Mathematical Biology at UBC...

Abstracts for 2006-2007 Mathematical Biology Seminars
Speaker: Lazar Z. Krsmanovic Title: Pulsatile Gonadotropin-Releasing Hormone Secretion: Roles of G Protein- Coupled Receptors, Second Messengers and Ion Channels Return to seminar page Abstract: The integrated activity of the hypothalamic gonadotropin-releasing hormone (GnRH) neuronal network, and the pulsatile release of GnRH at the median eminence, is essential for the episodic mode of pituitary gonadotropin secretion and for the maintenance of normal gonadal function. GnRH receptor was found to be expressed in GnRH neurons and their immortalized counterparts (GT1-7 cells). This suggested that GnRH released from hypothalamic GnRH neurons could exert autocrine actions upon its cells of origin and contributes to the pulsatile secretion of GnRH. Patch clamp recording from identified GnRH neurons showed irregular action potential (AP) firing with transition between narrow, high spike amplitude rhythmic firing, and intervals of broader, lower spike-amplitude, burst-like AP firing. Treatment of hypothalamic GnRH neurons with 10 nM GnRH increased the occurrence of high-frequency broad APs with unchanged decay constants for fast afterhyperpolarization (fAHP) and medium (mAHP). In contrast, treatment of hypothalamic GnRH neurons with 1 M GnRH abolished mAHP current, but did not affect the occurrence of fAHP current. That was followed by subthreshold afterdepolarization potential (ADP) and significant reduction of the frequency of AP firing. These data indicate that spontaneous firing of APs in hypothalamic GnRH neurons determines the profile of afterhyperpolarization currents and consequently mediates firing frequency and the spike-profile. Constitutive and agonist-induced hetero- oligomerization of GnRH receptor and G protein-coupled receptor 54 (GPR54), stimulation of GnRH secretion by kisspeptin, and the opposing effects of GnRH on kisspeptin secretion, indicates that GnRH receptor/GnRH and GPR54/kisspeptin autoregulatory systems are integrated by negative feedback to regulate GnRH and kisspeptin secretion from GnRH neurons.
Speaker: Joel Miller Title:Predicting the size and probability of epidemics on networks Return to seminar page Abstract: Many diseases periodically emerge into human populations. Many of these diseases have animal hosts, while others are diseases which have been eliminated from some parts of the world and are occasionally reintroduced by travelers. As a classic example, HIV probably began as a transmission from an infected monkey to a hunter or cook in West Africa around 1930. Perhaps many such introductions happened over the centuries, and there is evidence that they continue, but this was the first instance in which the disease managed sustained spread. When a disease emerges or is likely to emerge, public health responses need to devote limited resources to containing the spread. In this talk we will address three important questions: 1) How likely is an introduction to lead to an epidemic? 2) If an epidemic occurs, how quickly will it grow? 3) How many people will be infected by an epidemic. All of these questions depend on both the characteristics of the disease and the structure of the population. We will develop a relatively simple mathematical theory and show how its predictions compare with an epidemic spreading in a simulated urban population.
Speaker: Yue-Xian Li Title: Noise and Synchrony in Neuronal Networks Return to seminar page Abstract: A rich variety of rhythms in human brain have been observed through the electroencephalogram (EEG), ranging from low frequency (1-4 Hz) delta rhythms in deep dreamless sleep to high frequency (>14 Hz) beta rhythms in alert states. Rhythms picked up by electrodes on the surface of the scalp are synchronized oscillations of many neurons. A deterministic theory of coupled oscillators has been developed over the past decades in which individual neurons are treated as spontaneous oscillators. A novel mechanism for generating synchronized rhythms, called coherence resonance (CR), was discovered recently. It refers to coherent oscillations triggered by noise in a system that is quiescent in the absence of noise. In this talk, I will review several distinct examples of noise-induced synchrony and oscillations, including the spike-reset-recover (SRR) model recently proposed by myself and coworkers. In most known examples of CR, the oscillation frequency increases as the noise level increases. In our SRR model, however, the frequency is determined by the intrinsic properties of the neuron but not by the noise level. The significance of this model in understanding the origin of brain rhythms will be discussed together with some other intriguing effects of noise. Some preliminary results toward developing a stochastic phase theory of coupled oscillators will also be discussed. Collaborators in works presented here are S. Reinker, R. Kuske and N. Yu.
Speaker: Rafael Meza Title: Mathematical Modeling of Colon Carcinogenesis Return to seminar page Abstract: Mathematical modeling of carcinogenesis offers the opportunity to study in greater detail the effects of specific interventions that affect critical biological processes involved in cancer development. In this talk, I will present a mathematical model of colorectal carcinogenesis and discuss some applications. Careful mathematical analysis shows that the age-specific incidence of cancer predicted by the model exhibits 'phases' that reflect the carcinogenic process in reverse, with early events showing up late, and late events influencing the incidence at young age. In particular, calibration of our model to the colorectal cancers (CRC) in the SEER registry makes it evident that the age-specific incidence increases mostly linearly above age 60-65, reflecting the incidence (onset) of adenomatous polyps (adenomas) in the population, while it increases exponentially for mid ages due to "clonal expansion" of adenoma cells. Adenomas are the premalignant lesions associated with the large majority of colorectal cancers. These results contradict the long-held view that the cancer age-specific incidence increases as a power of age. Our findings have important implications for the design and analysis of CRC screening strategies. In particular, they allow us to use our model, which was only fitted to cancer incidence and not to adenoma data, to simulate the natural history of CRC and evaluate the effect of screening for adenomas on CRC risk. If time permits, I'll discuss some of the mathematical, computational and practical issues related to our analyses of CRC screening, and present evidence that current screening guidelines may be far from optimal.
