






Mathematical Biology and related seminars 

April, 2014
Thursday, April 17  Rebecca Tyson  3:00 pm in ? UBCO   The effect of extreme temperature events on developmental dynamics 
Thursday, April 3  John Stockie  3:00 pm in ESB 2012 SFU Math   Mathematical modelling of sap flow in maple trees 
 Abstract  
 The flow of sap in trees is such a common everyday phenomenon that it
is hard to believe that there is a lack of understanding in several
fundamental aspects of sap flow. This talk will demonstrate the role
that mathematics can play in dealing with the complex coupled physics
that govern sap flow in trees. More specifically, I will explain how
an improved understanding of fundamental aspects of sap flow in sugar
maple trees (Acer saccharum) can be applied to answer pressing
questions in the maple syrup industry.
This talk will focus on two mathematical modelling efforts. The first
aims to develop a macroscopic model for sap flow and heat transport in a
tree during the growing season when sap flow is driven by the process of
"transpiration". The tree is treated as an anisotropic porous medium
through which sap flow is driven by a given transpiration flux, and heat
transport is driven by daily variations in ambient temperature and solar
radiation.
The second project aims to explain the phenomenon of "sap exudation", in
which sugar maple (and a few related species) generate a positive stem
pressure during the spring thaw in the absence of leaves. Many
(bio)physical mechanisms have been proposed over the past century to
explain this phenomenon, yet there remains a great deal of controversy
over the precise mechanism driving sap exudation. We consider the
prevailing hypothesis due to Milburn and O'Malley that treats sap as a
twophase (gas/liquid) mixture whose dynamics are governed by the
combined effects of porous media flow, freezing/thawing, gas
dissolution, and osmotic pressure. We develop a nonlinear system of
differential equations that captures these effects at the cellular
scale, and we demonstrate through a combination of analytical and
numerical methods that the model is capable of reproducing qualitatively
many of the behaviours observed in maple trees. 
March, 2014
Thursday, March 20  Ignacio Rozada  3:00 pm in ESB 2012 BC Centre for Excellence in HIV/AIDS   Getting rid of Hepatitis C for good: Modelling the effect of a test and treat strategy for HCV prevention in British Columbia. 
Thursday, March 6  Joe Yuichiro Wakano  3:00 pm in ESB 2012 Meji Institute for Advanced Study of Mathematical Sciences   Evolutionary branching in demestructured populations 
 Abstract  
 Adaptive dynamics demonstrates that 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.” Evolutionary branching in spatial models such as island or metapopulation models is still not completely understood. One summary statistics representing the effect of population structure on selection is relatedness. It is thus expected that the branching condition can be described in terms of relatedness coefficients in combination with disruptive selection intensity. Here, by constructing a model of the trait variance dynamics in the population, we obtain such an analytic prediction for the criteria of evolutionary branching in a demestructured population. As an application of our theory, we evaluate the threshold migration rate below which evolutionary branching cannot occur in a pairwise interaction game. This agrees very well with the individualbased simulation results. 
February, 2014
Thursday, February 27  Jaroslav Ispolatov  3:00 pm in ESB 2012   Chaos and Unpredictability in Evolution 
Thursday, February 6  Nilima Nigam  3:00 pm in ESB 2012 SFU Math   A mathematical model of bone remodeling at the cellular level 
 Abstract  
 In this talk, we quickly review the physiological process of bone remodeling and some key characteristics of the process at the cellular level. We then construct a mathematical model which accounts for some of the observed features. We describe the (difficult) process of parameter estimation, and present some computational results. This is joint work with Prof. Svetlana Komarova (McGill) and Dr. Marc Ryser (Duke). We end by describing refinements and extensions of the model, including a model of bone metastasis. This latter work is by Prof. Komarova and Ryser. 
January, 2014
Thursday, January 30  Hildur Knutsdottir and Josh Scurll  3:00 pm in ESB 2012 UBC Math   Developing a personalized, adaptive treatment strategy for nonsmall cell lung cancer (NSCLC) 
Thursday, January 23  Carlos Castillo Chavez  3:00 pm in ESB 2012 Arizona State University   Behavior, Dispersal and Epidemics: A Challenging Frontier 
 Abstract  
 Persontoperson contacts drive human disease dynamics and managing epidemics has begun to focus on motivating people, via social distancing policies that alter behaviors aimed at reducing contacts and disease risk. However, individuals value such contacts and are willing to accept some disease risk to gain contactrelated benefits.
Epidemiological–economic model of disease dynamics that explicitly model the tradeoffs that drive personto person contact decisions need to be systematically developed. Preliminary results ((Adaptive human behavior in epidemiological models, PNAS 2011, Fenichel et al.) show, not surprisingly, that including adaptive human behavior significantly changes the course of epidemics a result with implications for parameter estimation and interpretation as well as for the development of social distancing policies. Acknowledging adaptive behavior requires a shift in thinking about epidemiological processes and parameters.
The cost–benefit tradeoffs that shape contact behavior and its dynamics are implicitly incorporated in epidemiological models making it difficulty to parse out the effects of adaptive behavior. We revisit and apply unpublished theoretical results by S.P. Blythe, the late K. Cooke and CastilloChavez (Steve Blythe, Kenneth Cooke and CastilloChavez) to the study of the impact of individuals’ adaptive responses to epidemics that account for epidemiological and economic factors. The resulting generalized SIR framework supports multiple equilibria and oscillatory epidemiological dynamics. Its analysis facilitates the study of disease dynamics as a complex adaptive system (Morin et al. 2013, RMA).
In this lecture, I will discuss multiple approaches for incorporating the role of behavior; highlight some preliminary results from Blythe et al (1991), E. Diaz (2011), Fenichel et al (2011) and Morin et al. (2013) and Yun Kang and CCC (2012, 2014) 
Monday, January 20  Carlos Castillo Chavez  3:00 pm in LSK 460 Arizona State   Computational and Theoretical Epidemiology: Challenges and Opportunities 
 Abstract  
 The marriage of mathematics and epidemics has a long and distinguished history with a plethora of successes that go back to the work of Daniel Bernoulli (1700 – 1782) and Nobel Laureate and physician Sir Ronald Ross (1911) and associates. These individuals, mostly physicians, created the field of theoretical/mathematical epidemiology in their efforts to meet their commitment to diminish health disparities; the consequences of poverty and the lack of access to health services. The last four decades have seen deep and extensive computational and theoretical advances in the fields of computational, mathematical and theoretical epidemiology and the connections of this theoretical research to public health policy and security have had significant impact. These advances have been driven by the dynamics of specific emergent or reemergent diseases including HIV, influenza, SARS and Tuberculosis as well as by bioterrorism concerns. Challenges and opportunities arise from the demands generated by the study of disease dynamics over multiple time scales and levels of organization and by the search for response to questions of importance to the fields of public health, homeland security and evolutionary biology. In this lecture, I will revisit some of the history of the field and discuss selected applications in the context of slow and fast diseases; highlight the differences between single and recurrent outbreaks and related issues.   This seminar is part of the IAM Colloquium Series. 
