






Abstracts for 20062007 Mathematical Biology
Seminars 
Speaker: Lazar Z. Krsmanovic Title:
Pulsatile GonadotropinReleasing Hormone Secretion: Roles of G Protein
Coupled Receptors, Second Messengers and Ion Channels Return to seminar page Abstract:
The integrated activity of the hypothalamic gonadotropinreleasing hormone
(GnRH) neuronal network, and the pulsatile release of GnRH at the median
eminence, is essential for the episodic mode of pituitary gonadotropin
secretion and for the maintenance of normal gonadal function. GnRH receptor
was found to be expressed in GnRH neurons and their immortalized
counterparts (GT17 cells). This suggested that GnRH released from
hypothalamic GnRH neurons could exert autocrine actions upon its cells of
origin and contributes to the pulsatile secretion of GnRH. Patch clamp
recording from identified GnRH neurons showed irregular action potential
(AP) firing with transition between narrow, high spike amplitude rhythmic
firing, and intervals of broader, lower spikeamplitude, burstlike AP
firing. Treatment of hypothalamic GnRH neurons with 10 nM GnRH increased
the occurrence of highfrequency broad APs with unchanged decay constants
for fast afterhyperpolarization (fAHP) and medium (mAHP). In contrast,
treatment of hypothalamic GnRH neurons with 1 M GnRH abolished mAHP
current, but did not affect the occurrence of fAHP current. That was
followed by subthreshold afterdepolarization potential (ADP) and
significant reduction of the frequency of AP firing. These data indicate
that spontaneous firing of APs in hypothalamic GnRH neurons determines the
profile of afterhyperpolarization currents and consequently mediates firing
frequency and the spikeprofile. Constitutive and agonistinduced hetero
oligomerization of GnRH receptor and G proteincoupled receptor 54 (GPR54),
stimulation of GnRH secretion by kisspeptin, and the opposing effects of
GnRH on kisspeptin secretion, indicates that GnRH receptor/GnRH and
GPR54/kisspeptin autoregulatory systems are integrated by negative feedback
to regulate GnRH and kisspeptin secretion from GnRH neurons.

Speaker: Joel Miller
Title:Predicting the size and probability of epidemics on networks
Return to seminar page Abstract:
Many diseases periodically emerge into human populations. Many of these
diseases have animal hosts, while others are diseases which have been
eliminated from some parts of the world and are occasionally
reintroduced by travelers. As a classic example, HIV probably began as
a transmission from an infected monkey to a hunter or cook in West
Africa around 1930. Perhaps many such introductions happened over the
centuries, and there is evidence that they continue, but this was the
first instance in which the disease managed sustained spread.
When a disease emerges or is likely to emerge, public health responses
need to devote limited resources to containing the spread. In this talk
we will address three important questions:
1) How likely is an introduction to lead to an epidemic?
2) If an epidemic occurs, how quickly will it grow?
3) How many people will be infected by an epidemic.
All of these questions depend on both the characteristics of the disease
and the structure of the population. We will develop a relatively
simple mathematical theory and show how its predictions compare with an
epidemic spreading in a simulated urban population.

Speaker: YueXian Li Title:
Noise and Synchrony in Neuronal Networks Return to seminar page Abstract:
A rich variety of rhythms in human brain have been observed through the electroencephalogram (EEG), ranging from low frequency (14 Hz) delta rhythms in deep dreamless sleep to high frequency (>14 Hz) beta rhythms in alert states. Rhythms picked up by electrodes on the surface of the scalp are synchronized oscillations of many neurons. A deterministic theory of coupled oscillators has been developed over the past decades in which individual neurons are treated as spontaneous oscillators.
A novel mechanism for generating synchronized rhythms, called coherence resonance (CR), was discovered recently. It refers to coherent oscillations triggered by noise in a system that is quiescent in the absence of noise. In this talk, I will review several distinct examples of noiseinduced synchrony and oscillations, including the spikeresetrecover (SRR) model recently proposed by myself and coworkers. In most known examples of CR, the oscillation frequency increases as the noise level increases. In our SRR model, however, the frequency is determined by the intrinsic properties of the neuron but not by the noise level. The significance of this model in understanding the origin of brain rhythms will be discussed together with some other intriguing effects of noise. Some preliminary results toward developing a stochastic phase theory of coupled oscillators will also be discussed.
Collaborators in works presented here are S. Reinker, R. Kuske and N. Yu.

Speaker: Rafael Meza Title:
Mathematical Modeling of Colon Carcinogenesis
Return to seminar page Abstract:
Mathematical modeling of carcinogenesis offers the opportunity to study in
greater detail the effects of specific interventions that affect critical
biological processes involved in cancer development. In this talk, I will
present a mathematical model of colorectal carcinogenesis and discuss some
applications.
Careful mathematical analysis shows that the agespecific
incidence of cancer predicted by the model exhibits 'phases' that reflect
the carcinogenic process in reverse, with early events showing up late,
and late events influencing the incidence at young age. In particular,
calibration of our model to the colorectal cancers (CRC) in the SEER
registry makes it evident that the agespecific incidence increases mostly
linearly above age 6065, reflecting the incidence (onset) of adenomatous
polyps (adenomas) in the population, while it increases exponentially for
mid ages due to "clonal expansion" of adenoma cells. Adenomas are the
premalignant lesions associated with the large majority of colorectal
cancers. These results contradict the longheld view that the cancer
agespecific incidence increases as a power of age. Our findings have
important implications for the design and analysis of CRC screening
strategies. In particular, they allow us to use our model, which was only
fitted to cancer incidence and not to adenoma data, to simulate the
natural history of CRC and evaluate the effect of screening for adenomas
on CRC risk. If time permits, I'll discuss some of the mathematical,
computational and practical issues related to our analyses of CRC
screening, and present evidence that current screening guidelines may be
far from optimal.

