MITACS/MathBiology (and related) Seminars (Year 2001/2003)

MITACS Mathematical Biology (and related) Seminars
2001/2003

Year 2002-2003:

Jan 27, 2003, 3-4 pm, IAM/Stats seminar Room (301 Leonard Klink bldg), IAM-PIMS Distinguished colloquium speaker: Leon Glass (Physiology, McGill): Dynamics of genetic networks

Time: Thursday, Dec 12, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Malgorzata Klosek Mathematical Sciences, University of Wisconsin, Milwakee
Title:An Application of Stochastic Processes: Mathematical Tools for Profile-Profile Alignment
Abstract:
We study ionic channel proteins which come from distinct but related families. Each of the families can characterized statistically by distributions of amino acids along positions of its sequence; that is, a profile. We build stochastic models to measure similarity and evolutionary distances between the families. Our models take into account correlations between residues at each position and substitution probabilities of one amino acid by another. [Back To Top]

Time: Thursday, Nov 28, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Jenny Read Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health
Title:Cortical computations that support stereo vision
Abstract: Our visual system fuses the images from left and right eyes into a single percept, while using the disparities between them to extract information about depth. Disparity-tuned neurons in primary visual cortex are believed to carry out the initial processing which ultimately makes this possible. A relatively simple model (the energy model) provides the most successful account of the mechanism by which these neurons signal disparity. Even this model fails to capture several properties of real neurons. We describe how a simple modification of the energy model enables us to account for three puzzling experimental observations.
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Time: Thursday, Nov 21, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Diana Jiang (UBC, undergrad) and Nathaniel Newlands (UBC, PDF)
Title:The Search for Realistic Simulated Fish Schools
Abstract: Under the guidance of Prof. Keshet a project was undertaken for Biology 448 (Directed Studies) this past summer, 2002. The goal of this project was to develop models to simulate fish schools based on individual decision-making rules. These models enabled an exploration of the relative effects of centroid pull, polarization, random turning rate, and individual attraction and repulsion within fish schools. School centroid pull, individual attraction and polarization contributed strongly to the compactness of schools, while individual random turning and repulsion had opposing effects. The tendency for individuals to align as they moved resulted in more polarized and faster traveling schools.

The talk will provide an overview of the project and summarize its main results. A hierarchical model that expands upon these simple rules by linking them to different sensory mechanisms, energetic trade-offs and behavioural modes is currently being developed by Dr. Newlands and Prof. Keshet to test alternative hypotheses and to identify unique rule-sets that produce different school formations. To search for realistic survival trade-offs that individuals make while schooling in the wild, simulation results of these individual-based models will be compared to data on the shape and structure of different formations of Atlantic bluefin tuna.

November 14, 2002, 12 - 1 pm, IRC 6: Dr. Ruedi Aebersold Institute for Systems Biology, Seattle UBC Systems Biology Lecture Series

Time: Thursday, November 14, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Nick Swindale Opthalmology, UBC
Title: The singular geometry of visual cortex maps
Abstract: The primary visual cortex of humans and higher mammals contains organised maps of visual features such as position in the visual field, edge orientation, direction of motion, and the eye in which the stimulus is present. In this talk I will describe the organisation of these maps and discuss the pattern-formation rules that may govern their early post-natal development.
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November 7, 2002, 12 - 1 pm, IRC 6: Dr. Tony Pawson Samuel Lunenfeld Research Institute, Toronto UBC Systems Biology Lecture Series

Nov 4, 2002, 3-4 pm, IAM/Stats seminar Room (301 Leonard Klink bldg) David Boal (Physics, SFU): Extraterrestrial cells

October 31, 2002, 12 - 1 pm, IRC 6: Dr. John Aitchison Institute for Systems Biology, Seattle UBC Systems Biology Lecture Series

Time: Thursday Oct 31, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Yue Xian Li Dept of Mathematics, UBC
Title: Symmetry-breaking and Bifurcation Caused by Spatial Inhomogeneity in a Reaction-diffusion Model for Biological Waves
Abstract: Waves have been observed ubiquitously a in a large variety of biological systems. Reaction-diffusion equations have been used to model many types of waves. In most models, spatial homogeneity was assumed. However, in many cases, spatial heterogeneity can occur and numerical studies have revealed some very interesting phenomenon in reaction-diffusion equations with spatial inhomogeneity. We used the FitzHugh-Nagumo equations as a model to study effects of spatial inhomogeneity on front solutions in reaction-diffusion systems. In particular, we study the effect of the gradient of spatial variations by using the slope of a linear ramp as the bifurcation parameter. A linear ramp breaks the translational invariance of the stationary front and stabilizes the front. The front becomes less stable as the slope decreases. At a critical value of the slope, the front becomes unstable through a Hopf bifurcation giving rise to oscillations at the front. This bifurcation can occur in regions of parameter space that are far from any other bifurcation points, and is caused exclusively by spatial inhomogeneity. The general condition for determining whether a particular spatial inhomogeneity is stabilizing is derived.
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Oct 25, 2002, 3-4 p.m.,Mathematics Colloquium: MATH ANNEX 1100, Jim Keener (Math, Utah), title: TBA

Time: Thursday, October 17, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Mary Lou Zeeman Applied Math, U Texas (San Antonio)
Title: Modeling the LH surge in the human menstrual cycle
Abstract: In vertebrates, ovulation is triggered by a surge of luteinizing hormone (LH) from the pituitary. The precise mechanism for initiating the surge in the human menstrual cycle remains a fundamental open question of physiology. Sampling of serum LH on a time scale of minutes reveals pulsatile release from the pituitary in response to pulses of gonadotropin releasing hormone (GnRH) from the hypothalamus. The LH pulse frequency and amplitude vary considerably over the cycle, with the highest frequency and amplitude at the midcycle surge. In this talk we discuss the physiological background, and we present a mathematical model of the human pituitary as a damped oscillator driven by the hypothalamic oscillator. The numerically simulated LH surge is consistent with existing data on the time scales of both minutes and days. We use the model to explain the surprising GnRH pulse frequency characteristics required to successfully treat human infertility disorders such as Kallmann's syndrome, and to make new experimental predictions.
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MATHEMATICS COLLOQUIUM:
Time: Friday, Oct 11, 2002, 3:00 pm
Location: Math Annex 1100
Speaker: Yue Xian Li
Title: A Minimal Network Model for Quadrapedal Locomotion Based on Symmetry and Stability
Abstract:
Four-legged animals move with several distinct patterns of rhythmic leg movements, called gaits. Standard quadrapedal gaits include walk, pace, trot, bound, and gallop. Networks of coupled oscillators have been used to model the central pattern generators (CPGs) that produce these patterns. In these models, symmetric gaits are related to phase-locked states of the network possessing the same symmetries. Pioneer works by Golubitsky et al were based on symmetry analysis that gave conditions for the existence of these states. We show that models based on symmetry alone cannot generate a model circuit of practical use, i.e., a circuit people can actually install in a four-legged robot capable of moving with different gaits. A functioning network should possess not only enough symmetry to guarantee the existence of these solutions but a mechanism to segregate each one of them dynamically. Our new theory, based on the analysis of both the existence and stability of these phase-locked states, allows us to achieve both goals. We show that a minimal network of four identical neurons is capable of generating dynamically independent patterns for all standard quadrapedal gaits. A circuit is designed based on this theory using a realistic neuronal model and synaptic currents. Numerical simulations of this model circuit confirmed the analytical results. (Others involved in part of this work: Drs. Yuqing Wang and Robert Miura)

