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Upcoming seminars
Mathematical Biology Seminar
Wedn Dec 7, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Anmar Khadra Dept. of Mathematics, UBC.
Title:
Modeling the Pulsatile and Synchronized Behaviour of GnRH Neurons
Abstract:
The hypothalamic GnRH (Gonadotropin Releasing Hormone) decapeptide is
essential for reproductive processes in vertebrates. GnRH plays key roles
in the onset and progression of reproductive maturation, and regulation
of hormonal changes that occur during menstrual and estrous cycle. It
mediates the reproductive system responses to seasonal or diurnal cues. In
primates, GnRH is secreted from synchronized GnRH neurons in a pulsatile
and episodic manner in the median eminence, e.g., in humans, the hormone
is released approximately every 60 mins. This pulsatile and episodic
pattern is crucial for normal reproductive function.
The underlying mechanism of the GnRH pulse generator that is responsible
for the episodic secretion of GnRH has yet to be established. It is clear,
however, that GnRH neurons have an intrinsic capacity for the generation
of pulsatile neurosecretion. Recent experiments revealed important
details of the molecular events underlying the GnRH pulsatility. It has
been shown that GnRH neurons express GnRH receptors allowing GnRH to exert
an autocrine action on them. Krsmanovic et al., proposed a mechanism
describing this autocrine effect via Calcium and cAMP. In this talk we
will present a mathematical model which reflects the properties of the
proposed mechanism. Furthermore, we illustrate how this hormone can act
as an agent or a "diffusible mediator" that is responsible for coupling
the GnRH neurons to generate synchronized release of itself. We also show
the robustness of synchronization to variations in the properties of the
GnRH neurons.
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Mathematical Biology Seminar
Wedn Nov 30, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Muhammad Arshad Chaudhry Michael Smith Laboratories, UBC.
Title:Influence of Culture pH and Osmolality on the Maintenance of
Pluripotentiality of Murine Embryonic Stem Cells
Abstract:
The clinical realization of stem cells based gene and tissue regeneration
therapies depends on the development of consistent, robust and scalable
processes to expand their numbers without compromising their developmental
potential. Murine embryonic stem (ES) cells provide a practical model for
stem cell culture process research as they can be readily obtained at
relatively high numbers and purities. Conventional ES cultures require daily
medium exchange and an understanding of their environmental tolerance ranges
is still lacking. We have now begun to explore these using a functional
assay (Embryoid body, EB, formation) to quantify the integrity of an ES cell
line, R1, exposed to various culture stresses. Based on the EB formation
assay, culture environment strongly influences the developmental potential
of two ES cell lines, R1 and EFC. A dose-response analysis of R1 cells
exposed to various medium pH and osmolalities was carried out and revealed
that within 48 h, the yield of EBs was ~ 3-fold decreased (p<0.05) when R1
cells were cultured in pH 7.0 or 400 mOsm/kg osmolality medium (compared to
a pH of 7.3 and 300 mOsm/kg osmolality). This was due to both a relative and
absolute decreases in the rate of EB-forming cell expansion. These studies
provide guidance in determining the optimal culture conditions and
environmental tolerances for stem cell bioprocess research and development.
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Mathematical Biology Seminar
Wedn Nov 23, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Fred Brauer Mathematics, UBC.
Title:Simple pandemic models
Abstract: Stochastic simulation of large network models have become the standard
approach to modelling epidemics and control measures, including anticipated
possible pandemics. We show that simple compartmental deterministic models
can give some of the predictions of such models simply and with better
understanding of critical dependence on some parameters. In particular, the
dependence on the initial number of infectives is critical, and this makes
predictions of the amount of treatment needed for control and the number of
disease cases completely unreliable. However, comparison of different
control strategies is still possible.
(work joint with Julien Arino, Pauline van den Driessche, James Watmough,
and Jianhong Wu).
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Mathematical Biology Seminar
Wedn Nov 16, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Neil Balmforth Mathematics and
Earth and Ocean Sciences, UBC
Title:Locomotion of Gastropods: Lubrication theory plus RoboSnail
Abstract: Many gastropods, such as slugs and snails, crawl via adhesive locomotion
in which the foot sends waves over a fluid layer between the creature
and the underlying surface. We investigate this method of propulsion
using two mathematical models, one for direct waves and one for retrograde
waves. We then test the effectiveness of both proposed mechanisms by
constructing two mechanical crawlers. Each crawler uses a different
mechanical strategy to move on a thin layer of fluid. The first uses
a flexible flapping sheet to generate lubrication pressures in a
Newtonian fluid which in turn propels the mechanical snail. The
second generates a wave of compression on a layer of Laponite, a
non-Newtonian, finite-yield stress fluid with characteristics similar
to those of snail mucus. This second design can climb smooth
vertical walls and perform an inverted traverse.