Speaker: Maria-Rita D'Orsogna Title: Patterns, stability and collapse for two-dimensional biological swarms Return to seminar page Abstract: One of the most fascinating biological phenomena is the self-organization of individual members of a species moving in unison with one another, forming elegant and coherent aggregation patterns. Schools of fish, flocks of birds and swarms of insects arise in response to external stimuli or by direct interaction, and are able to fulfill tasks much more efficiently than single agents. How do these patterns arise? What are their properties? How are individual characteristics linked to collective behaviors? In this talk we model a swarm as a non-linear system of self propelled agents that interact via pairwise attractive and repulsive potentials. We are able to predict distinct aggregation morphologies, such as flocks and vortices, and by utilizing statistical mechanics tools, to relate the interaction potential to the collapsing or dispersing behavior of aggregates as the number of constituents increases. We also discuss passage to the continuum and possible applications of this work to the development of artificial swarming teams.
Speaker: Pauline van den Driessche Title: Modeling the Spread of West Nile Virus Return to seminar page Abstract: West Nile virus was detected in New York State in 1999, and has spread rapidly across the continent causing bird, horse and human mortality. The aim of this lecture is to model this spread. Biological assumptions are summarized and lead to the development of a reaction-diffusion model for the spatial spread of West Nile virus with cross infection between birds and mosquitoes. For a simplified model, the existence of traveling waves is proved and the spatial spread of infection is calculated. Related models for West Nile virus spread are briefly discussed
Speaker: Hong Qian Title: Nonequilibrium Steady-state Theory of Phosphorylation-dephosphorylation Switch in Cellular Signaling Return to seminar page Abstract: We present a mathematical theory for a biochemical switch system, which can be either the phosphorylation-dephosphorylation cycle (PdPC) reactions catalyzed by a kinase and a phosphatase, or GTPase cycles catalyzed by a guanine exchange factor (GEF) and a GTPase activating protein (GAP). The theory is based on the recently developed open-system nonequilibrium thermodynamics, the chemical master equation, and the traditional enzyme kinetics. We show how ultrasensitivity, as a new form of cooperativity, arisies in an open system, and the role of cellular energy in the functioning of switches. We also investigate PdPC/GTPase systems with feedbacks and how it leads to various nonlinear bifurcations.
Speaker: Jianhong Wu Title: Neural Computation with Attractors: Memory, Dynamics and Time Lags Return to seminar page Abstract: This talk addresses the issue how to design and compute a network with feedback, that exhibits complex but desired dynamical behaviors for some particular cognitive tasks. We illustrate the linkage between neural computation with attractors and the memory storage/retrieval using the additive network of neurons, and discuss the simplicity-capacity dilemma arising from the requirement for a network to posses a large number of stable patterns and to be easily implemented. We then propose a novel approach based on signal processing delay and show the interaction of delay, feedback and refractoriness in a simple inhibitory network of two neurons can generate three basic types of oscillations and these three basic oscillations can then be pinned together to form a large number of interesting coexisting periodic patterns. Therefore, a simple and small network with delayed feedback can process a large amount of information. How connection topology of a large network enhances the network's capacity for memory storage and retrieval remains to be an interesting task.
Speaker: Adriana Dawes Title: Stable segregation of PAR proteins in the early C elegans embryo relies on a bistable switch mechanism Return to seminar page Abstract: PAR proteins, collectively termed the anterior and posterior PAR proteins, establish distinct intracellular spatial domains in the one cell C elegans embryo, polarizing the cell. This polarization is persistent, lasting approximately 10-20 minutes until first cleavage. It has been established experimentally that the anterior and posterior PAR proteins interact through mutual phosphorylation, and recent genetic studies indicate that the anterior PAR proteins are capable of oligomerizing. Using mathematical modelling, I show that known interactions between the PAR proteins give rise to a bistable switch that may account for the stable segregation of the PAR proteins. The presence of a bistable switch in the C elegans embryo is verified experimentally by depleting the anterior PARs using RNA interference, providing a direct test of the mathematical model.
Speaker: Joel Heath Title: Behavioural Dynamics of Arctic wintering eider ducks Return to seminar page Abstract:
Speaker: Rodrigo Restrepo Title: RNA and prebiotic evolution Return to seminar page Abstract: By considering many regularities in the occurrences of purines and pyrimidines in 6241 gene sequences for the tRNAs of the prokaryotes in the Bayreuth Database, this study uncovers a strand (collection) of long RNA segments that fit a large fraction of those tRNAs. This strand suggests a plausible data-based scenario for prebiotic evolution that may explain the relatively uniform size of the tRNAs, the fact that the messenger is RNA, not DNA, with a reason for its introns, suggesting a plausible conjecture about some steps in the origin of the genetic code.
Speaker: Suani Pinho Title: Mathematical and Computer Modelling of Diseases Return to seminar page Abstract: In this seminar, we present some results and projects of our research group (Statistical Physics and Complex Systems - FESC) concerning Mathematical and Computer Modeling of Diseases. We propose and analyse models of diseases using time delayed differential equations, cellular automata and, more recently, complex networks. Our focus is both on the intra-host dynamics of some diseases (for instance, cancer, malaria, HIV) and on the population dynamics of transmissible diseases (for instance, dengue, measles, tuberculosis). Our aim is to compare the model results with some clinical observations from the qualitative point of view and, when it is possible, with some actual data. In these themes, we collaborate with researchers of Universidade Federal de Pernambuco (Recife - Brazil) and Public Health Institute (ISC) of our University.
