The concept of genetic relatedness, the probability that social partners share a focal genotype above and beyond chance, is fundamental to the evolution of behaviour. As a consequence, numerous species - humans included - have evolved kin recognition systems, designed to condition behaviour upon relatedness. Here, we formalize a traditional, but troubled, mechanism of kin recognition known as "phenotype matching." By linking quantitative genetics to Bayes' formula, we provide a sound theoretical foundation for phenotype matching. Following this, we show how partner information (e.g. via phenotype matching) can lead to peculiar asymmetries in the perception of relatedness that, in conjunction with concepts pertaining to the distribution of competition, can help us to understand phenomena as diverse as familial love and ethnocentrism.

Repetition is one of the core ingredients of the evolution of cooperation. In a set of papers, we explore the evolutionary dynamics in repeated games, with and without discounting, with and without complexity costs, and with and without population structure. The usual shortcut to finding asymptotically stable states in the replicator dynamics is offered by equilibria being evolutionarily stable (ESS). In repeated games, there are no equilibria that are ESS, but there are very many that are neutrally stable (NSS). That, however, does not imply asymptotic stability in the replicator dynamics. In order to characterize the dynamics, we define and apply the concept of robustness against indirect invasions (RAII). Being RAII is equivalent to being an element of a minimal ES-set, and ES-sets are asymptotically stable in the replicator dynamics. In repeated prisoners dilemmas, with or without discounting, but without complexity costs, and without population structure, we show that no strategy is RAII. That implies that all equilibria are susceptible to indirect invasions and no ES-set exists. We should therefore expect populations playing repeated games to wander from one equilibrium to the other through a series of indirect invasions. This is indeed what we find in simulations with stochastic, finite population dynamics. Population structure is another core ingredient of the evolution of cooperation. RAII helps derive a "unified" prediction for repeated prisoners dilemmas in structured populations. The prediction contains Hamilton's rule from biology and the threshold discount factor implied by the folk theorem as special cases. (Joint work with Julian Garcia, Dave Rand and Martin Nowak) The talk will include elements of a few different papers: 1) a paper about Robustness against indirect invasions (RAII) and its properties http://www.sciencedirect.com/science/article/pii/S0899825611000960 2) a working paper about plain vanilla repeated games http://www.tinbergen.nl/discussionpapers/10037.pdf 3) a working paper about repeated games with complexity costs http://www.tinbergen.nl/discussionpapers/12089.pdf 4) a paper about repeated games and population structure http://www.pnas.org/content/109/25/9929.full

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.

Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic cytoplasmic model which leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this, a dynamic computational model of the cell was developed that includes mechanics of and the interactions between the intracellular fluid, the actin cortex, the cell membrane, and the cytoskeleton. The Immersed Boundary Method is modified to account for the relative motion between the cytoskeleton and the fluid. Results show the relative importance of cytoskeletal elasticity and drag in bleb expansion dynamics and support the hypothesis that pressure equilibrates slower than the timescale of bleb expansion time.

I will present a two-phase model for the solid cytoskeleton and fluid cytosol inside crawling nematode spermatozoa. Simulations demonstrate that entropy of the cytoskeletal polymer network can generate force that drives a cell forward. The drag force exerted by cytosolic fluid also plays a significant role. Simulations also show that cytoskeletal anisotropy is required to account for the dependance of cell speed on cell shape, as observed in experiments. I am using level set methods to provide an implicit representation of cell boundaries. Data analysis includes image processing as a minimization problem, leading to an Euler-Lagrange equation. Tracking cytoskeletal features makes use of correlations.

In all multicellular organisms one can find examples where a growing tissue divides up until some final fixed cell number ( e.g. in the worm C. elegans there are just 302 neurons). In most of these examples a cell divides asymmetrically where after division the two cells inherit different types or quantities of molecules. Often after asymmetric division the cells receive further extracellular cues that regulate their growth process as well. However, is it possible to find a cell autonomous mechanism that will yield any arbitrary final population size? Here we present a minimal model based on asymmetric division and dilution of a cell-cycle regulator that can generate any final population size that might be needed. We show that within the model there are a variety of growth mechanisms from linear to non-linear that can lead to the same final cell count. Interestingly, when we include noise at division we find that there are special final cell population sizes that can be generated with high confidence that are flanked by population sizes that are less robust to division noise. When we include further noise in the division process we find that these special populations can remain relatively stable and in some cases even improve in their fidelity. The simple model has a rich behaviour which will be discussed.

This meeting will run from Thursday 17 Jan to Saturday 19 Jan, 2013. See the event website for more details

Certain organisms can survive in the most extreme of living conditions by entering anhydrobiosis, a waterless hibernative state. Lyopreservation seeks to duplicate this process in mammalian cells as an alternative to cryopreservation. If successful, lyopreserved cells could be stored indefinitely at room temperature, eliminating the need for the extreme temperatures or cryoprotectants required for cryopreservation. However, current techniques fail to produce viable cells after the drying process. The problem is believed to lie with the formation of trehalose glass. When combined with water, trehalose can form a glassy substance that is believed to provide protection and support to the cell membrane and organelles during the drying process. However, uncontrolled formation of this glass can actually hinder the drying process. Thus, an understanding of trehalose glass formation is key to developing successful and efficient lyopreservation techniques. To this end, the diffusion of water through a trehalose glass is modeled using subdiffusion. The equations and boundary conditions are derived using a continuous-time random walk and solved numerically. Additionally, the effect of drying on the cell membrane is modeled using incompressible Navier-Stokes. Numerically simulated cell shapes give insight into the effectiveness of various drying approaches.

Speaker(s): Raibatak Das (UBC) Jun Allard (UC Davis) Jesse Goyette (Oxford) Spencer Freeman (UBC) Omer Dushek (Oxford)

Leukocytes play a critical role in recognising and responding to infections and cancerous cells. Central to this role is a diverse array of cell surface receptors that do not share sequence homology but do share many other features. These receptors have multiple tyrosine residues in their cytoplasmic tails that become phosphorylated following ligand binding but these receptors lack intrinsic catalytic activity. Instead, these Non-catalytic Tyrosine-phosphorylated Receptors (NTRs) are regulated by extrinsic membrane-confined Src-family tyrosine kinases (SFKs) and protein tyrosine phosphatase receptors (PTPRs). In this talk, I will introduce NTRs as a new family of surface receptors, review their shared properties and contrast them to existing receptor families, and discuss the role(s) of multisite phosphorylation in their regulation.