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Mathematical Biology Seminar
Wedn Nov 9, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Lin Wang University of Victoria
Title:Competition in the
chemostat.
Abstract: TBA
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Wedn Nov 2, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Nick Swindale UBC
Title:Coverage, Polymaps and the Visual Cortex
Abstract:
In this talk I will present some simple mathematical models that are able to
explain the structure of the maps that are found in the mammalian visual
cortex. These can be characterized as projections of a 2D surface into a high
dimensional feature space subject to completeness and local continuity
constraints.
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Wedn Oct 26, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Nima Geffen Mathematics, Tel Aviv
University.
Title:A micro helical organism revisited.
Abstract: TBA
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Wedn Oct 19, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Byron Goldstein Los Alamos National Laboratory,
Title:Immunoadhesins and monoclonal antibodies in the treatment of disease:
Modeling how they couple target cells to natural killer cells.
Abstract: Natural killer (NK) cells can destroy cells coated with antibody. The killing occurs at close range and requires that NK cells and target cells adhere. The antibodies mediate adhesion and bridge the two cells by binding to sites on the target cell through their Fab regions and by binding to Fc receptors on the NK cells through their constant region. A number of monoclonal antibodies and antibody like molecules have been developed and approved by the FDA to target over expressed normal proteins on tumor cells and cells that drive autoimmune diseases. We present a physical model of NK cell-target cell adhesion mediated by these drugs. We illustrate the properties of the model and determine important physical parameters by using it to fit quantitative data on adhesion of T cells to NK cells mediated by a drug, Alefacept, used in the treatment of psoriasis, an autoimmune disease of the skin. We discuss quantitative predictions of the model, focusing on how drugs can discriminate among cells expressing the same target molecules but with different surface densities. The model offers an explanation of how Alefacept can distinguish target from normal T cells.
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Mathematical Biology Seminar
Wedn Oct 12, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Nicola Fameli Dept. of Physics, UBC
Title:Modeling of Ca2+ transport in smooth muscle cells
Abstract:
I will present a stochastic numerical model simulating the transport of calcium ions (Ca 2+) within the junctional spaces between the plasma membrane and the sarcoplasmic reticulum of smooth muscle cells. In this type of cells, release of Ca 2+ from the sarcoplasmic reticulum (SR) is thought to be responsible for contractile activation. In this scenario, measurements of [Ca 2+] oscillations suggest that to replenish the sarcoplasmic reticulum and maintain contraction, Ca 2+ from the extracellular space are taken up by the sarcoplasmic reticulum having traversed the buffer spaces between the plasma membrane (PM) and the SR. These spaces are known as junctions. The model assumes the propagation of Ca 2+ occurs by diffusion through the junctional cytosol between the PM and the SR. The typical path of Ca 2+ diffusing inside the junctional space is therefore simulated as a three- dimensional random walk from ion sources to ion sinks, representing the ion transporters Na +/Ca2+ exchanger and SERCA pumps, respectively. Results of this study in conjunction with [Ca 2+], force transduction and electron microscopy measurements seem to reinforce the idea that Ca 2+ uptake via PM-SR junctions is a possible and plausible pathway to refilling SR calcium to maintain contractions in smooth muscle cells.
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Mathematical Biology Seminar
Wedn Oct 5, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Eric Cytrynbaum
Mathematics, UBC
Title:Finding the center - how to solve simple geometry problems at the cellular scale
Abstract: Fragments of fish melanophore cells can form and center
aggregates of pigment granules by dynein-motor-driven transport along a
self-organized radial array of microtubules (MTs). I will present a
quantitative model that describes pigment aggregation and MT-aster
self-organization and the subsequent centering of both structures.
The model is based on the observations that MTs are immobile and treadmill,
while dynein-motor-covered granules have the ability to nucleate MTs.
From assumptions based on experimental observations, I'll derive partial
integro-differential equations describing the coupled granule-MT interaction.
Scaling arguments and perturbation theory allow for analysis in
two limiting cases. This analysis explains the mechanism of aster
self-organization as a positive feedback loop between motor aggregation
at the MT minus ends and MT nucleation by motors. Furthermore, the centering
mechanism is explained as a global geometric bias in the cell
established by self-nucleated microtubules. Numerical simulations
lend additional supports to the analysis. The model sheds light on
role of polymer dynamics and polymer-motor interactions in
cytoskeletal organization.
