thymic medulla and the highly reduced time frame during which negative selection occurs (4-5days, instead of the formerly supposed 12-16 days). These findings support the assumption that T cells 'see' mixtures of (self and foreign) antigens rather than every antigen alone. This idea was already used in the probabilistic T cell activation model of van den Berg, Rand and Burroughs in 2001 [1] and further developed in [2]. Inspired by our own analysis of this model [3] and its extensions, we devise a new probabilistic T cell activation model which especially helps us to capture the different aspects of negative selection. In this model we have a set of self antigens and generate a repertoire of T cells. Every T cell is characterized by the stimulation rates induced by the single antigens, where we assume the stimulation rate distribution of an antigen over all T cells to be the same for all antigens. The T cells undergo negative selection and the surviving T cell repertoire is analyzed for changes in the stimulation rate distribution and its foreign-self discrimination capability. We propose different biologically reasonable ways to model the negative selection process in order to improve the foreign-self discrimination capability. [1] Van Den Berg, H.A., Rand, D.A., Burroughs, N.J.: A reliable and safe T cell repertoire based on low-affinity T cell receptors. J Theor Biol 209(4), 465-486 (2001) [2] Zint, N., Baake, E., den Hollander, F.: How T-cells use large deviations to recognize foreign antigens. J. Math. Biol. 57, 841-861 (2008). [3] Lipsmeier, F. and Baake, E.: Rare event simulation for T-cell activation. J Stat Phys 134, 537-566 (2009). | ||
| Coauthor(s): Ellen Baake | ||
| CTC1f | Lorz, Alexander | |
| University of Cambridge | ||
| Collective Motion of Swimming Microorganisms and Chemotaxis | ||
| We consider coupled chemotaxis-fluid models aimed to describe swimming bacteria, which are able exert bio-convective flow patterns on length scales much larger than the bacteria size. When looking at the microorganisms in detail, experimentalists have observed that high concentration of swimming microorganisms show collective behaviour, in the sense that each organism aligns its swimming direction with those of its neighbours. We discuss different PDE models for the phenomena, give results and challenges in analysing them. | ||
| Coauthor(s): Marco Di Francesco, Renjun Duan, Klemens Fellner, Peter Markowich | ||
| CTB6e | Lowengrub, John | |
| University of California, Irvine | ||
| Hybrid continuum-discrete multiscale models of vascular tumor growth | ||
| We present a hybrid continuum-discrete mathematical multiscale modeling framework for vascular solid tumor growth. A continuum model based on mixture theory is used to describe the evolution of volume fractions of multiple tumor cell clones, extracellular matrix (ECM), host cells, nutrients and water. The continuum model is coupled to an agent-based, lattice-free model that describes the evolution of discrete tumor cell clones. The models couple through mass and momentum exchange. In addition, a model for tumor-induced angiogenesis and vascular growth is incorporated. Simulations are presented that demonstrate the effectiveness of the hybrid approach in describing hypoxia-induced transitions from collective to individual based motion and vice-versa when cells are in oxygen-rich environments near the flowing, dynamic neovasculature network. | ||
| CTA6f | Lukeman, Ryan | |
| University of British Columbia | ||
| Inferring interaction rules from empirical data of collective motion in animal groups | ||
| Collective motion in animal groups has been studied rather extensively with a variety of models, but real data to test model hypotheses is scarce, owing to difficulty in gathering such data. Here, I discuss our empirical study to capture movements of surf scoters (a type of duck), collectively foraging in groups of a few hundred individuals near Vancouver, BC. We are able to reconstruct individual trajectories for each individual duck, giving a temporal dimension to the data that proves useful for comparing to dynamic models. We then test hypotheses for inter-individual interactions against the data to develop an individual-based zonal model that captures both the angular preference and overall spatial distribution of neighbors observed in the surf scoter data. | ||
| Coauthor(s): Yue-Xian Li, Leah Edelstein-Keshet | ||
| MSA2c | Lushnikov, Pavel | |
| University of New Mexico | ||
| Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact | ||
| A connection is established between a discrete stochastic model describing the microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards a chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. A nonlinear diffusion equation is derived from the microscopic dynamics in dimensions one and two using an excluded volume approach. The nonlinear diffusion coefficient depends on the cellular volume fraction and demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions of about 0.3. A combination of microscopic and macroscopic models are used to simulate growth of structures similar to early vascular networks. | ||
| MSG5d | Lutscher, Frithjof | |
| Department of Mathematics and Statistics, University of Ottawa, Canada | ||
| Approximations and rules of thumb for persistence and spread in heterogeneous landscapes | ||
| The spread of non-indigenous species and diseases poses a major risk to ecosystems and human health worldwide. The key challenges to management and control of such invasions are to understand the conditions of spread and the different factors influencing the speed of spread. Of particular interest is the effect of landscape heterogeneity on the spread of organisms. We formulate a discrete-time model for growth and dispersal, where both of these processes vary in space. We then present approximation formulas for the spread rate in such a heterogeneous landscape and demonstrate their validity by comparison with numerical simulation. We also give rules of thumb for the conditions under which a species is able to spread in a heterogeneous landscape. We separately consider the two cases with and without Allee effect in the population growth function. Our results provide simple recipes for calculation of spread rates in complex landscapes together with their limits of validity. | ||
| CTC7e | Mahaffy, Joseph | |
| San Diego State University | ||
| Marine Bacteria and Phage Model with Delays | ||
| A two compartment model for marine bacteria and phage is developed. The environment is divided into a small compartment where bacteria grow rapidly with abundant nutrients, and a large compartment where the bacteria have few nutrient resources. There are large epidemics in the compartment containing nutrients, while the no growth compartment serves as a refuge. Delays are introduced to account for the time between infection of a bacterium and when it lyses to produce new phage. New modeling techniques are required to account for the dynamics of the infected bacteria. Bifurcation analysis and parameter sensitivity are shown. Stable oscillatory phenomena are shown for the predator-prey system. | ||
| Coauthor(s): Beltran Rodriguez-Brito | ||
| CTA6d | Malchow, Horst | |
| Institute of Environmental Systems Research, University of Osnabrueck, Germany | ||
| Pattern Generation and Competition in Models of Population Dynamics | ||
| The formation and spread of spatiotemporal structures in a simple predation-diffusion model with Holling type II or III predator is demonstrated. The dynamics is modelled by reaction-diffusion equations. Spatial spread will be presented as well as competition of concentric and/or spiral population waves with non-oscillatory sub-populations for space, and long transients to spatially homogeneous population distributions. Environmental fluctuations are modelled as external multiplicative noise, using stochastic partial differential equations. The external noise can enhance the survival of a population that would go extinct in a deterministic environment. Noise can also induce local and global oscillations as well as local coherence resonance and global synchronization. The results are related to plankton dynamics, partly with viral infections of the prey population [1-3]. References [1] Sieber, M., Malchow, H. & Schimansky-Geier, L. (2007). Constructive effects of environmental noise in an excitable prey-predator plankton system with infected prey. Ecological Complexity 4, 223--233. [2] Siekmann, I., Malchow, H. & Venturino, E. (2008). Predation may defeat spatial spread of infection. Journal of Biological Dynamics 2, 40--54. [3] Malchow, H., Petrovskii, S.V. & Venturino, E. (2008). Spatiotemporal patterns in ecology and epidemiology: Theory, models, simulations. CRC Mathematical and Computational Biology Series. Boca Raton: CRC Press. | ||
| MSA3c | Marceau, Normand | |
| Centre de recherche en cancerologie, Laval University | ||
| Keratin involvement in simple epithelial cell response to a mechanical stress or a migratory stimulus | ||
| The capacity of cells to sense and adapt to mechanical stress applied on extracellular matrix (ECM)-integrin-cytoskeleton connections at focal adhesions (FAs) is crucial for basic cell behaviors, like migration. In migratory cells, new linkages between ECM and integrins are formed at FAs, and used as sites for the application of actin cytoskeleton-generated force at the cell front. Conversely, upon ECM deformation cells experience a mechanical stress that is transmitted to actin microfilaments through cytoskeletal linkers that also bind integrins. In the work reported here we assessed the contribution of keratin 8/18 (K8/K18) intermediate filaments (IFs) in simple epithelial cells in their response to a mechanical stress or a migratory stimulus, using monolayer cultures of K8-knockdown H4-II-E-C3 (shK8b1) rat hepatoma cells and their K8/K18-containing counterparts (H4ev). The mechanical stress was generated with a laser tweezer-mediated force applied on a fibronectin-coated microbead attached to integrins, and the cell response was assessed by the bead displacement. Notably, de-polymerization of actin microfilaments and microtubules led to increased bead displacements relative to untreated H4ev cells, whereas the loss of the K8/K18 IF network yielded a decrease in bead displacement in shK8b1 cells. In a comparable way, using scratch wound and single-cell migration assays, shK8b1 cells were found to migrate less than H4ev cells upon seeding on fibronectin. Finally, the K8/K18 loss was found to perturb the plectin/ receptor of activated C kinase 1(RACK1)/protein kinase C involvement in the integrin-mediated response to mechanical stress or migratory stimulus, in support of our model by which K8/K18 IFs, along with plectin and RACK1, constitute a versatile signaling platform in simple epithelial cells. Work supported by CIHR and NSERC (in collaboration with François Bordeleau1,2, Luc Galarneau1 and Yunlong Sheng2. 1Centre de recherche en cancérologie and 2Centre de recherche en optique, photonique et laser, Laval University, Quebec City, G1K 7P4, Canada.) | ||
| MSD6d | Marino, Simenone | |
| Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, Michiga | ||
| A multi-compartmental model of Mycobacterium tuberculosis infection in mice: the role of antigen dose in T cell priming | ||
| Infection with Mycobacterium tuberculosis (Mtb) induces a host cellular immune response capable of recognizing mycobacterial antigens, that leads to the production of type I cytokines, activating infected macrophages that kill or at least contain the bacterial infection. T cell priming (CD4+ and CD8+ T cells) that occurs in the lymph node is key to the successful development of a protective adaptive immunity and host resistance to Mtb infection. Once primed, these cells circulate to the lung to participate in the local immune response there. In an effort to understand these complex series of events including the involvement of multiple T cell subsets, we developed a mathematical model. Our goal was to elucidate which mechanisms are affecting T cell priming in Mtb infection and whether or not antigen dose plays any role in the quality of priming of T cells. Our non-linear ordinary differential equations system comprises two main physiological compartments (lung and lymph node), each one populated with different cell populations (macrophages, dendritic cells and lymphocytes), bacteria and cytokines. Mouse data from aerosol infection in respiratory chambers have been collected and extensively used to calibrate the model, which will be discussed. Model fitting and sensitivity analysis results inform us regarding similarities and differences between lung and lymph node biological mechanisms, as well as if and how antigen dose plays a role in T cell immunity. Key mechanisms are targets for designing vaccine or adjunctive treatment strategies. | ||
| MSC3d | Marshall, Wallace | |
| University of California, San Francisco | ||
| The Flagellar Length Control System | ||
| A major unanswered question in cell biology is how cells regulate the size of organelles. We are using the eukaryotic flagellum as a simple system to probe the nature of organelle size control. By analysis of flagellar growth dynamics, we have developed a simple model for length control based on the interplay between length-independent turnover of flagellar microtubules and length-dependent transport of fresh protein to the turnover site. Our model can recapitulate the main phenomenological features of flagellar length including the ability of the cell to equalize the lengths of its flagella following perturbations. We are now probing the fluctuations in the length control system, combining experimental measurements with a linear noise analysis. Finally, we have begun to integrate an additional transcription-based feedback control loop into the model. | ||
| MSD3b | Marée, Athanasius F. M. (Stan) | |
| University of Utrecht | ||
| Cell polarity in plants and animals: a conservation of principles | ||
| Animal cells display a fascinating ability to undergo cell shape changes and move. In contrast, plant cells are encased in a relatively rigid cellulose cell wall, which impedes cell motility. Even though plants and animals split up 1.6 billion years ago, molecular and genetic studies reveal that plant and animal cells still share the a similar core machinery required for cell shape changes. A fascinating similarity between animal and plant cells in the organisation of cytoskeletal elements in the regions of active protrusive growth and cell wall extension (the `leading edges'), is parallelled by a striking conserved molecular mechanism responsible for the creation and organisation of these `leading edges'. The key players underlying cell polarity in animals, the small G-proteins, are very similar to polarity determinants in plants, the Rho of Plants, ROPs. Both are switched between active, membrane-bound forms and inactive forms that can enter the cytosol. To unravel and understand the interplay and feedbacks which brings about animate cell motility, we have developed a multiscale model of a motile cell, describing small G-protein dynamics, PIPs, actin filament turnover, and cell deformation. By explicitly modelling the fish epidermal keratocyte, we study how the emergence of a single, stable front and directed motion. We then contrast this to the cell shape changes that occur in the pavement cells (PCs) in the leaves of plants. PCs develop complex forms that resemble pieces from a jigsaw puzzle. The cells grow multiple lobes, which fit perfectly into the indentations of the neighbouring cells, generating interdigitating patterns. We will show that similar modular principles as found in the keratocyte play a role. Here, however, it generates an interdigitating pattern between cells, generating multiple stable `leading edges'. Thus, we are able to unravel both mathematically and computationally a 1.6-billion-year-old principle of cell polarity. | ||
| CTB6f | Massey, Susan | |
| University of Washington | ||
| Paracrine PDGF signaling and progression in experimental gliomas | ||
| Gliomas are the most prevalent primary malignant brain tumors in adults and are currently incurable. Experimental work done by Assanah, et al, 2006 demonstrated that very similar tumors can be initiated in rats by infecting them with a retrovirus (PDGF-IRES-GFP) that lends the capacity to over-express platelet-derived growth factor (PDGF). The key observation from this study was that the majority of cells within all such tumors were glial progenitor cells uninfected with the retrovirus, comprising 70 – 85% of the tumors. Infected PDGF-IRES-GFP+ glial progenitors made up the remainder. This finding strongly suggested that the observed recruitment to the tumor was a direct result of paracrine PDGF signaling. Given this knowledge, we have created and parameterized a mathematical model of experimental glioma initiation and progression, incorporating the experimentally observed recruitment dynamic. In creating our model, we took a multi-scale continuous modeling approach, treating the various cell populations as densities in tissue and unbound PDGF as a concentration in the extracellular fluid. This model accounts for the dispersal and proliferation of both infected and uninfected glial progenitor populations due to PDGF signaling, the secretion of PDGF into the extracellular space by PDGF-IRES-GFP+ (infected) glial progenitors, and PDGF consumption by both infected and uninfected glial progenitor cell populations. Additionally, we assumed that while the PDGF-IRES-GFP+ cells receive both autocrine and paracrine PDGF signals, the other glial progenitor cells receive only paracrine signals. Recruitment model dynamics, after reaching an MRI-detectable density, exhibit the same velocity of linear radial expansion as displayed by a model tumor without recruitment; thus, our model confirms the reasonability of a recruitment mechanism acting in human glioma. Moreover, the differing effects of paracrine and autocrine signals on the glial progenitors described above could explain the differing rates of progression observed in glioma patients. Our model predicts faster rates of radial expansion at the MRI detectable level for more paracrine-driven tumors than autocrine-driven tumors, which exhibited slower expansion in simulations due to greater diffusivity. | ||
| Coauthor(s): Peter Canoll, MD PhD, Kristin R. Swanson, PhD | ||
| CTF4a | Masso, Majid | |
| George Mason University | ||
| Novel Pedagogical Resources Based on Protein Structure Analysis | ||
| Life science applications in undergraduate mathematics classes typically focus on ODE and PDE modeling of biological systems. Biomathematics courses may also illustrate the utility of graph theoretic, numerical, and statistical approaches in the study of DNA and RNA molecules. However, in-class examples and homework exercises based on protein structure analysis are rarely exploited despite an inherently large number of quantitative applications. This talk will begin with a basic overview of proteins and their 3D structures, followed by a description of one particular approach to protein structure analysis that draws on methods from computational geometry, finite mathematics, probability theory, computer programming, and statistical mechanics. The example provides a rich new source of pedagogical tools that are easily implemented in the mathematics classroom. | ||
| MSE3a | McCawley, Lisa | |
| Vanderbilt University Medical School | ||
| An integrative approach in modeling bio-mechanics of epithelial cancer initiation. Experimental view | ||
| To better understand the process of carcinogenesis more detailed knowledge of the origin of neoplastic growth is required. In particular we are interested in addressing questions of when the initiated cell begins to show altered behavior and what events lead to tissue deformations and tumors. We investigate these problems using the bio-mechanical models of simple and stratified epithelia, such as mammary breast glands or skin epidermis, due to their unique properties of frequent cell turnover and a finely define topology. We will present an integrated approach combining laboratory experiments and computational modeling showing normal tissue development and turnover, and discuss the possible events (molecular, bio-chemical, mechanical) that lead to disruption of this tightly controlled system and result in the formation of epithelial tumors. | ||
