IGTC Graduate Summer School in Mathematical Biology

A PIMS/Accelerate BC sponsored Summer School in Mathematical Biology

University of British Columbia, Vancouver, May 11-June 11, 2008

Abstracts for Talks

For a detailed daily schedule click HERE.

For a list of events by category and/or lecturer(s) click HERE.

For details of the main Course Content click HERE.

For an overview of the month-long schedule click HERE.

Unless otherwise indicated, events will take place at the UBC campus of PIMS. Directions for PIMS can be found HERE.

Sunday May 11, Opening Lecture:

Prof Michael Doebeli

Adaptive diversification: theory and experiments

Special Mathematical-Biology Guest Lectures

Friday May 16, 1:00PM

Prof Eirikur Palsson

Excitability of Dictyostelium discoideum is regulated by the ratio of membrane bound to secreted phosphodiesterase

Friday May 23, 1:00PM

Prof Daniel Coombs

Models of T cell activation

Tuesday May 27, 1:00PM

Prof Yue Xian Li

Tango Waves in Inhomogeneous Calcium Excitable Media

Monday June 2, 1:00PM

Prof Eric Cytrynbaum

Finding the center - how to solve simple geometry problems at the cellular scale

Student Research Seminars on Thursday May 15, 2:00PM

• William Holmes

  Department of Mathematics, Indiana University

  A 3-D model of the passive cochlea

  Abstract: The cochlea is the primary sound processing mechanism of the (inner) ear. The aim of this talk is to present a 3-D model of the passive (non-energetic) cochlear mechanism. A brief overview of the function of the ear will be included.

• Annabelle Ballesta

  INRIA de Rocquencourt, BANG Project, France

  Modeling The Pharmacokinetics and Pharmacodynamics of the anticancer drug Irinotecan at the intracellular level

  Abstract: Irinotecan is an anticancer drug which is currently used in chemother- apy against colorectal cancer. Here we are interested in its action on a cell population, at a molecular level. We model its Pharmacokinet- ics(PK),which is what the cells do to the drug (e.g. metabolization, trans- port), and its Pharmacodynamics(PD), which is what the drug does to the cells(e.g. DNA damages). The PK-PD of Irinotecan is largely influenced by the circadian rhythms: each living being has an internal clock that is responsible for rhythms over a 24-hour period. Its most obvious manifestation is the regular cycle of sleeping and waking, but body temperature and the concentration of en- zymes also vary over the day. Our mathematical model is based on ODEs and simulates the PK-PD of Irinotecan, taking into account the circadian variation of the chemi- cals. An aim of this modelization could be to optimize the schedule of administration of the drug.

• Heather Hardway

  Mathematics, Rice University

  Models for Robust Protein Gradients in the Drosophila Embryo

  Abstract: In early Drosophila development, one of the first specifications made in determining cell location is the formation of the anterior-posterior axis, and this event is carried out with incredible precision, despite many variations of the genetic regulatory network and environmental fluctuations. My focus is on the first step in this process, where the protein, Hunchback (Hb), forms a very sharp boundary at the midpoint of the embryo, despite receiving noisy information from its known upstream regulator, Bicoid (Bcd). Using systems of partial differential equations to model the gene network, we seek an answer to the following inverse problem: given the robust Hb boundary, what conditions does this place on the regulatory network? While a simple answer does not likely exist, we provide examples of such networks, as the result of both numeric searches and analytic techniques, and an interpretation of the conditions in terms of the biological system.

• Yanyu Xiao

  Department of Applied Mathematics, University of Western Ontario)

  Model for the dynamics of Malaria

  Abstract: The transmission and maintenance of malaria is considered between human being hosts and mosquitio vectors that are infected by protozoan parasites. On the basis of the simple Ross-Macdonald model, it considers a model both the incubation period in the disease circle of hosts and vectors, especially on the latency of the malaria in mosquito vectors. For the new model with an exposed class , the basic reproduction number R0 is identified and its threshold property is discussed. Numerical simulations re given to illustrate the dynamics of the population.