Time: Thursday, October 3, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Eirikur Palsson Dept of Biology, SFU
Title: The interplay of chemotaxis and cell adhesion on cell sorting in multicellular systems
Abstract: A biologically realistic three dimensional mathematical model that facilitates the simulation and visualization of cell movement in multicellular systems, has been developed. In this talk I will introduce the model, show examples of its applications, compare the results with experimental data and present results that highlight the interplay of chemotaxis and adhesion in cell sorting and movements. The building blocks of the model are individual deformable ellipsoidal cells; each cell having certain given properties, not neccesarily the same for all cells. The basic properties of a cell are: it conserves volume under deformation, it adheres to other cells, and it can generate an active motive force. The response of a cell depends on its internal parameter state, and on the information it recieves from the external environment. Since the model is based on known processes, the parameters can be estimated or measured exprimentally. The organism that I focus on here is the cellular slime mold Dictyostelium discoideum; A videly used model system for studying a variety of basic processes in development, including cell-cell signaling, signal transduction, pattern formation and cell motility. Here I will show that this model can reproduce the observations of the chemotactic behavior of single cells, streaming during aggregation, and the collective motion of an aggregate of cells driven by a small group of pacemakers. The model predicts that the motion of two-dimensional slugs results from the same behavior that are exhibited by individual cells; it is not necessary to invoke different mechanisms or behaviors. I will also demonstrate how differences in adhesion between pre-stalk and pre-spore cells, affect the sorting and separation of those cell types, that occurs during the slug stage, and I will suggest and explain why chemotaxis alone might not be sufficient to achieve complete sorting.
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October 3, 2002, 12 - 1 pm, IRC 6 Dr. Tim Galitski Institute for Systems Biology, Seattle UBC Systems Biology Lecture Series

Sept 30, 2002, 3-4 pm, IAM/Stats seminar Room (301 Leonard Klink bldg) Carl Bergstrom (Zoology, UW): Fighting the antibiotic resestant bacteria in hospitals.

Time: Thursday Sept 26, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof Nima Geffen School of Mathematical Sciences, Tel Aviv University, Israel
Title: The structure and Shape of a helical micro organism as a stable solution to a variational problem.
Abstract: The basic mathematics and physics underlying a phenomenological geometric model of the uniquely simple prokaryotic Spiroplasma are postulated. The geometrical implications of the model are discussed in the context of newly reported biological data.
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Time: Thursday, September 19, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. José-Leonel Torres (Institute of Physics and Mathematics, Universidad Michoacana de San Nicolás de Hidalgo, Mexico)
Title: Biological power laws and Darwin's principle
Abstract: It will be argued that ecological allometries (power laws) are the mathematical expression of a darwinian condition of 'good design': maximum adaptabilidy in a rapidly fluctuating environment. The argument leads in each case to a canonical function (one of R. Thom's 'catastrophes'), constructed from the available empirical allometries. This function allows identification of regions where the system shows enhanced susceptibility, related to phase transitions, hysteresis, etc. The method will be illustrated by applying it to systems that satisfy the 'self-thinning rule' from ecology.
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September 19, 2002, 1-2 pm, Wesbrook Building 100, 6174 University Boulevard Dr. Andrew Link Vanderbilt University, Tennessee UBC Systems Biology Lecture Series

September 16, 2002, 3.30-4.30 pm, Instructional Resources Centre 6, 2194 Health Sciences Mall (IRC 6) Dr. John Yates Scripps Institute, La Jolla UBC Systems Biology Lecture Series

Thursday, Sept 12, 2002, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Amy Norris, (IAM, UBC)
Title: Investigating signal transduction pathways
Abstract: I will review the biology of signal transduction pathways and several approaches to studying these pathways that are derived from previous studies of gene networks. These approaches include multivariate analysis and reverse engineering using genetic algorithms. New formulations of and approaches to the problem of reverse engineering pathways will be introduced.
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September 11, 2-3 pm, Forest Science Centre 1005, 2424 Main Mall Dr. Lee Hood Institute for Systems Biology, Seattle UBC Systems Biology Lecture Series

September 6, 2002, 3-4 p.m., MATH ANNEX 1100, Michael Ward (UBC Math), Beyond Turing: The Stability and Dynamics of Localized Patterns in Reaction-Diffusion Systems (Dept of Mathematics Colloquium).

Year 2001-2002:

July & August
No Math Biology seminars. Seminars will resume in September.
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Wednesday, June 5, 11:00 am
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Michael Mackey (Director, Centre for Nonlinear Dynamics, Department of Physiology, McGill University)
Title: Dynamics of Gene Control Networks: The Lactose and Tryptophan Operons
Abstract: This talk will introduce people to some of the problems inherent in the modeling of gene regulatory networks including model formulation, analysis, parameter estimation and simulation. Informal and presented mainly using a piece of chalk on a blackboard.
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Tuesday, June 4, 11:00 am
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Andrew Edwards (Research Associate, Bedford Institute of Oceanography and Dalhousie University)
Title: Biologically Induced Circulation - Can Phytoplankton Influence Ocean Physics?
Abstract: An intriguing question in oceanography concerns the extent to which the biological component of the ocean can influence the physical component. The presence of phytoplankton in a body of water affects the penetration of irradiance through the water column. This influences the temperature and hence the density distribution of the water. If the phytoplankton concentration varies horizontally, then the consequent density distribution will result in a horizontal pressure gradient.
I will consider two such horizontal gradients of phytoplankton. By means of a simple model, I will present analytical calculations of the induced velocities to ascertain whether the differential heating effects are significant. Finally, I will discuss the potential for the induced velocities to act as a mechanism for enhancing the supply of nutrients into the near-surface waters, such that the phytoplankton may (speculatively) modify the physical environment to 'feed themselves'.
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Friday, May 31, 11:00 am
Location: Rm 100 Mathematics Annex, UBC
Speaker: Dr. Réka Albert (School of Mathematics, University of Minnesota)
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Title:The Architecture of Complex Networks
Abstract: Many complex systems in nature and society have an underlying network topology. For example, metabolism can be thought of as a network of substances (metabolites and enzymes) connected by chemical reactions. The World Wide Web is a network of web pages and documents connected by hyperlinks, and groups of people form social networks in which the nodes are individuals and the edges are social relations. While traditionally large-scale networks were modeled by random graphs, it is increasingly recognized that their topology is much richer, and displays universal properties that suggest robust organizing principles. In this talk I will present the main advances in the theory of complex networks, focusing on evolving network models that concentrate on the principles governing the assembly and time-evolution of real networks
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Wednesday, May 29, 1:00 pm
Location: Rm 318 Hennings Bldg. (Physics & Astronomy), 6224 Agricultural Road, UBC
Speaker: Dr. Réka Albert (School of Mathematics, University of Minnesota)
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Title: Connections Matter: Boolean Modeling of Gene Regulatory Networks
Abstract: Biological systems often form complex networks of interaction. For example, external signals are detected and internalized by a signal transduction network. Or, the expression of genes is regulated by interactions with other genes and gene products. Recent experimental advances uncovered the qualitative structure of many gene control networks, creating a surge of interest in the quantitative description of gene regulation. In this talk I will focus on the segment polarity genes of the fruit fly Drosophila melanogaster, and the network of interactions determining the stability of their expression. I will present a Boolean representation of this network that assumes that genes and proteins are either ON or OFF, and their interactions can be formulated as logical functions. This simple model is able to reproduce the observed spatial patterns of the segment polarity genes, as well as the patterns obtained in gene mutation experiments. In addition, the Boolean representation allows us to determine the possible steady state patterns, and to identify the initial conditions that lead to certain steady states. I propose this type of modeling as a first, qualitative step in understanding complex networks. The success of a Boolean representation strongly suggests that the topology of the network is correctly taken into account, and a more quantitative approach can be used.
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Week of May 21-25: NO MATHEMATICAL BIOLOGY SEMINAR
Location: Woodward IRC, UBC Campus
Tuesday-Wednesday, May 21-22: MITACS Biomedical Theme Meeting