Speaker: Veronica Grieneisen Title: Morphogen Gradients Stable During Growth? an example in plant development Return to seminar page Abstract: In plant development, the phytohormone auxin plays a key-role, controlling cell identity, cell division and cell expansion. Interestingly, in both distal regions of plant roots and shoots, characteristic auxin maxima have been found which correlate with these developmental outputs. It is also known that auxin export facilitators (PINs) are associated with auxin maxima. Combining such empirical knowledge, we present a multilevel model for the Arabidopsis root that spans molecular and cellular levels describing diffusion and PIN-mediated transport in and across cells within a structured tissue layout. The modelling study allows us to pinpoint the necessary elements for the formation and maintenance of an auxin-maximum. It also permits us to draw connections between PIN-topology and macroscopic properties such as auxin-capacitance, auxin gradient properties and timescales. We explain how pattern formation and morphogenesis at timescales varying from seconds to days/weeks can be understood, and thus, how such morphogen gradients should be treated as out-of-equilibrium processes.
Speaker: Stan Maree Title: T-cell dynamics within Lymph Nodes Return to seminar page Abstract:
Speaker: Wouter-Jan Rappel Title: Which way to go? Modeling eukaryotic chemotaxis Return to seminar page Abstract: Chemotaxis is characterized by directed movement of cells up a chemical gradient. It is a key component in a multitude of biological processes, including neuronal patterning, wound healing, embryogenesis, and cancer metastasis. Even though many of the key components involved in chemotaxis are known it remains a poorly understood process. In this talk, I will present our modeling efforts aimed towards a better quantitative and mechanistic understanding of chemotaxis. In addition, I will discuss some of the new experimental techniques that should bring us closer to answering the question how cells know which way to go.
Speaker: James P. Keener Title: How cells make measurements Return to seminar page Abstract: A fundamental problem of cell biology is to understand how cells make measurements and then make behavioral decisions in response to these measurements. The full answer to this question is not known but there are some underlying principles that are coming to light. The short answer is that the rate of molecular diffusion contains quantifiable information that can be transduced by biochemical feedback to give control over physical structures. In this talk, this principle will be illustrated by two specific examples of how rates of molecular diffusion contain information that is used to make a measurement and a behavioral decision. Example 1: Bacterial populations of P. aeruginosa are known to make a decision to secrete polymer gel on the basis of the size of the colony in which they live. This process is called quorum sensing and only recently has the mechanism for this been sorted out. It is now known that P. aeruginosa produces a chemical whose rate of diffusion out of the cell provides information about the size of the colony which when coupled with positive feedback gives rise to a hysteretic biochemical switch. Example 2: Salmonella employ a mechanism that combines molecular diffusion with a negative feedback chemical network to "know" how long its flagella are. As a result, if a flagellum is cut off, it will be regrown at the same rate at which it grew initially.
Speaker: Claude Muller Title: The spread and evolution of highly pathogenic Avian Influenza (HPAI) H5N1 in Africa Return to seminar page Abstract: In Africa HPAI H5N1 virus was first detected in Northern Nigeria and since then in 7 other African countries: Niger, Egypt, Cameroon, Burkina Faso, C™te dÕIvoire, Sudan and Djibouti. The study of the Nigerian-Luxembourg Poultry Virus Network at the University of Ibadan showed high seroprevalences for some poultry viruses but antibodies against AIV were not found in farms in the Southwest of Nigeria at least until May 2004. Phylogenetic analysis and substitution rates of complete genome sequences of Nigerian strains from the South-West and the North showed that three sublineages were present in Nigeria as early as February 2006 and that three independent introductions of H5N1 into the country are likely. (MF Ducatez et al. Avian flu: multiple introductions of H5N1 in Nigeria. Nature 442, 37, 2006). These three sublineages include all African strains and by now have a distinct geographic distribution: sublineage A (southwest Nigeria, Lagos, Niger), B (southwest Nigeria, Lagos, Egypt, Djibouti) and C (Northern Nigeria, Burkina Faso, Sudan, C™te dÕIvoire) within Africa. Probable non-African ancestors within the West-Asian/Russian/European lineage distinct from the Southeast Asian lineages were identified for each sublineage. In 2006 all reported human cases in Africa (Egypt, Djibouti) were caused by sublineage B with a distinct but poorly understood amino acid signature. In 2006, this sublineage B has been found also in at least one farm in/near Lagos. Genetic analysis will reveal whether the same strain caused the recent human case in Lagos. We have also characterized the first avian influenza strains from Burkina Faso and the first strains from African wild birds (sublineage C). Between February and June 2006, 48 hooded vultures (Necrosyrtes monachus) were found dead or sick throughout Ouagadougou. We present here the first sequences from African wild birds and compare them to strain found in Burkina poultry. The sequences clustered with strains found in Ivory Coast, Northern Nigeria and The Sudan (sublineage C). We showed that the infection of scavenger birds in Africa is likely to cause spill-backs from poultry to wild birds, which is rarely seen in other countries and has important consequences for surveillance in Africa and beyond. As they scavenge on many dead species, they may also function as conspicuous sentinels in the African continent, similar to raptors or swans in Europe or cats in Indonesia. Proper disposal of infected carcasses must be carefully enforced on affected farms to avoid primary infections of carrion feeders.