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Mathematical Biology Seminar
Sept 28, 2005 Time:2:00
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Rodrigo A. Restrepo (Emeritus), Dept of Mathematics, UBC
Title:
A Plausible Ancestry for the tRNAs.
Abstract:
After examining the frequent occurrences
of some RNA
segments in 657
prokaryotic gene sequences, this work suggests
that the development of the tRNAs began with two
small RNA segments, specified here, formed in abundant numbers
early in the
history of the Earth. These segments may have grown larger and
diversified in the manner suggested here, becoming
able to interact with some
specific amino acids before the emergence of the
genetic code. These suggestions are supported here by
many statistical tests on the tRNAs of prokaryotes.
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Mathematical Biology Seminar
Wedn Sept 21, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Steven Plotkin Dept of Physics, UBC
Title:How does a protein fold? The effects of structure, and a segue into
differential geometry.
Abstract:
The elusive theory for how a protein folds up to a
biologically functional structure has occupied researchers for the
last few decades. The difficulties stem from an incomplete knowledge
of an accurate Hamiltonian, as well as non-trivial aspects of polymer
physics that complicate the kinetics of folding. Here I will describe
some recent results showing that relaxation rates increase
significantly as the folding mechanism becomes increasingly
heterogeneous. A search for a suitable reaction coordinate leads to an
unsolved problem in differential geometry, namely a precise
mathematical formulation of distance between objects of
dimension > 0. A distance metric for two non-crossing space curves can be
formulated as a variational problem, mapping to the solution of a
partial differential equation. I will describe these developments and
discuss some possible future directions.
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Mathematical Biology Seminar
Wedn Sept 7, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Lindi Wahl U Western Ontario
Title:Modelling Experimental Evolution
Abstract:
In experimental evolution, populations of microbes are grown under
laboratory conditions for thousands of generations -- enough time for
significant evolutionary change to occur. The results of these
experiments in the past several years have shed enormous light on the
trajectories and outcomes of evolution. In parallel with this
experimental effort, we have developed mathematical models of
experimental evolution, deriving in particular the probability that
rare, beneficial mutations will emerge and invade the population. I
will give an overview of our techniques and results to date,
highlighting some interesting predictions of the model. For example,
we derive an optimal dilution ratio, that is, the length of time
populations should be allowed to grow in order to maximize the rate of
evolution. In addition, we predict that mutations which allow the
microbe to reproduce more quickly, as opposed to reproducing more
prolifically, are less likely to invade.
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Mathematical Biology Seminar
Wedn Aug 17, 2005 Time: 2:00 pm
Location: Rm 110 (downstairs), PIMS main facility, 1933 West Mall, UBC
This will be a double-feature, with the following two guest speakers:
Speaker: Athanasius (Stan) F. M. Maree Theoretical Biology, Utrecht
Title:Modelling Cell Movement Patterns during Chick Gastrulation
Abstract:
During gastrulation, the primitive streak is the first axial structure
to appear. The tip of the ingressing streak, called Hensen's node,
moves more than halfway across the blastoderm, after which it
regresses again. From half-maximal extension onwards, cells in the
streak start to differentiate from epithelial into mesenchymal cells,
and move as individual cells into the blastocoel, the space in between
the epiblast and the hypoblast. The cells that move away from the
streak show characteristic, 'though complex, cell migration patterns:
the cells just behind the node moved outward laterally, away from the
streak, but once the node has regressed past these cells, they move
back in again; the cells that leave the streak more posteriorly, on
the other hand, move out in lateral and posterior direction, giving
rise to a fan-shaped pattern of cell movement. We have studied how the
ingressing and regressing motion of the streak is entangled with the
migratory patterns of the mesenchymal cells using the cellular Potts
model. The strength of this model formalism is that the basic scale is
subcellular, allowing for a straightforward integration of information
related to cell adhesion, deformation, motion, shape and
chemotaxis. In our model, we describe the different celltypes
involved, such as the Hensen's cells, streak cells and mesenchymal
cells, as well as the production and decay of morphogens such as FGF4
and FGF8. With our model we are able to reproduce the intricate cell
motions of both streak and mesenchymal cells. Moreover, the model
allows us to compare cell trackings of the simulations with those
observed experimentally. We show how the established positive and
negative chemotaxis to FGF4 and FGF8 (whose fields are dynamically
changing due to cell motility and cell differentiation) combined with
cell adhesion, differentiation and division properties, form the basis
of the observed intricate cell movements.