Of particular interest is the Session for Junior Investigators (May 21), organized by Stan Marée and Marek Łabęcki.
Thursday-Saturday, May 23-25: MITACS Annual General Meeting
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Thursday, May 16, 2:00 pm
NOTE Location: Rm 1102 Mathematics Annex, UBC
Speaker: Nathaniel Newlands (Fisheries Centre and Department of Mathematics, UBC)
Title: Spatially-Explicit Individual-Based Modeling of Bluefin Tuna, Integrating New Data from Acoustic Tracking, Satellite Tagging and Aerial Survey Experiments
Abstract: Biological interactions occur at specific locations involving the spatial redistribution of organisms. From initially homogeneous states, striking heterogeneous spatial patterns can emerge. Recognizing the importance of space, biologists have struggled with the difficulties of collecting data across spatial scales. Recent advances in ocean monitoring technology are generating new insights on how fish move and interact. Mathematical modeling facilitates the exploration of the complexities in observed dynamics and aid in addressing hypotheses difficult to test in laboratory studies or open-ocean experiments.
A spatially-explicit, individual-based model of bluefin tuna whereby interacting individuals coexist on a spatially heterogeneous ocean landscape will be presented. The model represents the population dynamics of schooling bluefin tuna seasonally resident in an important Northwestern Atlantic commercial fishing area. The model is structured based on new results obtained from the analysis of acoustic tracking, satellite tagging and survey data. Individual tuna move by adjusting their orientation and speed, responding to oceanographic gradients and the prey concentration. Foraging (intensive search) and travel (extensive search), two separable behavioural modes of movement are distinguished by different turning rates and cross-correlation strength between movement parameters. The movement dynamics of schools is considered to be a stochastic process whereby individual fish perceive and continually adjust their modes based upon an incomplete identification of the modes of their nth-order nearest-neighbours. These alterations are super-imposed on scheduled diurnal switching between behaviours and random fluctuations. Attractive and repulsive harmonic forces are considered to act only between first-order nearest-neighbours. The process describing how individuals collectively alter their movement behaviour while schooling is self-organizing and can lead to highly polarized and less organized groups, depending upon the fraction of tuna moving in each mode. The exchange of individuals between schools by fast behaviour alterations is considered to also be regulated by a longer-term, evolutionary fitness goal to maximize reproductive output. This goal is dependent on perceived feeding rate and predation risk which scale with such factors as age, weight, visual range, and metabolic rate. Individual fish continually make trade-offs between feeding rate and predation risk. Over time, specific rates of fusion and fission between interacting schools in the model may distinguish optimal trade-offs between feeding rate and predation risk as a function of school size. As leading changes in the size of schools occurs primarily when schools are in relative proximity to each other, the model may delineate separate foraging and travel zones predicted on the basis of the degree of behaviour mode adjustments of schooling individuals. With continued refinement and improvement, the model may lead to predictions of emergent patterns of bluefin spatial distribution, whereby spatial patterns are characterized on the basis of individual decision-making in schools, seeking to maintain survival and improve evolutionary fitness.
Selected results from analyses of new experimental data and model simulations will be presented. The talk will end by outlining several improvements required and two aspects of the model where further collaborative research will be focused.
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Thursday, May 9, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Clive Glover (Institute of Applied Mathematics and Biotechnology Laboratory, UBC)
Title: Optimization of Cell Culture Media through Gene Expression Profiling
Abstract: Mammalian cells have complex growth requirements and their culture media include over 50 components at concentrations from 0.4 mg/L to 4.5 g/L. Conventionally, media are developed empirically, by analyzing for depletion and adding components individually or in groups to determine if culture productivity can be increased. This optimization process consumes valuable time and labor. In the emerging field of cellular therapy, there is an increasing need to develop diverse new media and accelerating this process would provide patients with earlier access to cellular treatments.
We are investigating novel approaches to media optimization through monitoring the gene expression profile of cells in culture. It is hypothesized that cells experiencing a particular limitation will exhibit a characteristic gene expression profile corresponding to that limitation. We have analyzed human TF-1 cells under glucose limitation and also literature data on yeast cells under amino acid limitations. The expression level of genes in the pathways relevant to these two nutrients were analyzed at several times following exposure to the particular limitation. Ultimately, the knowledge developed here should lead to the development of a diagnostic tool for monitoring and optimizing cell culture.
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Thursday, April 25, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Marian Groenenboom (Department of Zoology, UBC)
Title: Local Interactions and the Coexistence of Multiple Male-Killers
Abstract: Male-killing bacteria are cytoplasmic sex-ratio distorters that are transmitted vertically through females of their insect hosts. In nature often perfectly transmitted male-killers are observed, as well as multiple male-killing bacteria infecting one single population. We use different model formalisms to explain these observations. In meanfield models a perfectly transmitted male-killer cannot be maintained, and coexistence between multiple male-killers within one population is impossible. In a spatially explicit model, however, it is possible to maintain a perfectly transmitted male-killer in the population, without driving the population to extinction. This is even the case without assuming any positive fitness effects for females that carry the male-killer. We show how the spatial pattern formation underlies these results: the bacteria are favoured in areas where infected hosts occur at low densities, but selected against when infected individuals occur at high densities. The spatial model also creates the opportunity for two male-killers to coexist within one population. This is caused by the creation of qualitatively different areas by different strains, which serve as different niches in the competition for hosts.
This work was carried out in collaboration with Prof. Paulien Hogeweg at the Department of Theoretical Biology/Bioinformatics, Utrecht University, the Netherlands.
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Thursday, April 18, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Danika Goosney (Finlay Lab, Biotechnology Laboratory, UBC)
Title: Exploitation of the Actin Cytoskeleton by Bacterial Pathogens
Abstract: Bacterial pathogens have evolved numerous strategies to exploit their host's cellular processes in order to survive and persist. Often, the bacterium must adhere very tightly to the cells and mediate its effects extracellularly or it must find a way to invade the host's cells and survive intracellularly. In either scenario, the pathogen subverts the host's cytoskeleton. The cytoskeleton provides a flexible framework for the cell and is involved in numerous cellular functions, ranging from cell shape and structure to programmed cell death. Altering the host cytoskeleton is crucial for mediating pathogen adherence, invasion, and intracellular locomotion. Data presented will focus on recent advances in the extracellular attachment and movement of enteropathogenic Escherichia coli on the host cell surface. Comparisons will be made to Salmonella typhimurium and Listeria monocytogenes, two intracellular pathogens. Each bacterium represents a novel way that pathogens can exert dramatic effects on the host cytoskeleton.
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Thursday, April 11, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Eric Cytrynbaum (PMMB Postdoctoral Fellow, Institute of Theoretical Dynamics, University of California at Davis)
Title: Centering Behaviour in Fish Melanophore Cells: A Quantitative Exploration of Cytoskeletal Dynamics
Abstract: Fish melanophore cells demonstrate a self-organizing behaviour that depends on the same cytoskeletal components that are at work in the centering of chromosomes during mitosis and therefore provide a good "warmup" problem for that more complicated and vital process. When a fragment of the melanophore cell is excised, eliminating the centrosome (the regular cytoskeletal organizer) and therefore the cytoskeletal structure, stimulating the cell with adrenaline somehow reintroduces cytoskeletal organization, leading to the formation of a microtubule aster and the aggregation of the cell's pigment particles at the center of the fragment. It is this centering behaviour that is analogous to the mitotic process of chromosome alignment and separation.
We use three different approaches to understand the problem of cytoskeleton reorganization and pigment aggregation. First, a 2D Monte Carlo simulation of microtubule and pigment dynamics provides evidence for the mechanism we propose. Next, we derive a system of non-linear diffusion-advection equations (1D) that describes the system under a particular parameter regime. The steady state solution to this system, which can be calculated analytically, has the desired "centered" structure. Finally, numerical simulation of an intergo-differential equation that describes a second parameter regime also demonstrates the centering behaviour we seek to explain.
This work was carried out in collaboration with Alex Mogilner (University of California at Davis, Mathematics) and Vladimir Rodionov (University of Connecticut, Physiology).
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Thursday, April 4, 2:00 pm
Location: Rm1102, Mathematics Annex, 1986 Mathematics Road, UBC
Speaker: Dr. Peter Lansdorp (Terry Fox Laboratory, BC Cancer Research Centre)
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Title: Molecular Markers of Aging: Loss of Telomeric DNA