| CTG7b | McDougall, Steven | |
| Heriot-Watt University | ||
| Modeling the impact of fibroblast migration and collagen alignment during dermal wound healing | ||
| In dermal wound healing, after the skin is injured, several interacting events are initiated including inflammation, tissue formation, angiogenesis, tissue contraction and tissue remodelling. Crucial to all of these events is the interaction of a variety of cells with the extracellular matrix (ECM). After the blood clot has formed during the inflammatory response, white blood cells invade the wound region by migrating through the ECM and fibroblasts subsequently migrate into the region and begin to replace the blood clot with collagen. These cells biochemically alter the ECM by degrading the fibrin and producing collagen and, while new tissue is being generated, endothelial cells migrate into the region forming a new vasculature in the process known as angiogenesis. In this paper we present a new model of wound healing angiogenesis that is coupled to a model of dermal tissue regeneration. Here, we incorporate discrete fibroblast migration through the fibrous matrix in response to a chemical produced in the wound. Whilst migrating, the fibroblasts degrade fibrin, deposit collagen and also realign the pre-existing fibres. Furthermore, a direct coupling between the spatial distribution of collagen to vessel migration during angiogenesis is considered, whereby collagen alignment affects the path taken by nascent capillaries. We investigate the potential impact of these processes on the speed and success of healing through measures of oxygen tension and collagen alignment within the wound area. Throughout all of the above, we discuss the clinical implications of our study at length. | ||
| Coauthor(s): Michael Watson and Mark Chaplain | ||
| MSB3a | Meier, Markus | |
| Department of Chemistry, University of Manitoba | ||
| Biophysical characterization of vimentin coil 1A, a molecular switch | ||
| Vimentin is an intermediate filament protein mainly found in fibroblast cells of the connective tissue. It has a tripartite structure consisting of a head domain, an α-helical rod domain and a tail domain. The rod itself is sub-segmented into four segments called coil 1A, coil 1B, coil 2A and coil 2B. The amino acid sequence contains a heptad repeat pattern that is characteristic for a coiled-coil structure. Interruptions ("stutters") in this pattern cause the sub-segmentation. The atomic structures of coils 1B, 2A and 2B are indeed dimeric parallel coiled coils (shown by the X-ray crystallography and/or analytical ultracentrifugation). Interestingly, the first published structure of the coil 1A fragment of the human intermediate filament protein vimentin turned out to be a monomeric α-helical coil instead of the expected dimeric coiled coil1. However, the 39 amino acids long helix had an intrinsic curvature compatible with a coiled coil. We have now designed four mutant variants of vimentin coil 1A, modifying key a and d positions in the heptad repeat pattern, with the aim to investigate the molecular criteria that are needed to stabilize the dimeric coiled-coil structure. We have analysed the biophysical properties of the mutants by circular dichroism spectroscopy, analytical ultracentrifugation and X-ray crystallography. All four mutants did exhibit an increased stability over the wild type as indicated by a rise in the melting temperature (Tm). At a concentration of 0.1 mg/ml, the Tm of the peptide with the single point mutation Y117L increased dramatically by 46 ℃ compared to the wild-type peptide. In general, the introduction of a single stabilizing point mutation at an a or d position did induce the formation of a stable dimer as we demonstrated by sedimentation equilibrium experiments. We also confirmed the dimeric oligomerisation state of the Y117L mutant peptide by X-ray crystallography, which yielded a structure with a genuine coiled-coil geometry. Most notably, when we introduced this mutation into the full-length vimentin, the filament assembly was completely arrested at the unit-length filament (ULF) level, thus impeding the longitudinal elongation reaction. We concluded that the low propensity of the wild-type coil 1A to form a stable two-stranded coiled coil is most likely a prerequisite for the end-to-end annealing of ULFs into filaments. Accordingly, the coil 1A domains might "switch" from a dimeric α-helical coiled coil into a more open structure, thus mediating, within the ULFs, the conformational rearrangements of the tetrameric subunits that are needed for the IF elongation reaction. References: 1. Strelkov, S. V., Herrmann, H., Geisler, N., Wedig, T., Zimbelmann, R., Aebi, U. & Burkhard, P. (2002). EMBO J. 21, 1255-1266. (in collaboration with G. Pauline Padilla, Harald Herrmann, Tatjana Wedig, Trushar R Patel, Jörg Stetefeld, Ueli Aebi, and Peter Burkhard) | ||
| CTF7c | Mendoza, Luis | |
| Instituto de Investigaciones Biomédicas, UNAM. | ||
| A virtual cell culture of T-helper lymphocytes | ||
| There is a wealth of cellular and molecular information regarding the differentiation of T-helper cells, as well as results of in vitro experimental treatments that modify the normal differentiation process. With the aid of such publicly available information, I inferred the regulatory network that controls the differentiation of T-helper cells. Such network was converted into a continuous dynamical system in the form of a set of coupled ordinary differential equations. The system has a set of fixed point attractors, but the basins of only five of them cover most of the state space. These attractors correspond to the activation states observed experimentally for the precursor (Th0), and effector (Th1, Th2, Th17 and Treg) T-helper cells. Moreover, the model is able to describe the differentiation from a precursor to an effector type due to specific molecular signals. Then, taking a network as a representation of a single cell, I constructed a model of a cell culture where cells respond to and produce different molecular signals. The dynamical behavior of this virtual cell culture was analyzed, showing that it leads to cultures containing subsets of undifferentiated and differentiated cells in appropriate proportions. This model will allow to study the mechanisms leading to imbalances of T-helper populations, which is the cause of several immune disorders. | ||
| PLEN6 | Michor, Franziska | |
| Memorial Sloan-Kettering Cancer Center | ||
| Towards the evolutionary trajectory causing tumorigenesis | ||
| Human cancer is caused by the accumulation of genetic alterations in cells. Many of these mutations are currently being catalogued in the context of large cancer genome projects, but it is not clear how to prioritize the functional validation of the biologically most relevant genetic events within the large number of candidate mutations. Of special importance are those changes that occur early during malignant transformation since they may result in rewiring of the signaling circuitry or confer a state of addiction to the new signal, and thus represent particularly promising targets for therapeutic intervention. I will describe a new computational approach, called Retracing the Evolutionary Steps In Cancer (RESIC), to deduce the temporal sequence of genetic events arising during tumorigenesis from cross-sectional genomic data of tumors at their fully transformed stage. This approach is tested with data from advanced colorectal cancer samples and then applied to primary glioblastoma and lung adenocarcinoma. | ||
| CTD7c | Miekisz, Jacek | |
| University of Warsaw | ||
| Stochastic models of gene expression with time delays | ||
| Many biochemical processes in living cells take place in small volumes and involve small number of molecules. Such systems are usually modeled by birth and death processes where products of various reactions appear or degrade immediately after corresponding reactions are triggered. However, many such reactions take a considerable amount of time. Therefore to describe them we have to introduce models with time delays. Reactions with delays are of two kinds: non-consuming and consuming. Reactants of unfinished consuming reactions cannot participate in new reactions, reactants of non-consuming reactions can participate in new reactions. We will discuss simple models of gene expression with time delays. We will analyze both kinetic rate equations and corresponding birth and death processes with both types of time delays. Many kinetic rate equations with non-consuming reactions undergo the Hopf bifurcation when the delay increases and crosses a critical value. For small time delays the system evolves into its stationary state with damped oscillations observed in transient states. We will show that such effects are not present in the case of consuming reactions where for all values of time delay the unique stationary state is asymptotically stable. In the stochastic models corresponding to deterministic rate equations, the variance of the number of protein molecules and autocorrelation functions will be calculated analytically. To deal with more complex models, we will develop a small delay approximation. We compare our results with those obtained earlier by Bratsun, Volfson, Tsimring, and Hasty, for models with delayed degradation and repression, PNAS 102: 14593-14598 (2005). | ||
| CTD7d | Mileyko, Yuriy | |
| Georgia Institute of Technology | ||
| Nonlinear effect of copy number variation on gene expression | ||
| The expression dynamics of interacting genes depends on the topology of the regulatory network, the quantitative nature of feedbacks and interactions between DNA, RNA and proteins, and the biochemical state of the intracellular and surrounding environment. In this talk we show that dynamics of a gene regulatory network can also depend sensitively on the copy number of genes and promoters. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number can cause a sequence of saddle-node bifurcations in the corresponding differential equations models, which leads to multiple orders of magnitude change in gene expression. A similar analysis of a 3-gene motif with successive inhibition (the "repressilator") reveals that changes in gene copy number can also cause a Hopf bifurcation, thus leading to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. Importantly, we show that these bifurcations exist over a wide range of parameter values, thus reinforcing our claim that copy number is a key control parameter in the expression dynamics of regulatory networks. | ||
| MSC5d | Miller, Jason | |
| Truman State University | ||
| Training Undergraduates in Mathematical Biology Using Research With Faculty | ||
| Since 2004, Truman State University has trained students to conduct interdisciplinary research in mathematical biology through a combination of research experiences with faculty collaborators, courses, and field trips. This program of experiences for undergraduates has been made possible by the National Science Foundation’s Interdisciplinary Training for Undergraduates in Biology and Mathematics (UBM) program. This talk will outline our courses and our research program (including a portfolio-based interdisciplinary minor in mathematical biology), what we have learned about assessing interdisciplinary learning, and the role field trips have played in the professional development of faculty and students. | ||
| CTF6c | Miller, Laura | |
| University of North Carolina at Chapel Hill | ||
| Scaling effects and fluid dynamics in heart development | ||
| When the heart tube first forms, the Reynolds number describing intracardial flow is only about 0.02. During development, the Reynolds number increases to roughly 1000. The heart continues to beat and drive the fluid during its entire development, despite significant changes in fluid dynamics. Early in development, the atrium and ventricle bulge out from the heart tube, and valves begin to form through the expansion of the endocardial cushions. As a result of changes in geometry, conduction velocities, and material properties of the heart wall, the fluid dynamics and resulting spatial patterns of shear stress and transmural pressure change dramatically. Recent work suggests that these transitions are significant because fluid forces acting on the cardiac walls, as well as the activity of myocardial cells which drive the flow, are necessary for correct chamber and valve morphogenesis. In this presentation, computational fluid dynamics was used to explore how spatial distributions of the normal forces and shear stresses acting on the heart wall change as the endocardial cushions grow, as the Reynolds number increases, and as the cardiac wall increases in stiffness. The immersed boundary method was used to simulate the fluid-structure interaction between the cardiac wall and the blood in a simplified model of a two-dimensional heart. Numerical results are validated against simplified physical models. We find that the presence of chamber vortices is highly dependent upon cardiac cushion height and Reynolds number. Increasing cushion height also drastically increases the shear stress acting on the cushions and the normal forces acting on the chamber walls. | ||
| MSC5c | Milton, John | |
| The Claremont Colleges | ||
| REBMI: Research Experiences at the Biology-Mathematics Interface | ||
| The goal of our REBMI program is to prepare undergraduate students to work on interdisciplinary teams that tackle “translational”, real-life challenges at the crux of biology and mathematics. By creating “unstructured, open-ended” environments within active research laboratories, we leverage the strong and uncommonly open-mindedness of liberal arts students while at the same time exposing them to “real world” research experiences. In our presentation we review the successes and failures of our program and how our experiences are re-shaping the ways we think about preparing biologists and mathematicians to work together. | ||
| MSG2a | Mincheva, Maya | |
| Department of Mathematical Sciences, Northern Illinois University | ||
| Oscillations in biochemical reaction networks | ||
| Understanding the dynamics of interactions in complex biochemical networks is an important problem in modern cellular biology. Biochemical reaction networks are usually modeled by large nonlinear dynamical systems with many unknown kinetic parameters, making the models challenging for analysis. However, important properties, such as the ability of a biochemical network to oscillate can be determined by the network structure. The structure of a bipartite graph associated with a biochemical reaction network can be used to predict oscillations without knowing the kinetic parameters. We will discuss the connection between the bipartite graph of the reaction network and the bipartite graph associated with the dynamical system model. | ||
| CTH3d | Miura, Robert M. | |
| New Jersey Institute of Technology | ||
| Migraine With Aura and Cortical Spreading Depression | ||
| Migraine with aura (classic migraine) is a debilitating disease that affects people around the world. The triggers of this condition are various and undiagnosed in most cases, and treatments are essentially ad hoc on a patient-by-patient basis. Migraine with aura has been linked to waves of cortical spreading depression (CSD) in the visual cortex of the brain. In spite of an enormous experimental and theoretical literature on the brain, we do not have a good understanding of how it functions on a gross mechanistic level. To devise rational treatments for migraine with aura, much more needs to be known about the brain and about CSD. In general, the brain maintains a homeostatic state with relatively small ion concentration changes, the major ions being sodium, potassium, and chloride, and a very important ion, calcium. We can learn a lot about the brain by studying extreme phenomena, and CSD is such a phenomenon. CSD was discovered 65 years ago by A.A.P. Leão, a Brazilian physiologist during his PhD research on epilepsy at the Harvard Medical School. CSD is characterized by nonlinear chemical waves that propagate at very slow speeds, on the order of mm/min, in the cortex of different brain structures in various animals, including humans. CSD waves generate massive changes in extracellular ion concentrations, but to date, we do not have a good explanation of how CSD occurs, although a number of mechanisms have been hypothesized to be important for CSD wave propagation. Some of these mechanisms are ion diffusion, membrane ionic currents, neurotransmitter substances, gap junctions, metabolic pumps, synaptic connections, osmotic effects, and the spatial buffer mechanism. In this talk, I will review some of the characteristics of CSD wave propagation, and describe some of the above mechanisms. Continuum models of CSD, consisting of coupled nonlinear diffusion equations for the ion concentrations, will be described. | ||
| PLEN4 | Mogilner, Alex | |
| Depts. of Mathematics and Neurobiology, Physiology and Behavior, University of California, Davis | ||
| Geometry and force of mitotic spindle assembly | ||
| Mitotic spindle is a molecular machine segregating chromosomes at the onset of cell division. The spindle self-assembles in prometaphase by the 'search-and-capture' process, in which dynamically unstable microtubules search in space until chromosomes are captured. Quantitative mechanistic understanding of how spindle assembly can be both fast and accurate is lacking. We used computer simulations to test plausible pathways of spindle assembly in realistic geometry. Our results suggest that chromosome movements and rotations is needed to complete prometaphase in 10-20 min while keeping erroneous attachments down to a few per cent. The simulations also suggest that molecular motor forces play an important role in stabilizing the spindle geometry. We compare the model predictions with experimental data for colorectal cancer cells. | ||
| MSG3b | Molavian, Hamid | |
| University of Waterloo | ||
| Cell metabolism and its relationship to hypoxia and acidity in solid tumors. Computational results | ||
| The tumor microenvironment plays an essential role in the growth and development of tumors. Among many microenvironmental parameters, acidity and hypoxia are two major factors which affect cell metabolism as well as the metastasis of cancer cells to other organs. In this talk, we first give a brief review of some experimental results on acidity and hypoxia and their relationship to cell metabolism. We then use a mathematical model to calculate PH and oxygen concentration inside a solid tumor and discuss implications and relevance to experimental work. | ||
| CTH5e | Molnár, Péter | |
| Centre for Mathematical Biology, University of Alberta | ||
| Using Dynamic Energy Budget Models to Predict Changes in Polar Bear Reproduction under Climate Change | ||
| Polar bears (Ursus maritimus) depend on sea ice for most aspects of their life history, including access to seals, their main prey. Climate warming induced losses in sea ice are therefore expected to result in a loss of feeding opportunities, with consequent reductions in polar bear body condition, survival, reproduction, and eventually population abundance. To date, no quantitative predictions for changes in body condition, reproduction, and survival under climatic warming exist despite long-term empirical research - largely because historic and predicted sea ice conditions differ substantially, making extrapolation from current observations difficult. Here, we develop a mechanistic dynamic energy budget model for adult female polar bears to quantitatively predict how their reproductive success, and specifically their litter size, would be affected by expected losses in sea ice and feeding opportunities. The model is based on a body composition model that allows estimating the amount of energy stored in the fat and protein reserves of individual bears, given their body mass and body length, and tracks changes in energy stores due to somatic maintenance, movement, and feeding. The litter size of pregnant females is predicted as a function of energy stores at maternity den entry, which in turn depend on previous feeding rates. We apply the dynamic energy budget model to the population of western Hudson Bay to predict changes in energy stores, and consequent changes in litter size, as a function of predicted changes in sea ice dynamics and feeding opportunities. We show that severe declines in litter size can be expected under climatic warming, but the precise rates of change can only be approximated due to a lack of data on current feeding rates. | ||