Speaker: Veronica Albers Grieneisen Theoretical Biology, Utrecht
Title:Modelling Tumour Growth Dynamics
Abstract:
We explore quantitatively, through both experiments and computer
simulations, how the relationship between tumour structure, cell
phenotype and cell cycle regulation brings forth feedback mechanisms
that determine growth and invasiveness of cancer lineages. It is well
established that, on a phenomenological level, some populational
growth models can be adjusted with much success to experimental growth
curves of tumour cells. For example, the Gompertz model is widely used
to fit experimental data and obtain parameters that describe different
tumour lineages. However, a physical or biological interpretation of
the parameters is lacking. Measuring and analyzing both the growth
curve and the phenotypical characteristics of six different tumour
lineages, we were able to establish a novel interpretation of these
growth parameters in the light of phenotypical characteristics of the
individual cells that constitute the tumour. This part of the study
strongly suggested that especially cell deformation can be closely
linked to tumour cell growth. To verify the predictions and
theoretically understand the implications of such a dependency, we
incorporate the experimentally obtained cell phenotype regulation
mechanism hypothesis in simulations using the Cellular Potts
Model. Because cells exist on a mesoscopic level within this model,
cell adhesions and cohesions with substratum naturally bring forth
differentiated cell spreading and cell forms. By postulating an
intrinsic cell shape dependent mitosis mechanism, we demonstrate that
a variation in cell form can indeed regulate population growth as a
result of the emergent topology of the tumour. Thus, we are finally
able to link adhesion, cohesion and mitosis regulation properties with
global characteristics of a tumour, such as growth rates and degree of
malignancy. On a higher level, this work shows how the evolution of a
tumour generates certain distributions of cell phenotypes within the
tumour, which, influenced by intrinsic properties of the cells, also
determines the topology of the tumour itself. The manner in which cell
division is controlled in the light of these morphological signals
makes one of the differences between normal cells and altered cells.
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Mathematical Biology Seminar
Monday, Aug 15, 2005 at 2:00 pm
Location: Rm 110 (downstairs), PIMS main facility, 1933 West Mall, UBC
Speaker: Ying-Hen Hsieh, Department of Applied Mathematics,
National Chung Hsing University.
Taichung, Taiwan
Title:Candidate Genes Associated with Susceptibility to SARS-CoV
Abstract:
Ho et al. (2005, unpublished) observed that clinical severity of SARS is significantly associated with three genes, Fgl2(+158), CXCL10/IP-10(-938), and HO-1(-497). Using a compartment model and SARS data from the outbreak in Taiwan, we show that SARS infection rates do not vary significantly with severity of illness as often assumed. However, particular genotypes are associated with susceptibility to SARS-CoV. Furthermore, we show that the joint effect of some genotypes could also be significant for an individual's susceptibility to SARS.
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Mathematical Biology Seminar
Wedn Aug 10, 2005 Time: 2:00 pm
Location: Rm 110 (downstairs), PIMS main facility, 1933 West Mall, UBC
Speaker: Shaoshan (Carol) Huang BSc.CS, UBC 2005
Title:Modelling the metal ion hypothesis of Alzheimer's Disease
Abstract:
The widely accepted amyloid cascade hypothesis of Alzheimer's disease (AD)
proposes that the aggregation of amyloid-beta protein is the key to AD
pathogenesis, and the hypothesis is continuously modified in light of new
experimental evidence. Bush (Trends Neurosci., 2003) describes such a
modified model which implicates the brain metal ions, in particular, iron and
zinc, in contributing to the disease. Here I will present our attempt in
formulating a mathematical model from Bush's verbal descriptions, the
assumptions that are made explicit in the modelling process, and some results
in analyzing a reduced version of the model with realistic parameter values.
(Note: Ms. Huang is a USRA student with Leah Keshet and this talk is a summary of her project.)
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Break for summer due to travel and conferences elsewhere
Mathematical Biology Seminar
Wedn June 8, 2005 at 2:00 PM
Location: Rm 110 (downstairs), PIMS main facility, 1933 West Mall, UBC
Speaker: Toby Elmhirst Department of Mathematics, University of
Houston
Title:Adaptive Radiation as Pattern Formation in Phenotype Space
Abstract:
Adaptive radiation in sympatric populations is generally preceded
by
the emergence of distinct morphological types. I will describe how this
phenotypic polymorphism can be seen as the formation of pattern in phenotype
space through the mechanism known as symmetry-breaking. The appearance of
patterns in many biological, chemical and physical systems
has been explained in terms of the loss, or breaking, of symmetries of a
uniform homogeneous state. Using statistical arguments, a monomorphic
population can be identified with the homogeneous state and a polymorphic
population with the patterned state. Furthermore, these same statistical
arguments can be used to characterize the structure of the competitive
interactions within the population in terms of symmetry, and this structure
puts severe constraints on any system of nonlinear ODEs used to model the
adaptive phenotype dynamics of the population. This class of models provides
a natural framework in which polymorphism appears through a
``symmetry-breaking bifurcation".
