MITACS Mathematical Biology (and related) Seminars
Acknowledgements:
This seminar series is supported by the Mathematics for
Information Technology and Complex Systems (MITACS) NCE,
by PIMS, and by NSERC grants to UBC faculty.
We are very grateful to PIMS and to the PIMS staff for
(a) providing space and seminar facilities (b) organizing
and providing refreshments and (c) handling local arrangements
for visiting speakers.
Seminars held in Year 2003
Mathematical Biology Seminar
Time: Wedn Dec 3, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Peter Cripton, Mechanical Engineering, UBC
Title:Kinematics of the Human Spine
Abstract:
The human spine must allow significant motion during such everyday
activities as bending, lifting, looking overhead or emphatically shaking
one's head no. In addition to allowing this motion, the spine must withstand
significant mechanical loads, in its role as a component of the
musculoskeletal structure, and protect a major component of the central
nervous system, the spinal cord, from mechanical insult. The loads in the
lumbar spine (low back) can range up to five thousand Newtons in some people
for some activities. This approaches half the weight of some small cars!
The spine is anatomically complex and its size and structure changes from
one part of the body to the next. The corresponding kinematics (motion)
allowed by the spine varies greatly depending on the region of the body of
interest. Physicians, bioengineers and other basic scientists have long
studied the spine's kinematics for the investigation of natural
biomechanical processes, to characterize pathologic motion or instability
and to evaluate the efficacy of surgical devices and techniques. I will
present a review of the experimental techniques and underlying mathematical
principals that have been used to measure and communicate results regarding
human spine kinematics. One focus of the presentation will be to identify
and compare the fundamental differences between spine motion in the
cervical(neck), thoracic and lumbar regions of the spine. I will also review
the overall research questions and themes that have been addressed using
these techniques.
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Mathematical Biology Seminar
Time: Wedn Nov 19, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Viktoria Hsu Applied Mathematics, University of Washington
Title: Mechanistic Modeling of Cell Membrane Potentials via a Quasi Steady-State
Approximation
Abstract:
Most mathematical models for signal generation in single neurons,
such as the classic Hodgkin-Huxley model, assume that the single neuron
is bathed in an infinite buffer solution. Thus the composition of
the bath never changes. This assumption is appropriate for the comparison
of model results to in vitro studies because in these studies the
cell preparation is actually bathed in a relatively fixed environment.
In their current state, such models are not able to take into account
large changes in the external environment of a cell during ischemia.
It is my goal to improve current neuron models so that the changing
extracellular conditions can be taken into account in a single cell
micro environment. The main challenges in this endeavor are due to
the necessity of creating a finite extracellular compartment. This
requires considering mass conservation and electroneutrality.
In this talk, I lay the foundation for a physically consistent model
based on a quasi-steady-state approximation. In the first part of the
presentation, an efficient numerical method for the solution of 1D
Poisson-Nernst-Planck (PNP) systems is developed. In the second part
of the talk, this numerical method is applied to solving the consecutive
steady-state dynamics of a two compartment system of ions. The results
of my approach are compared to the full PDE in order to confirm the
sensibility of the steady-state assumption. Finally, the quasi steady-
state approach is compared to a Hodgkin-Huxley type model for a cell
with intact gated channels but no ion pumps to maintain homeostasis.
In the future, I would like to incorporate active ion transport, applied
currents, and cell volume dynamics into my model.
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Mathematical Biology Seminar
Time: Wedn Nov 12, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Fred Brauer
Dept of Mathematics, UBC
Title:
Some simple models for disease outbreaks
Abstract:
The recent SARS epidemic has drawn attention back to the
classical Kermack - McKendrick epidemic model of 1927 (more precisely, to
the very special case which is usually called the Kermack - McKendrick
model). We study some natural extensions to include such aspects as an
exposed period, quarantine, and the reduction of contacts by susceptibles
in response to an epidemic.
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Mathematical Biology Seminar
Time: Wedn Nov 5, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Elena Braverman U Calgary
Title:Logistic equations with harvesting
Abstract:
[joint work with L. Berezansky
and L. Idels]
Population models with harvesting of various types are considered. The
following question is in the centre of our discussion:
when does the harvesting lead to the extinction of the population? When
can we provide that there is a positive solution of the system? Two models
are studied in detail: a delay logistic equation with continuous
(proportional or nonlinear) harvesting which may also be delayed and a
logistic equation with impulsive harvesting. In addition to non-extinction
of the population, for the continuous model with linear harvesting the
oscillation about a new equilibrium is studied; for a logistic equation
without delay and with impulsive harvesting the asymptotics of solutions
is described. It is demonstrated that the latter model can be reduced to
some difference equation.
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Mathematical Biology Seminar
Time: Wedn Oct 29, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
David Brian Walton Applied Mathematics, U Washington
Title:Using Hidden Markov Models to Analyze Single-Molecule Motor
Protein Experiments
Abstract:
Kinesin is a motor protein that uses the energy of ATP
hydrolysis to transport vesicles and organelles along microtubule
tracks within cells. Biophysicists interested in understanding how such
proteins can convert chemical energy into mechanical energy have
studied kinesin and other motor proteins extensively. Recent
experiments study the behavior of single kinesin motors using optical
traps and tethered glass beads. Records of bead positions provide an
indirect, noisy record of the progress of the motor protein. Hidden
Markov models provide a tool to analyze these records statistically to
infer model parameters for the motor's stepping cycle.
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Note: There will be no Math Biology seminar on October 22, 2003
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Applied Mathematics Colloquium
Time: Monday, Oct 20, 2003, 3:00 pm
Location: Rm301, LS Klink, 6356 Agricultural Road, UBC
Speaker: Dan Coombs, Dept of Mathematics, UBC
Title:
Periodic chirality inversions propagating on bacterial flagella.
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Mathematical Biology Seminar
Time: Wedn Oct 15, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Roy Adler IBM Watson Research
Center, Yorktown Heights, NY
Title: Scoliosis and modelling the spine
Abstract:
Scoliosis is an enigmatical disease (not so uncommon) which results in a three dimensional deformation of the spine. At present the only treatment for severe cases is spinal fusion, not a particularly desirable solution. The purpose of this study is to develop new tools for understanding this mystery and improving surgical procedures. We present preliminary results concerning a certain hypothesis about the three dimensional spinal configuration: namely, the static erect spine assumes a shape, which minimizes a hypothetical energy function. Ordinarily this type of minimization would be handled by Lagrange's method of undetermined multipliers. However due to the nature of the constraints, we obtain this minimum by an application of Newton methods on manifolds, which uses the group operations of orthogonal matrices to advantage.