| Coauthor(s): Andrew Derocher, Tin Klanjscek, Mark Lewis, Martyn Obbard | ||
| MSD5c | Morgan, John | |
| Purdue University | ||
| In silico prediction and experimental measurements of metabolic fluxes in photosynthetic organisms | ||
| Photoautotrohpic metabolism involves the utilization of light energy to fix available CO2 into complex organic molecules. A major goal of our research is to have a systems level understanding of metabolism that will enable the rational design of production of valuable metabolites from photosynthetic systems. To accomplish this goal, a key tool is the measurement of metabolic fluxes. The first task is to reconstruct the metabolic network for the organism of interest. We have done this for a model prokaryote, Synechocystis PCC6803, and a genome scale model for photosynthetic eukaryotic algae, Chalmydomonas reinhardtii. Predictions of metabolic fluxes are accomplished by specifying an objective function, such as maximize biomass synthesis, and performing linear programming to determine optimal fluxes satisfying stoichiometric constraints. We will present our findings for metabolic flux distributions under hetero-, mixo-, and autotrophic growth conditions. Metabolic flux analysis is widely used for quantification of phenotypes under varying environmental and genetic conditions. However, inherent limitations have prevented the application of steady state 13C-MFA to purely autotrophic metabolism, wherein CO2 is the sole carbon source. This is due to the fact that, in autotrophic systems under conditions of isotopic steady state, every single carbon atom in every downstream molecule has the same labeling percentage as the single input carbon (CO2), irrespective of flux distribution. However, the pattern of change in isotopic label distribution as the steady state is attained does depend on the fluxes. This type of labeling information is utilized in recently developed techniques of instationary 13C-MFA, which enable measurement of fluxes at a metabolic steady state, while following changes in 13C labeling patterns of metabolic intermediates as a function of time, in response to a step change in 13C label input. In this work, we utilize the instationary 13C- MFA technique with the elementary metabolite unit (EMU) formulation to measure central carbon fluxes under photoautotrophic conditions for the first time. We will compare in silico and experimental results for the cyanobacterium, Synechocystis sp. PCC 6803. | ||
| MSD1b | Murillo, David | |
| Arizona State University | ||
| Local vs. global behavioral change strategies for a two-strain dengue fever outbreak | ||
| There are various public education campaigns aimed at preventing the spread and prevalence of dengue fever. These generally employ the use of bednets, pesticides, and the removal of standing water near populated areas. We propose a comparison of these different techniques distinguishing between those techniques that provide benefits to the individual employing them (local behavioral change) and those that may benefit many individuals (global behavioral change). Although global strategies are more effective at preventing an outbreak, we suggest some incentives for the inclusion of both strategies in a public campaign to fight dengue fever. | ||
| CTG7c | Murphy, Kelly | |
| Queensland University of Technology | ||
| A fibrocontractive mechanochemical model of dermal wound closure incorporating realistic growth factor kinetics | ||
| Fibroblasts and their activated phenotype, myofibroblasts are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct components: the cells must be stimulated by transforming growth factor β (TGF-β) and experience mechanical tension. We review the experimental findings in detail and investigate an extension of the model of dermal wound healing developed by Olsen et al. (1995) to incorporate these phenomena. We also extend their model to include a more biologically realistic form of the growth factor kinetics, again using recent experimental observations. This new framework enables the exploration of the effect of strong interactions between the mechanics and growth factors in dermal wound healing which has not been explored in previous models. This model suggests that it is the strong coupling of the tissue mechanics and the growth factors that determine the quality and type of dermal wound healing and is the overriding driver for the appearance of pathological scarring. Olsen, L., Sherratt, J.A. and Maini, P.K. (1995) A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile, Journal of Theoretical Biology, 77, 113-28. | ||
| CTH5f | Myerscough, Mary | |
| University of Sydney | ||
| Why do so few choose for so many? Nonlinear decision-making by honey bees. | ||
| In the spring a swarm of honey bees may leave the hive and hang on a branch nearby while scouts go out and look for a new home. When a scout finds a suitable cavity, she returns to the swarm and performs a waggle dance on its surface to communicate the location and quality of the potential new nest site. Other scouts use this information to visit the nest site themselves and then they too return and dance and so recruit more scouts. At any given time, a number of nest sites may be being advertised on the surface of the swarm. Eventually the number of scouts at one site reaches a quorum. At that point the decision is made and the swarm prepares to take off and fly to its new home. Honey-bee swarms may contain up to 20,000 bees but only a few hundred scout bees participate in choosing a new home. This seems surprising given that choosing a good quality nest site is essential for the swarm's survival and that this decision needs to be made within a few days of the swarm leaving its original hive. Using both stochastic and differential equation models, I examine the dynamics of this decision-making process and present some hypotheses as to why keeping scout numbers low may enable the swarm to use a more flexible decision-making strategy and ultimately make a better decision. | ||
| MSA1c | Nag, Ambarish | |
| Los Alamos National Laboratory | ||
| Aggregation of membrane proteins by cytosolic cross-linkers: Modeling of LAT aggregation mediated by cytosolic complex of Grb2 and SOS1 proteins | ||
| Ligand-induced receptor aggregation is a well-known mechanism for initiating intracellular signals but oligomerization of distal signaling molecules may also be required for signal propagation. Formation of complexes containing oligomers of the transmembrane adaptor protein, linker for the activation of T cells (LAT) has been identified as critical in mast cell and T cell activation mediated by immune response receptors. Cross-linking of LAT arises from the formation of a 2:1 complex between the adaptor Grb2 and the nucleotide exchange factor SOS1, which bridges two LAT molecules through the interaction of the Grb2 SH2 domain with a phosphotyrosine on LAT. We model this oligomerization and find that the valence of LAT for Grb2, which ranges from zero to three, is critical in determining the nature and extent of aggregation. A dramatic rise in oligomerization can occur when the valence switches from two to three. For valence three, an equilibrium theory predicts the possibility of forming a gel- like phase. This prediction is confirmed by stochastic simulations, which make additional predictions about the size of the gel and the kinetics of LAT oligomerization. We discuss the model predictions in light of recent experiments on RBL-2H3 and Jurkat E6.1 cells and suggest that the gel phase has been observed in activated mast cells. We conclude with the extension of the mathematical model to account for the heterogeneity in the LAT population with respect to the number of Grb2 binding sites per LAT molecule. | ||
| CTH7e | Nahmad, Marcos | |
| California Institute of Technology | ||
| Steady-State Invariant Manifolds: A theoretical approach to the study of morphogen gradient dynamics | ||
| Patterning by morphogens is the predominant model by which cells acquire positional information during animal development. However, how cells respond to morphogen gradients that change with time, or how and when concentration thresholds are interpreted to form reproducible patterns of gene expression is largely unknown. Although recent studies have highlighted the importance of morphogen gradient dynamics, how these transient gradients contribute to developmental patterning has not been explored in detail, in part because the difficulty of isolating transient from steady-state effects. Here we present a mathematical method to identify perturbations on the gene networks controlling developmental patterning that affect the transient, but leave invariant the shape of the steady-state morphogen gradient. The set of these perturbations defines a geometric object in parameter space named Steady-State Invariant Manifold (SSIM). In many systems, SSIMs can be obtained analytically providing a tool to study the role of transient gradients in developmental pattern formation. As a case study, we demonstrate how this theoretical approach can be used to study the dynamic properties of Hedgehog signaling in the wing disc of the fruitfly Drosophila melanogaster. Finally, we discuss how this method can be employed to design experiments that permit to assay the function of morphogen gradients dynamics in a more general way. | ||
| CTF5c | Namba, Toshiyuki | |
| Osaka Prefecture University, Department of Biological Science | ||
| Multiple, not stable, but unstable, steady states may explain ungulate population dynamics | ||
| In recent decades, ungulate populations have strikingly increased and expanded their ranges in many countries. Ungulate population dynamics often follows a rapid increase to peak abundance and a subsequent crash to much lower abundance, a process known as irruption. Overabundant ungulate herds can extirpate palatable plant species and drive the natural plant communities into those dominated by unpalatable species. Although some mathematical models have explained ungulate dynamics by a limit cycle or a transition between multiple stable states, no models of ungulate outbreaks have included dynamics of palatable and unpalatable plants. Here, we consider a simple three-species Lotka-Volterra model of a palatable and an unpalatable plant species and an herbivore species to understand how competition between palatable and unpalatable plants affects herbivore dynamics. We assume that unpalatable plant species is inferior to the palatable in competition because of the cost of anti-herbivore defense. However, herbivores may reduce the abundance of palatable species and allow the unpalatable species to increase. Under the above assumptions, there exist steady states, at which (1) only the unpalatable plant survives, (2) only the palatable plant survives, (3) the palatable plant and herbivore coexist, and (4) three species of the palatable and unpalatable plants and herbivore coexist. The steady states (1) to (3) are always unstable and the steady state (4) becomes unstable if intraspecific competition of the palatable plant is weak. Then, all of the four steady states are unstable, and population oscillations occur. In these oscillations, the herbivore population increases rapidly when the palatable plant is initially abundant. Then, the herbivore extirpates the palatable plant and crashes. Then, unpalatable plant invades. The unpalatable plant dominates the plant community for long time until the palatable plant recovers from overgrazing. The cycles staying around some critical points for long time resemble homoclinic-like or heteroclinic-like cycles. These cycles seem to describe the irruptive dynamics of ungulates quite well. Thus, the existence of multiple unstable (not stable) steady states may be essential to explain the irruptive dynamics of ungulates and the resultant dominance of unpalatable plant species after the crash of the ungulate population. We will also consider a model that incorporates a carnivore species and investigate effects of the trophic cascade on the dynamics of herbivores and plants. | ||
| Coauthor(s): Aiko Ohno | ||
| CTH4c | O'Regan, Suzanne Marie | |
| University College Cork, Ireland | ||
| Chaos in a seasonally perturbed SIR model: numerical evidence and rigorous proof | ||
| Seasonality is a complex force in nature, and may affect multiple processes in a population. Seasonal variations may, therefore, have a considerable effect on the transmission dynamics of a pathogen. In this talk, a seasonally perturbed Susceptible-Infected-Recovered (SIR) model is considered. Such a system is known to exhibit complex dynamics as the amplitude of the seasonal perturbation term is increased. Furthermore, it has been long observed that chaotic solutions may appear in such a model. The results of computer simulations of this seasonally perturbed SIR system suggest evidence of the existence of chaos in the model. A rigorous proof of the existence of chaos in this system will be outlined. The proof is based on the concept of topological hyperbolicity, which will be discussed informally in this talk. To our knowledge, this is the first time that this technique has been used to prove the existence of chaos in an epidemiological model. | ||
| Coauthor(s): Thomas C. Kelly, Andrei Korobeinikov, Michael J. A. O'Callaghan and Alexei V. Pokrovskii | ||
| CTH3e | Olson, Sarah | |
| Tulane University | ||
| A model of CatSper channel-mediated Calcium dynamics in mammalian spermatozoa | ||
| CatSpers are Calcium (Ca) channels that are located along the principal piece of mammalian sperm flagella and are directly linked to sperm motility and hyperactivation. It has been observed that Ca induced entry through CatSper channels triggers a tail to head Ca propagation in mouse sperm, as well as a sustained increase of Ca in the head region. Here, we develop a mathematical model to investigate this propagation and sustained increase in the head region. A 1-d reaction-diffusion model tracking intracellular Ca with flux terms for the CatSper channels, a leak flux, and plasma membrane Ca clearance mechanism is studied. Results of this simple model exhibit tail to head Ca propagation, but no sustained increase in the head region. Therefore, in this model, diffusion alone cannot account for these experimentally observed results. It has been proposed that the Ca influx from the CatSper channels may induce Ca release in the head region. We test this hypothesis by examining the possible role of Ca induced Ca release from the Redundant Nuclear Envelope (RNE), an inositol-1,4,5-triphosphate (IP3) gated Ca store in the neck. The simple model is extended to include an equation for IP3 synthesis, degradation, and diffusion, as well as flux terms for Ca in the RNE. When IP3 and the RNE are accounted for, the results of the model exhibit a tail to head Ca propagation as well as a sustained increase of Ca in the head region. | ||
| CTH7f | Osborne, James | |
| University of Oxford | ||
| Multiscale Modelling in Systems Biology | ||
| Problems in systems biology are intrinsically multi-scale, with processes occuring on many disparate spatial and temporal scales. We present a multi-scale framework for mathematical modelling in systems biology. Utilising the natural structural unit of the cell, the framework consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level (micro-scale). Cells are modelled as discrete interacting entities using either an off-lattice tessellation, or a vertex based model. The behaviour at the tissue level is currently represented by field equations for nutrient or messenger diffusion, with cells functioning as sinks and sources. However, the versatility of the framework facilitates the implementation of more biologically realistic models, for example dynamic vascular networks. The sub-cellular level concerns numerous metabolic processes and is represented by interaction networks rendered into ODEs. The modular approach of the framework enables much more complicated sub-cellular behaviour to be considered. Interactions occur between all spatial scales. The multi-scale framework is implemented in an open source software library known as Chaste (http://web.comlab.ox.ac.uk/chaste). This software library consists of object orientated C++, developed using an agile development approach. All software is tested, robust, reliable and extensible. In this talk we introduce the Chaste computational framework and discuss both its functionality and development. This framework is illustrated by presenting possible applications in tissue growth, looking at colorectal cancer (within the geometry of the intestinal crypt) and the growth of tumour spheroids, developmental biology (with applications in cell sorting) and bacterial biofilms. An important consideration for any multi-scale framework is the propagation of error in the system: how coarse graining models at lower scales affects behaviour at the cell and tissue level. We use a pedagogical example to illustrate the behaviour of the overall system for varying sub-cellular models, identifying when such simplifications are possible and what levels of error are introduced. | ||
| Coauthor(s): Alex Fletcher, Professor David Gavaghan, Professor Philip Maini | ||
| PLEN1 | Oster, George | |
| Department of Molecular and Cellular Biology, University of California, Berkeley | ||
| What the thoughts of a mollusk tell us about memory in neural systems | ||
| I will present a model to explain how the neurosecretory system of aquatic mollusks generates their diversity of shell structures and pigmentation patterns. The anatomical and physiological basis of this model sets it apart from other models for shape and pattern. The model reproduces most known shell shapes and patterns, and accurately predicts how the pattern alters in response to environmental disruption and subsequent repair. The model provides a concrete example of how neural networks predict the future from memories of the past. | ||
| CTH3f | Oster, Andrew | |
| Mathematical Biosciences Institute | ||
| Mitochondrial Calcium Trafficking: excitability, waves, and oscillations | ||
| Mitochondria have long been known to sequester cytosolic Ca2+ and even to shape intracellular patterns of endoplasmic reticulum -based Ca2+ signaling. Accumulating evidence suggests that the mitochondrial network is an excitable medium which can demonstrate Ca2+ induced Ca2+ release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca2+ handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction. In this talk, we extend the modular Magnus-Keizer computational model for respiration-driven Ca2+ handling to include a transition pore and we demonstrate both excitability and Ca2+ wave propagation that is accompanied by depolarizations similar to those reported in cell preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function in a spatially extended fashion. | ||
| Coauthor(s): Balbir Thomas, David Terman, Christopher P. Fall | ||
| PLEN3 | Othmer, Hans | |
| School of Mathematics and Digital Technology Center, University of Minnesota | ||
| Robustness of Pattern Formation in Development | ||
| In many developing systems the outcome is buffered to numerous perturbations, ranging from major ones such as separation of the cells at the 2-cell stage in Xenopus (which can lead to one smaller, but normal adult, and an amorphous mass of tissue), to less severe ones such as changes in the ambient temperature or the loss of one copy of a gene. The general question is how systems are buffered against variations in such factors. We address this question in the specific context of scale-invariance: how different size embryos lead to normally-proportioned adults. | ||