Traveling waves in actin have recently been reported in many cell types. Fish keratocyte cells, which usually exhibit rapid and steady motility, exhibit traveling waves of protrusion when plated on highly adhesive surfaces. We hypothesize that waving arises from a competition between actin polymerization and mature adhesions for VASP, a protein that associates with growing actin barbed ends. We developed a mathematical model of actin protrusion coupled with membrane tension, adhesions and VASP. The model is formulated as a system of partial differential equations with a nonlocal integral term and noise. Simulations of this model lead to a number of predictions, for example, that overexpression of VASP prevents waving, but depletion of VASP does not increase the fraction of cells that wave. The model also predicts that VASP exhibits a traveling wave whose peak is out of phase with the F-actin wave. Further experiments confirmed these predictions and provided quantitative data to estimate the model parameters. We thus conclude that the waves are the result of competition between actin and adhesions for VASP, rather than a regulatory biochemical oscillator or mechanical tag-of-war. We hypothesize that this waving behavior contributes to adaptation of cell motility mechanisms in perturbed environments.

This will be an informal warm-up talk for Byron Goldstein's IAM Distinguished Colloquium on Monday, October 22nd (see http://www.iam.ubc.ca/colloq/DistinguishedColloquiumSeries.html). I will talk about some of the basics of HIV biology, antibodies, and modelling this kind of system.

I will talk about my research at the Laboratoire d'Ecologie Alpine in 2011, where I studied the coevolution of the globeflower Trollius europaeus and its specialized nursery pollinators Chiastocheta flies. These small flies feed, mate, and lay eggs on T. europaeus, and the larvae develop only on the host-plant seeds. The polination of T. europaeus is mainly carried out by Chiastocheta, since most other insects are to large to enter the flower. The interaction is therefore one of the few examples of extremely specialized reciprocal interaction. The emergence and stability of this apparent mutualism is still an open question, but my research has shown that it may have arrived unintentionally as an evolutionary trap. I will introduce a mechanistic population-genetical mean-field model, used for the numerical analysis of their coevolution. The model can be generalized to many similar multiple-species interaction systems. Reference: Louca et al. (2012), Specialized nursery pollination mutualisms as evolutionary traps stabilized by antagonistic traits, Journal of Theoretical Biology, vol 296, pp. 65-83

The presence of immune cells in breast tumors has been correlated with poor prognosis for years but it was not until recently that the role they play in promoting secondary tumors was understood. It has now been demonstrated experimentally that invasion of tumor cells into surrounding tissues and blood vessels is directly associated with immune cells. Gaining better understanding of the underlying mechanisms of this system is key in finding new targets in chemotherapy and to develop new breast cancer treatments. I will introduce a computational 3D individual cell based model that I developed to study the signaling pathway between breast cancer cells and immune cells. I will show that the model successfully reproduces results from both in vivo and in vitro experiments. A parameter sensitivity analysis has yielded insight into possible new targets in breast cancer chemotherapy.

Why do some individuals provide benefits to others at a cost to themselves? "The puzzle of altruism" has already generated thousands of studies, but the multiplicity of frameworks (game theory, kin selection, group selection) gives an overall impression of confusion. In addition, the conditions for the evolution of altruism sometimes seem to rely on artificial details, such as the "rule" (Birth-Death or Death-Birth) chosen to update the population. In this presentation, I show how going back to a mechanistic description of the process helps better understand what is really needed for the evolution of altruism, and why DB and BD are in fact symmetrical. I present a single condition for the evolution of altruism that unifies and generalizes most of the theoretical studies done in populations of fixed sizes and with additive games.

This will be an introductory talk on two approaches to studying evolutionary games on graphs. The "fixation probability" approach tracks the fate of a single, rare mutant by calculating the probability that the progeny of that mutant go on to take over the population. The "inclusive fitness" approach considers the instantaneous rate of change of the proportion of mutants in a population by evaluating the effect of the mutant behaviour on each member of the population. I will explore when these two approaches yield the same results and discuss when they differ.

My talk will culminate in a model for chemical gradient detection by migrating cells that change shape. I will first present a method for solving reaction-advection-diffusion equations inside a deforming region, with a moving boundary. The method employs a "distance map" that is constructed by storing the shortest distance to the boundary at each node on a grid. The gradient of the distance map provides a vector that points from each node to the boundary, which is a known distance away. These vectors and corresponding distances give exactly the displacements that will move nodes onto the boundary, from points nearby. This yields a structured, boundary-fitted grid that provides the basis for a finite-volume method

The diversity of form in living beings led Darwin to state that it is "enough to drive the sanest man mad". How can we describe this variety? How can we predict it? Motivated by biological observations on different scales from molecules to tissues, I will show how a combination of biological and physical experiments, mathematical models and simple computations allow us to begin to unravel the physical basis for morphogenesis.

TBA

Fragments of fish pigment cells can form and center aggregates of pigment granules by dynein-motor-driven transport along a self-organized radial array of microtubules (MTs). I will present a quantitative model that describes pigment aggregation and MT-aster self-organization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dynein-motor-covered granules have the ability to nucleate MTs. From assumptions based on experimental observations, I'll derive partial integro-differential equations describing the coupled granule-MT interaction. Analysis explains the mechanism of aster self-organization as a positive feedback loop between motor aggregation at the MT minus ends and MT nucleation by motors. Furthermore, the centering mechanism is explained as a global geometric bias in the cell established by spontaneously-nucleated microtubules. Numerical simulations lend additional support to the analysis. The model sheds light on role of polymer dynamics and polymer-motor interactions in cytoskeletal organization.

Polarization, where cells segregate specific factors to distinct domains, is a fundamental and evolutionarily conserved biological process. Polarizing cells often rely on the same toolkit of proteins and lipids, including actin, myosin, microtubules, and the Par and Rho protein families. In this talk, I will present experimental and theoretical work demonstrating the importance of Par protein oligomerization for stable spatial segregation in early embryos of C. elegans. I will discuss some current research directions in my lab, including the incorporation of Rho proteins into our theoretical and experimental frameworks.