Thursday, January 16  Caroline Colijn  3:00 pm in ESB 2012 Imperial College   Pathogen phylogenies reveal ecological competition 
 Abstract  
 Ecological competition between strains of a pathogen occurs when strains compete for hosts  either for susceptible hosts, host resources during coinfection, or the ability to reinfect hosts. Competition is important because when strains compete with each other, intervening against only some of them can pave the way for rises in others. This has happened, for example, with the introduction of polyvalent vaccines against Streptococcus pneumoniae. However, detecting ecological competition between strains of an infection is very challenging, because competition is by its nature revealed over relatively long periods of time and is a populationlevel phenomenon which we would not expect to observe in smallscale studies. Even populationlevel dynamical (ODE) models, which are frequently used in such situations, are hard to formulate and calibrate. Indeed, such models often make hidden assumptions about competition, rather than aiding in its estimation. I have therefore been motivated to ask: can sequence data for pathogens allow us to detect ecological competition? Large and rich datasets of pathogen gene sequences are now available, due to the development of nextgeneration sequencing; perhaps they can be of assistance if appropriately linked to models with and without competition. Here, I present a dynamical model in which there is a competition parameter which ranges continuously from 0 (where pathogen strains are independent of each other) to 1 (where competition is complete, and strain dynamics show competitive exclusion). It predicts that the branching rates in phylogenies for competing strains should be anticorrelated. A stochastic implementation of the model gives rise to pathogen phylogenies that are quantitatively different, both in their structures and their branch lengths, from phylogenies without competition. This leads to a distinct profile for a phylogeny under ecological competition: such trees have high imbalance early in the tree, greater topological distances from the root to the tips, lower widths and a characteristic skew in interbranch distances, among other properties. I analyse a phylogeny of withinhost HIV sequences and show that it fits the profile of ecological competition. I conclude with a discussion of other organisms and future directions for this work. 
November, 2013
Thursday, November 28  Matthew Miles Osmond  3:00 pm in ESB 2012 UBC Zoology   Using adaptive dynamics to predict evolution and extinction in changing environments 
 Abstract  
 Populations exposed to changing environments must adapt to
persist. Here we ask which factors determine a population's ability to
persist in changing environments through genetic adaptation. We
investigate the adaptive response to both a gradual, directional change in
the environment and a sudden, sustained shift. Throughout, we use the
canonical equation of adaptive dynamics, which allows us to derive
analytical expressions while including ecological processes neglected in
previous theory. 
Thursday, November 14  Christoph Hauert  3:00 pm in ESB 2012 UBC Math   Honour, Shame and Climate Change  Lessons from Public Goods Experiments 
 Abstract  
 In view of dwindling global resources, increased pressures on our social welfare states and the threat of climate change, the sustainable management of public goods becomes increasingly important and presents formidable challenges to human societies. In this talk I review two recent behavioural experiments on public goods interactions and the closely related collective risk dilemma. In both cases individuals are asked to contribute funds to a common pool, which benefits everyone but the share of benefits that return to the actor based on his or her contribution is insufficient to outweigh the costs of contributing. This generates a social dilemma where rational individuals withhold their contributions in an attempt to freeride on benefits generated by others  to the detriment of all. In the first set of experiments we show that revealing the identities of the two individuals that contributed least (shame), or that contributed most (honour), towards the end of repeated public goods interactions, both result in a significant increase of cooperation as compared to a fully anonymous setting (control) [1]. This setup reflects practices implemented, for example, by the state of California who mandates that restaurants display the results of their most recent health inspection and lists the top 250 tax delinquents with outstanding state taxes that exceed $100k. The former has lead to a significant decrease in hospitalizations based on food poisoning and the latter has generated millions in tax income. Interestingly, however, our experiments suggest that similar effects could be achieved by the socially more acceptable form of honouring compliant behaviour  and even have a more lasting impact. In the context of climate change, the problem of cooperation is significantly harder because the benefits of not contributing are immediate, whereas the rewards for successfully mitigating climate change are delayed by decades. Future rewards are naturally discounted due to the risk that the rewards may not get realized or the beneficiary may not life to enjoy them. In the second set of experiments we consider a collective risk dilemma framed around climate change where a group of participants has to raise a certain amount to avert dangerous climate change  if they succeed, the benefits of achieving the goal are paid out either the next day, seven weeks later, or, invested into planting oak trees [2]. In all treatments, participants could keep the capital that they did not invest. The three treatments compare inter and intragenerational discounting and the results reveal a sobering trend: the longer the delay the fewer groups reach the target  and, in fact, all eleven groups failed to reach the target in the third and most realistic setting. Our results experimentally confirm that international negotiations to mitigate climate change are unlikely to succeed if individual countries’ shortterm gains can arise only from defection.
References:
[1] Jacquet et al (2011) Shame and honour drive cooperation, Biol. Lett. 7 899901
[2] Jacquet et al (2013) Intra and intergenerational discounting in the climate game, Nature Climate Change, (online Oct 20) 
October, 2013
Thursday, October 31  Joe Mahaffy  3:00 pm in ESB 2012 San Diego State   Modeling Epidermal Sensory Neuron Development in Ascidians 
 Abstract  
 A mathematical model is developed for the morphogenesis of epidermal cells in the tunicate (Ciona intestinalis) into epidermal sensory neurons (ESNs). An introduction to the evolutionary significance of this morphogenesis problem is presented. A brief discussion of some neural development models is presented. Our model extends previous models of NotchDelta signaling for neurogenesis to explain the sparse spatial pattern seen on the tails of developing embryos. The model is compared to a series of experiments and analyzed mathematically, including some bifurcation results. 
Thursday, October 24  Sandy Rutherford  3:00 pm in ESB 2012 SFU   Disease Dynamics on Complex Networks with Applications to the HIV Epidemic in Vancouver 
 Abstract  
 Diseases such as HIV which spread through direct physical contact 
either sexual interaction or the sharing of needles by injection drug
users  may be modelled by treating transmission as a stochastic
contact process on the edges of a complex network. In addition, risk
behaviour which contributes to the spread of HIV may also spread
through social influence on this network. The example of the SIR model
on a network will be used to introduce some of the basic concepts of
disease dynamics on networks. Simulation studies are typically
required to understand the dynamics of more complicated disease
models. For this reason, our group has developed the software package
NepidemiX to simulate disease models on networks. A NepidemiX
simulation of a simplified model involving both risk behaviour and
disease transmission will be shown. We have developed a detailed model
of the HIV epidemic in Vancouver's Downtown Eastside to evaluate the
potential effectiveness of treatment and prevention strategies. This
model is being simulated using NepidemiX. Data to calibrate and
validate the model was supplied by the BC Centre for Excellence in
HIV/AIDS. Some preliminary results from this modelling study will be
presented. 