| CTF2c | Ougrinovskaia, Anna | |
| University of Sydney | ||
| Modelling the inflammatory response in early stage atherosclerosis | ||
| Within the past decade, inflammation has been determined as a crucial factor in all stages of formation of atherosclerotic plaques. The inflammatory response is initiated by the appearance and modification of cholesterol-carrying Low Density Lipoproteins (LDL) in the intima. Monocyte-derived macrophages then bind modified LDL and internalize it, via a variety of scavenger receptors. Eventually they become laden with lipid and take on a foamy appearance. These macrophage foam cells become trapped in the intima, and, moreover, continue to proliferate, becoming the main constituent of early plaques. Macrophage proliferation and uptake of modified LDL are mediated by an array of factors, including pro- and anti-inflammatory cytokines, T-cells, and High Density Lipoproteins (HDL). HDL is thought to have an athero-protective role and to enable plaques to regress with time. We present a simplified ODE model based on the interactions of modified LDL and macrophages, and allow these interactions to be modified by the presence of T-cells and HDL. The model uses general kinetic functions, as the exact mechanisms of modified LDL uptake and HDL activity are still a subject of debate. We are able to perform a phase plane analysis of the system without relying on parameter estimation. Our results indicate that the underlying mechanisms of macrophage uptake of modified LDL can have a deep impact on the cellular dynamics in the lesion. We demonstrate that it is macrophage proliferation and constant signalling, rather than an increasing influx of modified LDL, that drives lesion instability. We also identify cholesterol efflux and possibility of foam cell emigration as the main pathways through which HDL stabilizes the system and reduces the foam cell content. | ||
| Coauthor(s): Rosemary S. Thompson, Mary R. Myerscough | ||
| CTE6e | Palsson, Eirikur | |
| Simon Fraser University of | ||
| Excitability of Dictyostelium discoideum is regulated by the ratio of membrane bound to secreted phosphodiesterase | ||
| After onset of starvation Dictyostelium discoideum cells initiate formation of cooperative aggregation territories via propagating cAMP waves. Recruitment of a high number of cells is important, and it appears that formation of large territories has been selected for. These cAMP waves are generated by the means of an elaborate cAMP signaling system that makes the whole field of cells excitable. Dictyostelium cells respond chemotactically to these waves, guiding cell aggregation towards a signaling center. A crucial component of the signaling system, the PdsA phosphodiesterase (PDE), an enzyme, that breaks down the external cAMP. can be either membrane bound or secreted. I show that by utilizing both forms of PDE and by fine tuning the ratio, Dictyostelium extends the range of cell densities where cAMP waves can propagate and thus where aggregation can be successful. The membrane bound PDE reduces the likelihood the aggregation territory breaks up into many smaller territories at higher densities, while the secreted PDE is important for wave propagation at low cell densities. These findings have implications for other excitable systems such as the Oregonator model for the Beluzov-Zhabotinskii, Ca++ propagation in cardiac cells and propagation of electrical excitation in nerve axon. With discrete point sources located far apart, wave propagation is not possible if the sink is in the same location as the source. However, when the source and sink are in a different location, wave propagation is possible. | ||
| CTA7d | Parsons, Todd | |
| University of Pennsylvania | ||
| Stochastic Competition in Ecology, Epidemiology and Population Genetics | ||
| In this talk, I will present analytical results for a model of stochastic competition in multi-species population dynamics that incorporates density-dependent population regulation, and allows for mutation and migration. I will demonstrate how this framework allows us to obtain analogues to classical results in population genetics (fixation probabilities, fixation times and polymorphism spectra) without assuming fixed population sizes, study the evolution of virulence in multi-strain SIS epidemics, and may be used to determine species abundance distributions for neutral and near-neutral models with trade-offs in community ecology. | ||
| Coauthor(s): Christopher Quince, Joshua B. Plotkin | ||
| CTA7e | Parvinen, Kalle | |
| University of Turku, Finland | ||
| Evolutionary emergence of cooperators and defectors in a metapopulation | ||
| The possibility of evolutionary emergence of cooperators and defectors via evolutionary branching of a cooperative strategy has recently been demonstrated in the continuous snowdrift game. However, the required conditions on the cost and benefit functions are rather restrictive. In this work I show that in a metapopulation model with small local populations such evolutionary branching is essentially more common: it can occur also with linear cost and benefit functions. The observed effect of various parameters on the numerical value of the monomorphic singular strategy is intuitive. Their effect on the final coexisting cooperator-defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the relative population size of the cooperator increases such that the average strategy does increase. | ||
| CTE7d | Pasour, Virginia | |
| Duke University | ||
| A Dimensionless Number for Viral Evolution | ||
| Evolution of viral proteins involved in immune escape typically exhibits one of two strikingly different dynamical regimes: either lineage turnover with limited genetic diversity (cactus-like dynamics) or evolutionary branching with increasing genetic diversity (acacia-like dynamics). For example, the evolutionary dynamics of influenza A in humans is cactus-like, while in pigs it is acacia-like. Understanding why viral proteins exhibit cactus-like versus acacia-like dynamics will lead to better disease prediction and control, especially of new pandemic strains. To this end, we propose to distinguish between cactus-like and acacia-like evolution using a dimensionless number. The proposed number is given by the ratio of the time to extinction of the original variant to the time to generation of a second variant by the original variant. We expect this number to be < 1 for cactus-like viruses and >1 for acacia-like viruses and to depend on properties of the host as well as the virus. We present an analytic function, derived using the Moran model, for the numerator, the time to extinction of the original variant. This function depends on the selective advantage of a novel variant and on the population size of infected individuals. We use numerical simulations based on two epidemiological multi-strain models to address the relevance of this function. In spite of the assumptions inherent to the Moran model (namely, a constant selective advantage and a constant population size), the analytic expression matches the simulation results remarkably well. We also present simulations for the denominator of the dimensionless number and end with work in progress towards an analytic expression for this quantity. | ||
| Coauthor(s): Jonathan Mattingly, Katia Koelle | ||
| CTE6f | Pearson, Yanthe | |
| Rensselaer Polytechnic Institute | ||
| A Renewal Process Approach to Growth Cone Kinematics in Axonogenesis | ||
| Axonogenesis is the growth and differentiation of axonal processes by the developing neuron. Studies in vivo and in vitro have demonstrated that ethanol disrupts axonogenesis. Current studies use time lapse microscopy of live embryonic rat hippocampal neurons growing in cell culture to study the dynamics of axonal growth and its disruption by ethanol. Thus far we can analyze axonal trajectory data based on cells growing in an undisturbed environment. Due to the noisy nature of the data we develop filtering algorithms to smoothen out the paths while maintaining the underlying dynamics of the axonal growth process. We analyze the new paths and propose a model for growth cone kinematics during axonogenesis without a gradient field. We propose a general model that can be extended to accommodate steering effects, a consequence of adding gradients. We present a simple renewal process with the aim of reproducing certain path behaviors of the growth cone. Future development will include angle variability and gradients effects. | ||
| MSB4d | Peercy, Bradford | |
| University of Maryland, Baltimore County | ||
| Long Time Scale cAMP-Dependent Signaling by Protein Kinase A in Pancreatic Beta Cells | ||
| External signaling to pancreatic beta cells enhances glucose-dependent insulin secretion and biogenesis. This signaling pathway involves the ubiquitous second messenger cyclic adenosine mono-phosphate (cAMP) activation of protein kinase A. Compartmentalization of cAMP appears to be important in cells such as heart cells. Experiments that track the catalytic subunit of PKA (cPKA) during nuclear translocation show success that is dependent on cAMP stimulus profile. We develop both spatial and compartmental models to address cAMP distribution and nuclear translocation of cPKA in response to enhanced production of cAMP or enhanced inhibition of degradation of cAMP. We find that compartmentalization need not play a role in cPKA nuclear translocation and passive transport or rapidly buffering active transport across the nuclear membrane is sufficient to account for many of the observed experiments. | ||
| MSB4c | Periwal, Vipul | |
| Laboratory of Biological Modeling -NIDDK/NIH | ||
| Modeling Metabolism in Pancreatic Beta-Cell Mitochondria | ||
| Pancreatic beta-cells sense the ambient blood-glucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. We have developed a model of beta-cell mitochondrial respiration, ATP synthesis, and ROS production in response to glucose and fatty acid stimulation, based on available data in the literature and mathematical models derived from first principles. The model is consistent with a number of experimental observations reported in the literature. Most notably, it explains the non-ohmic rise in the passive proton-leak rate at high membrane potential and its dependence on increased ROS production. Results from our model suggest increasing mitochondrial density while decreasing uncoupling protein activity may be an effective way to increase glucose-stimulated insulin secretion while decreasing oxidative stress. It also predicts that glucose-stimulated insulin secretion may be inhibited by long-term fatty acid exposure. Using glucose and fatty acid profiles from individuals in a diet study, we find a negative correlation between the amount of ROS produced per ATP, as predicted by the model, and the individual insulin sensitivities. The model can also be applied in a clinical setting to predict the insulin secretion rate and quantify beta-cell function for a single individual. | ||
| CTF3a | Phipps, Colin | |
| University of Waterloo | ||
| Combination of chemotherapy and antiangiogenic therapies: The roles of angiogenic factors and interstitial fluid pressure | ||
| Clinical studies have shown that the combination of cytotoxic therapies and antiangiogenic agents is a more effective strategy in the treatment of malignant tumors than either alone. However, there are different outcomes depending on, at least partially, the drugs used, the delivery vehicle, the dosages of these agents and their treatment schedules. A mathematical model could help in predicting the results of a wide array of possible treatment strategies. In this direction, we have developed a medically relevant model including tumor cells, blood vasculature, interstitial fluid pressure (IFP), as well as proangiogenic and antiangiogenic factors. We discuss the effects of antiangiogenic agents and chemotherapy on tumor growth and its microenvironment. We also compare the efficacy of specific delivery vehicles (e.g. liposomes, nanospehres, etc.) that include single agents or various combinations of treatment with appropriate drug release profiles. | ||
| Coauthor(s): Mohammad Kohandel | ||
| MSC3b | Pilgrim, Dave | |
| University of Alberta | ||
| Genetic analysis of the forces involved in shaping the cells in the C. elegans germline | ||
| Our lab is interested in exploiting the C. elegans gonad as a model for the study of the regulation of contractive forces in cytokinesis. In particular, we are curious about the regulation of non-muscle myosins in the process that generates an ordered progression of meiotic germ cells from a multinuclear mitotic syncytium. Achieving this organization requires a series of protein folding and assembly steps. Both myosin folding and assembly require factors to coordinate the formation of the thick filament in the sarcomere and these factors include chaperone molecules. Myosin folding and sarcomeric assembly requires association of classical chaperones as well as folding cofactors such as UNC-45. Recent research has suggested that UNC-45 is required beyond initial myosin head folding and may be directly or indirectly involved in different stages of myosin thick filament assembly, maintenance and degradation. In my seminar, I will review what we now know about these processes and solicit your ideas about how to resolve some of the conundrums that have arisen when we have examined the processes in the earlier stages of cellularization. | ||
| MSD2b | Pineda-Krch, Mario | |
| Centre for Mathematical Biology, University of Alberta | ||
| Prediction of mountain pine beetle outbreaks using Markov process logistic regression | ||
| When the mountain pine beetle populations (Dendroctonus ponderosae) reach epidemic levels, large areas of old growth forests are destroyed. In British Columbia alone, the mountain pine beetles have affected more than 10 million ha of land. Recently the pine beetle infestation successfully crossed the Rocky mountain range and is now threatening to spread across the Prairie provinces. As a consequence there is an urgent need to predict potential outbreaks. Here we use a Markov process logistic regression model that integrates ecological, climatic, and topographic information to determine the probability of a mountain pine beetle outbreak one year ahead. The resulting model maximizes predictive ability by accurately identifying high-risk regions, is simple to implement, uses information that is readily available, and can easily be validated. We develop recommendations for how this model can support strategic planning by identifying high-risk areas for control and management. | ||
| CTC7b | Planque, Bob | |
| VU University Amsterdam | ||
| Recruitment strategies and colony size in ants | ||
| Ants use a great variety of recruitment methods to forage for food or find new nests, including tandem running, group recruitment and scent trails. It has been known for some time that there is a loose correlation across many taxa between species-specific mature colony size and recruitment method (Beckers et al 1989). Until now, explanations for this correlation have focused on the ants' ecology, such as food resource distribution. However, many species have colonies with workforces that grow from a single queen over several orders of magnitude, and little is known about how a colony's organization, including recruitment methods, may change during growth. After all, recruitment involves interactions between ants, and hence the size of the colony itself may influence which recruitment method is used. Here we show using mathematical models that the observed correlation can also be explained by recognizing that failure rates in recruitment depend differently on colony size in various recruitment strategies. Our models predict that ant colonies should use only one recruitment method (and always the same one) rather than a mix of two or more. We also show that certain recruitment features, such as group size in group recruitment, in fact should not depend on colony size. These results highlight the importance of the organization of recruitment and how it affects, and is affected by, colony size. Hence these results should also expand our understanding of ant ecology. | ||
| MSA3b | Portet, Stephanie | |
| Department of Mathematics, University of Manitoba | ||
| Modeling of the intermediate filament assembly | ||
| Intermediate filaments are one of the three main components of the cytoskeleton, which is a complex arrangement of structural proteins organized in networks involved in many major cellular functions. Here, a model is designed to study the kinetics of the assembly of individual filaments. The model deals with the dynamics of the length distribution of filaments by taking into account the diffusion properties of rod-like linear aggregates. Different hypotheses are tested by mathematical and computational analyses. | ||
| MSD5d | Potter, Laura | |
| Syngenta Biotechnology, Inc. | ||
| Perspectives on key modeling problems and challenges in the agricultural industry | ||
| As the world’s population continues to expand, the agricultural industry is encountering major challenges to meet the rapidly increasing demand in the face of limited farmland and water supplies. In order to meet these challenges, the industry must move beyond traditional breeding practices and help farmers produce more yield with less resources. One active area of research is the study of key biological pathways in crop species to improve yield and tolerance to drought. Major pathways of interest include photosynthesis, nitrogen uptake, water utilization and flowering time. By understanding the dynamics of these pathways and their connections to important traits, we can predict novel alterations in the pathways that will improve one or more traits. These predicted pathway interventions can then be implemented through crop breeding or genetic transformation. Mathematical models can be a powerful tool to help detail key biological pathways in crop species, and to predict optimal modifications to these pathways for trait improvement. This talk will provide an overview of these challenges, some key biological pathways of interest, the current state of modeling in this area, and opportunities for new models that can help suggest novel leads for improving traits in crops. | ||
| MSD4a | Poulin, Marc | |
| Departments of Physiology & Pharmacology and Clinical Neurosciences, University of Calgary | ||
| Physiological Responses to Intermittent Hypoxia in Healthy Humans | ||
| Relatively few studies have investigated the physiological responses to intermittent hypoxia in healthy humans, the changes that ensue with prolonged exposure to intermittent hypoxia, and the mechanisms that underlie these adaptive processes. This review will outline the physiological (cardiovascular, cerebrovascular, respiratory) responses to intermittent hypoxia in healthy humans. Moreover, new data emerging from our group and others will be presented to describe some of the proposed mechanisms (i.e., erythropoiesis, angiogenesis, oxidative stress, endothelial function) that may underlie the physiological adaptations that ensue after exposure to intermittent hypoxia in healthy humans. Finally, the implications for obstructive sleep apnea will be discussed | ||
| MSD2c | Powell, James | |
| Department of Mathematics and Statistics, Utah State University | ||
| Connecting tree-level phenology and lanscape-level outbreak dynamics for mountain pine beetle | ||