Topics include: -Local Perturbation Analysis - Bifurcation analysis of Reaction Diffusion Equations -Bifurcation analysis using Matcont -Wave pinning and Actin Waves - Models and analysis. http://www.math.ubc.ca/~wrholmes/teaching/MCB2012/MCB2012.html

Lecture 1: Motivation | The principle of maximum likelihood | Least squares regression | Linear regression Lecture 2: Nonlinear regression | Levenberg-Marquardt algorithm | Other likelihood-maximization methods | Parameter confidence intervals Lecture 3: Bootstrap confidence intervals | Assessing differences in parameter distributions using bootstrap Lecture 4: Model selection | Bias variance trade-off | F-test | Akaike's information criterion

In order for an immune cell, such as a T-cell to do its job (kill virus infected cells) it must first undergo an activation event. Activation requires the encounter of the cell surface T-cell receptors (TCRs) with bits of protein that are displayed in special complexes (peptide-MHC complexes) on the surface of a target cell. all cells of the body display such p-MHC complexes, but in normal circumstances only those perceived as infected will be destroyed by T-cells in the process of immune surveillance. In this seminar I will describe both theoretical and experimental work aiming to understand the events that culminate in the activation of the T-cell.

May 7: Bonds, springs, dashpots and motors May 8: Biopolymer mechanics May 9: Diffusion in a potential and thermal forces May 10: Thermal forces on biopolymers May 11: Mechanics of two- and three-dimensional structures May 11: Additional topics

In this talk, I will describe a smoothed particle hydrodynamics method for simulating the motion and deformation of red blood cells. After validating the model and numerical method using the dynamics of healthy red cells in shear and channel flows, we focus on the loss of red cell deformability as a result of malaria infection. The current understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of about 3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out 3D numerical simulations of RBC stretching tests by optical tweezers to demonstrate this mechanism. Our results show that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. Thus, the previous interpretation of RBC-deformation data in terms of membrane stiffness alone is flawed. With the solid inclusion, the apparently contradictory data can be reconciled, and the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.

Dorsal closure (DC) is a tissue-modeling process in the developing Drosophila embryo during which an epidermal opening is gradually closed. Experiment results using image analysis showed oscillatory (fluctuating) behavior of tissue as well as individual cells (AS cells) that cover the opening gap. Tissue oscillates with no obvious net contraction at early stages of DC, which is followed by a gradual damping in the amplitude of oscillation after the onset of net contraction. Finally, oscillation becomes weak and undetectable as AS cells contract rapidly. These evolutions are accompanied by progressive accumulation of actomyosin network, which is proposed as intracellular ratchet that aids the DC. To explore the mechanism behind, we model the cell network by a dissipative dynamical system that couples with myosin activity to reproduce these behaviors. Different ratchet mechanisms are implemented and discussed. Qualitative comparison is carried out between numerical results and experiments for different stages of dorsal closure.

Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation. The talk will give an introduction to multi-scale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, certain aspects particularly relevant in upscaling reaction-diffusion processes in biological cells will be discussed.

Locusts exhibit two interconvertible phases, solitarious and gregarious. Solitarious (gregarious) individuals are repelled from (attracted to) others, and crowding biases conversion towards the gregarious form. We construct a nonlinear partial integrodifferential equation model of the interplay between phase change and spatial dynamics leading to the formation of locust hopper bands. Analysis of our model reveals conditions for the onset of aggregation, characterized by a large scale transition to the gregarious phase. A model reduction to ordinary differential equations describing the bulk dynamics of the two phases enables quantification of the proportion of the population that will gregarize, and of the time scale for this to occur. Numerical simulations provide descriptions of the swarm structure and reveal transiently traveling clumps of gregarious insects. This is joint work with Maria D'Orsogna, Leah Edelstein-Keshet, and Andrew Bernoff.

I will present a biologically-based mathematical model that accounts for several features of human sleep and demonstrate how particular features depend on interactions between a circadian pacemaker and a sleep homeostat. The model is made up of regions of cells that interact with each other to cause transitions between sleep and wake as well as between REM and NREM sleep. Analysis of the mathematical mechanisms in the model yields insights into potential biological mechanisms underlying sleep and sleep disorders including stress-induced insomnia and fatal familial insomnia.

We consider the aggregation equation ρt = ∇ ⋅ (ρ∇K ∗ ρ) in ℜn, where the interaction potential K models short-range singular repulsion and long-range power-law attraction. Here, ρ represents the density of the aggregation and K is a social interaction kernel that models attraction and repulsion between individuals. We show that there exist unique radially symmetric equilibria supported on a ball. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model. This work is in collaboration with Razvan Fetecau (SFU) and Theodore Kolokolnikov (Dalhousie).

The inspiration for this work comes from wanting to understand more of infectious disease agents spreading in wildlife populations. Such populations often have a metapopulation structure, where groups of individuals living in suitable habitat patches are separated from each other in space, but linked through migration. A key example we have focussed on is the great gerbil, a rodent species from Kazakhstan forming vast metapopulations, and the spread of plague in this system. In the lecture I will use the plague-great gerbil system to illustrate various aspects of thresholds and spread, touching on both theoretical and biological insights. An example of the former is a non-linear relation between persistence time in a spatial metapopulation and migration, showing an optimum for intermediate migration activity. An example of the latter is using percolation to explain the spread of plague through a metapopulation landscape of great gerbils and threshold behaviour in that system from long-term data sets, including a possible threshold for zoonotic spread to humans.

Cells and tissues rearrange under the action of chemical signals. Numerous examples are found in eggshell development, wing disc remodeling, dorsal closure, wound healing, etc. In many cases, this can be attributed to changing local mechanical properties of cytoskeleton due to motor attachment/detachment and rearrangement of the actin network triggered by signaling. I consider in more detail the action of myosin motors on nonlinear viscoelastic properties of cytoskeleton. It turns out that motors activity may either stiffen the network due to stronger prestress or soften it due to motor agitation, in accordance with experimental data. Prestress anisotropy, which may be induced by redistribution of motors triggered by either external force or a chemical signal, causes anisotropy of elastic moduli. Based on this assumption, we developed a cellular mechano-diffusive model cell that describes reshaping of the Drosophila wing disc. Similar models may be applicable to other processes where mechanics is influenced by chemical signals through the action of myosin motors.

TBA

I plan to review several applications described by delay differential equations (DDEs) starting from familiar examples such as car following models to physiology and industrial problems. DDEs have the reputation to be mathematically difficult but there is a renewed interest for both old and new problems. I’ll emphasize the need for analytical tools in order to guide our numerical simulations and identify key physical phenomena. These ideas will be illustrated by problems in nonlinear optics and neurobiology.