Thursday, October 17  Isabell Graf  3:00 pm in ESB 2012 SFU   Sap flow in maple trees: Fine view and coarse view 
 Abstract  
 Each spring the pressure in maple tree stems is so high that, for several days, maple sap can be harvested by making simple holes in the stem. The mechanisms behind this high pressure are not entirely understood.
In collaboration with John Stockie and Maurizio Ceseri we developed a mathematical model which might describe the processes inside the maple tree.
The model is based on the ideas of Milburn and O'Malley, where during cold nights the sap is pulled out of the vessel into the usually gasfilled fibers for freezing, and during warm days the ice melts and moves back into the vessel by osmosis and gas pressure. Thereby the water pressure in the vessel increases.
The model is divided into the freezing and the thawing process, in this talk we will only consider the thawing process.
First we consider the interaction of one vessel and one fiber in the fine view, later we upscale this process to the whole tree stem and describe the events for many vessels and fibers in the coarse view. 
Thursday, October 10  Stilianos Louca  3:00 pm in ESB2012 UBC   Discerning externally forced oscillations and autonomous limit cycles using noisy ecological time series 
 Abstract  
 Population cycles are ubiquitous in nature and have triggered ecologist's interests for decades. Given a noisy time series exhibiting a spectral peak, how can one decide wether the observed cycles are driven by an external periodic force, or are part of an autonomously emerging limit cycle? First results indicate that as the sampling time increases, the spectra and autocorrelations of the two signal classes behave qulitatively different and can be used to separate the two cases. Furthermore, crossspectral analysis can be used to falsify or verify a concrete candidate signal as driving force. I use ROC curves and linear discriminant analysis to evaluate the fidelity of several classifiers. 
Thursday, October 3  Nathan Kuwada  3:00 pm in ESB 2012 University of Washington   The right place at the right time: Probing the mechanisms of physical organization in bacterial cells 
 Abstract  
 One of the most striking aspects of the cell is the broad range of cellcycle dependent patterning and partitioning of subcellular components. Despite its physiological importance, the biophysical mechanisms responsible for most of this complex spatiotemporal organization in bacteria are currently unknown. Our lab attempts to quantitatively characterize these mechanisms using a combination of highthroughput, complete cellcycle fluorescence microscopy and automated image analysis. I will present results from two projects that represent the power of this approach: (1) a measurement of the force profile on the E. coli chromosome throughout the cell cycle, including the dynamic segregation process following replication, and (2) the first proteomewide characterization of localization dynamics for every individual protein in E. coli. We expect this quantitative cellcycle imaging approach will be widely applicable to understanding the emerging role of physical organization in prokaryotic cellular function. 
Tuesday, October 1  Ronen Avni  2:00 pm in IAM Lounge Applied Mathematics, Technion, Israel   Mathematical model for cell motility driven by active gel 
 Abstract  
 Cell crawling is a highly complex integrated process involving three distinct activities: protrusion adhesion and contraction, and also three players: the plasma membrane (car body), the actin network (engine) and the adhesion points (clutch). The actin network consists of actin polymers and many other types of molecules, e.g. molecular motors, which dynamically attach to and detach from the network, making it a biological gel. Furthermore, energy is consumed in the form of ATP due to both the activity of molecular motors and the polymerization at the filament tips; thus the system is far from thermodynamic equilibrium. These characteristics make the above system unique and responsible for a wide range of phenomena (different forcevelocity relationships) and behaviors (contraction, elongation, rotation, formation of dynamic structures)
Like the story on the blind men and the elephant, previous works considered only parts of the complex process, neglecting other subprocesses, or using unrealistic assumptions. Our goal was to derive a mathematical model for the whole system that can predict the rich variety of behaviors. For this purpose we had to identify the major players and integrate previous works into a one coherent mathematical model with no (or almost no) arbitrary constraints, adding our own mathematical description where needed. The model we derived consists of several temporal and spatial scales, relating processes on the molecular scale e.g. capping / branching to processes on the macro scale; furthermore, we used a hydrodynamic approach, hence accounting for both local dynamic events on the boundary and the bulk inside the domain. We focused on the processes near the leading edge that drive the system, i.e. the complexity comes in the b.c., and termed this filamentsmembrane dynamics “the polymerization machinery”.
In my talk I will describe the mathematical model we derived and its relation to previous works.
I will also describe the proprietary numerical simulation we derived for a freesurface flow of complex fluid in arbitrary geometries.
Finally I will discuss open questions and opportunities in this line of research.  Comment:  This is an irregular seminar, by a visiting scientist 
September, 2013
Thursday, September 26  Nancy Forde  3:00 pm in ESB2012 SFU physics   Probing multiscale mechanics of collagen 
 Abstract  
 In this talk, I will give an overview of my group's research interests in collagen, the predominant structural protein in vertebrates, and our progress towards understanding how its chemical composition influences its mechanical properties. I hope to inspire interest in this system and future discussions with colleagues here at UBC during my sabbatical year.
We use optical tweezers to measure forces in a variety of collagen systems: stretching single molecules of collagen to learn about their elasticity and flexibility at the molecular level; and probing the local viscoelastic environment in microrheology experiments on collagens in solution, as they selfassemble into fibrillar matrices, and as gelatin. We find that collagen's chemical composition influences the dynamics and strength of interactions between collagens, which we quantify with simple viscoelastic models. We furthermore characterize the development of microscale mechanical heterogeneity as collagen undergoes selfassembly into fibrillar networks. 
Thursday, September 19  Wes Maciejewski  3:00 pm in ESB 2012 UBC   Evolutionary game theory in heterogeneous, structured populations 
 Abstract  
 TBA 
Thursday, September 5  Peter Kim  3:00 pm in ESB2012 University of Sydney   Mathematical model of self/nonself discrimination from localized T cell dynamics 
 Abstract  
 In a healthy immune system, the T cell response discriminates between self and nonself cells. Medical research has shown that this phenomenon is not blackandwhite, since the immune system always contains T cells that could react against self antigens, but are kept suppressed by other immune cells.
The solution also cannot only involve a simple bistable system that shifts between immune and tolerant modes, because the T cell response has to be immunogenic to nonself and tolerogenic to self at the same time. We propose that the immune system resolves this difficulty by producing T cell responses that are localized in the vicinity of antigenpresenting cells (APC), which act as information collectors and T cell interaction hubs in the lymph node.
We develop an ordinary differential equation model that considers helper, killer, and regulatory T cells. Helper T cells stimulate the immune response, while regulatory T cells suppress it. All T cells interact with each other and with APCs and migrate among APC microenvironments. 
July, 2013
Thursday, July 11  Bernhard Konrad  2:00 pm in ESB 2012 UBC   Recovering parameters and unobserved states of an epidemic model with missing observations 
Thursday, July 4  Alejandra Herrera and Stilianos Louca  2:00 pm in ESB 2012 UBC   TBA 
 Abstract  
 Alejandra and Stilianos will give short presentations on research projects conducted at the summer school on Biological Invasions (held in Alberta over the past few weeks). 
