Program
Poster Session A
| Poster session A is generously sponsored by the IMA's journal Mathematical Medicine and Biology and Oxford Journals.
The poster sessions will take place in the lobby of the Woodward building. Poster session A will be held from 5.30pm-7pm on Monday, July 27. Poster session B will be held from 5.30pm-6.45pm on Wednesday, July 29. Refreshments will be served. |  |
| PS01A | Afsharnezhad, Zahra | |
|---|---|---|
| Ferdowsi University of Mashhad-Iran | ||
| Bifurcation and Permanent DNA Damage Region for P53 Model | ||
| The P53 protein is recently a subject of interest for both mathematicians and biologists. It is known that one of the key players in cancer development is P53, a tumor suppressor. P53 is a transcription factor encoded by a gene whose disruption is associated with approximately 50 to 55 percent of human cancers. In this paper, we stydy bifurcation of the DNA Damage signal for P53 madel which is based on ordinary differential equation model. We show that change of parameters may cause bifurcation switching Damge signal off. Also the region in which the covergence of the DNA Damage signal changes repair to permanent Damage is indicated. | ||
| PS26A | Agarwala, Edward K. | |
| Case Western Reserve University | ||
| Food for Thought: When Infomax Fails to Optimize Utility | ||
| Information maximization criteria have been used to account for the physiology of sensory systems as diverse as receptive fields in the primary visual and auditory cortices, the organization of saccades by the oculomotor system, and olfaction. We investigated a simple model of an organism searching for food by taking successive samples from an environment in which food particles diffuse stochastically from a slowly randomly moving source. In the limit of large food concentrations we reduced our high dimensional model system to a Markov chain on a small number (<= 5) of equivalence classes on the state space. In this system were are able to make rigorous quantitative comparisons of the relative benefit to the organism of pursuing a search strategy based on (i) maximizing the searcher's information about the location of the food source, (ii) maximizing the expected concentration of food at the searcher's next location, and (iii) hybrid strategies combining aspects of (i) and (ii). The relative success of the different strategies in terms of long-term expected food benefit depended on parameters such as the variability of the source movement. To our surprise we found that each strategy was superior to the others for a certain set of parameters. Therefore any claim that the principles of information maximization or immediate utility optimization provide an explanation of creature behavior should be met with suspicion. | ||
| Coauthor(s): Peter J. Thomas | ||
| PS03A | Aubert, Marine | |
| University of Dundee | ||
| A hybrid continuum-discrete mathematical model of the developing retinal vasculature: A combined experimental and theoretical study | ||
| Angiogenesis is the process of blood vessel growth and is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis (neovascularization) also plays a crucial role in pathological situations such as the growth and development of solid tumours and in the developing retina where it impacts on diseases such as retinopathy. Although tumour-induced angiogenesis has been well-studied experimentally and has received a lot of attention in the mathematical modelling community there has been less modelling work in the other areas. Our current work is to create mathematical models of the developing retinal vasculature. The first step was to establish a continuum model consisting of a system of partial differential equations. These equations describe the migratory response of astrocytes and endothelial cells to molecular cues and haptotaxis. We then discretized the partial differential equations to develop a hybrid continuum-discrete modelfor cell migration. This model enables us to track individual cells (astrocytes and endothelial cells) and to incorporate the dynamic remodelling effects of blood perfusion on the architecture of the developing vascular plexus. Our approach is closely coupled to an associated experimental programme to parametrise our model effectively. The simulations of the discrete model are compared with the astrocyte and the vascular networks observed in in vivo experiments. Our aim is to use this model to elucidate the impact of molecular cues upon vasculature development and the implications for various eye diseases such as retinopathy. | ||
| PS05A | Baron, Marc | |
| Ryerson University | ||
| Differences in cell receptor preference is sufficient to explain differences in virulence between human and avian influenza. | ||
| Influenza is a growing concern for health authorities worldwide. Annual influenza epidemics result in an estimated 3-5 million cases of severe illness every year. With the looming threat of pandemic influenza and the recent emergence of virulent avian (H5N1) and swine (H1N1) strains, it is critical to understand the factors that lead to severe influenza viral infections. Recent publications have shown that avian and human influenza strains target different cell types in the lung. Specifically, human influenza strains seem to preferentially bind to cell receptors found mainly on nonciliated, mucus producing cells, while avian influenza strains appear to preferentially bind cell receptors found predominantly on ciliated cells. It is unclear, however, how this difference in cell tropism between the two strains affects the dynamics of influenza viral infection in humans. We developed a mathematical model describing the spread of influenza within a population of cells consisting of two different cell types. Our results show that the presence of two different cell types can lead to a high viral load which is sustained for long periods of time, which is believed to be a characteristic of severe avian influenza virus infections in human. I will discuss under which conditions this behavior can arise out of the proposed model and how it relates to human versus avian infection severity. | ||
| PS07A | Benson, James | |
| University of Missouri | ||
| Stability and Optimal Control of an Extended General Model of Cell Volume | ||
| Cell volume and concentration regulation are universal in biology, and examples of active and passive transport of water and solutes across the cell membrane can be drawn from all areas of both plant and animal biology. Recently a general model encompassing multiple transport phenomena for cell volume and concentration regulation of water and a single solute with applications in several areas of biology was published and a local stability result was shown (Hernandez 2007). Here, we extend this model to the case with water and multiple solutes and solute pathways (e.g.~both active and passive transport), and extend the previous stability result by proving global asymptotic stability at the rest point. Because it is often useful in biology to understand the optimal way to modify the concentration of intracellular solutes, we use this stability result together with some classic results from optimal control theory to show that the system is controllable and an optimal control exists in the case of multiple solutes or solute pathways. Finally we determine explicitly the optimal control protocol (that is, synthesize the time optimal control problem) for the commonly encountered water-single permeating and single non-permeating solute case. | ||
| Coauthor(s): John Critser, Carmen Chicone | ||
| PS08A | Bernard, Branka | |
| University Lyon 1, France | ||
| Mathematical Modelling of Tumour Response to Hadron Therapy | ||
| Carbon ion beam used in cancer radiotherapy is characterized by better precision, dose distribution and higher biological effect than that in conventional radiation. Therefore, hadrontherapy by carbon ions offers the possibility to treat tumours that are resistant to standard radiation protocols. In France, this method is being introduced by the Centre ETOILE in Lyon, which should start treating its first patients by 2014. Within the ETOILE project, we are developing a dynamical multiscale mathematical model of tumour growth to predict the efficacy of radiotherapy by carbon ions relative to conventional radiotherapy in individual patients. Such a model will allow integrating available molecular and clinical data in order to select patients that will benefit most from hadrontherapy, and to use the individualized models to optimize treatment protocols for hadrontherapy in the selected patients. | ||
| Coauthor(s): Benjamin Ribba, Claire Rodriguez-Lafrasse, Jean-Pierre Boissel | ||
| PS02A | Bishop, Lisa | |
| University of Washington | ||
| Stochastic Bistability and Bifurcation in a Signaling System with Autocatalytic Kinase | ||
| Deterministic chemical kinetics studied in the past has shown that bistability occurs in systems with strong (cubic) nonlinearity. For certain mesoscopic, weakly nonlinear (quadratic) biochemical reaction systems in a small volume, however, stochasticity can induce bistability and bifurcation that have no macroscopic counterpart. We report the simplest yet known reactions involving driven phosphorylation-dephosphorylation cycle (PdPC) kinetics with autocatalytic kinase. We show that the noise-induced phenomenon is correlated with free energy dissipation thus conform with the open-chemical system theory. | ||
| PS09A | Boone, Addie | |
| University of Washington | ||
| The Clinical Significance of Mathematical Models in the Treatment and Management of Gliomas: A Case Study in Translating Applied Mathematics Research into Clinically Relevant Solutions | ||
