






Abstracts for 2009 Mathematical Biology
Seminars 
Speaker: Eldon Emberly
Title: Optimization of Mutual Information in Genetic Networks
Return to seminar page
Abstract:
Cellular decisions rely upon a cell making some measurement
of its surroundings and then regulating its behaviour based on this
measurement. For many cellular processes this decision is regulated by
the transcriptional output of a gene which is regulated by a single
input which may exist in several possible states. Given the noise
inherent in the input signal and the chemical processes coupling the
input to the output, how well can the input states be measured by the
genetic network and is the genetic network optimized to maximize the
likelihood of determining the correct input state? Recently, this
problem has been analyzed in the context of mutual information. I will
discuss the application of mutual information to the problem of
morphogen readout in developing organisms, and will compare the
predicted optimal morphogen gradient for the early drosophila factor
Bcd to its experimental profile. Lastly, I will show how optimizing
mutual information for an organism that needs to infer a two state
environment which varies, leads to an optimal transcriptional response
with biologically realistic kinetic parameters.

Speaker: Prof. PikYin Lai
Title: Synchronization of cardiac cells growing in culture.
Return to seminar page
Abstract:
Synchronization of heterogeneous systems consisted of oscillatory
and passive elements are studied in cardiac myocytes
(CM)/fibroblasts (FB) cocultures. It is found that beating
clusters of CM surrounded by FB will be formed. The beatings of
the CM clusters are not correlated at early times but get
synchronized as the cultures mature. This synchronization can be
understood by a Kuramoto model with a time increasing coupling
strength. Our findings show that the growth of the coupling
strength between clusters is linear while the overall wave
dynamics of the system is controlled by the passive FB in the
system which presumably is growing exponentially. The variations of the frequencies towards synchronization are also modeled b
y the "frequency enhancement" effect for coupled excitable/oscillatory elements.

Speaker: David Drubin
Title: A mechanochemical model for endocytic vesicle formation
Return to seminar page
Abstract:
Formation of endocytic vesicles is a complex, dynamic process that couples
sequential protein recruitment and lipid modifications with dramatic shape
transformations of the plasma membrane. How the proper timing and
coordination of these events is achieved, and the vesicle scission
mechanism, are not understood. We address these questions by constructing
an integrated mathematical model based on four key ideas: (1) membrane
curvature and PI(4,5)P2 hydrolysis are mechanochemically coupled; (2)
curvaturesensing and curvaturedeforming activities constitute a positive
feedback loop for BAR domain protein recruitment; (3) the mechanochemical
coupling of events ensures the proper and robust temporal and spatial
sequence of endocytic events; and (4) vesicle scission is the result of an
interfacial force that develops at a lipid phase boundary. The model
quantitatively recapitulates the endocytic events in budding yeast in a
coherent manner, and explains key aspects of endocytosis in mammalian
cells.

Speaker: Anmar Khadra
Title: Investigating the role of IGRPspecific low avidity T cells in the
protection against T1D
Return to seminar page
Abstract:
Recent experimental observations have revealed that during the onset of
autoimmune Type 1 Diabetes (T1D), different clones of T cells with various T
cell avidities and protein specificities are naturally generated in diabetic
animal models. One particular protein, IGRP, is considered to be the most
dominant autoantigen, responsible for activating low and high avidity
IGRPspecific T cells via APCs. Although high avidity T cells destroy ~90%
of beta cell repertoire, leading to the abolishment of insulin secretion
crucial for glucose metabolism, low avidity T cells appear to play a
protective role. Several hypotheses concerning the kinetics of these low
avidity T cells and the effects of certain drug treatments on this
populations have been suggested. In this talk, we shall present series of
mathematical models that investigate these hypotheses and the outcome of
certain drug treatments. We shall examine the experimental data available so
far and explain certain features exhibited by the various clones of T cells.

Speaker: Nessy Tania
Title: Mathematical models of calcium regulation in cardiac cells
Return to seminar page
Abstract: Calcium is a ubiquitous signaling molecule involved in the regulation of a
wide range of processes. In cardiac cells, calcium plays a key role in
mediating the electricalexcitation and contraction processes. Three
mathematical models of calcium regulation are derived and analyzed. Using a
simplified model, we first show that release localization, diffusion, and
singlechannel activity modulate the onset of calcium oscillations. These
factors are of particular importance in cardiac cells where calcium release
is spatially inhomogeneous and inherently stochastic. However, models that
take these effects into account are computationally expensive to simulate.
Using a variety of asymptotic approximations, we derive a simplified yet
reliable model of stochastic calcium flux through a release unit. Finally,
we use a wholecell model to explore the role of calcium oscillations in the
generation of periodic action potentials based on recent experimental
studies on the sinoatrial node and embryonic cardiac cells.