If time permits, we shall discuss a connection of the scolitic deformity with the geometry of space curves. On one hand, the erect scoliotic spine is usually non-planar and involves twisted vertebrae. On the other hand, the normal spine is planar with no vertebral rotations, but rotation occurs upon bending. The medical literature gives a physiological explanation of this phenomena. We shall present a purely geometrical one.
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Department of Mathematics Colloquium, UBC
Time: Friday Oct 10, 3-4 pm
Location: Math Annex room 1100, UBC
Speaker: Yue Xian Li, Dept of Mathematics, UBC
Title:A Model of Calcium Waves and a Theory of Waves in Inhomogeneous Media
Abstract:
Many living creatures, including humans start their life when an egg cell is
penetrated by a sperm. One of the events immediately following sperm entry
is the occurrence of one or more waves of elevated Ca2+ concentration that
travel from the site of sperm entry to the opposite end of the egg cell. These
waves, called fertilization Ca2+ waves, are vital for the subsequent
development of the fertilized egg. In egg cells of some species, the first
few waves propagate further and further into the cellular space but fail
to reach the opposite end. These waves are called ``incomplete'' waves. In
this talk, I present a bidomain model of reaction-diffusion type that
explains how such incomplete waves can occur. The model reveals that
traveling fronts that propagate in an oscillatory manner, called tango
waves, can occur in an excitable medium in the presence of spatial
inhomogeneity. A preliminary theory is developed for studying stationary
and traveling fronts and pulses in a more general model for excitable
media. This study predicts a variety of experimental conditions under
which tango waves can occur. Other areas of biology in which this theory
may also apply will be discussed.
(A more technical talk closely related to this one will be presented
at the Applied Math/Scientific Computing seminar on Oct 1.)
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Mathematical Biology Seminar
Time: Wedn Oct 8, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Thomas Hillen Dept of Mathematics, U Alberta
Title:L^2-moment closure of transport equations and applications
in biology
Abstract:
We consider the moment-closure approach to transport equations which arise
in mathematical biology.
We show that the negative L2-norm is an entropy in the sense of
thermodynamics, and it satisfies an H-theorem.
With an L2--norm minimization procedure we formally
close the moment hierarchy.
The 2-moment closure leads to semilinear Cattaneo systems, which are
closely related to damped wave equations. We derive estimates for the
accuracy of this moment approximation.
The method is used to study reaction-transport models and transport
models for chemosensitive movement.
In addition, the closure procedure allows us
to derive appropriate boundary conditions
for the Cattaneo approximation.
Finally, we discuss applications to pattern formation in
Dictyostelium discoideum and Salmonella typhimurium (joint
with Yasmin Dolak, Vienna).
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The applied math/scientific computing seminar
Time: Wedn Oct 1, 2003, 12-13 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:Yue Xian Li, Dept of Mathematics, UBC
Title:A Theory of Forced Pattern Formation in Excitable Media
Abstract:
An excitable medium generally refers to a medium that is capable
of generating traveling waves. It has been widely encountered
in biology, chemistry, and physics. Many excitable media have been modeled
by systems of PDEs of reaction-diffusion type. Excitable neural media are
often modeled by integro-differential equations (IDEs). In both PDE and
IDE models of excitable media, stationary spatial patterns of Turing's
type can occur under certain conditions. Such patterns have been used to
explain a variety of biological pattern formation processes including
morphogenesis and hallucination. In this talk, I'll discuss a pattern
formation mechanism that is different from Turing's, called
inhomogeneity-induced pattern formation. Such patterns occur in an
excitable medium due to the existence of an inhomogeneous but stationary
forcing. The interesting thing we found is: introducing a stationary
bump into such a medium does not always produce just a simple bump-shaped
output pattern. A complex bifurcation scenario can occur
giving rise to the co-existence of multiple patterns. Stability analysis
shows that instability of such patterns often occur through a Hopf
bifurcation giving rise to oscillatory pulse solutions. Such
oscillatory pulses can behave like a pulse-generator that emits
traveling pulses periodically into the medium. Possible areas in biology
where this theory can be applied will be discussed.
(This talk is closely related to my math colloquium talk on Oct 10.)
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Math-Biology workshop
Times: Tuesday Sep 30, 2003 11:00
Location: IAM lab, 306 Leonard Klinck building, UBC
Speaker: Stefan Reinker, Dept of Mathematics, UBC
Title: Software for ODE models
Abstract:
To complement Fred Brauer's workshop on qualitative analysis of
ODE models (see below), I will offer a workshop on software that is useful
for numerical, phase plane and bifurcation analysis of ODEs.
Just drop by if you are interested. I will first show some of
the standard software, including XPP and Matlab, and then we can address
specific questions. There is also a
website
with descriptions of the programs and some example files that
will be discussed.
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Math-Biology workshops
Times: Monday September 29, 11.00 AM - 12.00 noon, and
Wednesday October 1, 11.00 AM - 12.00 noon
Location: Monday at: Rm216, PIMS main facility, 1933 West Mall, UBC
NOTE CHANGE: Wedn at: 140 West Mall Annex
Speaker: Fred Brauer, Dept of Mathematics, UBC
Title: Review: Qualitative analysis of ODE models
Abstract:
There will be two lectures on qualitative properties of ordinary
differential equations to serve as review and background for dealing with
ODE models in mathematical biology. They will concentrate on two -
dimensional systems covering equilibrium analysis, local asymptotic
stability, and global properties. Everyone with possible interest is
invited to attend.
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MITACS/Mathematical Biology 1/2-day workshop
Time: Wedn Sept 24, 2003, 1:00 PM
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speakers: MITACS students, faculty
Title:Semi-annual local MITACS team workshop
Abstract:
See Schedule for full details.
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Mathematical Biology Seminar
Time:Wedn Sept 17, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Brian Grenfell Dept of Zoology, University of Cambridge, UK
Title:Childhood infections in space and time
Abstract:
Childhood infections give us an unusually detailed empirical picture of natural
enemy dynamics in space and time. I use wavelet analysis and models to
explore the spatio-temrpoal dynamics and control by vaccination of measles and
whooping cough in England and Wales. The results indicate marked hierarchical
travelling waves of measles, driven by 'forest fire-like' dynamics and
markedly different nonlinear behaviour of the measles and whooping cough
attractors in the face of vaccination, despite the similarity of their natural
history. A final study also explores waves. The talk also explores the impact
of waves, sparks and vaccination in the control of foot and mouth disease.