Speaker: Alex Mogilner Title: System Level Mathematical Analysis of Mitosis Return to seminar page Abstract: Mitotic spindle goes through distinct morphological states characterized by increasing spindle length and distances between chromosomes. A complete picture of how the spindle assembles is still lacking. We performed an In Silico model screen to identify all potential mechanisms of spindle self-organization. We trained' the computer to assemble a set of models and screened the models in a multi-dimensional parameter space. To identify models that fit experimental data we used stochastic optimization and genetic algorithms. We found multiple models quantitatively describing the spindle in which the timing of force activity must be fine tuned, in contrast to the kinetic and mechanical parameters that show robustness to change.
Speaker: Joe Tien Title: Geometric approaches to parameter estimation for differential equations. Return to seminar page Abstract: Parameter estimation for differential equations is a fundamental problem, but work in this area is incomplete. One difficulty is the presence of local minima which trap optimization algorithms, resulting in poor fits. Incorporating geometric features of the differential equations into the optimization algorithms can alleviate this problem. These structural features are combined with numerical improvements via automatic differentiation, and applied to neural models and data related to breathing. This work has resulted in my becoming interested in statistical inference. If time permits, I will mention some HIV data I have been working on with viral strains which have escaped immune system recognition.
Speaker: Junling Ma Title: Evolutionary Branching Return to seminar page Abstract: Evolutionary branching is sympatric speciation driven by competition between dominant species and their mutants. The traditional approach to study evolutionary branching is to use pairwise-invasibility plot (PIP). However, PIP is only suitable for the branching of a single species with a single trait. With multiple co-evolving traits or species, this method breaks down because the evolution/branching in one trait changes the PIP of other traits. In this talk, I introduce a dynamical method to study the branching of multiple co-evolving traits and species, and give the branching conditions.
Speaker: Stewart Chang Title: Multi-scale modeling of antigen presentation with applications to tuberculosis. Return to seminar page Abstract: Antigen presentation is the process by which cells of the immune system display peptides from pathogens on their surface after binding the peptides to major histocompatibility complex (MHC) molecules. T helper cells recognize peptides from pathogens in this context then secrete cytokines that activate other cells, initiating an immune response. Antigen presentation is therefore a requisite for immunity to several pathogens including Mycobacterium tuberculosis (Mtb). To approach questions related to antigen presentation and disease, I represented antigen presentation at different scales using a series of mathematical and statistical models. At the molecular scale, I asked whether heterogeneity in peptide length affects binding to MHC class II, the class of MHC responsible for binding peptides from bacteria such as Mtb. By developing statistical models of peptide-MHC binding, I found that length has a nonlinear effect on binding affinity and that this information could improve the accuracy of binding prediction. At the cellular scale, I asked why Mtb possesses multiple mechanisms to inhibit antigen presentation on the cell surface. My mathematical model shows that these mechanisms may be acting on different timescales and therefore complementary rather than merely redundant. Finally, at the multi-cellular level, I asked how polymorphisms in multiple genes related to antigen presentation might affect T cell response and susceptibility to infectious diseases such as tuberculosis. Using a multi-scale model representing both the antigen-presenting cell and T cell, I found that polymorphisms in two different genes may exert the same influence on the output, potentially canceling out their effects. Future work with these models may include evaluation of candidate peptide-based vaccines to ensure high-affinity binding, T cell response, and broad efficacy in diverse populations.
Speaker: Josef Ackerman Title: The role of mathematics in physical ecology. Return to seminar page Abstract: The natural link between mathematics and ecology is evident in the field of physical ecology, which uses physical models to explore some fundamental issues. These include how aquatic organisms use the constraints imposed by physical environment to satisfy their biological processes. This seminar will present examples of the physical ecology approach to sexual reproduction and trophic dynamics in marine, lake and river systems.
Speaker: Arthur Sherman Title: Ionic and Metabolic Mechanisms in Pulsatile Insulin Secretion Return to seminar page Abstract: Insulin is secreted in pulses with a period of about 5 minutes from the beta-cells of the pancreas. These pulses are in turn driven by oscillations of cytosolic calcium. Two parallel streams of investigation over more than two decades have studied metabolic oscillations and ionic mechanisms as possible sources of the calcium oscillations. We propose that the two are linked by a potassium channel, K(ATP), that senses the ATP and ADP levels in the cell. This directly transduces metabolic oscillations into oscillations of membrane potential and calcium. However, calcium can also affect metabolism by stimulating ATP-consuming pumps, by depolarizing the mitochondria, and by directly activating Krebs cycle enzymes. A unified model that combines the above elements and can thereby explain a diverse set of experimental observations using only a few simple assumptions will be presented.
Speaker: Bill Kath Title: Models of Initiation and Propagation of Dendritic Spikes in Hippocampal CA1 Pyramidal Neurons Return to seminar page Abstract: In computational models of hippocampal CA1 pyramidal neurons with active dendrites, distal synaptic inputs trigger dendritic spikes, but in many cases these spikes do not propagate reliably to the soma to produce output action potentials in the axon. The computational models show, moreover, that the probability of axonal action potential initiation increases dramatically if the distal dendritic inputs are accompanied by small amounts of more proximal synaptic input. In this case, the propagation of the dendritic spikes appears to be gated by the more proximal inputs. The mechanisms for this phenomenon, as well as experimental results designed to test the predictions of the computational models, will be discussed.