Speaker: Kurt Haas
Title: Imaging single neuron growth and circuit activity in the awake
developing brain: How does activity sculpt structure and function?
Return to seminar page
Abstract:
Using techniques to label individual neurons within intact brains and
in vivo twophoton rapid timelapse microscopy we image dynamic growth
of neuronal dendritic arbors in awake Xenopus tadpoles. Our result
suggest a strong role of neuronal transmission in directing dendrite
growth by influencing synapse formation, which in turn, stabilize new
dynamic dendritic branches. By loading the entire brain with calcium
sensitive dyes, we find that brain neuron responses to sensory stimuli
can be increased or decreased by training with sensory input.
Combining single neuron morphometric and network activity analysis we
hope to understand how neuronal transmission and developmental
experience influences brain circuit form and function.

Speaker: Scott Grandison
Title: It's tough at the tip: Mechanical models of polar growth.
Return to seminar page
Abstract:
From cell morphogenesis to protein docking, shape and shape dynamics
have a vital role to play in our understanding of biological systems.
In this talk we will discuss a novel method
for extracting important shape information based on image processing,
minimum energy surfaces and the calculus of variations which allows us
to infer some of the mechanical properties of a tip growing
Arabidopsis root hair
from timelapse image data. We have developed a computer simulation,
based on a network of interconnected springs which enable our
formulation to be validated against further experimental data.

Speaker: Paul Tian
Title: Mathematical Study of Brain Tumor Therapies.
Return to seminar page
Abstract:
Glioma is the most serious malignant brain tumor. In order to improve the
efficacy of therapies, it is important to understand its progression with
therapies and its genesis. In this talk, I will first present our effort in
understanding of glioma progression with different therapies in terms of
mathematical models. The first model is about virotherapy of glioma, which
is a free boundary problem with five nonlinear partial differential
equations. Virotherapy is a promising treatment for malignant solid tumors,
and it is now in animal experimental stage. In order to treat human glioma
by virotherapy, it is critical to understand all factors involved in the
therapy. Our model finds an important factor burst size of virus, and the
effect of immunosuppression drug cyclophosphamide in animal experiments.
The model prediction has been verified by experimental results. The second
model is about radiotherapy plus chemotherapy after surgical resection,
which is a twocomponent free boundary problem. After surgery, the tumor
progression depends on the degree of resection and radiation, and a
particular drug. We use human data to estimate parameter values, and the
model can predict the mean survival times of patients who undergo different
protocols of treatments.

Speaker: PikYin Lai
Title: Synchronized Bursting and Growth of cultured neuronal network: experiments & model.
Return to seminar page
Abstract:
Synchronized bursting is observed in cortical neuronal cultures in vitro when the neuronal network is incubated
for a sufficiently period of time. The synchronized bursting frequency of the network is found to be much slower than the
characteristic time scale of a neuron and increases with the network connectivity. We present a detailed analysis and
theoretical growth models to account for the experimental data on the growth of cortical neuronal networks. The bursting
frequency (f) during SF of the networks is found to be an increasing function of k. In particular, the special form of
P(k)~ exp(k/ko) gives the experimental observed result that f is characterized by a critical age tc and a critical
frequency (fc) as: f = fc + fo log(t/tc). The growth of the network is consistent with the model of an early enhanced
growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Our electrophysiological
measurements using doublepatch techniques reveal that even though the bursting frequencies are synchronized, the
intraburst spikes are not. We present a mean field model of the neural network that combines a FitzHugh Nagumo (FHN)
model with an additional dynamic variable. This new variable is slower than those in the FHN model. It enables the neuron
firing to be inhibited and generates interspike intervals (ISI) with long time scales resulting in bursting.