A crucial element for life is fertilization and for this to take place a sperm must meet an egg. The question is how does the sperm locate and swim towards the egg. Here, we consider the case of sea urchins for which fertilization is external and communication between egg and sperm is achieved by means of molecules secreted by the egg, that diffuse to the sperm. Once they reach the sperm they attach to its flagellum and trigger a biochemical signaling pathway that produces oscillations in the internal calcium concentration. These fluctuations are known to reorient the sperm navigation. Our main concern is to increase our understanding of this activation process. We achieve this by means of a network model with linked nodes representing the pathway elements and their interactions. In our approach nodes take discrete values and time evolution is dictated by regulatory tables. With this logical network we have been able to identify unforeseen elements for the regulation of the onset and periodicity of the calcium oscillations, which we have corroborated experimentally. These time evolution characteristics affect sperm navigation properties such as the presence or absence of chemotaxis. Our study also reveals that the network dynamics operates in a critical regime, this meaning that it strikes a balance between evolvability and robustness, a condition that favors the adaptation to different environments and that has probably been achieved throughout evolution. Our work hence provides a new instance for the proposition that life takes place at criticality.

TBA

The immune response involves cells of various types, including B, T and Natural Killer (NK) lymphocytes expressing a large diversity of receptors which recognize foreign antigens and self-molecules. The various cell types interact through a complicated network of communication and regulation mechanisms. These interactions enable the immune system to perform the functions of danger recognition, decision, action, memory and learning. As a result, the dynamics of lymphocyte repertoires are highly complex and non-linear. The humoral (antibody-generating) immune response is one of the most complex responses, as it involves somatic hypermutation of the B cell receptor (BCR) genes and subsequent antigen-driven selection of the resulting mutants. This process has been and still is extensively studied using a variety of experimental methods, ranging from intravital imaging to studying the mutations in BCR genes, and has also been one of the most often modeled phenomena in the theoretical immunology community. The problem for modelers, however, is that until recently kinetic data on the humoral immune response were so limited that all models could fit those data. We have addressed this and the challenge of following individual clones by combining modeling with a novel immunoinformatical method of generation and quantification of lineage trees from B cell clones undergoing somatic hypermutation. We applied these new analyses to the study of humoral response changes in aging, chronic or autoimmune diseases and B cell malignancies. Finally, we used simulations to answer some theoretical questions regarding the evolution of BCR genes.

Tuberculosis (TB) granulomas are organized collections of immune cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro‐inflammatory cytokine, tumor necrosis factor‐α (TNF). We have developed a multi‐scale computational model that includes molecular, cellular and tissue scale events that occur during TB granuloma formation. At the molecular scale, we focus on TNF. TNF receptor internalization kinetics are predicted to play a critical role in infection outcome, controlling whether there is clearance of bacteria, excessive inflammation, containment of bacteria in a stable granuloma, or uncontrolled growth of bacteria. Our results suggest that there is an inter‐play between TNF and bacterial levels in a granuloma that is controlled by the combined effects of both molecular and cellular scale processes. We also use the model to explain what mechanisms lead to differential effects of TNF-neutralizing drugs (generally used to treat anti-inflammatory diseases) on reactivation of TB. Ultimately, these results can help to elaborate relevant features of the immune response to Mtb infection, identifying new strategies for therapy and prevention.

Since the historic first applications of the “standard model of viral dynamics” in 1994, mathematical modelling has been shifting paradigms about the HIV infection by identifying unexpected mechanisms behind observed patterns. The aim of our group is to take advantage of the already accumulated experimental results to test the validity of accepted explanations and theories, by formulating corresponding mathematical models and comparing the predictions to existing experimental findings. If none of the existing theories proves acceptable, we seek to formulate a satisfactory alternative model. Our simple models, so far based on ordinary differential equations, do not aspire to contain all factors influencing the course of infection, but aim to identify the main, necessary or sufficient mechanisms and offer testable predictions. I shall present the results of several of our modelling studies, which have led to novel insights in viral escape and reversion, effects of vaccination, early prediction of disease outcome, different dynamics of infection in blood and mucosal tissues, and the role of immune activation for differences in pathogenesis in humans and “natural hosts”.

Dr. Sinha's talk will cover both genome analysis of pathogens (HIV-1 in particular), SIR type models, and statistical modelling of disease prevalence data (of Malaria).

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, new jury decision-making experiments are developed. The results of these experiments are used to compare the quantum model to the belief-adjustment model and suggest that the belief-adjustment model faces limitations whereas the quantum inference model does not.

Recent developments have revealed that, by means of the inclusive fitness theory, the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. However, understanding the inclusive fitness theory requires a deep intuition and hence mathematically explicit expression of the theory is required. We provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. We show that key concepts of the theory, such as fitness, relatedness and inclusive fitness, are all derived from the probability distribution of an "offspring-to-parent map" in a straightforward manner. We prove theorems showing that inclusive fitness provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in Wright's island model. We also show the existence of the critical mutation rate, that does not depend on the number of islands, below which a positive dispersal rate evolves.

Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in formation of various dynamical patterns. Examples of these patterns include fruiting bodies - aggregates in which tens of thousands of bacteria self-organize to sporulate under starvation conditions and ripples - dynamical bacterial density waves propagating through the colony during predation. Relating these complex self-organization patterns in M. xanthus swarms to motility of individual cells is a complex-reverse engineering problem that cannot be solved solely by traditional experimental research. Our group addresses this problem with a complementary approach - a combination of biostatistical image quantification of the experimental data with agent-based modeling. To illustrate our approach we discuss our methods of modeling predatory traveling waves - ripples, quantifying emergent order in developmental aggregation under starvation conditions and discovering features that affect the aggregation dynamics.

What dynamic processes are responsible for the development of complex body plans? I will approach this from a chemical perspective, looking at what types of dynamics can form spatial concentration patterns. I will discuss two areas in which we are exploring the conditions for chemical patterning in development. At the fine scale, stochastic modelling of gene regulation in early fruit fly embryos shows the degree to which self-feedback can limit noise in protein patterns - a key component for reliable development. At a broader scale, plants are continuously growing over their life cycles, and here we are looking at how the interaction of chemical pattern (3D reaction-diffusion modelling) and domain growth can create the shapes of plants.

The atmosphere and the oceans are the two largest and most important global commons. No one has a strong individual economic incentive to protect and preserve these vital resources. Indeed, quite the opposite! Present discussions centre mainly around human impacts on the environment (global warming), or on the oceans (oil spills), with little recognition that these systems are intricately interwoven. In this talk I will briefly describe some aspects of atmosphere-ocean coupling.