June, 2013
Thursday, June 27  Mark Zajac  2:00 pm in ESB 2012 UBC   Modeling collisions between moving cells and rigid, immobile obstacles 
 Abstract  
 I will give an impromptu presentation on using level set methods to simulate collisions between migrating cells and rigid, immobile obstacles. Time permitting, I might also cover some more technical issues of using level set methods in general. 
Thursday, June 20  Eric Cytrynbaum  2:00 pm in ESB4127 UBC   Mechanisms of maltose transport in E. coli 
Thursday, June 13  Christopher Angstmann  2:00 pm in ESB4127 University of New South Wales   A parsimonious model for the dynamics of Min proteins. 
 Abstract  
 Oscillations of the Min protein system are in part responsible for the correct placement of the FtsZ ring during cell division in E. coli. All existing models of this patterning in the Min proteins introduce nonobserved effective interactions in order to produce the pattern. We show that this is unnecessary as the nonlinearity induced by the dimerisation of MinD is sufficient to induce Turing patterns in the dynamics. This fits with the experimentally observed molecular interactions of the Min protein system. The model compares well to experimental data taken from E. coli. The model has been solved through the whole cell cycle starting from a small cell that grows and then divides. The model in the growing cell is also consistent with experiments from filamentous E. coli with the transition to higher order modes that lead to the formation of multiple FtsZ rings. The transition of the Min patterning to a higher mode during cell division is shown to give rise to two daughter cells with acceptable Min protein levels to maintain patterning without the need for regulation of protein synthesis and degradation. This work has been a collaboration with James Walsh and Paul Curmi from University of New South Wales. 
Thursday, June 6  Cindy Greenwood  2:00 pm in ESB 4127 UBC   A stochastic model for avian flu 
 Abstract  
 This is about an SIR + virus model with ducks and virus, no humans. I start with a stochastic model from a recent paper where sustained oscillations are found through a nice bump in the power spectral density function. In fact considerable additional insight into the epidemic pattern (the stochastic dynamics) can be obtained through analysis of the associated stochastic process. The paper is not yet written, and I am looking for an author or coauthor. 
May, 2013
Thursday, May 16  Maziyar Jalaal  2:00 pm in ESB 2012 UBC   A model for the controlled release of nanoencapsulated tissue plasminogen activator using shear activation 
 Abstract  
 A model is presented for the controlled release of Tissue Plasminogen Activator tPA from nanoparticles, using shear stress as a trigger. The present model resolves blood flow in a partially blocked vessel, motion of microscale particles (aggregated nanoparticles), and the subsequent release of nanoparticles encapsulating tPA due to shear activation. Assumptions and results will be described and comments made regarding the further development of this class of nanomedicine. 
Thursday, May 9  Antoine Baker  2:00 pm in ESB 2012 SFU Physics   Linking the DNA strand asymmetry to the spatiotemporal replication program 
 Abstract  
 The replication process is known to be strand asymmetric:
it requires the opening of the DNA double helix and acts differently on the two DNA strands,
which generates different mutational patterns and in turn different nucleotide compositions on
the two DNA strands (compositional asymmetry). During my PhD thesis, we modeled the
spatiotemporal program of DNA replication and its impact on the DNA sequence evolution.
I will show how this model helps understand the relationship between compositional asymmetry
and replication in eukaryotes and explains the patterns of compositional asymmetry observed in
the human genome. During the last part of my talk, I will present our ongoing project: inferring the
spatiotemporal replication program from experimental replication kinetics data. 
March, 2013
Thursday, March 28  Daniel Krupp  2:00 pm in SWING 121 Queen's University   New problems of kin recognition 
 Abstract  
 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.  Comment:  Note unusual location  on west mall just south of university blvd. 
Wednesday, March 27  Matthijs van Veelen  3:30 pm in BRC 224 University of Amsterdam   In and out of equilibrium: evolution of cooperation in repeated games with population structure. 
 Abstract  
 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 ESset, and ESsets 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 ESset 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  Comment:  Special seminar, note special time and place 
Thursday, March 21  May Ann Mata  2:00 pm in ESB 4133 UBC   Nonlinear stability analysis of intracellular actin waves model 
Thursday, March 14  Karthika Raghavan  2:00 pm in ESB 4133 SFU   Modeling implications of Epigenetics Mechanisms  from cancer associated genes networks to chromatin remodelling 
Thursday, March 7  Joe Wakano  2:00 pm in SWNG 121 Meiji University   Evolutionary branching in a finite population: Deterministic branching versus stochastic branching 
 Abstract  
 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 branchingout times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individualbased model.  Comment:  Note unusual location "Swing space" building, on West Mall just south of University Blvd. 
February, 2013
Thursday, February 28  Lidan You  2:00 pm in ESB 4133 U Toronto   TBA 
Thursday, February 21  Wanda Strychalski  2:00 pm in ESB 4133 UC Davis   Insights into cytoplasmic rheology gained from modeling cellular blebbing 
 Abstract  
 Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressuredriven 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. 
Thursday, February 14  Mark Zajac  2:00 pm in ESB 4133 UBC   Polymer Entropy Can Drive Cell Migration 
 Abstract  
 I will present a twophase 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 EulerLagrange equation. Tracking cytoskeletal features makes use of correlations. 
Thursday, February 7  Jia Guo  2:00 pm in ESB 4133 UBC   TBA 
January, 2013
Thursday, January 31  Alejandra HerreraReyes  2:00 pm in ESB 4133 UBC   TBA 
Thursday, January 24  Eldon Emberly  2:00 pm in ESB4133 SFU Physics   Controlling the final size of a cell population using asymmetric division 
 Abstract  
 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 cellcycle 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 nonlinear 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. 
Thursday, January 17  Disease Dynamics 2013: Immunization, a true multisca  9:00 am in TBA   
 Abstract  
 This meeting will run from Thursday 17 Jan to Saturday 19 Jan, 2013. See the event website for more details  More info:  Event website 
Thursday, January 10  Chris Vogl  2:00 pm in ESB 2012 Northwestern   Various Approaches to Modeling the Lyopreservation of Cells 
 Abstract  
 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 continuoustime random walk and solved numerically. Additionally, the effect of drying on the cell membrane is modeled using incompressible NavierStokes. Numerically simulated cell shapes give insight into the effectiveness of various drying approaches. 