| Maintaining an appropriate seasonality is a basic ecological requirement for insects living in seasonal environments. Critical life history events (the timing of which is termed phenology) must mesh with seasonal cycles, and it is often selectively advantageous for individuals in the population to synchronize their activities with one another as well. In most terrestrial insects, some explicit physiological mechanism, such as diapause (hibernation which ends with a specific environmental cue, as when day-length exceeds a fixed duration), maintains both aspects of seasonality. However, many ecologically important insects, such as the mountain pine beetle (Dendroctonus ponderosae), apparently lack an explicit physiological timing mechanism. Seasonality of such insects is said to be under direct temperature control. How such insects maintain seasonality has been a mystery, since their physiological clocks move at a rate nonlinearly dependent on environmental temperatures. In this talk, we first discuss the mechanistic basis for direct temperature control of seasonality in the mountain pine beetle, which is responsible for more forest damage across North America than all other disturbances together, including fire. This bark beetle attacks healthy pine trees; successful reproduction is contingent on host mortality. Pines under attack defend themselves strongly using toxic resin, which can repel a fixed number of attacking beetles. This creates strong selective pressure for populations of beetles to mature and emerge simultaneously (synchrony), and at an appropriate time of year (seasonality); synchrony of adult emergence is absolutely necessary for the mass-attack strategy that overcomes tree defenses. We connect a distributional model describing mountain pine beetle phenology with a model of population success measured using annual growth rates derived from aerially detected counts of infested trees. This model bridges the gap between phenology predictions and population viability/growth rates for mountain pine beetle. The model is parameterized and compared with 10 years of data from a recent outbreak in central Idaho, and is driven using measured tree phloem temperatures from north and south bole aspects and cumulative forest area impacted. A model driven by observed south-side phloem temperatures and that includes a correction for forest area previously infested and killed is most predictive and generates realistic parameter values of mountain pine beetle fecundity and population growth. Extensions of this model to include spatial and demographic structure of host forest (both leading to outbreak `waves’) are discussed. | ||
| MSD3d | Rafelski, Susanne | |
| University of California, San Francisco | ||
| Mitochondrial Morphology: Quantifying Topological Network Properties in 3 Dimensions | ||
| A fundamental unsolved question in the post-genomic era is how the 3-dimensional geometry of cellular structures is generated by networks of molecular interactions. Mitochondria are an ideal system in which to approach this question. Mitochondrial morphology ranges from small individual organelles to giant reticular networks and affects mitochondrial functions. In budding yeast mitochondria compose a dynamic tubular network at the cell periphery, which undergoes subtle, consistent changes in morphology under different physiological conditions. We aim to understand the mechanisms that regulate the normal range of reticular structures. We have developed a method to quantify the 3D interconnected morphology of the mitochondrial network by considering the mitochondria as a network of edges (the tubules) and nodes (the branch points where tubules connect). Live mitochondria are rapidly imaged in 3D at high resolution using Spinning-disk Confocal microscopy. Specialized segmentation and 3D skeletonization methods are applied to the image stacks to extract the 3D mathematical graph of the mitochondrial network. For validation we create theoretical microscope images from pre-determined skeletonized structures and compare these to the 3D skeletons obtained by our “mito-graph” methodology. These tests are used to optimize the accuracy of the 3D skeletons and determine their limits, imposed by microscopy imaging. We then apply concepts and methods from complex networks research to characterize the connectivity and clustering of the tubules. This quantification technique provides us with measurements of the arc lengths, density, and connectivity of mitochondrial tubules in the cell and how the connections change as individual tubules undergo constant fusion and fission dynamics or individual cells progress through the cell cycle. In our first analysis we focus on how the properties of the network change with tubule density at the surface and which properties depend on fusion and fission dynamics. We also compare measurements of real mitochondrial networks with simulated networks created by joining points (nodes) on the surface of a sphere with edges following a set of rules to explore the minimum requirements necessary to generate quantitatively realistic mitochondrial networks. | ||
| CTH4d | Rebarber, Richard | |
| University of Nebraska - Lincoln | ||
| Integral projection model analysis of an endangered plant species | ||
| We analyze the population dynamics of blowout penstemon (Penstemon haydenii). In Nebraska this endangered plant naturally occurs in "blowouts", which are sparsely vegetated depressions in active sand dunes created by wind erosion. Our goal is to identify factors limiting the population size and to make recommendations for its management. We use discrete time integral projection models to predict plant population dynamics, and to determine how the dynamics depend upon the life history parameters and initial conditions. The kernel for the integral operator is obtained by estimating the size-dependent survival, growth, seed production, and recruitment probability (the probability that a seed will become a seedling in the following year) from a large data set spanning 13 blowout sites in western Nebraska. This model is density-dependent, since the recruitment probability is dependent upon the number of seeds produced. We do a numerical analysis of the transient and asymptotic dynamics, and a mathematical analysis of the asymptotic dynamics. The novel aspect of the mathematical proofs involves writing the projection operator as a closed-loop feedback operator (where the recruitment probability is a feedback of the population) and using control theoretic small-gain techniques to obtain convergence. We find that there is an asymptotic population and stage structure, which is independent of the nonzero initial population and stage structure. This is observed numerically and proved mathematically. We give formulas for the asymptotic population density and quantity in terms of the parameters, and provide global convergence proofs. We also analyze the transient dynamics that are predicted if the population deviates from the stable stage distribution. Our model predicts that in the early phase of blowout colonization population density drops to very small numbers before increasing to the asymptotic population size. This suggests a very small colonization success of this plant since small populations have a high extinction risk because of demographic and environmental stochasticity and Allee effects. We use robustness analysis to evaluate different management strategies. | ||
| Coauthor(s): Brigitte Tenhumberg, Kay Kottas, Stuart Townley, Joseph Briggs, Kathryn Dabbs, Daniel Riser-Espinoza | ||
| MSH2d | Rejniak, Kasia | |
| Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, USA | ||
| Revealing the Mechanisms Underlying Formation of Carcinomas using the Multiscale IBCell Morphocharts | ||
| A disruption of epithelial morphogenesis is thought to be involved in the initiation of cancer, however, little is known about the cell biology of early neoplastic lesions. Computational models can facilitate in the study of early cancer lesions by directing essential empirical data collection and by integrating results in quantitative outcomes. Here, we present IBCell, a computational model of epithelial acinar structures that predicts the disruptive effects of altered cell-microenvironment interactions on epithelial morphogenesis. A systematic investigation using IBCell reveals a range of model parameters (in terms of cell sensitivity to external cues) for which robust acinar structures form, and the ranges of parameters leading to abnormal geometrical forms resembling tumor-like morphologies, such as: acini with filled lumen or cell clusters with uncontrolled growth. The results obtained from computational simulations are compared (in both, a qualitative and quantitative way) to three-dimensional in vitro experiments on a non-tumorigenic MCF10A cells and some mutants derived from this cell line. | ||
| MSE3b | Rejniak, Kasia | |
| H. Lee Moffitt Cancer Center & Research Institute | ||
| An integrative approach in modeling bio-mechanics of epithelial cancer initiation. Bio-mechanical view | ||
| To better understand the process of carcinogenesis more detailed knowledge of the origin of neoplastic growth is required. In particular we are interested in addressing questions of when the initiated cell begins to show altered behavior and what events lead to tissue deformations and tumors. We investigate these problems using the bio-mechanical models of simple and stratified epithelia, such as mammary breast glands or skin epidermis, due to their unique properties of frequent cell turnover and a finely define topology. We will present an integrated approach combining laboratory experiments and computational modeling showing normal tissue development and turnover, and discuss the possible events (molecular, bio-chemical, mechanical) that lead to disruption of this tightly controlled system and result in the formation of epithelial tumors. | ||
| CTB7d | Reluga, Timothy | |
| Penn State | ||
| Recent results in game-theoretic epidemiology | ||
| One potentially valuable contribution of mathematical analysis to epidemiology is the characterization of the costs of infectious diseases to people and communities. In many situations, the costs align, so that what's good for individual patients is also good for the communities, but in some cases, these costs diverge, creating dilemmas for policy and practice. Mathematical models, particularly those based on game-theory, can help us understand these problems. In this talk, I'll summarize some recent results including models of ``policy failure'' and the calculation of trembling-hand perfect equilibria as they apply to epidemiology. | ||
| MSD5b | Rockne, Russ | |
| University of Washington | ||
| Predictive modeling of brain tumor growth and invasion: optimizing treatment in individual patients | ||
| Gliomas are notoriously aggressive primary brain tumors with limited treatment options. A primary reason for their therapeutic resistance is the diffuse invasion of individual gliomas cells throughout the normal appearing brain tissue peripheral to any abnormality seen on imaging. We have developed a series of bio-mathematical models to quantify this diffuse invasion in individual patients. I will discuss the application of such modeling to patient-specific imaging (e.g., MRI, PET) to illustrate how these models can be used to not only predict the extent of diffuse invasion but also quantify and predict response to therapy in individual patients. | ||
| CTF3b | Rockne, Russ | |
| University of Washington | ||
| The role of delay and observation timing in assessing glioma response to radiation therapy. | ||
| Gliomas are malignant brain tumors characterized by their high proliferation rate and diffuse invasion of surrounding tissue. High grade gliomas known as glioblastoma multiforme (GBM) are uniformly fatal with a median survival of 12 months from diagnosis. Radiation therapy is widely considered a first-line treatment for gliomas and is conventionally given in daily doses, with target volumes based on the imageable disease burden assessed on post surgical magnetic resonance imaging (MRI). Response to radiation therapy is typically quantified clinically as the change in MRI imageable tumor volume from pre to post therapy -in addition to mental status and the doctor's clinical experience. The problem of quantifying disease response to therapy is compounded by the delay between the administration of therapy and the resulting changes in tumor volume in conjunction with the timing of the MRI observations relative to treatment. Moreover, increases in tumor volume immediately post treatment, known as 'pseudo progression' of disease, have been attributed to treatment effect rather than actual disease progression. We extend a model for glioma response to radiation therapy previously presented by us (model I) (Rockne et al) and others (Powathil et al) to include a sub population of tumor cells affected by radiation therapy–determined by a spatially defined survival probability–that decay at a rate related to the pre-treatment proliferation rate (model II). Using the brainweb brain atlas (Cocosco et al) and in vivo parameter values taken from an actual glioma patient, we construct a fully 3 dimensional, anatomically accurate in silico virtual glioma patient. Using the clinically-defined spatial and temporal radiation dose prescription for that patient, we simulate radiation therapy on the virtual patient using both models I) and II). Results from model II) suggests that an optimal time for observing tumor response to therapy can be assessed on a patient-specific basis such that pseudo progression or treatment effect can more accurately be distinguished from actual tumor progression. Moreover, pseudo progression may be the result of observation timing relative to the rate of treatment response. Results from both model implementations are systematically compared and contrasted to each other and also to the actual patient data. ________________________________________ Rockne R, Alvord EC, Jr., Rockhill JK, Swanson KR. A mathematical model for brain tumor response to radiation therapy. J Math Biol 2009; 58: 561-78. Powathil G, Kohandel M, Sivaloganathan S, Oza A, Milosevic M. Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy. Phys Med Biol 2007; 52: 3291-306. Cocosco CA, Kollokian V, K.-S. KR, Evans AC. Brainweb: Online interface to a 3D simulated brain database. Neuroimage 1997; 5: S425. | ||
| Coauthor(s): Kristin R Swanson | ||
| MSB2c | Rodriguez, Ignacio | |
| Courant Institute of Mathematical Sciences | ||
| A mathematical model of telomere length regulation and cellular senescence | ||
| Telomeres play an essential role in chromosomal function and cell viability by preventing chromosome ends from being interpreted by the DNA damage response machinery as DNA breaks. In normal somatic cells telomere length shortens with each cell replication and correlates with the onset of senescence or apoptosis. Germ cells, stem cells and the majority of cancer cells express telomerase, an enzyme that extends telomere length and when expressed at sufficient levels can immortalize or extend the life span of a cell line. It is believed that telomeres switch between two states: capped and uncapped. The telomere state determines its accessibility to telomerase and the onset of senescence. One hypothesis is that the t-loop, a large lariat-like structure, represents the capped state. In this talk we present a model telomere state based on the biophysics of the t-loop and the effects of TRF2, a telomere binding protein implicated in t-loop formation. We provide a mathematical description of a telomere length sensing feedback loop for telomerase positive cells and a model of cellular senescence for normal somatic cells. The model predicts the steady state length for telomerase positive cells, describes the time evolution of telomere length, and computes telomere length and the life span of a cell line based on the levels of TRF2 and telomerase expression. By fitting the model to a variety of experimental data we show that a model of telomere length regulation and cellular senescence based on the t-loop is capable of replicating a wide range of experimental results. | ||
| CTB7e | Rogalsky, Tim | |
| Canadian Mennonite University | ||
| Continuous Parameterization for Optimal Control of Epidemiological and Biomedical Models by Differential Evolution | ||
| For many epidemiological and biomedical models, the dynamics can be described by a system of ordinary differential equations, that is controlled by an independent function of time known as the control function. Optimal control is the problem of finding the best control function for a given objective. For example, in an epidemic disease model, the control function might be the percentage of susceptible individuals being vaccinated per unit time. An optimal control problem for this situation is: Find the vaccination rate that minimizes both the number of infectious persons and the overall cost. Direct solution methods treat optimal control as a global optimization problem. A global search is performed, for the control function that minimizes the objective functional. Increasingly, Differential Evolution (DE) is being recognized as a powerful global optimizer for multimodal optimal control problems. However, like other evolutionary algorithms, it operates on discrete n-dimensional vectors, and becomes computationally unmanageable for large values of n. Evolutionary direct methods thus require a technique to represent control functions with a small number of real-valued parameters. This is known as Control Vector Parameterization (CVP). To date, solutions for epidemiological and biomedical models have used piecewise constant or piecewise linear parameterization. These have obvious limitations for approximating arbitrary functions. We introduce a new CVP, using Bezier curves, which can accurately represent continuous control functions, using only a few parameters. The new technique is shown to be robust and efficient when paired with DE, providing global, near optimal, continuous solutions, with reasonable computational cost. The effectiveness and versatility of the method is demonstrated by application to a range of models, including public health strategies for epidemics, and drug administration schedules for HIV and cancer. | ||
| MSA5c | Rogers, Lisa | |
| Rensselaer Polytechnic Institute | ||
| Neurochemically Based Model of the Human Sleep Wake System | ||
| A physiologically based mathematical model of the human sleep/wake system is presented that improves upon previously established models. Our approach is to use the known properties of the neurotransmitters associated with wake and sleep, and the regions of the brain in which they function, to derive the model. Specifically, we use neurochemical interactions in the VLPO, eVLPO and ascending arousal system (brainstem, hypothalamus, basal forebrain and ventral tegmental area) to determine the dynamics. Also used are mechanisms of neuron function and chemical kinetic reactions. It is through studying the neurochemical inner-workings of mammalian sleep/wake cycles that we hope to obtain a physiological realistic human sleep/wake cycle model, and from this gain further insight into the elusive function of sleep. | ||
| MSG1d | Rojas, Enrique | |
| Department of Organismic and Evolutionary Biology, Harvard University, USA | ||
| Tip Growth Morphogenesis: From Molecules to Cell Shape | ||
| Many features of tip growth are shared across a wide range of organisms and seem therefore to transcend differences in wall composition and subcellular architecture. Based on this observation, we suggest a generic model of tip growth and show how it can account for many aspects of cell morphogenesis in fungi, oomycetes, and plants. One of the most difficult issues remains to formulate a set of equations for cell surface expansion that includes both the addition of new wall material and its stretching into a functional shape. We will discuss how our model unites these two processes and show how it can account for the steady growth of cells as well as non-steady responses. (Joint work with Enrique Rojas) | ||
| MSD2a | Roland, Jens | |
| Department of Biological Science, University of Alberta | ||
| Periodicity and spread in cyclic dynamics of forest tent caterpillar populations | ||
| Forest tent caterpillar populations exhibit eruptive dynamics with a periodicity that varies geographically. Variable dynamics could result from differing environment, differing components of the ensemble of agents thought to drive dynamics, or the interaction between agents and environment. I will present data on the effect of habitat structure (forest fragmentation) and presence/absence of a specialist parasitoid on the large-scale dynamics of this forest defoliator. | ||