| Malignant gliomas account for approximately 70% of the 22,500 new cases of malignant primary brain tumors diagnosed in adults in the U.S. each year and are associated with a disproportionately high morbidity and mortality presenting a significant clinical challenge (Wen, et al; N Engl J Med. 2008 Jul 31;359(5):492-507). Currently, treatment options for newly diagnosed glioma patients vary little from one patient to the next. Standard protocol of surgical resection, radiotherapy, and chemotherapy is prescribed with high incidence of tumor recurrence, neurological and/ or cognitive deficit, and poor quality of life with modest survival improvement. Recently, notable progress has been made in the application of mathematical models to clinical data in understanding the in vivo dynamics of malignant glioma growth and invasion patterns (Harpold, et al; J Neuropathol Exp Neurol. 2007 Jan;66(1):1-9.). These mathematical models use patient-specific clinical data to assess net rates of glioma cell migration and proliferation in vivo, in combination with known variation in migration rates between grey and white matter (Swanson et al; Cell Prolif. 2000 Oct;33(5):317-29.). In this respect, applications of patient-specific modeling offer a significant opportunity to individualize malignant glioma treatment and management by assessing patient-specific growth kinetics and therapy response non-invasively, using only clinically available data (Szeto et al; Cancer Res. 2009 May 15;69(10):4502-9). In this case study we present two clinical cases: 1) a pre-treatment malignant glioma comparison using current clinical MRI diagnostic imaging with the same lesion rendered leveraging the mathematical model and the surgical resection and radiation oncology opportunities available based on each image, and 2) a post treatment abnormal image leveraging current clinical MRI diagnostic imaging and the same lesion rendered leveraging the mathematical model with the model showing a clear differentiation between XRT effect vs. actual tumor recurrence. Thus, we see that mathematical modeling translates readily to offer a clinically relevant solution in the treatment and management of malignant gliomas. These mathematically based patient-specific models would complement existing clinical diagnostic tools to provide vital data not currently available by quantifying more fully the extent of glioma cell infiltration offering opportunities for clinicians to achieve maximal surgical resection and radiotherapy coverage. Furthermore, these patient-specific models would make it possible to assess tumor response to various treatment options through virtual control simulations obtaining response metrics before any treatment has been implemented leading to improved clinical decision making and outcomes as measured by tumor recurrence, extent of surgical resection, response to radio and chemotherapy, and overall quality of life for the patient. | ||
| Coauthor(s): Russ Rockne, MS, Maciej M. Mrugala MD, PhD, MPH, Jason K. Rockhill, MD, PhD, Ellsworth C. Alvord, Jr, MD, Kristin R. Swanson, PhD | ||
| PS10A | Bordeleau, Francois | |
| Université Laval | ||
| Keratin 8/18 regulation of simple epithelial cell sensing and reaction to mechanical stress | ||
| Force interplay between the extracellular environment and the actin cytoskeleton at the surface membrane regulates several key biological processes, such as the ability of cells to sense and react to mechanical stimuli as they progress through differentiation during development. Mechanical cues largely result from external forces applied by deformation of the extracellular matrix (ECM) or internal forces generated through actin-myosin contraction, which in turn exerts a traction force on ECM. In both cases, the mechanical stimuli converge on integrins, which are transmembrane receptors composed of two subunits, α and β, that cluster within specialized focal adhesions (FAs) at the surface membrane and link the ECM and the actin cytoskeleton. Hepatocyte and H4-II-E-C3 (H4) hepatoma cell intermediate filaments (IFs) consist of the keratin 8/18 pair (K8/K18) only, and since the loss of one keratin leads to the degradation of its partner, these hepatic cells provide unique models to address K8/K18 functions in simple epithelial cells. Using cultured K8-knockdown H4-(shK8b) cells and their K8/K18-containing counterparts (H4ev), we assessed the contribution of K8/K18 in their response to mechanical stress generated either at the dorsal or ventral cell surface. In the first case, the stress was generated with a laser tweezer-mediated force applied on a fibronectin-coated polystyrene microbead attached to integrins on the surface, and the cell response was assessed by the bead displacement. Of particular interest, the loss of K8/K18 IFs in shK8b cells revealed an immediate reduction in bead displacements characteristic of a sudden increased in the FA elastic stiffness. In addition, the use of pharmacological inhibitors point to a key role for “novel” PKC as intermediary in the K8/K18 IFs contribution. In the second case, cells were seeded on fibronectin-coated polyacrylamide gel substrata of different rigidity to generate a variable mechanical stress at the basal interface. It involved the addition o f 0.03, 0.05 and 0.08 % bisacrylamide to 5 % acrylamide, which provided substrata exhibiting a Young modulus of 800, 1400 and 3000 Pa, respectively. This rigidity range mimicked the in vivo situation for tissues like liver, and was very much lower than the 3 GPa for a polystyrene substratum. Notably, shK8b cells exhibited a prominent spreading impairment for substratum rigidity below 1400 Pa. Moreover, as the substratum rigidity was decreased, a comparable reduction of FA components, like talin, was found in both H4ev and shK8b cells. In addition, the 3D arrangements of the actin cytoskeleton and the cytolinker plectin were differentially perturbed following the K8/K18 loss in shk8b cells. Overall, K8/K18 IFs appear to be important regulatory players in epithelial cell sensing and reaction to mechanical stress. Work supported by NSERC and CIHR | ||
| Coauthor(s): Anne Loranger, Yunlong Sheng, Normand Marceau | ||
| PS11A | Brakken-Thal, Christina | |
| University of Minnesota | ||
| Stochastic Models for DV Patterning in Drosophila | ||
| Dorsal Ventral patterning in drosophila helps determine the boundary between amnioserosa and the dorsal ectoderm. The major morphogen involved is a heterodimer comprising Short gastrulation (Sog) and Twisted gastrulation (Tsg). These proteins are secreted into the perivitteline space, react together and diffuse. The metaloprotease Tolloid (Tld) inactivates Sog when it is bound to Dpp/Scw. In the early blastoderm, Dpp levels are moderate throughout the dorsal ectoderm and pMad, a downstream component, is broadly distributed. Later the maximum pMad concentration increases and localizes at the dorsal midline. Wang and Ferguson suggested that positive feedback might be involved in the contraction and this was demonstrated by computational analysis of a detailed reaction-diffusion model using both a surface binding protein (SBP) and endocytosis. We have extended this model to study how stochastic fluctuations effect the boundary formation. We created three stochastic models: a single cell model, a spatial model, and a downstream network model using a modified Gillepsie algorithm. In the single cell model we found bistability only with endocytosis and SBP. In this model we additionally found that endocytosis reduces the maximal coefficient of variation in BMPs. In the spatial model we found that positive feedback allows for the amniosersa to contract and creates a sharper boundary. We also found contraction in the spatial model with and without endocytosis, however without endocytosis there was a larger variation in the threshold position. In our final model we analyzed the downstream network that creates the positive feedback loop. We found that as we decrease the strength of the positive feedback, the level of compartment differentiation decreases. With the stronger positive feedback we also found the noise in pMad is amplified compared to the upstream level and the differences of noise among compartments are large. In conclusion the single cell model, spatial model, and downstream network model showed that the stochastic fluctuations effect both the location and the strength of the contraction in the boundary between the amnioserosa and dorsal ectoderm. | ||
| Coauthor(s): Likun Zheng, Hye-Won Kang, Xiao Xiao, Michael O'Connor, and Hans Othmer | ||
| PS12A | Brown, David | |
| Colorado College | ||
| Signal Transduction by the Gac/Rsm Quorum Sensing System of Pseudomonas fluorescens | ||
| Many bacteria modify their behavior in response to the concentration of a diffusible signal molecule that they produce. This signal is commonly believed to be an indicator of local cell density, so the phenomenon is known as quorum sensing. In the soil dwelling bacterium Pseudomonas fluorescens, quorum sensing is regulated by the Gac/Rsm network of genes; similar networks are found in many other γ-proteobacteria. These systems are noteworthy in part because of the central role played by small untranslated RNAs, which are involved in the post-transcriptional regulation of target genes. I am presenting a model of the Gac/Rsm regulatory network, consisting of nonlinear differential equations for the cell population and the concentrations of proteins and RNAs in the system. The model can be parameterized to agree with published reporter protein data, despite the fact that aspects of the system are not yet well understood. I have investigated the signal-processing behavior of the network, which allows the bacteria to be hyper-sensitive to fluctuations in the signal concentration, while remaining robust to the noise inherent in gene regulation. This provides clues about the function of feedbacks within the rather complex network. Like other models of quorum sensing, this one predicts a hysteretic response to population density. However, hysteresis can be achieved by a much simpler positive feedback loop. By focusing on the effects of transient fluctuations in signal concentration, I show that the complex structure of quorum sensing systems may result from the conflicting demands of amplifying external signals while filtering out internally generated noise. | ||