Abstract: The DNA ends of chromosomes in mammalian cells are characterized by G-rich repeats synthesized by the reverse transcriptase enzyme telomerase. Most human cells express insufficient telomerase enzyme to compensate for the loss of telomere repeats that invariably follows DNA replication. As a result telomeres shorten in most cells with accumulated cell divisions and with age. We have developed novel methods to measure the telomere length in different blood cells and have shown that most human and baboon blood cells show a non-linear decline in telomere length with age that fits a polynomial curve. We are looking to expand our earlier work on mathematical models that may help explain telomere decline with age in relation to cell turnover with the long term goal to develop a better understanding of the biological and genetic variables that underpin aging.
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Thursday, March 21, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Sima Setayeshgar (Science and Technology Council Postdoctoral Fellow, Applied and Computational Mathematics, Princeton University)
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Title: Monte Carlo Evolution of Bacterial Chemotaxis
Abstract: We present a new, efficient numerical evolution scheme for a class of stochastic problems where the dynamics can be expressed in terms of a finite number of moments of the full distribution. Although such a low-dimensional description may not be a priori known, we show how coarse integration on time scales long compared to that of the microscopic dynamics can be applied to an appropriate low-dimensional projection of the full distribution, leading to fast approach to steady state. We apply this numerical scheme to Monte Carlo evolution of bacterial chemotaxis.
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Thursday, March 14, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Stan Marée (IAM Postdoc, UBC)
Title: Type I Diabetes: Avidity Maturation of the Immune System and Treatment with Altered Peptide Ligands
Abstract: Autoimmune diseases such as type 1 diabetes develop after prolonged periods of inflammation of target tissues. Santamaria and others have shown that the progression of pancreatic islet inflammation to overt diabetes in non-obese diabetic (NOD) mice is driven by the avidity maturation of a prevailing, pancreatic beta-cell-specific, CD8+ T-lymphocyte population. The same group has treated pre-diabetic NOD mice with peptides which to a certain extent resemble the ones that are recognized by these CD8+ T cells - so called altered peptide ligands (APLs). Such a treatment either accelerates or blunts the avidity maturation, and therewith the development of diabetes. The outcome depends in a highly non-linear way on both the dose and the affinity of the APL.
Using their data, we here develop a number of ordinary differential equation models, to explore the possible underlying mechanisms of the affinity maturation, as well as the modulation of the progression by APLs. We show that a rich set of known immunological interactions could explain the observed data, as long as they fulfill certain essential characteristics, either directly or indirectly. Such a model study forces to make implicit assumptions explicit, which allows us to test the feasibility of competing explanations, and leads to suggestions for experiments to discriminate between them.
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Monday, February 18, 3:00 pm
IAM-PIMS Distinguished Colloquium Speaker
Location: Rm301, Klinck Bldg, 6356 Agricultural Road, UBC
Speaker: Dr. Adam Arkin (Assist. Prof., Department of Bioengineering and Chemistry, University of California at Berkeley and Lawrence Berkeley National Laboratory)
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Title: Signal Processing in Cellular Regulatory Networks: Physical Models, Formal Abstractions and Applications
Abstract: Cellular behavior is controlled by highly interconnected networks of chemical and physical interactions. The networks process signals from the environments and from internal subsystems in order to perform complex tasks such as when an immune cell locates a bacterium in complex tissue, or chooses to follow one path of development or another. The physical mechanisms underlying these decisions range in time from milliseconds to hours and include mechanical, chemical, and transport processes. They are highly nonlinear and often stochastic. Molecular biology has progressed to the point wherein the questions being addressed seem to require that the detailed functioning of these networks be understood in great detail. However, building models of these processes is extremely difficult: both physical theory and the ability to observe all the parameters and interactions is lacking. Thus, there is need to develop more abstract models of these networks that are nonetheless able to aid in prediction, control and design of cellular systems. In support of this, theories of biological network decomposition and regulatory motif detection need to be developed so that analysis of pieces of the system can proceed without explicitly including every interaction in the cell. All the while, these analyses must drive experiment and be validated in detail by the experimental data. Here we describe some of our approaches to all these different problems and demonstrate them on particular bacterial and eukaryotic systems. The suite of tools we are developing are designed to fit into an integrated framework for biological systems analysis called Bio/Space. Progress on this tool and its theory will also be discussed.
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Friday, February 15, 3:00 pm
Department of Mathematics Colloquium
Location: Rm1100, Mathematics Annex, 1986 Mathematics Road, UBC
Speaker: Dr. Alex Mogilner (Assoc. Prof., Department of Mathematics, University of California at Davis)
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Title: How Mathematics Help Us Understand Cell Motion
Abstract: The motion of animal cells is a complex and important process that affects growth, development, wound healing, as well as disease processes (such as cancer). Cell motility is known to depend on protrusion, adhesion, and retraction of parts of the cell, which, in turn, stem from both chemical and mechanical changes in a structure called the cytoskeleton. Polymerization of components of this structure (usually actin) is one of the important processes underlying motility. Generation of force by "molecular motors" such as myosin is also important. Mathematical models (ordinary and partial differential equations) and simulations (in 2D and 3D) can help to understand the roles of the components, their interactions, and how they are controlled to produce motion in the cell.
I will present a mechanochemical analysis of a crawling cell and describe a finite element model wherein (a) localized protein polymerization and bundling generate the force for extension, and (b) energy stored in the gel formed from the polymers at the leading edge is subsequently used to produce the contraction that pulls the rear of the cell forward. While this model has features of general interest, I apply it to a specific example, the crawling of the nematode sperm cell. These cells crawl using a specialized "major sperm protein", rather than actin, in their cytoskeleton. Their simplicity provides a 'stripped down' version of a crawling cell in which to examine the basic mechanism of cell locomotion, independent of other cellular functions. I show how results of the models and simulations, based on realistic values of known biological parameters agree with the experimental observations.
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Thursday, February 14, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Alex Mogilner (Assoc. Prof., Department of Mathematics, University of California at Davis)
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Title: The Rippling of Myxobacteria: Mathematical Model
Abstract: In the first few hours of starvation, myxobacterial swarms develop a phenomenon called 'rippling'. Ripples appear as a pattern of waves on the surface of the colony that propagate continuously for long periods. The wave crests appear to pass through one another with no interference. In certain circumstances the waves can persist with no net mass transport, analogous to water waves. Development of the ripple phase requires both the social (S) and adventurous (A) motility systems, as well as intercellular communication by way of cell contact. I will present a model for the rippling phenomenon based on the observation that individual cells posses an internal cycle that manifests itself in individuals as periodic reversals in direction with no net progress in either direction. Understanding the mechanism of ripple formation reveals how intracellular dynamics, intercellular communication, and cell motility can coordinate to produce collective behavior. This pattern of waves is quite different from that observed in other social organisms, especially Dictyostelium discoideum, that depend on diffusible morphogens.
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Thursday, February 7, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Fred Brauer (Department of Mathematics, UBC)
Title: Qualitative Analysis of Dynamical Systems with Two Time Scales
Abstract: Many biological systems may be separated into components which act on very different time scales. For example, when the HIV virus attacks the immune system there are radical changes in viral load and number of infected T cells in a few weeks but the decline in the T cell population takes place over several years. The analysis of such systems is often simplified greatly by viewing them as singular perturbation problems and essentially decomposing them into fast and slow time systems. We will give an elementary exposition of some of the relevant facts about singular perturbations, avoiding such gory details as asymptotic expansions, and show how to apply them to some simple models of HIV dynamics to obtain qualitative information which would be much more difficult or impossible to obtain from analysis of the full system. The presentation will be on an expository level and will not be intended as a research progress report.
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Thursday, January 10, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Tim Lewis (Courant Institute and the Center for Neural Science, New York University)
Title: The Effects of Nonexcitable Regions on Signal Propagation in Excitable Media: Propagation Failure and Reflection
Abstract: Many physical excitable media contain regions of substantially decreased excitability. For instance, regions of this nature can arise in neural and cardiac tissue due to ischemia. The presence of these regions can lead to pathological activity such as propagation failure and reflection. I present a model in which regions of reduced excitability are idealized as nonexcitable (i.e. strictly diffusive). I show that the phenomena of propagation failure and reflection can occur in the model and I attempt to elucidate the dynamical mechanisms underlying these behaviors.
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Year 2001:

Thursday, November 29, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Gerald Lim (Bio-Physics Group, Department of Physics, SFU)
Title: Three-Dimensional Simulation of the Shapes and Shape Transformations of the Human Red Blood Cell (the Stomatocyte-Discocyte-Echinocyte Cycle and More)
Abstract: A mature human red blood cell (RBC) normally assumes the shape of a doubly dimpled disc. However, it has been known for more than 50 years that, under a variety of chemical or physical treatments in vitro, the cell undergoes a quasiuniversal sequence of transformations which preserve its volume and surface area but result in quite different overall shapes. The new shapes belong predominantly to one of two classes: Stomatocyte and Echinocyte. The former refers to an RBC with a single invagination, whereas the latter refers to an RBC studded with multiple protrusions. We describe these so-called Stomatocyte-Discocyte-Echinocyte Transformations using a simple nonlinear mechanical model, based on the bending elasticity of the plasma membrane and the dilational and shear elasticities of the membrane-bound cytoskeleton. This model is capable for the first time of describing all the different shapes and of giving a good account of the sequence of transitions between them. The central control parameter is the area difference between the two leaflets of the bilayer (plasma) membrane. However, the cytoskeletal elasticity and the undeformed shape of the cytoskeleton both play crucial roles in selecting finer details of the cell's ultrastructural features and shape sequence. A rather surprising and notable aside is the presence of other stable shapes, such as the triconcave Knizocytes, in the model's prediction.
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Thursday, November 22, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Colin Clark (Department of Mathematics, UBC)
Title: The Logic of Fisheries Management Failures
Abstract: It is now widely recognized that the majority of attempts to manage marine fisheries in Canada and elsewhere have been far less successful than was hoped. Various reasons for this have been proposed, including failure to consider the whole marine ecosystem, lack of understanding and consideration of oceanography, inadequate "Science" of some sort, etc. I will argue that the main cause of minimal success may have been a kind of "leakage," and that most systems of regulation contain the seeds of their own demise. Simple models will be used to illustrate the argument, and a case study will be discussed. The level of mathematics will be close to trivial, but this need not imply that the subject matter is so.
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Thursday, November 15, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Donald Ludwig (Departments of Mathematics and Zoology, UBC)
Title: Ecology, Conservation, and Public Policy
Abstract: A new sense of urgency about environmental problems has changed the relations between ecology, other disciplines, and public policy. Issues of uncertainty and scientific inference now influence public debate and public policy. Considerations that formerly may have appeared to be mere technicalities now may have decisive influence. When science is used in support of policy-making, it cannot be separated from issues of values and equity. In such a context the role of specialists diminishes, since nobody can be expert in all the aspects of complicated environmental, social, ethical, and economic issues. The disciplinary boundaries that have served science so well in the past are not very helpful in coping with the complex problems that face us today, and ecology now finds itself in intense interaction with a host of other disciplines. A sense of urgency has affected not only ecology, but other disciplines that influence environmental problems: they are undergoing a similar transformation of their outlook and objectives. The next generation of environmentalists must be prepared to interact with such disciplines as history, religion, philosophy, geography, economics, and political science.
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Thursday, November 8, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Muhammad A. S. Chaudry (Ph.D. Student, Biotechnology Laboratory, UBC)
Title: Mathematical Modeling of Epidermal Growth Factor Signal Transduction Pathway
Abstract: Cells receive information from their environment affecting their growth motility, differentiation and apoptosis. Signal transduction is the study of the mechanism by which an extra-cellular signal is transmitted to the nucleus to elicit a biological response. As our comprehension of cellular function has grown, it has become clear that understanding signal transduction events is crucial to developing cures for various human diseases. Numerical simulations of signaling pathways will be useful to develop a mechanistic understanding of how cells respond to various stimuli. In this talk, a brief overview of various aspects of signal transduction pathways will be provided. Results of numerical simulations of the early events in epidermal growth factor receptor signal transduction pathway will be presented.Various biological questions important in the signaling events that are difficult to answer experimentally will be addressed via simulations.
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Thursday, October 25, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Stan Marée (IAM Postdoc, UBC)
Title: Small Variations in Multiple Parameters Account for Wide Variations in HIV-1 Set Points: A Novel Modelling Approach
Abstract: Steady-state levels of HIV-1 viraemia in the plasma vary more than a 1000-fold between HIV-positive patients and are thought to be influenced by several different host and viral factors such as host target cell availability, host anti-HIV immune response and the virulence of the virus. Previous mathematical models have taken the form of classical ecological food-chain models and are unable to account for this multifactorial nature of the disease. These models suggest that the steady-state viral load (i.e. the set-point) is determined by immune response parameters only. We have devised a generalised consensus model in which the conventional parameters are replaced by so-called 'process functions'. This very general approach yields results that are insensitive to the precise form of the mathematical model. Here we applied the approach to HIV-1 infections by estimating the steady-state values of several process functions from published patient data. Importantly, these estimates are generic because they are independent of the precise form of the underlying processes. We recorded the variation in the estimated steady-state values of the process functions in a group of HIV-1 patients. We developed a novel model by providing explicit expressions for the process functions having the highest patient-to-patient variation in their estimated values. Small variations from patient to patient for several parameters of the new model collectively accounted for the large variations observed in the steady-state viral burden. The novel model remains in full agreement with previous models and data.
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Thursday, October 18, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dan Reinders (Grad. Student, Department of Chemical and Biological Engineering, UBC)
Title: Computer Modelling of Endometrial Thermal Ablation for Menorrhagia
Abstract: Menorrhagia, excessive menstrual bleeding, is a common disorder for peri-menopausal women. A relatively new treatment cauterises the inner lining of the endometrium using heated fluid in a silicone balloon. A computer model of the heat transfer and tissue burning processes has been developed to guide the optimisation of the treatment protocol and to investigate safety issues. The implications of supra-boiling fluid temperatures on water vaporisation and the associated effect on treatment results are addressed. Two treatment approaches, constant temperature and constant initial heat, are investigated and their effectiveness and safety is compared.