• Omer Dushek

  Dept of Mathematics and Institute of Applied Mathematics, UBC

  Receptor clustering is required for accurate detection of ligands

  Abstract: T cells discriminate between pMHC ligands using their T cell receptors. Accurate pMHC discrimination is critical to defend against forgein pathogens while avoiding autoimmunity. The mechanism of accurate detection has remained elusive. T cell receptors have recently been shown to cluster on the surface of T cells. The role of T cell receptor clusters is discussed controversially. I will use physical arguments and mathematical modeling to show that T cell receptor clustering is critical for accurate pMHC discrmination.

  SKILL: Stochastic simulation of reaction-diffusion system

  For this work I needed to perform accurate simulations of diffusing and reacting proteins on a 2D membrane. I also needed to relate all parameters in the stochastic model to the relevant PDE model since experiments were carried out in the PDE regime (i.e. high concentration). I can use a simplified example to show how one can simulate diffusion and reaction and how to pick the parameters so that the simulation converges to a PDE.

• Shaun Strohm

  Dept of Mathematics, UBC Okanagan

  The effects of fragmentation of habitat on cyclic population dynamics

  Abstract: We investigate how fragmentation of habitat affects cyclic population dynamics by constructing a spatially explicit predator-prey model in which predators and prey orient their movement toward high quality patches. For our reaction terms, we use four different pairs of functions found in the literature. Our study is motivated by cyclic mammalian populations such as the Snowshoe Hare and Canada Lynx that exhibit high amplitude, 8-11 year population cycles. We investigate whether increasing anthropogenic fragmentation of habitat could affect the population dynamics and persistence of cyclic populations. This fragmentation of habitat could be attributed to temporary disturbances such as forest harvesting, or more permanent disturbances such as roads and agricultural or urban development. We use a Partial Differential Equation (PDE) model to describe the dispersal of predators and prey in a heterogeneous landscape made of high quality and low quality habitat patches. We show that habitat fragmentation affects the amplitude and average densities of both predator and prey in high quality patches. This result may be important to conservation efforts for species with cyclic population dynamics in fragmented habitats.

  SKILL: Determining critical patch size for multi-species population dynamics with dispersal

  In my research, I had to determine critical patch size for predators and prey for my spatially-explicit model. I could present an example on how to determine critical patch size for one of the models I used.

Student Research Seminars on Thursday May 22, 2:00PM

• Raluca Apostu

  Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University

  Galactosemia: a mathematical approach based on the impairment of galactose metabolism in Saccharomyces cerevisiae

  Abstract: In organisms ranging from E. coli to mammals, galactose is metabolized through a series of sequentially reactions known as the Leloir pathway. In humans, the deficiency in any of the Leloir enzymes leads to a potentially lethal disorder called galactosemia. Despite decades of study, the underlying bases of galactosemia pathophysiology remain unknown, limiting the development of novel and potentially more effective treatments. The difficulties in understanding this inborn error of metabolism created an impetus for a model organism susceptible to metabolic changes and genetic engineering, and for an investigation based on advanced computational methods. We address the problem of galactosemia by employing a model system with high relevance for human health (S. cerevisiae) and through mathematical modeling. Our main goal is to propose a comprehensive kinetic model of galactose signaling pathway in yeast and to investigate the mechanisms underlying galactosemia. We plan to examine the effect of the Leloir enzymes impairment on the cell ability to metabolize galactose, to follow the flux distribution through the biochemical routes, and to define the role of the transferase-independent routes of galactose metabolism in this disorder. The potential physiological impact of metabolites accumulation, questions of great importance from a therapeutic point of view (e.g. the maximum amount of exogenous galactose tolerated by a galactosemic patient) as well as the logical connection between the metabolic abnormality and the long-term complications in galactosemia are further research goals.