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Mathematical Biology Seminar
Wedn April 27, 2005 at 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Amil Shah, MDCM, FRCPC, FACP Medical Oncologist, Vancouver Cancer Centre
Title: In Search of the Achilles Heel of Cancer
Abstract:
Normal cell growth is controlled by special groups of regulatory genes
(oncogenes and tumor suppressor genes), whose protein products convey
signals across the cell membrane to the cellular DNA. The signal pathways
interact with one another to form networks. These networks are complex
systems and each element of the network responds to various regulatory
molecules. All the different elements in the network may respond at the
same time to their regulatory molecules, and as such behave as a parallel-
processing network. To understand the integrated behavior of the network,
it is necessary to consider the simultaneous activity of all of the
elements at each moment as well as the temporal progression of their
activity patterns. There are two key features of the network.
i. Each element is directly regulated by only a few other molecular
variables; that is, they are sparsely connected.
ii. Almost all the elements are regulated according to a special class of
Boolean rules that govern their activity as a function of the activity of
the regulators acting on them; that is there are canalyzing functions.
Cancer develops through a multistage process that involves accumulation of
abnormalities in the function of several key regulatory genes. As a
consequence, the signal pathways are deregulated and the circuitry is
scrambled. Two possible outcomes are possible: the cell collapses and dies
or it reaches a new steady state (homeostasis) and survives. Thus, cancer
arises through disruptions in the signalling system with formation of a
new, albeit bizarre, homeostatic state.
Recently, a new class of molecularly targeted drugs have been crafted that
interact with the cellular biochemical signals. An understanding of the
topology of the cell-signalling network - its functional structure and the
architecture of its control modules - and how this is disrupted in cancer
would help in the rational design of therapy. The issues germane to this
include:
i. What is the best strategy to correct aberrant signalling in a network
with numerous pathways linked by intermediate nodes?
ii. Should serially connected processes be inhibited?
iii. What is the optimal combination of upstream and downstream target
nodes that must be blocked?
iv. What are the implications of the nonlinear relationships between the
signals and network parameters?
Prof Shah is also the
Chair, Gastrointestinal Tumor Group, BC Cancer Agency, and
Clinical Professor of Medicine, UBC, and
Clinical Skills Course Director (Year 2), UBC
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Mathematical Biology Seminar
Time: Wedn April 20, 2005 at 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Don Ludwig Emeritus, Dept of Matheamtics, UBC
Title:Uncertainty in Discount Models and Mitigation of Environmental Change
Abstract:
Recent analyses of economic discounting invalidate the customary
practice of discounting at a constant exponential rate, and reveal
large uncertainties in long-term discount rates. A proper treatment of
this uncertainty requires that we consider returns over a plausible
range of assumptions about future discounting rates. When returns are
averaged in this way, the schemes with the most severe discounting have
a negligible effect on the average after a long period of time has
elapsed. This re-examination of economic uncertainty provides support
for policies that prevent or mitigate environmental damage. We examine
these effects for three examples: a stylized renewable resource,
management of a long-lived species (Atlantic Right Whales), and lake
eutrophication.
This is joint work with W. A. Brock, and S. R. Carpenter.
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Mathematical Biology Seminar
Time: Wedn April 13, 2005 at 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Christopher Kribs Zaleta U Texas, arlington
Title:Vector consumption and contact process saturation
in sylvatic transmission of T. cruzi
Abstract:
Recent research in the transmission of the protozoan parasite Trypanosoma
cruzi, some strains of which cause Chagas' disease, suggests that consumption
of vectors by sylvatic hosts such as raccoons may play a role in maintaining
the transmission cycle in the wild. Since both hosts and vectors have been
observed to invade new ecological niches, it is important to consider the
effect vector consumption may have on vector density. For this reason we
consider a per capita contact rate which rises roughly linearly for low vector
densities and saturates for high densities. This paper analyzes the effects
of these features by superimposing a predator-prey structure on a host-vector
infection model (with first one, and then multiple, hosts). Outbreak behavior
follows classical threshold behavior via the reproductive number R_0, which
allows evaluation of this transmission avenue's relative importance.
For sufficiently sharp contact rate saturation, two locally stable vector
densities may exist.