Speaker: MariaRita D'Orsogna Title:
Patterns, stability and collapse for twodimensional biological swarms Return to seminar page Abstract:
One of the most fascinating biological phenomena is the selforganization
of individual members of a species moving in unison with one another,
forming elegant and coherent aggregation patterns.
Schools of fish, flocks of birds and swarms of insects
arise in response to external stimuli or by direct interaction, and are
able to fulfill tasks much more efficiently than single agents.
How do these patterns arise? What are their properties?
How are individual characteristics linked to collective behaviors?
In this talk we model a swarm as a nonlinear system of
self propelled agents that interact via pairwise attractive and repulsive
potentials. We are able to predict distinct
aggregation morphologies, such as flocks and vortices, and by
utilizing statistical mechanics tools,
to relate the interaction potential to the collapsing or
dispersing behavior of aggregates as the number of constituents
increases.
We also discuss passage to the continuum and possible applications
of this work to the development of artificial swarming teams.

Speaker: Pauline van den Driessche Title:
Modeling the Spread of West Nile Virus
Return to seminar page Abstract:
West Nile virus was detected in New York State in 1999, and has spread
rapidly across the continent causing bird, horse and human mortality.
The aim of this lecture is to model this spread. Biological assumptions
are summarized and lead to the development of a reactiondiffusion model
for the spatial spread of West Nile virus with cross infection between
birds and mosquitoes. For a simplified model, the existence of traveling
waves is proved and the spatial spread of infection is calculated.
Related models for West Nile virus spread are briefly discussed

Speaker: Hong Qian Title:
Nonequilibrium Steadystate Theory of Phosphorylationdephosphorylation
Switch in Cellular Signaling
Return to seminar page Abstract:
We present a mathematical theory for a biochemical switch system,
which can be either the phosphorylationdephosphorylation cycle
(PdPC) reactions catalyzed by a kinase and a phosphatase, or GTPase
cycles catalyzed by a guanine exchange factor (GEF) and a GTPase
activating protein (GAP). The theory is based on the recently
developed opensystem nonequilibrium thermodynamics, the chemical
master equation, and the traditional enzyme kinetics. We show how
ultrasensitivity, as a new form of cooperativity, arisies in an
open system, and the role of cellular energy in the functioning of
switches. We also investigate PdPC/GTPase systems with feedbacks
and how it leads to various nonlinear bifurcations.

Speaker: Jianhong Wu Title:
Neural Computation with Attractors: Memory, Dynamics and Time Lags
Return to seminar page Abstract:
This talk addresses the issue how to design and compute a network with
feedback, that exhibits complex but desired dynamical behaviors for some
particular cognitive tasks. We illustrate the linkage between neural
computation with attractors and the memory storage/retrieval using the
additive network of neurons, and discuss the simplicitycapacity dilemma
arising from the requirement for a network to posses a large number of
stable patterns and to be easily implemented. We then propose a novel
approach based on signal processing delay and show the interaction of delay,
feedback and refractoriness in a simple inhibitory network of two neurons
can generate three basic types of oscillations and these three basic
oscillations can then be pinned together to form a large number of
interesting coexisting periodic patterns. Therefore, a simple and small
network with delayed feedback can process a large amount of information. How
connection topology of a large network enhances the network's capacity for
memory storage and retrieval remains to be an interesting task.

Speaker: Adriana Dawes Title:
Stable segregation of PAR proteins in the early C elegans embryo relies on a
bistable switch mechanism Return to seminar page Abstract:
PAR proteins, collectively termed the anterior and posterior PAR proteins,
establish distinct intracellular spatial domains in the one cell C elegans
embryo, polarizing the cell. This polarization is persistent, lasting
approximately 1020 minutes until first cleavage. It has been established
experimentally that the anterior and posterior PAR proteins interact through
mutual phosphorylation, and recent genetic studies indicate that the anterior
PAR proteins are capable of oligomerizing. Using mathematical modelling, I show
that known interactions between the PAR proteins give rise to a bistable switch
that may account for the stable segregation of the PAR proteins. The presence of
a bistable switch in the C elegans embryo is verified experimentally by
depleting the anterior PARs using RNA interference, providing a direct test of
the mathematical model.

Speaker: Joel Heath Title: Behavioural Dynamics of Arctic wintering eider ducks Return to seminar page Abstract:

Speaker: Rodrigo Restrepo Title: RNA and prebiotic evolution Return to seminar page Abstract:
By considering many regularities in the occurrences of purines and pyrimidines in 6241 gene sequences for the tRNAs of the prokaryotes in the Bayreuth Database, this study uncovers a strand (collection) of long RNA segments that fit a large fraction of those tRNAs. This strand suggests a plausible databased scenario for prebiotic evolution that may explain the relatively uniform size of the tRNAs, the fact that the messenger is RNA, not DNA, with a reason for its introns, suggesting a plausible conjecture about some steps in the origin of the genetic code.

Speaker: Suani Pinho
Title: Mathematical and Computer Modelling of Diseases
Return to seminar page Abstract:
In this seminar, we present some results and projects of our research group
(Statistical Physics and Complex Systems  FESC) concerning Mathematical
and Computer Modeling of Diseases. We propose and analyse models of
diseases using time delayed differential equations, cellular automata and,
more recently, complex networks. Our focus is both on the intrahost
dynamics of some diseases (for instance, cancer, malaria, HIV) and on the
population dynamics of transmissible diseases (for instance, dengue,
measles, tuberculosis). Our aim is to compare the model results with some
clinical observations from the qualitative point of view and, when it is
possible, with some actual data. In these themes, we collaborate with
researchers of Universidade Federal de Pernambuco (Recife  Brazil) and
Public Health Institute (ISC) of our University.