| MSE2a | Roussel, Marc | |
| Department of Chemistry and Biochemistry, University of Lethbridge | ||
| Simultaneous experimental study of multiple clocks in yeast | ||
| Yeasts have become an important group of model organisms for eukaryotic structure and function because they are easy to culture. In particular, they have become a popular system in which to study cellular clocks. Here I will discuss the advantages and limitations of working with yeast for the study of metabolic networks, using the recent discovery of a four-minute oscillation in yeast cultures as a case study. | ||
| CTF2b | Rubchinsky, Leonid | |
| Indiana University - Purdue University Indianapolis | ||
| Dynamics of synchronized oscillations of neuronal activity in Parkinson’s disease | ||
| The low-dopamine state as is seen in Parkinson’s disease (PD) is marked by an increase of oscillatory and synchronous activity in the beta frequency band. While casual relationship between oscillatory synchronized activity in the beta band and motor symptoms of PD is not completely certain, multiple recent experimental results suggest that this activity is closely related to the pathologies of motor behavior. Understanding the dynamical nature of this synchronization is essential for the understanding of its function as well as for determining potentially efficient therapeutic ways to suppress this synchrony in PD. The present study explores this dynamical nature of synchronous oscillations in PD as well as its potential mechanisms. We simultaneously record spikes and LFP from subthalamic nucleus of PD patients, analyze the phase synchronization between these signals as it develops in time and use mathematical modeling to study the network mechanisms of the observed dynamics. To explore synchrony patterns on a fine time scale we analyzed the first-return plots of the phase differences between recorded signals. Observed synchronized dynamics is interrupted by desynchronization events. These events are irregular, although not completely random – there is a predominance of short desynchronization events. The signals go out of phase for just one cycle of oscillations more often than for two or a larger number of cycles. The chances of longer desynchronization events decrease with the duration of these events. An alternative scenario (longer but less frequent desynchronization events) would produce the same degree of average synchronization, however, it is not supported by the data analysis. Numerical simulation of conductance-based models of subthalamo-pallidal circuits allowed us to identify the parameter domains, where the model without any external input or plasticity effects reproduces imperfect synchronization with the same characteristic fine temporal structure. This dynamics is robust to the small noise perturbations and persists in simplified model of two synaptically coupled neurons. The parameter values correspond to the relatively strong synaptic strengths in the model, which is realistic for PD (in a healthy state these synaptic connections would be inhibited by dopaminergic action). The computational results indicate that this variability can be generated intrinsically in pallido-subthalamic circuits without any external inputs due to moderately large strength of synaptic coupling. The dominance of the short desynchronization events indicates that even though the synchronization in parkinsonian basal ganglia is fragile enough to be frequently destabilized, it has the ability to reestablish itself very quickly, which may be important for the development of the therapeutically relevant methods to suppress this synchrony. | ||
| Coauthor(s): Choongseok Park, Robert Worth | ||
| MSC2d | Régnière, Jacques | |
| Laurentian Forestry Centre, Canada Forest Service | ||
| Comparative Empirical Models of Local Population Dynamics for Three Conifer-Feeding Budworms | ||
| We have been working on a comparative modeling approach to the dynamics of three damaging species of conifer-feeding budworms (Choristoneura fumiferana, the eastern spruce budworm; C. occidentalis, the western spruce budworm; and C. pinus pinus, the jack pine budworm). Over the years, a large amount of population data has amassed and an overall understanding of their dynamics has crystallized. These three species share very similar life systems, yet exhibit very different outbreak dynamics. Our explanation focuses on the differences between species in the intensity of the feedback between defoliation and population performance, around a concept that call the Risk of Dispersal. This is an empirical modeling approach, of course, which makes for simple math but very complex (messy) systems. These models are intended to describe the essential aspects of population dynamics of the three budworms All three budworm species are univoltine, with discrete generations. All three undertake two larval dispersal phases. In the fall, they leave the egg mass laid on host foliage in search of overwintering sites (anywhere in the stand). They spend winter in the 2nd instar. In the spring, they must disperse again to find host foliage and start feeding. They all undergo a total of 6 larval stages. They share the same (or very similar) natural enemy complexes and are exposed to much the same environmental factors. It is in the details of their relationships with their host plants that they differ most. Jack pine budworm cannot mine old needles of its host prior to bud break in the spring. It therefore requires the presence of staminate flowers to survive until succulent foliage is available. Western spruce budworm can mine old needles of its main host, Douglas fir. But it requires adjacent needle pairs to do so. Thus, past defoliation greatly decreases survival during the needle-mining period. Eastern spruce budworm is much less fussy: it will readily accept to mine old needles, or staminate flowers, on either of its main hosts (balsam fir and white spruce). However, once trees start dying from severe defoliation, it become increasingly risky to disperse in search of food. Our discrete, empirical models integrate available knowledge in an attempt to account for differences in the frequency, intensity and duration of outbreaks of these three species. This is the first step, before these models are placed in a spatial context where movement between populations can be included. | ||
| MSE2b | Schnell, Santiago | |
| Department of Molecular & Integrative Physiology, University of Michigan Medical School | ||
| How is protein load sensed in the endoplasmic reticulum? | ||
| One of the main functions of the endoplasmic reticulum (ER) is to serve as the cell protein-folding factory. The ER is responsible for the synthesis, folding, assembly and modification of one third of the eukaryotic proteome. Proteins enter the ER as unfolded polypeptide chains with variable fluxes depending on the physiological state of the cell. A sudden increase in the demand for a protein or the disruption of a folding reaction causes an imbalance between protein-folding load and capacity of the ER, which can lead to the accumulation of unfolded protein in the ER lumen. The ER protein balance is regulated by several signaling pathways, which are collectedly termed the unfolded protein response. The unfolded protein response is activated by three transducers, which are enzymes whose oligomerization-induced activation is linked to perturbed protein folding in the ER. Three model mechanisms for how these enzymes sense the unfolded protein load have been proposed: (i) the direct recognition model, (ii) indirect recognition model and (iii) hybrid recognition model. We developed mathematical formulations for these mechanisms. We found that mathematical formulations of both directed and indirect recognition models have serious discrepancies with the experimental data. However, a mathematical formulation of hybrid recognition model tests against most experimental results. We suggest a set of experiments that have not been yet carried out to test our model mechanism of protein load sensing. This is a joint work with Miguel Rodríguez. | ||
| MSH6a | Schwartz, Elissa | |
| Washington State University | ||
| A Stochastic Model of HIV-1 Escape from the Cytotoxic T Lymphocyte Response | ||
| Knowledge of the correlates of viral escape from the cytotoxic T lymphocyte (CTL) response is needed for HIV-1 vaccine development. Mathematical models of this process have been constructed using deterministic equations, but the appearance of CTL escape mutants reported in the published data is not well approximated by deterministic models of viral escape. This finding motivated us to model viral escape as a stochastic process, with the aim of predicting parameter sets likely to prevent escape. Our model takes into account viral infection, mutation, CTL killing, and viral production and includes parameters for viral burst size, mutation rate, and probabilities of recognition and elimination by CTLs. We used the model to simulate viral production by both wild type and mutant strains in 50 to 500 individuals over 25 years. We found that our model reproduced the CTL escape phenomena seen in clinical data, with varying waiting times before the emergence of escape mutants. The model can be used to determine under what conditions we see escape frequencies like those observed in the data. We can also estimate the number of mutations needed for an escape mutant that arises after x years. Model results were consistent with a scenario in which mutant virus has a competitive advantage when CTL pressure against the wild type strain is strong, and when the number of infected cells is greater. In this way, a vaccine that stimulates a CTL response that incompletely eliminates wild type infected cells can promote escape by mutant virus. Such results may aid in the development of vaccines. | ||
| CTG7d | Segal, Rebecca | |
| Virginia Commonwealth University | ||
| Analyzing Complexities of Wound Healing | ||
| Emergency room physicians do not understand why patients with similar traumas experience different outcomes (up to and including death.) An extensive series of human subject tests are being conducted at the VCU Medical Center to improve the understanding of the complex biochemical and cellular processes which are involved in the mechanics of healing a wound. We plan to use mathematical models in conjunction with the experiments to shed light on which processes are most important in healing and why negative outcomes are observed. Two modeling paradigms are being used to attack the problem. The first is an ODE model describing the healing of a local wound which includes a parameter for a systemic oxygen level. This is the first step to understand the role systemic parameters (such as cortisol and estrogen) will play in predicting the outcome of the wound and of the patient. The second model is a PDE based model to analyze spatial cell migration. The experimental study is using porous tubes to collect migrating cells and this model aims to capture cell migration under chemotaxis through the porous medium. | ||
| CTA6e | Seo, Gunog | |
| University of Ottawa | ||
| The effect of temporal variability on persistence conditions in rivers | ||
| There has been great interest in the persistence and invasion of algal and insect populations in rivers. Most recent modeling approaches assume that the flow speed of the river is constant. In reality, however, flow speeds in rivers vary significantly on various temporal scales due to seasonality, weather conditions, or human generated disturbance such as hydroelectric dams. In this talk, I consider a simple reaction-advection-diffusion model with variable flow speed chosen to be a periodic step function. The density of the population at discrete times turns into an integrodifference equation. Without Allee effect, the asymptotic speed of spread is obtained by the minimum traveling wave speed of a linearized equation. The key idea to derive the minimum traveling wave speed is to take a Laplace transform with respect to space. I apply the same technique to revisit some known results for constant flow speed. Our results can provide informative management strategies for water release schedules to maintain populations downstream of dams. | ||
| Coauthor(s): Frithjof Lutscher | ||
| MSA3d | Seow, Chun, Y. | |
| Department of Pathology and Laboratory Medicine, University of British Columbia | ||
| Intermediate filaments in smooth muscle | ||
| Intermediate filaments are abundant in smooth muscle and they can be found in the cytoskeletal network of the cells. It is commonly believed that intermediate filaments are not part of the contractile apparatus, and therefore do not contribute to the generation of active force in the muscle. However, intermediate filaments, together with other cytoskeletal elements, are believed to play an important role in maintaining the shape of the cells and their structural integrity. Details of the structural role played by the intermediate filaments in smooth muscle are nonetheless very sketchy. In this presentation, three-dimensional ultrastructure of aggregates of intermediate filaments and dense bodies in airway smooth muscle is examined. Dense bodies are commonly believed to be the skeletal muscle Z-disks equivalents in smooth muscle. Our 3-D ultrastructure however showed dense bodies strung together by intermediate filaments in a cable-like structure, casting doubts on the role of dense bodies as the "Z-disks". Measurements of the waviness of the intermediate-filament, dense-body cables in the cells revealed an inverse relationship between passive tension borne by the muscle cells and the cable waviness, suggesting that these cables may be able to bear tension in resting muscle. It is known that the passive length-tension relationship in smooth muscle is not elastic, but can be shifted plastically by adapting the muscle at different lengths. Examination of the lengths of the dense-body cables in the muscle cells adapted at different lengths revealed that the cables were able to adjust their lengths rapidly to accommodate the cell length. These length-adjustable cables are therefore likely responsible for the dynamic and plastic length-tension relationship observed in resting smooth muscle and are likely the major regulator of resting smooth muscle length. Because smooth muscle cells are mostly found in the walls of hollow organs, controlling smooth muscle length regulates organ dimension and function, for example, the diameter and resistance of airways. Interaction of intermediate filaments with dense bodies therefore could have an important regulatory role in organ function. Supported by the Canadian Institutes of health Research. | ||
| MSB4b | Sherman, Arthur | |
| Laboratory of Biological Modeling -NIDDK/NIH | ||
| The Highly Calcium Sensitive Pool and Newcomer Vesicles: Buy One Get One Free | ||
| Insulin secretion from pancreatic beta-cells shares many features with neural transmitter release. For example, both are triggered by calcium entry through voltage-dependent calcium channels. Beta-cells also have unique features, particularly the dependence of calcium elevation on glucose metabolism and the division of release into two phases, an intense but transient first phase and a sustained second phase. Loss of first phase is an early predictor of type 2 diabetes. Grodsky and colleagues proposed forty years ago that the first phase was mediated by a readily releasable pool of vesicles docked at the plasma membrane whereas the second phase was mediated by the slow delivery of new vesicles from a reserve pool. This model has stood up well over time but needs modification. Recent models have distinguished the calcium-raising and vesicle mobilizing effects of the glucose stimulus. We will discuss a new model which goes a step further to show that the second phase may be carried mainly by a newly discovered pool of vesicle with enhanced calcium sensitivity. These vesicles may coincide with another, more controversial, pool of vesicles claimed to fuse rapidly after arrival at the plasma membrane, avoiding a prolonged period of being docked and ready. | ||
| MSC3c | Sherrard, Kristin | |
| University of Washington | ||
| From so simple a beginning: How cells conspire to construct an embryo | ||
| Cells are the basic units of life, and one of their most awe-inspiring roles is to generate the signals and forces that build an embryo from an unstructured ball of cells--a process called morphogenesis. We use the ascidian, a basal chordate, as a simple model of morphogensis. Ascidians undergo the same gastrulation and neurulation movements as other chordates, but with tens of cells instead of thousands. This means that individual cells are large in proportion to embryo size and their contributions to global deformations during morphogenesis can be observed at high resolution. We take a multi-faceted approach to explore the mechanisms by which cells change shape, rearrange, and cleave to drive morphogenetic movements, using confocal microscopy, micromanipulation, laser ablation, pharmacological inhibition, and computer simulations of localized cortical contractility and adhesion. We found that endoderm invagination occurs by a mechanism of "collared rounding" by which apically narrow and columnar cells rapidly round to cause the invagination. Further, searches of tension parameter space in a two-dimensional computer simulation indicate that this is the only mechanism by which localized cortical contractilty can drive endoderm invagination on the ascidian geometry. Although these results contradict the textbook view that apical constriction drives invagination, the similarity of ascidian endoderm invagination to the well-studied ventral furrow and posterior midgut invaginations in Drosophila suggests it may be a general mechanism. We have recently begun to investigate neural plate invagination and closure in ascidians. Our preliminary results suggest that neural plate invagination requires basal crawling and that closure requires a coordination of localized cortical contractility, cell crawling, and formation of new adhesive contacts. The ascidian embryo, long seen as a model system for cell fate determination, is revealing itself to be an equally excellent system in which to investigate the cellular basis for morphogenesis. | ||
| CTB7c | Shim, Eunha | |
| Yale University | ||
| The influence of altruism on influenza vaccination decisions | ||
| Epidemiological game theory models assume that individuals are selfish and make decisions that maximize their personal utilities. Contrary to this fundamental assumption, our psychological study shows that altruism plays an important role in the decision to receive influenza vaccination. We parameterize an epidemiological game theoretic model of influenza vaccination with questionnaire data on actual perceptions of influenza and its vaccine that takes into account the influence of altruism. We find that this altruism has a dramatic impact on the model predictions. Altruism shifts community vaccination away from the Nash equilibrium and towards the utilitarian strategy, with reduced morbidity and mortality. We determine the benefit that community interventions that emphasize benefit to others of one’s vaccination could have in helping to achieve optimal community vaccination. | ||
| MSH1b | Shipman, Patrick | |
| Colorado State University, USA | ||
| Shapes and Symmetries: Patterns in Plants and Mollusks | ||
| Tiling planforms dominated by diamonds (such as the diamond-shaped seeds on a sunflower head), hexagons, or ridges (such as those on saguaro cacti) are observed on many plants. Similar patterns are observed in mollusk shells. We analyze PDE models for the formation of these patterns that incorporate the effects of growth and biophysical and biochemical mechanisms. The aim is to understand both the underlying symmetries and the information specific to the mechanisms. | ||
| MSA2a | Simpson, Matthew | |
| University of Melbourne | ||