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Mathematical Biology Organizational Meeting
Time: Wed Sept 10, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Organizational Meeting
There will not be a formal seminar on this day, but we will
meet at our usual venue at PIMS to introduce
new students and faculty, and to chat over coffee, tea, and
refreshments.
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Applied Mathematics Colloquium
Time: Mon Sept 8, 2003, 3:00 pm
Location: Rm301, LS Klink, 6356 Agricultural Road, UBC
Speaker: Michael Ward, Dept of Mathematics, UBC
Title: Oscillatory and competition instabilities of localized
patterns in the Gierer-Meinhard and Gray-Scott Models.
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Mathematical Biology Seminar
Time: Tues Aug 26, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Euiwoo Lee,
Dept of Mathematics, Soongsil University, Korea
Title:Singular perturbation methods in bursting phenomenon
Abstract:
Neurons and other excitable cells often exhibit bursting oscillations;
this behavior is characterized by alternations of silent phase of
near steady state and active phase of rapid, spike-like oscillations.
Mathematical models for bursting oscillations often display a rich
structure of dynamic behavior. Besides periodic bursting oscillations,
these systems may exhibit other types of periodic solutions, such as
continuous spiking, as well as more exotic behavior including chaotic
dynamics.
The models contain multiple time scales and this often leads to
very interesting issues related to the theory of singular perturbations.
We introduce some different classes of bursting oscillations and
discuss the underlying mathematical mechanisms responsible for these
oscillations.
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Mathematical Biology Seminar
Time: Thur Aug 21, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Laurent Pujo-Menjouet
and Samuel Bernard
Centre for Nonlinear Dynamics, McGill U
Title:
Analysis of Cell Kinetics Using a Cell Division Marker:
Mathematical Modeling of Experimental Data
Abstract:
We consider an age-maturity structured model arising from a blood cell
proliferation problem. This model is ``hybrid" i.e., continuous in
time and age but the maturity variable is discrete. This is due to the
fact that we include the cell division marker CarboxyFluorescein
diacetate Succinimidyl
Ester (CFSE). We use our mathematical analysis in conjunction with
experimental data taken from the division analysis of primitive
murine bone marrow cells to characterize the maturation/proliferation
process. Cell cycle parameters such as proliferative
rate, cell cycle duration, apoptosis rate and
loss rate can be evaluated from CFSE+ cell tracking
experiments.
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Mathematical Biology Seminar
Time: Mon Aug 18, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Ryan Gutenkunst Cornell University
Title:Analysis of Movement
pattern of Bluefin Tuna in homogeneous and heterogeneous environments
Abstract:
Ryan is a visiting graduate student working with Nathaniel
Newlands and Leah Keshet on a summer research project.
He is modelling random motion and comparing data for
tuna fish tracks with the simulated random walks. The goal is
to
learn more about how to characterise aspects of the
individual behaviour given the record of the individual's
motion.
He will tell us about this project in this seminar.
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Mathematical Biology Seminar
Time: Thurs July 24, 2003, 2:00 pm
Location: Note unusual venue!!Rm 1102, Mathematics Annex, UBC
Speaker: Nadine Wolff, Department
of Mathematics, University of British Columbia
Title:Recent Results in the Study of Complex Networks
Abstract:
This is intended to be a survey talk about the recent results in the
theory of complex networks. Many real-world networks can be modelled
using graphs, and their structure can be analyzed using graph
theoretical results. Examples of such networks are: food webs,
communication networks, social networks, protein interaction networks,
etc. In the past, it was thought that random graphs, which are nearly
regular, provide sufficient models for complex networks. However, in
the late nineties, Barabási and Albert showed that complex
networks are far from random. In fact, we now know that most networks
have a degree distribution that follows a power law, i.e. many
vertices of very low degree and few vertices of very large degree. So
complex networks are best modelled using so called scale-free
networks. Furthermore, Watts and Strogatz showed that real-world
networks also exhibit high clustering and short characteristic path
length, which defines a class of networks now known as small-world
networks. In the past few years much research has focused on finding
models that display both the scale-free and the small-world behavior
to provide better ways to represent real-world networks. Attention has
also been drawn to several particularly interesting properties of
real-world networks such as path lengths, communities, and
connectivity. Studying these properties promises to give insight into
the structures underlying human interaction, gene interaction, and
many other networks of significance to a wide variety of fields of
research.
This talk will present an overview on recent results regarding models
and properties of small-world and scale-free networks using real-world
network examples. Furthermore, I will talk about the centrality of the
notion of clustering and some common misconceptions in the literature
about the definition of the clustering coefficient. The talk will also
give some insight about results from algebraic graph theory, in
particular, how the spectra of the Laplacian and normal matrices can
be used to study the structure of complex networks.
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There will be no seminar on the week of July 7-11 due to
out-of town events.
Special Mathematical Biology Seminar
Time: Wedn, July 2, 2003, Reception: 4:00 pm, Seminar 4:30 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Albert Goldbeter,
Unite de Chronobiologie theorique, Faculte des Sciences,
Universite Libre de Bruxelles, B-1050 Brussels, Belgium
Title:
Computational models for the Drosophila and mammalian circadian clocks
Abstract:
Most living organisms are capable of displaying spontaneously sustained oscillations with a period close to 24 h. These circadian rhythms can occur in constant environmental conditions, e.g. constant darkness, and are therefore endogenous. Recent experimental advances have shed much light on the molecular mechanism of circadian rhythms. While the most studied organisms were initially Drosophila and Neurospora, molecular studies of circadian rhythms have since been extended to cyanobacteria, plants and mammals. The picture that emerges from these experiments is that in all cases investigated so far, the molecular mechanism of circadian oscillations relies on negative autoregulation of gene expression. I will address the mathematical modeling of circadian rhythms, based on these experimental observations. Three models of increasing complexity will be considered. The first model accounts for autonomous oscillations of the PER protein in Drosophila. A second model incorporates the formation of a complex between the PER and TIM proteins and the effect of light, which is to trigger TIM degradation in Drosophila. In addition to periodic oscillations this model predicts the occurrence of more complex dynamics such as chaos. It also accounts for the suppression of circadian rhythms by a single light pulse. Third, I will present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erba genes. The model uncovers the possible existence of multiple sources of oscillatory behavior in the genetic regulatory network controlling the circadian clock. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles and for a number of human physiological disorders related to circadian rhythms, such as advanced or delayed sleep phase syndrome, or the non-24h sleep-wake syndrome.