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Thursday, October 11, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Leah Keshet (Department of Mathematics, UBC)
Title: Applications of Mathematical Modelling to Social Aggregation and Swarming Behaviour
Abstract: I will briefly survey a few results on the modelling of social aggregations. I will discuss both an Eulerian (pde) approach that focuses on the ability of a swarm to stay together despite random motion (or turbulence) in the flight of individual insects, and a Lagrangian (ode) model for spacing behaviour in a group. This represents work joint with James Watmough and Danny Grunbaum, as well as more recent ongoing work with Alex Mogilner (and simulations by Athan Spiros). This lecture is in preparation for a similar presentation at the 2001 International Symposium on Nonlinear Theory and its Applications (NOLTA 2001) to be held October 28 - November 1, 2001 in Miyagi, Japan. Comments and suggestions for improving the talk are requested.
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Thursday, October 4, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Kerry Landman (Department of Mathematics and Statistics, University of Melbourne)
Title: Part I. Can You Still Read the Fine Print?
Abstract: In spite of extensive research on changes in the human eye lens that occur with age, the causes of presbyopia and senile cataract remain unclear. The transport of water through the lens is believed to play an important role in the processes that give rise to these age-related disorders. Mathematical modelling of some NMR experiments indicate that the observed decrease in the lens water transport rate with age is due to two factors, namely the continuous increase in the lens size with age and a change in the lens physiology causing a decrease in apparent diffusivity of water within the lens nucleus.
Title: Part II. Development of the Nervous System of the Gut
Abstract: A complex nervous system extends the length of the gastro-intestinal tract. The precursor cells to these nerve cells migrate into the intestine from its oral end in an anal direction. Once in the intestine, the precursor cells differentiate and generate patterned networks. Failures in these developmental processes cause several common birth defects in humans, such as Hirschsprung's Disease. This new project will build a mathematical model to unravel the dynamics of the cell migration and differentiation, based on the results of existing experiments.
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Thursday, September 13, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall
Speaker: Prof. Nima Geffen (Tel-Aviv University)
Title: Line and Point Singularities for Sources in Two and Three Dimensions
Abstract: Decaying solutions are sought for the equation: Laplacian u = k² u, with a source at the origin. The boundary value problem for r in [0, infinity) is treated for the radially symmetric case. This leads to an ordinary differential equation in cylindrical and spherical coordinates that is compared with the one-dimensional case. Special attention is paid to the singularity at the origin and the decay at infinity. An overview of the problem is given in the general three-dimensional, coordinate-free formulation. This is a survey talk. It is related to modeling for the Alzheimer project of Dr. Leah Keshet and the summer-work of Taneia Wong.
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Thursday, September 6, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Marek Łabęcki (IAM Postdoc, UBC)
Title: Protein Transport in Hollow-Fibre Bioreactors for Mammalian Cell Culture
Abstract: Cultivation of mammalian cells in the extracapillary space (ECS) of ultrafiltration membrane hollow-fibre bioreactors (HFBRs) is increasingly used for the production of useful proteins such as monoclonal antibodies. One of the greatest challenges in the operation of HFBRs is the maintenance of a uniform cell growth environment. In particular, the distributions of growth-factor proteins can be highly heterogeneous, leading to poor performance or failure of the culture. Considering the high costs of the media as well as product proteins, there is a strong motivation for studies that will provide a better understanding of protein behaviour in HFBRs.
The main focus of this project was the development of mathematical models describing different aspects of protein transport in HFBRs. The models were validated using protein concentration data collected during cell-free HFBR experiments. A one-dimensional Krogh cylinder model was employed to analyse hindered transmembrane transport relevant to the leakage of smaller proteins from the ECS. A two-dimensional porous medium model (PMM) was used to simulate open-shell operations such as product harvesting from the ECS. An extended, three-dimensional PMM formulation permitted a more advanced analysis of gravity-influenced free-convective ECS protein transport at different HFBR orientations.
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Tuesday, August 28, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Taneia Wong (USRA Student with L. Keshet, UBC)
Title: Alzheimer's Disease in Silico
Abstract: Alzheimer's Disease (AD) is irreversible dementia characterized by intellectual deterioration, disorganization of the personality, and functional disabilities in carrying out the tasks of daily living. Dr. Leah Edelstein-Keshet and Dr. Athan Spiros of the Department of Mathematics at the University of British Columbia have developed a minimal model that accounts for the formation of senile plaques.To gain a deeper understanding of the model and hence AD, simplified versions of the original model were analyzed. This paper summarizes the five major aspects of the model that were explored: the one-dimensional phase portrait of the model was analyzed for four values of I, the injury: I = 0, 0 < I < r/4, I = r/4, and I > r/4; the phase-plane behaviour of the system for three functions of f(h), the rate of production of chemical by neurons at health h: linear, exponential, and exponential with an inflection point near the origin; the value of neuron health, h, at which neurons die or survive and the conditions for the steady state, (h,C), to exist for the system corresponding to linear functions for f(h); the stability properties of the steady states; and the size of the killing zone of neuronal tissues' distance from the source of toxic chemical.
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Tuesday, August 21, 2:00 pm
Location: Rm301, Klinck Bldg, 6356 Agricultural Road, UBC
Speaker: Magdalena Luca (MITACS Ph.D. Student, UBC)
Title: Application of Chemotaxis Models to Alzheimer's Disease
Abstract: In this talk, we present several chemotaxis models for biological systems. Our work was motivated by the complex interactions between glial cells, cytokines and proteins that cause neuronal death and eventual dementia in Alzheimer's disease (AD). We investigate conditions that lead to periodic patterns and aggregation of glial cells that are observed in senile plaques. We have examined a hierarchy of models, starting with models in which there is a single (attractant) inflammatory agent, and microglia, and then models in which multilple cell types and both chemoattractants and chemorepellents occur. We studied linear stability, dispersion equations, and numerical methods for the models. Using real biological parameters available in the literature, we discuss the applicability of the models to the pattern formation observed in AD.
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Tuesday, August 16, 2:00 pm
Location: Rm301, Klinck Bldg, 6356 Agricultural Road, UBC