Humans are currently jeopardizing the other species in life's fabric and potentially our own future due to our overuse of common resources. Over the last two decades, a large effort has focused on trying to persuade individuals to consume differently. These conservation efforts largely appeal to guilt - an individual's willingness to do the right thing. What about the role of shame in solving the tragedy of the commons? I will explore the differences between guilt and shame and then present results from a recent public goods experiment conducted with Christoph Hauert and others that tests the effects of shame on cooperation. I will also examine our findings in the context of shame's real world applications and concerns.

Efforts to control the Mountain Pine Beetle infestation in British Columbia and Alberta include large-scale landscape manipulations such as clearcutting, and cost-intensive techniques such as green attack tree removal. Unfortunately, it is unclear just how effective these techniques are in practice. In order to determine and predict the effectiveness of various management strategies, we need to understand how MPB disperse through heterogeneous habitat, where heterogeneity is measured in terms of species composition and tree density on the landscape. In this talk I will present a spatially-explicit hybrid model for the Mountain Pine Beetle (MPB) dispersal and reproduction. The model is composed of reaction-diffusion-chemotaxis PDEs for the beetle flight period and discrete equations for the overwintering stage. Forest management activities are also included in the model. I will discuss the formation of beetle attack patterns and the impacts of management in the PDE model.

This presentation starts with a quick epidemiological overview that puts emphasis on neglected diseases and health disparities in the context of developing and/or poor nations. The primary emphasis is however on Tuberculosis (TB). A review of mathematical models and results on issues related to the transmission dynamics and control of TB, under various degrees of complexity is provided. The presentation continues with a discussion on the relationship between urban growth and TB decline in the USA. The observations are supported using demographic and TB epidemiological time series that capture the observed patterns of disease prevalence in growing urban centers in the States of Massachusetts and a large aggregate of cities in the USA, over a long window in time.

Cooperation has been often studied in the framework of evolutionary game theory. Usually each player adopts a single strategy against everyone: cooperation or defection. But humans can discriminate and adopt different strategies against different opponents. In this talk I am going to present some analytical and simulational results for the case where the players can distinguish the opponents and, in the second part, I am going to talk about the extension of these ideas that has been developed jointly with prof. Christoph Hauert.

Tuberculosis is a very widespread disease; about one third of the world's population is infected at any given time although most will not develop symptoms or transmit infection. It is a curable disease but kills more than a million people annually, most in Africa. It has a very complicated compartmental structure, and models are complicated. We describe some of the models that have been formulated and suggest, but do not carry out, methods for analyzing them. The analyses are left as exercises.

Most tissues are hierarchically organized into lineages, which are sets of progenitor-progeny relationships where the cells differ progressively in their character due to differentiation. It is increasingly recognized that lineage progression occurs in solid tumors. In this talk, we develop a multispecies continuum model to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages and lead to the development of heterogenous cell distributions and formation of niche-like environments for stem cells. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression, the development of morphological instability, and response to treatment.

I will provide an overview of recent modeling work on acute HIV infection stimulated by new experimental findings. I will discuss new deterministic models that incorporate a time-varying infectivity parameter. I will also discuss stochastic models of early infection and show how one can compute the probability of the infection going extinct. Alternatively, when the infection "takes" the model allows one to compute the delay from time virus enters to the time of appearance of detectable viremia. Unlike deterministic (ODE) models the stochastic model has different formulations depending upon whether virus production occurs continuously or if it occurs in a burst at the end of an infected cell's lifespan. Both will be dicussed.

Animal cells crawl on surfaces using the lamellipod, a flat dynamic network of actin polymers enveloped by the cell membrane. Recent experiments showed that the cell geometry is correlated with speed and with actin dynamics. I will present mathematical models of actin network self-organization and viscoelastic flow explaining these observations. According to this model, a force balance between membrane tension, pushing actin network and centripetal myosin-powered contraction of this network can explain the cell shape and motility. In addition, I will discuss Darci flow of cytoplasm and its role in the cell movements.

Reproduction in mammals is controlled by the pulsatile release of gonadotropin-releasing hormone (GnRH). About 800~2000 GnRH neurons participate in the generation of GnRH pulses. Their cell bodies are distributed in a scattered manner in designated areas of the hypothalamus. Although several experimental models including cultured hypothalamic tissues, placode-derived GnRH neurons, and GT1 cell lines have been developed and studied, a mechanistic explanation for the origin of GnRH pulsatility remains elusive. One major obstacle is identifying the mechanism for synchronizing scattered neurons. This talk is aimed at studying the viability of autocrine regulation in synchronizing GnRH neurons using mathematical models describing diffusely distributed GnRH neurons in two-dimensional space. The models discussed here are developed based on experiments in GT1 cells as well as hypothalamic neurons in culture. These experiments revealed that GnRH neurons express GnRH receptors that allow GnRH to regulate its own secretion through an autocrine effect. GnRH binding to its receptors on GnRH neurons triggers the activation of three types of G-proteins of which two activates and one inhibits GnRH secretion (Krsmanovic et al, 2003, PNAS 100:2969). These observations suggest GnRH secreted by GnRH neurons serve as a diffusive mediator as well as an autocrine regulator. A mathematical model has been developed (Khadra-Li, 2006, Biophys. J. 91:74) and its robustness and potential applicability to GnRH neurons in vivo investigated (Li-Khadra, 2008, BMB 70:2103). In this talk, I will introduce some key experimental and modeling results of this rhythm-generating system, focusing on the effects of intracellular distance, rate of hormone secretion, and spatial distribution on the ability of diffusely distributed GnRH neurons to synchronize through autocrine regulation. Based on the modeling results, one plausible explanation for why GnRH neurons are distributed in a scattered manner is proposed. (Results presented in here are based on works in collaboration with Anmar Khadra, Atsushi Yokoyama, and Patrick Fletcher.)

We present a computational platform for the simplified Mammalian Cochlea with the standard coupled fluid-plate equations as a base. Physiological data shows a clear wave nature in the response of the basilar membrane to stimulus. We explain the presence of this wave nature and use it as inspiration for a 3D numerical solver. Additionally, a parallel asymptotic model with simulations is presented and qualitatively validated. Results from these models are used to propose relationships between mechanical properties of the cochlea and observed function. In one such case, results are compared with physiological data.

Polarization occurs when cells segregate specific proteins and other factors to opposite ends of the cell in response to some signal. A cell with a symmetric distribution of proteins must have a symmetry breaking event in order to become polarized, resulting in a stable asymmetric protein distribution. In this informal talk, I will discuss possible mechanisms used by embryos of the nematode worm C. elegans to initiate the process of polarization, including new experimental evidence produced this summer.