| PS13A | Buford, Glenna | |
| Murray State University | ||
| Using Population Dynamic Models to Assess the Spread of an Invasive Species, Alligator Weed (Alternanthera philoxeroides) | ||
| Alligator Weed (Alternanthera philoxeroides) is an invasive perennial plant of the Amaranthaceae family that is found in multiple climates. It was originally discovered in the Parana River region of South America, but has been studied the most in China. The concern for the invasion of alligator weed is due to the economic and environmental threats it poses. Our hypothesis is that the adaptability of populations affects the spread of the aquatic species. We looked at the population dynamics of alligator weed in three states: Mississippi, Kentucky, and Tennessee. The population dynamics were compared to see if there is a significant difference between the growth rates, suggesting adaptation. A population that has greater adaptation will be more invasive. We expected to find that Mississippi has greater adaptability to different climates, because its population has been in the United States longer. | ||
| PS14A | Callier, Viviane | |
| Duke University | ||
| A mathematical model for larval molting in the tobacco hornworm, Manduca sexta | ||
| Insects grow until they reach a species-specific size before they begin metamorphosis. During this growth phase they molt several times in order to increase the size of their exoskeleton, which limits the size that can be attained during each molt. In addition, the exoskeleton limits the feeding and growth rates during the intermolt period. We hypothesize that molts are initiated when the fixed size of the exoskeleton becomes growth-limiting. We present a mathematical model to formalize this hypothesis, and test this model against experimentally recorded growth trajectories of larval stages of the tobacco hornworm, Manduca sexta. | ||
| Coauthor(s): H. Frederik Nijhout | ||
| PS16A | Chakraborty, Gargi | |
| University of Washington | ||
| Predicting metabolic growth patterns from patient-specific anatomic imaging and mathematical modeling of glioblastomas | ||
| Glioblastomas (GBMs) are World Health Organization classified – grade IV brain tumors exemplified by their ability to rapidly proliferate and diffusely infiltrate surrounding tissue. Harsh microenvironments have been implicated in increasingly aggressive behavior of gliomas, which leads to lower survival across the brain tumor patient population (1). We present a metabolic mathematical model based on five partial differential equations to assess how angiogenesis or formation of nascent, irregular vasculature and hypoxia or phenomenon of oxygen depletion drive anatomical growth of GBMs. This expands upon the original model by Swanson that represented only the tumor cell population (2). The populations deterministically simulated include tumor cells, hypoxic cells, necrotic cells, vasculature, and tumor angiogenic factors. This model incorporates two patient-specific parameters, diffusion (D) and proliferation (ρ), derived from tumor volume measurement of two MRI scans conducted prior to treatment. We show that the resulting two-dimensional simulations parallel clinical imaging such as gadolinium-labeled T1-weighted MRI, T2-weighted MRI, and hypoxia-detecting [18F]-Fluoromisonidazole (FMISO) labeled PET imaging. We quantitatively compare the virtual and true MRI and FMISO-PET scans to assess how well the model predicts clinical imaging and whether it can be utilized as a tool to predict hypoxic growth patterns from MRI-based parameters. ------- 1. Szeto MD, Chakraborty G, Hadley J, Rockne R, Muzi M, Alvord EC Jr, Krohn KA, Spence AM, Swanson KR. Quantitative Metrics of Net Proliferation and Invasion Link Biological Aggressiveness Assessed by MRI with Hypoxia Assessed by FMISO-PET in Newly Diagnosed Glioblastomas. Cancer Research. 69: (10). 2009. 2. Swanson KR, Alvord EC Jr, Murray JD. Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. British Journal of Cancer. 86,14-18. 2002. | ||
| Coauthor(s): Stanley Gu, Russell Rockne, Kristin Swanson | ||
| PS24A | Chuechote, Suparat | |
| Case Western Reserve University | ||
| Effects of Fluctuations in a 2D Model of Gradient Sensing | ||
| Chemotaxis is the directed migration of cells guided by chemical gradients. This process plays a role in embryogenesis, immune response, wound healing and tumor metastasis. During chemotaxis, a cell detects extracellular chemoattractants and translates these signals into a complex cellular response resulting in morphological reorganization and motility. The accuracy with which a cell can determine an external chemical gradient is limited by fluctuations arising from the discrete nature of second messenger release and diffusion processes within the small volume of a living cell. These sources of intrinsic noise have the potential to attenuate or disperse gradient information contained in the membrane bound receptors. At the same time, models of the intracellular signaling network have been devised that use a combination of local excitation and global inhibition to sharpen the intracellular gradient signal. In this study, we implement a stochastic version one such model, the "balanced inactivation" model (Levine et. al. 2006), in a two dimensional geometry. We develop a fixed timestep approach in which the probabilities of individual molecules making spatial or chemical transitions is handled as a system of multinomial random variables. With this numerical platform we investigate the relationship between the amplification of the gradient signal, the propagation of noise in the signaling pathway, and fundamental limits on the accuracy of the gradient sensing mechanism. | ||
| Coauthor(s): Peter J. Thomas | ||
| PS17A | Comar, Timothy | |
| Benedictine University | ||
| Motivating and Preparing Undergraduates to Pursue Research Through Biocalculus Courses | ||
| Biocalculus courses are designed to provide quantitative techniques and approaches that will be useful to students majoring in the biological and health sciences in the future coursework and careers. The mathematics must be presented in engaging manner in which the students see the need for the mathematics. To achieve these goals, the mathematics must be appropriately motivated using concepts and problems from biology. Additionally, these courses can help prepare students to partake in undergraduate research activities in mathematical biology or other quantitatively oriented areas of the biological sciences. We will present examples of materials and activities from our biocalculus courses that motivate the mathematics and help prepare to pursue research. | ||
| PS18A | cordoleani, flora | |
| Université de la méditerranée | ||
| Heterotrophic bacteria dynamics in a simplified microbial foodweb chemostat system | ||
| The dynamics of heterotrophic bacteria within the microbial loop is very complex and depends particularly on the predation by protozoan species which control directly their abundance.To better understand what biological processes have an impact on the microorganisms trophic interactions, we studied a bi-trophic microbial food chain model in chemostat. We first consider general formulations for the resource utpake, satisfying biological relevant asumptions and provide the mathematical analysis of the model. We extend well known results on the bifurcations ocurring in such systems, in the parameter space defined by the dilution rate and the substrate concentration in the reservoir. On the basis of the paper by Fussman and Blasius (2005), we shown that the choice of the functional response formulation may have a strong impact on the dynamics of the system, even for a class of functions which statisfy the same set of phenomenological assumptions, and which are quantitatively very close. In other words the sensitivity to the structure of the model is important. | ||
| Coauthor(s): Mathias Gauduchon, David Nerini, Jean-Christophe Poggiale | ||
| PS19A | Crowl Erickson, Lindsay | |
| University of Utah | ||
| Understanding the effect of red blood cells on lateral platelet motion | ||
| Platelets play an essential role in blood clotting; they adhere to damaged tissue and release chemicals that activate other platelets. Yet in order to adhere, platelets, which account for only 0.3% of the blood's volume, must first come into contact with the injured vessel wall. Fortunately, fluid dynamics have created a solution to this problem. Under arterial and arteriolar flow conditions, platelets have an enhanced concentration near blood vessel walls. This has been seen both in vitro and in vivo. This non-uniform cell distribution depends on the fluid dynamics of blood as a heterogeneous medium; no such effect occurs in a Newtonian fluid. Although lateral platelet motion has been well documented, the fluid dynamics are poorly understood. We use a parallelized lattice Boltzmann-immersed boundary method to solve the flow dynamics of red cells and platelets in a 2D vessel with no-slip boundary conditions. Red cells are treated as biconcave immersed boundary objects with isotropic Skalak membrane tension and an internal viscosity five times that of the surrounding plasma. Using this method we analyze the influence of shear rate, hematocrit and red cell membrane properties on lateral platelet motion. Insight gained from this work could lead to significant improvements to current models for platelet adhesion where the presence of red blood cells is neglected due to computational intensity. | ||