Speaker: Veronica Grieneisen Title: Morphogen Gradients Stable During Growth? an example in plant development Return to seminar page Abstract:
In plant development, the phytohormone auxin plays a keyrole,
controlling cell identity, cell division and cell
expansion. Interestingly, in both distal regions of plant roots and
shoots, characteristic auxin maxima have been found which correlate
with these developmental outputs. It is also known that auxin export
facilitators (PINs) are associated with auxin maxima. Combining such
empirical knowledge, we present a multilevel model for the Arabidopsis
root that spans molecular and cellular levels describing diffusion and
PINmediated transport in and across cells within a structured tissue
layout. The modelling study allows us to pinpoint the necessary
elements for the formation and maintenance of an auxinmaximum. It
also permits us to draw connections between PINtopology and
macroscopic properties such as auxincapacitance, auxin gradient
properties and timescales. We explain how pattern formation and
morphogenesis at timescales varying from seconds to days/weeks can be
understood, and thus, how such morphogen gradients should be treated
as outofequilibrium processes.

Speaker: Stan Maree Title: Tcell dynamics within Lymph Nodes Return to seminar page Abstract:

Speaker: WouterJan Rappel Title: Which way to go? Modeling eukaryotic chemotaxis Return to seminar page Abstract:
Chemotaxis is characterized by directed movement of cells up a chemical gradient. It is a key component in a multitude of biological processes,
including neuronal patterning, wound healing, embryogenesis, and cancer metastasis. Even though many of the key components involved in chemotaxis
are known it remains a poorly understood process. In this talk, I will present our modeling efforts aimed towards a better quantitative and mechanistic understanding of chemotaxis. In addition, I will discuss some of the new experimental techniques that should bring us closer to answering the question how cells know which way to go.

Speaker: James P. Keener Title: How cells make measurements Return to seminar page Abstract:
A fundamental problem of cell biology is to understand how cells make measurements and then make behavioral decisions in response to these measurements. The full answer to this question is not known but there are some underlying principles that are coming to light. The short answer is that the rate of molecular diffusion contains quantifiable information that can be transduced by biochemical feedback to give control over physical structures.
In this talk, this principle will be illustrated by two specific examples of how rates of molecular diffusion contain information that is used to make a measurement and a behavioral decision.
Example 1: Bacterial populations of P. aeruginosa are known to make a decision to secrete polymer gel on the basis of the size of the colony in which they live. This process is called quorum sensing and only recently has the mechanism for this been sorted out. It is now known that P. aeruginosa produces a chemical whose rate of diffusion out of the cell provides information about the size of the colony which when coupled with positive feedback gives rise to a hysteretic biochemical switch.
Example 2: Salmonella employ a mechanism that combines molecular diffusion with a negative feedback chemical network to "know" how long its flagella are. As a result, if a flagellum is cut off, it will be regrown at the same rate at which it grew initially.

Speaker: Claude Muller Title: The spread and evolution of highly pathogenic Avian Influenza (HPAI) H5N1 in Africa Return to seminar page Abstract:
In Africa HPAI H5N1 virus was first detected in Northern Nigeria and since then in 7 other African countries: Niger, Egypt, Cameroon, Burkina Faso, C™te dŐIvoire, Sudan and Djibouti. The study of the NigerianLuxembourg Poultry Virus Network at the University of Ibadan showed high seroprevalences for some poultry viruses but antibodies against AIV were not found in farms in the Southwest of Nigeria at least until May 2004. Phylogenetic analysis and substitution rates of complete genome sequences of Nigerian strains from the SouthWest and the North showed that three sublineages were present in Nigeria as early as February 2006 and that three independent introductions of H5N1 into the country are likely. (MF Ducatez et al. Avian flu: multiple introductions of H5N1 in Nigeria. Nature 442, 37, 2006). These three sublineages include all African strains and by now have a distinct geographic distribution: sublineage A (southwest Nigeria, Lagos, Niger), B (southwest Nigeria, Lagos, Egypt, Djibouti) and C (Northern Nigeria, Burkina Faso, Sudan, C™te dŐIvoire) within Africa. Probable nonAfrican ancestors within the WestAsian/Russian/European lineage distinct from the Southeast Asian lineages were identified for each sublineage. In 2006 all reported human cases in Africa (Egypt, Djibouti) were caused by sublineage B with a distinct but poorly understood amino acid signature. In 2006, this sublineage B has been found also in at least one farm in/near Lagos. Genetic analysis will reveal whether the same strain caused the recent human case in Lagos. We have also characterized the first avian influenza strains from Burkina Faso and the first strains from African wild birds (sublineage C). Between February and June 2006, 48 hooded vultures (Necrosyrtes monachus) were found dead or sick throughout Ouagadougou. We present here the first sequences from African wild birds and compare them to strain found in Burkina poultry. The sequences clustered with strains found in Ivory Coast, Northern Nigeria and The Sudan (sublineage C). We showed that the infection of scavenger birds in Africa is likely to cause spillbacks from poultry to wild birds, which is rarely seen in other countries and has important consequences for surveillance in Africa and beyond. As they scavenge on many dead species, they may also function as conspicuous sentinels in the African continent, similar to raptors or swans in Europe or cats in Indonesia. Proper disposal of infected carcasses must be carefully enforced on affected farms to avoid primary infections of carrion feeders.

Speaker: Alex Mogilner Title: System
Level Mathematical Analysis of Mitosis Return to seminar page Abstract:
Mitotic spindle goes through distinct morphological states characterized
by increasing spindle length and distances between chromosomes. A
complete picture of how the spindle assembles is still lacking. We
performed an In Silico model screen to identify all potential mechanisms
of spindle selforganization. We trained' the computer to assemble a set
of models and screened the models in a multidimensional parameter
space. To identify models that fit experimental data we used stochastic
optimization and genetic algorithms. We found multiple models
quantitatively describing the spindle in which the timing of force
activity must be fine tuned, in contrast to the kinetic and mechanical
parameters that show robustness to change.