Note: Prof Goldbeter is arriving from a trans-Atlantic flight
at 2:30 pm on this same date. We plan to honor him with a reception
around 4:00 pm followed by a seminar that will start between 4:30 and 5:00.
In the event of flight delays that affect his arrival, we
will hold the reception in any case.
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Mathematical Biology Seminar
Time: Tues June 24, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Fred Brauer, Department
of Mathematics, University of British Columbia
Title:Population harvesting
Abstract:
We consider some simple models for constant yield harvesting of single
species populations and of predators in a predator - prey system. There
are some situations in which the critical harvest rate beyond which a
system collapses must be obtained from the dynamics of the model and is
much smaller than can be deduced from equilibrium analysis.
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Mathematical Biology Seminar
Time: Thurs June 19, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Dr. Leonardo Huato, Vancouver, B.C., Canada
Title:
Predicting migratory route and behavior of migratory fishes: A
fitness-based approach to the modelling of the juvenile migration of
sockeye salmon.
Abstract:
Here I present a modelling investigation of the factors that define the
migratory route and behavior of sockeye salmon from the Fraser River. The
model is fitness based and spatially explicit, and it is based on the
hypothesis that fish behavior is constrained by the state of the
individual and the environment. It also has a trade-off between foraging
time and migration time. The environment here was defined as monthly
fields of sea surface temperature, currents, prey density, and predation
risk.
The model predicts the following characteristics of the sockeye salmon
migration: 1) Juveniles migrate along the coast and then move into the
Alaska Gyre where they stay for the rest of their oceanic residence.
Model predictions do not support the commonly held hypothesis of an
annual circuit around the Alaska Gyre. 2) The juvenile migration arises
as a response to high zooplankton density in the coast at the time of the
migration, although the high risk of mortality there creates a bottleneck
in their life cycle. 3) The model predicts a seasonal growth pattern as a
response to the seasonality of zooplankton density. 4) Juvenile fish
display higher swimming migration activity than adults. 5) Individuals
behaving optimally distribute below observed thermal limits, however
their distribution follows that of prey density.
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Mathematical Biology Seminar
Time: Tues June 10, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Ross Cressman,
Department of Mathematics, Wilfrid Laurier University
Title:
Coevolution and the Stationary Density Surface
Abstract:
Coevolution is a broad topic connecting the study of individual
traits within separate biological populations (e.g. separate species) to
the study of ecosystems based on interactions among these populations. An
early success in the analysis of stability in coevolutionary models
introduced some twenty years ago was to separate evolutionary and
ecological effects by assuming population densities track their
equilibrium values (what I call the stationary density surface) for a
given set of species' traits. This assumption is a more sophisticated
version of the intuitively appealing idea that, since the evolution of
population densities takes place on a much faster time scale (ecological
time) than that of species' traits (evolutionary time), trait values can
be taken as fixed parameters when studying the evolution of population
densities (or vice versa). It has since been well documented that both
assumptions have the potential to give misleading insights into the
eventual outcome of general coevolutionary systems.
The main purpose of this talk is to show that, notwithstanding the
preceding statement, the stationary density surface remains of central
importance. Moreover, there is no need for some artificial assumption of
different coevolutionary time scales. This will initially be shown by
considering coevolutionary Lotka-Volterra systems where individual fitness
functions are assumed to be linear in the population state. If time
permits, I will also connect the theory to more recent coevolutionary
models based on adaptive dynamics where there continues to be a widespread
conviction that the stationary density surface technique can be used to
predict stable trait distributions.
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Mathematical Biology Seminar
Time: Thur June 5, 2003, 2:00 pm
Location:Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Leah Edelstein-Keshet,
University of British Columbia,
Title:
Mathematical Biology of cellular and biomedical problems
Abstract:
(This is a practice talk, in preparation for a lecture to be given
at CMS in Edmonton. Feedback is desired and would be appreciated.)
I will survey a few problems and areas on which my research has
focused in recent years. One area is that of the molecular machinary that
controlls motility of living cells: the actin cytoskeleton. I will
describe how work has proceeded from the small scale investigations of the
"parts list" to more global modelling of dynamics of actin filaments
and how these lead to the force of protrusion in cell motility. (This work
has been joint with G.B. Ermentrout and A. Mogilner)
I will then briefly survey some of the more recent biomedically related
projects, including modelling of Alzheimer's Disease (joint with A. Spiros)
and Type 1 Diabetes (with AFM Maree and Diane Finegood).
The common thread in the latter projects is the involvment of inflammation
and the immune system. My main goal will be to highlight the synergy between
the mathematical models and insight or understanding of underlying mechanisms
in the biological systems. (These project have been funded by MITACS.)
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Mathematical Biology Seminar
Time: Thur May 22, 2003, 2:00 pm
Location:Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Professor Linghai Zhang (Math Dept, Lehigh University,
Pennsylvania)
Title:
On the stability of travelling wave solutions of integral-differential
equations arising from synaptically coupled neuronal networks
Abstract:
I study the asymptotic stability of traveling wave solutions
of integral-differential equations arising from synaptically coupled
neuronal networks. By using complex analytic functions, I prove that there
is no nonzero spectrum of some linear operator $L$ in the region
Re$\lambda\geq 0$, and $\lambda=0$ is a simple eigenvalue. By applying
linearized stability criterion, I show that the traveling wave solutions
are asymptotically stable. Furthermore, some explicit analytic functions
are found for a scalar integral-differential equation.
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Mathematical Biology Seminar
Time: Tue May 20, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
David Sean Kirby,
Senior Fisheries Scientist (Modeller),
Oceanic Fisheries Programme, Secretariat of the Pacific Community
Noumea, New Caledonia, South Pacific
Title:
Fisheries Ecology & Oceanography in the Western and Central Pacific Ocean:
an individual based modelling approach
Abstract:
The Secretariat of the Pacific Community is an International Organization
providing technical support to Pacific Island Countries and Territories
across a range of sectors. The Oceanic Fisheries Programme (OFP) collects,
manages and analyses data for the Western and Central Pacific Ocean tuna
fisheries and carries out biological research and modelling studies to
further understand the dynamics of the resources.
This talk presents the work of the OFP's Tuna Ecology and Biology (TEB)
section with particular emphasis on the development of individual-based
models (IBM's) for the movement and population dynamics of Pacific tunas.