| PS21A | Davis, Courtney | |
| University of Utah | ||
| Mathematically Modeling the Impact of a Population Bottleneck on the Immune Memory Repertoire | ||
| Certain viruses kill off memory T-cells early in infection and thus create lymphopenic conditions in a process called active attrition; following this, memory and naïve T-cells proliferate (and differentiate if necessary) to refill the memory T-cell compartment. I mathematically examine how active attrition and subsequent lymphopenic proliferation impact the memory CD8+ T-cell repertoire using a combination of hypergeometric distributions and Markov birth processes. This gives insight into how the immune memory repertoire changes with infections. | ||
| PS22A | de Silva, U. Chandimal | |
| RCC-ERI, Department of Medical Sciences, Ministry of Public Health, Thailand. | ||
| Strong positive selection of HIV-1 within host is not reflected in its macro-evolution | ||
| It has been established that HIV-1 undergoes extensive changes in the genome – particularly in the env region – due to positive selective pressure in the host as well as neutral evolution resulting from erroneous reverse transcription. The major circulating viral population within the host several years after infection would therefore have genetically distanced itself considerably from the initial infecting strain. However, it is doubtful whether these “evolved” viral populations are the major players responsible in the event of infecting a third party, due to differences – phenotypic and genotypic – between viruses from the newly infected and patients from the later stages. Using a model that incorporates evolutionary dynamics at the population level as well as evolution within the host, we provide empirical evidence for the proposition that HIV strains that survive selective evolution and persist in the host as a minority are mainly responsible for infecting a third party. | ||
| Coauthor(s): \"Jiranan Warachit, Nerisa Sattagowit, Chanin Jirapongwattana, Sumolrat Panthong, Piraporn Utachee, Masanori Kameoka, Shota Nakamura, Teruo Yasunaga, Naphatsawan Boonsathorn\" | ||
| PS25A | Dougherty, Daniel | |
| Michigan State University | ||
| Wedge: A Bayesian Smoothing Algorithm For Neuronal Models | ||
| A robust Bayesian smoothing algorithm for the estimation of parameters in neuronal models is presented. The algorithm constitutes a useful addition to the computational neuroscience toolbox and an alternative to typically data-hungry spectral and information-theoretic methods. In particular, the algorithm has been designed to perform well for noisy data sets consists of a relatively short time-series (perhaps only a few periods observed), data is completely missing on one or more variables (latency), and model mis-specification is almost certain (simplifying assumptions). Simulation studies using Wedge estimation are performed for some well-known neuronal oscillators. The posterior coverage intervals from these studies support the recommendation that the Wedge algorithm is appropriate for hypothesis generation and exploration but should be used with caution when the goals of analysis are inferential. | ||
| Coauthor(s): Johannes Reisert, Haiqing Zhao | ||
| PS27A | El-Borai, Mahmoud Mohammed | |
| Faculty of Science Alexandria University Egypt | ||
| Application of control theory in modeling of brain cancer | ||
| In this paper a mathematical model is presented that describes the concentration of tumor cells of the brain. The treatment of the brain cancer is interpreted as an optimal control problem. Evolution of the disease is characterized by a parabolic partial differential equation that describes the growth of a tumor brain. While biomedical research concentrates on the development of new drugs and experimental and clinical determinations of their treatment schedules, the analysis of mathematical models can assist in testing various treatment strategies and searching for optimal ones. Using the considered mathematical model, we try to solve some medical problems in brain cancer. Keywords: Optimal control, tumor cells,brain cancer, parabolic partial differential equations. | ||
| PS28A | El-Nadi, Khairia El-Said | |
| Faculty of Science Alexandria University Egypt | ||
| On some stochastic dynamical systems and cancer | ||
| Different models of tumor growth are considered. Some mathematical methods are developed to analyze the dynamics of mutations enabling cells in cancer patients to metastize. The mathematical models consist of some stochastic dynamical systems describing tumor cells and immune effectors. It is also considered a method to contrast the ideal outcomes of some treatments. The results of the considered model predict continuous under which some suitable treatment can be successful in returning an aggressive tumor to its passive, non-immune evading state. The principle goal of this paper is to find ways to treatment the cancer tumor before they can reach an advanced stage development. Keywords: Stochastic dynamical systems, tumor cells, treatment of cancer. | ||
| PS29A | Fitzpatrick, Ben | |
| Loyola Marymount University | ||
| Dynamic Models of College Drinking and the Amethyst Initiative | ||
| To address heavy episodic drinking on college campuses college presidents have endorsed the Amethyst Initiative, a call to lower the minimum legal drinking age (MLDA). Our objective is to forecast the effect of the Amethyst Initiative on college drinking using a systems approach. A system model of college drinking called SimHED was adapted to simulate two hypothesized effects that would result from lowering the MLDA: 1) a decrease in heavy episodic drinking (HED) due to the lower likelihood of students drinking in unsupervised settings where they model irresponsible drinking (i.e., misperception decrease), and 2) an increase in overall drinking among currently underage students due to increased social availability alcohol (i.e., wetness increase). Simulations on a variety of campus types predicted similar results. In terms of the proportion of heavy episodic drinkers on campus large decreases in misperception of responsible drinking behavior were more than offset by modest increases wetness. In terms of the effect of lowering the MLDA increasing the social availability alcohol has a stronger impact on drinking behavior than decreasing misperceptions. | ||
| Coauthor(s): R. Scribner, A. Ackleh, J. Rasul | ||
| PS30A | Flann, Nicholas | |
| Utah State University | ||
| Lateral Inhibition coordinates endothelial stalk-tip cell type transitions during sprouting angiogenesis to produce self-symmetric vessel networks | ||
| Angiogenesis, the development of new blood vessels from existing vessels, is critical in wound repair, tissue development and the progression of many important diseases including cancer. Under normal conditions in sprouting angiogenesis, the growing vessel network extends along a frontier distal to the existing vessel and forms a regular self-symmetric pattern of lumina. Many mechanisms are known to contribute to the correct formation of the new vessel network such as Vegf signaling and activation, adherens junctions, basement membrane restructuring, and endothelial tip cell chemotaxis and haptotaxis, but their coordination and interaction are poorly understood. This poster reports on a modeling study using an extended Glazier-Graner-Hogeweg Model, (GGH) that implements a high fidelity simulation of sprouting angiogenesis. The GGH is detailed enough so that individual endothelial cells have shape and extend over space and time. Sprout formation and anastomosis are not modeled explicitly, but emerge from the independent behavior of each cell. Cell mechanisms include those listed above and growth, adhesion, extracellular matrix (ECM) fiber adhesion and degradation, and filopodia extension and retraction. Protein signaling and regulation are represented as ODEs and capture critical behaviors such as VegF secretion, diffusion through tissue, and uptake and activation by endothelial cells. This poster studies the role of internal signaling cascades and membrane signaling in coordinating the spatial and temporal behavior of the endothelial cells during sprouting angiogenesis. Endothelial cells in the growing vessels are known to change their type from stalk to tip, and from tip to stalk using some form of VegF activated Notch-based lateral inhibition. Since the two types of endothelial cells have distinct cell properties (e.g. proliferation, adhesion, growth, chemotactic sensitivity, proteases secretion), changing the specific pattern of type transitions produces distinct vessel morphologies. The study implements a plausible set of signaling networks and type transition rules (that map protein expression levels to type transitions) then evaluates the regularity of the resulting vessel network. In particular, measures of vessel network connectedness and self symmetry are computed from the simulated tissue morphology. Results show that membrane signaling appears to be critical in constructing regular vessel networks. | ||
| Coauthor(s): Gregory Podgorski | ||
| PS31A | Fleming, Stephen | |
| Case Western Reserve University | ||
| Accuracy of Gradient Sensing Based on Maximum Likelihood | ||