Speaker: Dr. Yue-Xian Li (Department of Mathematics, UBC)
Title: Phase-Clustered States in Networks of Excitatory Neurons with Heterogeneous Coupling Strengths
Abstract: Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is generally unstable in networks of excitatory neurons. Furthermore, phase-clustered states in which neurons are divided into multiple synchronized clusters have also been found unstable in numerical studies of excitatory networks. To examine whether stable phase-clustered states can occur in excitatory networks, we derive analytically conditions for the existence and stability of such states in small networks of weakly-coupled neurons with heterogeneous distribution of coupling strength. Each neuron in a multi-cluster state receives "in-cluster" inputs from neurons within the same cluster and "out-cluster" inputs from neurons in other clusters. A multi-cluster state can be stable in excitatory networks if the overall out-cluster interactions are stabilizing and strong enough to counter-act the destabilizing in-cluster interactions. These conditions can be satisfied in excitatory networks with heterogeneous distribution of coupling strength but rarely satisfied when the coupling strength is homogeneous. The difference in coupling strengths is a determinant factor in these stability conditions. Numerical results on small networks of three types of model neurons are presented to support the analytical results.
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Tuesday, June 5, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. James Watmough (Department of Mathematics, University of New Brunswick)
Title: Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission
Abstract: Classical disease transmission models typically have only a single stable equilibrium. There is a threshold level of the reproduction number, R_o, such that if R_o< 1, then the disease dies out and if R_o> 1, then the disease approaches an endemic level. In this simple case, disease control is a 'simple' matter of reducing the reproduction number. Many recent models show bistability over a range of reproduction numbers, where both the disease free equilibrium and an endemic equilibrium are stable. These results have important consequences for disease control. We present a general compartmental disease transmission model based on a system of ordinary differential equations. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R_o near one. This criterion, together with the definition of R_o, is illustrated by several models, including multiple group, multiple strain, staged progression and vector-host models.
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Tuesday, May 29, 1:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Leah Keshet (Department of Mathematics, UBC)
Title: Alzheimer's in Silico
Abstract: In this talk, I will review work done jointly with Athan Spiros over the past year on modeling Alzheimer's Disease in Silico (www.math.ubc.ca/~ais). We have developed an interactive simulation environment that can be used to experiment with some of the biological parameters, assumptions, and hypotheses for causes and development of this disease. I will discuss what are the things we can learn from the simulation, what are its current problems and defects, and what this bodes for the idea of In Silico Biology in general. This talk will be a practice run for a presentation later this summer at the Beyond Genome Conference in San Francisco.
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Tuesday, May 1, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Stan Marée (Theoretical Biology and Bioinformatics, University of Utrecht)
Title: From Pattern Formation to Morphogenesis: Multicellular Coordination in the Cellular Slime Mould
Abstract: Upon starvation, solitary amoebae of the cellular slime mould Dictyostelium discoideum aggregate and form migrating multicellular slugs, which behave as a single organism. Slugs show a pronounced thermo- and phototaxis, which direct them towards the soil surface, where migration halts and the whole process culminates in the formation of a fruiting body consisting of a globule of spores on a slender stalk.
We have simulated the whole developmental process using a hybrid cellular automata/partial differential equation model. In the model, individual cells are represented as a group of connected automata, i.e. the basic scale of the model is subcellular. Therefore amoebae can slide past one another, and deform themselves and adjoining amoebae by means of small changes in their boundaries.
With our model we have been able to reproduce and understand the dynamics that emerge during the morphogenesis. I will show that cyclic AMP signalling (which is a special kind of exitable medium) and differential adhesion are sufficient to produce many self-organizing and self-correcting properties, and how the entire development is enacted by means of the above mentioned building blocks.
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Tuesday, April 17, 1:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall
Speaker: Prof. Diane Finegood (Diabetes Research Lab and School of Kinesiology, SFU)
Title: The Initiation of Autoimmune Diabetes
Abstract: Diane Finegood will describe an ongoing experimental project which is ripe for modelling. The dynamics of beta cells and their interaction with the immune system (macrophages, T cells, cytokines) will be described, and potential modelling problems posed.
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Tuesday, April 10, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Adriana Dawes (Grad. Student, Department of Mathematics and IAM, UBC)
Title: Estrogen Biosynthesis: A Modelling Approach
Abstract: Estrogen biosynthesis occurs when androstenedione, a hormone secreted by the adrenal cortex, is converted to 17-beta estradiol, a very potent form of estrogen. This process occurs in healthy tissue and is essential for many physiological processes such as spermatogenesis and bone calcification. Unfortunately it can also occur in hormone-dependent disease such as breast cancer. This allows the diseased tissue to thrive and proliferate despite suppression of endogenous hormone production. In this talk I will give the background for the problem and discuss some possible directions for modelling it.
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Tuesday, March 27, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speakers: Magdalena Luca (MITACS Ph.D. Student, UBC) and Dr. Alexandra Chavez Ross (MITACS Postdoc, UBC)
Title: Application of Chemotaxis Models to Alzheimer's Disease
Abstract: In this talk, we present several chemotaxis models for biological systems. Our work was motivated by the complex interactions between glial cells, cytokines and proteins that cause neuronal death and eventual dementia in Alzheimer's disease (AD). We investigate conditions that lead to periodic patterns and aggregation of glial cells that are observed in senile plaques. We have examined a hierarchy of models, starting with models in which there is a single (attractant) inflammatory agent, and microglia, and then models in which multilple cell types and both chemoattractants and chemorepellents occur. We constructed a minimal PDE model similar to the Keller-Segel model for the chemotaxis of microglia and their involment in secretion and uptake of various inflammatory factors. Stationary solutions of the minimal system are investigated using a method developed by Schaaf. Models with a greater level of detail are reduced in dimensionality using quasi-steady state approximations and explicit solutions for chemical diffusion using the Green's function method. We studied linear stability, dispersion equations, and numerical methods for the models. Using real biological parameters available in the literature, we discuss the applicability of the models to the pattern formation observed in AD.