• Vivi Andasari

  Division of Mathematics, University of Dundee

  Mathematical Modelling of Cancer Cell Invasion of Tissue

  Abstract: When solid tumour cells are no longer contained in their primary compartment, they acquire an ability to break out of the compartment and invade the surrounding tissue locally. The ability of tissue invasion gives solid tumours a defining deadly characteristic where they become malignant cancerous cells by growing rapidly and establishing a new colony in distant organs, a process that is known as metastasis. A mathematical model of cancer cell invasion of tissue with overcrowding prevention mechanism is formulated and analysed. The model includes the role of urokinase plasminogen activation (uPA) system with a system of 5 taxis-diffusion-reaction partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin or matrix degrading enzyme, and host tissue. In this model, cell motility is expressed by random motion and local continuum model based on chemotaxis and haptotaxis terms. Further, the effect of cell-cell and cell-matrix adhesions is incorporated by replacing local taxis flux terms by nonlocal flux terms.

• Jun Allard

  Institute of Applied Math, UBC

  Models of the actin-like MreB helix in prokaryotes

  Abstract: MreB is an actin-like protein that forms a helix running the length of cylindrical bacterial cells. I will present a model of the helix. Individual polymers that make up the helical cables are represented by simple force-dependent polymer models bundled into a supramolecular array. Boundary conditions and external forces are provided by a global elasticity model representing the cables as flexible rods buckled into a helix inside the confinement of the cell wall. The model produces a relationship between the pitch of the helix, the thickness of the cables and the total abundance of MreB, and has implications for cell growth, macromolecule trafficking and the polarization of Caulobacter crescentus.

• Ehsan Ellahi Ashraf

  Department of Mathematics, University of Glasgow

  Resistive Force Theory and the swimming of Biflagellated Green Algae

  Abstract: Green Algae plays an important role in the development of the Earth's atmosphere by photosynthesizing and acting as a sink for carbon dioxide. They are estimated to make up more than half of the Earth's biomass and acts as a potential source for Hydrogen gas production. They can be the most efficient source of feedstock for Biofuel or Biodiesel industry.

  The green biflagellated algae Chlamydomonas nivalis has a prolate spheroidal body and has two long, thin flagella attached at one end which are propelled to cause the swimming of the organism. The length of the cell body and flagella is approx. same as 10 micro meter and the flagella beat at approx. 50 hertz. C. nivalis is usually considered to swim in a human breast-stroke manner with an effective-recovery style, approximately in the direction of its axis of symmetry. However, the latest research proved that this is not exactly the accurate swimming stroke.

  The approximation known as Resistive Force Theory (RFT) was established by Gray & Hancock (1953) and states that the normal and tangential components of force and torque on an element of a flagellum is directly proportional to the normal and tangential components of the fluid velocity relative to that element. RFT was used by Jones et al. (1994) to model the swimming of a single cell of C. nivalis in a viscous flow of low Reynolds number. Analytical and numerical techniques were used to calculate the magnitude and direction of the cell's swimming velocity and angular velocity.

  The aim of our work is to extend the Jones et al. model to calculate the the cell's swimming velocity and angular velocity in the vicinity of a stationary no-slip boundary or sphere using appropriate image system techniques. Finally, we will model interactions of two algae cells using RFT and image systems and calculate the magnitude and direction of both cell's swimming velocity and angular velocity.

• Anne Yust

  Department of Mathematical Sciences, Carnegie Mellon University

  Probabilistic Modeling of the Immune System

  Abstract: Our ultimate goal is to obtain a reasonable model of the gene interactions within the immune system. From the data we have which contains time plots of the growth of specific proteins produced by classified immune system genes, we want to determine the inhibiting and catalyzing interactions between those genes. We are specifying these interactions as stochastic in nature. The probabilities we are attempting to determine are defined by the likelihood that a gene affects another gene, positively or negatively. In our attempt to realize these interactions, we have produced various models that show protein production. Here we try to solve the forward problem: given a specified number of probabilities, create a time plot of the protein productions. These models consider single genes producing one protein, simple two gene interactions producing two proteins, and random n gene interactions producing n proteins. After creating these models, we use them to solve the backward problem: given a time plot of protein productions, find the inhibiting and catalyzing interactions between specific genes and their associated probabilities.

• Sarah Lukens

  Department of Mathematics, Tulane University

  Introduction to Projection Methods

  Abstract: Projection Methods are a numerical method for solving the full incompressible Navier Stokes equations, based on decoupling the momentum and continuity equations and solving two separate systems within a single time step. In the talk, I will give an overview of the method applied to a staggered grid, and show an example with periodic boundary conditions.