The talk will briefly describe the work of the section and then focus on the
development of an IBM for Pacific skipjack tuna, Katsuwonus pelamis.
The model has been developed in collaboration with colleagues in Bergen,
Norway, and uses the Lagrangian IBM paradigm to track individual properties
(e.g. movement, physiological state, feeding history, reproductive activity)
of a population of model fish in an ocean simulated by prior numerical
modelling of currents, temperature, primary production and tuna forage. Tuna
larvae behave as passive drifters but juveniles and adults exhibit directed
movement in relation to their environment, location, time and internal
state. Movement and spawning behaviour is output from an artificial neural
network with weights that are unique to each individual. A genetic algorithm
is used to allow the weights to be passed on to offspring by sexual
reproduction. Therefore life-cycle closure is achieved and both individual
behaviour and large-scale spatial dynamics are emergent within the model
without reference to a pre-determined fitness measure or a prescriptive
rule-set.
The model is designed for eventual comparison with other population dynamics
and stock assessment models and may be used to explore individual behaviour
in comparison to data from archival and conventional tags.
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Mathematical Biology Seminar
Time: Thurs May 1, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
PROJECT PRESENTATION DAY:
On this day several students
will present short summaries of work that they will take to the
MITACS Annual General Meeting in Ottwa in May 2003.
Speaker:
Carol Huang
(joint work with Stan Maree, Leah Keshet)
Title:A Cellular Automata Model in Alzheimer's Disease Senile PlaqueFormation
Abstract:
Plaques composed of amyloid-beta, an abnormal fibrilar protein,
are believed to play a major role in the pathophysiology of Alzheimer's
Disease. This investigation aims to understand the processes that give
rise to the formation of Alzheimer's Disease senile plaques as a balance
of deposition and removal of amyloid-beta. By refining previous coarse
grained simulations (Edelstein-Keshet and Spiros, 2002) to reveal more
accurate 2 and 3D plaque ultrastructure, we hope to investigate
hypotheses about the mechanisms of removal of amyloid by microglia as
well as details of how fiber deposits nucleate further deposition. Our
investigation starts from simple cellular automata simulations based on
Cruz et al (1997, 1999), who modeled aggregation-disaggregation
phenomena and were able to produce plaques with similar structure to
that of experimental observations and predict the time dependency of
amyloid-beta deposition. However, the aggregation and disaggregation
rules that produce those plaques remained largely unexplained. We would
include more realistic parameter values from our previous simulations
and biological details such as soluble amyloid-beta peptide diffusion
and microglia movement. The effects of a rather artificial "surface
diffusion" mechanism, which is required to form the correct morphology
of plaques in the original model, will also be assessed.
Speaker:Adriana Dawes,
(joint with Stan Maree, Leah Keshet)
Title:
Listeria Propulsion by Actin Polymerization
Abstract:
Actin is a ubiquitous protein and is found in all eukaryotic
cells. Pathogens such as Listeria hijack actin to propel themselves
through infected cells. Listeria, as well as specially treated polystyrene
beads, causes the growth of an actin "comet tail" through the process of
polymerization where actin is built into thin filaments. As more actin is
polymerized at the rear of the obstacle (bacterium or bead), it pushes the
obstacle forward. We use a simple mathematical model to describe the
dynamics of actin polymerization on a spatial grid to investigate this
system. We will look at various parameters and whether they affect the
formation of the actin comet tail and the velocity of the obstacle.
Speaker:Clive Glover
(joint with Jamie Piret)
Title:
Gene expression as a means of monitoring cell culture requirements
Abstract:
From the emerging field of cellular therapy, there is an increasing demand
for new media to provide optimal expansion of cells in culture.
Hematopoietic stem cells have complex growth requirements and serum free
media include over 50 components at concentrations from near zero to 7
g/L. Conventionally, media are developed empirically, either by depletion
analysis or component addition to determine if culture productivity can be
increased. This optimization process consumes valuable time and labour.
We are investigating medium optimization through monitoring the gene
expression profile of cells in culture based on the hypothesis that cells
experiencing a particular limitation will exhibit a characteristic gene
expression profile. We have analyzed gene expression of human TF-1 cells
under nutritional stress and literature data on yeast under amino acid
limitations. The expression levels of genes in pathways relevant to these
stresses were monitored at several time points following limitation
exposure. As part of this study we are developing statistical methods to
detect perturbations of entire pathways. Rather than focusing on
differential expression of individual genes, we combine p-values across
subsets of genes, grouped using gene ontology. An attractive property of
this approach is the potential to detect an expression change for a
pathway, when the gene-specific changes are subtle. Results show that
genes coding for enzymes involved in the biosynthesis of limiting
nutrients are generally upregulated. In TF-1 cells exposed to limiting
glucose, genes coding for three key regulatory enzymes in the glycolysis
pathway (hexokinase, phosphofructokinase and pyruvate kinase) were
significantly upregulated. Furthermore, yeast exposed to histidine
starvation showed a strong upregulation in genes involved in both the
histidine and arginine biosynthesis pathways. Genes involved in protein
biosynthesis were downregulated upon amino acid limitation. In the latter
case, while individual genes did not show statistically significant
shifts, statistical confidence was obtained from the pattern observed in
functionally related genes. Ultimately the knowledge developed by this
work should contribute to the development of diagnostic tools for
monitoring and rapidly optimizing stem cell cultures.
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Mathematical Biology Seminar
Time: Thurs April 17, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Dr. Nathaniel Newlands, Department of Mathematics, UBC
Title:Fishery-independent abundance estimation of Atlantic bluefin tuna
(Thunnus thynnus) in the Gulf of Maine:
integrating tracking, tagging and aerial survey data
Abstract:
From 1993-1997, the New England Aquarium conducted
fishery-linked aerial surveys with spotter pilots to document
the surface abundance, distribution, and environmental associations
of bluefin tuna schools in the Gulf of Maine. The long-term goal
of this program is to develop fishery-independent estimates of
abundance. Information obtained by direct monitoring of surface
schools allowed us to conduct spatial analyses, modeling and
simulations that are not usually available in CPUE based approaches.
Our presentation will address measurement bias and uncertainty
in population abundance estimation from bluefin tuna movement,
spatial aggregation and distribution data. We used an integrated
approach to analyze, calibrate, and correct the aerial survey
data in order to obtain more reliable estimates of regional
abundance. Bias and uncertainty in the size and aggregation
of schools were directly estimated from the survey data,
adjusted by additional data on movements and dispersal from
electronic and hydro-acoustic tagging studies.