Speaker: Geoff Wasteneys
Title: Dynamic Properties of Microtubules in Plant Cells, with Implications for Spatial Organization, Growth and Development.
Return to seminar page
Abstract:
Microtubules are dynamic polymers found in all eukaryotic organisms that build the cellular machines that separate chromosomes, polarize the cytoplasm, direct expansion and divide cells. Interestingly, plant cells lack the central microtubuleorganizing centres common in animal cells but still manage to organize microtubules into complex arrays.
The research in my laboratory explores how the dynamic properties of microtubules, which we can now quantify in live cells using fluorescent reporter proteins, help to determine the spatial organization of microtubule arrays, and how these arrays in turn control the growth, morphology and performance of plants. I will outline how genetic approaches to identify key accessory proteins that modulate microtubule dynamics are generating experimental tools for understanding the mechanisms that drive organization of the microtubule arrays. Comparing the dynamic behaviour of microtubules in mutant lines that are defective in one or more of these accessory proteins enables us to test models of the molecular mechanisms that drive microtubule organization. We are currently using this knowledge to explore the role microtubules play in the mechanical properties of the cellulosic cell wall, the helical handedness of elongating organs, and even the polar transport of the hormone auxin.

Speaker: Matthew Onsum
Title: Analysis of immune cell chemotaxis and signal integration
Return to seminar page
Abstract:
In response to an injury, immune cells are recruited to fight off infecting microbes and clear cellular damage. A number of chemicals, called chemoattractants, are produced at or near sites of infection and inflammation and diffuse into the surrounding tissue. Immune cells sense these chemoattractants and move in the direction where their concentration is greatest, a process termed chemotaxis, and thus locate the source of the attractants and associated targets. In this talk I will present my work using mathematical modeling and experiments to understand how immune cells detect and interpret multiple chemoattractants and convert these signals into directed migration. I will conclude my talk by discussing the application of this work, and mathematical modeling in general, to the drug discovery process in the pharmaceutical industry.

Speaker: Ryan Gutenkunst Title:
Sloppiness in biochemical modeling and evolution
Return to seminar page Abstract:
The dynamics of complex biochemical networks typically depend on many
parameters (e.g. reaction rate constants). I show that mathematical models
of such networks exhibit a universal "sloppy" pattern of parameter
sensitivities; their dynamics are exponentially more sensitive to changes in
some combinations of parameters than others. For model builders this
suggests that predictions will be much more efficiently constrained by
fitting parameters than by directly measuring them. I also explore the
evolutionary consequences of sloppiness in the context of Fisher's
geometrical model. Sloppiness has little affect on the first step in an
adaptive walk, but it may substantially slow the longterm pace of
adaptation.

Speaker: Vered RomKedar Title:
Novel strategies for GCSF support of severe prolonged neutropenia.
Return to seminar page Abstract:
We develop, in an axiomatic fashion, structurally stable mathematical
equations that describe the GCSFneutrophil dynamics (the majority
of the white blood cells are neutrophils. G CSF is a factor that may
be injected to help patients produce more neutrophils). We then show
that a variant of this model adequately describes the neutrophils
dynamics after chemotherapy treatments with various support protocols.
A grading for neutropenia (the dangerous drop in the neutrophil's
level) and corresponding tailored GCSF treatments are proposed and
are shown to be robust to parameter variability. Our results clarify
and revise the current American Society of Clinical Oncology
recommendations for GCSF administration in neutropenia following
intensive chemotherapy regimens. As all our recommendations correspond
to clinically available protocols, a framework for a prospective
randomized clinical trial is proposed.

Speaker: Babak Pourbohloul Title:
Emerging Infectious Disease, Pandemic Preparedness and Mathematical Models: How to Prepare When We Don't Know the Enemy?
Return to seminar page Abstract:
The underlying contact structure among individuals that determines the pattern of disease transmission and the progression in time of this pattern are two crucial elements in understanding and controlling communicable disease spread within a social setting. Mathematical models of infectious disease that are in principle analytically tractable, have taken two general approaches in incorporating these elements. The first approach, generally known as compartmental models, addresses the time evolution of disease spread at the expense of simplifying the pattern of transmission. On the other hand, the second approach  contact networks  incorporates detailed information of underlying contact structure among individuals. While providing accurate estimates on the final size of outbreak/epidemics, this approach in its current formalism, loses track of the time progression of outbreaks. So far, the only alternative to integrate both aspects of disease spread simultaneously, has been to abandon the analytical approach and rely on computer simulations. Although, powerful modern computers can perform an enormous amount of simulations at an incredibly rapid pace, the complex structure of `realistic' contact networks along with the stochastic nature of disease spread pose a serious challenge to the ability of the computational techniques to the robust analysis of disease spread in large populations in real time. An analytical alternative to this approach is lacking. We offer a new analytical framework, which incorporates both complexity of contact network structure and time progression of disease spread. Furthermore, we demonstrate that this framework works equally effective for finite and `infinite'size networks.