Speaker: Joe Tien
Title: Geometric approaches to parameter estimation for differential equations.
Return to seminar page Abstract:
Parameter estimation for differential equations is a fundamental problem, but work in this area is incomplete. One difficulty is the presence of local minima which trap optimization algorithms, resulting in poor fits. Incorporating geometric features of the differential equations into the optimization algorithms can alleviate this problem. These structural features are combined with numerical improvements via automatic differentiation, and applied to neural models and data related to breathing.
This work has resulted in my becoming interested in statistical inference. If time permits, I will mention some HIV data I have been working on with viral strains which have escaped immune system recognition.

Speaker: Junling Ma Title:
Evolutionary Branching Return to seminar page Abstract:
Evolutionary branching is sympatric speciation driven by competition between dominant species and their mutants. The traditional approach to study evolutionary branching is to use pairwiseinvasibility plot (PIP).
However, PIP is only suitable for the branching of a single species with a single trait. With multiple coevolving traits or species, this method breaks down because the evolution/branching in one trait changes the PIP of other traits.
In this talk, I introduce a dynamical method to study the branching of multiple coevolving traits and species, and give the branching conditions.

Speaker: Stewart Chang Title:
Multiscale modeling of antigen presentation with applications to tuberculosis. Return to seminar page Abstract:
Antigen presentation is the process by which cells of the immune system display peptides from pathogens on their surface after binding the peptides to major histocompatibility complex (MHC) molecules. T helper cells recognize peptides from pathogens in this context then secrete cytokines that activate other cells, initiating an immune response. Antigen presentation is therefore a requisite for immunity to several pathogens including Mycobacterium tuberculosis (Mtb). To approach questions related to antigen presentation and disease, I represented antigen presentation at different scales using a series of mathematical and statistical models. At the molecular scale, I asked whether heterogeneity in peptide length affects binding to MHC class II, the class of MHC responsible for binding peptides from bacteria such as Mtb. By developing statistical models of peptideMHC binding, I found that length has a nonlinear effect on binding affinity and that this information could improve the accuracy of binding prediction. At the cellular scale, I asked why Mtb possesses multiple mechanisms to inhibit antigen presentation on the cell surface. My mathematical model shows that these mechanisms may be acting on different timescales and therefore complementary rather than merely redundant. Finally, at the multicellular level, I asked how polymorphisms in multiple genes related to antigen presentation might affect T cell response and susceptibility to infectious diseases such as tuberculosis. Using a multiscale model representing both the antigenpresenting cell and T cell, I found that polymorphisms in two different genes may exert the same influence on the output, potentially canceling out their effects. Future work with these models may include evaluation of candidate peptidebased vaccines to ensure highaffinity binding, T cell response, and broad efficacy in diverse populations.

Speaker: Josef Ackerman
Title: The role of mathematics in physical ecology.
Return to seminar page Abstract:
The natural link between mathematics and ecology is evident in the field of physical ecology, which uses physical models to explore some fundamental issues. These include how aquatic organisms use the constraints imposed by physical environment to satisfy their biological processes. This seminar will present examples of the physical ecology approach to sexual reproduction and trophic dynamics in marine, lake and river systems.

Speaker: Arthur Sherman Title: Ionic and
Metabolic Mechanisms in Pulsatile Insulin Secretion Return to seminar page Abstract:
Insulin is secreted in pulses with a period of about 5 minutes from the
betacells of the pancreas. These pulses are in turn driven by
oscillations of cytosolic calcium. Two parallel streams of
investigation over more than two decades have studied metabolic
oscillations and ionic mechanisms as possible sources of the calcium
oscillations. We propose that the two are linked by a potassium
channel, K(ATP), that senses the ATP and ADP levels in the cell. This
directly transduces metabolic oscillations into oscillations of membrane
potential and calcium. However, calcium can also affect metabolism by
stimulating ATPconsuming pumps, by depolarizing the mitochondria, and
by directly activating Krebs cycle enzymes. A unified model that
combines the above elements and can thereby explain a diverse set of
experimental observations using only a few simple assumptions will be
presented. 
Speaker: Bill Kath Title: Models of
Initiation and Propagation of Dendritic Spikes in Hippocampal CA1
Pyramidal Neurons Return to seminar
page Abstract: In computational models of hippocampal
CA1 pyramidal neurons with active dendrites, distal synaptic inputs
trigger dendritic spikes, but in many cases these spikes do not
propagate reliably to the soma to produce output action potentials in
the axon. The computational models show, moreover, that the probability
of axonal action potential initiation increases dramatically if the
distal dendritic inputs are accompanied by small amounts of more
proximal synaptic input. In this case, the propagation of the dendritic
spikes appears to be gated by the more proximal inputs. The mechanisms
for this phenomenon, as well as experimental results designed to test
the predictions of the computational models, will be discussed.

Speaker: David Lloyd Title: Nucleation of
localised pattern in continuous media Return to seminar page Abstract:
The formation of patterns from quiescence under the continuous variation
of a parameter has long been of interest across the physical and life
sciences since the pioneering work of Alan Turing. We describe how
spatially localised patches of pattern arise spontaneously in
experiments in a wide variety of nonlinear media including liquid
crystals, autocatalytic chemical reactions, gas discharge systems,
optical crystals and in solidification. Perhaps the most intriguing
examples of such patterns are small circularly symmetric spatially
localised subharmonic excitations (dubbed \emph{oscillons}) that occur
in vertically vibrated granular materials, viscous fluids and plasmas.
Oscillons tend to form tightly packed strongly interacting clusters
which coexist with an undeformed background and cannot be captured by
theories of weakly interacting localised atoms. Here we present a
predictive theory for the nucleation and pattern selection of
\emph{multidimensional} localised structures in quite general
continuous media, via the interplay between linear instability and
nonlinear bistability. We show how specific kinds of localised patterns
(spots, targets, hexagonal arrays etc.) are selected and emerge
subcriticality depending on the amount of bistability between the
background and finiteamplitude cellular patterns. These parameter
regions of localised pattern overlap as the amount of hysteresis in the
system is increased, explaining experimental results showing competition
between different localised patterns. Furthermore, using a Maxwell point
argument that goes well beyond onedimensional theory, we reveal a
complex {\em snaking} transition diagram that provides the mechanism by
which larger localised clusters form and self completion occurs.