| Studies of neutrophil chemotaxis have revealed that chemotactic signals are mediated by extracellular chemokines such as interleukin-8 and fMLP. Single-cell imaging has revealed that receptor-specific binding occurs at the cell membrane, and that this process triggers several intracellular signaling pathways. These signaling cascades transmit information about the cell’s surroundings to the machinery that directs cell motility. We propose that maximum likelihood estimation based on the state of a cell’s receptors at a given moment in time can be used to construct a guess of the direction of a chemoattractant gradient surrounding the cell and describe the direction of cell migration. The information a cell receives from its receptors thus limits the accuracy of its best estimate of the true gradient direction. For any given value of the relative concentration gradient, maximum likelihood estimates predict an optimal value of the mean concentration for movement accuracy as measured by chemotactic index. This optimal value corresponds to the equilibrium constant assumed for the receptor-ligand interaction, as observed experimentally. We also construct a maximum likelihood estimate based on receptor states that fluctuate over time. The distribution of estimates obtained via a maximum likelihood procedure appears to be well fit by a von Mises angular distribution. For shallow gradients we obtain an analytic approximation for the von Mises concentration parameter as a function of relative gradient steepness. | ||
| Coauthor(s): Heather McGinnis, Peter Thomas, Harihara Baskaran, Saheli Sarkar | ||
| PS32A | Fletcher, Patrick | |
| University of British Columbia | ||
| Electrical activity, calcium dynamics, and autocrine regulation in GnRH neurons | ||
| Gonadotropin-releasing hormone (GnRH) neurons secrete in a circhoral pulsatile pattern required for normal reproductive function. Their electrophysiology and second messenger signaling has been extensively studied. A plausible mechanism for GnRH pulsatility has been proposed, involving autoregulation of GnRH neurons through GnRH receptors (hereafter referred to as the autocrine mechanism). Mathematical models have been developed to explain certain features of each of these, separately. The slow nature of the GnRH rhythm suggests that many faster processes in these neurons could be involved. In particular, the role of electrical activity and calcium dynamics in rhythmogenesis is not clear. The goals of the present work are twofold. First, we examine two mechanisms for phasic electrical activity in GnRH neurons. Second, we present some preliminary findings from coupling the electrophysiological model to an existing model for GnRH pulsatility. | ||
| Coauthor(s): Yue-Xian Li | ||
| PS35A | Gadgil, Chetan | |
| National Chemical Laboratory, Pune, India | ||
| Exploring robustness of the Drosophila segment polarity network using a Boolean model | ||
| Continuous and Boolean models for the Drosophila segment polarity network have shown that the system is able to maintain the wild-type pattern when subjected to sustained changes in the interaction parameters and initial conditions. Embryo development is likely to occur under fluctuating environmental conditions. We use a well-established Boolean model (Albert and Othmer, 2003) to explore the ability of the segment polarity network to resist transient changes. We identify paths along which alternate unviable states are reached, and hence critical nodes whose state changes lead the system away from the wild-type state. We find that the system appears to be more sensitive to changes that involve activation of normally inactive nodes. Through a simulation of the heat shock response, we show how a localized perturbation in one parasegment is more deleterious than a global perturbation affecting all parasegments. We identify the sequence of events involved in the recovery of the system from a global transient heat shock condition. Finally we discuss these results in terms of the robustness of the system response. | ||
| Coauthor(s): Kartik Subramanian | ||
| PS36A | Galante, Amanda | |
| University of Maryland, College Park | ||
| Mathematical Model of B7-H1-positive Tumor and Cytotoxic T Cell Interaction | ||
| A costimulatory molecule B7-H1, which is ever-present in carcinomas of the lung, ovary and colon and in melanomas but not in most normal tissues, has been experimentally determined to be an anti-apoptotic receptor on cancer cells. B7-H1-positive cancer cells have been shown to be immune resistant, whereas in vitro experiments and mouse models have shown B7-H1-negative tumor cells are significantly more susceptible to being repressed by the immune system. B7-H1 is believed to form a molecular shield which inhibits production and induces apoptosis of cytotoxic T cells. A better understanding of this relationship may allow medical researchers to develop a cancer treatment specifically targeting this molecular shield, allowing the immune system to more effectively repress a tumor. In this work, using experimental data and “first principles” arguments regarding the immune system and tumor growth, we derive and simulate a mathematical model in order to elucidate the immune system, surface protein B7-H1, and tumor cell interaction dynamics. | ||
| Coauthor(s): Doron Levy | ||
| PS37A | Galsworthy, Stephen | |
| University of Oxford | ||
| Modelling the role of seed dispersal and a seed bank on the regional dynamics of annual plants | ||
| Understanding the dynamics of multiple populations of a species within a region is a problem of fundamental importance in ecology. However plant ecologists are divided as to the utility of existing metapopulation frameworks. We develop an integrodifference equation model to describe the large-scale spatial dynamics of an annual plant with a long lived seed bank. Our model describes the balance between persistence of local populations assisted by a seed bank, and the colonisation of new areas via seed dispersal. Our model is parameterised with data taken from our experiments on natural populations of annual Brassica species in Southern England. Our dispersal experimentation has suggested that anthropogenic dispersal is a potential dispersal vector in addition to the primary dispersal vector (wind) for this species. Informed by these experimental results we investigate mathematically the effect of a variety of realistic dispersal kernels to describe the distribution of dispersal distances of seeds about their parent plant. We determine the effect of the seed bank on the spread and persistence of the plant population via the analysis of the speed of invasion and critical patch sizes. We calibrate our model by comparison with data from the natural plant populations. Moreover, we compare our model with an agent-based simulation model, as part of the on-going challenge of investigating the strengths and weaknesses of different modelling approaches. | ||
| Coauthor(s): Rosie S. Hails, James M. Bullock, Philip K. Maini | ||
| PS39A | Garlick, Martha | |
| Utah State University | ||
| Homogenization of large-scale movement models in ecology with application to the spread of chronic wasting disease in ungulate populations | ||
| A difficulty in using diffusion models to predict large scale population behaviors is that individuals move differently in differing habitat types. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion (in which an individual’s motility is based on local qualities of the environment as opposed to gradients) and apply it to a simplified model of the spread of chronic wasting disease in mule deer in the La Sal Mountains of Utah. Homogenization allows us to determine the impact of small scale (~10-100m) habitat variability on large scale (~10-100km) movement and interactions without solving on the small scale. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. Chronic wasting disease is a contagious, fatal neurological disease which could greatly impact deer and elk populations. | ||
| Coauthor(s): James Powell, Mevin Hooten | ||
| PS40A | Gaudreault, Mathieu | |
| McGill University | ||
| Bifurcation in stochastic differential equations with delayed feedback | ||
| The bifurcation diagram of a model nonlinear Langevin equation with delayed feedback is obtain numerically. This model relates to a common motif in genetic regulatory networks, and we study the effect of fluctuating parameters on the bifurcation diagram of the network. We observe both direct and oscillatory bifurcations in different ranges of model parameters. Below threshold, the stationary distribution function p(x) is a delta function at the trivial state x = 0. Above threshold, p(x) is a polynomial function at small x, where the exponent is -1 at threshold, and monotonously increasing with the value of the control parameter above threshold. Unlike the case without delayed feedback, the bifurcation threshold is shifted by fluctuations by an amount that scales linearly with the noise intensity. With numerical information about time delayed correlations, we derive an analytic expression for p(x) which is in good agreement with the numerical results. | ||
| PS41A | Grandison, Scott | |
| University of East Anglia | ||
| On growth and force | ||
| A central theme in D'Arcy Thompsons' book 'On Growth and Form' is that the biologists of his day were overemphasising evolution as the most important aspect of development but were neglecting the mechanics and physical laws that govern both organisms and the environment in which they exist as a fundamentally important when considering growth. To some extent the same can be said today. A large body of excellent work has been published in recent years that discusses the role of genetics in growth with scant regard to the physical processes that genes must initiate in order for development to occur. In this poster we will present a method that combines a finite element solver for diffusive processes on a three-dimensional sheet, along with an elasto-mechanical finite-element solver which can simulate growth on the same sheet. This technique is motivated by specific examples, along with experimental data. | ||
| PS42A | Gu, Stanley | |
| University of Washington | ||
| Spatiotemporal Pharmacokinetic/Pharmacodynamic Radioactive Tracer and Brain Tumor Modeling: A Method for Generating Patient-specific Simulated PET Images | ||