| Multi-scale tools for interpreting experimental cell biology data | ||
| Trajectory data from observations of a random walk process are often used to characterize macroscopic transport coefficients and to infer motility mechanisms in cell biology. New continuum equations describing the average moments of the position of an individual agent in a population of interacting agents are derived and validated. Unlike standard noninteracting random walks, the new moment equations explicitly represent the interactions between agents as they are coupled to the macroscopic agent density. Key issues associated with the validity of the new continuum equations and the interpretation of experimental data will be explored. | ||
| MSH6d | Smith?, Robert | |
| The University of Ottawa | ||
| When zombies attack!: Mathematical modelling of an outbreak of zombie infection | ||
| Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all. | ||
| CTA7f | Strelioff, Christopher | |
| Michigan State University | ||
| Dynamics of Biological Information in Epistatic Fitness Landscapes | ||
| Biological information connects evolutionary dynamics with the tools of information theory by focusing on the distribution of alleles at each locus. At a neutral locus all possible alleles are equally likely in the long-term, resulting in a maximum entropy (minimum information) distribution. For loci with fitness effects, a preference for particular alleles, created by mutation and natural selection, results in less entropy and more information. Previous research has primarily treated loci as non-interacting by making specific approximations in the calculation of biological information. In the present research, we refine previous approximations to include epistasis or interactions between loci. To understand the results of the new approximation, we consider evolutionary dynamics using the discrete time quasispecies equation. This model describes mutation and selection in an infinite population, removing the need for statistical inference in the current investigation. Application of the improved form for the biological information demonstrates that mutual information between loci is only present when considering evolution on epistatic fitness landscapes. Examples of two-locus, two-allele fitness landscapes with and without epistatic interactions will be presented. Finally, we consider modular four-locus, two-allele fitness landscapes. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides great insight into the underlying structure of the fitness landscape. | ||
| Coauthor(s): Charles Ofria, Richard Lenski | ||
| MSE4c | Sun, Sean | |
| Johns Hopkins University | ||
| Condensation of FtsZ filaments can drive bacterial cell division | ||
| Bacterial cell division coincides with a gradual contraction of a ring of FtsZ filaments (Z-ring) at the mid cell. The mechanism of Z-ring contraction is unknown. Mechanical estimates and in vitro experiments show that the Z-ring can generate forces. Using computational modeling and fluorescence experiments, we investigate the molecular mechanism of Z-ring contraction. We show that the weak lateral attraction between filaments is sufficient to generate contractile forces. The contraction process does not require a motor mechanism. Possible experiments are proposed to test the model. | ||
| CTF4b | Svoboda, Julia | |
| University of California, Davis | ||
| Undergraduates’ Conceptions of Mathematical Models in Biology | ||
| As biologists increasingly embrace mathematical modeling techniques, many scientists and science educators are calling for the inclusion of mathematical and computer modeling in biology curricula (Bialek & Botstein, 2004; Gilbert, 2004; Goldstone, 2006; May, 2004; Metzger & Zare, 1999; NRC, 2003). In addition to preparing students for the changing discipline, curricula based on models and modeling can potentially provide opportunities for students to engage with sophisticated themes surrounding the nature of scientific knowledge by highlighting the role models play in knowledge creation and evaluation. However, education research suggests that undergraduate students struggle with epistemological themes such as these, often holding simplistic views of scientific knowledge as the end-product of a linear “Scientific Method” (Windschitl, Thompson, & Braaten, 2008). Thus, a shift towards model-based curricula creates a need to understand how to support opportunities for learning as well as address a new set of curricular challenges. In this study we examine the ways in which a yearlong NSF-sponsored training program, Collaborative Learning at the Interface of Mathematics and Biology (CLIMB), was able to support students’ engagement with challenges of model construction and evaluation. We conducted an extended in-depth qualitative study of the CLIMB students, faculty, and curriculum. We collected the following data sources: questionnaires, semi-structured interviews, field notes of group problem solving sessions, video of group problem solving, students' journal entries, and written work (both group and individual). We relied on triangulation among these data sources to uncover important themes relating to the generation and evaluation of knowledge from mathematical models. We report on both the level of sophistication with which students were able to engage with these themes and the particular features of the CLIMB curriculum that were likely to have supported students’ epistemological development. We present a conceptual framework of modeling curricula that includes the importance of explicit faculty discourse, task structure, and the opportunity for collaborative problem solving in helping support students’ conceptualization of models as important components of biological research. We also display evidence that students were able to identify criteria for constructing and evaluating scientific models in practice as they worked as a cohort to solve problems. This work has important implications for the structure of biology curricula that foreground mathematical modeling. It suggests that an emphasis on modeling may create a rich context in which students can expand their repertoires with respect to the nature of scientific knowledge and the ways in which it is produced in practice. | ||
| Coauthor(s): Cynthia Passmore, Carole Hom, Rick Grossberg | ||
| MSG4c | Tarazona, Pedro | |
| Universidad Autonoma de Madrid | ||
| Theoretical modeling of dynamic FtsZ filaments imaged with atomic force microscopy. | ||
| We present a theoretical lattice model for FtsZ that incorporates the information gained from the high resolution AFM images, taken under dynamic polymerization of the protein filaments. The model includes the longitudinal bond energy, the flexibility and spontaneous curvature of the filaments, and their lateral attractions as the essential interactions underlying the polymorphic filamentary shapes observed experimentally. Monte Carlo computer simulations of the model are used to identify the relevant interaction parameters for wild type and mutant FtsZ. The extrapolation of the model to cylindrical geometry shows that the lateral attractions between the filaments allow the condensation of the filaments in contractile ring structures. | ||
| CTB7f | Tchuenche, Jean M. | |
| University of Guelph | ||
| Outbreak Control through Voluntary First-order and Second-order Ring Vaccination | ||
| In ring vaccination, the contacts of an index case are identified and vaccinated. This has been applied in modelling the control of various infectious diseases. However, a form of ring vaccination where both contacts of index cases and some fraction of the contacts of the contacts of the index cases (second-order contacts) has not been explored. This may be a successful policy option for diseases where individuals are infectious before exhibiting symptoms, such as influenza, in health care systems with well-developed contact tracing capabilities. Herein, we derive and analyze a simple mathematical model that represents the conditions for control of an infectious disease through first-order and second-order ring vaccination, where individuals are free to choose whether or not to vaccinate and decide according to utility (health) maximization in the context of the vaccination decisions of others with whom they are in contact. | ||
| Coauthor(s): A. Galvani, L. Ancel-Meyers, C.T. Bauch | ||
| MSD6c | Textor, Jophannes | |
| Institute of Theoretical Computer Science, Universität zu Lübeck, Germany | ||
| Antigen detection as a distributed randomized search process: A multiscale approach | ||
| The important role of stochastic effects in the immune system in general has been investigated for a long time, and the interest in this topic has increased further by the finding that the search of B and T cells search for antigen in lymph nodes is apparently realized by a random walk. Several groups have constructed computational models of this microscopical search process in lymphoid tissue. Our modelling approach links these efforts to stochastic effects observed on the macroscopic scale: Lymphocytes continuously recirculate through lymph nodes, blood and lymph, the lung and other tissues, and thus the microscopic random walk through lymph nodes is coupled with a macroscopic random walk through the organism. We derive a quantitative model that integrates the two levels. Using techniques borrowed from randomized algorithm analysis, we show how both tissue-level and anatomical factors determine the efficiency and robustness of the search process. A good agreement between the optimal T cell residence time predicted by our model and the value found in mice indicated that the kinetics of lymphocyte recirculation have evolved as a solution to a two-level combinatorial optimization problem. Finally, we discuss implications of our work for the currently debated problem of how lymphocytes exit from the lymph node. | ||
| MSA4a | Thibodeaux, Jeremy | |
| University of Central Oklahoma | ||
| Seeking Optimal Treatment Strategies for Malaria Infection | ||
| The malaria parasite inhibits erythropoiesis in two major ways. The first, and obvious way, is the preying upon erythrocytes. But it has been recently discovered that a toxic by-product of digested hemoglobin, called hemozoin, inhibits the development of erythroid precursors. A mathematical model accounting for both of these effects will be presented along with model predictions concerning combined treatments for both of the effects of malaria infection on the erythropoietic system. | ||
| CTD7e | Thomas, Peter | |
| Case Western Reserve University | ||
| On the Information Capacity of Diffusion Mediated Signal Transduction | ||
| Diffusion mediated signaling is ubiquitous in biology, playing a role in processes as diverse as chemotaxis, quorum sensing, mate seeking, gene regulation, and homeostasis. How much ``information'' can a diffusion based signaling system signal? This talk will describe a framework for posing and answering questions about the information processing performance of a broad class of signal transduction systems. The ingredients include (1) a source of diffusible molecules, (2) a physical medium through which they diffuse, and (3) a ligand-receptor interaction by which the signal is transduced. The source, medium and receptor form a model of a biochemical communications channel. As in classical information theory, the performance of this channel is measured by its capacity, the maximal mutual information between its input and output ensembles. We investigate the capacity of a class of biochemical communications channels through a combination of computer simulations and analytic investigation of limiting cases. The capacity behaves in some respects like that of a classical AWGN (additive white Gaussian noise) channel, although in our case it depends on biochemical parameters such as the diffusion constant and decay rate of ligand molecules, the forward and reverse rate constants for the ligand-receptor binding interaction, and the geometry of the physical medium through which signaling takes place. Contributors to this work include Case Western Reserve graduate students Matthew Garvey, Suparat Chuechote and Edward Agarwala, and CWRU undergraduates Stephen Fleming and Heather McGinnis. Supported by NSF grants DMS-0720142 and DUE-0634612. | ||
| Coauthor(s): Edward Agarwala, Suparat Chuechote, Stephen Fleming, Matthew Garvey, Heather McGinnis | ||
| MSE5c | Thomason, Sarah | |
| Murray State University | ||
| Undergraduate Biomathematics Research at Murray State University | ||
| [Jointly presented by Sarah Thomason and Glenna Buford.] Mathematical applications are becoming widely used for research in biology, providing Murray State undergraduates the opportunity to conduct research in a variety of topics, including invasive alligator weed and tiger salamanders. Using Matlab, we compiled data on three populations of alligator weed and computed population dynamics statistics on them. A population of tiger salamanders has also been studied to perform a pedigree analysis and track the evolutionary significance of facultative paedomorphosis. | ||
| CTH5d | Tokita, Kei | |
| Osaka University | ||
| Species abundance distributions, the species-area relationships and the Zipf's law | ||
| In many complex systems such as an ecosystem, a metabolic system, an immune system, a human social system, an economic system, a linguistic system etc, common "general community structures" have been widely observed. A mechanism to generate such patterns, e.g. abundance distributions of components, is not only a main topic in each discipline but also have aroused controversy independently. The current study aim to explore a uniform view and methodology for the patterns by theoretically approaching to complex systems essentially containing diverse components, e.g. species in an ecosystem, genes in a cell, currencies, products or companies in a economic system, words in a book, etc. First, some examples of the general community structure will be presented: species abundance distributions (SAD) and the species-area relationships (SAR) in ecology, and the Zipf's law in linguistics and social sciences. Second, I relate SAD and SAR to the Zipf's law which may be best known as the power distribution of word frequency. Its characteristic power exponent is ubiquitously observed in many distributions such as in benthos population, proteins or mRNAs in a cell, economic system, population of cities, names in a population, etc. Various mechanisms of the Zipf's law have been suggested in each discipline, while there is few discussions on a general principle to generate such a ubiquitous exponent. Reconsidering the relations between SAD and SAR, I present a novel scenario for the origin of the Zipf's law in connection with the "generalized island biogeography" which can be applied to populations, molecules, products, words, etc. In particular, it is suggested that the ubiquitous value of the power exponent is due to a self-organized critical state at which some function of species richness is maximized, and therefore, the Zipf's law can be explained by a general mechanism which is independent from the details of the characteristics of each system. | ||
| Coauthor(s): Haruyuki Irie | ||
| CTF3c | Tomasetti, Cristian | |
| University of Maryland | ||
| Modeling Drug Resistance in Cancer | ||
| Resistance to drugs has been an ongoing obstacle to a successful treatment of many diseases. In this work we consider the problem of drug resistance in cancer, focusing on random genetic point mutations. Most previous works on mathematical models of such drug resistance have been based on stochastic methods. In contrast, our approach is based on a compartmental system of ODEs. The simplicity of our model allows us to obtain analytic results for resistance to any number of drugs. Our main result is that the amount of resistance generated before the start of the treatment, and present at some given time afterward, always depends on the turnover rate, no matter how many drugs are simultaneously used in the treatment. This result seems to contradict some results in the literature, and a detailed discussion is provided. | ||
| Coauthor(s): Doron Levy | ||
| MSC4a | Topor, Zbigniew | |
| Department of Cell Biology & Anatomy, University of Calgary | ||
| Transient ventilatory intervention reverses central sleep apnea - a model study | ||
| We developed a computational model of the human respiratory control system and its chemoreflex control during sleep. Our model, which is an extension of the model of Grodins et al. (J. Appl. Physiol. 22(2):260-276, 1967), combines an accurate description of a plant with a novel controller design. The controller consists of two negative feedback loops (central and peripheral) each with its own delay and gain. The peripheral chemoreceptor (PCR) loop operates with short delay and the central chemoreceptor (CCR) loop operates with long delay. Both delays are state-dependent that is they depend on the partial pressures of oxygen and carbon dioxide in the arterial blood – state variables of the system. Periodic breathing – an oscillatory limit cycle behavior, indicative of instability in the respiratory control system, is commonly seen during sleep in premature infants, in patients with heart failure, and during exposure to high altitude. These periodicities appear to relate to the operation of, and interaction between, the two chemoreflex loops. Precisely how the gains and delays of the two loops interact to determine overall stability of the system is uncertain, however. The mathematical analysis of the control system having one negative feedback loop indicates that the oscillatory limit cycle behavior develops when feedback gain and/or delay exceed critical level. Similar analysis of the system having multiple feedback loops, each having state-dependant delay, has proven more challenging with positive results restricted to few special cases. To draw some general conclusions about stability of the respiratory control system during sleep, we employed a two dimensional plot similar in concept to the phase plane, with the chemosensitivities of the two loops serving as coordinates of each point. The plain contains a region of stability with the normal operating point for the system lying well inside its boundaries. For the normal operating point, or any other operating point from the stability region, the system exhibits stable steady state behavior. Changes to the sensitivities of either loop caused by known pathologies displace the operating point toward the border of the stability region and further into the region of bi-stability. While operating in this region, the system characterized by the same values of all parameters may exhibit either stable steady state or oscillatory limit cycle behavior. The actual behavior depends on the past history of the system. An appropriately timed transient perturbation can shift the behavior of the system from the oscillatory limit cycle to steady state or vice versa. We postulate that in many pathophysiological conditions the respiratory control system can be stabilized by means of transient intervention without changing its fundamental characteristics. | ||
| MSB5c | Tyson, Rebecca | |
| University of British Columbia Okanagan | ||
| The effect of habitat fragmentation on cyclic predator-prey populations | ||
| It is well-known that predator prey populations can exhibit regular, large-amplitude cycles, and existing models suggest that this behaviour is due to a predator-prey limit cycle. We will examine the effect of habitat fragmentation on the predator-prey cycles by adding diffusion to existing models, and examining solution behaviour on a domain consisting of alternating good and bad habitat patches. We will see that habitat fragmentation tends to decrease cycle amplitude, though the pattern of decrease is very model dependent. Numerical results and theoretical arguments will be presented. | ||
| CTD7f | Uriu, Koichiro | |
| Kyushu University | ||
| Synchronized oscillation of the segmentation clock gene in vertebrate development | ||