Speaker: Richard Bertram Title:
Mathematical Analysis of the Neural Control of Hormone Secretion Return to seminar page Abstract:
The pituitary is one of the primary glands of the body. Many hormones
are released from a variety of cells within the pituitary, and these
hormones regulate the release of hormones from other glands and have
direct actions on the brain, muscles, and organs. The timing of hormone
release from the pituitary is important, and is determined largely
through interactions with a region of the brain called the hypothalamus.
These interactions are quite complex, and serve as a good application
area for mathematical modeling and computer simulations. The focus of
this seminar is recent mathematical modeling and analysis of
interactions between the hypothalamus and pituitary lactotrophs,
pituitary cells that secrete the hormone prolactin. We discuss possible
mechanisms for circadian oscillations in prolactin secretion in pregnant
rats, and the much faster oscillations (period of several seconds) in
electrical activity of the lactotrophs, using models of cellular
dynamics at very different temporal and spatial scales. 
Speaker: Michael Doebeli Title: Evolution
of diversity: Pattern formation in phenotype space Return to seminar page Abstract:
Understanding the origin of diversity is one of the fundamental
conceptual problems in biology. Traditional evolutionary theory predicts
uniformity: natural selection acting on organisms under given
environmental conditions and developmental constraints produces a
unique, optimally adapted phenotype. According to this view, different
types only come about through a change in conditions over space or time.
In particular, the process of diversification, that is, the split of an
ancestral population into distinct descendent lineages, is a byproduct
of geographical separation. This traditional view misses out on the
important perspective that diversification itself can be an adaptive
process triggered by ecological interactions within an ancestral
population. In this perspective, diversification is a process of pattern
formation in phenotype space, during which frequencydependent selection
splits unimodal phenotype distributions into multimodal distributions,
with the different modes corresponding to different descending species.
In this talk I will review recent theoretical work on adaptive
diversification from the general perspective of pattern formation. I
will start out showing how diversity can evolve in the framework of
adaptive dynamics due to the phenomenon of evolutionary branching. I
will then consider PDE models of continuous phenotype distributions,
showing that speciation due to pattern formation is a plausible outcome
in such models. Finally, I will briefly introduce a general framework
for understanding pattern formation in PDE models that is based on
equivariant bifurcation theory.

Speaker: Daniel Coombs Title: Virus
Competition at Multiple Scales Return to
seminar page Abstract: Viruses compete and are subject
to natural selection at multiple levels: withincell, withinhost and
withinpopulation (of hosts). We looked at how viruses can optimally
exploit their hosts and how this behaviour may influence the most
successful strategy at the betweenhost, or epidemiological level. I
will present a fairly general way to consistently combine models of
disease process and disease spread with the goal of understanding the
net selection pressure on a model virus. The method is illustrated using
two popular models at the within and betweenhost levels. 
Speaker: Yoichiro Mori Title TBA Return to seminar page Abstract:
The immersed boundary method is a general framework used to handle
fluidstructure interactions. One computational bottleneck of the
immersed boundary methods is that the elastic structures are often very
stiff, necessitating the use of a very fine time step.
In this talk, we will present an immersed boundary scheme in which the
position of the immersed elastic structure is treated implicitly. We
show that the resulting implicit method allows much greater time steps
to be used compared with an explicit method, and that the computational
cost is greatly reduced in certain test situations. We shall also show
that the implicit method provides a natural way in which to add
addtional mass to the immersed elastic structure.

Speaker: Lin Wang Title: Impact of Travel
Between Patches for Spatial Spread of Disease Return to seminar page Abstract:
A patch model is proposed to study the impact of travel on the spatial
spread of disease between patches. The basic reproduction number for the
ith patch in isolation, is obtained along with the basic reproduction
number of the system, $\mathcal{R}_0$. Inequalities describing the
relationship between these numbers are also given. For a twopatch model
with one high prevalence patch and one low prevalence patch, results
pertaining to the dependence of $\mathcal{R}_0$ on the travel rates
between the two patches are obtained. For parameters relevant for
influenza, the effects of travel restrictions are also discussed.
Results show that if border control is properly implemented, then it
could contribute to stopping the spatial spread of disease.

Speaker: Kevin Painter Title Modelling
cell migration in the ECM and its role in tumour invasion Return to seminar page Abstract:
Cell migration plays an essential role during both embryonic development
(e.g. gastrulation, neural crest migration) and in the normal
physiological responses of the adult (e.g. immune response, wound
healing). The extracellular matrix (ECM) plays a vital role in
regulating movement by both providing a scaffold through which cells can
generate traction and imparting specific migratory cues through
ECMbound proteins. The ECM also provides specific guidance to cells
through preferential movement by the cells along the matrix fibres, a
process known as contact guidance. The acquired ability of tumour cells
to break free from the main mass and migrate into the surrounding ECM is
a key stage in increased tumour malignancy.
Individual cell migration in the ECM can be classified into two main
groups: amoeboid and mesenchymal. In the former, cells move quickly and
have negligible effect on the structure of the surrounding ECM.
Mesenchymal migration, however, is much slower and extensive matrix
degradation takes place through the focussed expression of specific
matrix degrading proteins by the cells (pericellular proteolysis).
In this talk, I will describe both discrete and continuous models for
amoeboid and mesenchymal cell migration. Numerical investigations will
be used to demonstrate a potential role of contact guidance and matrix
degradation in directing the macroscopic organisation of cells and the
matrix. I will consider applications in the context of models for tumour
invasion.