Results of simulations will be presented for different
survey designs, including random, systematic, stratified,
adaptive and spotter-search aerial sampling.
Recommendations for achieving greater precision in
abundance estimation in aerial surveys will be discussed.
The work demonstrates how fishery-independent data can be
integrated to provide more reliable estimates of bluefin
tuna abundance, and a broader understanding of spatial
heterogeneity in fish populations.
This talk will be presented at the
International Tuna Conference, Lake Arrowhead, CA,
U.S.A. May, 2003. (20 minutes). Feedback and comments
are welcomed.
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Mathematical Biology Seminar
Time: Thurs April 10, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:Dr. Chad Topaz, Department of Mathematics, Duke University
Title: Dynamics of a two-dimensional continuum model for swarming
Abstract:
A biological swarm is a group of organisms undergoing large-scale
coordinated movement. Typically, this movement is not due to
centralized control, but rather to social interactions which occur on a
length scale smaller than that of the global swarm formation. Swarms
occur in populations of ants, locusts, fish, birds, wolves, and others,
and are often observed to have sharp boundaries and a roughly
spatially-constant population density. In this talk, I will discuss
preliminary results for a simple continuum model for swarming in two
dimensions. The population density $\rho$ satisfies an advection
equation. The velocity depends nonlocally on $\rho$ by means of a
convolution with a spatially decaying kernel $K$, which describes the
social interaction between organisms. Using the Hodge decomposition
theorem, the velocity field may be decomposed into a divergence-free
component and a gradient component. This framework provides a
convenient way to characterize the two-dimensional dynamics. The
gradient component controls the expansion or contraction of the
population, while the divergence-free component is responsible for its
rotational motion. Numerical simulations of the model reveal vortex
states similar to those observed in nature.
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Mathematical Biology Seminar
Time: Thurs April 3, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:Dr. Daniel Promislow,
Title:A network
perspective on the evolutionary genetics of aging
Abstract:
Classical evolutionary theories of aging make few
assumptions about how many genes are involved in the aging process,
or about the magnitude of their effects on rates of aging. I will
discuss my recent work with gene networks. This work is an attempt to
create a more genetically realistic model for the evolution of aging.
In addition, I will discuss ways in which we might use networks to
aid molecular biologists in predicting what types of genes might
influence longevity.
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Mathematical Biology Seminar
Time: Thurs March 20, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:Dr. Fred Brauer, Department of Mathematics, UBC
Title: Backward Bifurcations in Simple Vaccination Models
Abstract:
We describe and analyze by elementary methods some simple models for
disease transmission with vaccination. In particular, we give conditions
for the existence of multiple endemic equilibria and backward
bifurcations. We also extend the results to include the possibility of
adaptive systems in which the parameter values may depend on the level of
infection.
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Mathematical Biology Seminar
Time: WEDN(!) March 12, 2003, 2:00
pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dr. Anders
E. Carlsson, Department of Physics, Washington University, St. Louis,
Missouri
Title: Growth of Branched
Actin Networks: Theory and Simulation
Abstract:
Actin filaments often form branched network structures which provide
stable propulsion for cells or for intracellular parasites such as
Listeria. We study the growth of such networks using a combination of
stochastic simulation and kinetic rate equations. The stochastic
simulations use a model of static, rigid filaments to which monomers
and branches are added at random positions according to specified
rates. They show that a simple model based on five basic unit
processes produces three-dimensional network structures quite similar
to those observed by electron microscopy. Surprisingly, the growth
velocity of the network is independent of the opposing force, even
though the velocity of a free filament depends exponentially on the
force. To understand this effect, we study a rate-equation model based
on the density of free filament tips near the cell membrane (or
intracellular pathogen). The force-independence of the velocity
results from the linearity of the rate equation, and holds under a
broad range of plausible assumptions. Experiments testing the
predictions are proposed.
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Mathematical Biology Seminar
Time: Thurs March 6, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Dr. Stan Marée
, Department of Mathematics, UBC
Title:
Modelling Slime Mould Morphogenesis: the Culmination
Abstract:
Culmination of the morphogenesis of the cellular slime mould
Dictyostelium discoideum involves complex cell movements which
transform a mound of cells into a globule of spores on a slender
stalk. The movement has been likened to a "reverse fountain",
whereby prestalk cells in the upper part form a stalk that moves
downwards and anchors itself to the substratum, while prespore cells
in the lower part move upwards to form the spore head. We will
demonstrate that the processes that are essential during the earlier
stages of the morphogenesis are in fact sufficient to produce the
dynamics of the culmination stage. These processes are cyclic AMP
signalling, differential adhesion, cell differentiation and production
of ECM.
We have simulated the culmination using a hybrid CA/PDE model. In the
model, individual cells are represented as a group of connected
automata, i.e. the basic scale of the model is subcellular. Initially
we simulated in 2D, describing transverse sections through the
culminant. Recently we have extended the model to 3D, in order to
prove feasibility of the full model, and to open the road to describe
the whole development as one continuous process.
With our model we are able to reproduce the main features that
occur during culmination, namely the straight downward elongation of
the stalk, its anchoring to the substratum and the formation of the
long thin stalk topped by the spore head. We show that periodic
upward movements, due to chemotactic motion, are essential for
successful culmination, because the pressure waves they induce squeeze
the stalk downwards through the cell mass, a mechanism which has a
number of self-organising and self-correcting properties and can
explain many experimental observations.
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Time: Mon Jan 27, 2003, 3:00 pm
Location: Rm 301, Leonard Klink bldg
IAM-PIMS Distinguished Colloquium Speaker:
Leon Glass, Physiology, McGill
Title: Dynamics of Genetic Networks
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Mathematical Biology Seminar
Time: Tues Jan 21, 2003, 10:00 am
Location: Room WMAX 240, 1933 West Mall (down the hall from
PIMS seminar room)
Speaker:
Dan Coombs, Theoretical Biology and Biophysics Group, Los Alamos National Laboratory
Title: Modeling T Cell Activation
Abstract:
In this talk I will present some ways in which mathematical modeling has
been helpful in studying T cell activation, and outline challenges for the
future. No prior knowledge of the immune system will be assumed.
The activation of T cells is an essential part of the immune response to
viruses and bacteria. Fragments ("antigens") of these enemies are
presented to T cells on the surfaces of antigen-presenting-cells, but an
individual T-cell carries receptors (TCR) that recognize only a few
possible antigens. After the T cell becomes activated, it may kill the
presenting cell (in the case of viral infection) or activate other
components of the immune system (in the case of bacterial infection).