| In vertebrate somitogenesis, "segmentation clock" genes (her in zebrafish, hes in mouse and hairy in chick) show oscillation, synchronized over nearby cells through intercellular interaction. In zebrafish neighboring cells interact by Delta-Notch system and realize synchronization. Under Delta-Notch system, however, a cell with a high expression of the segmentation clock gene tends to suppress the expression in its adjacent cells, which might produce spatial heterogeneity, instead of synchronized oscillation. Here we study the condition for pre-somitic mesoderm cells to show the synchronized oscillation of gene expression mathematically. We adopt a model which considers kinetics of mRNA and proteins of segmentation clock gene and cell-cell interaction by Delta-Notch system explicitly. From statistical study of the model with randomly generated parameters, we conclude that synchronized oscillation tends to be stable when reactions included in the intracellular negative feedback loop of her gene are fast and when reactions included in the intercellular interaction are slow. Further we discuss mechanisms for cells to achieve synchronization in a sufficiently short time. | ||
| Coauthor(s): "Yoshihiro Morishita, Yoh Iwasa" | ||
| CTE7e | van Gaalen, R D | |
| University of Western Ontario | ||
| Antioxidant supplementation as a potential therapy for HIV-positive injected drug users on HAART | ||
| HIV-infected individuals are known to suffer from micronutrient deficiencies and oxidative stress. Therefore, as a therapy to be used alongside a drug treatment regimen, antioxidant supplementation has been proposed. Substantial evidence is available to support the use of antioxidant supplementation in patients not receiving highly active antiretroviral therapy (HAART); however, intervention trials in patients receiving HAART have had mixed results. In this talk, a mathematical model is developed to explore this potential therapy in patients on HAART. Clinical data from both HIV-negative and HIV-positive injected drug users (IDUs) are used to estimate model parameters; these groups have lower baseline concentrations of antioxidants than controls. Our model suggests that moderate levels of daily antioxidant supplementation can produce increases in CD4+ T cell concentrations in HIV-positive IDUs, although excessive supplementation has the potential to cause periods of immunosuppression. | ||
| Coauthor(s): L M Wahl | ||
| CTG7e | Van Schepdael, An | |
| Catholic University Leuven | ||
| The biology of bone formation in orthodontic tooth movement: a mathematical model | ||
| The primary aim of orthodontic treatment is maintaining a functional dentition, including chewing, aesthetics and comfort. Under the influence of an orthodontic force, the pressure side of the tooth root will experience bone resorption and bone formation will take place on the tension side. The experience of the orthodontist determines the nature and the length of the treatment. Although some typical movements and treatment plans are known, the reaction to the treatment is different for every patient and the treatment plan is adjusted regularly. Most existing models describing tooth movement are based on an empirical bone remodeling function in which the biological activity in the periodontal ligament and the alveolar bone is not taken into account. This study presents an onset to a mechanobiological model for bone formation in orthodontic tooth movement. Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. The bone remodeling is done by osteoclasts and osteoblasts, who coordinate their actions by communicating by means of the RANKL-RANK-OPG signalling pathway. Together with the alveolar bone remodeling, extensive remodeling of the periodontal ligament (PDL) takes place to ensure the attachement of the tooth root to the alveolar bone. This process is regulated by periodontal ligament fibroblasts, which have a high proliferation rate and are highly active cells, mainly due to the continued mechanical stimulation from occlusal contacts. The amount of tooth movement is regulated by the cellular respons to a mechanical stimulus. Both osteocytes, present in the alveolar bone, and fibroblasts, present in the periodontal ligament, have a high sensitivity for mechanical signals. However, since osteocytes are present in the stiffer alveolar bone, in contrast to the PDL, they are subjected to a much smaller strain. Therefore, this model only takes into account the reaction of fibroblasts to the applied force. Fibroblasts respond to mechanical stretching by producing the osteogenic growth factor TGF-β and by upregulating the production of nitric oxide. The developped model consists of 15 non-linear partial differential equations describing the concentration of various cells, growth factors, cytokines and matrix-components. The PDL has a large concentration of fibroblasts and its precursors, mesenchymal stem cells. The bone mainly consists of osteocytes and has a smaller concentration of osteoblasts and osteoclasts. The production of RANKL and OPG by osteoblasts is determined by the levels of NO in the bone. The osteogenic differentiation of mesenchymal stem cells into osteoblasts is regulated by TGF-β, present in an active and a latent form. Multinucleated osteoclasts are formed through the fusion of hematopoietic stem cells, which are present in the vascular matrix. Vascular endothelial cells are responsible for the formation of bloodvessels. | ||
| Coauthor(s): Jozef Vander Sloten, Liesbet Geris | ||
| MSE4d | Vélez, Marisela | |
| Universidad Autónoma de Madrid | ||
| Polymerization of individual FtsZ filaments observed with atomic force microscopy | ||
| Observing bacterial FtsZ GTP dependent polymerization in vitro is challenging experimentally given the dynamic nature of the process and the small size of the individual filaments. We present results obtained from observing the depolymerization process of individual filaments formed under GTP hydrolyzing conditions with atomic force microscopy. Observation of the structures formed at different protein densities and under different nucleotide hydrolysing conditions indicates the curved, dynamic and flexible character of the filaments and provides insight into the way filaments assemble and disassemble. | ||
| CTF4c | Wallace, Dorothy | |
| Dartmouth College | ||
| Six Short Weeks: A classroom strategy for supporting undergraduate research in mathematical biology | ||
| Dartmouth's "Calculus with Applications in Biology and Medicine" course is designed to integrate undergraduate research into the introductory mathematics curriculum, within six weeks. Students progress from remembering simple exponential growth models in week one to reading research papers with multiple ordinary differential equations, reading these critically, testing hypotheses by altering equations or designing new ones, and using the computer to draw conclusions about real world problems. In order to achieve these results, Wallace has developed a highly interactive teaching strategy that quickly puts students in charge of developing their own models, evaluating them critically, and posing their own research questions. | ||
| MSB2a | Wang, Hongyun | |
| University of California Santa Cruz | ||
| How to convert reciprocal motions to a unidirectional motion? | ||
| In molecular motors, each cycle of chemical reaction is coupled to some conformational change, which is used to directly drive the motion or rectify thermal fluctuations. Strictly speaking, the conformational change also goes through a cycle. But the conformational change may be very close to a reciprocal motion. I will discuss several possible mechanisms of converting reciprocal motions to a unidirectional motion. | ||
| CTG7f | Watson, Michael | |
| Heriot-Watt University | ||
| Wound healing in the murine panniculus carnosus: mathematical modelling and numerical simulation | ||
| Whilst it is well known that angiogenesis plays a pivotal role in various mammalian growth processes such as embryogenesis and tumourigenesis, obtaining reliable experimental data from such processes for use in models is fraught with difficulty. However, wound analysis provides a more tractable approach for quantitative benchmarking of angiogenesis models, as corresponding experimental data can be obtained with relative ease. To this end, the main aim of this work is to develop a mathematical model of angiogenesis during wound healing in the murine panniculus carnosus. A mathematical model of wound healing in the murine panniculus carnosus is presented and compared against experimental stereology data associated with burn injury. The hybrid model incorporates the discrete in-growth of new vessels in response to growth factors such as TGF-β and the subsequent flow of blood within the nascent vasculature. By allowing dynamic adaptation of the new vessels in response to both haemodynamic and metabolic stimuli, network architectures comparable to the experimental observations are obtained. The model is then extended to examine the role of pericyte recruitment in wound healing. In particular, we assess the healing potential of wounds under the assumption of different plasticity windows in vascular remodelling. | ||
| Coauthor(s): S R McDougall, M A J Chaplain | ||
| CTF1c | Wei, Guowei | |
| Michigan State University | ||
| Differential geometry based multiscale modeling of biomolecules | ||
| We report new muliscale models for describing biomolecular systems. Under physiological condition, about 70 percent of body mass is water. Therefore, most biomolecules live and function at aquatic environment. Full scale description of an interacting biomolecular system, including the aquatic environment, is very expensive. We propose a multiscale approach which treats the aquatic environment as mesoscopic continuum and describes the biomolecule in atomic and electronic detail. We use differential geometry theory of surfaces to describe the interface between the continuum and discrete domains. A total free energy functional is proposed to account for interactions both between the continuum and discrete, and among particles within the biomolecules. The former are described by surface tension energy in classical theory of thermodynamics. While the latter are of both bonding and non-bonding types. The energy minimization using the Euler-Lagrange equation leads to coupled geometric and potential driving evolution partial differential equations (PDEs). The solution of these coupled equations can result in biomolecule surfaces and a variety of other physical quantities, including solvation free energy, electrostatic potential, pKa values, protein-protein binding free energy and molecular dynamics, depending on the choice of the interaction potentials. Applications are discussed to proteins, DNA-protein interaction, and virus complex. | ||
| MSG1a | Wells, Darren | |
| Centre for Plant Integrative Biology, University of Nottingham, UK | ||
| Plant root cell expansion | ||
| Plant root cells elongate anisotropically with deposition of new material and modification of cell wall properties occurring over the entire wall (with the exception of root hairs which exhibit tip growth). This anisotropic growth pattern is dependent on directional mechanical properties of the cell wall, conferred by a tightly regulated network of cellulose microfibrils embedded in the wall matrix. Experimental techniques to analyse the structure of the elongating cell wall and the potential mechanisms whereby walls are modified will be presented, together with techniques to parameterize current models for the control of cell expansion in roots. | ||
| CTE7f | White, Steven | |
| Centre for Ecology & Hydrology | ||
| Modelling multiple within-host insect virus dynamics | ||
| Pathogens play an important role for many host organisms, ranging from population regulation to species invasion, which in turn, have applications for issues such as disease control, pest control and biodiversity. However, much of our empirical understanding of host-pathogen ecology and evolution is derived from scenarios where the host is infected by a single pathogen or parasite. Molecular techniques have revealed that many infections in insect hosts are caused by several pathogen genotypes which differ phenotypically in their interaction with the host. This raises the question of how competing genotypes co-exist in the field. The simplest assumption would be that competition between genotypes within a host is a race to gain the greatest share of resources (host tissues), as in the tragedy of the commons. However, this would act to reduce genetic diversity rather than to maintain it. In this talk we aim to build upon recent developments in the literature by conducting single infection bioassays to obtain data on within-host growth and fitness parameters for phenotypically different and similar strains of nucleopolyhedroviruses in the Lepdipoteran host Spodoptera exigua. Using these data, a simple mechanistic mathematical model (a coupled system of differential equations) is derived and fitted. Predictions from this model agree with empirical findings, such as increased virus doses leading to decreased virus yields. Extending the single infection model, we assume that in mixed infections viruses compete for host resources, but otherwise act independently. The outcome of these simple assumptions leads to multiple infections producing some non-intuitive outcomes. For example, we predict that multiple infections can lead to significantly increased or decreased virus yield when compared to single infections. This resource mediated competitive synergistic or antagonistic relationship depends crucially on the composition of the multiple infections and the time-lag between infections, which potentially has great importance for understanding pathogen coexistence and for biocontrol design. | ||
| MSG4b | Wolgemuth, Charles | |
| University of Connecticut Health Center | ||
| The Shape and Dynamics of the Spirochetes | ||
| In this talk I will discuss the shape and motility of a unique group of bacteria, the spirochetes. These bacteria use helical polymer filaments (flagella) encased between their cell wall and outer membrane to maintain their cell shape and to drive motility. Consideration of the coupling between the cellular and flagellar elasticity leads to a model that describes the shape and dynamics of a number of these bacteria, such as Borrelia burgdorferi and the Leptospiraceae. | ||
| MSB5d | Yakubu, Abdul-Aziz | |
| Howard University | ||
| Asynchronous and synchronous dispersals in spatially discrete population models | ||
| This talk is on the role of synchronous and asynchronous dispersals in a discrete-time single-species population model with dispersal between two patches, where pre-dispersal dynamics are compensatory or overcompensatory, and dispersal is synchronous or asynchronous or mixed synchronous and asynchronous. | ||
| MSB2d | Yamada, Richard | |
| University of Michigan | ||
| Error Correcting Mechanisms During Transcriptional Elongation | ||
| Transcription is a complex process consisting of 3 distinct steps: initiation, elongation and termination. Out of these steps, elongation is the most natural step in transcription to be modeled in a quantitative manner. During elongation, the RNA polymerase rapidly adds ribonucleotide triphosphates (rNTPs) to the nascent RNA chain. Surprisingly, this process is remarkably accurate (error of ~1 base per 100,000 bases transcribed). The look-ahead model, proposed by Yamada and Peskin, is a model that governs the dynamics of elongation during transcription. An important integer parameter of the look-ahead model is the window size (in bases). In this talk, we investigate the effect of this window size in the error rate during transcription. We show an example in which there is dramatic reduction in the error rate as the window size increases, especially for small window sizes. We conclude by discussing the model's fit to experimental data and by making further experimental predictions from the model. | ||
| MSA5a | Yamada, Richard | |
| University of Michigan | ||
| Molecular Noise Enhances Oscillations in SCN Network | ||
| In this talk, we will discuss a detailed mathematical model for circadian timekeeping within the SCN. Our proposed model consists of a large population of SCN neurons, with each neuron containing a network of biochemical reactions involving the core circadian components. Using mathematical modeling, our results show that both intracellular molecular noise and intercellular coupling (nonlinear in nature) are required to sustain stochastic oscillations in the SCN oscillator network. Our work focuses on the problem of overcoming noise in oscillator systems, and our results highlight the importance of transcriptional noise in enhancing oscillations rather than dampening them. Surprisingly, our predictions have been confirmed experimentally, and we conclude with a short discussion of these results. | ||
| MSD1a | Yang, Hyun | |
| UNICAMP | ||
| Control of mosquitoes by the the Sterile Insect Technique (SIT) | ||
| We propose a mathematical model to describe the dynamics of a mosquito population when the Sterile Insect Technique (SIT) is used as a biological control. This technique consists in the introduction of sterile insects (produced by irradiation) in a previously infested region. We use optimal control theory to evaluate the effectiveness of the application of SIT, together with insecticide to a mosquito population. We want to find the minimal effort necessary to reduce the fertile female mosquitoes considering the cost of insecticide application, the cost of production of irradiated mosquitoes, and social cost. Coauthors: Roberto Thome, Lourdes Esteva Peralta | ||
| MSA4b | Yuster, Thomas | |
| Department of Mathematics, Lafayette College | ||
| A Mathematical Model of the Within-Vector Dynamics of the Plasmodium Falciparum Protozoan Parasite | ||
| A Mathematical Model of the Within-Vector Dynamics of the Plasmodium Falciparum Protozoan Parasite Abstract: Based upon experimental data, we developed a mathematical model that simulates the within-vector dynamics of P. falciparum in an Anopheles mosquito. The model takes as input a mosquito blood meal and the final output is the salivary gland sporozoite load, a probable measure of mosquito infectivity. Sensitivity analysis of the model parameters suggests that reduction of gametocyte density in the blood meal most significantly lowers mosquito infectivity, and is thus an attractive target for malaria control. The model was used to investigate the implication of incomplete fertilization on optimal gametocyte sex ratio, which appears to be significantly impacted by this effect. (Coauthors: Miranda I. Teboh-Ewungkem; Nathaniel H. Newman) | ||
| CTC7f | Zhang, Xu-Sheng | |
| University of Edinburgh | ||
| Dynamics of E. coli O157 infection among Scottish cattle farms: Stochastic models and selection | ||
| Escherichia coli O157 emerged about two decades ago; Scotland has had among the highest incidences of human infection in the world. Two recent surveys (Chase-Topping et al 2007; Gunn et al 2007) concluded that E. coli O157 was present on c. 20% Scottish cattle farms, though with large variation in on-farm prevalence. Here, we considered dynamical processes for the spread of E. coli O157 infection between farms using stochastic models, and fitted the models by maximum likelihood to epidemiological survey data. Based on Akaike information Criterion (AIC), the most likely dynamical process is identified. The best model incorporates spread by the movement of cattle and by other routes including infection from an environmental reservoir. Adding decay of transmission with distance, seasonality, or the presence/absence of other livestock animals did not improve model fit. However, there was evidence of an effect of farm size. Further, a distribution of sets of parameter for the best model was generated by Markov Chain Monte Carlo methods. Using this distribution, the potential impacts of different control measures were simulated and sensitivity to changes in model parameters was explored. Reducing cattle movement between farms had only a small effect. Measures to reduce transmission rates (e.g. improved biosecurity) may be most effective if targeted at larger farms. |