Speaker: Nick Hill Title: Modelling Abdominal Aortic Aneurysms
Return to seminar page
Abstract:
This is the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is treated as a twolayer, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural recruitment and fibre density
variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm agree with those observed in vivo. An asymmetric aneurysm with spinal contact is also considered, and the stress distributions are consistent with previous studies. Additionally,
the dynamic properties of the AAA are calculated for different stages in its development, and the evolution of clinically measurable mechanical properties compare well with published physiological data.
Watton, P.N., Hill, N.A. & Heil, M. ``A mathematical model for the growth of the abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 3, pp. 98113, 2004
Watton, P.N. & Hill, N.A. ``Evoloving mechanical properties of a model of abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 2007, DOI: 10.1007/s1023700701159

Speaker: Xiaoyu Luo Title: Dynamic simulation of mitral valve using the immersed boundary method
Return to seminar page
Abstract:
The dynamic behaviour of a novel chorded mitral prosthesis is studied using an immersed boundary model. To investigate the mechanical behaviour of the mitral design under physiological flow conditions without having to model the left ventricle, we make use of in vivo magnetic resonance images of the left ventricle. The relative motion of the mitral annulus and the papillary muscle regions of the ventricle determined from these MRI images is then used as a prescribed boundary condition for the chorded mitral valve in a dynamic cycle. Results show that without the proper functioning of the papillary muscle, the mitral prosthesis can suffer from an intolerable overstretch during systole compared with laboratory tests in which the mitral chordae are fixed in space. This turns out to be the key weakness of the current design. The mechanical performance of the prosthesis is compared with recent studies of native porcine valves; differences in mechanical behaviour are observed. Potential improvements for the design and future research projects are also discussed.

Speaker: Angela Reynolds Title: Mathematical Models of Acute Inflammation
Return to seminar page
Abstract: Acute inflammation involves both pro and anti inflammatory
components. The balance between these responses is key to the survival
of an insult. In severe cases, unbalance can result in multiple organ
dysfunction (MODS). MODS is characterized by sequential organ failure
caused by an overactive immune system that persists despite treatment
of the initial insult. In order to explore treatments for MODS we have
developed multiple models of acute inflammation.
These models were constructed through a modular approach where the
dynamics of multiple subsystems were analyzed. The subsystems were
then merged to form the full model. This approach ensures that known
dynamical features of component interactions, such as bistability,
excitability, and bifurcation structures, are present in the model
dynamics.
We will consider three models accounting for various aspects of
acute inflammation. The first will focus on the dynamics between pro
and antiinflammation. The second models the communication between the
tissue and blood, which is essential in mounting a successful response
to pathogen. The third models acute inflammation in the lung and its
effects on gas exchange. Creating these models is the first step in
simulating the spread of inflammation between organs.

Speaker: Richard Allen Title: Modelling the Endothelial Cell Response to Fluid Flow
Return to seminar page
Abstract: Following the onset of shear stress due to fluid flow endothelial
cells polarise and elongate in the direction of flow. How the
mechanical signal is transformed into an organised and directed
response is poorly understood. A multiscale cellular Potts model
promises to aid investigation of this question. A 3D virtual cell
defines the fluid flow via a boundary integral representation,
solution of which gives the force over the surface of the cell. A
framework of how to link this to models of Rho GTPase
interaction, actin filament alignment and Arp2/3 induced actin
polymerisation will be described.

Speaker: Jessica Conway Title: Superlattice Patterns in Oscillatory Systems Forced at Multiple Resonant Frequencies
Return to seminar page
Abstract:
Superlattice patterns and quasipatterns have been wellstudied in waves on the
surface of
vertically vibrated
viscous fluids (Faraday waves). We show that such patterns, comprised of 4 or more
Fourier modes at
different orientation, can also be obtained in systems undergoing a Hopf bifurcation
to spatially
homogeneous oscillations if they are exposed to a spatially homogeneous forcing with
judiciously
chosen time dependence with frequencies near the 1:1, 1:2, and 1:3resonance. For
weak forcing
such systems can be described by a suitably extended complex GinzburgLandau
equation with time
periodic coefficients. Using
Floquet theory and weakly nonlinear analysis we obtain the amplitude equations for
simple patterns
(comprised of 1, 2, or 3 modes) as well as superlattice patterns comprised of more
modes.
Exploiting spatiotemporal resonances we stabilize subharmonic 4 and 5mode
patterns. We confirm
our analysis through direct numerical simulations of the GinzburgLandau equation.
We also show the
possibility of such
complex patterns in the laboratory setting by using system parameters reported for
experiments on
the oscillatory BelousovZhabotinsky reaction and explicitly demonstrating that the
forcing
parameters can
be tuned such that 4mode patterns are the preferred patterns.