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Mathematical Biology Seminar
Time: Wedn, April 6, 2005 at 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Adriana Dawes , Dept of mathematics, UBC
Title:
Modelling the spatial profile of barbed ends and filament density behind
the leading edge of a motile cell
Abstract:
Cells that move in response to an external signal are crucial for diverse
physiological processes such as embryogenesis, wound healing and immune
surveillance. Many such cells extend a long, flat, and broad lamellipod
which consists mainly of the protein actin. Actin polymerizes into polar
filaments with most filament barbed ends (the filament end favoured for
monomer addition) pointing toward the leading edge of a motile cell. I
will discuss a novel model that incorporates known biochemical events,
nucleation, capping, filament growth and depolymerization, to investigate
the spatial distribution of barbed ends and filament density behind the
leading edge. Parameter values in this model can have a spatial dependence
which we use to investigate the existence of a special zone near the
leading edge where capping is inhibited and nucleation is enhanced.
When some simplifying assumptions are made, we obtain an analytic solution
for the spatial profiles as well as an expression for the membrane speed
in terms of kinetic parameters. We perform numerical experiments that
produce experimentally testable predictions and compare the output of our
model to experimental data.
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Mathematical Biology Seminar
March 30, 2005, 1:30 pm --
Note: 1/2 an hour earlier than usual!
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Gustavo Carrero, Dept of Mathematics, University of Alberta
Title: Modelling the Compartmentalization of Splicing Factors
Abstract: Splicing factor compartments (SFC's) are heterogeneously
distributed compartments within the nucleus of eukaryotic cells
that are enriched in pre-mRNA splicing factors. We derive a
fourth-order aggregation-diffusion model that describes a possible
mechanism underlying the organization of splicing factors into
speckles. The model incorporates two hypotheses, namely (1) that
self-organization of dephosphorylated splicing factors, modulated
by a phosphorylation-dephosphorylation cycle, is responsible for
the formation and disappearance of speckles, and (2) that an
underlying nuclear structure plays a major role in the
organization of splicing factors. A linear stability analysis
about homogeneous steady-state solutions of the model reveals how
the self-interaction among dephosphorylated splicing factors can
result in the onset of spatial patterns. A detailed bifurcation
analysis of the model describes how phosphorylation and
dephosphorylation modulate the onset of the compartmentalization
of splicing factors.
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Mathematical Biology Seminar
March 23, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Yue Xian Li, Dept of Mathematics, UBC
Title: Pulsatile hormonal signals generated by networks of endocrine neurons: a review of recent development
Abstract:
The concentrations of many hormones in the blood show pulsatileX
oscillations with a period of a few hrs., called the ultra-dian rhythms.
These rhythms are usually superimposed on the well-known circa-dian rhythm
with a period close 24 hrs. The best studied example is the pulsatile
rhythm of GnRH (gonadotropin-releasing hormone) which drives the
rhythmicity in two hormones, LH (luteinizing hormone) and FSH
(follicle-stimulating hormone). LH and FSH control the reproductive
organs in both male and female in mammals. The period is about one hour
per pulse.
The GnRH pulses are generated by about 1,500 neurons specialized to
secrete GnRH in the hypothalamus of the brain. This rhythmicity was
revealed in early 70s. In early 80s, it was shown obligatory and
permissive for sexual maturity and reproduction in mammals.
Obligatory because the whole reproductive system is shutdown down if this
rhythm is missing or even if the frequency is not correct. Permissive
because introducing this rhythm in ``baby'' female monkeys prematurely
induces sexual maturation and menstruation. For this reason, some people
call puberty a Hopf bifurcation to dramatize the importance of the occurrence
of this rhythmicity around puberty.
A tumorized cell line of the GnRH neurons was successfully cultured in
1990. They have since been pulsing once per hour in lab cultures. Fifteen
years have passed, the mechanism underlying this rhythm remains obscure.
One recent experimental work by an old friend caught my attention
recently. It was a similar idea that he tried to sell me 10 years ago but
with one crucial addition. This new development made me believe that we
are very close to solving this puzzle. I will present this new development
in my talk.
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Mathematical Biology Seminar
March 16, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Jens Rademacher, Dept of Mathematics, UBC
Title: Global bifurcations, spectra and dynamics of travelling waves
Abstract:
Methods for the study of travelling waves that move with constant
speed and shape in one space dimension are presented. The main approach is
spatial dynamics, which views the spatial direction as the time axis. ODE
techniques allow to study the existence and bifurcation of such travelling
waves. Moreover, these methods allow to study the PDE spectra, and hence
stability, of travelling waves under different boundary conditions, in
particular large bounded and unbounded domains.