December, 2012
Thursday, December 13  Anais Khuong  2:00 pm in ESB4192   TBA 
Comment:  Note different location than usual 
November, 2012
Thursday, November 22  Joshua Zukewich  2:00 pm in ESB 2012 UBC   Learning Grammar with Neural Nets 
Thursday, November 15  William Carlquist  2:00 pm in ESB 2012 UBC   A computationally Efficient Method for Solving Reaction Diffusion Equations in RodCell Geometry 
Thursday, November 8  PIMSIGTC Symposium on Immune Cell Modeling  10:00 am in PIMS (ESB 4th floor)   
 Abstract  
 Speaker(s):
Raibatak Das (UBC)
Jun Allard (UC Davis)
Jesse Goyette (Oxford)
Spencer Freeman (UBC)
Omer Dushek (Oxford)  More info:  Event website at PIMS (more information) 
Comment:  Event is from 10am3pm (including regular seminar by Omer Dushek at 2pm). There will be some sandwiches provided for lunch. Please sign up for your sandwich by email to Ruth Situma, ruths@pims.math.ca with subject line: PISoICM2012 Attendance. 
Thursday, November 8  Omer Dushek  2:00 pm in ESB 2012 Oxford University   Noncatalytic tyrosinephosphorylated receptors 
 Abstract  
 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 Noncatalytic Tyrosinephosphorylated Receptors (NTRs) are regulated by extrinsic membraneconfined Srcfamily 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. 
Thursday, November 1  Jun Allard  2:00 pm in ESB 2012 University of California, Davis   Actin traveling waves in motile cells 
 Abstract  
 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 Factin 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 tagofwar. We
hypothesize that this waving behavior contributes to adaptation of
cell motility mechanisms in perturbed environments. 
October, 2012
Thursday, October 25  Cindy Greenwood  2:00 pm in ESB 2012 UBC   Genesis of gamma bursts in neural local field potentials 
Monday, October 22  Byron Goldstein  3:00 pm in LSK 460 Los Alamos National Lab   Estimating the probability of polyreactive antibodies disabling a gp41 trimer after T cellHIV adhesion 
More info:  IAM Distinguished Colloquium 
Thursday, October 18  Dan Coombs  2:00 pm in ESB 2012 UBC   HIV, antibodies and neutralization 
 Abstract  
 This will be an informal warmup 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. 
Thursday, October 11  Stilianos Louca  2:00 pm in ESB 2012 UBC   Nursery pollination mutualisms as evolutionary traps  A populationgenetical meanfield model. 
 Abstract  
 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 hostplant 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 populationgenetical meanfield model, used for the numerical analysis of their coevolution. The model can be generalized to many similar multiplespecies 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. 6583 
Thursday, October 4  Hildur Knutsdottir  2:00 pm in ESB 2012 SFU/UBC   A 3D computational individual cell based model to study the motility of breast cancer cells 
 Abstract  
 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.  Comment:  (use stairs from 1st floor to access room) 
September, 2012
Thursday, September 27  Florence Debarre  2:00 pm in ESB 2012 UBC Zoology   Evolution of social behaviour in spatially structured populations 
 Abstract  
 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" (BirthDeath or DeathBirth) 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.  Comment:  Enter ESB 2012 (in the new earth science building) by going up the stairs from the ground floor. 
Thursday, September 20  Wes Maciejewski  2:00 pm in PIMS UBC   Fixation Probability and Inclusive Fitness 
 Abstract  
 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. 
Thursday, September 13  Mark Zajac  2:00 pm in ESB 2012   Modeling Cell Boundary Dynamics 
 Abstract  
 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 reactionadvectiondiffusion 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, boundaryfitted grid that provides the basis for a finitevolume method 
May, 2012
Thursday, May 24  Lakshminarayanan Mahadevan  2:00 pm in Math 100 Harvard University   On growth and form: geometry, physics and biology 
 Abstract  
 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.  More info:  Math Department Colloquium Page 
Comment:  This is the 2012 Department of Mathematics Niven Lecture.
Students of Mathematical Biology, and of the 2012 Math Cell Biology course are encouraged to attend. 
Tuesday, May 22  Dimitrios Vavylonis  9:45 am in WMAX 110 Lehigh University   TBA 
 Abstract  
 TBA  More info:  Link to MCB 2012 Course Homepage 
Comment:  This is a series of 4 talks, one each day from May 2225 that are part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center)

Thursday, May 17  Adriana Dawes  10:00 am in WMAX 216 Ohio State University (Mathematics/Molec Genetics)   Spatial segregation of polarity determinants in embryos of the nematode worm C. elegans 
 Abstract  
 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.  Comment:  Note special time and place.
This talk is part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center) 
Thursday, May 17  Eric Cytrynbaum  2:00 pm in WMAX 110 UBC Mathematics   Selforganization in cells  how to use proteins to solve a geometry problem 
 Abstract  
 Fragments of fish pigment cells can form and center aggregates of pigment granules by dyneinmotordriven transport along a selforganized radial array of microtubules (MTs). I will present a quantitative model that describes pigment aggregation and MTaster selforganization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dyneinmotorcovered granules have the ability to nucleate MTs. From assumptions based on experimental observations, I'll derive partial integrodifferential equations describing the coupled granuleMT interaction. Analysis explains the mechanism of aster selforganization 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 spontaneouslynucleated microtubules. Numerical simulations lend additional support to the analysis. The model sheds light on role of polymer dynamics and polymermotor interactions in cytoskeletal organization.  Comment:  This talk is part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center) 
Tuesday, May 15  William R Holmes  11:00 am in WMAX 216 Dept of Mathematics, UBC   ReactionDiffusion Pattern formation 
 Abstract  
 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  Comment:  This is a series of talks from May 15  18 that are part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center) 
Monday, May 14  Dodo (Raibatak) Das  10:00 am in WMAX 110 Dept of Mathematics, UBC   Biological Data Analysis 
 Abstract  
 Lecture 1: Motivation  The principle of maximum likelihood  Least
squares regression  Linear regression
Lecture 2: Nonlinear regression  LevenbergMarquardt algorithm  Other
likelihoodmaximization methods  Parameter confidence intervals
Lecture 3: Bootstrap confidence intervals  Assessing differences in
parameter distributions using bootstrap
Lecture 4: Model selection  Bias variance tradeoff  Ftest  Akaike's
information criterion  Comment:  This is a series of talks from May 14  18 that are part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center)

Thursday, May 10  Daniel Coombs  2:00 pm in WMAX 110 Department of Mathematics, UBC   Models of T cell activation based on TCRpMHC bond kinetics 
 Abstract  
 In order for an immune cell, such as a Tcell to do its job (kill virus infected cells) it must first undergo an activation event. Activation requires the encounter of the cell surface Tcell receptors (TCRs) with bits of protein that are displayed in special complexes (peptideMHC complexes) on the surface of a target cell. all cells of the body display such pMHC complexes, but in normal circumstances only those perceived as infected will be destroyed by Tcells 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 Tcell.  Comment:  This talk is part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center) 
Monday, May 7  Jun Allard  9:45 am in WMAX 216 UC Davis   Cell Mechanics 
 Abstract  
 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 threedimensional structures
May 11: Additional topics  More info:  Link to MCB 2012 Course Homepage 
Comment:  This is a series of 5 talks, one each day from May 711 that are part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS. (IGTC=International Graduate Training Center) 
Thursday, May 3  James J. Feng  2:00 pm in WMAX 110 Department of Mathematics and Department of Chemical and Biological Engineering UBC   A particlebased model for healthy and malariainfected red blood cells 
 Abstract  
 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 10fold increase in membrane stiffness caused by extra crosslinking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of about 3fold 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 RBCdeformation 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.  Comment:  This talk is part of the monthlong Mathematical Cell Biology Graduate course, sponsored by the IGTC in Mathematical Biology and PIMS.