Activation appears to rely on the formation of a stable region of close
apposition between the cells, termed the "immunological synapse". Within
the synapse, each TCR may individually be activated and labeled for
internalization by interaction with presented antigen. A key parameter
controlling individual TCR activation and internalization is the lifetime
of the bond between the TCR and a presented antigen.
We have developed a mathematical model consisting of reaction-diffusion
equations describing spatial and temporal changes that take place within
the synapse. From comparison of model predictions with experimental data,
we draw conclusions about the requirements for T cell activation as well
as the cellular internalization and degradation of TCR.
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Mathematics Colloquium
Time: Mon Jan 20, 2003, Time: 4:00 pm
Location: Math 203
Speaker:
Dan Coombs, Theoretical Biology and Biophysics Group, Los Alamos National
Laboratory
Title:
Chirality Inversions Propagating on Bacterial Flagella
Abstract:
Many experimental investigations have shown that bacterial flagella (the
long, whip-like structures that provide thrust during swimming) take on a
variety of helical forms under differing mechanical and chemical
conditions. During the 1980s a series of experiments examined the response
of a single, detached flagellum to simple fluid stresses. In particular,
when a flagellum is clamped at one end and placed in an axial external
flow, it is observed that regions of the flagellum transform to the
opposite chirality and travel as pulses down the length of the filament,
the process repeating periodically.
We propose a theory for this phenomenon based on a treatment of the
flagellum as an elastic object with multiple stable configurations. This
theory is expressed in terms of coupled PDEs for the filament shape and
twist configuration, and involves only physical, measurable properties of
the flagellum. We generate simulations that quantitatively reproduce key
features seen in experiment.
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Mathematical Biology Seminar
Time: Thurs Jan 16, 2003, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Peter J. Thomas,
Computational Neurobiology Laboratory,
The Salk Institute for Biological Studies;
Title:
Inside the Mind of the Amoeba: Simulation and Analysis of
Biochemical Signal-Transduction Networks.
Abstract:
In lieu of nervous systems, single-celled organisms use complex
networks of biochemical reactions to sense the world around them,
make decisions, and take action. A wealth of quantitative
biological data from bioinformatics to fluorescence microscopy
has created the possibility of building biophysically realistic
models of the information processing occurring inside cells, in
analogy to models of biological neural networks. Biochemical
networks present several unique mathematical challenges.
Chemical reactants are localized within subcellular volumes,
requiring PDE rather than ODE treatments of their behavior.
Small numbers of interacting molecules make the typical
biochemical network inherently noisy, leading us to consider
approximations to stochastic PDEs. Finally, chemical systems
typically occupy state spaces of large dimension, forcing us to
look for effective means of "coarse-graining" the representation
of chemical states. We have constructed a finite-element model
for solving arbitrary boundary-coupled PDEs as a platform for
studying spatially heterogeneous signal-transduction networks,
and used it to develop a model for the orienting response of a
eukaryotic cell during directed cell movement (chemotaxis)*. We
are building on this finite-element framework to accommodate the
effects of fluctuations as an approach to stochastic PDEs, and as
a way of formalizing dimension-reduction of chemical state
spaces.
*Eukaryotic chemotaxis will also be discussed in the context of Turing
pattern formation in the 1/15 Wednesday Mathematics Colloquium.
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Mathematics Colloquium
Time: Wedn Jan 15, 2003, 3:00 pm
Location:Math Annex 1100
Speaker:
Peter J. Thomas,
Computational Neurobiology Laboratory,
The Salk Institute for Biological Studies
Title:
Applications of Turing Pattern Formation, from Geometric Visual
Hallucinations to Eukaryotic Chemotaxis.
Abstract:
In 1952 Alan Turing proposed a mechanism for the development of
spatial patterns, such as animal coat patterns, from spatially
homogeneous initial conditions, such as a presumably uniform
embryo. Many systems have invited analogous treatments, from
segmentation of the Drosophila embryo to Meinhardt's model for
establishing direction in eukaryotic chemotaxis. The two
essential elements underlying the Turing mechanism, a short-range
activator and a long-range inhibitor, have not always been easily
identified as the biology underlying pattern formation becomes
better understood. In this talk I will explore two systems in
which the biological details gave new insights into the
possibilities of pattern formation. In the cerebral cortex, the
local connectivity of nervous tissue gives an effective
long-range inhibitory and short-range excitatory interaction that
can lead to the creation of spontaneous patterned activity in the
cortical sheet. In the visual cortex this spontaneous activity
gives rise to a distinct set of geometric visual hallucinations.
Careful analysis of the geometry of cortical connectivity allows
classification of the observed patterns in terms of a particular
class of subgroups of the Euclidean motions of the plane. As a
second example, I will return to the problem of eukaryotic
chemotaxis. An unbiased single-celled organism must respond to a
weak gradient of a chemical attractant, organizing its internal
chemistry in order to initiate movement in the direction of the
gradient (chemotaxis). Using data from mutant cells showing
anomalous chemotaxis, we have identified a rapidly diffusing
intracellular inhibitory molecule that facilitates sharpening of
the directional response. In addition to amplifying the weak
spatial gradient signal, this variant of the Turing mechanism
also exploits timing characteristics of the extracellular
signal. (The Mathematical Biology Seminar on Thursday 1/16 will
discuss biochemical networks in more detail.)
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Mathematical Biology Seminar
Time: Tues Jan 14, 2003, 2:00pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Duane Nykamp, UCLA Mathematics Department
Title:
Assessing the inherent nonlinearity of visual neurons:
simple cells versus complex cells
Abstract:
Investigators typically divide neurons of the primary visual cortex
(V1) into two classes: simple and complex. Neurons with an
approximately linear response to a visual stimulus are classified as
simple; the remainder are classified as complex. Standard analysis
methods lead to the view that V1 neurons fall neatly into these two
categories. I develop a method to analyze neural response based on an
explicit mathematical model that captures the nonlinear
sign-independence of an idealized complex cell. When V1 neurons are
analyzed by this method, one observes evidence of a broad continuum of
nonlinear response without a division into two discrete classes.
Discrete classes are observed with standard analysis methods because
the methods do not account for the effect of a spike generating
nonlinearity. I discuss how this modeling approach can be used to
better understand the nonlinear response properties of visual and
other stimulus-driven neurons.