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Mathematical Biology Seminar
Wedn Mar 9, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Artem Cherkasov Division of Infectious Diseases, Faculty of Medicine, UBC.
Title: Reliability and network analysis in genomics
Abstract:
We establish that the occurrence of protein folds among genomes can be
accurately described mathematically with a Weibull function. Systems which
exhibit Weibull character can be interpreted with reliability theory
commonly used in engineering analysis. For instance, Weibull distributions
are widely used in reliability, maintainability and safety work to model
time-to-failure of mechanical devices, mechanisms, building constructions
and equipment.
Thus, we have found that the Weibull function describes protein fold
distribution within and among genomes more accurately than conventional
power functions which have been used in a number of structural genomic
studies reported to date and that relate protein fold distribution to the
scale-free architecture of fold evolutionary network.
The results of this work demonstrate that reliability analysis can provide
useful insights and testable predictions in the fields of comparative and
structural genomics.
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There will be no Mathematical Biology seminar on Mar 2, 2005 due to an
all-day meeting of diabetes researchers (beta-CAAN).
Mathematical Biology Seminar
Wedn Feb 23, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Colin Clark, Professor Emeritus, Dept of Mathematics, UBC
Title:A potpourri of Fishy Models
Abstract:
I will describe some new-ish models that pertain to fisheries
management. The models, mostly very simple, arose while I was writing
a book on fisheries. They relate to ITQs (Individual Transferable
Quotas) and MPAs (Marine Protected areas), and stuff like that. The
models could be extended in useful ways, given that fisheries
management seems to be headed in these directions. If you get tired
of fish models, I might switch to ant economics (but probably not).
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There will be no Math-Biology seminar on the week of Feb 16, 2005
due to mid-term break.
Mathematical Biology Seminar
Please NOTE special time and alternate room for this event!!
Wedn, Feb 9, 2005, 3:00 pm
Location: WMAX 110, PIMS main facility, 1933 West Mall, UBC
Speaker: Babak Pourbohloul, BC Center for Disease Control
Title:Control of Respiratory-borne disease outbreaks in populations: A Contact Network Theory Approach
Abstract:
A large class of infectious diseases spread through direct
person-to-person contacts. Respiratory-borne diseases like influenza,
tuberculosis and SARS, spread through the exchange of respiratory
droplets between people in close physical proximity to each other. The
patterns of these contacts tend to be highly heterogeneous. Explicit
models of the patterns of contact among individuals in a community,
contact network models, underlie a powerful approach to predicting and
controlling the spread of such infectious disease. Effective control of
respiratory infectious diseases requires quantitative comparisons of
quarantine, infection control precautions, case identification and
isolation, and immunization interventions. We use contact network
epidemiology to predict the impact of various control policies for both
a mildly contagious disease such as SARS and a more highly contagious
disease such as smallpox. The success of an intervention depends on the
transmissibility of the disease and the contact pattern among people
within a community. We illustrate that contact network epidemiology can
provide detailed and valuable insight into the fate and control of an
outbreak. Integrating these tools into public health decision-making
should facilitate more rational strategies for managing newly emerging
diseases, bioterrorism and pandemic influenza in situations where
empirical data are not yet available to guide decision making.
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Mathematical Biology Seminar
Wedn Feb 2, 2005 Time: 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Jonathan Alberts UW Biology, and Center for Cell Dynamics, FHL
Title:In silico reconstitution of Listeria motility exhibits complex
biological behaviors
Abstract:
We believe that fully understanding the complex (emergent) behavior
of cells requires mathematical modeling/simulation of the small-scale
details. I will describe our computer model of the motility of the
bacteria Listeria monocytogenes, a system well studied experimentally.
Our model simulates both the biochemical kinetics (often measured by
experiment) and the mechanical dynamics (which obey the laws of
classical mechanics) of this system in hopes of capturing and
understanding the complex system behaviors.
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Mathematical Biology Seminar
Wedn January 26, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dan Beamish, York University
Title: 50 Years Later: A Neurodynamic Explanation of Fitts' Law
Abstract:
Fitts' law is a robust model of the speed-accuracy trade-off inherent in human
movement developed by applying information theory to the sensory-motor system.
However, there are some major inconsistencies between the predictions of the
information-theoretic model and experimental data. We present an alternative
formulation of Fitts law, based instead on the neurodynamic assumption of
delayed perceptual feedback, and show that the experimental inconsistencies are
explainable as a consequence of delay within the nervous system.