Speaker: David Lloyd Title: Nucleation of localised pattern in continuous media Return to seminar page Abstract: The formation of patterns from quiescence under the continuous variation of a parameter has long been of interest across the physical and life sciences since the pioneering work of Alan Turing. We describe how spatially localised patches of pattern arise spontaneously in experiments in a wide variety of nonlinear media including liquid crystals, autocatalytic chemical reactions, gas discharge systems, optical crystals and in solidification. Perhaps the most intriguing examples of such patterns are small circularly symmetric spatially localised subharmonic excitations (dubbed \emph{oscillons}) that occur in vertically vibrated granular materials, viscous fluids and plasmas. Oscillons tend to form tightly packed strongly interacting clusters which coexist with an undeformed background and cannot be captured by theories of weakly interacting localised atoms. Here we present a predictive theory for the nucleation and pattern selection of \emph{multi-dimensional} localised structures in quite general continuous media, via the interplay between linear instability and nonlinear bistability. We show how specific kinds of localised patterns (spots, targets, hexagonal arrays etc.) are selected and emerge subcriticality depending on the amount of bistability between the background and finite-amplitude cellular patterns. These parameter regions of localised pattern overlap as the amount of hysteresis in the system is increased, explaining experimental results showing competition between different localised patterns. Furthermore, using a Maxwell point argument that goes well beyond one-dimensional theory, we reveal a complex {\em snaking} transition diagram that provides the mechanism by which larger localised clusters form and self completion occurs.
Speaker: Richard Bertram Title: Mathematical Analysis of the Neural Control of Hormone Secretion Return to seminar page Abstract: The pituitary is one of the primary glands of the body. Many hormones are released from a variety of cells within the pituitary, and these hormones regulate the release of hormones from other glands and have direct actions on the brain, muscles, and organs. The timing of hormone release from the pituitary is important, and is determined largely through interactions with a region of the brain called the hypothalamus. These interactions are quite complex, and serve as a good application area for mathematical modeling and computer simulations. The focus of this seminar is recent mathematical modeling and analysis of interactions between the hypothalamus and pituitary lactotrophs, pituitary cells that secrete the hormone prolactin. We discuss possible mechanisms for circadian oscillations in prolactin secretion in pregnant rats, and the much faster oscillations (period of several seconds) in electrical activity of the lactotrophs, using models of cellular dynamics at very different temporal and spatial scales.
Speaker: Michael Doebeli Title: Evolution of diversity: Pattern formation in phenotype space Return to seminar page Abstract: Understanding the origin of diversity is one of the fundamental conceptual problems in biology. Traditional evolutionary theory predicts uniformity: natural selection acting on organisms under given environmental conditions and developmental constraints produces a unique, optimally adapted phenotype. According to this view, different types only come about through a change in conditions over space or time. In particular, the process of diversification, that is, the split of an ancestral population into distinct descendent lineages, is a by-product of geographical separation. This traditional view misses out on the important perspective that diversification itself can be an adaptive process triggered by ecological interactions within an ancestral population. In this perspective, diversification is a process of pattern formation in phenotype space, during which frequency-dependent selection splits unimodal phenotype distributions into multimodal distributions, with the different modes corresponding to different descending species. In this talk I will review recent theoretical work on adaptive diversification from the general perspective of pattern formation. I will start out showing how diversity can evolve in the framework of adaptive dynamics due to the phenomenon of evolutionary branching. I will then consider PDE models of continuous phenotype distributions, showing that speciation due to pattern formation is a plausible outcome in such models. Finally, I will briefly introduce a general framework for understanding pattern formation in PDE models that is based on equivariant bifurcation theory.
Speaker: Daniel Coombs Title: Virus Competition at Multiple Scales Return to seminar page Abstract: Viruses compete and are subject to natural selection at multiple levels: within-cell, within-host and within-population (of hosts). We looked at how viruses can optimally exploit their hosts and how this behaviour may influence the most successful strategy at the between-host, or epidemiological level. I will present a fairly general way to consistently combine models of disease process and disease spread with the goal of understanding the net selection pressure on a model virus. The method is illustrated using two popular models at the within- and between-host levels.
Speaker: Yoichiro Mori Title TBA Return to seminar page Abstract: The immersed boundary method is a general framework used to handle fluid-structure interactions. One computational bottleneck of the immersed boundary methods is that the elastic structures are often very stiff, necessitating the use of a very fine time step. In this talk, we will present an immersed boundary scheme in which the position of the immersed elastic structure is treated implicitly. We show that the resulting implicit method allows much greater time steps to be used compared with an explicit method, and that the computational cost is greatly reduced in certain test situations. We shall also show that the implicit method provides a natural way in which to add addtional mass to the immersed elastic structure.
Speaker: Lin Wang Title: Impact of Travel Between Patches for Spatial Spread of Disease Return to seminar page Abstract: A patch model is proposed to study the impact of travel on the spatial spread of disease between patches. The basic reproduction number for the i-th patch in isolation, is obtained along with the basic reproduction number of the system, $\mathcal{R}_0$. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of $\mathcal{R}_0$ on the travel rates between the two patches are obtained. For parameters relevant for influenza, the effects of travel restrictions are also discussed. Results show that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease.