TBA

Somitogenesis is a process for the development of somites which are transient, segmental structures that lie along the anterior-posterior axis of vertebrate embryos. The pattern of somites is traced out by the ``segmentation clock genes" which undergo synchronous oscillation over adjacent cells. In this presentation, we analyze the dynamics for a model on zebrafish segmentation clock-genes which are subject to direct autorepression by their own products under time delay, and cell-to-cell interaction through Delta-Notch signaling. For this system of delayed equations, we present an ingenious iteration approach to derive the global synchronization and global convergence to the unique synchronous equilibrium. On the other hand, by applying the delay Hopf bifurcation theory and the method of normal form, we derive the criteria for the existence of stable synchronous oscillations. Our analysis provides the basic range of parameters and delay magnitudes for stable synchronous, asynchronous oscillation, and oscillation-arrested dynamics. Based on the derived criteria, further numerical findings on the dynamics which are linked to the biological phenomena are explored for the considered system.

Probably the most thoroughly studied mechanism that can explain the evolution and maintenance of costly cooperation among selfish individual is population structure. In the past years, hundreds of papers have mathematically modeled how cooperation can emerge under various dynamical rules and in more and more complex population structures [1,2]. However, so far there is a significant lack of experimental data in this field. Milinski et al. have conducted an experimental test to address how humans are playing a particularly simple spatial game on a regular lattice [2]. The data shows that the way humans choose strategies is different from the usual assumptions of theoretical models. Most importantly, spontaneous strategy changes corresponding to mutations or exploration behavior is more frequent than assumed in many models. This can strongly affect evolutionary dynamics [4] and decrease the influence of some spatial structures.
This experimental approach to measure properties of the update mechanisms used in theoretical models may be useful for mathematical models of evolutionary games in structured populations.

[1] Ohtsuki, Hauert, Lieberman, and Nowak, Nature (2006)
[1] Szabo and Fath, Evolutionary games on graphs, Physics Reports (2007)
[3] Traulsen, Semmann, Sommerfeld, Krambeck, and Milinski, PNAS (2010)
[4] Traulsen, Hauert, De Silva, Nowak, and Sigmund, PNAS (2009)

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Mathematical models of infectious disease dynamics have helped to advance our basic understanding of the epidemiology and pathogenesis of some diseases. Models have been used to predict the impact of prevention efforts or to assess host-pathogen mechanisms. Efforts are currently underway to develop both pre-exposure and post-exposure vaccines for several viral infections, including Human Immunodeficiency Virus type 1 (HIV-1) and Herpes Simplex Virus type 2 (HSV-2). In this talk, I will present models of vaccination strategies for these viral infections. Results using deterministic models of the HSV-2 epidemic showed that imperfect vaccines could reduce new infections, but vaccines providing therapeutic benefits that do not lower transmission are likely to have little impact on epidemic control. For HIV-1 infection, I will show a stochastic model of viral mutation and the immune response that reproduces phenomena seen in clinical data; such a model can be used to predict conditions under which a vaccine would be most effective. These studies are potentially useful to guide future strategies for the development of vaccines and other preventative or therapeutic interventions.

Microtubules are intracellular polymers that dynamically grow and shorten at their ends via the stochastic addition and loss of αβ-tubulin heterodimers, a highly regulated process that underlies many fundamental cellular processes, including chromosome segregation and cell polarization. Previously, the rates of tubulin subunit exchange at the ends of growing microtubules have been estimated using a 1D linear growth theory, which assumes that tubulin dissociation occurs at a constant rate regardless of the free subunit concentration. We now find via 2D molecular-level simulations that the tubulin dissociation rate during microtubule growth is not expected to be constant, but rather will increase with increasing free subunit concentration. This effect is due to a concentration-dependent bias in simulated microtubule tip structures, as has been experimentally observed. As a consequence, we predict theoretically that the published subunit addition and loss rates at growing microtubule ends in vitro have been consistently underestimated in the literature by an order-of-magnitude. We then test this prediction experimentally via TIRF-microscopy and via a laser-tweezers assay with near-molecular resolution, and find that the variance in the assembly rate in vitro is too high to be consistent with the previous low kinetic rate estimates. In contrast, the 2D model, with kinetic rates that are an order-of-magnitude higher than the 1D model kinetic rates, quantitatively predicts a priori the variance and its concentration dependence. We conclude that net assembly is the result of a relatively small difference between large rates of subunit addition and loss, both of which occur at near-kHz rates, far faster than previously believed. More generally, our theoretical analysis demonstrates that the fixed off rate originally used in the 1D model of Oosawa, and assumed in most subsequent models, is problematic for self-assembled polymers having both lateral and longitudinal bonding interactions between subunits. Our results imply a major revision of how microtubule assembly is likely regulated in vivo.

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Two topics will covered in this talk. The first part concerns the dynamics of coupled excitable FitzHugh-Nagumo elements in the presence of noise, which is used to model the frequency variations in beating cardiac cultures. As the coupling strength increases, the frequency increases with a peak which is associated with the synchronization of the elements. The physical mechanism of frequency enhancement is due to the variation of the potential barrier for firing as the coupling changes and can be estimated by Kramer's escape rate theory which shows good agreement with simulations. The second part is about waves in phase coupled excitable medium. The corresponding phase diagrams for stable plane waves and spiral waves are obtained by simulations. This discrete model corresponds to an excitable medium with zero-refractoriness and in the continuum limit supports zero-core spiral waves.

POSTPONED! NEW DATE TBA. An environment contains distinct groups of individuals, where individuals are either Cooperators or Defectors. Individuals propagate asexually within their groups, and groups propagate by fissioning. A discrete stochastic model of the population dynamics of groups and individuals is proposed, and then a continuous deterministic model is derived from the stochastic model. The continuous deterministic model takes the form of a PDE, where the partial derivative terms correspond to individual population dynamics and the other terms correspond to group level dynamics. The equations can be solved to obtain evolutionary trajectories and equilibrium configurations. An example based on hunter-gatherer tribes will illustrate the techniques.

