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.
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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)
Home Page
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)
Home Page
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)
Home page
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)
Home page
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)
Home page
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.
[Back To Top]
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)
Home Page
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.
[Back To Top]
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)
Home Page
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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, Ro,
such that if Ro< 1, then the disease dies out and if Ro> 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 Ro
near one. This criterion, together with the definition of Ro, is
illustrated by several models, including multiple group, multiple strain, staged
progression and vector-host models.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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.
[Back To Top]
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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