Speaker: Kevin Painter Title Modelling cell migration in the ECM and its role in tumour invasion Return to seminar page Abstract: Cell migration plays an essential role during both embryonic development (e.g. gastrulation, neural crest migration) and in the normal physiological responses of the adult (e.g. immune response, wound healing). The extracellular matrix (ECM) plays a vital role in regulating movement by both providing a scaffold through which cells can generate traction and imparting specific migratory cues through ECM-bound proteins. The ECM also provides specific guidance to cells through preferential movement by the cells along the matrix fibres, a process known as contact guidance. The acquired ability of tumour cells to break free from the main mass and migrate into the surrounding ECM is a key stage in increased tumour malignancy. Individual cell migration in the ECM can be classified into two main groups: amoeboid and mesenchymal. In the former, cells move quickly and have negligible effect on the structure of the surrounding ECM. Mesenchymal migration, however, is much slower and extensive matrix degradation takes place through the focussed expression of specific matrix degrading proteins by the cells (pericellular proteolysis). In this talk, I will describe both discrete and continuous models for amoeboid and mesenchymal cell migration. Numerical investigations will be used to demonstrate a potential role of contact guidance and matrix degradation in directing the macroscopic organisation of cells and the matrix. I will consider applications in the context of models for tumour invasion.
Speaker: Peter Borowski Title: A stochastic two-state signalling module with negative feedback Return to seminar page Abstract: Motivated by the negative feedback calcium exerts on the gating dynamics of a calcium-conducting ion channel in olfactory receptor neurons, we develop an abstract two-state (open/closed) signalling module with negative feedback. The coupling between the gating dynamics of the channel and the conducted ion makes the effective dynamics of the channel non-Markovian and difficult to treat in a Langevin-approach. We make use of two different techniques to describe the stochastic dynamics of the module. First, we calculate the steady state probability distribution using a Master/Fokker-Planck-type equation. Second, a path-integral formulation based on the temporal statistics of the channel state-flips is developed to calculate dynamical properties of the module. The feedback effect is built into the model in a systematic way in the form of a weak perturbation. Analytic results are obtained for the open probability of the channel as well as the auto-correlation and response functions (both for the discrete channel variable and the continuous calcium concentration). Monte Carlo simulations are performed which support the analytical predictions in the weak feedback limit and provide results beyond linear perturbation theory.
Speaker: Jason Haugh Title: Analysis of Intracellular Signal Transduction at Various Scales of Biological Abstraction Return to seminar page Abstract: An ongoing challenge in mammalian cell biology is to bridge the gaps in our understanding of processes at the molecular, cellular, and tissue levels. Central to the hierarchy of biological complexity is the field of /signal transduction/, which deals with the biochemical mechanisms and pathways by which cells respond to external stimuli, such as soluble growth factors/cytokines, extracellular matrix, and mechanical forces. Intracellular signaling processes control the growth, survival, and migration of cells in normal physiological contexts, and defects in signaling form the molecular basis for cancer, immune system disorders, and other diseases. Using a quantitative approach that combines biochemical measurements, fluorescence imaging, and mathematical modeling, our group characterizes signal transduction networks through analysis of their kinetics and spatial patterns in cells. Based on analysis of experimental data and informed where appropriate by knowledge of protein domain structure, we develop mechanistic models that may be embedded in mathematical representations of cell population dynamics, with the goal of evaluating hypotheses regarding the concerted responses of cells in tissues. As an example of this approach, I will describe our efforts to characterize signal transduction mediated by cell surface receptors for platelet-derived growth factor (PDGF), a soluble factor that accelerates dermal wound healing by directing the migration and proliferation of dermal fibroblasts.
Speaker: Gerda deVries Title: Mathematical models in radiation biology Return to seminar page Abstract: In this talk, I will review concepts in radiation biology that allow us to model the effectiveness of radiation therapy in the treatment of cancer. In particular, I will focus on the Tumour Control Probability (TCP), which is the probability that no cancerous cells survive the treatment. Early TCP formulae are based on simple binomial and Poissonian statistics. They are of limited value, since they do not take cell proliferation during the treatment period into account. Recent TCP formulae are based on dynamic models of a cell population, taking cell proliferation into account. I will conclude with a discussion of how and when the TCP formulae are related to each other, and how they can be used to compare the efficacy of different treatment schedules.
Speaker: Gail Wolkowicz Title:An alternative formulation for a delayed logistic equation Return to seminar page Abstract: After a brief review of the history and dynamics of the classical logistic and delayed logistic equation models, an alternative expression for a delayed logistic equation is derived assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model. A complete global analysis shows that unlike the dynamics of the classical logistic delay differential equation model,no sustained oscillations are possible. Instead, the dynamics of this model are more reminiscent of the classical logistic ordinary differential equations growth model, but with some important differences. Implications for incorporating delays in population models are considered.
Speaker: Mark Lewis Title TBA Return to seminar page Abstract:
Speaker: Bob Guy Title: A multiphase flow model of calcium induced morphology changes in true slime mold Return to seminar page Abstract: The true slime mold Physarum polycephalum is a single cell organism reaching up to meters in size. The cytoplasm shows periodic shuttle streaming through a network of tubular structures attaining velocities up to 1 mm/s. The motion is driven by the periodic contraction of an actin-myosin gel that is regulated by a calcium oscillation. When the organism is small (< 100 microns) no streaming is observed, but as it gets larger regular rhythmic steaming suddenly emerges. We present a mechanochemical multifluid model which is used to explore how the sensitivity to changes in calcium concentration is related to the stability of the sol/gel mixture. Stability of the homogeneous mixture is explored analytically in one-dimension, and computational results are presented for higher dimensions. The model demonstrates that as the organism grows, a calcium-induced spatial instability occurs which may be responsible for the initiation of streaming. The overall goal of this work is to understand the interplay between chemistry and fluid mechanics which is necessary to transmit chemical signals and organize structures over very large distances. In addition to streaming, some other problems related to spatial organization of structure will be discussed.