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Infectious agents play a significant role in the etiology of several cancers. Notable examples are the increase of cervical cancer risk due to Human Papillomavirus infection (HPV), and the association of gastric cancer risk with the colonization of the gut by Helicobacter pylori. In many cases, although the association between an infectious disease and cancer is well established, the biological mechanisms are not completely understood. A new methodology designed to i) study the mechanisms by which infectious agents cause cancer and ii) predict the the impact of infectious disease dynamics on future cancer trends will be presented. This framework couples traditional mathematical models of infectious disease dynamics with stochastic models of carcinogenesis, therefore capturing the time-scales of both disease processes adequately. Some examples will be discussed.

We seek to build a computational model for the simplified Mammalian Cochlea with the standard coupled fluid-plate equations as our base. Physiological data shows a clear wave nature in the response of the basilar membrane to stimulus. We seek to explain the presence of this wave nature and use it as inspiration for a 3D numerical solver. The results of simulations along with asymptotic arguments suggest a relationship between the form and function of the cochlea which we compare to physiological data.

Essentially all cellular processes depend on spatially localized proteins. Some proteins localize to cell poles, others to the particular cell membranes, and yet others to specific cytoplasmic regions. This localization is often dynamic, with proteins shuttling between different regions. The Smoldyn biochemical simulator helps researchers study this intracellular organization; Smoldyn represents each protein as an individual point-like particle that diffuses, reacts, and interacts with membranes, all in continuous space. It was surprisingly difficult to make these processes quantitative, such as for finding the "binding radius" for bimolecular reactions and the adsorption probability for molecules that adsorb to membranes. Smoldyn has enabled a variety of research projects over the last several years. In one example, Smoldyn simulations showed that yeast cells appear to secrete a protease (called Bar1) which degrades extracellular pheromone so that, paradoxically, they can sense the pheromone gradient more accurately. This helps cells improve their mating success.

The emergence of novel infectious diseases has become a major public health concern, with zoonotic diseases such as avian and swine flu providing prominent examples. Although initially poorly adapted to their new host, such pathogens have the potential to adapt over the course of a chain of transmissions and thus may cause a major epidemic. In this talk, I will present a branching process model of the between-host spread of an evolving pathogen. This stochastic model allows us to address the probability of events such as evolutionary steps and major epidemics, and identify risk factors influencing these probabilities.

I will begin by reviewing single-type branching processes as applied to disease spread, and then introduce a multi-type process that can capture several strains of pathogen which may arise. Through a fairly general framework, we can investigate the impact of contact distribution in the host population and of the mutational pathway(s) among pathogen strains on the probability of pathogen emergence (adaptation and non-extinction). Time permitting, I will also present preliminary results on the probability of specific strains arising and the distribution of time to extinction or evolution.

In animal cells, a "bleb" is a balloon-like protrusion of the plasma membrane that forms when the membrane separates from the underlying cytoskeletal network and is pushed outward by pressure-driven cytosol. The protrusion later retracts due to the formation and subsequent myosin-II driven contraction of a new actin cortex within the bleb. Blebs are one of a number of cell motility mechanisms and they also play a key role in apoptosis and mitosis.

We have developed a computational model of this phenomenon. This two-dimensional fluid-structure interaction model includes the motion of the actin filaments, the actin and myosin monomer concentrations, the plasma membrane, and the cytosol. The membrane is modeled by a damped wave equation with a strain-dependent elasticity modulus. The cytosol is modeled by Stokes flow and the protein concentrations are modeled via advection-diffusion equations. The cytoskeleton is represented by a set of filaments each governed by Hooke?s law. This discrete representation is a departure from the commonly utilized notion of treating the cytoskeleton as a continuum. A volume constraint is also included in the model to maintain the overall cell volume at a constant value. The simulation is carried out via an operator splitting procedure where the components of the model interact through external forces and boundary conditions.

However, the cytoskeleton is a dynamic structure whose overall mechanical properties change due to underlying biochemical reactions and thus exhibits non-equilibrium behavior. In particular, the stiffness of the filaments in the above model are coarse-grained representations of the microscopic actin network. I will present preliminary results on coupling the time evolution of coarse-grained and microscopic descriptions by statistical sampling of the dynamics of the cytoskeletal network.

The energy metabolism is a tight regulated system providing energy for the organism. Dysfunctions in this system lead to pathologies like obesity or diabetes. The new Selfish Brain theory treats the brain as the main controller of the energy metabolism. Mathematical models are able to describe and analyze this system. Quantifying parameter values by comparing the model with real world data is an classical inverse problem. Additionally, in biological and medical disciplines the choice of the design of an experiment (e.g when and how often should data be measured) is most important to recover model parameter. The strong interplay between the accuracy of the results and efficiency of experiment need to be considered carefully. Here, I will present the general framework of computational methods for ordinary differential equations, optimization, parameter estimation, and optimal experimental design and apply these methods to target the questions arising from the energy metabolism.

Biological aggregations such as insect swarms, bird flocks, and fish schools are arguably some of the most common and least understood patterns in nature. In this talk, I will discuss recent work on swarming models, focusing on the connection between inter-organism social interactions and properties of macroscopic swarm patterns. The first model is a conservation-type partial integrodifferential equation (PIDE). Social interactions of incompressible form lead to vortex-like swarms. The second model is a high-dimensional ODE description of locust groups. The statistical-mechanical properties of the attractive-repulsive social interaction potential control whether or not individuals form a rolling migratory swarm pattern similar to those observed in nature. For the third model, we again return to a conservation-type PIDE and, via long- and short-wave analysis, determine general conditions that social interactions must satisfy for the population to asymptotically spread, contract, or reach steady state.

Subcellular oscillations of Min proteins within individual cells of E. coli serve to localize division to midcell. While significant progress has been made to understand the Min oscillation both experimentally and in modeling, I will present three outstanding Min mysteries. I will also present our ongoing work to develop generic submodels of the Min oscillation, and to systematically manipulate the Min oscillation experimentally. In particular, we find that the period of the Min oscillation responds dramatically to temperature and to the concentration of extracellular multivalent cations (including antimicrobial peptides).

In Africa the HPAI H5N1 ("birdflu") virus was first detected in Northern Nigeria in early 2006, and since then in 10 other African countries. In this talk, I will describe how we relocated a high-tech laboratory from Luxembourg to the African countryside, where we worked with local scientists to track and characterize this disease.

Within days of the first report that H5N1 had reached the African continent, we received a request from FAO and the University of Ibadan, Nigeria to help set up a laboratory to detect this deadly virus. Within 1 week we had flown a ton of specialized biosafety equipment to Lagos; 1 week later the laboratory was operational.