(IGTC=International Graduate Training Center) 
April, 2012
Thursday, April 5  Rebecca Tyson  2:00 pm in WMAX 110 UBCOkanagan   A diffusionbased model to predict transgenic seed contamination in beepollinated crops 
March, 2012
Thursday, March 29  Qiming Wang  2:00 pm in WMAX 110 UBC   Modeling and simulation of dorsal closure 
 Abstract  
 Dorsal closure (DC) is a tissuemodeling 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. 
Tuesday, March 27  Malte Peter  12:30 pm in WMAX 110 University of Augsburg   A multiscale approach to reactiondiffusion processes in domains with microstructure 
 Abstract  
 Reactiondiffusion 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 multiscale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.
The talk will give an introduction to multiscale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, certain aspects particularly relevant in upscaling reactiondiffusion processes in biological cells will be discussed.  More info:  UBC SCAIM 
Comment:  Note unusual time and date 
Thursday, March 15  Chad Topaz  2:00 pm in WMAX 110 Macalester College   Locust dynamics: Behavioral phase change and swarming 
 Abstract  
 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 EdelsteinKeshet, and Andrew Bernoff. 
February, 2012
Thursday, February 16  Michael Rempe  2:00 pm in WMAX 110 Whitworth University   A mathematical model of human sleep and insomnia 
 Abstract  
 I will present a biologicallybased 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 stressinduced insomnia and fatal familial insomnia. 
October, 2011
Monday, October 31  Yanghong Huang  3:00 pm in LSK 301 SFU   A Nonlocal Aggregation Model with RepulsiveAttractive Kernels 
 Abstract  
 We consider the aggregation equation ρt = ∇ ⋅ (ρ∇K ∗ ρ) in ℜn, where the interaction potential K models shortrange singular repulsion and longrange powerlaw 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 powerlaw 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).  Comment:  IAM colloqium / math bio seminar 
September, 2011
Thursday, September 22  Hans Heesterbeek  2:00 pm in TBA Utrecht University   Threshold behaviour and infection dynamics in spatial metapopulations of hosts 
 Abstract  
 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 plaguegreat gerbil system to illustrate various aspects of thresholds and spread, touching on both theoretical and biological insights. An example of the former is a nonlinear 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 longterm data sets, including a possible threshold for zoonotic spread to humans. 
August, 2011
Monday, August 8  Len Pismen  2:00 pm in WMAX 216 Technion   Malleable Cytoskeleton: Mechanics Guided by Chemistry 
 Abstract  
 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 mechanodiffusive 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.  Comment:  PIMS Upstairs 
Thursday, August 4  Miles Davenport  2:00 pm in WMAX 110 University of New South Wales   TBA 
 Abstract  
 TBA  Comment:  Note Thursday seminar 
July, 2011
Tuesday, July 12  Thomas Erneux  2:00 pm in WMAX 110 Universite Libre de Bruxelles   Applications of Delay Differential Equations 
 Abstract  
 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. 
June, 2011
Thursday, June 16  JeanFrancois Ganghoffer  2:00 pm in WMAX 110 LEMTA  ENSEM, Nancy, France   Equivalent properties of biological membranes from lattice homogenization 
Comment:  Note Thursday seminar 
May, 2011
Monday, May 2  Beth Kochin  2:00 pm in WMAX 110 Emory University   Control of Acute Infections 
April, 2011
Tuesday, April 26  Jesus Espinal  2:00 pm in WMAX 110 UNAM, Mexico   Discrete Dynamics Model for the SperactActivated Ca2+ Signaling Network Relevant to Sperm Motility. 
 Abstract  
 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. 
Tuesday, April 19  Janak Wedagedera  2:00 pm in WMAX 110 University of Ruhuna, Sri Lanka   Some aspects on stochastic Modelling of Tcell activation problem 
 Abstract  
 TBA 
Monday, April 11  Ramit Mehr  1:55 pm in WMAX 110 Bar Ilan University   The complexity of the humoral immune response 
 Abstract  
 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 selfmolecules. 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 nonlinear. The humoral (antibodygenerating) immune
response is one of the most complex responses, as it involves somatic hypermutation of the B cell receptor (BCR)
genes and subsequent antigendriven 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.  Comment:  * We are starting a few minutes early as there is a seminar in the same room at 3:00pm 
March, 2011
Wednesday, March 30  Mohammad FallahiSichani  1:00 pm in Math 126 University of Michigan   Multiscale analysis of TNFregulated immune response to Mycobacterium tuberculosis infection 
 Abstract  
 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 TNFneutralizing drugs (generally used to treat antiinflammatory 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.  Comment:  Note unusual time and place 
Tuesday, March 29  Somdatta Sinha  2:00 pm in WMAX 110 Centre for Cellular & Molecular Biology (CSIR), Hyderabad   Modelling infectious disease  from genomes to populations 
 Abstract  
 Dr. Sinha's talk will cover both genome analysis of pathogens
(HIV1 in particular), SIR type models, and statistical modelling of disease prevalence data (of Malaria). 
Tuesday, March 29  Janka Petravic  11:00 am in IAM Lounge University of New South Wales   Inhost modelling of HIV infection 
 Abstract  
 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”.  Comment:  Note unusual time and place 
Tuesday, March 15  Jennifer Trueblood  2:00 pm in WMAX 110 Cognitive Science Program, Indiana University, Bloomington   A Quantum Probability Model of Order Effects in Human Inference 
 Abstract  
 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 beliefadjustment 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 decisionmaking task. To further test the quantum inference model, new jury decisionmaking experiments are developed. The results of these experiments are used to compare the quantum model to the beliefadjustment model and suggest that the beliefadjustment model faces limitations whereas the quantum inference model does not. 
Thursday, March 10  Joe Yuichiro Wakano  2:00 pm in WMAX 110 Meji Institute for Advanced Study of Mathematical Sciences   Mathematical expression of inclusive fitness theory 
 Abstract  
 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 "offspringtoparent 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. 
Thursday, March 3  Oleg Igoshin  2:00 pm in WMAX 110 Dept. of Bioengineering, Rice University   Uncovering selforganization mechanisms in Myxococcus xanthus swarms with modeling and image processing 
 Abstract  
 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 selforganize to sporulate under starvation conditions and ripples  dynamical bacterial density waves propagating through the colony during predation. Relating these complex selforganization patterns in M. xanthus swarms to motility of individual cells is a complexreverse 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 agentbased 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. 