Speaker: Claus Rueffler Title:Work in progress: The evolution of phenotype determination and an attempt to classify simple life-history models Return to seminar page Abstract: In this talk I will present two pieces of work in progress. In the first half of the talk I will speak about the evolution of phenotype determining mechanisms. Many heterogeneous environments favour different phenotypes in different places or at different times. Phenotypic diversity can either result from genetic diversity of from a single genotype capable of producing different phenotypes. A single genotype might produce different phenotypes for example in response to an environmental cue (phenotypic plasticity), through a randomization mechanism (bet-hedging), or through a combination of the two. A large part of the existing theoretical literature attempts to give conditions under which one of these specific mechanisms is favoured over a phenotypically monomorphic population. However, in many circumstances different evolutionary responses are favoured simultaneously and the real question becomes which of these different responses might evolve first and possibly pre-empt any selection driving one of the alternative responses. I will address this question by presenting some preliminary results derived from a model designed to study evolution in a temporarily heterogeneous environment. In the second half of the talk I will present a classification of the evolutionary dynamics for a class of simple life-history models. The aim of this classification is to find principles governing the evolutionary dynamics that are valid beyond a single specific model. The family of models considered is characterized by discrete time population dynamics, density-dependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a trade-off. Individual models differ in the choice of traits that are presumed to be evolving and in the way population regulation is incorporated. I classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimization criterion. The first classification allows me to infer whether trait combinations that are characterized by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequency-independent from models that give rise to frequency dependence. I will conclude by summarizing some general patterns emerging from this analysis.
Speaker: Claus Rueffler Title: The evolutionary ecology of resource specialization Return to seminar page Abstract: In the presence of different resources, when should we expect the evolution of a generalist phenotype versus specialized phenotypes? While this question has a long history in evolutionary ecology the evolutionary dynamics of a single consumer type in the presence of two kinds of renewable resources has not yet been studied in great detail. I will present a model of one evolving consumer feeding on two resources and analyse the evolutionary dynamics of different consumer traits using a set of techniques known as `` adaptive dynamics''. I show that, depending on the type of trait considered, selection is either frequency-independent or frequency-dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency-dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Traits with frequency-independent selection follow Levins' classical prediction stating that convex phenotype sets favour generalists while concave phenotype sets favour specialists. In a second step I extend the model by allowing consumers to choose their diet so as to maximize resource uptake. This version of the model allows for the study of the dynamic interplay between adaptive choice behaviour and the evolutionary dynamics of morphological and physiological foraging traits. The model predicts that flexible diet choice behaviour can guide the direction of evolutionary change in a foraging trait and that flexible behaviour can mediate the coexistence of different consumer types where coexistence would not be possible otherwise. Such polymorphisms can evolve from a monomorphic population at evolutionary branching points and also at points where a small genetic change in a trait can provoke a drastic and non-genetic change in choice behaviour. The added feature of diet choice behaviour can lead to alternative evolutionarily stable communities.
Speaker: Christoph Hauert Title: Evolutionary Dynamics: Structured Populations and the Problem of Cooperation Return to seminar page Abstract: Evolutionary dynamics in finite populations reflects a balance between Darwinian selection and random drift. For a long time population structures were assumed to leave the evolutionary outcome unaffected, i.e. to leave the fixation probability of a single mutant type in a resident population unchanged, provided that the fitness of mutants and residents is constant and independent of the population configuration. This result indeed holds for a certain (large) class of population structures or graphs. Quite intriguingly, however, other structures can tilt the balance to the extent that either selection is eliminated and drift rules or drift is eliminated and only selection matters. These results have recently been extended to include frequency-dependent selection on graphs where individuals engage in game theoretical interactions. The most important case refers to the problem of cooperation in social dilemmas, i.e. to behavioral patterns that are beneficial to the group but costly to the individual. For the prisoner's dilemma, this yields a simple rule under which selection can favor cooperation in structured populations that range from regular lattices to scale-free networks. In well-mixed populations, i.e. in the absence of spatial structure, defectors reign. Spatial structure has long been recognized to support cooperation because it allows cooperators to form clusters and thereby to reduce exploitation by defectors. However, this does not hold for social dilemmas in general. In fact, under relaxed conditions of the social dilemma, i.e. if cooperators and defectors can co-exist in well-mixed populations, spatial structure often turns out to be detrimental and may even eliminate cooperation altogether.