The first incursion of H5N1 happened in the North of the country, leading to Government containment measures. However, preliminary tests from the South were also positive, necessitating culling of poultry farms vital to the economy. Despite containment measures, the virus had apparently jumped more then 1000 km to the South! In my talk, I will describe how our team discovered genetic evidence for three independent introductions of the virus, and what this implies about its mode of transmission. These 3 strains have later been found in a number of African countries, continuing to threaten the human population as well as the economy of the African poultry industry.

The Min system in E.coli -- a group of three interacting proteins playing a role in cell division -- has attracted a lot of attention by modellers, some claiming it to be the 'measurement stick' in the rod-shaped bacterium. Different models have been proposed to explain the observed dynamical patterns -- oscillations, standing and travelling waves. Here, we will focus on a simple polymerisation/depolymerisation model. The model provides an interesting example of a stochastic hybrid dynamical system and we use probabilistic maps to compute probability distributions of experimentally accessible quantities. As a step towards model discrimination I will report on experiments we conducted on GFP-labelled E.coli.

TBA

The simplest models of population genetics, useful as they are in analyzing data, often have obvious shortcomings. Such models might ignore the effects of natural selection, mutation, or, as we will be concerned with in this talk, geography and migration. We will briefly look at the Wright-Fisher model of evolution of a single population; then, we will look at a so-called stepping stone model, where instead of a single population living all in one place, we model several populations living on discrete islands, with migration between the islands. It is often useful to consider these models' associated dual processes, which correspond to tracing the lineages of a current-day sample backwards through history. We will discuss these dual processes as well.

We will then discuss two models of evolution with *continuous* geography. Unlike the previous models, which describe directly the dynamics of a population evolving as time moves forward, the continuous geography models are instead defined in terms of prescribed dual processes. Time permitting, we will also discuss some properties of these models, such as continuity.

This is joint work with Steve Evans.

This talk presents some coherent though incomplete conjectures for the emergence, replication and abundance of some chemical structures found in each prokaryote, with special emphasis on the trines and the rRNA filaments that constitute a large part of the ribosomes.

In addition to the consideration of the data, two guiding principles for the formulation of these conjectures are Occam's razor, and the idea of uniformitarianism introduced with great success by the geologists of the 19th century. These ideas, aided by the empirical data, suggest that the abundance of the relevant cell structures should be regarded as a clue for their emergence. Also, in this talk, the distinction between the purines and the pyridines is emphasized, while distinguishing each purine (or each pyrimidine) from the others is often ignored; and the conjectures advanced in this talk also suggest some experiments that may justify or falsify their ideas.

Nonlinear dynamical systems are prevalent in systems biology, where they are often used to represent a biological system. Its dynamical behaviour is often impossible to understand by intuition alone without such mathematical models. Ideas and methods from systems and control engineering can help us to understand how the pathway architecture and parameter choices produce the desired performance and robustness in the observed dynamics. In this talk, we first show the direct interaction of a theoretical analysis with efficiently setting up experiments. We present the application of tools from engineering for designing biological experiments to elucidate the signalling pathway in the chemotactic system of /Rhodobacter sphaeroides/. In the second part, we focus on the problem of finding experimental setups that allow for full state observability and parameter identifiability of a nonlinear dynamical system; that is, whether the values of system states and parameters can be deduced from output data (experimental observations). This is an important question to answer as often observability and identifiability are assumed, which might lead to costly repetitions of experiments. We present a novel approach to check a priori for parameter identifiability and use new, state of the art computational tools for the implementation. Examples from biology are used to illustrate our method.

Weakly electric fish are fascinating animals that have evolved an electric sense that blends aspects of our senses of touch, vision and audition. Much is known about the relatively simple (compared to higher mammals) circuitry of their brains, the kinds of stimuli they respond to and their social communications/interactions. They are particularly well-suited to study principles of neural encoding and decoding because of the availability of electrophysiological recordings at many successive processing stations, enabling mathematical modeling of information transfer between stations. This talk will review past and current research on this topic from the experimental-theoretical collaboration of Len Maler, John Lewis and Andre Longtin at the University of Ottawa. We will focus especially on the role of feedback and how it interacts with stochastic spatio-temporal stimuli to induce oscillatory neural activity.

The basic reproductive number, R_0, which is generally defined as the expected number of secondary infections per primary case in a totally susceptible population, is an important epidemiological quantity. It helps us to understand the possible outcome of an initial infection seeding in a social setting: whether it leads to a small outbreak, or it evolves into a large-scale epidemic. The basic reproductive number encapsulates the information about the biology of disease transmission as well as the structure of human social contacts. We use concepts from network theory to present a novel method for estimating the value of the basic reproductive number during the early stage of an outbreak. This approach will greatly enhance our ability to reliably estimate the level of threat caused by an emerging infectious disease.

Social learning is an important ability seen in a wide range of animals. Especially, humans developed the advanced social learning ability such as language, which triggered rapid cultural evolution. On the other hand, many species, such as viruses, rely on genetic evolution to adapt to environmental fluctuations. Here we propose an evolutionary game model of competition among three strategies; social learning, individual learning, and genetic determination of behavior. We identify the condition for learning strategies to evolve.

Breathing is an interesting and essential life-sustaining behavior for humans and all mammals. Like many rhythmic motor behaviors, breathing movements originate due to neural rhythms that emanate from a central pattern generator (CPG) network. CPGs produce neural-motor rhythms that often depend on specialized pacemaker neurons or alternating synaptic inhibition. But conventional models cannot explain rhythmogenesis in the respiratory preBötzinger Complex (preBötC), the principal central pattern generator for inspiratory breathing movements, in which rhythms persist under experimental blockade of synaptic inhibition and of intrinsic pacemaker currents. Using mathematical models and experimental tests, here we demonstrate an unconventional mechanism in which metabotropic synapses and synaptic disfacilitation play key rhythmogenic roles: recurrent excitation triggers Ca2+-activated nonspecific cation current (ICAN), which initiates the inspiratory burst. Robust depolarization due to ICAN also causes voltage-dependent spike inactivation, which diminishes recurrent excitation, allowing outward currents such as Na/K ATPase pumps and K+ channels to terminate the burst and cause a transient quiescent state in the network. After a recovery period, sporadic spiking activity rekindles excitatory interactions and thus starts a new cycle. Because synaptic inputs gate postsynaptic burst-generating conductances, this rhythm-generating mechanism represents a new paradigm in which the basic rhythmogenic unit encompasses a fully inter-dependent ensemble of synaptic and intrinsic components.