| Gliomas are diffuse and highly invasive primary brain tumors that account for approximately half of all conditions of this nature [1]. Due to its motility within the brain tissue, the border defining the separation between tumor and healthy tissue is nebulous and gliomas are consequently difficult to treat. In addition, this characteristic of gliomas make them difficult to model with simple exponential models [2]. Work by the Swanson group has produced an angiogenesis-based model that is simple enough to use in principle but accounts for both the diffusivity and proliferative aspects of spatio-temporal glioma growth [3]. There is a distinct difference from the quantitative mathematical model of glioma spatio-temporal growth and the qualitative results from clinical imaging modalities. In the case of positron emission tomography (PET) scans, typically a short-lived radioactive tracer is injected into the the patient\'s bloodstream, whereupon a circular detector monitors the tracer\'s positron emission decay. This work presents a potential tool for simulating clinically observable PET images from glioma model results. This is done by creating a pharmacokinetic/pharmacodynamic (PK/PD) model of tracer activity in the brain and by performing the same data manipulations done in PET acquisitions to the model results, such as filtered backprojection. The PK/PD model was inspired by previous work done in radioactive tracer modeling [4]. The tracer concentration solution is solved using the kinetic model at each voxel of the virtual brain. The tracer activity at each voxel is combined with information provided by an model for angiogenesis and hypoxia in glioma growth and invasion [5] that describes the differing types of tissue at each voxel. Combing these two models, along with filtered backprojection, allows for more realistic simulations of clincially observable PET scans. This may serve as method of validating the glioma model and providing biological insight to the PK/PD action of the FMISO tracer in the brain. [1] E.C. Alvord, Jr. and C.M. Shaw, Neoplasms affecting the nervous system of the elderly. In: S. Duckett, Editor, The Pathology of the Aging Human Nervous System, Lea and Fabiger, Philadelphia (1991), pp. 210–86. [2] F.G. Blankenberg et al., The influence of volumetric tumor doubling time, DNA ploidy, and histologic grade on the survival of patients with intracranial astrocytomas. AJNR Am. J. NeuroRad. 16 (1995),1001–12. [3] Swanson, K. R., et al. (2003). Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. Journal of the Neurological Sciences. 216 (1), 1. [4] Thorwarth, D., et al. (2005). A kinetic model for dynamic [18F]-Fmiso PET data to analyse tumour hypoxia. Physics in Medicine & Biology. 50 (10), 2209-24. [5] H. Harpold, et al. (2006) Silico Model Integrating the Angiogenic Cascade Accurately Simulates Low and High-Grade Human Gliomas. Brain Pathology 16: S4-S4 007 | ||
| Coauthor(s): Stanley Gu, Gargi Chakraborty, Russel Rockne, Kristin R. Swanson | ||
| PS43A | Hamlet, Christina | |
| University of North Carolina | ||
| Drag and flutter reduction strategies in broad leaves using qualitative flow visualization techniques and particle image velocimetry | ||
| Flutter, a self-excited vibration with a sustained amplitude, often leads to structural failure especially in engineered structures such as buildings, plane wings, and bridges. Due to the potential for catastrophic failure with serious consequences, flutter analysis is of primary concern in engineering design. Natural structures such as leaves have the ability to reconfigure themselves in order to reduce the forces experienced by the structure. Analysis of the properties of these natural structures could provide insight into designing artificial structures that exhibit reduced flutter. Here we present preliminary data demonstrating the behavior of leaves in response to fluid forces. Leaves from a tulip poplar (Liriodendron tulipifera) are subjected to laminar and turbulent flow in a wind tunnel in order to observe the reconfiguration of the leaf structure to reduce drag and flutter. Similarly, wild ginger (Asarum canadense) is subjected to flow in a water tank to observe the reconfiguration and to examine of trapped vortices. Preliminary data suggest natural leaves more readily reconfigure into drag reducing and flutter reducing shapes than do morphologically similar artificial leaves constructed from homogeneous materials such as cardboard. Artificial leaves are used to compare biological structures with simple flexible models. Quantitative data on the wake structure within and behind the leaves in water using particle image velocimetry (PIV) will be presented here. | ||
| Coauthor(s): Laura Miller | ||
| PS44A | Haskell, Evan | |
| Nova Southeastern University | ||
| Undergraduate Mathematical Biology without a Mathematics Major | ||
| Nova Southeastern University is the nation’s sixth largest independent university with more than 26,000 students and 6,000 undergraduate students served by the Farquhar College of Arts and Sciences. The college offers 18 intensive major programs and a varied roster of more than 30 complementary minor programs. The college offers large undergraduate programs in pre-medical biology and experimental psychology yet offers very limited Mathematics courses. Fewer than 10% of those completing Calculus I continue their Mathematics studies. Over the past four years Mathematics at NSU has experienced tremendous growth in both student interest and new full-time PhD faculty showing a keen interest in application of their diverse backgrounds from functional analysis to complex geometry towards modeling in Biology. Over the past two years with Mathematical backgrounds ranging from coursework in Calculus II to Ordinary Differential Equations; students have completed successfully completed independent study courses in statistical genetics, modeling of retinal disorders, computational neuroscience, and nonlinear dynamics and chaos with a focus on nonlinear oscillators in biological systems. In this presentation I overview the Mathematics program at NSU and Mathematical Modeling projects in Biology that students have successfully completed with minimal Mathematics backgrounds. I discuss some of the challenges the students overcame, the role of technology in these projects, and the students successful presentations in the NSU Undergraduate Student Symposium. | ||
| PS45A | Hernandez, Yvonne | |
| University of Houston-Downtown | ||
| Building a Diatom Succession Model for a Fresh Water Marsh | ||
| The richness and diversity of a diatom assemblage can be used to measure wetland stability in both natural wetlands and in artificial mitigation banks. The goal of this project is to develop a Diatom Succession Model which can then be used to analyze the path of succession of mitigated wetlands as the diatom death assemblage converges toward that of a natural wetland. This will also indicate if the Greens Bayou Wetland Mitigation Bank (Greens) is providing sustainable ecological benefits to counter the adverse impacts on local wetland loss caused by humans. The Anahuac National Wildlife Refuge is an undisturbed natural wetland so it provides a good example of a climax community which will serve as our reference point to study the succession of the diatom death assemblage found in Greens. Data mining techniques will be utilized to discover if patterns occur within and among the various assemblages. | ||
| Coauthor(s): Justine Onyedebelu | ||
| PS46A | Ho, Ernest | |
| University of Toronto; Toronto Western Research Institute | ||
| Slow population rhythms emerge in noisy inhibitory network models | ||
| The hippocampus is a brain region chiefly responsible for memory consolidation. Its functions are thought to be associated with neuronal population activities of various frequencies. Of the different types of neuronal networks, inhibitory interneuronal networks are known to underlie high-frequency population oscillations (~40 Hz).However, recent experiments on rodent hippocampal slices demonstrate that these same networks can exhibit robust spontaneous slow rhythms (0.5-4Hz) [1-2]. While we have gathered a relatively rich knowledge about the mechanism underlying high-frequency oscillations, a mechanistic understanding of the corresponding slow population activities is still absent. With a smaller circuitry, these in vitro slow rhythms provide an ideal platform for us to gain insight into similar but behaviourally significant in vivo slow rhythms such as neocortical UP and DOWN state transitions and large irregular activities in the hippocampus. Since the majority of hippocampal interneurons fire at a high frequency without adaptation, how is it possible for a network to exhibit slow oscillations when there is no slow time scale at the individual neuron level? We address this question from a mathematical and computer simulation standpoint. Through simulations,we show that slow rhythms can emerge without any explicit slow time scale on the part of individual neurons and synapses.However, two crucial prerequisites are required for their occurrence.First,the network should possess a suitable amount of synaptic background activity,and second, the network should consist fast spiking constituent interneurons. From our simulations we have determined that the optimal rate of spike onset of constituent interneurons should be approximately ten times the rate of the commonly used Wang-Buzsaki model [3]. Furthermore, in order to understand why a fast onset of spiking is required for slow oscillations, we have mathematically analyzed the network equations in terms of firing rates of individual neurons. Results of our analysis indicate that a rapid onset of spike initiation of individual interneurons is necessary for the network to exhibit multi-stability. Slow oscillations occur as a result of the network with suitable synaptic background activity switching from one stable state to another. Our novel results underscore, for the first time, the importance of the fast-spiking character of interneurons in slow rhythms. It is possible that the `fast-spiking'-ness of interneurons may be a generic requirement for the occurrence of many slow population activities of which the mechanisms are yet unknown. [1] Papatheodoropoulos and Kostopoulos 2002. [2] Wu et al 2005. [3] Wang and Buzsaki 1996. | ||