February, 2011
Tuesday, February 22  David Holloway  2:00 pm in WMAX 110 BC Institue of Technology   Chemical patterning in development: from gene regulation in flies to growth control in plants 
 Abstract  
 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 selffeedback 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
reactiondiffusion modelling) and domain growth can create the shapes
of plants. 
Tuesday, February 8  Colin Clark  2:00 pm in WMAX 110 UBC (emeritus)   Oceanatmosphere coupling and the likelihood of doom 
 Abstract  
 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 atmosphereocean coupling. 
January, 2011
Thursday, January 27  Jennifer Jacquet  2:00 pm in WMAX 110 UBC Fisheries   Guilt, shame, and the tragedy of the commons 
 Abstract  
 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.  Comment:  Cosponsored with the W. Maurice Young Centre for Applied Ethics. 
Tuesday, January 18  Shaun Strohm  2:00 pm in WMAX 110 UBCOkanagan   Dispersal of Mountain Pine Beetle and Impacts of Management 
 Abstract  
 Efforts to control the Mountain Pine Beetle infestation in British Columbia and Alberta include largescale landscape manipulations such as clearcutting, and costintensive 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 spatiallyexplicit hybrid model for the Mountain Pine Beetle (MPB) dispersal and reproduction. The model is composed of reactiondiffusionchemotaxis 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. 
November, 2010
Tuesday, November 30  Carlos CastilloChavez  2:00 pm in WMAX 110 Arizona State University   Growth of Urban Centers and Tuberculosis Decline in the USA 
 Abstract  
 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. 
Tuesday, November 23  Lucas Wardil  2:00 pm in WMAX 110 Universidade Federal de Minas Gerais   Coevolution of strategy and network 
 Abstract  
 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. 
Tuesday, November 16  Fred Brauer  2:00 pm in WMAX 110 UBC   Some models for tuberculosis 
 Abstract  
 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.  Comment:  Fred Brauer has agreed to give this informal survey talk about TB modeling. There will be a reading list advertised later on for students who would like to read up about these interesting problems.This lecture on disease modeling fits into a theme that will be followed up by Carlos CastilloChavez later on. 
October, 2010
Friday, October 29  John Lowengrub  1:45 pm in WMAX 110 UC Davis   Feedback, lineages and cancer 
 Abstract  
 Most tissues are hierarchically organized into lineages, which are sets of
progenitorprogeny 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
selfrenewal and differentiation of the different cells within the lineages
and lead to the development of heterogenous cell distributions and formation
of nichelike 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.  Comment:  Special talk in Dept of Mathematics. Note unusual time and day. 
Thursday, October 21  Alan Perelson  2:00 pm in WMAX 110 Los Alamos National Laboratory   HIV Dynamics 2010: New Models of Acute HIV Infection 
 Abstract  
 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 timevarying 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. 
Thursday, October 14  Alex Mogilner  2:00 pm in LSK 301 UC Davis   Mechanics of cell migration 
 Abstract  
 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 selforganization and viscoelastic flow explaining these observations. According to this model, a force balance between membrane tension, pushing
actin network and centripetal myosinpowered 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. 
Tuesday, October 5  YueXian Li  2:00 pm in WMAX 110 UBC   Viability of Autocrine Regulation in Synchronizing Diffusely Distributed Endocrine Neurons Producing Pulsatile Hormonal Signals 
 Abstract  
 Reproduction in mammals is controlled by the pulsatile release of gonadotropinreleasing 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, placodederived 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 twodimensional 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 Gproteins 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 (KhadraLi, 2006, Biophys. J. 91:74) and its robustness and potential applicability to GnRH neurons in vivo investigated (LiKhadra, 2008, BMB 70:2103). In this talk, I will introduce some key experimental and modeling results of this rhythmgenerating 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.) 
September, 2010
Tuesday, September 28  William Holmes  2:00 pm in WMAX 110 UBC   A 3D computational model of the Mammalian Cochlea with Asymptotics 
 Abstract  
 We present a computational platform for the simplified Mammalian
Cochlea with the standard coupled fluidplate 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. 
Tuesday, September 21  Adriana Dawes  2:00 pm in Math 125 U Alberta   Symmetry breaking in the early C. elegans embryo 
 Abstract  
 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.  Comment:  (Note the meeting place!) 
Tuesday, September 14  Isabell Graf  2:00 pm in WMAX 110   TBA 
 Abstract  
 TBA 
August, 2010
Tuesday, August 17  Prof. ChihWen Shih  2:00 pm in WMAX 110 Dept of Applied Math, National Chiao Tung University, Hsinchu, Taiwan   Synchronized Oscillation for Segmentation Clock Gene of Zebrafish 
 Abstract  
 Somitogenesis is a process for the development of somites which are transient, segmental structures that lie along the anteriorposterior 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 clockgenes which are subject to direct autorepression by their own products under time delay, and celltocell interaction through DeltaNotch 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 oscillationarrested 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. 
June, 2010
Thursday, June 10  Arne Traulsen  2:00 pm in WMAX 110 MaxPlanck Institute for Evolutionary Biology   Human strategy updating in a spatial game 
 Abstract  
 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) 
Tuesday, June 1  Jose Faro  2:00 pm in WMAX 110 University of Vigo   Analysis of TcR diversity in CD4+ T cells 
 Abstract  
 TBA 
April, 2010
Tuesday, April 6  Elissa Schwartz  2:00 pm in WMAX 110 Washington State University   Using Mathematical Models to Predict Vaccine Strategies for Viral Infections 
 Abstract  
 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 hostpathogen mechanisms. Efforts are currently underway to develop both preexposure and postexposure vaccines for several viral infections, including Human Immunodeficiency Virus type 1 (HIV1) and Herpes Simplex Virus type 2 (HSV2). In this talk, I will present models of vaccination strategies for these viral infections. Results using deterministic models of the HSV2 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 HIV1 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. 
March, 2010
Tuesday, March 16  David Odde  2:00 pm in WMAX 110 Department of Biomedical Engineering, University of Minnesota   Microtubule assembly dynamics at the nanoscale 
 Abstract  
 Microtubules are intracellular polymers that dynamically grow and shorten at their ends via the stochastic addition and loss of αβtubulin 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 molecularlevel 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 concentrationdependent 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 orderofmagnitude. We then test this prediction experimentally via TIRFmicroscopy and via a lasertweezers assay with nearmolecular 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 orderofmagnitude 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 nearkHz 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 selfassembled 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. 
Tuesday, March 2  Joe Wakano  2:00 pm in WMAX 110 Meiji University   Chaotic Dynamics in Spatial Public Goods Games 
 Abstract  
 TBA 
February, 2010
Tuesday, February 9  PikYin Lai  2:00 pm in WMAX 110 National Central University, Taiwan   Frequency Variation and Waves in Coupled Excitable Systems 
 Abstract  
 Two topics will covered in this talk. The first part concerns the dynamics of coupled excitable FitzHughNagumo 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 zerorefractoriness and in the continuum limit supports zerocore spiral waves. 
January, 2010
Thursday, January 14  Burt Simon  2:00 pm in WMAX 216 University of Colorado   POSTPONED! NEW DATE TBA 
 Abstract  
 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 huntergatherer tribes will illustrate the techniques. 
Tuesday, January 12  Omer Dushek  2:00 pm in WMAX 110 Oxford University   Doseresponse reveals the importance of T cell receptor  peptideMHC kinetics in T cell activation 
 Abstract  
 TBA 
December, 2009
Tuesday, December 8  Rafael Meza  2:00 pm in WMAX 110 BCCDC   Infectious Diseases and Cancer 
 Abstract  
 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 timescales of
both disease processes adequately. Some examples will be discussed. 
Thursday, December 3  William Robert Holmes  2:00 pm in WMAX 216 Indiana, Mathematics   A 3D computational model of the Mammalian Cochlea with Asymptotics 
 Abstract  
 We seek to build a computational model for the simplified Mammalian Cochlea with the standard coupled fluidplate 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.  Comment:  Note unusual time and date 
November, 2009
Tuesday, November 24  Steve Andrews  2:00 pm in WMAX 110 Fred Hutchinson Cancer Research Institute   Simulating cell biology with spatial accuracy and single molecule detail 
 Abstract  
 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 pointlike 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. 
Tuesday, November 17  Helen Alexander  2:00 pm in WMAX 110 Queen's University   Branching Processes in Evolutionary Epidemiology 
 Abstract  
 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 betweenhost 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 singletype branching processes as applied to disease spread, and then introduce a multitype 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 nonextinction). Time permitting, I will also present preliminary results on the probability of specific strains arising and the distribution of time to extinction or evolution. 
Tuesday, November 10  Jennifer Young  2:00 pm in WMAX 110 UNC, Chapel Hill, NC   A Numerical Model of Cellular Blebbing 
 Abstract  
 In animal cells, a "bleb" is a balloonlike protrusion of the plasma
membrane that forms when the membrane separates from the underlying
cytoskeletal network and is pushed outward by pressuredriven cytosol.
The protrusion later retracts due to the formation and subsequent
myosinII 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
twodimensional fluidstructure 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 straindependent elasticity modulus. The
cytosol is modeled by Stokes flow and the protein concentrations are
modeled via advectiondiffusion 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 nonequilibrium behavior. In particular, the stiffness of
the filaments in the above model are coarsegrained representations of
the microscopic actin network. I will present preliminary results on
coupling the time evolution of coarsegrained and microscopic
descriptions by statistical sampling of the dynamics of the cytoskeletal
network. 
Tuesday, November 3  Matthias Conrad  2:00 pm in WMAX 110 Emory University   Optimal experimental design and parameter estimation for the energy metabolism 
 Abstract  
 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. 
October, 2009
Thursday, October 22  Chad HigdonTopaz  2:00 pm in WMAX 110 Department of Mathematics/Computer Science, Macalester College   Biological aggregation patterns and the role of social interactions 
 Abstract  
 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 interorganism social interactions and properties of macroscopic swarm patterns. The first model is a conservationtype partial integrodifferential equation (PIDE). Social interactions of incompressible form lead to vortexlike swarms. The second model is a highdimensional ODE description of locust groups. The statisticalmechanical properties of the attractiverepulsive 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 conservationtype PIDE and, via long and shortwave analysis, determine general conditions that social interactions must satisfy for the population to asymptotically spread, contract, or reach steady state.  Comment:  This week's seminar will take place on Thursday! 
Tuesday, October 6  Andrew Rutenberg  2:00 pm in WMAX 110 Dept. of Physics, Dalhousie Univeristy   Models and manipulations: Min oscillations inside an E. coli bacterium 
 Abstract  
 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). 
Friday, October 2  Claude Muller  1:30 pm in PWI Conference Room National Public Health Laboratory, Luxembourg   The spread and evolution of Highly Pathogenic Avian Influenza H5N1 virus in poultry, wild birds and humans in Africa 
 Abstract  
 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 hightech
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.  More info:  Peter Wall Events 
Comment:  This special lecture is part of the Peter Wall Institute Colloquium Series. Refreshments will be served at 1:30pm,
and the lecture will begin at 2:00pm. The event takes place in the Peter Wall Inst conference room, University Center. 
September, 2009
Tuesday, September 22  Peter Borowski  2:00 pm in WMAX 110 University of British Columbia   The Min system in E.coli: A stochastic polymer model and new ideas for experiments 
 Abstract  
 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 rodshaped 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 GFPlabelled E.coli. 
Monday, September 21  Alain Goriely  3:00 pm in LSK 301 University of Arizona   The Mechanics and Mathematics of Growth and Remodeling in Biological Systems 
 Abstract  
 TBA   This seminar is part of the IAM Colloquium Series. 
Wednesday, September 16  Richard Liang  3:00 pm in WMAX 216 Mathematics, UBC   Models in population genetics with continuous geography 
 Abstract  
 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 WrightFisher model of evolution of a single population; then, we will look at a socalled 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 currentday 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 seminar is part of the Probability Seminar Series. 
Tuesday, September 15  Rodrigo Restrepo  2:00 pm in WMAX 110 University of British Columbia   On the Emergence, Replication and Abundance of some Early Cell Structures 
 Abstract  
 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. 
August, 2009
Monday, August 31  Elias August  2:00 pm in WMAX 216 Department of Computer Science, Swiss Federal Institute of Technology (ETH) Zurich   Elucidating pathways in bacterial chemotaxis & a novel method for checking parameter identifiability 
 Abstract  
 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. 
July, 2009
Thursday, July 16  Andre Longtin  2:00 pm in WMAX 216 University of Ottawa   Neural Coding in Electric Fish 
 Abstract  
 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 wellsuited 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 experimentaltheoretical 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 spatiotemporal stimuli to induce oscillatory neural activity. 
April, 2009
Thursday, April 23  Bahman Davoudi Dehaghi  2:00 pm in WMAX 216 BC Centre for Disease Control   Early Realtime Estimation of the Basic Reproductive Number 
 Abstract  
 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
largescale 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. 
Thursday, April 16  Joe Yuichiro Wakano  2:00 pm in WMAX 216 Meiji Institute for Advanced Study of Mathematical Sciences   Origin of culture: an evolutionary model of social learning 
 Abstract  
 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. 
Wednesday, April 15  Christopher A. Del Negro  2:00 pm in WMAX 216 The College of William and Mary   Emergent network properties in the preBotzinger Complex: the cellular and synaptic mechanisms of respiratory rhythm generation 
 Abstract  
 Breathing is an interesting and essential lifesustaining 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 neuralmotor 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 voltagedependent 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 burstgenerating conductances, this rhythmgenerating mechanism represents a new paradigm in which the basic rhythmogenic unit encompasses a fully interdependent ensemble of synaptic and intrinsic components.  Comment:  This is not the usual mathbiology seminar time. 