Speaker: Peter Borowski Title: A
stochastic twostate signalling module with negative feedback Return to seminar page Abstract:
Motivated by the negative feedback calcium exerts on the gating dynamics
of a calciumconducting ion channel in olfactory receptor neurons, we
develop an abstract twostate (open/closed) signalling module with
negative feedback. The coupling between the gating dynamics of the
channel and the conducted ion makes the effective dynamics of the
channel nonMarkovian and difficult to treat in a Langevinapproach.
We make use of two different techniques to describe the stochastic
dynamics of the module. First, we calculate the steady state probability
distribution using a Master/FokkerPlancktype equation. Second, a
pathintegral formulation based on the temporal statistics of the
channel stateflips is developed to calculate dynamical properties of
the module. The feedback effect is built into the model in a systematic
way in the form of a weak perturbation. Analytic results are obtained
for the open probability of the channel as well as the autocorrelation
and response functions (both for the discrete channel variable and the
continuous calcium concentration). Monte Carlo simulations are performed
which support the analytical predictions in the weak feedback limit and
provide results beyond linear perturbation theory.

Speaker: Jason Haugh Title: Analysis of Intracellular Signal Transduction at Various Scales of Biological Abstraction Return to seminar page Abstract:
An ongoing challenge in mammalian cell biology is to bridge the gaps in our understanding of processes at the molecular, cellular, and tissue levels. Central to the hierarchy of biological complexity is the field of /signal transduction/, which deals with the biochemical mechanisms and pathways by which cells respond to external stimuli, such as soluble growth factors/cytokines, extracellular matrix, and mechanical forces. Intracellular signaling processes control the growth, survival, and migration of cells in normal physiological contexts, and defects in signaling form the molecular basis for cancer, immune system disorders, and other diseases. Using a quantitative approach that combines biochemical measurements, fluorescence imaging, and mathematical modeling, our group characterizes signal transduction networks through analysis of their kinetics and spatial patterns in cells. Based on analysis of experimental data and informed where appropriate by knowledge of protein domain structure, we develop mechanistic models that may be embedded in mathematical representations of cell population dynamics, with the goal of evaluating hypotheses regarding the concerted responses of cells in tissues. As an example of this approach, I will describe our efforts to characterize signal transduction mediated by cell surface receptors for plateletderived growth factor (PDGF), a soluble factor that accelerates dermal wound healing by directing the migration and proliferation of dermal fibroblasts.

Speaker: Gerda deVries Title: Mathematical models in radiation biology
Return to seminar page Abstract:
In this talk, I will review concepts in radiation biology that allow us to model the effectiveness of radiation therapy in the treatment of cancer. In particular, I will focus on the Tumour Control Probability (TCP), which is the probability that no cancerous cells survive the treatment. Early TCP formulae are based on simple binomial and Poissonian statistics. They are of limited value, since they do not take cell proliferation during the treatment period into account. Recent TCP formulae are based on dynamic models of a cell population, taking cell proliferation into account. I will conclude with a discussion of how and when the TCP formulae are related to each other, and how they can be used to compare the efficacy of different treatment schedules.

Speaker: Gail Wolkowicz Title:An alternative formulation for a delayed logistic equation Return to seminar page Abstract:
After a brief review of the history and dynamics of the classical
logistic and delayed logistic equation models, an alternative
expression for a delayed logistic equation is derived assuming that the
rate of change of the population depends on three components: growth,
death, and intraspecific competition, with the delay in the growth
component. In our formulation, we incorporate the delay in the growth
term in a manner consistent with the rate of instantaneous decline in
the population given by the model. A complete global analysis shows
that unlike the dynamics of the classical logistic delay differential
equation model,no sustained oscillations are possible. Instead, the
dynamics of this model are more reminiscent of the classical logistic
ordinary differential equations growth model, but with some important
differences. Implications for incorporating delays in population
models are considered.

Speaker: Mark Lewis Title TBA Return to seminar page
Abstract:

Speaker: Bob Guy
Title: A multiphase flow model of calcium induced morphology changes
in true slime mold
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Abstract:
The true slime mold Physarum polycephalum is a single cell
organism reaching up to meters in size. The cytoplasm shows periodic
shuttle streaming through a network of tubular structures attaining
velocities up to 1 mm/s. The motion is driven by the periodic
contraction of an actinmyosin gel that is regulated by a calcium
oscillation.
When the organism is small (< 100 microns) no streaming is observed,
but as it gets larger regular rhythmic steaming suddenly emerges. We
present a mechanochemical multifluid model which is
used to explore how the sensitivity to changes in calcium
concentration is related to the stability of the sol/gel mixture.
Stability of the homogeneous mixture is explored analytically in
onedimension, and computational results are presented for higher
dimensions. The model demonstrates that as the organism grows, a
calciuminduced spatial instability occurs which may be responsible
for the initiation of streaming.
The overall goal of this work is to understand the interplay between
chemistry and fluid mechanics which is necessary to transmit chemical
signals and organize structures over very large distances. In
addition to streaming, some other problems related to spatial
organization of structure will be discussed.