| Coauthor(s): Liang Zhang, Frances Skinner | ||
| PS47A | Holder, Ben | |
| Ryerson University | ||
| Characterizing virulence of influenza strains from viral plaque assays | ||
| Influenza A is an annual public health threat which has also been responsible for some of the deadliest pandemics in history. Rapid evolution and reassortment of its genetic structure allow the virus to subvert or delay an effective immune response, merge with strains natural to different host species (a characteristic of this years swine-avian-human outbreak), and develop resistance to anti-viral drugs. What had been the most reliable anti-influenza drug only two years ago, oseltamivir (or Tamiflu), faced resistance in 20% of H1N1 strains last year and preliminary data on this year's flu season shows a nearly 100% resistance to the drug. In order to understand the development of this resistance and to potentially avoid or reverse these effects in the future, it is important to understand how the genetic differences between resistant and non-resistant strains translate to differences in their infection kinetics. The virulence of a particular virus strain is typically assessed via in vitro plaque assay experiments. The initial infection of a single cell results in a circular plaque of infected or dead cells, whose rate of growth is an indication of the infection's virulence. In an effort to study how this growth depends on virus-cell interaction parameters including adsorption rate, production rate and time of latent infection, we have developed a reaction-diffusion model and a related spatially-discrete stochastic simulation. We apply the model results to the experimental plaque growth of three circulating influenza A H1N1 strains and their oseltamivir-resistant counterparts (including both natural and synthetic isolates). We map growth differences between the two strains to specific changes in key infection parameters and discuss the implications for the emergence of drug resistance. | ||
| PS48A | Huynh, Giao | |
| University of Utah | ||
| Modeling the association of EBV infection with the development of nasopharyngeal carcinoma | ||
| Epstein-Barr virus (EBV) is one of the most widespread human viruses, infecting over 90% of humans worldwide and persisting for the lifetime of the person. Most people infected with EBV are asymptomatic, but the virus has been associated with many diseases and cancers including infectious mononucleosis, Burkitt's lymphoma, Hodgkin's lymphoma, and nasopharyngeal carcinoma (NPC). NPC is a cancer of epithelial cells, with the so-called undifferentiated type being strongly associated with EBV. In these cases, EBV genomes are found in almost all tumor cells and, in concert with genetic and environmental factors, play an important role in the development of cancer. In healthy carriers, the persistence of EBV infection at a low level is tightly regulated by the virus and the host immune response. We propose a mathematical model to describe this regulation, and the steps leading to the breakdown of regulation in the development of NPC. | ||
| Coauthor(s): Frederick Adler | ||
| PS49A | Ibargüen-Mondragón, Eduardo | |
| Universidad Nacional Autónoma de México (UNAM)- Universidad de Nariño (UDENAR) | ||
| Modeling the Dynamics of Mycobacterium tuberculosis (Mt) | ||
| We formulate a model to describe the dynamics of Mycobacterium tuberculosis (Mt.) considering only four populations: uninfected macrophages, infected macrophages, T cells and Mt. Our objective is to capture the essential features of the phenomenom, trying to simplify the great number of variables involved in the immunological mechanisms induced by Mt. While our model is overly simple comparing to the complexity of the immune response to Mt., it has interesting predictions, and the results of the model reproduce basically the cellular response. The dynamics of the model is given in terms of the basic reproduction number Ro, a threshold that has been used largely in understanding the persistence of viral or bacterial infections within individuals. Analysis of the model reveals the existence of two equilibria: the infection-free equilibrium in which the bacteria is cleaned, and the infected equilibrium. Depending on the amount of bacteria, this state might represent a latent state or an active infection. | ||
| Coauthor(s): Lourdes Esteva | ||
| PS50A | James, Alex | |
| University of Canterbury | ||
| Is this insect too lazy to crap? | ||
| Sugar-rich honeydew production by phloem-feeding sooty beech scale insects (Ultracoelostoma spp.) is a keystone ecological process in New Zealand beech (Nothofagus) forest. However, very little is known about the role of the insect, particularly whether it is passive or active during the production process. Using some simple models we have tried to determine whether these bugs are, indeed, too lazy to crap. | ||
| PS51A | Joshi, Hem | |
| Xavier University | ||
| Optimally Controlled Treatment Strategy Using Interferon and Ribavirin for Hepatitis C | ||
| In this work we determine an optimal treatment strategy for hepatitis C virus (HCV) using interferon and ribavirin, through mathematical modeling. We formulate a mathematical model using a system of ordinary differential equations, which describes the interaction of target cells (hepatocytes), infected cells, infectious virions, non-infectious virions, and the two drugs, namely, interferon and ribavirin. Our goal is to minimize the viral load as well as the side effects of treatment. Finally we derive an optimal treatment strategy and then solve it numerically. | ||
| PS54A | Kempf, Harald | |
| Frankfurt Institute for Advanced Studies | ||
| Spatio-temporal dynamics of tumour spheroid irradiation | ||
| We present an agent-based approach to the modelling of cellular dynamics within tumour spheroids during irradiation treatment. Our model aims at bridging the gap between theory and experiment and thus is based on experimentally accessible parameters. Within our agent-based approach cells are represented as instances of a C++ cell-class. Each cell advances through a realistic cell cycle in response to external and internal stimuli such as the concentration of nutrients and the pressure upon the cell by neighbouring cells. The model makes use of a dynamic Delaunay triangulation in order to derive the cell neighbourhood topology while its dual, a Voronoi tessellation, is employed in order to calculate the contact surfaces between adjacent cells. Cell-cell interaction is handled within the contact model of Johnson, Kendal and Roberts which employs experimentally accessible parameters such as cell elastic modulus and Poisson\'s ratio. Forces acting on a cell are summed up and integrated using Newton\'s equation in an overdamped approach. An adaptive integration stepsize algorithm is employed in order to maximize performance. In a first approach we use a stochastic model for cell damage upon irradiation: Defined probabilities exist for the occurrence of cluster damage or non-lethal damage to a cell\'s DNA. Affected cells show a reaction depending on the radiation characteristics, local tissue oxygenation, DNA content and cell status. After irradiation cells with complex cluster damage to their DNA will undergo interphasic death. Cells with non-lethal damage to their DNA will rest at the G2/M-checkpoint until successfully repaired or undergo clonogenic death if repair failed multiple times. Damage repair capability depends on availability of nutrients amongst other factors. Accumulation of multiple repairable hits to the DNA in a cell will also lead to interphasic death. As a results of irradiation treatment a dynamic reaction is triggered in the tumour system which can be studied in detail. Reoxygenation of the tumour volume and a decrease in pressure due to cell necrosis lead to excessive regrowth after irradiation as previously quiescent cells are reactivated. A distinct resynchronisation of the cell cycle is observed which can be exploited within fractionated irradiation treatment. The inability of DNA-damaged cells to pass the G2/M-checkpoint leads to an accumulation of cells in the G2 phase interchanging the ratio of cells in G1 to cells in G2. Fractionation of the radiation dose changes the degree of tumour control considerably depending on the applied fractionation scheme. Results of our simulation environment are directly comparable to experimental results. Ultimate goal is a model which is able to relate the deposited radiation dose to the dynamical effects of partial tumour destruction. Such a model could be used to optimise treatment planning and to determine a tumour control probability. | ||
| Coauthor(s): Marcus Bleicher, Michael Meyer-Hermann | ||
| PS56A | Kielbassa, Janice | |
| Laboratory of Biometry and Evolutionary Biology, University Claude Bernard Lyon 1 (France) | ||
| A temperature-dependent von Bertalanffy growth model applied to bullhead (Cottus gobio) | ||