Speaker: Ben Vanderlei Title: Error Estimates for Numerical Solutions of Interface Problems
Return to seminar page
Abstract:
In order to make numerical approximations more useful in
application settings it is important to understand and, if possible, to
quantify the error introduced by approximating the solution of the problem
using numerical methods. I will discuss the results of applying a
modification of the Method of Nearby Problems to compute error estimates.
I will present first the results for a continuous problem and then discuss
interface problems. The model interface problem will be an elliptic PDE
with a coefficient which is discontinuous across an internal boundary. I
will present the Immersed Interface solution of this problem and the
development of an error estimate. We will also look at solutions obtained
using regularization methods and the additional error introduced by
regularizing the problem.

Speaker:Somdatta Sinha Title: Collective Behaviour in Multicell Systems
Return to seminar page
Abstract:
Robust synchronized functional dynamics are commonly observed in biological
cell populations and spatially extended biological systems, e.g., tissues.
These are fascinating examples of collective behaviour. To investigate the
roles of local cellular dynamics and interaction strength in the
spatiotemporal dynamics of cellcollectives of different sizes, we studied a
model system consisting of a ring of coupled cells incorporating an
autoregulated, threestep biochemical pathway. The isolated individual
cells can display complex dynamics as a result of the nonlinear interactions
common in cellular processes. On coupling the cells to nearest neighbours,
through diffusion of the pathway end product, the ring of cells yields a
host of interesting and unusual dynamical features for varying interaction
strengths and system sizes. But robust complete synchronization can be
induced in these coupled cells with a small degree of random coupling among
them even where regular coupling yielded only intermittent synchronization.
The example of beta cell dynamics in pancreatic islets will be discussed.

Speaker: Sido Nagano Title: Receptors as a master key for synchronization of rhythms
amoebae know the strategy of the crystal growth?
Return to seminar page
Abstract:
Unicellular amoeba called Dictyostelium discoideum has attracted a lot of atten
tion recently
as a model system for the study of multicellular morphogenesis and pattern form
ation. When
starved, they aggregate and form a multicellular organism. During the aggregati
on process,
amoebae communicate by periodically producing and relaying cAMP signals (chemic
al signals).
From the modeling study of Dictyostelium's survival strategy, we have derived a
simple, but
general scheme to achieve synchronization of rhythms, and clarified that biolog
ical receptors
work as apparatuses that can convert external stimulus to the form of nonlinear
interaction
within individual oscillators. The derived scheme is very simple mathematically
, but surprisingly
powerful. We can apply an essence of Dictyostelium's survival strategy not only
to other
biological systems (for example, pancreas), but also to crystal growth and elec
tric circuit design.

Speaker: Gideon Ngwa
Title: The population dynamics of the malaria vector
Return to seminar page
Abstract:
A deterministic differential equation model for the
population dynamics of the human malaria vector is derived and studied.
Conditions for the existence and stability of a
nonzero steady state vector population density are derived.
These reveal that a
threshold parameter, the vectorial basic reproduction
number, exist and the vector can established itself in the
community if and only if this parameter exceeds unity.
When a nonzero steady state population density exists,
it can be stable but it can also be driven to instability
via a Hopf Bifurcation to periodic solutions, as a
parameter is varied in parameter space. By considering
a special case, an asymptotic perturbation analysis is
used to derive the amplitude of the oscillating solutions
for the full nonlinear system. The present modelling
exercise and results show that it is possible to study the
population dynamics of disease vectors, and hence
oscillatory behaviour as it is often observed in
most indirectly transmitted infectious diseases of humans,
without recourse to external seasonal forcing. In this
communication, we derive and study a simple model for
the dynamics of the human malaria vector based on the
simple idea that the mosquito has a human biting habit.
Since it is the mosquito that actively seeks and bites human beings, this assumption, which has been used successfully to model the
dynamics of malaria transmission Ngwa et al. [1, 2, 3],
may be seen as a restricted form of homogeneous mixing
based on the idea that the mosquito has a human biting habit.
The concept of the existence of a basic reproduction number,
R0, in models has been addressed by Porphyre et al. [4],
Diekmann et. al. [5]. In our formulation, R0 depends
on a mass action contact rate tau* as well as on the
probability of the mosquito obtaining a successful
blood meal p in the sense that R0 goes to 0 whenever p goes to 0
or tau* goes to 0, and saturates to a positive nonzero value when
p goes to 1 and tau* becomes infinite .
[1] Ngwa, G. A., Modelling the dynamics of endemic malaria in growing populations. Discrete and Continuous Dynamical SystemsÐSeries B Vol 4 No. 4 (2004), 11731202. [2] Ngwa, G. A., Ngonghala, C. Ngeh and Sama Wilson, N.B, A model for endemic malaria with delay and variable populations. Journal of the Cameroon Academy of Sciences, Vol. 1 No. 3 (2001), 168186. [3] Ngwa, G. A and Shu, W. S., A mathematical model for endemic malaria with variable human and mosquito populations. Math. and Comp. Modelling, 32(78) (2000), 747763. [4] Porphyre T. Bicout D. J., Sabatier P., Modelling the abundance of mosquito vectors versus flooding dynamics. Ecological Modelling 183 (2005) 173181. [5] Diekmann O., Heesterbeek J.A.P and Metz J.A.J. On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365382.