Speaker: Claus Rueffler Title:Work in progress: The evolution of phenotype determination and an attempt to classify simple lifehistory models Return to seminar page Abstract:
In this talk I will present two pieces of work in progress. In the first half of the talk I will speak about the evolution of phenotype determining mechanisms. Many heterogeneous environments favour different phenotypes in different places or at different times. Phenotypic diversity can either result from genetic diversity of from a single genotype capable of producing different phenotypes. A single genotype might produce different phenotypes for example in response to an environmental cue (phenotypic plasticity), through a randomization mechanism (bethedging), or through a combination of the two. A large part of the existing theoretical literature attempts to give conditions under which one of these specific mechanisms is favoured over a phenotypically monomorphic population. However, in many circumstances different evolutionary responses are favoured simultaneously and the real question becomes which of these different responses might evolve first and possibly preempt any selection driving one of the alternative responses. I will address this question by presenting some preliminary results derived from a model designed to study evolution in a temporarily heterogeneous environment.
In the second half of the talk I will present a classification of the evolutionary dynamics for a class of simple lifehistory models. The aim of this classification is to find principles governing the evolutionary dynamics that are valid beyond a single specific model. The family of models considered is characterized by discrete time population dynamics, densitydependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a tradeoff. Individual models differ in the choice of traits that are presumed to be evolving and in the way population regulation is incorporated. I classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimization criterion. The first classification allows me to infer whether trait combinations that are characterized by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequencyindependent from models that give rise to frequency dependence. I will conclude by summarizing some general patterns emerging from this analysis.

Speaker: Claus Rueffler Title: The evolutionary ecology of resource specialization Return to seminar page Abstract:
In the presence of different resources, when should we expect the evolution of a generalist phenotype versus specialized phenotypes? While this question has a long history in evolutionary ecology the evolutionary dynamics of a single consumer type in the presence of two kinds of renewable resources has not yet been studied in great detail. I will present a model of one evolving consumer feeding on two resources and analyse the evolutionary dynamics of different consumer traits using a set of techniques known as `` adaptive dynamics''. I show that, depending on the type of trait considered, selection is either frequencyindependent or frequencydependent. This difference is explained by the effects different foraging traits have on the consumerresource interactions. If selection is frequencydependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Traits with frequencyindependent selection follow Levins' classical prediction stating that convex phenotype sets favour generalists while concave phenotype sets favour specialists.
In a second step I extend the model by allowing consumers to choose their diet so as to maximize resource uptake. This version of the model allows for the study of the dynamic interplay between adaptive choice behaviour and the evolutionary dynamics of morphological and physiological foraging traits. The model predicts that flexible diet choice behaviour can guide the direction of evolutionary change in a foraging trait and that flexible behaviour can mediate the coexistence of different consumer types where coexistence would not be possible otherwise. Such polymorphisms can evolve from a monomorphic population at evolutionary branching points and also at points where a small genetic change in a trait can provoke a drastic and nongenetic change in choice behaviour. The added feature of diet choice behaviour can lead to alternative evolutionarily stable communities.

Speaker: Christoph Hauert Title: Evolutionary Dynamics: Structured Populations and
the Problem of Cooperation Return to seminar page Abstract:
Evolutionary dynamics in finite populations reflects a balance
between Darwinian selection and random drift. For a long time population
structures were assumed to leave the evolutionary outcome unaffected, i.e.
to leave the fixation probability of a single mutant type in a resident
population unchanged, provided that the fitness of mutants and residents is
constant and independent of the population configuration. This result
indeed holds for a certain (large) class of population structures or
graphs. Quite intriguingly, however, other structures can tilt the balance
to the extent that either selection is eliminated and drift rules or drift
is eliminated and only selection matters. These results have recently been
extended to include frequencydependent selection on graphs where
individuals engage in game theoretical interactions. The most important
case refers to the problem of cooperation in social dilemmas, i.e. to
behavioral patterns that are beneficial to the group but costly to the
individual. For the prisoner's dilemma, this yields a simple rule under
which selection can favor cooperation in structured populations that range
from regular lattices to scalefree networks. In wellmixed populations,
i.e. in the absence of spatial structure, defectors reign. Spatial
structure has long been recognized to support cooperation because it allows
cooperators to form clusters and thereby to reduce exploitation by
defectors. However, this does not hold for social dilemmas in general. In
fact, under relaxed conditions of the social dilemma, i.e. if cooperators
and defectors can coexist in wellmixed populations, spatial structure
often turns out to be detrimental and may even eliminate cooperation
altogether.

Speaker: Christoph Hauert Title: Cooperation in Social Dilemmas: The Role of Punishment and Volunteering Return to seminar page Abstract:
The emergence and maintenance of cooperative behavior that
is beneficial to others but costly to the individual represents a major
conundrum in evolutionary biology. Punishment represents an efficient
mechanism to stabilize and maintain cooperation in social dilemmas and is
ubiquitous in animal and human societies  ranging from toxin producing
microorganisms to law enforcement institutions  but it remains unresolved
how initially rare costly punishment can gain a foothold and spread through
the population. In nature, animals and humans often select their interaction
partners or adjust their behavior in response to them. In the simplest case
they simply refuse to participate in risky enterprises. Such voluntary
participation in social dilemmas is an efficient mechanism to prevent
deadlocks in states of mutual defection, and thus represents a potent
promoter of cooperation that nevertheless fails to stabilize it. However, the
combined efforts of punishment and volunteering may change the odds in favor
of cooperation. Interestingly, even the combined efforts fail in infinite
populations, but provide a most efficient mechanism to stabilize cooperation
(and punishment) in the stochastic dynamics of finite populations under
mutation and selection. Thus the freedom to withdraw leads to prosocial
coercion. This implements Hardin's principle: mutual coercion mutually (and
voluntarily) agreed upon.