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Tuesday, March 20, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Leah Edelstein-Keshet (Department of Mathematics, UBC)
Title: Spatial Regulation of Actin Dynamics in Cell Motion
Abstract: This is joint work with Alex Mogilner (University of California at Davis). We have developed a mathematical model that describes key details of actin dynamics in the lamellipod that governs cell motility. We consider a set of partial differential equations for diffusion and reactions of actin monomers, nucleation, and growth by polymerization of actin filaments, as well as capping and depolymerization of the filaments. The mechanical aspect of protrusion is based on an elastic polymerization ratchet mechanism due to Mogilner and Oster. An output of the model is a relationship between the rate of motility ('protrusion velocity') and the number of filament ends pushing the membrane. Significantly, this relationship has a local maximum: too many ends deplete the available monomer pool, too few are insufficient to generate protrusive force, so that motility is stalled at either extreme. Our results suggest that to achieve rapid motility, some tuning of parameters affecting actin dynamics must be operating in the cell.
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Tuesday, March 13, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Yue-Xian Li (Assist. Prof., Department of Mathematics, UBC)
Title: Paradoxical Role of Ca²⁺-activated K⁺ (BK) Channels in Controlling the Firing Patterns of Anterior Pituitary Cells: A Modelling Study
Abstract: Activation of high conductance, Ca²⁺-activated K⁺ (BK) channels normally limits action potential (AP) duration and voltage-gated Ca²⁺ entry by facilitating membrane repolarization. Recent experiments in rat pituitary cells found exactly the opposite: the activation of BK prolongs membrane depolarization leading to the generation of plateau-bursting activity and facilitated Ca²⁺ entry. In order to provide an in depth understanding of this paradoxical role of BK channels, a mathematical model was developed based on the experimental finding that BK channels in these cells are activated by domain Ca²⁺ but not the bulk Ca²⁺. The analysis of the model shows that rapid activation of BK channels truncates the AP amplitude and thereby limits the participation of delayed rectifying K⁺ channels. When the reduction in the rectifying K⁺ current exceeds the added BK current at a depolarized membrane potential, plateau-spiking occurs. Increased Ca²⁺ entry during the plateau phase activates another K⁺ current that terminates the plateau phase resulting in the occurrence of burst oscillation patterns in these cells.
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Tuesday, February 27, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Amy Norris (Grad. Student, Department of Mathematics and IAM, UBC)
Title: Survey of Methods for Studying Large Scale Gene Expression Data
Abstract: The talk will be an introduction to and overview of several methods that are currently being applied to the study of large scale gene expression data (data obtained using microarrays). The methods discussed will include clustering, multivariate analysis, and the elucidation of gene networks.
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Tuesday, February 13, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Discussion organized by Dr. Yu-Qing Wang (PIMS Postdoc)
Title: Learning and Associative Memory of Neural Networks
Abstract: During this session, Dr. Yu-qing Wang, a PIMS postdoc with Miura and myself, will give us a demonstration of how a simple neural network can perform the task of recognizing a very noisy pattern after it has learned and remembered the pattern. After that, we will discuss the problem of whether is it possible to extend Hopfield's theory on binary neural nets to networks of neurons which are themselves a dynamical system capable of generating action potentials with Hodgkin-Huxley-like ionic currents.
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Tuesday, January 30, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Prof. Nima Geffen (Tel-Aviv University)
Title: A Simple Geometric Model for a Simple Unicellular Organism
Abstract: Under consideration is the shape and motion of Spiroplasma Melliferum BC3, a wall-less prokaryotic cell with a cholestrol membrane, the smallest, simplest, self-sustaining, self-replicating cell. Its free motion is controlled by a protein ribbon, attached to the membrane. Minimal information from optical-microscope films and biochemical analysis was use to describe the geometry of the moving cell. Basic geometric constraints were used for the general description and elementary differential geometry for getting the picture of the moving cell, which can be summarized in one equation, ready for graphical and numerical simulation. Results of this simple description are compared with the results of elaborate experiments and measurements (some suggested by the mathematical considerations), verifying the validity of the model. Remaining basic questions, one in particular, will be presented, more needed steps pointed out.
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Tuesday, January 23, 2:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Cheryl McDonald (M.Sc. Student, School of Engineering Science, SFU)
Title: A Model of Pulsatile Insulin Secretion with Novel Insights into Possible Beta Cell Function
Abstract: Endogenous insulin is secreted in 5-15 minute pulses. Loss of regular insulin pulses is associated with the pathogenesis of type 2 diabetes, but the mechanism underlying pulsatile insulin secretion is unknown. Insulin has been observed to inhibit insulin secretion, although recent data also suggest a paradoxical insulin induced stimulation of insulin secretion. The results lead us to reconsider the hypothesis that insulin is an important controller of insulin secretion, and to postulate that the insulin secretory oscillations are a consequence of conflicting stimulatory and inhibitory actions of insulin on its own secretion. To test this hypothesis we derived a mathematical model of insulin synthesis and secretion based on a two-pool structure widely accepted to describe the biphasic nature of insulin secretion. The model we derived has many important characteristics similar to endogenous insulin secretion: spontaneous oscillation, entrainment to an applied oscillatory glucose signal, and coordination of pulses from separate "beta cells".
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Monday, January 15, 3:30 pm
Location: Rm100, Math, UBC
Speaker: Dr. Sergey Gavrilets (Assoc. Prof., University of Tennessee)
Title: Evolutionary Dynamics on Holey Adaptive Landscapes
Abstract: The world as we perceive it is three dimensional. Physicists currently believe one needs on the order of a dozen dimensions to explain physical world. However, biological evolution occurs in a space with millions dimensions. Sewall Wright's powerful metaphor of rugged adaptive landscapes with its emphasis on adaptive peaks and valleys is based on analogies coming from our three-dimensional experience. Because the properties of multidimensional adaptive landscapes are very different from those of low dimension, for many biological questions Wright's metaphor is not useful or is even misleading. A new unifying framework that provides a plausible multidimensional alternative to the conventional view of rugged adaptive landscapes is emerging for deepening our understanding of evolution and speciation. The focus of this framework are percolating (nearly) neutral networks of well-fit genotypes which appear to be a common feature of genotype spaces of high dimensionality. A variety of important evolutionary questions have been approached using the new framework.
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