Speaker: Heather Hardway Title: Modeling Genetic Networks in the Fruit Fly
Return to seminar page
Abstract:
Over the past century, the Drosophila melanogaster (fruit fly) gene network has become one of the most studied and well
understood. This is especially true of the genes involved in the anteriorposterior axis specification, the first step
in spatially organizing the developing embryo. However, a new feature of this system was recently discovered:
positional noise filtering. Gene products were shown to have high specificity with respect to positional location,
despite receiving noisy information from upstream regulators. I will discuss reactiondiffusion models for this system
and the results of a parameter search for such robust networks. In addition, I will present some unexpected nonlinear
phenomenon possible in these gene networks, including tango waves in an activatorinhibitor system.

Speaker: Caz Taylor Title: Finding optimal behavior using decision rules in an individualbased model
Return to seminar page
Abstract:
We describe a modeling approach in which individuals are able to use
information about their state and the environment to formulate
behavioural rules that optimize fitness. We model the decision
probability as a function of weighted input or state variables. We then
use a search optimization algorithm (simulated annealing) to find the
rule weights so that a series of decisions made by an individual
maximize a known fitness function. The advantage of this individual
rulebased approach is that we can optimize behaviour in an environment
that includes complex interactions, such as densitydependence. We
apply this approach to the migration behavior of Western Sandpipers
(Calidris mauri), moving sequentially through a set of stopover sites
along the North American Pacific coast and optimizing arrival time at
the breeding grounds. The departure probability of each individual at
each stopover site is a function of four state variables (i) whether or
not the individual is on time, (ii) the individual fuel load, (iii)
availability of food, and (iv) risk of predation. The latter two
variables depend not only on the individual but on the density of
conspecifics and therefore on the behavior of all other
individuals. We investigate how different types of density dependence
affects the patterns of migration.

Speaker: Sally Otto and Rich FitzJohn
Title: Inferring the past for traits that alter speciation and extinction
rates
Return to seminar page
Abstract:
We will describe work by ourselves and coauthors Wayne Maddison and
Peter Midford to build a likelihoodbased approach to infer how
speciation and extinction rates depend on the state of a particular
character. The phylogenetic tree of a group of species contains
information about character transitions and about diversification:
higher speciation rates, for example, give rise to shorter branch
lengths. The likelihood method that we have developed uses all of
the information contained in a phylogeny and integrates over all
possible evolutionary histories to infer the speciation and
extinction rates for species with different character states. Our
method can be used to provide more detailed information than previous
methods, allowing us to disentangle whether a particular character
state is rare because species in that state are prone to extinction,
are unlikely to speciate, or tend to move out of that state faster
than they move in.

Speaker: Jana Gevertz
Title: Multiscale Mathematical Modeling of Heterogeneous Tumor Growth
Return to seminar page
Abstract:
An in silico tool that can be utilized in the clinic to
predict neoplastic progression and propose individualized treatment
strategies is the holy grail of computational tumor modeling. As we
have the longterm goal of developing such a simulation tool, we have
worked over the years to address a number of tumorrelated questions
using variations of one theoretical model. In this talk, I will focus
on both the implementation of, and the results drawn from, several of
the model variants. Questions we have addressed through our modeling
efforts include:
1. How do we develop a minimalistic quantitative model of tumor
progression?
2. What effects do organ geometry and topology have on tumor size,
shape and spread?
3. How does an evolving vasculature impact tumor dynamics?
4. What effects do genetic mutations have on patient prognosis?
After looking at a set of model variants that allows us to answer each
of these questions, I talk about recent efforts to merge these models
into one comprehensive cancer simulation tool. I use the merged model
to highlight biological features that must be considered in a
clinicallyrelevant tumor growth algorithm and to test the impact of
vasculartargeting treatment strategies.

Speaker: YueXian Li
Title: Modeling Hormonal Rhythms in a Network of Endocrine Neurons
Return to seminar page
Abstract:
The regulation of reproductive function and fertility is ultimately controlled by
a pulsatile signal of gonadotropinreleasing hormone (GnRH). GnRH is synthesized and secreted by a
few hundred GnRH neurons in the hypothalamus that work in synchrony to produce this pulsatile rhythm.
The mysteries surrounding the rhythmogenesis in GnRH neurons remain defiant
to any conventional knowledge of rhythmgeneration in neuronal networks.
Efforts to crack this puzzle have been pushing the frontier of classical neuroscience that traditionally
only focused on ionotropic channel events with time scales of milliseconds to the inclusion of metabotropic
receptors, second messengers, vesicle transportation and docking,
autocrine/parcrine regulations, as well as genetic events. Mathematical modeling of this rhythm
gives rise to challenging nonlinear mathematical problems one has never encountered before.
This talk will present a brief summary of important progress in recent years including our own contributions
to solving this puzzle.

Speaker: Alexander Verkhovsky
Title: Organization and dynamics of motile machinery in a simple
cell
Return to seminar page
Abstract:
Understanding cell migration as an integrated physical phenomenon
requires a combination of experimental and theoretical studies, and
appropriate model systems. Fish epidermal keratocytes exhibit a
simple and regular organization and motion pattern and therefore
represent a favorable system to understand how the molecular
machinery is orchestrated to produce coordinated behavior at a
cellular level. We use a combination of experimental imaging,
micromanipulation, and computational approaches to evaluate
structural and dynamical parameters of actin network, map assembly
and motion of actin and myosin II during migration, and to
investigate the relationship between cytoskeletal dynamics and
generation of motile forces. The results indicate the mechanism of
generation of contractile forces and suggest several redundant modes
of cell migration.

Speaker: Gareth Leng
Title: Modeling a model system; bursts and pulses in neuroendocrine neurones
Return to seminar page
Abstract:
Peptides in the hypothalamus are not like conventional neurotransmitters; their release is not particularly associated with synapses, and their long halflives mean that they can diffuse to distant targets. Peptides can act on their cells of origin to facilitate the development of patterned electrical activity, they can act on their neighbours to bind the collective activity of a neural population into a coherent signalling entity, and the coordinated population output can transmit waves of peptide secretion that act as a patterned hormonal analogue signal within the brain. At their distant targets, peptides can reprogramme neural networks, by effects on gene expression, synaptogenesis, and by functionally rewiring connections by priming activitydependent release.
My lab has studied mainly the oxytocin and vasopressin neurones of the hypothalamus, these neurones fire in distinctive patterns that govern and in turn are governed by the peptide secretion that they induce. Oxytocin cells display remarkable synchronised bursts, that arise through emergent properties of an interactive network; vasopressin cells also burst, but asynchronously in a very different way and for very different reasons. In their different ways, these two neuronal systems have become important model systems in neuroscience; in this talk I will talk about modelling these model systems.
(1) Leng G, Brown C, Sabatier N, Scott V (2008) Population dynamics in vasopressin neurons. Neuroendocrinology PMID: 18667805.
(2) Leng G, Ludwig M (2008) Neurotransmitters and peptides: whispered secrets and public announcements. Journal of Physiology Oct 9. [Epub ahead of print].
(3) Rossoni E, Feng J, Tirozzi B, Brown D, Leng G, Moos F (2008) Emergent synchronous bursting of oxytocin neuronal network. PLoS Computational Biology Jul 18;4(7):e1000123.PMID: 18636098.
(4) Leng G, Macgregor D (2008) Mathematical modelling in neuroendocrinology Journal of Neuroendocrinology 20: 713718 PMID: 18513205.