Speaker: Christoph Hauert Title: Cooperation in Social Dilemmas: The Role of Punishment and Volunteering Return to seminar page Abstract: The emergence and maintenance of cooperative behavior that is beneficial to others but costly to the individual represents a major conundrum in evolutionary biology. Punishment represents an efficient mechanism to stabilize and maintain cooperation in social dilemmas and is ubiquitous in animal and human societies - ranging from toxin producing microorganisms to law enforcement institutions - but it remains unresolved how initially rare costly punishment can gain a foothold and spread through the population. In nature, animals and humans often select their interaction partners or adjust their behavior in response to them. In the simplest case they simply refuse to participate in risky enterprises. Such voluntary participation in social dilemmas is an efficient mechanism to prevent deadlocks in states of mutual defection, and thus represents a potent promoter of cooperation that nevertheless fails to stabilize it. However, the combined efforts of punishment and volunteering may change the odds in favor of cooperation. Interestingly, even the combined efforts fail in infinite populations, but provide a most efficient mechanism to stabilize cooperation (and punishment) in the stochastic dynamics of finite populations under mutation and selection. Thus the freedom to withdraw leads to prosocial coercion. This implements Hardin's principle: mutual coercion mutually (and voluntarily) agreed upon.
Speaker: Kristan Schneider Title: Long-term evolution of polygenic traits under frequency-dependent intraspecific competition Return to seminar page Abstract: We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a `largest' element, an LTE, which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large.
Speaker: Kristan Schneider Title: A Multilocus-Multiallele Analysis of Frequency-Dependent Selection Induced by Intraspecific Competition Return to seminar page Abstract: The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system.
Speaker: Jung Kyung Kim Title : Function Follows Form - Transport Phenomena Coupled with Mechanics in Biological Systems Return to seminar page Abstract: As the systems approaches are actively adopted in biology, studies for revealing the link between physical dynamics and corresponding molecular mechanism will be crucial to better understanding of the inherent complexity and dynamics of biological phenomena. Macromolecule diffusion in cells and tissues is important for cell signaling, metabolism and locomotion. Non-invasive or minimally invasive in-vivo photobleaching and single quantum-dot tracking techniques combined with mathematical modeling have been used for quantifying macromolecule diffusion in cells and living tissues, including central nervous system and tumors. My extensive experience in manipulating the tiny volume of liquids and small biological objects with micro/nanofluidic systems has been stimulating me to think that cells can respond to chemically patterned and topologically textured substrates by sensing the modulated surface forces. More specifically, my current aim is to find the role of membrane tension in spreading and self-propulsion during cell migration by applying fluid dynamics approaches to describing the motion of droplets and thin films on the substrates with chemical or topological patterns. Interdisciplinary collaborations between engineers and biologists would also lead to continuous advancement in engineering by applying uncovered design principles and intrinsic strategies in biological systems.
Speaker: Michael Gilchrist Title Predicting Protein Production Rates from Codon Usage Patterns: A Nested Model Approach Return to seminar page Abstract: Genes are often biased in their use of particular codons. The degree of bias displayed changes as a function of expression level and intra-genic position. Numerous indices measuring such bias have been developed. While the expression level of a gene and such indicies are often correlated, the huristic nature of these metrics precludes a deeper understanding between expression and bias. Here I employ mechanistic models of cellular and population processes to develop a framework for evaluating codon usage bias in an explicitly evolutionary framework.
Speaker: Joshua Weitz Title: Evolutionary and Population Dynamics of Bacteria and Phage Return to seminar page Abstract: Bacterial viruses, aka bacteriophage or phage, are ubiquitous in nature, yet many central aspects of host-phage biology have not been integrated into mathematical models. In this talk I present a series of theoretical efforts to understand the diversity, population dynamics and life history of phage. First, I discuss an evolutionary ecology model of host-phage diversification using the framework of adaptive dynamics and show how the principle of competition exclusion is modified in the context of coevolutionary arms races. Second, current models of host-phage population dynamics neglect to include the reduction of lytic effectiveness as hosts approach stationary phase. Incorporating reduced lysis into dynamics leads to a prediction of alternative stable states, which are discussed in the context of simple experiments. Finally, I explore ongoing experimental and theoretical efforts to understand how phage may optimally exploit their hosts by utilizing a variety of life history strategies.
Speaker: Matthew Onsum Title: Analysis of immune cell chemotaxis and signal integration Return to seminar page Abstract: In response to an injury, immune cells are recruited to fight off infecting microbes and clear cellular damage. A number of chemicals, called chemoattractants, are produced at or near sites of infection and inflammation and diffuse into the surrounding tissue. Immune cells sense these chemoattractants and move in the direction where their concentration is greatest, a process termed chemotaxis, and thus locate the source of the attractants and associated targets. In this talk I will present my work using mathematical modeling and experiments to understand how immune cells detect and interpret multiple chemoattractants and convert these signals into directed migration. I will conclude my talk by discussing the application of this work, and mathematical modeling in general, to the drug discovery process in the pharmaceutical industry.
Speaker: Fred Brauer Title: Epidemic models with heterogeneous mixing Return to seminar page Abstract: The classical compartmental epidemic models are too simple, because they assume homogeneous mixing of all members of the population. The modern network models are too complicated because they assume too much knowledge of the population and are too difficult to analyze. We seek something in between, starting with a population consisting of two groups with different activity levels, assuming proportionate mixing between the groups, calculating the basic reproduction number and using the final size relation to determine what the size of the epidemic would be if there were no disease deaths. We show that if the disease death rate is small, this is a good approximation. We compare numerical simulations for one - group and two - group models to examine whether the extension to more groups is worthwhile. We show how to extend to models with treatment and other compartments, more general mixing (in which case there is a final size relation even though the reproduction number can not be calculated explicitly), and more groups.
Speaker: Title: TBA Return to seminar page Abstract:
Speaker: Title: TBA Return to seminar page Abstract: