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The COVID-19 pandemic has passed its initial peak in most countries in the world, making it ripe to assess whether the basic reproduction number (R0) is different across countries and what demographic, social, and environmental factors other than interventions characterize vulnerability to the virus. In this talk, I will show the association (linear and non-linear) between COVID-19 R0 across countries and 17 demographic, social and environmental variables obtained using a generalized additive model. Moreover, I will present a mathematical model of COVID-19 that we designed and used to explore the effects of adopting various vaccination and relaxation strategies on the COVID-19 epidemiological long-term projections in Ontario. Our findings are able to provide public health bodies with important insights on the effect of adopting various mitigation strategies, thereby guiding them in the decision-making process.

Epithelial-mesenchymal transition (EMT), a process in which immotile cells that line surfaces in the body become motile mesenchymal cells, play a crucial role in major processes such as wound healing, embryo development, and cancer growth; therefore, examining the dynamics behind individual and collective cell migration would allow for a better understanding of these processes. It has been previously observed that the protein YAP is activated by external mechanical stimuli and affects the expression and activation of the proteins E-cadherin and Rac1, which are involved in intercellular adhesion and migratory ability respectively. It has also been demonstrated that the mechanical stimulation of expanding cell sheets leads to the formation of finger-like projections and EMT, as well as quantitative differences in properties between cells near the sheet edge and cells away from it. Such cell sheets can be simulated using Morpheus, an agent-based modelling and simulation environment. In this talk, I will propose an ODE model for YAP/Rac1/E-cadherin dynamics and demonstrate that the resulting Morpheus simulation gives results consistent with several observations seen in vitro.

For cells to divide, they must undergo mitosis: the process of spatially organizing their copied DNA (chromosomes) to precise locations in the cell. This procedure is carried out by stochastic components that manage to accomplish the task with astonishing speed and accuracy. New advances from our collaborators in the New York Dept of Health provide 3D spatial trajectories of every chromosome in a cell during mitosis. Can these trajectories tell us anything about the mechanisms driving them? The structure and context of this cutting-edge data makes utilizing classical tools from data science or particle tracking challenging. I will discuss my progress with Alex Mogilner on developing analysis for this data and mathematical modeling of emergent phenomena.

Cells in tissue can communicate short-range via direct contact, and long-range via diffusive signals. In addition, another class of cell-cell communication is by long, thin cellular protrusions that are ~100 microns in length and ~100 nanometers in width. These so-called non-canonical protrusions include cytonemes, nanotubes, and airinemes. But, before establishing communication, they must find their target cell. Here we demonstrate airinemes in zebrafish are consistent with a finite persistent random walk model. We study this model by stochastic simulation, and by numerically solving the survival probability equation using Strang splitting. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive (highly curved, random) search. We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme’s source, finding the experimentally observed parameters to be at a Pareto optimum balancing directional sensing with contact initiation.

To initiate movement, cells need to form a well-defined "front" and "rear" through the process of cellular polarization. Polarization is a crucial process involved in embryonic development and cell motility and it is not yet well understood. Mathematical models that have been developed to study the onset of polarization have explored either biochemical or mechanical pathways, yet few have proposed a combined mechano-chemical mechanism. However, experimental evidence suggests that most motile cells rely on both biochemical and mechanical components to break symmetry. I will describe a mechano-chemical mathematical model for emergent organization driven by both cytoskeletal dynamics and biochemical reactions. We have identified one of the simplest quantitative frameworks for a possible mechanism for spontaneous symmetry breaking for initiation of cell movement. The framework relies on local, linear coupling between minimal biochemical stochastic and mechanical deterministic systems; this coupling between mechanics and biochemistry has been speculated biologically, yet through our model, we demonstrate it is a necessary and sufficient condition for a cell to achieve a polarized state.

Cell division is a vital mechanism for cell proliferation, but it often breaks its symmetry during animal development. Symmetry-breaking of cell division, such as the orientation of the cell division axis and asymmetry of daughter cell sizes, regulates morphogenesis and cell fate decision during embryogenesis, organogenesis, and stem cell division in a range of organisms. Despite its significance in development and disease, the mechanisms of symmetry-breaking of cell division remain unclear. Previous studies heavily focused on the mechanism of symmetry-breaking at metaphase of mitosis, wherein a localized microtubule-motor protein activity pulls the mitotic spindle. Recent studies found that cortical flow, the collective migration of the cell surface actin-myosin network, plays an independent role in the symmetry-breaking of cell division after anaphase. Using nematode C. elegans embryos, we identified extrinsic and intrinsic cues that pattern cortical flow during early embryogenesis. Each cue specifies distinct cellular arrangements and is involved in a critical developmental event such as the establishment of the left-right body axis, the dorsal-ventral body axis, and the formation of endoderm. Our research started to uncover the regulatory mechanisms underlying the cortical flow patterning during early embryogenesis.

Cellular polarization plays a critical during cellular differentiation, development, and cellular migration through the establishment of a long-lived cell-front and cell-rear. Although mechanisms of polarization vary across cells types, some common biochemical players have emerged, namely the RhoGTPases Rac and Rho. The low diffusion coefficient of the active form of these molecules combined with their mutual inhibitory interaction dynamics have led to a prototypical pattern-formation system that can polarizes cell through a non-Turing pattern formation mechanism termed wave-pinning. We investigate the effects of paxillin, a master regulator of adhesion dynamics, on the Rac-Rho system through a positive feedback loop that amplifies Rac activation. We find that paxillin feedback onto the Rac-Rho system produces cells that (i) self-polarize in the absence of any input signal (i.e., paxllin feedback causes a Turing instability) and (ii) become arrested due to the development of multiple protrusive regions. The former effect is a positive finding that can be related to certain cell-types, while the latter outcome is likely an artefact of the model.

At the cortex of Dictyostelium, the actin cytoskeleton localizes in discrete patches which have been shown to oscillate at different phases. Recent findings suggest that the spatial coordination of actin oscillators is regulated by the G protein subunit G$\beta$, which diffuses rapidly throughout the cell. Upon G$\beta$ sequestration, the following phenomena are observed: (1) higher fraction of actin patches becomes oscillatory; (2) phase difference between different sectors becomes smaller. To understand these observations, we model each actin patch as a conditional oscillator, which is governed by an excitable activator-inhibitor model coupled by bulk diffusion of G$\beta$. Assuming that G$\beta$ promotes the actin activator Arp2/3 in each actin patch, we find that actin oscillations can emerge when the G$\beta$ concentration is low. We show that spatial heterogeneity of G$\beta$ can lead to phase differences in actin oscillators. We consider how additional spatial coupling by Arp2/3 can influence spatial patterning in this system.

Why do organelles have their particular sizes, and how does the cell maintain them given the constant turnover of proteins and biomolecules? To address these fundamental biological questions, we formulate and study mathematical models of organelle size control rooted in the physicochemical principles of transport, chemical kinetics, and force balance. By studying the mathematical symmetries of competing models, we arrive at a hypothesis describing general principles of organelle size control. In particular, we consider flagellar length control in the unicellular green algae Chlamydomonas reinhardtii, and develop a minimal model in which diffusion gives rise to a length-dependent concentration of depolymerase at the flagellar tip. We explain how the same principles may be applied to other examples of organelle size and scaling such as the ratio of nucleus to cell volume.

Fibrin polymerization, an important component of blood clotting, involves the conversion of soluble fibrinogen molecules in the blood plasma to fibrin monomers. These monomers can then polymerize to form a gel that is a major structural component of a blood clot. Oligomers of fibrinogen and fibrin have been observed experimentally and are thought to impact the kinetics of the fibrin gelation process. Fibrinogen plays a dual role in fibrin polymerization; it can occupy available binding sites by binding to fibrin, inhibiting gelation, and it can be converted to fibrin in monomeric or oligomeric form thus facilitating gel formation. In this talk, I will overview two kinetic polymerization models that we developed to study the effects of fibrin-fibrinogen interactions on fibrin polymerization. These models can help characterize the conditions under which a gel forms and examine the impact of fibrinogen-fibrin binding and fibrinogen conversion to fibrin on the gel structure, if one forms. Finally, I will briefly discuss current directions that involve incorporating other processes involved in blood clot formation into our modeling framework.

The reproducibility crisis has emerged as an important concern across many fields of science including life science, since many published results failed to reproduce. Systems biology modelling, which involves mathematical representation of biological processes to study complex system behaviour, was expected to be least affected by this crisis. While lack of reproducibility of experimental results and computational analysis could be a repercussion of several compounded factors, it was not fully understood why systems biology models with well-defined mathematical expressions fail to reproduce and how prevalent it is. Hence, we systematically attempted to reproduce 455 kinetic models of biological processes published in peer-reviewed research articles from 152 journals.Our investigation revealed that about half (49%) of the models could not be reproduced using the information provided in the published manuscripts. With further effort, an additional 12% of the models could be reproduced either by empirical correction or support from authors. The other 37% remained non-reproducible models due to missing parameter values, missing initial concentration, inconsistent model structure, or a combination of these factors. Among the corresponding authors of the non-reproducible model we contacted, less than 30% responded. Our analysis revealed that models published in journals across several fields of life science failed to reproduce, revealing a common problem in the peer-review process. Hence, we propose an 8-point reproducibility scorecard that can be used by authors, reviewers and journal editors to assess each model and address the reproducibility crisis.

Actin filaments are polymers that interact with myosin motor proteins inside cells and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We also develop tools based on topological data analysis to understand time-series data extracted from these filamentous network interactions. We use these tools to compare the filament organization resulting from myosin motors with different properties. Moving forward, we are interested in gaining insights into myosin motor regulation and the resulting actin architectures during cell cycle progression. This work also raises questions about how to assess the significance of topological features in common topological summary visualizations.

The form and function of tissues and organs emerge out of cell-to-cell interactions. Cell interaction dynamics take place on a variety of temporal and spatial scales, and reflect processes—diffusion, migration, force production/sensing, growth, and proliferation. In this talk, we develop a multiscale framework where directly measurable quantities at the discrete cell-scale inform the model parameters at the continuum tissue scale through upscaling. In principle, this enables the model to be truly predictive because the data used for calibration (e.g., at the cell scale) is distinct from that used for validation (e.g., at the tissue scale). This model borrows ideas from statistical physics, materials science and applied mathematics and follows the framework of dynamic density functional theory. This approach provides a strategy for coarse-graining systems of stochastically interacting particles. By appropriately accounting for cell size and shape variability, we obtain a system of continuum equations that are able to capture plastic, viscoelastic and elastic deformations in the clusters while providing single-cell resolution. We validate this approach by comparisons with recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. We then use this framework to develop a new continuum elastic model for tissues that contains microscale information, including cell-cell correlations. The governing equations are obtained by using a 1-mode approximation and coarse-graining. We simulate the system numerically and analyze the system using matched asymptotic expansions to relate the new model with previously developed approaches.

During development, cellular self-organization by cell segregation leads to boundary formation and is critical for the organization of morphogenetic movement and tissue patterning. Signaling between membrane-bound EPHRINS and EPH receptor tyrosine kinases is essential in boundary formation, driving segregation between EPHRIN-expressing and EPH-expressing cells. Here we examine the basic cellular mechanistic drivers of EPH/EPHRIN cellular self-organization and boundary formation. Using a cell culture system to model EPH/EPHRIN cell segregation we analyzed the contact angle of cells to estimate the interfacial tension between EPHB2- and EPHRIN-B1-expressing cells. Heterotypic cell pairs exhibited increased interfacial tension relative to homotypic cell pairs. Inhibitors of actomyosin contractility significantly diminished this increase, suggesting that actomyosin contractility drives heterotypic interfacial tension. Cell segregation assays revealed that EPH/EPHRIN driven segregation is actomyosin contractility dependent. Further, atomic force microscopy showed that EPH/EPHRIN signaling results in increased cortical tension during cell segregation. Actomyosin contractility also drives increased EPHB2:EPHB2 homotypic contacts through an increase in tension away from the cell contact. Using a mouse model we demonstrated that actomyosin contractility is critical for EPH/EPHRIN cell segregation in vivo as well. Finally, we demonstrated that tissue-wide changes in cellular organization and tissue shape are driven by minimization of heterotypic contact. These data suggest a model for cell segregation and tissue organization in which Eph/ephrin signaling results in a cortical actin differential that prevents cells from making stable contacts and drives cell segregation to affect tissue morphology by modulating interfacial tension.

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. While biochemical models of adaptation have been previously proposed, here we discuss a different mechanism based on mechanosensing, where the interaction between biochemical signaling and cell tension facilitates adaptation. In this talk, we develop and analyze a model of mechanochemical-based adaptation consisting of a mechanics-based physical model coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. We use Local Perturbation Analysis to predict how cells adapt signaling parameters via feedback from mechanics to maintain polarity in response to chemoattractant levels. To confirm this prediction, we simulate the mechanochemical model in moving cells, demonstrating how mechanosensing results in persistent cell polarity when cells are stimulated with wide-ranging levels of chemoattractant in silico. These results demonstrate how mechanosensing may help cells adapt to maintain polarity in variable environments.

ODE models are widely used, and often derived or interpreted as a mean field approximation of some (often unspecified) continuous time stochastic model. Such ODE models often implicitly assume that, under the corresponding stochastic model, the time individuals spend in a given state is exponentially distributed. The linear chain trick (LCT) is a well-known technique for replacing exponentially distributed dwell times with Erlang distributions (i.e., gamma distributions with integer shape parameters). We have recently extended this technique beyond Erlang distributions to the much broader family of univariate, matrix exponential distributions known as phase-type distributions. These are the absorption time distributions for continuous time Markov chains, and include exponential, Erlang, and Coxian distributions, among others. This generalized linear chain trick (GLCT) helps clarify connections between individual-level stochastic model assumptions and the structure of corresponding mean field ODE models, and serves as a bridge allowing for the application of tools and concepts from Markov chain theory in the analysis and interpretation of mean field ODE models. In this talk, I will (1) introduce the GLCT framework and some related concepts from Markov chain theory; (2) describe a procedure for using the GLCT to quickly generalize or approximate some existing ODE, DDE, or distributed delay equation models; and (3) illustrate some benefits of viewing ODE models from the perspective of the GLCT.

The more we come to understand collective cell behaviors, the more we realize how central they are to multicellular life. This fundamental importance makes such behaviors as collective migration potent targets for strategies that would allow us to harness and direct collective cell behaviors for practical purposes. However, realizing such control requires approaching cellular collectives from an engineering and swarm theoretic perspective to first define relevant, fundamental rules governing a given collective process, and then build experimental tools to program these collective behaviors. Here, we will look at several case studies of this approach from my group: tissue tessellation based on multi-tissue interactions; bioelectric sheepdogs to literally herd and program collective migration; and cell-mimetic materials to reprogram tissue dynamics from the inside-out.

Insulin sensitivity in the body is an important part of modeling glucose homeostasis, however insulin sensitivity in the beta cells of the pancreas, where insulin is produced, has not previously been studied. In this talk, I will present a modified version of the Topp model that describes insulin negative feedback on its own production in beta cells. With this model and data from beta cell insulin receptor knockout mice, we are able to show that this effect does exist and begin to estimate insulin sensitivity for different genotypes, sexes and ages of mice. I will also present a preliminary model for the progression of insulin resistance in pre-diabetes.

As a disease spreads through a population, the pool of people still susceptible to the disease decreases. Eventually, it becomes unlikely that an infectious person will contact a susceptible person and as a result the number of infectious people starts to decrease. At this point, the fraction of people who are not susceptible is called the herd immunity threshold. The herd immunity threshold can be calculated for simple models and approximated or determined via simulation for more complex models. There has been an ongoing debate about where the herd immunity threshold might lie for the current pandemic. In this talk I will try to summarize the debate, and supply various other opinions.

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The advances in bioimaging techniques have enabled us to access the 3D shapes of a variety of structures: organs, cells, proteins. Since biological shapes are related to physiological functions, statistical analyses in biomedical research are poised to incorporate more shape data. This leads to the question: how do we define quantitative descriptions of shape variability from images? Mathematically, landmarks’ shapes, curve shapes, surface shapes, or shapes of objects in images are data that belong to non-Euclidean spaces, for example to Lie groups or quotient spaces. In this context, we introduce “Geometric statistics”, a statistical theory on non-Euclidean spaces. We present several studies showing the theory and applications of Geometric Statistics to the analysis of biomedical shape data.

In this talk, we will discuss two studies performed by the SMILE group (Collège de France/Sorbonne Université) in the beginning of the pandemic. (1) We study a model where infected individuals can be symptomatic or asymptomatic, use a contact tracing mobile app or not. We investigate the effect of non-digital interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of digital interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities. We show that moderate rates of adoption of a contact tracing app can reduce R0 but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions. (2) We present a general and tractable framework for modeling and "nowcasting" the epidemic at a national scale. Our approach is based on a fairly general stochastic model for complex diseases using an arbitrarily large number of types (e.g., infective stage, clinical state, risk factor class). We show how structuring the infected population by its infection age, i.e., time elapsed since infection, allows us to decouple dependencies between stages and to time. In the large population limit (obtained either by assumption or as a spontaneous effect of the outbreak), the global scale of the epidemic is well captured by a deterministic McKendrick-Von Foerster 1-d PDE, and such an approximation allows us to make robust predictions on the fate of the epidemic.

Nessy Tania Principal Scientist Quantitative Systems Pharmacology, Pfizer Worldwide Research, Development, and Medical In this talk, I will share some of my personal journey as a math biologist who had pursued a tenure-track position in academia and is now working as a research scientist in the biopharma industry. I will discuss similarities and differences, rewards and challenges that I have encountered in both positions. On a more practical aspect, I will discuss how current trainees can prepare for a career in industry (specifically biopharma) and how to seek those opportunities. I will also describe the emerging field of Quantitative Systems Pharmacology (QSP): its deep root in mathematical biology and how it is currently shaping the drug development process. Finally, I will share some of my own ongoing work as a QSP modeler who is supporting the Rare Disease Research Unit at Pfizer. As a key takeaway, I hope to share that there are multiple paths to success and a rewarding and stimulating career as a math biologist.

Election dynamics are a rich complex system, and forecasting next months U.S. elections is an exciting, high-stakes problem with many sources of subjectivity and uncertainty. In this talk, we take a dynamical-systems perspective on election forecasting, with the goal of helping to shed light on the forecast process and raise questions for future work. By adapting a well-studied model from epidemiology, we show how to combine a compartmental approach with polling data to produce forecasts of presidential, senatorial, and gubernatorial elections at the state level. Our results for the last 16 years of U.S. elections are largely in agreement with those of popular analysts, and we apply our model to forecast the upcoming U.S. elections on 3 November 2020. We also use our modeling framework to explore how different methods for handling polling data and accounting for uncertainty affect forecasts. This is joint work with Samuel Chian, William He, Christopher Lee, Daniel Linder, Mason Porter, and Grzegorz Rempala.

In general, the mechanisms by which walled cells specify their shapes are not fully understood. This project aims to understand the cell-shape formation during tip-cell elongation at the early developmental stage of moss. To do so, we have developed a mathematical method that decomposes cell wall “active” growth and cell wall “passive” stretching due to turgor pressure. We demonstrate that it is possible to map the active and passive physical effects using cell outline data and cell-wall marker techniques such as quantum dots. Joint work with: Luis Vidali, Giulia Galotto, Danush Chelladurai, Yaqi Deng, Chaozhen Wei, and Kamryn Spinelli.

Nature has evolved many mechanisms for achieving directed motion on the subcellular level. The burnt-bridges ratchet (BBR) is one mechanism used to achieve superdiffusive molecular motion over long distances through the successive cleavage of surface-bound energy-rich substrate sites. The BBR mechanism is utilized throughout Nature: it can be found in bacteria, plants, humans, as well as non-life forms such as influenza. Motivated to understand how fundamental design principles alter BBR kinetics, we have built both computer models as well as synthetic experimental systems to understand BBR kinetics. In this talk I will present the results of our modelling work where we explore how multivalency, leg length, hub topology, landscape dimension, and landscape elasticity affect BBR kinetics. I will also present the preliminary results of our experimental work where we have created a micron-sized BBR that has achieved superdiffusive motion on a two-dimensional landscape. Our work provides insight into the mechanistic origin for the observed velocities and persistence found in both synthetic and biological (eg. Influenza and ParA/ParB) systems.

Developing effective cancer treatment presents a unique challenge due to the overwhelming variability in tumour cell behaviour and spatial heterogeneity. Virotherapy is a type of cancer treatment that uses genetically engineered viruses to infect and lyse cancerous cells. When these viruses are administered with immune cells or immunostimulatory cytokines, an antitumour immune response is instigated. Developing a hybrid PDE/agent-based modelling for the treatment of glioblastoma (a type brain cancer), we predicted the variability in glioblastoma cells that hinders the efficacy of oncolytic virotherapy. We then show how this treatment could be improved for the majority of patients. Recently, gel-based mediums have been used to improve the efficacy of oncolytic virotherapy by providing a sustained therapeutic delivery of the vectors . Using a system of ODEs and a genetic algorithm, we show how this treatment could be further optimised by changing the gel-material to reduce the immune cell release rate. Overall, this talk aims to demonstrate complementing mathematical models and their applications in oncolytic virotherapy.

The mammalian hippocampus, comprised of serially connected subfields, participates in a variety of functions involving memory. It has been postulated that parallel circuitry embedded within hippocampal subfields may underlie such functional diversity. Here, I will present our work spanning experimental, computational, and mathematical neuroscience that shows distinct processes of memory that can emerge from parallel hippocampal circuits.

Wild-type zebrafish (Danio rerio) are characterized by black and yellow stripes, which form on their body and fins due to the self-organization of thousands of pigment cells. Mutant zebrafish and sibling species in the Danio genus, on the other hand, feature altered, variable patterns, including spots and labyrinth curves. The longterm goal of my work is to better link genotype, cell behavior, and phenotype by helping to identify the specific alterations to cell interactions that lead to these different fish patterns. Using a phenomenological approach, we develop agent-based models for cell interactions and simulate pattern formation on growing domains. In this talk, I will overview our models and highlight some topological techniques that allow us to quantitatively compare our simulations to in vivo images. I will also discuss current directions and open questions related to taking a more mechanistic and quantitative approach to describing cell behavior in zebrafish.

Cells often chemotax, directing their motion in response to a chemical signal. We develop models of strategies for chemotaxis in complex environments. Groups of cells may cooperate to sense a chemical signal. One strategy is to specialize into leader cells that sense the gradient and follower cells that follow the clusters direction. We find that this specialization can speed up cluster migration in steep gradients, where a few cells have much more information than the other cells in the cluster. Surprisingly, specialization may also be optimal in shallow gradients. There are tradeoffs between cluster speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters. In addition, single cells can express multiple types of receptors with varying affinities for the same signal. Will this help chemotactic accuracy? If the environment is not variable, using multiple receptor types is less effective than a single receptor type tuned to the environment. However, as environmental variability increases, cells should hedge their bets by expressing multiple receptor types adapted to varying environments. Cells can make several measurements of the signal over time, combining them to make a consistent estimate. Remarkably, time-integration for multiple receptor types is qualitatively different from a single type, allowing cells to extract orders of magnitude more information by using a maximum likelihood estimate.

It has been well established that the mechanical stiffness of the substrate with which cells interact affects various intracellular processes, including cell spread areas, speeds at which motile cells translocate, and the number and strength of cell-substrate adhesions. This mechanosensitivity is modulated through conformational changes in cell-substrate adhesion proteins that in turn regulate downstream processes, including processes involving proteins required for motility, actin and myosin. The aim of this work is to better understand how substrate stiffness affects actin dynamics and myosin activity in cell spreading. We present an axisymmetric model of a flat cell spreading on a two-dimensional substrate. The actin network is modeled as a viscous gel, and actin spreading and contraction dynamics are incorporated into the model as a local active rate of deformation. The model also incorporates membrane tension and stress-dependent focal adhesion dynamics, which in turn modulate a cell’s protrusive activity and speed of actin retrograde flow, thereby controlling the spreading rate. Using this model, we are able to recapitulate the three phases of cell spreading dynamics described in Gianonne et al. (Cell, 2004), and we predict how the balance of protrusive activity, actin retrograde flow, adhesion strength, and local actomyosin contractions are affected by substrate stiffness.

Malaria is a leading cause of death in many low-income countries despite being preventable, treatable and curable. One of the major roadblocks to malaria elimination is the emergence and spread of antimalarial drug resistance, which evolves when malaria parasites are exposed to a drug for prolonged periods. In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. Results will be presented from a Bayesian geostatistical model that have generated spatio-temporal predictions of resistance based on prevalence data available only at discrete study locations and times. In this way, the model output provides insight into the spatiotemporal spread of resistance that the discrete data points alone cannot provide. I will discuss how the results of these models have been used to update public health policy.

Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature, dense and fibrous extracellular matrix, irregular cellular architecture, metabolic gradients, and non-uniform expression of the cell membrane receptors. This can impede the transport of therapeutic agents to tumor cells in quantities sufficient to exert the desired effect. In addition, tumor microenvironments undergo dynamic spatio-temporal changes during treatment, which can also obstruct the observed drug efficacy. To examine ways to improve drug delivery on a cell-to-tissue scale (single-cell pharmacology), we developed the microscale pharmacokinetics/pharmacodynamics modeling framework “microPKPD”. I will present how this framework can be used to design optimal schedules for various treatments and to investigate the development of drug-induced resistance.

The first response of epithelial cells to local wounds is a dramatic increase in cytosolic calcium. This increase occurs quickly – calcium floods into damaged cells within 0.1 s, moves into adjacent cells over ~20 s, and appears in a much larger set of surrounding cells via a delayed second expansion over 40-300 s – but calcium is nonetheless a reporter: cells must detect wounds even earlier. Using the calcium response as a proxy for wound detection, we have identified an upstream G-protein-coupled-receptor (GPCR) signaling pathway, including the receptor and its chemokine ligand. We present experimental and computational evidence that multiple proteases released during cell lysis/wounding serve as the instructive signal, proteolytically liberating active ligand to diffuse to GPCRs on surrounding epithelial cells. Epithelial wounds are thus detected by the activation of a protease bait. We will discuss the experimental evidence and a corresponding computational model developed to test the plausibility of these hypothesized mechanisms. The model includes calcium currents between each cell’s cytosol and its endoplasmic reticulum (ER), between cytosol and extracellular space, and between the cytosol of neighboring cells. These calcium currents are initiated in the model by cavitation-induced microtears in the plasma membranes of cells near the wound (initial influx), by flow through gap junctions into adjacent cells (first expansion), and by the activation of GPCRs via a proteolytically activated diffusible ligand (second expansion). We will discuss how the model matches experimental observations and makes experimentally testable predictions. Supported by NIH Grant 1R01GM130130.

Comparisons are constantly being made between the 1918 influenza pandemic and the present COVID-19 pandemic. We will discuss our previous work on influenza pandemics, and the tools we have used to understand the temporal patterns of those outbreaks. Applying similar tools to the COVID-19 pandemic is easier in some respects and harder in others. We will describe our current approach to modelling the spread of COVID-19, and some of the challenges and limitations of epidemic forecasting.

Cells make fate decisions in response to dynamic environmental and pathological stimuli as well as cell-to-cell communications. Recent technological breakthroughs have enabled to gather data in previously unthinkable quantities at single cell level, starting to suggest that cell fate decision is much more complex, dynamic, and stochastic than previously recognized. Multiscale interactions, sometimes through cell-cell communications, play a critical role in cell decision-making. Dissecting cellular dynamics emerging from molecular and genomic scale in single-cell demands novel computational tools and multiscale models. In this talk, through multiple biological examples we will present our recent effort in the center to use single-cell RNA-seq data and spatial imaging data to uncover new insights in development, regeneration, and cancers. We will also present several new computational tools and mathematical modeling methods that are required to study the complex and dynamic cell fate process through the lens of single cells.

Throughout the lifespan of an organism, tissues are remodeled to shape organs and organisms and to maintain tissue integrity and homeostasis. Apical constriction is a ubiquitous cell shape change of epithelial tissues that promotes epithelia folding and cell/tissue invagination in a variety of contexts. Apical constriction promotes tissue bending by changing the shape of constituent cells from a columnar-shape to a wedge-shape. Drosophila gastrulation is one of the classic examples of apical constriction, where cells constrict to fold the primitive epithelial sheet and internalize cells that will give rise to internal organs. The actin cytoskeleton is organized in both time and space to facilitate apical constriction. We found that upstream signals that regulate apical constriction and myosin II activity exhibit a radially polarized spatial organization within the apical domain, which is critical for cell shape change. Furthermore, the cytoskeleton undergoes pulsatile dynamics, which are required for force transmission between cells. Finally, tissue wide forces orient cytoskeletal fibers to promote anisotropic force generation that promotes correct fold orientation.

Diffusion is the enemy of life. This is because diffusion is a ubiquitous feature of molecular motion that is constantly spreading things out, destroying molecular aggregates. However, all living organisms, whether single cell or multicellular have ways to use the reality of molecular diffusion to their advantage. That is, they expend energy to concentrate molecules and then use the fact that molecules move down their concentration gradient to do useful things. In this talk, I will show some of the ways that cells use diffusion to their advantage, to signal, to form structures and aggregates, and to make measurements of length and size of populations. Among the examples I will describe are signalling by nerves, cell polarization, bacterial quorum sensing, and regulation of flagellar molecular motors. In this way, I hope to convince you that living organisms have made diffusion their friend, not their enemy.

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Multiscale multicellular models combine representations of subcellular biological networks, cell behaviors, tissue level effects and whole body effects to describe tissue outcomes during development, homeostasis and disease. I will briefly introduce these simulation methodologies, the CompuCell3D simulation environment and their applications, then focus on a multiscale simulation of an acute primary infection of an epithelial tissue infected by a virus like SARS-CoV-2, a simplified cellular immune response and viral and immune-induced tissue damage. The model exhibits four basic parameter regimes: where the immune response fails to contain or significantly slow the spread of viral infection, where it significantly slows but fails to stop the spread of infection, where it eliminates all infected epithelial cells, but reinfection occurs from residual extracellular virus and where it clears the both infected cells and extracellular virus, leaving a substantial fraction of epithelial cells uninfected. Even this simplified model can illustrate the effects of a number of drug therapy concepts. Inhibition of viral internalization and faster immune-cell recruitment promote containment of infection. Fast viral internalization and slower immune response lead to uncontrolled spread of infection. Existing antivirals, despite blocking viral replication, show reduced clinical benefit when given later during the course of infection. Simulation of a drug which reduces the replication rate of viral RNA, shows that a low dosage that provides only a relatively limited reduction of viral RNA replication greatly decreases the total tissue damage and extracellular virus when given near the beginning of infection. However, even a high dosage that greatly reduces the rate of RNA replication rapidly loses efficacy when given later after infection. Many combinations of dosage and treatment time lead to distinct stochastic outcomes, with some replicas showing clearance or control of the virus (treatment success), while others show rapid infection of all epithelial cells (treatment failure). This switch between a regime of frequent treatment success and frequent failure occurs is quite abrupt as the time of treatment increases. The model is open-source and modular, allowing rapid development and extension of its components by groups working in parallel.

Binocular rivalry explores the question of how the brain copes with contradictory information. A subject is shown two different pictures – one to each eye. What images does the subject perceive? Results from rivalry experiments usually lead to alternation of percepts and are often surprising. Hugh Wilson proposed modeling rivalry in the brain by using structured networks of differential equations. We use Wilson networks as modeling devices and equivariant Hopf bifurcation as a tool to both post-dict and predict experimentally observed percepts. This work is joint with Casey Diekman, Zhong-Lin Lu, Tyler McMillen, Ian Stewart, Yunjiao Wang, and Yukai Zhao.

Until very recently most cancer biologists operated with the assumption that the most common route to metastasis involved cells of the primary tumor transforming to a motile single-cell phenotype via complete EMT (the epithelial-mesenchymal transition). This change allowed them to migrate individually to distant organs, eventually leading to clonal growths in other locations. But, a new more nuanced picture has been emerging, based on advanced measurements and on computational systems biology approaches. It has now been realized that cells can readily adopt states with hybrid properties, use these properties to move collectively and cooperatively, and reach distant niches as highly metastatic clusters. This talk will focus on the accumulating evidence for this revised perspective, the role of biological physics theory in instigating this whole line of investigation, and on open questions currently under investigation.

In this talk, we will use compartmental models to examine the power of age-targeted mitigation strategies for COVID-19. We will present evidence that, in the context of strategies which end with herd immunity, age-heterogeneous strategies are better for reducing direct mortalities across a wide parameter regime. And using a model which integrates empirical data on age-contact patterns in the United States and recent estimates of COVID-19 mortality and hospitalization rates, we will present evidence that age-targeted approaches have the potential to greatly reduce mortalities and ICU utilization for COVID-19, among strategies which ultimately end the epidemic by reaching herd immunity. This is joint work with Maria Chikina.

Narnaviruses have been described as positive-sense RNA viruses with a remarkably simple genome of 3 kb, encoding only a highly conserved RNA-dependent RNA polymerase (RdRp). Many narnaviruses, however, are "ambigrammatic" and harbor an additional uninterrupted open reading frame (ORF) covering almost the entire length of the reverse complement strand. No function has been described for this ORF, yet the absence of stops is conserved across diverse narnaviruses, and in every case the codons in the reverse ORF and the RdRp are aligned. The > 3 kb ORF overlap on opposite strands, unprecedented among RNA viruses, motivates an exploration of ambigrammatic sequences in general.

In this talk I will present a "dynamical paradigm" for modeling networks of interacting genes and proteins that regulate every aspect of cell physiology. The paradigm is based on dynamical systems theory of nonlinear ODEs, especially one- and two-parameter bifurcation diagrams. I will show how we have used this paradigm to unravel the mechanisms controlling "multiple fission" cycles in the photosynthetic green alga Chlamydomonas. While most eukaryotic cells maintain a characteristic size by executing binary division after each mass doubling, Chlamydomonas cells can grow more than eight-fold during daytime before undergoing rapid cycles of DNA replication, mitosis and cell division at night, which produce up to 16 daughter cells. We propose that this unusual strategy of growth and division (which is clearly advantageous for a photosynthetic organism) can be governed by a size-dependent bistable switch that turns on and off a limit cycle oscillator that drives cells through rapid cycles of DNA synthesis and mitosis. We show that this simple ‘sizer-oscillator’ arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model makes unexpected predictions about the size-dependence of the time of onset of cell-cycle oscillations after cells are transferred from light to dark conditions, and these predictions are confirmed by single-cell experiments. Collaborators: Stefan Heldt and Bela Novak (Oxford Univ) on the modeling; Fred Cross (Rockefeller Univ) on the experiments.

Zoom - see PIMS remote seminars for details

The closest point method (CPM) is a numerical method that was originally developed to solve partial differential equations (PDEs) on smooth, static surfaces using standard finite difference and interpolation methods. In this talk, we describe a recent generalization of the CPM to evolving surfaces. In our approach, the desired surface motion is obtained by evolving the underlying surface representation via the grid based particle method. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for reaction-diffusion, advection-diffusion and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.

The many different cell types and states result in large part from the different sets of genes they express. Gene expression level is encoded in the DNA sequence of the genome, and is interpreted by sequence-specific proteins called "transcription factors" (TFs). While characteristics of how TFs work are known, we lack a quantitative understanding of their function. Here, I describe a strategy using random DNA for building such a quantitative understanding, using yeast as a model system. I will provide a basic overview of how TFs recognize DNA, and why random DNA provides ideal gene regulatory "big data" for learning the relationship between DNA sequence and expression level. Using this strategy, we train highly complex models that learned a great deal about the biochemistry of transcriptional regulation, and gain insight into the activities of regulatory mutations.

In many bacteria, the segregation of their DNA is actively transported by a two protein system. One of the proteins acts as a substrate and binds to DNA in an ATP bound form, while the other stimulates its phosphatase activity, causing it to unbind after conversion to an ADP bound form. The result is a burnt-bridges style locomotion where the activity of the proteins generates a spatial gradient of the substrate that can drive motion. When this machinery is segregating low-copy plasmids, experiments show that the plasmids oscillate along the cell length, eventually placing themselves regularly along the cell. However it is unclear whether these oscillations persist as plasmids continue to replicate, or if system moves to a stable fixed point? Here I will present a deterministic model for the spatial dynamics of plasmids under the control of this two protein system. We find that over the course of the cell cycle, through a competition between spatial confinement and fluctuations in the amount of free substrate protein, the system can transition from a stable point to oscillations, then back to a stable point again. The prediction is that the system measures cell length via oscillations but eventually gets pushed into a fixed point that faithfully partitions the genetic information.

In vector-borne epidemic models there is often a substantial difference between the vector (usually insects) and host (usually humans) time scales. This makes it possible to view the model as a singular perturbation problem and use the quasi-steady state (equilibrium for the vector population in terms of the host population) to decompose the model into two problems of lower dimension and obtain a final size estimate for the epidemic.

Bacteria collective migration can spontaneously emerge when individuals follow common rules of interaction (chemotaxis), and a biased leakage during the migration can be observed, but it remains unclear how these behaviors are achieved. The traditional Keller-Segel model is successful in modeling chemotactic migration of a single phenotype in population/distribution level, in this talk we will introduce diversity to the model to study the collective migration. We reveal the mechanism behind collective migration through ‘analysis’ and numerical simulations. And we also make a connection to the Ornstein-Uhlenbeck process and Langevin equation to investigate the biased leakage. This is a joint-work with Xiongfei Fu and Yang Bai.

I will talk about modelling reports from around the world for the emerging novel coronavirus epidemic. I will explain their mathematical methods, findings and potential significance. At the moment I am not working on my own model, but this is a rapidly evolving situation so by Friday, who knows?

Breast cancer remains the second leading cause of cancer-related death with metastasis accounting around 90% of the total deaths. Specialized subcellular structures termed invadopodia play a critical role in metastasis, aiding tumor cell dissemination to distant sites. Invadopodia have documented roles in aiding tumor cells movement into (intravasation) and out of (extravasation) the blood vessels. While movement through the hematogenous system is well characterised, we are limited in our understanding of dissemination through the lymphatics. In this study we explore the role of invadopodia in aiding tumor cells invasion through the lymphatics. To impair invadopodia formation, knockout (KO) of key invadopodial regulatory protein Tks5 was performed in human breast cancer cells MDA-MB-231. Invadopodia formation in Tks5-KO cells was found to be completely abolished. We assessed cell invasion across a lymphatic monolayer and found a significant reduction in lymphatic invasion for Tks5-KO cells. Next, using transendothelial electrical resistance (TEER) we measured lymphatic tight junction integrity and found that control cells were able to reduce lymphatic tight junctions but this was significantly impaired in Tks5-KO. Overall, the inability of Tks5-KO cells to form invadopodia compromised their ability to invade through the lymphatics suggesting that invadopodia aid tumor cells invasion through the lymphatic system. Current studies are expanding on this work to better understand the role of invadopodia in lymphatic dissemination through the use of live cell imaging and bioluminescent imaging of progression and lymphatic invasion in mice.

Epithelial cells organize themselves into tubes for the necessary functions of gas and nutrient transport, and the production and secretion of hormones and enzymes. Such tubes result from the organization and collective motion of a flat sheet of polarized epthelial cells through either a wrapping or budding process. The Drosophila Salivary Gland is one such tube that results from the budding of a 2D placode of cells. Through orchestrated cell movements and cell rearrangements, the nascent tube begins to form. In this talk, we develop a novel 3D-vertex model that allows for the investigation and quantification of the role that cellular mechanics and cellular rearrangements play during this vital morphogenetic process.

Different mathematical models (direct and indirect transmission models) were used to understand and analyze different infectious diseases dynamics and possible prevention and/or elimination strategies. As a first step, an age of infection model with heterogeneous mixing and indirect transmission was considered. The simplest form of SIRP epidemic model was introduced and served as a basis for other models. Most mathematical results in this part were based on the basic reproduction number and the final size relation. The epidemic model was further extended to incorporate the effect of diffusion and how the coupled PDE-ODE system could be reduced to an ODE system with a diffusion term. A novel approach to modeling air-transmitted diseases using an ODE system was proposed, and showed how the reduced ODE system approximates the coupled PDE-ODE system. In addition, a deterministic compartmental model of the co-interaction of HIV and infectious syphilis transmission (direct transmission) among gay, bisexual and other men who have sex with men (gbMSM) was developed and used to examine the impact of syphilis infection on the HIV epidemic, and vice versa. Analytical expressions for the reproduction number and necessary conditions under which disease-free and endemic equilibria are asymptotically stable were established. Numerical simulations were performed and used to support the analytical results. Finally, the co-interaction model was modified to assess the impact of combining different HIV and syphilis interventions on HIV incidence, HIV prevalence, syphilis incidence and all-cause mortality among gbMSM in British Columbia from 2019 to 2028. Plausible strategies for the elimination of both diseases were evaluated. According to our model predictions and based on the World Health Organization (WHO) threshold for disease elimination, we suggested the most effective strategies to eradicate the HIV and syphilis epidemics over a 10-year intervention period. The results of the research suggest diverse ways in which infectious diseases could be modeled, and possible ways to improve the health of individuals and reduce the overall disease burden, ultimately resulting in improved epidemic control.

Swimming bacteria with helical flagella are self-propelled micro-swimmers in nature, and the swimming strategies of such bacteria vary depending on the number and the position of flagella on the cell body. In this talk, I will introduce two microorganisms, multi-flagellated E. coli and single-flagellated Vibrio A. The Kirchhoff rod theory is used to model the elastic helical flagella and the rod-shaped cell body is represented by a hollow ellipsoid that can translate and rotate as a neutrally buoyant rigid body interacting with a surrounding fluid. The hydrodynamic interaction between the fluid and the bacteria is described by the regularized version of Stokes flow. I will focus on how bacteria can swim and reorient swimming course for survival and how Mathematics can help to understand the swimming mechanism of such bacteria.

The green sea turtle Chelonia midas travels for thousands of miles from the coast of Brazil to a small island in the Atlantic Ocean, Ascension Island. There the turtles lay their eggs into the warm sand on the beach. It is a classic scientific challenge to understand the navigational skills of the turtles and several orienteering mechanisms are discussed, such as geomagnetic information, chemotaxis, Atlantic flow patterns etc. In this talk I will present a mathematical model for the homing of sea turtles and discuss how it can be used to identify the navigational mechanisms of sea turtles. (joint work with K.J. Painter).

Different types of cells, i.e. from different tissues, typically look quite different from each other. Even when cultured on two-dimensional surfaces like glass slides or tissue culture polystyrene under identical conditions, cells adopt different shapes. These shapes are in general functions of the cytoskeletal properties of those cells, itself a subset of what we can call the “state” of the cell. Experimental evidence over several decades has indicated that for some cell types, imposed changes in shape lead to changes in cellular differentiation and other properties. Conversely there is increasing evidence that some changes in cell state can lead to stereotypical changes in cell shape. We have developed a large number of morphological parameters to quantify cell shape and cytoskeletal morphology. Using these parameters to quantify morphologies of different cell lines, as well as cells in different experimental conditions, we show that quantifiers of cell shape and cytoskeletal texture can be used to discriminate between different cell states. A neural network is able to correctly classify different cell states with high accuracy. Using projections of the data to lower-dimensional shape space, we find that we can distinguish between similar and dissimilar changes in shape. We use this method to identify similarities in shape changes between breast cancer and osteosarcoma cell lines accompanying the acquisition of invasive characteristics. Our data indicates that cellular morphology is a powerful and sensitive window into the physiological state of the cell, and underline the need to develop mechanistic models that relate cell state to cell shape.

A major challenge in mathematical analysis of infectious diseases is that the epidemic process is usually only partially observed. Although we might be able to identify when an individual became symptomatic, rarely can we observe when infection began or from whom it was transmitted. This means that the likelihood of the observed data is computationally intractable for any more than a handful of infected cases. Although data-augmented Markov Chain Monte Carlo methods are generally considered the gold standard for analysis of partial epidemic data since they employ a tractable augmented likelihood, they also often struggle for large population sizes. I will describe a new approach which seeks to instead approximate the likelihood by exploiting the underlying structure of the epidemic model, without the need for augmentation. We regard this approach as a useful and adaptable addition to the toolkit for analysing infectious disease data, and I will provide examples of applications to real outbreaks and a variety of disease transmission models.

Reptiles have the ability to replace their teeth continuously throughout life. Replacement occurs in highly patterned waves passing from the back to the front of the mouth, in alternating tooth positions. Although this pattern has been recognized for over 100 years, the formation and maintenance of this pattern is not well understood. In this presentation, I will present work being undertaken in the Richman lab at UBC to attempt and understand the mechanisms of continuous tooth replacement in a reptile model organism, the leopard gecko. We performed tooth removal surgeries on adult geckos and tracked tooth replacement for over one year post-surgery. The pattern of tooth replacement was analyzed, and preliminary results suggest that signaling between adjacent teeth might be the primary control over the alternating replacement pattern.

A key question in population biology is understanding the conditions under which the species of an ecosystem persist or go extinct. Theoretical and empirical studies have shown that persistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n interacting species that live in a stochastic environment. Our models are described by n dimensional piecewise deterministic Markov processes. These are processes (X(t), r(t)) where the vector X denotes the density of the n species and r(t) is a finite state space process which keeps track of the environment. In any fixed environment the process follows the flow given by a system of ordinary differential equations. The randomness comes from the changes or switches in the environment, which happen at random times. We give sharp conditions under which the populations persist as well as conditions under which some populations go extinct exponentially fast. As an example we look at the competitive exclusion principle from ecology and show how the random switching can rescue species from extinction.

A diffusion-type operator biologically significant in neuroscience is a difference of Gaussian functions used as a spatial-convolution kernel (Mexican-Hat operator). We are interested in the dynamics inherent in a neural structure such as visual cortex modeled by stochastic neural field equations, a class of stochastic differential-integral equations using the Mexican-Hat kernel. We find that spatially smoothed noise, in a field of Ornstein-Uhlenbeck processes, without direct spatial coupling, causes pattern formation. Our analysis of the interaction between coupling and noise-sharing yields optimal parameter combinations for the formation of spatial pattern. Joint work with PH Baxendale and LM Ward, recently on line, Phys.Rev.E

The Hedtrich lab is developing human-based organ models with a current focus on skin and lung. They are specifically interested in the modeling of inflammatory and genetic diseases in vitro and use the organ models to study (patho)physiological mechanism. In this talk, Dr. Hedtrich will give an overview of the different approaches in her lab has with emphasize on their work done in atopic diseases and the atopic march.

One of the best studied experimental models for selforganization in embryonic development is the formation of skeletal elements in tetrapod limbs, in particular in the chicken and the mouse. Here cells aggregate to form chondrogenic condensations, which later turn into cartilage, then bone. This behavior is also seen in vitro in so-called micromass experiments. Several models for the underlying pattern forming mechanism have been proposed, notably Turing-type reaction-diffusion mechanisms and positional information mechanisms based on spatiotemporal gradients of signaling molecules. However the exact regulatory mechanisms for this process are far from understood. We present a model based on the experimentally established dynamics of a multiscale regulatory network consisting of two glycan-binding proteins expressed early in chick limb development: CG (chicken galectin)-1A, CG-8 and their counterreceptors. The model consists of a system of partial differential equations containing a nonlocal term to represent cell-cell adhesion, adapted from the work of Armstrong, Painter and Sherratt. Due to the high dimensionality of the problem, published results have only been in one spatial dimension. We present new results in two spatial dimensions, which allow for exploration of the topology of two dimensional patterns that can be generated. The full model recapitulates qualitatively and quantitatively the experimental results of network perturbation and leads to new predictions. This talk is based on joint work with S. A. Newman (NY Medical College), R. Bhat (Indian Institute of Science, Bangalore) and J. Zhang (West. Wash Univ.) .

The growth regulator auxin plays a central role in development across plants. Auxin spatial patterning is critical in the phyllotactic arrangement of leaves along a stem, the shapes of the leaves themselves, and venation within leaves. These patterns depend on polar auxin transport (PAT) at the cellular level, particularly the preferential allocation of PIN efflux proteins to certain areas of the plasma membrane. Two general mechanisms have been studied: an up-the-gradient (UTG) allocation dependent on neighbouring-cell auxin concentrations, and a with-the-flux (WTF) allocation dependent on the flow of auxin across walls. We developed a combined UTG+WTF model for leaf venation. The model simulates intracellular and membrane kinetics and intercellular transport, and is solved for a 2D leaf of several hundred cells. We find that vein initiation in the leaf margin and cell polarization towards new veins is UTG-driven, while WTF is critical for vein extension. UTG is important for joining veins to form a network structure. The model produces the experimentally observed succession of effects when PAT is increasingly inhibited by NPA treatment. Venation patterns are highly correlated with leaf shape; this model enables the investigation of how PAT dynamics contribute to the diversity of leaf shapes across plants.

A coupled PDE-ODE model used to describe communication between dynamically active signaling compartments (biological cells) is analyzed using strong localized perturbation theory. In the limit D >> 1, the coupled model is reduced into a nonlinear system of ODEs, which is then used to study global coupling and synchronous oscillations among the cells. In addition, this reduced system is used to study quorum sensing and phase synchronization among the cells.

The translation of proteins is a key part of the central dogma of biology that underlies life. Thus, unraveling the dynamics of translation and understanding how this process is regulated across scales, systems and species, is fundamental. In light of recent experimental data, I will present theoretical and computational tools, which we developed for the past few years, to study translation at the molecular, mesoscopic (single rNA), and macroscopic levels. By combining methods and models from computational geometry, stochastic analysis and systems biology, with sequencing, Cryo-EM and other experimental data, our results highlight the fundamental and complex role played by the ribosomes in modulating the dynamics of translation and its efficiency, which also leads to many challenging and still open questions.

In this talk we introduce a mathematical model to describe temporal processes like embryonic development and cellular reprogramming. We consider stochastic processes in gene expression space to represent developing populations of cells, and we use optimal transport to recover the temporal couplings of the process. We apply these ideas to study 315,000 single-cell RNA-sequencing profiles collected at 40 time points over 18 days of reprogramming fibroblasts into induced pluripotent stem cells. To validate the optimal transport model, we demonstrate that it can accurately predict developmental states at held-out time points. We construct a high-resolution map of reprogramming that rediscovers known features; uncovers new alternative cell fates including neural- and placental-like cells; predicts the origin and fate of any cell class; and implicates regulatory models in particular trajectories. Of these findings, we highlight the transcription factor Obox6 and the paracrine signaling factor GDF9, which we experimentally show enhance reprogramming efficiency. Our approach provides a general framework for investigating cellular differentiation, and poses some interesting theoretical questions.

Cellular movement plays important roles in many (patho)physiological processes, such as immune cell response, growth of neuronal axons and cancer. The regulation of this movement depends on the interaction of several key proteins implicated in the development of cellular polarity (consisting of a front and a back) and the formation of protein complexes called adhesions. Adhesions anchor the cell to its substrate, allowing it to migrate. In CHO cells, three classes of adhesion can be identified based on size and dynamic properties: nascent adhesions, focal complexes and focal adhesions. When cells extends forward at the front, nascent adhesions assemble and anchor the leading edge to the substrate, while focal adhesions at the back disassemble, allowing detachment, retraction and forward movement. The dynamics of these processes are controlled by a number of regulatory factors, occurring on both cell-wide and adhesion-level scales. The coordination of these regulatory factors is complex, but insights into their dynamics can be gained from the use of mathematical/biophysical modeling techniques which integrate many of these components together. In this talk, I will present our recently developed molecularly-explicit and mechanosensitive models of cell polarity and adhesion dynamics to explore how local regulation of key adhesion proteins (including paxillin, rho family of GTPases and integrin) produce cell-wide polarization and nascent adhesion assembly/disassembly. The dynamics associated with various parameter regimes will be presented and insights into the mechanisms regulating adhesion dynamics will be provided.

First, we review recent experiments on and biophysical modelling approaches for the early stages of osmotically spreading biofilms at an agar-air interface (e.g. [1,2]). Doing so, we highlight important experimental features and successes/limitations of the various models. In particular, it is pointed out that modelling has paid little attention to the physico-chemical interactions of the film and the agar (adhesion, wettability, etc) [3]. We propose to incorporate these surface forces in the form of a wetting potential that accounts for finite contact angles at the three-phase contact line where biofilm, agar and gas phase meet. Second, we establish the basic modelling principles of thin-film hydrodynamics for the dynamics of free surface films of mixtures and suspensions where all aspects of capillarity and wettability may, in principle, depend on the local film composition. We argue that in a passive (non-bioactive) limit one has to be able to write all such models in the form of a gradient dynamics. The passive model is then extended by bioactive terms like bacterial proliferation and matrix or biosurfactant production to reach a set of simplified models for the growth dynamics of biofilms [4]. Finally, we employ such models to investigate two phenomena: (i) It is shown that surface forces determine whether a biofilm can expand laterally over a substrate. In particular, we discuss modelling results and experimental evidence related to a transition between continuous and arrested spreading for Bacillus subtilis biofilms [5]. In the case of arrested spreading, the lateral expansion of the biofilm is confined, albeit the colony is biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading. (ii) As second phenomenon we discuss the relation of fingering instabilities of an advancing biofilm edge and the production of biosurfactant within the biofilm. As a result we distinguish four dynamical (morphological) modes of biofilm growth [6]. We conclude with an outlook. [1] Fauvart, M. et al., Surface tension gradient control of bacterial swarming in colonies of Pseudomonas aeruginosa, Soft Matter, 2012, 8, 70-76. [2] Seminara, A. et al., Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 1116-1121. [3] Tuson, H., Weibel, D. Bacteria-surface interactions, Soft Matter, 2013, 9, 4368-4380. [4] Trinschek, S.; John, K.; Thiele, U., From a thin film model for passive suspensions towards the description of osmotic biofilm spreading, AIMS Materials Science, 2016, 3, 1138-1159. [5] Trinschek, S.; John, K.; Lecuyer, S.; Thiele, U., Continuous vs. arrested spreading of biofilms at solid-gas interfaces - the role of surface forces, Phys. Rev. Lett., 2017, 119, 078003. [6] Trinschek, S.; John, K.; Thiele, U.; Modelling of surfactant-driven front instabilities in spreading bacterial colonies Soft Matter, 2018, 14, 4464-4476.

Cellular organization is regulated by a complex network of interactions between cytoskeletal regulators and the cytoskeleton itself. Here I will utilize mathematical modeling discuss how these complex interactions can give rise to a range of morphological cellular behaviors. I’ll discuss 1) how Rho GTPase dynamics give rise to a diverse array of cellular morphologies observed experimentally. 2) How feedback interactions between the cytoskeleton and the proteins responsible for its remodeling influence the dynamics of actin remodeling. 3) How interactions between the extra cellular matrix and Rho GTPase signaling modulate cellular migration. And 4) how feedbacks between GTPase signaling and membrane tension provide a mechanical means for cells to adapt to high concentration signaling environments. Together these investigations paint a picture where Rho GTPases form a signaling hub of cytoskeletal regulation and feedbacks between them and cellular remodeling lead to a diverse array of cellular dynamics.

Tissue growth requires cells of various types to organise themselves into the appropriate patterns and structures to produce viable, functional tissue. Similar processes occur in tissue repair (e.g. wound healing) or in biofilms (communities of bacteria or yeast cells). Understanding how this organisation is coordinated is therefore an important basic problem in biology. I will present a brief overview of recent work on pattern formation in vitro (in biofilms, and in interacting cell populations) using both continuum and individual-cell based models. A particular focus of our work has been on using image processing methods and spatial statistics (such as pair-correlation functions) to quantify both experimental data and model outputs, to facilitate comparisons between the two.

A primary goal of evolution biology is to understand the mechanisms that generate and shape the vast diversity of life. From stable polymorphisms at susceptibility loci to the maintenance of sexual reproduction, pathogens are thought to play an import role in the maintenance of genetic diversity of their hosts. Indeed as evidenced by the death toll of the Plague in 14th century Europe to the decimation of African undulates by Rinderpest, infectious pathogens can exert strong selective pressures on their hosts. Using methods from Epidemiology we modelled coevolution between hosts and their infectious pathogens. We explore how coevolution, epidemiology, and stochasticity shape the genetic diversity of hosts.

As climate warms, different phenotypes, such as different flowering time in plants or breeding date in birds, are favored by natural selection. To persist, species must therefore change their geographical distribution to track the climate to which they were adapted to, and/or their phenotypic distribution to adapt to new climates. Quantitative genetics models describing joint changes in phenotypic and geographical distributions have been developed in the nineties to better understand the challenges faced by species under climate change. We have built on this work by examining how the life cycle of species affects and jointly evolves with these dynamics: I will present a few examples of work in progress where collaboration between mathematicians and evolutionary biologists have led to new insights on how age-structure, mode of reproduction, mutation and dispersal affect the response of species to climate change.

Identifying and visualizing meaningful clusters within high-dimensional (HD) data is an important but challenging problem with applications to molecular biology and biomedicine. For example, mass cytometry (CyTOF) is a high-throughput single-cell technology that can quantify the abundance of >30 proteins simultaneously in single cells. CyTOF is commonly used to to investigate phenotypic heterogeneity in tumours, but this demands identification of biologically meaningful clusters from CyTOF data. The "curse of dimensionality" poses computational challenges when analyzing HD data. Another major difficulty common to most clustering algorithms is choosing optimal values for input parameters such as the number of clusters, K. I will present a new measure of similarity between clusters in HD data using local dimensionality reduction followed by triangulation of alpha shapes. Using this new approach, which I call ASTRICS, HD data can initially be over-clustered using an existing clustering algorithm with a very conservative choice of K. ASTRICS then generates a K x K similarity matrix, which can also be interpreted as a weighted graph, for the K clusters. In turn, this can be used as input for any similarity- or graph-based clustering algorithm, and force-directed layout of the graph can be used to visualize the initial K clusters in two or three dimensions. The introduction of ASTRICS as a fully automated, intermediate step in clustering or visualization of HD data alleviates some of the difficulties of parameter selection. Some community detection (i.e. clustering) algorithms for graphs do not require any input parameters to be specified by the user. Otherwise, the visualization afforded by ASTRICS can be used to guide parameter selection for the final clustering step. In this talk, I will demonstrate application of ASTRICS to clustering and visualizing CyTOF data. I will also illustrate the broader utility of ASTRICS beyond biology by applying it to the popular MNIST digital image dataset.

Single particle tracking is a powerful tool to study the mobility of molecules in the cell membrane. The most common approaches in analyzing these kinds of data are mean squared displacement and analyses with one or more hidden Markov states. However, in most experiments, positional measurements contain systematic and random errors, and to achieve proper fits, we must take these errors into account. In this work, we develop a hidden Markov model with multiple diffusive states. Our goal is to estimate the diffusion coefficients and transition probabilities between different states incorporating uncertainty due to measurement error in a rational way. Moreover, we also develop a Bayesian nonparametrics framework to estimate the number of states in the hidden Markov model, and then using information from the data we find the optimal Markov Model that describes that data. We test our methods using simulated data and present results using particle tracks obtained from surface receptor molecules on B cells.

Epstein-Barr virus (EBV) is a ubiquitous infection worldwide and is associated with the development of several kinds of cancers. Rates of EBV replication and disease are higher in individuals who are co-infected with HIV-1; however, the causes of this remain unknown. Here, we developed a mathematical model to describe the dynamics of EBV infection within the tonsils and analyzed oral EBV shedding data in a cohort of adults from Uganda to predict the role of HIV-1 in determining infection severity.

STORM is a super-resolution technique that uses photoswitchable fluorophores to achieve resolutions at or below 20nm. A downside of STORM is the possibility of recording several blinks from one fluorophore, affecting the estimation of the number of molecules detected in the image. I constructed a mathematical model to identify unique fluorophores in STORM images by independently using the localization and the time series of the observations. The temporal sequence is described with a Markov chain approach and their spatial distribution with a Gaussian mixture model. To estimate the parameter values, I implemented a maximum likelihood procedure which requires a mixed optimization. I have tested my protocol in simulated data and I will use it to improve STORM images of B-cell surface receptors. B-cell receptors distribution on the membrane has been related to B-cell activation. This model will enhance a microscopy technique that is already widely used in biological applications and will allow to deeper analyze immune cells signaling.

The neural crest offers a unique model system to study cell migration mechanisms during vertebrate embryogenesis since migrating cells are accessible to in vivo time-lapse imaging and manipulation. We recently discovered by single cell profiling that lead cells of neural crest migratory streams express a distinct set of genes. By combining agent-based modeling and experiment, we are testing the function of novel genes for their role in cell invasion. I will discuss the function of two of these genes in the context of our current cell-induced gradient model of neural crest cell migration.

My research program is motivated by fascination with bird flight. My laboratory group uses a multi-disciplinary approach that includes biomechanics, physiology, and neuroscience to examine flight ability. Our current research is organized around two topics: 1) how birds morph their wings and what benefits this provides; and 2) how optic flow signals are encoded in the avian brain and used to guide their flight. As we gain understanding of flight mechanisms, we further endeavor to apply comparative approaches that provide deeper insight into avian ecology and evolution.

Insulin is an essential hormone that regulates nutrient homeostasis. Insufficient insulin results in diabetes, one of the most prevalent and costly diseases. Although the primary actions of insulin are to induce glucose uptake and metabolism in distant tissues, including muscle, fat and liver, the insulin secreting pancreatic beta-cells contain a high number of insulin receptors and known to respond to the hormone. On a minute-to-minute time-scale, insulin has been reported to have negative feedback effects on its own secretion, and we have data suggesting that the actions of insulin may be context-dependent, potentially depending on the ambient glucose levels (which are primarily controlled by glucose). Insulin has also been reported to have positive effects on its own synthesis and on the survival of the beta-cells over a timescale of months. Within beta-cells, insulin production is inherently stressful and exerts a negative effect on beta-cell proliferation that is most pronounced at a young age. We have also recently found that single beta-cells can exist in ‘bursting’ states of elevated insulin production that account for a significant proportion of the previous described heterogeneity in this cell type. Thus, using a variety of experimental approaches, we seek to understand context-dependent insulin feedback signalling on single beta-cells and their collective populations and we are interested in collaborating to build quantitative and testable models that could be used to explain the pathogenesis of diabetes. We also interested in expanding models to include other tissues and other soluble factors that are also relevant in nutrient homeostasis and diabetes.

There are numerous genetic, molecular and physical factors that all need to be carefully orchestrated to create the face. When one or more of these processes goes awry during embryonic development, birth defects such as cleft lip result. In the past, our work has focused on several molecular signals and how they regulate facial growth. Here we investigate in an unbiased manner, the extrinsic and intrinsic factors contributing to shaping of the face. This presentation will describe new methods to track embryonic mesenchymal cells by marking cell nuclei in a defined culture system. These tracking data were analyzed over time and space to determine the order and disorder in the tissue. K-means clustering revealed a surprising degree of coordination in regions of the tissue. The normalization of the data throughout the whole centre of the face showed that there was a high degree of right-left symmetry. These reflected data support strong genetic control over cell movements. Furthermore, the block of intrinsic cytoskeletal remodeling with a drug, completely disrupted these conserved patterns of cell movements. Taken together the collaboration between biologists and mathematicians has shed new light on the fundamental mechanisms driving facial morphogenesis.

The Min protein system is critical for correct cell division, and is observed to produce a variety of interesting patterns, both in vitro and in vivo. I explore the behavior of a model of the min system far from the parameter regime where they were originally, and go onto to study the process of "Burst formation", using the techniques of Large Deviation theory to determine the time of burst formation, along with the predicted shape of bursts formed.

When two identical nonlinear oscillators are coupled through a 1-D bulk diffusion field, new patterns of synchronization occur that would be absent in the uncoupled system. Furthermore, if the two oscillators are quiescent, the effect of the coupling can be to turn the oscillations on. Mathematically, the models consist of systems of nonlinear ODEs coupled with linear diffusive PDEs. Through a detailed bifurcation analysis of three different examples, we reveal some of the underlying mechanisms behind phenomena as diverse as the diffusion sensing of reacting agents, the synchronization of chaotic oscillations and the formation of membrane-bound patterns at the cell-scale level.

Human milk production is controlled by a variety of internal and external factors, including hormones, neurons, suckling stimulus and milk removal. One method for increasing milk production colloquially suggested to mothers who want to produce more milk is cluster feeding: feeding more frequently during certain periods of the day rather than leaving equal time between feedings. Models have been proposed to describe average weekly milk production rates in dairy cattle, but these models do not take into account the effect of the milk removal schedule used. In this talk, I will present a model for describing milk production in response to set feeding regimens and introduce a model for infant metabolism.

Microbial communities routinely have several alternative stable states observed for the same environmental parameters. A possibility of sudden and irreversible transitions between these states (regime shifts) complicates external manipulation of these systems. Can we predict which specific perturbations may induce such regime shifts and which would have only a transient effect? Here I will describe several new conceptual models that exhibit these emergent phenomena. Two of our models [2,3] were inspired by a decades-old economics work: the stable marriage or stable allocation problem, developed by Gale and Shapley in the 1960s and awarded the Nobel prize in economics in 2012. Using only the ranked tables of nutrient preferences and competitive abilities of microbes, we can determine all stable states and specific perturbations driving the system from one state to another.

Cell migration is a fundamentally important phenomenon underlying wound healing, tissue development, immune response and cancer metastasis. Understanding basic physics of the cell migration presented a great challenge until, in the last three decades, a combination of biological, biophysical and mathematical approaches shed light on basic mechanisms of the cell migration. I will describe models, based on nonlinear partial differential equations and free boundary problems, which predicted that individual cells do not linger in a symmetric stationary state for too long, but rather spontaneously break symmetry and initiate motility. The cells can either crawl straight, or turn, depending on mechanical parameters. I will show how experimental data supported the models, and I will also review current computational challenges.

The Min system in E. coli is one of the simplest known biological systems that demonstrates diverse complex dynamic behavior or transduces local interactions into a global signal. Various mathematical models of the Min system show behaviors that are qualitatively similar to dynamic behaviors of the Min system that have been observed in experiments, but no model has been quantitatively compared to time-course data. In this talk, I will discuss extracting time-course data for model fitting from experimental measurements of the Min system and fitting established and novel biochemistry-based models to the time-course data using a homotopy-minimization method for parameter estimation in differential equations. Comparing models to time-course data allows me to make precise distinctions between biochemical assumptions in the various models. I will discuss how my modeling and fitting supports a novel model, which suggests that a regular, ordered, stability-switching mechanism underlies the emergent, dynamic behavior of the Min system.

Microbial communities play major roles in human health and disease and dominate global biochemi­cal cycles. Many proper­ties of these communities emerge from interactions between its mem­ber species and cannot be understood based on the properties of its members living in isolation. The ubiquity of these emergent properties has led some researchers to conclude that microbial commu­nities evolve by multi-level selection (MLS) where selection acts at both the levels of individuals and communi­ties. However, this view is controversial and whether MLS plays a role in natural microbial communities has been heatedly debated in the recent literature. The main controversy in the de­bate is whether community level properties can be inherited. Whether this is the case will depend on the quantitative details of how communities are assembled. For example, the community composition of host-associated communities that are vertically-transmitted between host generations will remain relatively constant through time, allowing for high degrees of heritability of community level traits. In contrast, the composition of communities assembled from the environment can fluctuate strongly in time, leading to low levels of heritability. In general, we need a quantitative method to predict the degree of heritability based on the dynamics of community assembly. Here we present such a method which is based on a recently published MLS framework that explicitly models both individual and community level dynamics. We are attempting to extract generalized rules that can predict the degree of heritability of community level traits for naturally occurring microbial communities. With this framework, we hope to change the focus of the ongoing debate from the question of whether microbial communities can evolve by MLS to the more productive question of which communities can evolve by MLS.

Geoff plans to talk about the transition from proliferation to differentiation, which is work following up on the paper that his group recently published in Current Biology. See: https://phys.org/news/2018-08-secrets.html

GTPases are a family of signalling proteins that controls cell shape by regulating the actin cytoskeleton. Understanding the dynamics of GTPase activity is essential toward deciphering the mechanisms behind cell motility and filopodia formation. In this talk, I will present several modelling approaches with ODEs and PDEs, numerical simulations and analytical results on their bifurcation behaviors.

Chikungunya is a viral disease transmitted to humans by infected mosquitoes: Aedes aegypti and Aedes albopictus. It causes fever and severe joint pain. Other symptoms include muscle pain, headache, nausea, fatigue and rash. Joint pain is often debilitating and can vary in duration. Some of the main mathematical methods to simulate Chikungunya spread are set as ordinary differential equations over compartmental models, SEIR for host and sei for vectors. We propose a spatio-temporal description of chikungunya spread using a cellular automata over unstructured triangular meshes.

While vaccines are available and are effective in protecting against colonisation and disease with Streptococcus pneumoniae, their effectiveness is limited by strain (serotype) replacement following widespread vaccination. Understanding the post-vaccination balance of serotypes would present the opportunity to achieve a final population composed of the most benign (non-invasive) strains. However, the complex ecology of the pneumococcus makes it difficult to predict the post-vaccination balance of strains. Recently, Corander et al proposed that there is widespread apparent negative frequency-dependent selection (NFDS) in the pneumococcus (Corander et al 2017 Nat. Ecol. Evol.). Here, we use this principle to develop a deterministic model of pneumococcal strain dynamics, and use the model to make predictions about the ecological response of the pneumococcal population to new candidate vaccine strategies. We find that we can identify formulations that out-perform existing formulations in the model. Furthermore, it is possible to obtain a final model population that scores as well as the currently used formulation, using a vaccine strategy with fewer serotypes -- these formulations would be much less costly to produce than current vaccines. We suggest that this approach could provide a template for principled vaccine design based on global surveillance data and genomics. This is joint work with N. Croucher.

A traditional population-genetics approach studies geneaologies in a population of a fixed size, which forms the basis of several spectral theories of finite samples. In contrast, a population of tumor cells typically experiences an exponential growth phase in its initial progression, which is far from constant population size. In this work, I develop two different numerical procedures, one of which is based on forward-in-time and the other is based on backward-in-time treatment, to derive allele frequency spectrum in such exponentially growing cancer cell populations. We find significance bias toward singletons both analytically and numerically, which reflects the fact that most observed mutations have recent origins in a growing population.

During early vertebrate embryogenesis, neural crest cells (NCCs) migrate in clusters from the neural tube to various target locations over long distances. Their collective migration is tightly regulated by environmental signals and intercellular interactions. Curiously, NCC clusters are capable of spontaneously developing a persistent migration down migratory corridors in the absence of chemoattractants. To understand this phenomenon, we built a vertex-dynamics model that predicts the key modes of cell interactions—contact inhibition of locomotion (CIL) and co-attraction (COA)—through the modulation of Rho GTPase biochemistry. Using such a signaling-based model, as opposed to implementing hard-coded simulation rules, we find that CIL and COA conspire to suppress Rac1 activity, leading to the persistence of polarization (POP) of clustering cells and thus the spontaneous directional migration in the absence of chemical gradients.

We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individual-based model which includes frequency dependent selection caused by m-player game interactions and stochastic fluctuations due to random genetic drift and mutation. We prove that under a proper scaling limit as the population size increases the system converges to the solution of replicator-mutator equations. Our result establishes an affirmative mathematical base to the adaptive dynamics formulation employed in the theory of the mathematical biology.

TBA

Mathematical models for population dynamics have a long history in biomathematics. They are tools to explore the effects of birth and death, species interaction, landscape quality and spatial movement on the persistence, spread and spatial distribution of a species. One particular question is how spatial variation in landscape attributes affects the dynamics of populations, for example in the context of species invasions. A relatively recent approach to this question divides a landscape into "patches" and incorporates small-scale individual movement information to predict large-scale population dynamics. In this talk, I will review several aspects of this growing body of literature. I will include empirical evidence, model derivation, basic model outcomes, analytical challenges and some future ideas. The talk is aimed at a general mathbio audience.

Hepatitis B virus (HBV) infection is a liver disorder that can result in cirrhosis, liver failure and hepatocellular carcinoma. HBV infection remains a major global health problem, as it affects more 350 million people chronically and kills roughly 600,000 people annually. Drugs currently used against HBV include IFN-α that decreases viremia, inflammation and the growth of liver fibrosis, and adefovir that decreases the viral load. Each of these drugs can have severe side-effects. In the present paper, we consider the treatment of chronic HBV by a combination of IFN-α and adefovir, and raise the followingquestion: What should be the optimal ratio between IFN-α and adefovir in order to achieve the best ‘efficacy’ under constraints on the total amount of the drugs; here the efficacy is measured by the reduction of the levels of inflammation and of fibrosis? We develop a mathematical model of HBV pathogenesis by a system of partial differential equations (PDEs) and use the model to simulate a ‘synergy map’ which addresses the above question.

Changes in cell-substrate adhesion are believed to signal the onset of cancer metastasis, but such changes must be quantified against background levels of intrinsic heterogeneity between cells. Variations in cell-substrate adhesion strengths can be probed through biophysical measurements of cell detachment from substrates upon the application of an external force. I will describe theoretical and experimental investigations of the detachment of cells adhered to substrates when these cells are subjected to fluid shear. I will present a theoretical framework within which we calculate the fraction of detached cells as a function of shear stress for fast ramps as well as for the decay in the fraction of detached cells at fixed shear stress as a function of time. Using HEK and 3T3 fibroblast cells as experimental model systems, characteristic force scales for cell adhesion as well as characteristic detachment times are extracted. Variations in adhesion across cell types are especially prominent when cell detachment is probed by applying a time-varying shear stress. These methods can be applied to characterizing changes in cell adhesion in a variety of contexts, including metastasis.

Model approaches to nuclear architecture have traditionally ignored the consequences of ATP-fueled active processes acting on chromatin. However, such activity is a source of stochastic forces that are substantially larger than the Brownian forces present at physiological temperatures. I will describe a first-principles approach to large-scale nuclear architecture in metazoans that incorporates such activity. The model predicts the statistics of positional distributions, shapes and overlaps of each chromosome. Our simulations reproduce common organising principles underlying large-scale nuclear architecture across human cell nuclei in interphase. These include the differential positioning of euchromatin and heterochromatin, the territorial organisation of chromosomes including both gene-density-based and size-based chromosome radial positioning schemes, the non-random locations of chromosome territories and the shape statistics of individual chromosomes. I will argue that the biophysical consequences of the distribution of transcriptional activity across chromosomes should be central to any chromosome positioning code.

We propose a mathematical model based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent. When activated, these motors attach to the chains of the polymer network and shorten them creating a global contraction of the gel, which mimics the active behavior of a cytoskeleton. The power generated by these motors is obtained by ATP hydrolysis reaction, which transduces chemical energy into mechanical work. The model is based on the Flory and Rehner theory for polymer network swelling and considers species diffusion to describe the transient passive behavior of the gel. The active behavior is modeled defining a volumetric density of mechanical power generated by the motors, through ATP hydrolysis, which increases the strain energy of the polymer network. The latter is depicted by an increment of the crosslink density in the polymer network, reducing the entropy of the polymer network. The model is finally adapted to the problem of uniaxial contraction of a slab of gel and compared with experimental results, showing good agreement.

Environmental challenges, such as pollution and anti-biotics, can cause populations to decline towards extinction. But declining populations can also be rescued from extinction by sufficiently fast adaptive evolution. In this talk I’ll describe some simple mathematical models we’ve created and analyzed to predict when and how evolutionary rescue will occur. In particular I’ll talk about how we’ve used branching process theory and a geometrical representation of trait space to predict how many mutations evolutionary rescue is likely to take and what the characteristics of these mutations will be given population survival.

Dr. Denise Daley PhD, is an Associate Professor in the Department of Medicine at the University of British Columbia. Dr. Daley is trained as a statistical geneticist with PhDs in Epidemiology and Biostatics and she currently holds a Canada Research Chair in Genetic Epidemiology of Complex Diseases. Dr. Daley is a Principal Investigator at the Centre for Heart and Lung Innovation at St. Paul’s Hospital in Vancouver, where she currently studies complex diseases such as asthma, food allergies, cancer, heart disease, and healthy aging. In particular, she has focused on why some children get asthma/allergic disease and others do not. Dr. Daley is currently investigating genes that may predispose children to developing asthma, and how a ombination of genetic variations can interact with gender and the environment to produce the condition. This presentation will focus on the concepts, principles and results of genetic association studies both candidate gene and genome-wide association studies, and the statistical models used to identify associations. A brief discussion of how this information can be used to identify individuals at risk for disease and the implications for clinical risk management.

STORM is a super-resolution technique that uses photoswitchable fluorophores to achieve resolutions at or below 20nm. A downside of STORM is the possibility of recording several blinks from one fluorophore, affecting the estimation of the number of molecules detected in the image. I constructed a mathematical model to identify unique fluorophores in STORM images by independently using the localization and the time series of the observations. The temporal sequence is described with a Markov chain approach and their spatial distribution with a Gaussian mixture model. To estimate the parameter values, I implemented a maximum likelihood procedure which requires a mixed optimization. Initially, I solved the mixed optimization problem with an extensive search algorithm on integers and a continuous optimizer for the rest of the parameters. I am currently investigating MCMC and Bayesian methods to speed up the optimization. I have tested my protocol in simulated data and I will use it to improve STORM images of B-cell surface receptors. B-cell receptors distribution on the membrane has been related to B-cell activation. This model will enhance a microscopy technique that is already widely used in biological applications and will allow to deeper analyze immune cells signaling.

Human African Trypanosomiasis (HAT) is a vector-borne disease endemic to rural areas of Sub-Saharan Africa. Over the last 150 years the disease has been a serious challenge to the people of Africa, with multiple outbreaks resulting the deaths of hundreds of thousands of people. Recent work by local programs and NGOs has had a large impact on controlling HAT through interventions like screening and vector control, and has brought the total number of recorded cases of HAT to its lowest point ever. However, this low number of cases brings with it a peculiar set of challenges in the pursuit of elimination of HAT. In this talk we will discuss how mathematical modeling and new data analysis methods can be brought to bear on some of these challenges. In particular, we will be using traditional models to assess the future impact of various interventions, to demonstrate the need for finer case data, and we will be using an equation-free data analysis method (Dynamic Mode Decomposition) to identify hotspots of disease activity and areas of low treatment coverage in the Democratic Republic of the Congo.

Predicting the impacts of environmental change on species requires a mechanistic understanding of biological processes such as foraging, migration, and reproduction. However, the continuous behavioural data needed to assess how these processes change through time is often impossible to gather, particularly for Arctic and marine species. Thus, ecologists increasingly rely on animal telemetry to monitor activity patterns. In this talk, I will demonstrate how emerging statistical methods and movement data can be used to model the behaviour of a range of species (e.g. polar bear, rhinoceros auklet), and discuss how the information provided by movement models can help us answer fundamental ecological questions and solve conservation problems.

In growing plant cells, parallel ordering of microtubules (MTs) influences the direction of cell expansion. Models of MT growth in the plane and on polyhedral surfaces have shown that growing-MT encounters lead to the formation of ordered arrays. The polyhedral surfaces models assume that when a MT crosses an edge, it emerges on the adjacent face at the same angle with the edge as the incident angle (i.e. following geodesics). This assumption ignores the MT mechanics - an elastic rod constrained to a rigid surface ought to deflect away from a geodesic when such a deflection decreases its energy. Here, we show this principle for a growing elastic rod on a cylindrical surface with one end clamped. We write down an energy functional that accounts for the bending energy of the rod and derive the associated Euler-Lagrange equation getting a two-variable boundary value problem. Minima and their stability can be found analytically in some cases. The system has a locus of saddle-nodes with a pitchfork in the symmetric case. In general, growing rods deflect away from high curvature directions and toward the flat axial direction, as expected. A rod growing circumferentially continues to grow circumferentially until a critical length (the pitchfork) after which it buckles up or down the cylindrical wall. Our results indicate that, for consistency with observations, the growing tip of MTs ought to be no longer than the radius of curvature of the cell.

Morphogenesis, the shaping of organisms, organs and tissues is driven by chemical signals and physical forces. It is still poorly understood how cells are able to collectively form intricate patterns, like for instance vascular networks. In particular, we were concerned with how interactions between the cell and the extracellular matrix (a protein network surrounding tissues that supports cells and guides cell migration) regulates morphogenesis. My PhD has mainly focused on how physical forces may drive morphogenesis. Lab experiments have shown that the mechanical properties of the matrix, such as its stiffness, regulate morphogenesis. In this presentation I will focus on my work on mechanical cell-matrix interactions. We developed a multiscale model that describe cells and the matrix and their interactions through physical forces. In this model, cells are represented by the Cellular Potts Model. The deformations in the ECM are calculated using a Finite Element Method. We model a mechanical feedback between cells and the ECM, where 1) cells pull on the ECM, 2) strains are generated in the ECM, and 3) cells preferentially extend protrusions oriented with strain. Similar to lab experiments, simulations show that cells are able to generate vascular like patterns on matrices of intermediate stiffness. Lab experiments where the matrix is uniaxially stretched, show that cells orient parallel to stretch. Model results on cells on a stretched matrices with and without traction forces indicate that cell traction forces amplify cell orientation parallel to stretch. Furthermore, they allow cells to organize into strings in the direction of stretch. I will also show an extension of this model. Stiffness sensing is mediated by transmembrane integrin molecules, which behave as ‘catch bonds’ whose strength increases under tension. Focal adhesions, which are large assemblies of these integrins, grow larger on stiffer substrates. We included such dynamics in our multiscale model. This second model explains how cell shape depends on matrix stiffness and how cells are able to durotact (move up a stiffness gradient). This model gives a more molecular understanding of how cells respond to matrix stiffness.

As biotechnologies for data collection become more efficient and mathematical modeling becomes more ubiquitous in the life sciences, analyzing both high-dimensional experimental measurements and high-dimensional spaces for model parameters is of the utmost importance. We present a perspective inspired by differential geometry that allows for the exploration of complex datasets such as these. In the case of single-cell leukemia data we present a novel statistic for testing differential biomarker correlations across patients and within specific cell phenotypes. A key innovation here is that the statistic is agnostic to the clustering of single cells and can be used in a wide variety of situations. Finally, we consider a case in which the data of interest are parameter sets for a nonlinear model of signal transduction and present an approach for clustering the model dynamics. We motivate how the aforementioned perspective can be used to avoid global bifurcation analysis and consider how parameter sets with distinct dynamic clusters contrast.

Frequently, the interests of a group do not align with those of its members. An individual could, for instance, do well by considering the collective needs in its actions but many times, it can gain even more benefits within the group by pursuing personal interests to the detriment of the entire community. This social dilemma is at the heart of public good interactions, and of particular importance when the production of a public resource is essential for the survival of a population. This scenario occurs, for example, when microbes secrete substances which grant microbial communities resistance to antibiotic drugs. The arising dynamics for the public good producing cooperative and the freeriding non-cooperative subpopulations have previously been analyzed by Professor Hauert and Professor Doebeli and extended by Wakano et al. into a spatial setting, in which the diffusing microbes form clusters and showcase rich patterns. As many microbes sense chemical gradients - and with that the public good - directional movement can lead to the aggregation of cooperative clusters and the exploitation through the defective subpopulation alike. In this talk, I will incorporate chemotactic migration in the aforementioned models and discuss how this extension affects the composition of the subpopulation, and whether cooperation can be maintained. This talk also showcases some parts of my research that are still in progress, and I’m happy to hear your feedback.

Diffuse Large B-Cell Lymphoma (DLBCL), a non-Hodgkin lymphoma, is the most common blood cancer and comprises more than two subtypes. The Activated B-Cell like (ABC) subtype has inferior survival rates, and is typically characterized by constitutive signalling that resembles B-cell activation following antigen engagement. However, there is significant heterogeneity observed clinically within the ABC subtype of DLBCL, with various mutations able to give rise to this oncogenic signalling. When present within an individual patient’s tumour, this kind of heterogeneity can lead to drug resistance due to evolutionary selection for cells with mutations that confer drug resistance. Optimized personalized therapies should therefore account for any underlying intratumour heterogeneity to prevent or delay the onset of drug resistance. In this work-in-progress talk, I will present our work towards developing a pipeline using mass cytometry -- a technique that enables the measurement of over 30 proteins simultaneously in single cells -- and computational analysis to study proteomic heterogeneity, especially at the level of intracellular signalling, in DLBCL samples. Since the ‘ground-truth’ cellular populations (clusters in proteomic or mutational feature space) that make up a heterogeneous tumour are not known for real tumours, we have devised novel mass cytometry experiments to simulate a heterogeneous DLBCL sample using cell lines as ‘ground-truth’ populations. This novel data will facilitate the improvement of existing, and development of new, computational algorithms for analysing heterogeneity and signalling in tumours.

Understanding incidence, spread, prevalence and control of an infectious disease requires a multidisciplinary approach that encompasses many fields of inquiry in Natural and Social Sciences. Several biological, environmental and economic/social/demographic factors govern the disease spread in a population. The overall pattern of a disease incidence is an outcome of the interaction of all these processes acting at different scales - from genetic epidemiology to public health - making it a complex multi-scale and interdisciplinary study. Mathematical modelling of the disease process has been one of the oldest areas of study in Mathematical Biology. It has contributed significantly to the understanding of basic infection process, predicting future incidence to aid in taking immediate control measures, drug discovery, and health policy development. It uses application of concepts from different areas in mathematics, statistics and computational algorithms for data analysis and visualization. Each theoretical approach incorporates information from the biological, environmental, and social sciences, and offers understanding at different scales. In this talk I will outline studies at three different scales to highlight the type of data required, variety of methods of analysis, and kinds of inferences/information that the analysis offers. I will show that comparative whole genome analysis of HIV-1, the pathogen responsible for AIDS, offers some insights into the differential evolution of HIV-1 genes; Understanding HIV-1 Reverse Transcriptase (RT) wild-type and mutant protein structures using graph theory allows us to uncover the drug resistance mechanisms in RT-drug mutants. Finally, at the population level modelling of disease spread, I will discuss our studies of Malaria using mathematical, statistical, and graphical approaches suitable for a diversity of fine and coarse-grained data from India.

How Xenopus brain neurons can improve or shift their encoding in response to experience? The present work is in collaboration with the Haas lab, which recent innovations in two-photon calcium imaging allows the simultaneous sampling of all visual-evoked synaptic input and firing output of individual neurons before, during and after visual training that enhanced evoked responses. In order to analyze and interpret these data, I am currently building several models for calcium dynamics in neurons. The purpose being to understand the origins of calcium transients, the integration of synaptic input to action potential output underlying encoding, and finally how neurons alter these properties to improve encoding with experience.

We present a mathematical model of the core mechanism responsible for the regulation of polarized growth dynamics by the small GTPase Cdc42. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate (inactive Cdc42) that diffuses in the cytosol. We consider several potential ways of implementing negative feedback between Cd42 and its GEF in this model that would be consistent with the observed oscillations of Cdc42 in fission yeast. We analyze the bifurcations in this model as the cell length increases, and total amount of Cdc42 and GEF increase. Symmetric antiphase oscillations at two tips emerge via saddle-homoclinic bifurcations or Hopf bifurcations. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. Our model suggests that negative feedback is more likely to be acting through inhibition of GEF association rather than upregulation of GEF dissociation.

Locust swarms pose a major threat to agriculture, notably in North Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust hopper bands that incorporates intermittent motion, alignment with neighbors, and social attraction, all behaviors that have been validated in experiments. Using a particle-in-cell computational method, we simulate swarms of up to a million individuals, which is several orders of magnitude larger than what has previously appeared in the locust modeling literature. We observe hopper bands in this model forming as a fingering instability. Our model also allows homogenization to yield a system of partial integro-differential evolution equations. We identify a bifurcation from a uniform marching state to columnar structures, suggestive of the formation of hopper bands.

My research program is motivated by fascination with bird flight. My laboratory group uses a multi-disciplinary approach that includes biomechanics, physiology, and neuroscience to examine flight ability. Our current research is organized around two topics: 1) how birds morph their wings and what benefits this provides; and 2) how optic flow signals are encoded in the avian brain and used to guide their flight. As we gain understanding of flight mechanisms, we further endeavor to apply comparative approaches that provide deeper insight into avian ecology and evolution.

The problems of estimation of state of a high dimensional chaotic system such as the atmosphere or estimation of parameters of models of highly nonlinear real life phenomena involving multiple parameters can both be considered in the Bayesian framework as problems of the study of the posterior distributions of the state or the parameters, conditioned on the observed data. The former is commonly known as data assimilation in the earth sciences. This talk will focus on discussing the connection between the properties of this posterior distribution and the characteristics of the dynamics of the system, in particular the unstable subspace (in the context of data assimilation [1,2]) and the bifurcations of the system as well as the characteristics of the data sets (in the context of parameter estimation [3]). Ref: [1] doi:10.1137/15M1025839, [2] doi:10.1137/16M1068712, [3] arXiv:1705.03868

TBA

In both health and disease, cells interact with one another through cellular adhesions. Normal development, wound healing, and metastasis all depend on these interactions. These phenomena are commonly studied using continuum models (partial differential equations). However, a mathematical description of cell adhesion in such tissue models had remained a challenge until 2006, when Armstrong et. al. proposed the use of an integro-partial differential equation (iPDE) model. The initial success of the model was the replication of the cell-sorting experiments of Steinberg. Since then this approach has proven popular in applications to embryogenesis, wound healing, and cancer cell invasions. In this talk, I present a first derivation of the non-local (iPDE) model from an individual description of cell movement. The key to the derivation is the extension of the biological concept of a cell’s polarization vector to the mathematical world. This derivation allows me to elucidate in detail how cell level properties such as cell-size of density of adhesion molecules affect tissue level phenomena. I will also present a study of the steady-states of the non-local cell adhesion model on an interval with periodic boundary conditions. The importance of steady-states is that these are the patterns observed in nature and tissues (e.g. cell-sorting experiments). I combine global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the mathematical properties of the non-local term to obtain a global bifurcation result for the first branch of non-trivial solutions. I will extend the non-local cell adhesion model to a bounded domain with no-flux boundary conditions.

In the past five years biotechnological innovations have enabled the measurement of transcriptome-wide gene expression in single-cells. However, the destructive nature of the measurement process precludes genuine time-series analysis of e.g. differentiating cells. This has led to the pseudotime estimation (or cell ordering) problem: given static gene expression measurements alone, can we (approximately) infer the developmental progression (or "pseudotime") of each cell? In this talk I will introduce the problem from the typical perspective of manifold learning before re-casting it as a (Bayesian) latent variable problem. I will discuss approaches including nonlinear factor analysis and Gaussian Process Latent Variable Models, before introducing a new class of covariate-adjusted latent variable models that can infer such pseudotimes in the presence of heterogeneous environmental and genetic backgrounds.

I will present a new quantitative genetic model of adaptation to a changing environment. The mathematical analysis will use small variance asymptotics introduced by Diekmann et al in 2005 to derive information on the equilibrium. The framework can handle sexual and asexual reproduction. Heuristics can be made to guess the lineages of the population inside the equilibrium, as shown by numerical simulations.

PDE models can be a powerful tool for understanding emerging structures and patterns, such as aggregates and traveling waves formed by large populations of cells. As a specific example, I will discuss myxobacteria, which, due to their co-operative nature, lie on the boundary between uni- and multicellular organisms. I will present a novel age-structured, continuous macroscopic model. The derivation is based on simple interaction rules and set within the SOH (Self-Organized Hydrodynamics) framework. The strength of this combined approach is that microscopic information can be incorporated into the particle model in a straight-forward manner, whilst the continuous model can be analyzed using mathematical tools, such as stability and asymptotic analysis. It has been suggested that myxobacteria are not able to react to signals immediately after they have reversed their direction. Our analysis reveals that this insensitivity period is not necessary for wave formation, but is essential for wave synchronization. A more mathematical focus will be the existence and stability of such traveling waves moving in two opposing waves frames. Fascinatingly, while the wave profiles do not change, the wave composition does, and the fractions of reversible and non-reversible bacteria form waves traveling in the opposite direction. I will discuss the explicit construction of such waves and show simulation results. This is joint work with Pierre Degond and Hui Yu.

Many types of large cells have multiple nuclei. In long muscle cells, nuclei are distributed almost uniformly along their length, which is crucial for cell function. However, the underlying positioning mechanisms remain unclear. We examine computationally the hypothesis that a force balance generated by microtubules positions the nuclei. Rather than assuming what the forces are, we allow for various types of forces between pairs of nuclei and between the nuclei and the cell boundary. Mathematically, this means that we start with a great number of potential models. We then use a reverse engineering approach by screening the models and requiring their predictions to fit imaging data on nuclei positions from hundreds of muscle cells of Drosophila larva. Computational screens result in a small number of feasible models, the most adequate of which suggests that the nuclei repel each other and the cell boundary with forces that decrease with distance. This suggests that microtubules growing from nuclear envelopes push on neighboring nuclei and the cell boundary. We support this hypothesis with stochastic microscopic simulations. Using statistical and analytical tools such as correlation and bifurcation analysis, we make several nontrivial predictions: An increased nuclear density near the cell poles, zigzag patterns in wider cells, and correlations between the cell width and elongated nuclear shapes, all of which we confirm by image analysis of the experimental data. This is joint work with Mary Baylies, Alex Mogilner and Stefanie Windner.

Biological populations facing severe environmental change must adapt in order to avoid extinction. This so-called “evolutionary rescue” scenario is relevant to many applied problems, including pathogen evolution of drug resistance during the treatment of infectious diseases. Understanding what drives the rescue process gives rise to interesting mathematical modelling challenges arising from two key features: demographic and evolutionary processes occur on the same timescale, and stochasticity is inherent in the emergence of rare well-adapted mutants. In this talk, I will present recent work on population dynamics in changing environments, merging biological realism with tractable stochastic models. Firstly, I will describe a model of drug resistance evolution in chronic viral infections, which serves as a case study for a novel mathematical approach yielding analytical approximations for the probability of rescue. Secondly, I will present a combined theoretical and experimental investigation of the classical problem of establishment (non-extinction) of new lineages, using antibiotic-resistant bacteria as a model system. Finally, I will discuss some future directions in modelling antibiotic treatment to predict optimal dosing strategies, and in developing a general theoretical framework for evolutionary rescue that unites approaches to distinct applied problems.

As the source of new genetic variation, mutations constitute a fundamental process in evolution. While most mutations lower fitness, rare beneficial mutations are essential for adaptation to changing environments. Thus, understanding the effects of mutations and estimating their rate is of strong interest in evolutionary biology. The necessity to treat rare mutational events stochastically has also stimulated a rich mathematical literature. Typically, mutations are modelled simply as an instantaneous change of type, occurring at a fixed rate. However, the underlying biology is more complex. I will present two recent projects delving deeper into mutational mechanisms and their consequences. Firstly, mutations can exhibit a multi-generational delay in phenotypic expression. Secondly, individuals within a population can vary in their propensity to mutate. Through analytical and simulation methods, we investigated the impact of these biological complexities on (a) population fitness and capacity to evolve, and (b) our ability to accurately infer mutation rates from data. I will conclude by discussing some future directions to incorporate these insights into more realistic models and to quantify the distribution of mutation rate empirically.

Ectodermal derivatives such as teeth, hair, feathers or scales share similar morphological features and spatial patterning mechanisms. From the mathematical point of view, pioneering works of Alan Turing showed that spatial-temporal self-organization structures can emerge from reaction-diffusion systems. However, recent biological and mathematical studies give evidence that there is a substantial difference in pattern generation between static and growing domains. The latter may contain a key to understanding the problem of sequential patterning in developmental biology. In this talk we present a macroscopic model of gene expression dynamics in the growing field where molars appear sequentially. Our model mimics the expression of the Edar gene during the formation of signaling centers, from where future teeth originate. We rely on a reaction-diffusion system of an activator-inhibitor type on a dynamically evolving tissue. The key element is not only the tissue growth but also its non-constant properties, which affect the reaction kinetics, depending on the presence of the activator. The purpose of the model is twofold. On one hand it describes a sequential formation of individual spots through Turing instability mechanism. On the other hand, it produces the activator up-regulation waves starting at distal field thanks to reaction functions containing bistable solutions. We present numerical studies of two dynamics on growing domain: under wild conditions and under a mutation regulating the inhibitor concentrations. For a fixed and fully matured domain, we analyze the effect of chemotaxis on the wavelength of Turing patterns and, as a consequence, on the merging of signaling centers that is observed in some biological conditions.

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Gender equality is a major issue within science communities. While efforts to be proactive and bring awareness to gender inequality have been made in recent years, still only 1/8th of academic scientists are women. A recent paper published in PLOS Computational Biology (Hashe et al. 2017) highlights the under-representation of women in biology, computational biology, and computer science. Here, I will present their findings and lead a general discussion on women in science and ways we may help to close the gender gap.

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Regulators of the actin cytoskeleton such Rho GTPases can modulate forces developed in cells by promoting actomyosin contraction. At the same time, through mechanosensing, tension is known to affect the activity of Rho GTPases. What happens when these effects act in concert? Using a minimal model (1 GTPase coupled to a Kelvin-Voigt element), we show that two-way feedback between signaling (“RhoA”) and mechanical tension (stretching) leads to a spectrum of cell behaviors, including contracted or relaxed cells, and cells that oscillate between these extremes. When such “model cells” are connected to one another in a row or in a 2D sheet (“epithelium”), we observe waves of contraction/relaxation and GTPase activity sweeping through the tissue. The minimal model lends itself to full bifurcation analysis, and suggests a mechanism that explains behavior observed in the context of development and collective cell behavior.

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The interactions of cancer cell with the environment play an important role in cancer cells migration and the formation of secondary tumors. In this talk, I will present a discrete model, motivated by these cancer cell interactions, to gain further insights into cancer cells aggregate conditions and how chemotaxis (migration up a chemical gradient) alters the cells’ behavior. I will show how the equivalent continuum model is derived and compare the resulting parameters to the original model. By deriving a continuum limit of the discrete model, analytical tools can be used to study the model dynamics and the parameter sensitivity. Finally, since the analysis of my seemingly simple model quickly gets complicated, I will solve the system numerically to demonstrate the rich dynamical properties of the model.

B cells integrate signals from multiple activating and inhibitory receptors in a highly regulated spatiotemporal manner to regulate B cell receptor (BCR) signaling and B cell activation. Marginal Zone (MZ) B cells are unique subset of B cells that exist in a partially activated ‘primed’ state, allowing them to rapidly respond to small amounts of antigens. The molecular basis for this priming is not fully understood. We propose that the priming of MZ B cells reflects altered lateral mobility and nanoscale organization of the BCR and other cell surface proteins, as compared to resting circulating follicular (FO) B cells. We have used high-speed single particle tracking and multi-color super-resolution microscopy to quantify receptor mobility and spatial organization, on the plasma membrane of FO and MZ B cells. We found that IgM, but not IgD BCRs in MZ B cells possess, (i) higher lateral mobility, (ii) larger confinement radius, and (iii) higher slowfast state transition rates, when compared to FO B cells. Using a novel graph-theory based hierarchical clustering algorithm (StormGraph), we found that both IgM and IgD BCRs exist in larger nanoclusters on the surface of MZ B cells, when compared to FO B cells. Although both BCR isotypes exist in discrete and heterogeneous nanoscale protein islands in both B cell types, signaling BCRs predominantly overlap with IgM containing nanoclusters, when compared to IgD. Our data propose that interaction of IgM BCRs and ‘signaling hub’ protein islands in MZ B cells may result in greater antigen-independent tonic BCR signaling, contributing to the partially-activated ‘primed’ state of MZ B cells.

For a differential equation model of some data, the controlled relaxation from data values to the state values of the best fitting numerical solution provides a means for precise parameter estimation. In this talk, I will discuss the theory, benefits, and examples of a relaxation approach to differential equation parameter estimation.

Two models involving bulk diffusion coupled to nonlinear reactions localized to the boundary are presented. For each of them, a combination of analytical and numerical methods exhibits a variety of exotic dynamics including in-phase and anti-phase oscillations between two compartments (1D model), Turing patterns and rotating waves (2D model).

The rapid increase of fentanyl and fentanyl analogues in British Columbia has led to a public health emergency being declared and a rapid increase in overdoses and overdose-related deaths in the province. Numerous interventions have been proposed in response, however it is not clear how to evaluate these interventions where the rate of overdoses is rapidly changing. We introduce a Poisson hidden Markov model to incorporate knowledge on ambulance-attended overdoses, fentanyl-related deaths and illicit-drug related deaths. We explicitly model the use of Take Home Naloxone kits (THN), an opioid agonist used in reversing an overdose that has been widely distributed. The model was fit using a Bayesian framework with informative priors, taking into account expert knowledge and literature-based rate estimates. We use the fitted model to estimate the total number of deaths averted due to the use of THN and explore a number of counterfactual scenarios including if THN was distributed sooner and if the size of the at-risk population was reduced.

Concentration waves of swimming bacteria Escherichia coli were described in his seminal paper by Adler (Science 1966). These experiments gave rise to intensive PDE modelling and analysis, after the original model by Keller and Segel (J. Theor. Biol. 1971), and the work of Alt (J. Math. Biol. 1980) and his co-authors. Together with Bournaveas, Perthame, Raoul and Schmeiser, we have revisited this old problem from the point of view of kinetic transport equations. This framework is very much adapted to the so-called run-and-tumble motion, in which bacteria modulate the frequency of reorientation (tumble) -- and thus the duration of free runs -- depending on chemical variations in the environment. I will present some recent analytical and numerical results about the existence of traveling wave solutions for a coupled kinetic-parabolic system describing concentration waves of bacteria in a micro-channel. The parabolic-parabolic problem obtained in the diffusive limit admits unique traveling wave solutions without any restriction on the parameters. This is in opposition to the kinetic-parabolic system for which solutions may be not unique, or may not exist for some extreme range of parameters.

A precise regulation of gene expression is required for virtually all biological processes, such as cell and tissue development or response to external stimuli. Mis-regulation of gene expression can lead to diseases, such as cancer. It is therefore crucial to improve our understanding of the components underlying the process of gene regulation. Enhancers are genomic regions (sequences) that act as regulatory elements by cooperating with core promoter regions to recruit the transcription machinery to drive gene expression. Recently emerged, genome-wide experimental assays, such as STAP-seq, aim to quantify the ability of genomic fragments to respond to an enhancer and drive the transcription of a gene. In this seminar, I will outline how statistical learning models enable us to extract biological insights from large, genome-wide assays, such as STAP-seq. As the vast majority of DNA sequences are unable to respond to enhancers and drive gene expression, we employ a zero-inflated model to address the challenge of many zeros in the data set. We harness convolutional neural networks (ConvNets) to automatically discover which DNA sequence motifs serve as ingredients of a responsive promoter. Our interpretable, zero-inflated, nonlinear Poisson regression model allows us to delineate minimal, core promoter properties from those that cooperate with the enhancer to modulate the level of gene expression.

Tumors consist not only of cancer cells, but also stromal and immune cells that constitute the tumor microenvironment. Clinical outcome and response to therapy depend on the complex interplay between these cell populations within the tumor microenvironment. Beyond numerical values, spatial organization of cells within tumors (and tumor-draining lymph nodes) also impacts biological behavior. These can now be collectively addressed via a quantitative image analysis approach that incorporates 1) multi-color tissue staining (Opal, Perkin Elmer), 2) high-resolution, automated whole-slide spectral imaging (Vectra, Perkin Elmer), 3) image analysis algorithms that utilize machine-learning to identify cell types and locations (InForm, Perkin Elmer), and 4) spatial statistical analysis to understand relationships between cell populations within tissue samples. This novel approach provides objective assessment of immune-stromal-cancer interactions within tumors and tumor-draining lymph nodes, and data generated are of prognostic and mechanistic value.

The hybrid method allows us to investigate the multi-scale (space and time) nature of tumor progression in many cancers including breast cancer and glioblastoma, brain tumor, at intracellular, cellular and population levels. We develop various mathematical models of tumor cell infiltration that may lead to metastasis. Ductal carcinoma in situ (DCIS) is an early stage noninvasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix (ECM) surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. Here we develop a mathematical model that incorporates the cross-talk between stromal and tumor cells, which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-beta signaling pathways and show how up or down-regulation of components in these pathways affects cell growth and proliferation. We then study a hybrid model for the interaction of cells with the tumor microenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a continuum, and show how these interactions affect the early development of tumors. Finally, we incorporate breakdown of the epithelium into the model and predict the early stages of tumor invasion into the stroma. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression. Glioblastoma (GBM) is one of the most lethal type of brain cancer with poor survival time. GBM is characterized by infiltration of the cancer cells through the brain tissue while lower grade gliomas and other non-neural metastatic types form self-contained non-invasive lesions. GBMs are highly invasive and difficult to treat because cells migrate into surrounding healthy brain tissue rapidly, and thus these tumors are difficult to completely remove surgically. We investigate the basic mechanisms of glioma infiltration through the extracellular matrix and other cells in the absence and presence of blood vessels. We show that the model’s predictions agree with experimental results for a glioma. We also develop new therapeutic strategies to eradicate the infiltrative glioma cells via the miR-451-AMPK-mTOR-cell cycle signaling network. Reactive astrocytes and microglia (M1 and M2 types) also play a significant role in regulation of cell infiltration. It is also shown that heavy CSPGs can drive the exodus of resident reactive astrocytes from the main tumor mass, and direct inhibition of tumor invasion by the astrogliotic capsule, leading to encapsulation of non-invasive lesions. The mathematical model presents the clear role of the key tumor microenvironment in brain tumor invasion.

This talk will describe a novel model for coupling continuous chemical diffusion and discrete cellular events inside a biologically inspired simulation environment. Our goal is to define and explore a minimalist set of features that are also expressive, enabling the creation of complex and plausible 2D patterns using just a few rules. By not being constrained into a static or regular grid, we show that many different phenomena can be simulated, such as traditional reaction-diffusion systems, cellular automata, and pigmentation patterns from living beings. In particular, we demonstrate that adding chemical saturation increases significantly the range of simulated patterns using reaction-diffusion, including patterns not possible before such as the leopard rosettes. Our results suggest a possible universal model that can integrate previous pattern formation approaches, providing new ground for experimentation, and realistic-looking textures for general use in Computer Graphics.

Alzheimer’s disease (AD) is a burgeoning threat to Canada. With nearly 15% of Canadian elderly affected presently by AD and numbers expected to roughly double by 2040, the disease could potentially cost the country as much as $300 billion annually. Therefore, treating this debilitating disease is an urgent priority. There are no therapies on the market and none on the horizon. The absence of therapies stems from the lack of efficient pre-clinical screens available for discovering drugs against AD. Current available models for drug screening include cells grown on petridishes and mice; are very limited in scope. The former suffers from loss of context and does not adequately capture the complexity of the human brain. For instance, besides lacking 3D complexity, cell cultures do not incorporate key constituent tissues such as the protective barrier, which has long been the Achilles’ heel of therapies targeting the brain. As a consequence, penetration through barrier is never actually evaluated until the molecules are tested in diseased animal models. The latter, which is a better model, is still not equivalent to human brains. The dissimilarity between the 2D cell cultures and the animal models causes a mismatch between the clinical and pre-clinical results. To this end, the pre-clinical discovery platform we seek to develop could ultimately lead to improved clinical approval rates and lower drug development costs, which, in turn, could potentially translate to lower government expenditures on therapeutics. The proposed work combines concepts and insights from stem cell bioengineering, neuroscience and biomedical instrumentation. Our proposal to construct brain tissue models in order to test drugs could eventually lead to the development of one of the first ever drugs to treat neurodegenerative disorders, which will directly benefit Canadians, and may prove to be a game changer for pharmaceutical testing and molecular medicine.

The emergence of HIV resistant mutation is of concern during the treatment of infected individuals. In this talk, I will present deterministic and stochastic mathematical models of HIV viral dynamics in lymphoid tissues, focusing in particular on the role of the latent reservoir. The models describe the interactions between within-host HIV, CD4+ T cells, latently and productively infected cells for both sensitive and resistant strains after administration of both reverse transcriptase and protease inhibitor drugs. We used Gillespie Algorithm to study the effect of key parameters and treatment in a continuous time stochastic process. Second scenario, when the resistant mutant population size distributions have stabilized, the distribution and the probability generating function for population size are approximated using a birth-death-immigration (BDI) process. Analytical expression for the probability of extinction with latency reversing agent for a single progenitor using constant birth-death process under the pre-treatment case conditions will presented.

In this talk, I will give an overview of the Drosophila Dorsal Closure phenomenon in which a developing embryo is able to close an opening in the epidermis. I will present recent experimental work and prior modelling efforts. Both of these will inform the model that I am developing which proposes a biochemical signal coupled to tissue dynamics to successfully complete the process. This talk will emphasize the work in progress nature of the seminar.

Immune cells are activated when receptors on their surface bind to target pathogenic molecules. This leads to receptor phosphorylation, initiating a cascade of downstream signals. Advances in fluorescence microscopy have made it possible to watch this process unfold in real time on single cells. These experiments reveal a dynamic spatial reorganization of signaling molecules on the cell membrane: kinases (that phosphorylate receptor tyrosines) preferentially colocalize with the receptors, while phophatases are excluded away from them. This spatial reorganization is believed to promote receptor phosphorylation. In my talk, I will describe how we used single molecule tracks to quantify such spatial exclusion. We tracked molecules of CD45, a major tyrosine phosphatase in macrophages, around micropatterned, geometrical arrays of aggregated Fc receptors. We used molecular trajectories to compute detailed spatial statistics of CD45 and compared them with biophysical simulations. We inferred that aggregated receptors are surrounded by a molecular barrier that effectively restricted the diffusion of nearly 80% of CD45 molecules that would have otherwise entered these regions. I will present the details of this analysis and discuss the role of spatial segregation on signaling.

In many current applications scientists can easily measure a very large number of variables (for example, several thousands of gene expression levels) some of which are expected be useful to explain or predict a specific response variable of interest. These potential explanatory variables are most likely to contain redundant or irrelevant information, and in many cases, their quality and reliability may be suspect. We developed a penalized robust regression estimator that can be used to identify a useful subset of explanatory variables to predict the response, while protecting the resulting estimator against possible aberrant observations in the data set. Using an Elastic Net penalty, the proposed estimator can be used to select variables, even in cases with more variables than observations or when many of the candidate explanatory variables are correlated. In this talk, I will present the new estimator and an algorithm to compute it. I will also illustrate its performance in a simulation study. This is joint work with Professor Matias Salibian­Barrera and my student David Kepplinger, both from the Department of Statistics.

In analysis of single particle tracking data, identifying and estimating the rate of absorption on a partially permeable boundary may be challenging. In this talk, I will present a technique for estimating the rate of absorption on these type of boundaries. This technique is based on calculating the probability of finding a particle performing Brownian motion in a region and maximum likelihood estimation. I will also talk about approximation of switching boundary with partially absorbing boundary.

From the common cold to crop blights, the consequences of host-parasite interactions on our daily lives are unavoidable. Beginning with an overview of the diversity and abundance of host-parasite interactions I will explore several of the evolutionary consequences of host-parasite coevolution, including the maintenance of sexual reproduction and the evolution of gene expression. I will then present results from two projects illustrating the impact of host-parasite coevolution on disease epidemiology. First, I explore how host-parasite interactions can alter disease dynamics, affecting when disease will spread as well as the long term abundance of infection. Second, by modeling genetic-association studies, I will illustrate how host-parasite coevolution can alter our understanding of the genetic basis of infectious disease.

The FitzHugh-Nagumo system of partial differential equations (FHN) is a generic model for excitable media, often used to build a qualitative understanding of electrophysiological phenomena. A well-characterized traveling-pulse solution to FHN serves as a model for action potentials in cardiac tissue and other contexts. The stability of the traveling pulse has been well-studied but the more global problem of predicting when an arbitrary initial condition will converge to the uniform rest solution and when it will converge to the traveling pulse remains unsolved. In this talk, I will present a proof of the existence of an invariant winding number in an asymptotic limit of the FHN system (the singular FHN system - SFHN) on a circular 1D domain that provides a crucial step toward a global convergence result. I will also provide evidence that this SFHN winding number result extends with limitations to FHN and outline conditions under which the SFHN approximation fails. The invariant winding number provides explanations for several observations of physiological relevance. For example, it explains the requirements on stimulus protocols that allow the formation and elimination of reentrant rhythms in cardiac tissue. This is joint work with Kelly Paton.

Understanding the spatial organization and dynamics of receptors at the cell membrane is an important step towards a full mechanistic model of cell activation. Single particle tracking (SPT) is an important experimental technique for analyzing receptor motion and confinement. Briefly, low densities of receptors are labeled and then tracked via video microscopy. In this talk, I am going to show a critical comparison between two different ways of labeling receptors: cyanine dyes or quantum dots, and how they can influence the mobility of B cell receptors. Moreover, I will show some initial analysis of SPT data of labeled pMHC on a supported lipid bilayer, where a T cell is placed on top of it.

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. I will present in this talk a hybrid discrete-continuum model that takes into account both a stochastic regime governed by rare events and a continuous regime in the bulk, in the context of vesicular release at chemical synapses. In a first part, I computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. This models the binding of calcium ions on the SNARE complex, a process that triggers vesicular release. Using this result, I developed a model to study how vesicles and calcium channels organization shape such process. In a second part, I will present a model for the pre-synaptic terminal built using the results described above. This model was formulated in an initial stage as a reaction-diffusion problem in a confined microdomain, where Brownian particles have to bind to small target sites. I coarse-grained this model into a system of mass action equations coupled to a set of Markov equations, which allows to obtain analytical results and to realize fast stochastic simulations.

The decline of the Earth's biodiversity is a threat to the ecosystems in the planet. Ecological systems are faced with species extinctions and invasions and one fundamental question is how systems vary when they suffer these changes. In particular, a major problem in theoretical ecology is to resolve how ecosystem features such as resilience, resistance, robustness, or in wider terms, stability respond to changes in species diversity, richness, connectivity, or in wider terms, complexity. This question is known as the Complexity-Stability problem.

We propose a novel formalism to deal with this problem. Chemical Organization Theory (COT) is a formalism for modeling self-organizing systems. Although COT is inspired by problems in biochemical systems, it has much broader applicability. The elements of the formalism are resources and reactions, where a reaction (e.g. a+b-> c+d) maps a combination of resources (in an abstract sense) onto a new combination. Thus, a reaction represents an elementary process that converts resources into new resources.

Reaction networks tend to self-organize into invariant reaction sub-networks, called organizations. They represent all the possible attractors of the reaction networks dynamics. Thus, COT provide a simple model that links the structure and dynamics of stable community systems: an organization is able to constantly recreate its own components.

In this seminar, we introduce the mathematical framework of COT, explain how to model ecological relationships and ecosystems using COT, and present some illustrative examples.

A pandemic subtype of influenza A sometimes replaces (e.g., in 1918, 1957, 1968) the previous seasonal subtype. However, the reintroduced subtype H1N1 in 1977 has been co-circulating with H3N2 since then. To understand these alternatives, we formulate a hybrid model for the dynamics of influenza A epidemics. Our model takes into account the cross-immunity between seasonal strains and the cross-immunity between seasonal and pandemic subtypes. A combination of theoretical and numerical analyses shows that for very strong cross-immunity between seasonal and pandemic subtypes, the pandemic cannot invade, whereas for strong and weak cross-immunity there is coexistence, and for intermediate levels of cross-immunity the pandemic may replace the seasonal subtype. This is joint work with Junling Ma and P. van den Driessche.

Signalling networks of Rho GTPases regulate single and collective cell migration. Mechanical effects, such as membrane tension and cell-cell pulling forces, also play a role in these networks. We couple a 1D ODE model for GTPase signalling within a cell with a simple model of cell mechanics. By coupling GTPase activation to membrane tension or pulling forces, we characterize the possible feedback loops that regulate cell length. We extend the single-cell model to a multicellular group by assuming that cell-cell junctions are responsible for transmitting forces to neighbouring cells. The interplay between cell-cell mechanics and GTPase signalling is responsible for the emergence of coordinated migratory behaviour in the model. This suggests that a core network of mechanical signals and GTPase signalling can organize multicellular migration.

Unsupervised learning by clustering is a key tool for analyzing single-cell biological data. StormGraph is a clustering algorithm that we have developed to analyze protein clustering in single cells imaged using super-resolution microscopy. I will introduce the StormGraph algorithm and discuss its application to studying the nanoscale biology of Diffuse Large B-Cell Lymphoma (DLBCL), a clinically heterogeneous, aggressive blood cancer. I will also briefly discuss how we are looking to study heterogeneity in DLBCL tumours by clustering high-throughput, high-dimensional single-cell proteomic data, with implications for personalized medicine.

We formulate and analyze an age of infection model for epidemics of diseases transmitted by a vector, such as malaria or dengue fever, including also the possibility of direct transmission, as in the Zika virus. We show how to determine a basic reproduction number. While there is no explicit final size relation as for diseases transmitted directly, we are able to obtain estimates for the final size of the epidemic.

The production and control of blood cells is regulation by an intricate system of coupled mechanisms built around differentiation and proliferation of cells emerging from a common pool, with hormonal feedback at various stages of the maturation process. By developing physiologically correct models of this system, and its perturbation under pharmaceutical interventions, such as oncological treatments, we are lead to the investigation of nonlinear systems of delay-differential equations, some with state-dependent delays. I will review the evolution of models for erythropoiesis (red blood cell production), and present recent models for neutrophils (white blood cells), incorporating the pharmacokinetics and pharmacodynamics of an oncological drug, together with the main regulating hormone, G-CSF, and platelets.

Individual cells regulate their morphology in response to environmental cues, selective pressures and signalling. The precise mechanism(s) through which cells control their shape is not well understood. Studies have shown that cell morphology has important implications for nutrient uptake, motility, proliferation, etc. For example, a change in bacterial cell diameter of 0.2 μm can change the energy required for chemotaxis by a factor of 10^5. Automatic classification and counting can facilitate a systematic investigation of cell morphology. Furthermore, it is a useful tool for diagnosis of diseases like leukemia that are characterized by cell shape deformation. In this talk, I will describe techniques for image segmentation and feature extraction that we use to build a descriptor of cell shape. This descriptor is used to classify cells using unsupervised learning (PCA, hierarchical clustering) methods. I will briefly discuss the advantages and limitations of supervised learning (deep neural networks, convolutional neural networks) methods.

A (brief) intro to the Min system of cell division, a slightly less brief introduction to some exciting data from recent experiments, and a discussion of plans for what to do with the stuff (several plans already running, but suggestions welcome). Note: everyone is free to come, but those who saw my thesis proposal will see very little that is new here).

A deterministic model may sometimes seem to be a good description of the dynamics of an observed system but may have a long-term stable constant limit, whereas observations of the system itself show a noisy pattern. An example is semi-arid vegetation patterns. Adding noise to the model may well reveal the pattern. In this talk I show some photos, talk about some math, and show some simulations. This is not a magic show.

We investigate the dynamical behavior arising from a coupled model of bulk diffusion and surface reaction. For the 2D case, implementation of the closest point method suggests the existence of Turing patterns for equal diffusion coefficients.

Cellular adhesions are one of the fundamental biological interactions between cells and their surroundings. However, the continuum modelling of cellular adhesions has remained mathematically challenging. In 2006 Armstrong et al proposed a mathematical model in the form of an integro partial differential equation. This model was successful at replicating Steinbergs cell sorting experiments and since has been used in models of cancer invasion and morphogenesis. In this talk we derive models of cell-cell adhesion from an underlying stochastic random walk. Through this derivation we are able to include micro biological properties in the model. It is shown that a particular choice of these properties yields the original Armstrong model.

We present an approximate description of sustained oscillations produced by a linear stochastic differential equation (SDE) of the form: dx(t)=A(t) x(t) dt + C(t) dW(t), a linear diffusion equation in two dimensions with a time-dependent periodic parameter, i.e. periodic forcing. Our work uses Floquet theory and a stochastic approximation by Baxendale and Greenwood (2011). Here we show that x(t), in an approximate sense, follows a cyclic path whose periodicity is related to the frequency of A(t) and the frequency predicted by the Floquet exponents. The radius of this approximate process is modulated by a slowly-varying bi-variate standard Ornstein-Uhlenbeck process. Moreover, we find that the typical amplitude of the approximate process is directly proportional to the square-root of the variance of the noise. We demonstrate the theory using a simulated stochastic model for a driven harmonic oscillator with noise. We discuss the applicability of our approximation in the context of stochastic epidemic model with seasonal forcing (e.g. avian flu).

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Formation of a composite material that constitutes bone tissue is a tightly regulated and highly non-linear process. Bone-forming osteoblasts first deposit an extracellular matrix (osteoid) that contains collagenous and noncollagenous proteins that require assembly and maturation. After an initial lag phase, when osteoid is present but no mineralization is evident − a fast primary mineralization occurs, which later turns into a secondary mineralization characterized by a continuous slow increase in bone mineral content. I will describe our studies aimed at development and validation of a mathematical model describing the dynamics of bone mineralization and the roles of individual processes in generating normal and abnormal mineralization patterns. Finally, I will discuss an algorithm for predicting the potential functions for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.

In order to understand the precise mechanisms used by cancer cells to transmigrate through blood vessels (covered by endothelial cells), physical experiments and models are designed to investigate such processes. In particular, two different techniques are presented: traction force microscopy (TFM) allows to measure forces exerted by cells during migration on a deformable substrate [1]. Atomic Force Microscopy (AFM) will be used for the investigation of receptor-ligand bonds between cancer cells and endothelial cells [2]. It may alternatively act as a probe to measure local cell rheology by dynamic indentation. This allows us to obtain elastic and viscous cell component responses. Cells of different invasiveness are thus chosen so that such methods can possibly help differentiate cells with respect to their metastatic potential. [1] V. Peschetola et al., Cytoskeleton, 70, 201 (2013) [2] V.M. Laurent et al., 9, e98034, PLOS One (2014) [3] Y. Abidine et al. EPJ Plus, in press (2015)

Cells provide highly crowded environments for the processes governing life to play out. We have been exploring some contexts, involving the transport of vesicle-encapsulated material down axons in nerve cells, where crowding appears to be crucial to healthy function. I will discuss how and why this might happen, describing some subtleties that must be accounted for when cellular motor-driven transport is modelled. Our work suggests that the robustness of cargo transport in crowded environments is an emergent property of the interaction of cargo vesicles with other vesicles as well as with crowding elements, and thus depends crucially on the milieu in which such vesicles move.This is joint work with the laboratory of Sandhya Koushika of TIFR, Mumbai and centres around a close collaboration between computational modelling and experiment.

DNA in the form of chromosomes is packaged by histones, proteins that help to compact the approximately 2m of DNA in our nuclei into a nuclear space of a few microns in extent. The combination of DNA, and the proteins and RNA which bind to it, is chromatin. I will describe recent theoretical work from my group on models for the architecture of chromatin in the mammalian cell nucleus. These models describe chromatin as "active matter", a term which emphasizes the central role of non-equilibrium (energy-consuming) processes, or "activity". Our results address several long-standing questions in nuclear architecture, among them the large-scale territorial organization of chromosomes and their non-trivial positioning patterns, suggesting a simple, yet general, framework within which they may be understood.

During morphogenesis, the organization of cells into tissues, cells respond to mechanical cues in the extracellular matrix (ECM) but also continuously deform it by pulling on it. To study how traction forces applied by cells influence self organization, we use a computational model, where cells are represented by the Cellular Potts Model. The deformations in the ECM are calculated using a Finite Element Method. We model a mechanical feedback between cells and the ECM, where 1) cells pull on the ECM, 2) strains are generated in the ECM, and 3) cells preferentially extend protrusions oriented with strain. Similar to experiments, cells in our model become small and round on compliant substrates, elongate on substrates of intermediate compliancies and spread on stiff substrates. With just this mechanical cell-substrate feedback in the Cellular Potts Model, simulations show that cells are able to generate vascular like patterns on substrates of intermediate stiffness. Again, this behavior has been observed in experimental conditions as well with cells on compliant substrates. Experiments where the ECM is uniaxially stretched, show that cells orient parallel to stretch. Model results on cells on a stretched ECM with and without traction forces indicate that cell traction forces amplify cell orientation parallel to stretch. Furthermore, they allow cells to organize into strings in the direction of stretch. The ability of cells to form strings is dependent on the balance between stretch force and traction forces. Also, string formation is enhanced when cell-cell adhesion is decreased. The model increases our understanding of how mechanical cell-ECM interactions influence self-organization and may guide tissue engineering experiments.

In this talk I will present details about a moving mesh finite element method for the approximate solution ofpartial differential equations on an evolving bulk domain in two dimensions, coupled to the solution of partial differential equations on the evolving domain boundary. Problems of this type occur frequently in the modeling of eukaryotic cell migration and chemotaxis - for these applications the bulk domain is either the interior or exterior of the cell and the domain boundary is the cell membrane. Fundamental to the success of the method is the robust generation of bulk and surface meshes for the evolving domains. For this purpose we use a moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known solutions which indicate second-order spatial and temporal accuracy. The method is then applied to a model of the two-way interaction of a migrating cell with an external chemotactic field.

Coauthors: Damian Dalle Nogare, Jeffery Head, Katherine Somers, Miho Matsuda and Ajay B Chitnis. The posterior Lateral Line primordium (pLLp) migrates from the ear to the tip of the tail in the zebrafish embryo periodically depositing neuromasts to pioneer establishment of the posterior lateral line system. We have developed three sets of agent-based models of the pLLp to visualize how interactions between cells coordinate morphogenesis of the pLLp system. The first explores how the polarized expression of chemokine receptors, CXCR4b and CXCR7b, facilitates directed migration of the pLLp along a stripe of chemokine expression. A second model explores how polarized Wnt and FGF signaling systems coordinate morphogenesis and cell fate in the pLLp. A Wnt signaling system that dominates in the leading domain, helps maintain the mesenchymal morphology of leading cells, while driving expression of FGF ligands that periodically initiate FGF signaling centers in a trailing zone. FGF signaling initiates formation of protoneuromasts by promoting morphogenesis of epithelial rosettes and expression of atoh1a to determine specification of a hair cell progenitor at the center of protoneuromasts. Our model explores how interactions between Wnt and FGF signaling systems could establish a reaction diffusion system to initiate center-biased FGF signaling and atoh1a expression in developing protoneuromasts. In the context of this center-biased expression, Notch-mediated lateral inhibition ensures atoh1a and hair cell fate is restricted to the central cell. Finally, we have used high-resolution time-lapse imaging to track movement, fate and lineage of every cell in the pLLp. These observations are used to develop a quantitative agent-based model that illustrates how proliferation and a progressively shrinking Wnt system determine the deposition pattern of neuromasts from the migrating pLLp. Together, our models provide a platform to integrate what has been learnt from a wide range of experimental studies and they allow us to evaluate if current hypotheses are adequate to account for various phenomena. Failure of our models identifies gaps in our understanding and helps define testable hypothesis that can be evaluated by future experiments.

One major scientific challenge in human health is developing effective vaccines to block T-cell responses in spontaneous autoimmune disorders, such as type 1 diabetes (T1D). The ability of these T cells to recognize host cells (e.g., insulin-secreting pancreatic β cells in T1D) and to exert cytotoxicity on self-tissue is dictated by the binding affinity (avidity) of T-cell receptors (TCR) with surface molecules on host cells, called peptide-major histocompatibility complexes (pMHC). Recent findings have shown that in T1D, and other autoimmune disorders, low-avidity autoreactive T cells spontaneously differentiate into memory autoregulatory T-cells that can blunt autoimmunity. These autoregulatory T cells can be selectively expanded using nanovaccines, or nanoparticles (NPs) coated with pMHC, in a PMHC-density- and dose-dependent manner. By using multistep Markov models and continuum avidity model of T cells, one can optimize the efficacy of NPs and identify the causes of abnormalities exhibited by this system. In this talk, we will present our recent work deciphering the kinetics of TCR-interaction with pMHC-coated NPs, and elucidate the role of immunomodulation in altering disease dynamics.

In this talk, I will discuss applications of statistical and mathematical models to study two different human herpesviruses. First, I will demonstrate how viral load data can be used to estimate viral load thresholds required for transmission of genital herpes infection. This information provides a vital link between viral pathogenesis at the single host level and epidemiologic spread of the virus. Second, using data collected from a study in Uganda, I analyze primary cytomegalovirus (CMV) infections in infants, where little is known about the natural history of infection. In this cohort, infants with primary CMV infection persistently shed virus for extended periods of time (> 180 days) with characteristic kinetics. Here, a mathematical model is employed to explain different phases of primary infection.

Individual-based models are widely used to describe the characteristics and dynamics of single organisms or particles in a population. A useful feature of these models is the ability to easily incorporate stochasticity and spatial structure at the individual level and, as a result, these models are well-suited to addressing questions in evolutionary biology and infectious diseases. In this talk, I will describe two models we have developed that incorporate these features. In the first project, we developed a stochastic, mechanistic model to predict the effectiveness and toxicity of therapies currently being developed to cause targeted disruption of latent viral genomes for the cure of diseases like HIV. We fit our model to flow cytometry data from multiple experiments aimed at optimizing engineered DNA cleavage enzymes delivered to cells using adeno-associated viruses (AAV) vectors. The model predicts the number of transgenes delivered, the level of expression and amount of cytotoxicity produced as a function of dosage for a given AAV serotype. We then use the model to predict the therapeutic index for a candidate therapeutic molecule and determine the optimal dosage, serotype and promoter for delivering the molecule to infected cells. In the second project, we developed a spatially structured, individual-based model of HSV spread in epithelial tissue with the goal of understanding how tissue-resident memory CD8+ T-cells (TRMs) control a reactivating HSV infection. CD8+ TRMs are a relatively recent discovery and characterizing their role and interactions with other T-cell compartments is vital for designing effective vaccine strategies against HSV. Our model incorporates mechanisms like viral diffusion, cell-cell spread, patrolling by TRMs, trafficking of effector memory T-cells (TEMs) from lymph nodes and effector functions of CD8s including tissue-wide alarm functions.

In infectious diseases, traditional pharmacokinetic (PK) and pharmacodynamic (PD) models are routinely used to establish concentration dependent effects of a drug on pathogen replication. Yet, these models ignore the complex and dynamic interplay between a pathogen and the host immune system. Using chronic HSV-2 infection as an example, I will demonstrate that synthesis of viral dynamic models with PK / PD equations allows for highly predictive in silico clinical trials. Model simulations allow for a more precise estimation of drug parameters necessary for complete viral containment, and may allow for optimized dosing strategies in future antimicrobial trials. I will conclude by highlighting similar approaches that are in development to inform the design of future therapeutic vaccine and viral eradication studies.

Scintillating Scotoma is a phenomenon in the visual cortex which may signal the onset of migraine, or may happen for no apparent reason. Initial steps to model this use a stochastic reaction diffusion system. A stochastic version of Turing patterns, called quasi-patterns is introduced. This idea is analogous to oscillations sustained by noise in a stochatic ODE setting.

In this mathematical modeling talk, we discuss two projects on socially aggregating insects. The first project models desert locusts with an eye towards hopper band aggregations. Via analysis and simulation of a nonlinear partial integrodifferential equation model, we find conditions for the formation of population density clumps, demonstrate transiently traveling pulses of insects, and discover hysteresis in the aggregation's existence. The second project uses motion tracking experiments on the pea aphid to construct a random walk model for their motion. The random walk parameters depend strongly on distance to an aphid’s nearest neighbor. For large nearest neighbor distances, when an aphid is isolated, its motion is ballistic and it is less likely to stop. For short nearest neighbor distances, an aphid moves diffusively and is more likely to become stationary; this behavior constitutes a simple aggregation mechanism.

Human African Trypanosomiasis (HAT) or Sleeping sickness and Nagana in cattle, which is generally known as the sleeping sickness is a deadly disease that affects 36 sub-Saharan Africa countries, threatening life of millions of people in rural settlements. In the absence of treatment, the outcome is always fatal. The tsetse fly which is responsible for transmitting the disease has very unusual life cycle. In this talk, we present a deterministic model of the transmission of Trypanosomiasis between human hosts and vectors in a natural environment. The model takes into account the unusual life cycle of the tsetse fly, since its larval stage to the adult stage with the different states of the fly relative to the infection. The host population is modelled by a SIR compartmental model. Analyse of the coupled model and measures of control/eradication will be discussed.

Tuberculosis continues to afflict millions of people and causes over a million deaths a year worldwide. Multi-drug resistance is also on the rise, causing concern among public-health experts. This talk will give an overview of my work on modeling tuberculosis at various scales. On the cellular side I will describe models of the metabolism of M. tuberculosis, where insights from duality led to a consistent analysis of existing models, a systematic method for reconciling discrepant models, and the identification of putative drug targets. On the population side I will describe models of strain evolution, where a new metric combined with an optimization-based approach resulted in an accurate classification of complex infections as originating from mutation or mixed infection, as well as the identification of the strains composing these complex infections.

Asthma is a surprisingly serious disease which exhibits a number of interesting dynamic phenomena. Because of challenges in making direct experimental measurements, mathematical modelling is a valuable tool for integrating the incomplete information available and exploring hypotheses about the underlying mechanisms at work. One such area is the phenomenon of clustered ventilation defects, where imaging of the lung during an asthma attack typically yields not just areas of reduced ventilation, as expected, but also some areas of increased ventilation. Moreover these clusters vary from event to event and are thought to be a dynamic, rather than structural phenomenon. In this talk I will discuss both general challenges in modelling asthma, and recent results from a model of clustered ventilation defects.

Current treatment of glioblastoma brain tumors offers lots of room for improvement, with the current expected survival being about a year with treatment. A model which describes the distribution of cancer cells within the brain tissue would offer potential for improved treatment regions, and subsequently improved survival and quality of life. I will present a model which makes use of brain architecture to predict the patterns of invasion. This is done by assuming that the cancer cells migrate preferentially along the white matter tracts of the brain, and adjusting the diffusion coefficient both spatially and directionally. We refer to this as anisotropic diffusion. We make use of Diffusion Tensor Imaging (DTI) to measure the diffusion tensors at each location within the brain and show simulations using real patient data.

The measurement of dynamic persistence of a population has been a long standing problem in Ecology. For spatial processes, fractal measurements such as the Korcak exponent or the boundary dimension have often been proposed as indicators of the persistence of the underlying dynamics. Recently it has been shown that the value of the Korcak exponent does not necessarily correlate with persistence. I shall explore under what conditions there does exist a strong relationship between persistence and fractal measures. I show that theoretically a Korcak-persistence relationship is expected under fairly generic conditions. I will then introduce a model of spatial vegetative growth with non-local competition and use numerical simulation to elucidate this relationship and find that environmental factors strongly affect both return rate and fractal measures. The theory and model are then supported by a long-term study of Seagrass in the Scilly Isles,UK.

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 two-phase (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.

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 meta-population 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 deme-structured 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 individual-based simulation results.

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.

Person-to-person 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 contact-related benefits. Epidemiological–economic model of disease dynamics that explicitly model the trade-offs that drive person-to- 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 trade-offs 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 Castillo-Chavez (Steve Blythe, Kenneth Cooke and Castillo-Chavez) 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)

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 re-emergent 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.

Ecological competition between strains of a pathogen occurs when strains compete for hosts -- either for susceptible hosts, host resources during co-infection, or the ability to re-infect 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 population-level phenomenon which we would not expect to observe in small-scale studies. Even population-level 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 next-generation 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 anti-correlated. 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 inter-branch distances, among other properties. I analyse a phylogeny of within-host 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.

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.

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 free-ride 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 intra-generational 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’ short-term gains can arise only from defection. References: [1] Jacquet et al (2011) Shame and honour drive cooperation, Biol. Lett. 7 899-901 [2] Jacquet et al (2013) Intra- and intergenerational discounting in the climate game, Nature Climate Change, (online Oct 20)

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 Notch-Delta 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.

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.

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 gas-filled 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.

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, cross-spectral 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.

One of the most striking aspects of the cell is the broad range of cell-cycle 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 high-throughput, complete cell-cycle 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 proteome-wide characterization of localization dynamics for every individual protein in E. coli. We expect this quantitative cell-cycle imaging approach will be widely applicable to understanding the emerging role of physical organization in prokaryotic cellular function.

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 force-velocity 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 sub-processes, 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 filaments-membrane 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 free-surface flow of complex fluid in arbitrary geometries. Finally I will discuss open questions and opportunities in this line of research.

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 self-assemble 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 self-assembly into fibrillar networks.

TBA

In a healthy immune system, the T cell response discriminates between self and nonself cells. Medical research has shown that this phenomenon is not black-and-white, 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 antigen-presenting 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.

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).

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.

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 non-observed effective interactions in order to produce the pattern. We show that this is unnecessary as the non-linearity 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.

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 co-author.

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 micro-scale particles (aggregated nanoparticles), and the subsequent release of nano-particles encapsulating tPA due to shear activation. Assumptions and results will be described and comments made regarding the further development of this class of nano-medicine.

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 spatio-temporal 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 on-going project: inferring the spatio-temporal replication program from experimental replication kinetics data.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

TBA

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

TBA

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

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

TBA

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

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

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

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”.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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