Speaker: Kristan Schneider Title: Longterm evolution of polygenic traits under frequencydependent
intraspecific competition
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We analytically investigate the longterm evolution of a continuously
varying quantitative character in a diploid population that is determined
additively by a finite number of loci. The trait is under a mixture of
frequencydependent disruptive selection induced by intraspecific
competition and frequencyindependent stabilizing selection. Moreover, the
trait is restricted to a finite range by constraints on the particular
loci. Our investigations are based on explicit analytical on the
shortterm dynamics under the assumption of linkage equilibrium. We show
that the population always reaches a longterm equilibrium (LTE), i.e., an
equilibrium that is resistant against perturbations of mutations of
sufficiently small effect. In general, several LTEs can coexist. They can
be calculated explicitly, and we provide necessary and sufficient
conditions for their existence. In the case that more than one LTE exists,
we exemplify numerically that the evolutionary outcome depends crucially
on the initial genetic architecture, on the joint distribution of
mutational effects across loci, and on the particular realization of the
mutation process. Therefore, longterm evolution cannot be predicted from
the ecology alone. We further show that a partial order exists for the
LTEs. The set of LTEs has a `largest' element, an LTE, which is reached
during longterm evolution if the effects of the occurring mutant alleles
are sufficiently large.

Speaker: Kristan Schneider Title: A MultilocusMultiallele Analysis of FrequencyDependent Selection Induced
by Intraspecific Competition
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The study of the mechanisms that maintain genetic variation has a long
history in population genetics. We analyze a multilocusmultiallele model
of frequency and density dependent selection in a large randomly mating
population. The number of loci and the number of alleles per locus are
arbitrary. The n loci are assumed to contribute additively to a
quantitative character under stabilizing or directional selection as well
as under frequencydependent selection caused by intraspecific
competition. We assume the strength of stabilizing selection to be weak,
whereas the strength of frequency dependence may be arbitrary.
Densitydependence is induced by population regulation. Our main result is
a characterization of the equilibrium structure and its stability
properties in terms of all parameters. It turns out that no equilibrium
exists with more than two alleles segregating per locus. We give necessary
and sufficient conditions on the strength of frequency dependence to
ensure the maintenance of multilocus polymorphism. We also give explicit
formulas on the number of polymorphic loci maintained at equilibrium.
These results are based on the assumption that selection is sufficiently
weak compared with recombination, so that linkage equilibrium can be
assumed. If additionally the population size is assumed to be constant, we
prove that the dynamics of the model form a generalized gradient system.

Speaker: Jung Kyung Kim Title : Function Follows Form  Transport Phenomena Coupled with Mechanics in Biological Systems Return to seminar page Abstract:
As the systems approaches are actively adopted in biology, studies for revealing the link between physical dynamics and corresponding molecular mechanism will be crucial to better understanding of the inherent complexity and dynamics of biological phenomena.
Macromolecule diffusion in cells and tissues is important for cell signaling, metabolism and locomotion. Noninvasive or minimally invasive invivo photobleaching and single quantumdot tracking techniques combined with mathematical modeling have been used for quantifying macromolecule diffusion in cells and living tissues, including central nervous system and tumors.
My extensive experience in manipulating the tiny volume of liquids and small biological objects with micro/nanofluidic systems has been stimulating me to think that cells can respond to chemically patterned and topologically textured substrates by sensing the modulated surface forces. More specifically, my current aim is to find the role of membrane tension in spreading and selfpropulsion during cell migration by applying fluid dynamics approaches to describing the motion of droplets and thin films on the substrates with chemical or topological patterns.
Interdisciplinary collaborations between engineers and biologists would also lead to continuous advancement in engineering by applying uncovered design principles and intrinsic strategies in biological systems.

Speaker: Michael Gilchrist Title Predicting Protein Production Rates from Codon Usage Patterns: A
Nested Model Approach Return to seminar page Abstract:
Genes are often biased in their use of particular codons. The
degree of bias displayed changes as a function of expression level and
intragenic position. Numerous indices measuring such bias have been
developed. While the expression level of a gene and such indicies are often
correlated, the huristic nature of these metrics precludes a deeper
understanding between expression and bias. Here I employ mechanistic models
of cellular and population processes to develop a framework for evaluating
codon usage bias in an explicitly evolutionary framework.

Speaker: Joshua Weitz Title:
Evolutionary and Population Dynamics of Bacteria and Phage
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Bacterial viruses, aka bacteriophage or phage, are ubiquitous in
nature, yet many central aspects of hostphage biology have not been
integrated into mathematical models. In this talk I present a series of
theoretical efforts to understand the diversity, population dynamics and
life history of phage. First, I discuss an evolutionary ecology model of
hostphage diversification using the framework of adaptive dynamics and
show how the principle of competition exclusion is modified in the context
of coevolutionary arms races. Second, current models of hostphage
population dynamics neglect to include the reduction of lytic
effectiveness as hosts approach stationary phase. Incorporating reduced
lysis into dynamics leads to a prediction of alternative stable states,
which are discussed in the context of simple experiments. Finally, I
explore ongoing experimental and theoretical efforts to understand how
phage may optimally exploit their hosts by utilizing a variety of life
history strategies.

Speaker: Matthew Onsum
Title: Analysis of immune cell chemotaxis and signal integration
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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: Fred Brauer Title: Epidemic models with heterogeneous mixing
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Abstract:
The classical compartmental epidemic models are too simple, because they assume homogeneous mixing of all members of the population. The modern network models are too complicated because they assume too much knowledge of the population and are too difficult to analyze. We seek something in between, starting with a population consisting of two groups with different activity levels, assuming proportionate mixing between the groups, calculating the basic reproduction number and using the final size relation to determine what the size of the epidemic would be if there were no disease deaths. We show that if the disease death rate is small, this is a good approximation. We compare numerical simulations for one  group and two  group models to examine whether the extension to more groups is worthwhile.
We show how to extend to models with treatment and other compartments, more
general mixing (in which case there is a final size relation even though the
reproduction number can not be calculated explicitly), and more groups.

Speaker: Title: TBA
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Speaker: Title: TBA
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