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Mathematics Colloquium
Time: Mon Jan 13, 2003 Time: 4:00 pm
Location: Math 203
Speaker:
Duane Nykamp, UCLA Mathematics Department
Title:
Reconstructing the coupling of neurons from spike times
Abstract:
Reconstructing the connectivity patterns of neural networks in higher
organisms has been a formidable challenge. Most neurophysiology data
consist only of spike times, and current analysis methods are unable
to resolve the ambiguity in connectivity patterns that could lead to
such data. I present a new method that can determine the presence of
a connection between two neurons from the spike times of the neurons
in response to spatiotemporal white noise. The method successfully
distinguishes such a direct connection from common input originating
from other, unmeasured neurons. Although the method is based on a
highly idealized linear-nonlinear approximation of neural response,
simulations demonstrate that the approach can work with a more
realistic, integrate-and-fire neuron model. I propose that the
approach exemplified by this analysis may yield viable tools for
reconstructing neural networks from data gathered in neurophysiology
experiments.
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Mathematics Colloquium
Time: Fri Jan 10, 2003: 3:00 pm
Location:Math Annex 1100
Speaker:
Eric Cytrynbaum, Mathematics Dept,
UC Davis
Title:
Aggregation and centering in fish melanophore cells -
a quantitative exploration of cytoskeletal dynamics
Abstract:
I study a process of self-organization that occurs inside a
cell called a fish melanophore in which pigment particles
are seen to aggregate. The process is mediated by subcellular
components called microtubules, which form part of
the cytoskeleton. The same components are at work in
the centering of chromosomes during cell division,
and therefore provide a good
"warmup" problem for that more complicated but fundamentally
important biological process.
When a fragment of the cell is excised to eliminate
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 chromosome alignment
during cell division.
We derive a system of seven non-linear PDEs (1D) that describes
the biological system. Numerical simulations of the equations
demonstrate certain observed features (aggregation) but not others
(centering). The system can be reduced so as to facilitate analysis
which allow for an understanding of the successes and failures of the
original model. Finally, we generalize the reduced model to 2D,
incorporating a stochatic element, and present numerical results.
In this talk, I will also briefly mention some of my previous work
on the phenomenon of ventricular fibrillation in the heart, and
the analysis of wave phenomena in
the Fitzhugh Nagumo equations that formed the focus of
my PhD work.
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Mathematical Biology Seminar
Time: Thurs Jan 9, 2003 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Eric Cytrynbaum, Mathematics Dept, UC Davis
Title:
Cytoskeletal mechanics and spindle morphogenesis during mitosis in
Drosophila embryos
Abstract:
Mitosis, the process by which a cell segregates two identical copies of
its genome in preparation for division, is fundamental to cell replication
and hence to life as we know it. In order to separate the two copies of
the genome, a self-assembling protein machine, the mitotic spindle,
employs several force generating molecules known as molecular motors.
These motors, through interaction with spindle microtubules (semi-rigid
protein filaments), aid in spindle assembly as well as chromosome
segregation.
It has been proposed that mitosis occurs by progression through a sequence
of steady states defined by a balance of motor forces. In close
collaboration with experimentalists, we have developed a quantitative
model describing this balance of forces during the process of spindle
formation in Drosophila embryos. In particular, we describe how dynein
and Ncd exert opposing forces on the spindle poles, moving them to
opposite sides of the nucleus where they reach a steady-state separation
distance. Complementing dynein is a polymerization force that explains
the rapid initial separation that is seen in experimental measurements.
The model compares favorably to data from both wildtype and mutant
phenotypes.
In this talk, I will describe the details of the quantitative model as
well as ongoing experimental work which was motivated by the quantitative
study. Although more experimental work is required, I will also describe
future plans for incorporating these new results into a "second
generation" model.
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Mathematics Colloquium
Time: Wedn Jan 8, 2003: 3:00 pm
Location: Math Annex 1100
Speaker:
Christoph Hauert, Department of Zoology,
UBC
Title:
Cooperation in social dilemmas: Volunteering in public goods games
Abstract:
Cooperative behavior among unrelated individuals is one of the
fundamental problems in biology and social sciences. Reciprocal
altruism fails to provide a solution if interactions are not repeated
often enough or groups are too large. Punishment and reward can be very
effective but require that defectors can be traced and identified. Here
we present a simple but effective mechanism operating under full
anonymity. Voluntary participation in public goods games can foil
exploiters and overcome the social dilemma. This natural extension
leads to rock-scissors-paper type cyclic dominance of the three
strategies cooperate, defect and loner i.e. those unwilling to
participate in the public enterprise.
In voluntary public goods interactions the three strategies can
co-exist under very diverse assumptions on population structure and
adaptation mechanisms. In particular, spatially structured populations,
where players interact only with their nearest neighbors, lead to
interesting dynamical properties and intriguing spatio-temporal
patterns. Variations of the value of the public good result in
transitions between one-, two- and three-strategy states which are in
the class of directed percolation.
Although volunteering is incapable of stabilizing cooperation, it
efficiently prevents successful spreading of selfish behavior and
enables cooperators to persist at substantial levels.
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Mathematical Biology Seminar
Time: Tues Jan 7,2003, 3:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Christoph Hauert, Department of Zoology, UBC
Title:
Cooperation in social dilemmas: Punishment and Reputation
Abstract:
Humans and animals display a high readiness to help their fellows in
need - even if such assistance involves substantial costs in terms of
money or fitness. Recently, economists became increasingly interested
in this apparently irrational behavior. Extensive experiments suggest
that fairness considerations, punishment and reputation play a crucial
role. It now poses a challenging task to embed such mechanisms in an
abstract game theoretical framework.
Various different games were designed to capture the essence and to
highlight different aspects of such interactions between pairs or
groups of individuals. The most prominent games are certainly the
prisoner's dilemma, the public goods game as well as the ultimatum
game. We show that from a mathematical point of view all three games
are closely related and share a common core. In particular, the
ultimatum game turns out to be a special case of a pairwise prisoner's
dilemma interaction followed by punishment opportunities. This leads to
a general class of two-stage games where an interaction is followed by
a reaction. The replicator equation allows for a full analysis of the
resulting game dynamics - even in the non-linear case of groups of
interacting individuals.
The threat of punishment is efficient in creating incentives to
cooperate, but punishment alone is not sufficient for persistence of
cooperation. Additional mechanisms such as reputation or spatially
structured populations are required to achieve highly social and fair
outcomes related to the experimental evidence.
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Mathematical Biology Seminar
Time:
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker:
Title:
Abstract:
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