Student Research Seminars on Tuesday May 27, 2:30PM

• Jiafen Gong

  University of Alberta

  Optimal Cancer Radiotherapy Treatment Schedule under Cumulative Radiation Effect constraint

  Abstract: Radiotherapy is a very important method to treat malignant cancer. Usher (1980) derived some optimal fractionated cancer radiotherapy treatment schedules by minimizing the total survival fraction of cancerous cells. But his method has two restrictions: 1) His optimization method is not a global optimization, 2) his method can only be used for uniform treatment, i.e. the treatment schedule with the same dose per fraction and same intertreat- ment time between two fractions. In this report, first we use both analytic and numerical methods to get global optimal treatment schedules for uniform treatment, which confirm that Usher's results are almost right. Furthermore, we generalized the cumulative radiation effect and total survival fraction model to nonuniform treatment with variable intertreatment time, use them to rank ten universally used protocols in prostate cancer treatment and compare with the rank obtained by tumor control probability model, which is another universal model used to determine the treatment schedule, they are almost the same.

• Ignacio Rozada

  Institute of Applied Mathematics, UBC

  Pattern formation on growing domains

  Abstract: Domain growth plays a central role in robustly selecting a pattern in reaction-diffusion systems. In this talk I will derive the generalized reaction-diffusion equations on growing domains for 1 and 2-D. I will show an example, and discuss the implications on pattern selection.

• Vishaal Rajani

  Department of Mathematical and Statistical Sciences, University of Alberta

  Applying a Correlated Random Walk Model to LFA-1 Protein Receptors

  Abstract: Single Particle Tracking (SPT) and Fluoresence Recovery After Photobleaching (FRAP) are two methods used to study the diffusion of membrane proteins in cells. SPT involves tagging proteins with fluorescent labels and observing their individual trajectories, while FRAP involves photobleaching a subcellular region of the cell membrane, creating a bleached population of proteins and allowing the observation of the fluorescence recovery in this region. Both methods provide important information about protein interactions through the measurements of diffusion. The methods provide estimates of diffusion coefficients from an ensemble (in the case of FRAP) or from the trajectories of single molecules (SPT). While these methods generally agree in a qualitative sense, it has been generally observed that they rarely agree quantitatively. As an early investigation into this problem, I will introduce a conventional method used to estimate a diffusion coefficient from a series of SPT trajectories, and try a different approach (measuring and analyzing turning angles) to uncover characteristics about protein diffusion. In particular, I will analyze a data set for LFA-1, an integral membrane protein found on cells associated with the immune system.

• Majid Hosseini

  Dept of Chemical and Biological Engineering, UBC

  Smoothed particle hydrodynamics

  Abstract: In several human diseases like cancer and malaria, an external factor (such as malarial parasites) changes the mechanical behavior of living cells by starting some biochemical reactions. This single-cell biomechanical response, such as increasing or decreasing the elastic modulus due to membrane or cytoskeleton reorganization (in the case of red blood cell infection), facilitates disease progression in the body. We first present a new model of a living cell based on Smoothed Particle Hydrodynamics (SPH) method. The particle-based nature of SPH method allows us to go beyond the continuum approaches and move toward micro/nano structural approaches for a mechanical model of living cells. This model is utilized to investigate two important phenomena: the interaction between living cells and external factors of disease; the molecular/structural changes inside the cells and in the cell membranes during the disease development.

• Tanny Lai

  National University of Singapore

  Periodic contractions of the lamellipodium

  Abstract: Lamellipodium dynamics have been shown to be important in the sensing of rigidity of the extracellular environment to guide in the motility of cells. Sheetz's group have discovered local contractions in the lamellipodium as the cell moves towards its target (eg an area of higher rigidity) and this is in contrast to past perception that cell migration is composed only of protrusion due to actin polymerization. In addition to identifying various factors involved in this phenomenon, a simple mechanism has also been proposed. In my project, I intend to develop a 1D system of equations to reflect the dynamics of the proteins in the cell and evaluate the model numerically. The model should be able to predict the effect of rigidity of the substrate on cell migration, and in 2D, provide some insights into the ruffling phenomenon seen in certain cellular movement.