| Global change, in particular climate warming is known to have a strong impact on aquatic populations. Water temperature is one of the most important environmental factors for the life cycle of fish due to direct effects on growth, survival and reproduction. In this respect, understanding and modelling of temperature effects on life-history characteristics of aquatic organisms can significantly contribute to ongoing attempts to predict climate-change effects at population and community levels. The most studied growth model among length-age models in fish is the von Bertalanffy equation. Although the von Bertalanffy equation is a suitable descriptor for length-at-age data, it can not be used to predict fish growth given changing environmental conditions. The main objective of our study was thus to propose a temperature-dependent form of the von Bertalanffy growth model. We included mean annual water temperatures in the von Bertalanffy growth equation by correlating the growth coefficient and the growth performance with the water temperature. The growth coefficient was related to temperature via Rosso's equation, and the growth performance was related to temperature via an increasing linear equation. These relationships included parameters with an obvious biological relevance that facilitated their identification. The asymptotic length was also linked to the water temperature via the growth performance that related the growth coefficient and the asymptotic length. We used our model to fit growth data of bullhead (Cottus gobio). The population we studied was that living in different locations of the River Bez network (France); this species appeared to be particularly sensitive to temperature fluctuations and field sampling sites along the river network corresponded to different mean annual temperatures. We proposed different assumptions to describe temperature correlations between parameters leading to several competing von Bertalanffy growth models. Graphical analyses as well as rigorous statistical methods and model selection criteria were combined to compare, to evaluate and to validate our models. We showed that our temperature-dependent growth model was an appropriate descriptor for the data set. Furthermore, we showed that this model fitted significantly better than other tested models assuming no dependency between temperature and the growth coefficient as well as between temperature and the growth performance. Such a temperature-dependent model may have broad implications if applied to data sets from other river networks or other species. | ||
| Coauthor(s): Marie Laure Delignette-Muller, Sandrine Charles | ||
| PS57A | Kim, Yangjin | |
| Mathematical Biosciences Institute | ||
| Interaction between a tumor and its environment | ||
| Tumor proliferation depends on its microenvironment. We shall consider two examples. In the first example, we have isolated tumor epithelial cells (TEC) on one side of a membrane and fibroblasts on the other side of the membrane. Cells cannot cross the membrane, but cytokines can cross over. We set up a mathematical model, and then show good fit of the simulation results with experimental results. In the second example, we analyze the migration patterns of glioma cells from the main tumor, and show that the various patterns observed in experiments can be obtained by a model\'s simulations, by choosing appropriate values for some of the parameters of the PDE model; these parameters are the chemotaxis and haptotaxis coefficients, and the cells adhesive forces which act on the migrating cells. | ||
| Coauthor(s): Avner Friedman, Julie Wallace, Fu Li, Michael Ostrowski, Sean Lawler, Michal O. Nowicki, E. Antonio Chiocca | ||
| PS58A | Kojouharov, Hristo | |
| The University of Texas at Arlington | ||
| Compatible Discretizations for Dynamical Systems in Ecology | ||
| A new class of one-step compatible finite difference methods is developed for first-order ordinary differential equations. The proposed numerical techniques are based on a nonlocal modeling of the right-hand side function and a nonstandard discretization of the time-derivative. This approach leads to significant qualitative improvements in the behavior of the numerical solution. For multi-dimensional autonomous dynamical systems, positive and elementary-stable nonstandard finite difference methods are formulated and analyzed, based on an extension of nonstandard discretization rules. Applications of the proposed new finite difference methods to specific biological systems are also presented. | ||
| Coauthor(s): Dobromir Dimitrov | ||
| PS59A | Krenz, Gary | |
| Marquette University, Zablocki VAMC and Medical College of Wisconsin | ||
| Evidence of a NAD(P)H:Quinone Oxidoreductase 1 (NQO1) Reduction Activity Threshold in Intact Pulmonary Arterial Endothelial Cells: Experimental Data and Mathematical Model | ||
| One putative pulmonary endothelial metabolic function is the reduction of blood borne redox compounds via NQO1, wherein phase II enzyme induction is a potential means to optimize this function. In other cell lines, there appears to be a threshold above which increases in intact cell NQO1 enzyme does not support further increases in NQO1 substrate reduction. The goal of this study was to evaluate whether pulmonary arterial endothelial cells (PAEC) also exhibit an NQO1 activity threshold. PAECs were grown to confluence on biosilon microcarrier beads thereby providing a cellular bioreactor for the investigation of PAEC NQO1 activity. PAEC NQO1 activity in cell cytosol fraction was induced about 6 fold (measured using a DCPIP assay: 46.2 +/- 3.4 vs. 268.1 +/- 28.5 nmol/min/mg cell protein; mean +/- SEM) by exposure to sulforaphane (5 microM;24 hours). However, when intact cell NQO1 activity was measured by addition of duroquinone (0-50 microM) to the extracellular medium, the maximal reduction rate was only about 3 fold higher in sulforaphane-treated than control cells (10.0 +/- 0.6 vs. 32.2 +/- 1.3 nmol/min/mg cell protein). The possibility that NADPH availability was limiting NQO1 activity in sulforaphane-treated cells was examined via a steady-state mathematical model of NOQ1 ping pong bi-bi kinetics interacting with the cytosolic NADPH donor system and is consistent with the observation that glucose-6-phosphate dehydrogenase was induced only 1.2 fold in sulforaphane-treated cells (19.6 +/- 1.2 vs. 23.9 +/- 1.6 nmol/min/mg cell protein). This study demonstrates, via experimental evidence and modeling of NOQ1 and NADPH interaction, a threshold effect for intact PAEC NQO1 activity. This implies that pulmonary endothelial NQO1 capacity to activate blood borne cell membrane permeant anticancer drugs or detoxify xenobiotics is potentially limited by factors other than enzyme activity measured in cytosol fractions. Supported by NIH HL-65537 and the Department of Veterans Affairs. | ||
| Coauthor(s): Robert Bongard, Brian Lindemer, Marilyn Merker | ||
| PS60A | Lade, Steven | |
| Nonlinear Physics Centre, The Australian National University | ||
| Kramers-Moyal analysis applied to the dynamics of myosin-V | ||
| The operation of biological molecular motors such as myosin and kinesin have long been debated. Within the last decade, experiments tracking single molecules have allowed for improved understanding of such motors' dynamics, and coarse details of these dynamics are now known. For example, myosin-V walks in a hand-over-hand, as opposed to inchworm, manner [1]. More precise details of the motor's dynamics, however, are still a matter of speculation. Recently, single-molecule time series for the motion of myosin-V of extraordinary precision were published [2]. Meanwhile, Craig et al. [3] have been simulating a simplified mechanical model of myosin V, based on current biophysical data, and validating their model by comparing coarse performance characteristics with experimental results such as those of Cappello et al. [2]. Kramers-Moyal analysis, introduced over the last decade by Friedrich et al. [4] allows for more detailed characterisation of molecular motor walking time series, which are typically stochastic, and thereby more inferences to be made about the motor itself, than is usually performed. It reconstructs directly from data the Kramers-Moyal coefficients, which furnishes the drift and diffusion coefficients of a Fokker-Planck (or, equivalently, Langevin) equation, an equation which we might expect a molecular motor to approximately follow since they usually operate in an overdamped, Brownian environment. The method permits these Kramers-Moyal coefficients to be position-dependent, so unlike some other methods of time series analysis can recover arbitrary nonlinearities; further, the nonlinearity which the method recovers can be easily visualised. Even if the time series is not (first-order) Markovian, and a model like the Langevin equation not appropriate, the Kramers-Moyal coefficients can still yield useful information about the system. This Kramers-Moyal analysis, which likely has wide applicability as a method of stochastic time series analysis, will be reviewed, along with our own work on geometrical and finite-time effects, which can alter the apparent shape of the Kramers-Moyal coefficients. In the context of molecular motors, we aim to use the Kramers-Moyal method to characterise and compare Craig et al.'s simulated and Cappello et al.'s experimental time series, and also to compare against our own semi-analytical calculations. This will provide further evidence with which to evaluate Craig et al.'s model and the hypotheses it embodies, for example that the motor moves through a diffusional search state, the dynamics of which should be distinguishable in the Kramers-Moyal coefficients. Progress towards this end, and preliminary conclusions, will be presented. 1. A. Yildiz et al. (2003), Science 300 2061-65 2. G. Cappello et al. (2007), PNAS 104 15328-33 3. E.M. Craig & H. Linke (2009), in preparation 4. R. Friedrich et al. (2000), Phys. Lett. A 271 217-22; R. Friedrich & J. Peinke (1997), Phys. Rev. Lett. 68 863-66 | ||
| Coauthor(s): Erin Craig, Heiner Linke, Yuri Kivshar |