Speaker: Sohrab Shah
Title: Model based approaches to array CGH data analysis
Return to seminar page
Abstract:
DNA copy number alterations (CNAs) are genetic changes that can produce
adverse effects in numerous human diseases, including cancer. CNAs are
segments of DNA that have been deleted or amplified and can range in size
from one kilobases to whole chromosome arms. Development of array
comparative genomic hybridization (aCGH) technology enables CNAs to be
measured at submegabase resolution using tens of thousands of probes.
However, aCGH data are noisy and result in continuous valued measurements of
the discrete CNAs. Consequently, the data must be processed through
algorithmic and statistical techniques in order to derive meaningful
biological insights. We introduce modelbased approaches to analysis of aCGH
data and develop stateoftheart solutions to three distinct analytical
problems.
In the simplest scenario, the task is to infer CNAs from a single aCGH
experiment. We apply a hidden Markov model (HMM) to accurately identify
CNAs from aCGH data. We show that borrowing statistical strength across
chromosomes and explicitly modeling outliers in the data, improves on
baseline models.
In the second scenario, we wish to identify recurrent CNAs in a set of aCGH
data derived from a patient cohort. These are locations in the genome
altered in many patients, providing evidence for CNAs that may be playing
important molecular roles in the disease. We develop a novel hierarchical
HMM profiling method that explicitly models both statistical and biological
noise in the data and is capable of producing a representative profile for a
set of aCGH experiments. We demonstrate that our method is more accurate
than simpler baselines on synthetic data, and show our model produces output
that is more interpretable than other methods.
Finally, we develop a model based clustering framework to stratify a patient
cohort, expected to be composed of a fixed set of molecular subtypes. We
introduce a model that jointly infers CNAs, assigns patients to subgroups
and infers the profiles that represent each subgroup. We show our model to
be more accurate on synthetic data, and show in two patient cohorts how the
model discovers putative novel subtypes and clinically relevant subgroups in
two types of lymphoma.

Speaker: Vipul Periwal
Title: Dynamics of Adipose Tissue Growth
Abstract:
Return to seminar page
Adipose tissue grows by two mechanisms: hyperplasia (cell number increase) and hypertrophy (cell size increase). Genetics and diet affect the relative contributions of these two mechanisms to the growth of adipose tissue in obesity. To address adipose tissue growth precisely, we developed a mathematical model describing the evolution of the adipose cellsize distributions as a function of the increasing fat pad mass, instead of the increasing chronological time. Our model describes the recruitment of new adipose cells and their subsequent development in different strains, and with different diet regimens, with common mechanisms, but with diet and geneticsdependent model parameters. Hyperplasia is enhanced by highfat diet in a straindependent way, suggesting a synergistic interaction between genetics and diet. Moreover, highfat feeding increases the rate of adipose cell size growth, independent of strain, reßecting the increase in calories requiring storage. Additionally, highfat diet leads to a dramatic spreading of the size distribution of adipose cells in both strains; this implies an increase in size ßuctuations of adipose cells through lipid turnover.
Speaker: Will Heuett
Title: Modeling Metabolism in Pancreatic BetaCell Mitochondria
Abstract:
Pancreatic betacells sense the ambient bloodglucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. I will present a model of betacell mitochondrial respiration, ATP synthesis, and ROS production in response to glucose and fatty acid stimulation, based on available data in the literature and mathematical models derived from first principles. The model explains experimental observations of the nonohmic rise in the passive protonleak rate at high membrane potential and its dependence on increased ROS production. It also predicts that glucosestimulated insulin secretion is inhibited by longterm fatty acid exposure, but can be enhanced by inhibiting uncoupling protein activation and promoting mitochondrial biogenesis. Using glucose and fatty acid profiles from individuals, I will show that there is a negative correlation between the amount of ROS produced per ATP, as predicted by the model, and the individual insulin sensitivities. Finally, I will discuss how the model can be used to predict the cpeptide and insulin secretion rate and provide a quantitative description of betacell function for a single individual.
Return to seminar page

Speaker: Joe Yuichiro Wakano
Title: Origin of culture: an evolutionary model of social learning
Abstract:
Social learning is an important ability seen in a wide range of animals. Especially, humans developed the advanced social learning ability such as language, which triggered rapid cultural evolution. On the other hand, many species, such as viruses, rely on genetic evolution to adapt to environmental fluctuations. Here we propose an evolutionary game model of competition among three strategies; social learning, individual learning, and genetic determination of behavior. We identify the condition for learning strategies to evolve.
Return to seminar page




 