• Jennifer Hubbarde

  Dept of Mathematics and Institute of Applied Mathematics, UBC

  Modelling Drug Resistance in HIV

  Abstract: Mathematical modelling of HIV, both within-host and between-host, is a very well studied and still fast moving field. In this talk, I will develop the pre-existing basic model for within-host HIV, including drug therapy and resistance, and look at some possible extensions and improvements of this model. The focus will be on the best ways to model the emergence of drug resistance in the early stages of HIV.

Student Research Seminars on Wednesday June 4, 2:00PM

• Jennifer (Jen) Lindquist

  University of Victoria

  Bayesian Markov Chain Monte Carlo Parameter Estimation: Application to Stochastic Epidemic Models

  Abstract:

  Maximum likelihood (ML), and least squares (LS) techniques, while incredibly common, are not the only methods available for parameter estimation. In this talk I will introduce Markov Chain Monte Carlo (MCMC) methods; these are especially useful in high dimensional (of order 10,000) models, and situations where data is missing or incomplete. While I will work exclusively in a Bayesian framework, MCMC is also applicable in frequentist settings. I will focus on key ideas in Bayesian and Markov theory, with attention to MCMC implementation algorithms and a discussion of stochastic epidemic models (SEIR type) with missing data.

• Atsushi Yokoyama

  Ritsumeikan University, Kyoto, Japan

  Biological Receptor Scheme for the External Synchronization of Mutually Coupled Oscillator Systems.

  Abstract: Recently, we have proposed a generalized theory of the synchronization of rhythms based on the concept of biological receptors. The theory can achieve both mutual synchronization and external synchronization. However, previous work has neglected the particular case of the external control of a group of mutually coupled oscillators. In nature, we often encounter complex systems that consist of many subsystems, e.g., organs that consist of many cells. However, without proper control, it is likely for an external field to break the synchronous behavior of systems. In this study, we generalize the biological receptor scheme such that external synchronization can be achieved without breaking the mutual synchronization of coupled oscillators.

• Vasthi Alonso Chavez

  School of Mathematics, University of Southampton

  Mathematical Studies of conservation and extinction in inhomogeneous environments.

  Abstract: A fragmented (or patchy) ecosystem is an ecological community constituted by those organisms who have a preferred living habitat with some emergent discontinuities (frag- mentation) within. In this work we will model this type of ecosystems using some concepts from Solid State Physics. Specifically, we will use some diffusion concepts to understand how individuals of a given species can diffuse out of the preferred habitat toward dangerous regions around the safe habitat. We also want to find an accurate expression to estimate the critical patch size in order to assure the endurance of the ecosystem, and extend this work to discover the ecological properties of extended inhomogeneous regions. This results are expected to be applied directly in two specific ecosystems in Argentina and Belize.

• Gabriel Mitchell

  Department of Physics, Georgia Institute of Technology

  Networks in Biology

  Abstract:

  One of the main goals in theoretical biology is to discover or explain unifying organizational principles across a wide range of observed structures and functions. Assigning subunits of these structures and their interactions to nodes and edges of a graph can often prove helpful in the development of such theories. In fact, much understanding can often be directly obtained by studying the properties of the resulting graph, or network. This mode of investigation is called "network biology." In this SURVEY I will highlight several results in network biology that I am familiar with and discuss some tools that prove useful for studying networks.

• Sara Sadeghi

  Simon Fraser University

  Swarm intelligence

  Abstract: Many different animal species, such as ants and honeybees, live in colonies as socialized organisms. These organisms are observed to have intellectual behavior. What is in charge of their behavior? How are the ant's duties in the morning allocated? How do they communicate? Are they really smart? If they are not smart, how do the simple actions of individuals add up to the complex behavior of a group? One of the current theories attributes this behavior to "swarm intelligence". According to this theory, each organism follows simple rules and acts on local information. No ant explicitly tells the other ants what to do. They use different optimization strategies to solve various problems, many of which can be exploited as templates for solving complex human problems such as scheduling airlines or routing trucks.