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Mathematical Biology Seminar
Wedn January 19, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Dan Luciani Biophysics & Complex Systems Group, Department of Physics, Technical University of Denmark
(Lyngby, Den.)
Title: Self-sustained and forced oscillations of cytosolic Ca2+ and glucose metabolism in pancreatic islets
Abstract:
Over the years the basis of glucose-stimulated pulsatile insulin
secretion has been fruitfully studied through a combination of
experiments and mathematical modeling. We now know that the periodic
release of insulin from pancreatic islets is driven mainly by
synchronous oscillations in the concentration of cytosolic Ca2+ of
the electrically coupled beta-cells within the islets. These
oscillations are due to bursts of beta-cell electrical activity,
which stimulate Ca2+ entry through voltage-gated channels. Evidence
suggests that oscillatory metabolism may underlie the bursting
electrical behavior through modulation of ATP regulated potassium
(KATP) channels, but it remains unresolved to what extent
oscillations of beta-cell metabolism arise through a feedback
relationship with Ca2+.
In this seminar, I will present recordings that elucidate the
interrelation of glucose-induced oscillations in islet Ca2+ with
concurrent oscillations of islet NAD(P)H autofluorescence and
mitochondrial membrane potential. The experimental findings will be
compared to predictions made by existing beta-cell models.
Furthermore, I will briefly discuss results pertaining to the
in-vitro entrainment of endogenous islet oscillations by an
externally applied, sinusoidally varying, glucose forcing. Such
nonlinear frequency locking phenomena may conceivably be of
importance for inter-islet synchronization within the pancreas.
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Mathematical Biology Seminar
Wedn Jan 12, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Fred Brauer, Dept of Mathematics, UBC
Title:The Kermack-McKendrick epidemic model revisited
Abstract:
The Kermack-McKendrick epidemic model of 1927 is an age of infection model.
A special case, which is formulated as a two-dimensional system of
ordinary differential ordinary differentila equations, has often been
called the Kermack-McKendrick model. One of the products of the SARS
epidemic of 2002-3 was a variety of epidemic models including general
contact rates, quarantine, and isolation which can be viewed as age of
infection epidemic models and analyzed using the approach of the full
Kermack-McKendrick model. These models share the basic properties
that there is a threshold between disappearance of the disease and an
epidemic outbreak, and that an epidemic will pass through a population
without infecting the entire population.
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Applied Math/Mathematical Biology Seminar
Time: Wedn Jan 5, 2005, 2:00 pm
Location: Rm216, PIMS main facility, 1933 West Mall, UBC
Speaker: Anmar Khadra
Ph.D. Applied Math/Electrical Eng,
University of Waterloo
Title:The Synchronization of Chaos-Generating Systems Using
Impulsive Control Techniques with Applications to Communication
Security
Abstract:
When two or more chaotic systems are coupled, they may
exhibit synchronized chaotic oscillations. The synchronization of chaos is
usually understood as the regime of chaotic oscillations in which the
corresponding variables or coupled systems are equal to each
other. This kind of synchronized chaos is most frequently observed in
systems specifically designed to be able to produce this behaviour. One
particular type of synchronization, called
impulsive synchronization, which is based on impulsive control
techniques, has been recently applied to low
dimensional chaotic, hyperchaotic and spatiotemporal chaotic
systems. This synchronization technique requires driving one chaotic
system, called response system, by samples of the state variables of
the other chaotic system, called drive system, at discrete
moments. Lagrange stability of the synchronization error between
the chaotic systems involved, becomes the major
concern when discussing the dynamics of impulsive synchronization
theoretically. However, when dealing with this phenomenon numerically, the
concept of Lyapunov exponents of the synchronization error becomes the
main tool for analysis.
Due to the fact that chaos exhibits pseudo-random behaviour, it is
believed that it may be a promising tool in designing chaos-based secure
communication schemes with the aid of impulsive synchronization.
Therefore, the issue of robustness of synchronized chaotic
oscillations with respect to parameter variations and time delay, is a
very important issue when dealing with impulsive
synchronization and chaos-based secure communication. Since it is
impossible to design two identical
chaotic systems and that transmission and sampling delays in impulsive
synchronization are inevitable, robustness becomes a fundamental issue
in the models considered. Therefore analyzing robustness theoretically and
numerically is quite essential to understand the behaviour of
impulsive synchronization and to investigate the trade-off that occurs
between robustness and security in these chaos-based communication
schemes.
In this talk, we shall present the concept of impulsive
synchronization of chaos-generating systems, and give a description of its
applications to secure communication by discussing its robustness
and security.
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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.
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