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Friday, January 31, 2014 - 11:00 ,
Location: Skiles 005 ,
Chi-Jen Wang ,
Iowa State ,
Organizer: Christine Heitsch

Spatially discrete stochastic models have been implemented to analyze cooperative behavior in a variety of biological, ecological, sociological, physical, and chemical systems. In these models, species of different types, or individuals in different states, reside at the sites of a periodic spatial grid. These sites change or switch state according to specific rules (reflecting birth or death, migration, infection, etc.) In this talk, we consider a spatial epidemic model where a population of sick or healthy individual resides on an infinite square lattice. Sick individuals spontaneously recover at rate *p*, and healthy individual become infected at rate O(1) if they have two or more sick neighbors. As *p* increases, the model exhibits a discontinuous transition from an infected to an all healthy state. Relative stability of the two states is assessed by exploring the propagation of planar interfaces separating them (i.e., planar waves of infection or recovery). We find that the condition for equistability or coexistence of the two states (i.e., stationarity of the interface) depends on orientation of the interface. We also explore the evolution of droplet-like configurations (e.g., an infected region embedded in an all healthy state). We analyze this stochastic model by applying truncation approximations to the exact master equations describing the evolution of spatially non-uniform states. We thereby obtain a set of discrete (or lattice) reaction-diffusion type equations amenable to numerical analysis.

Intra-Host Adaptation and Antigenic Cooperation of RNA Viruses: Modeling and Computational Analysis.

Wednesday, January 22, 2014 - 11:05 ,
Location: Skiles Bld Room 005 ,
Pavel Skums ,
CDC ,
Organizer:
Understanding the mechanisms responsible for the establishment of
chronic viral infections is critical to the development of efficient
therapeutics and vaccines against highly mutable RNA viruses, such as
Hepatitis C (HCV). The mechanism of intra-host viral evolution assumed
by most models is based on immune escape via random mutations. However,
continuous immune escape does not explain the recent observations of a
consistent increase in negative selection during chronic infection and
long-term persistence of individual viral variants, which suggests
extensive intra-host viral adaptation.
This talk explores the role of immune cross-reactivity of viral variants
in the establishment of chronic infection and viral intra-host
adaptation. Using a computational prediction model for
cross-immunoreactivity of viral variants, we show that the level of HCV
intra-host adaptation correlates with the rate of cross-immunoreactivity
among HCV quasispecies. We analyzed cross-reactivity networks (CRNs)
for HCV intra-host variants and found that the structure of CRNs
correlates with the type and strength of selection in viral populations.
Based on those observations, we developed a mathematical model
describing the immunological interaction among RNA viral variants that
involves, in addition to neutralization, a non-neutralizing
cross-immunoreactivity. The model describes how viral variants escape
immune responses and persist, owing to their capability to stimulate
non-neutralizing immune responses developed earlier against preceding
variants. The model predicts the mechanism of antigenic cooperation
among viral variants, which is based on the structure of CRNs. In
addition, the model allows to explain previously observed and
unexplained phenomenon of reappearance of viral variants: for some
chronically infected patients the variants sampled during the acute
stage are phylogenetically distant from variants sampled at the earlier
years of infection and intermixed with variants sampled 10-20 years
later.
(Joint work with Y. Khudyakov, Z.Dimitrova, D.Campo and L.Bunimovich)

Monday, January 6, 2014 - 15:00 ,
Location: Skiles 006 ,
Katherine St. John ,
Lehman College, CUNY ,
Organizer: Christine Heitsch

Evolutionary histories, or phylogenies, form an integral part of much work in biology. In addition to the intrinsic interest in the interrelationships between species, phylogenies are used for drug design, multiple sequence alignment, and even as evidence in a recent criminal trial. A simple representation for a phylogeny is a rooted, binary tree, where the leaves represent the species, and internal nodes represent their hypothetical ancestors. This talk will focus on some of the elegant mathematical and computational questions that arise from assembling, summarizing, visualizing, and searching the space of phylogenetic trees, as well as delve into the computational issues of modeling non-treelike evolution.

Wednesday, November 13, 2013 - 10:30 ,
Location: Skiles Bld Room 005 ,
Vladimir E. Bondarenko ,
GSU ,
Organizer:

A comprehensive mathematical model of β1-adrenergic
signaling system for mouse ventricular myocytes is developed. The model myocyte
consists of three major compartments (caveolae, extracaveolae, and cytosol) and
includes several modules that describe biochemical reactions and electrical
activity upon the activation of β1-adrenergic receptors. In the
model, β1-adrenergic receptors are stimulated by an agonist
isoproterenol, which leads to activation of Gs-protein signaling
pathway to a different degree in different compartments. Gs-protein,
in turn, activates adenylyl cyclases to produce cyclic AMP and to activate
protein kinase A. Catalytic subunit of protein kinase A phosphorylates cardiac
ion channels and intracellular proteins that regulate Ca2+ dynamics.
Phosphorylation is removed by the protein phosphatases 1 and 2A. The model is
extensively verified by the experimental data on β1-adrenergic
regulation of cardiac function. It reproduces time behavior of a number of
biochemical reactions and voltage-clamp data on ionic currents in mouse
ventricular myocytes; β1-adrenergic regulation of the action
potential and intracellular Ca2+ transients; and calcium and sodium fluxes
during action potentials. The model also elucidates the mechanism of action
potential prolongation and increase in intracellular Ca2+ transients
upon stimulation of β1-adrenergic receptors.

Wednesday, September 25, 2013 - 11:05 ,
Location: Skiles Bld Room 005 ,
D. Murrugarra ,
SoM, GaTech ,
Organizer:

Modeling stochasticity in gene regulation is an important and complex
problem in molecular systems biology due to probabilistic nature of gene
regulation. This talk will introduce a stochastic modeling framework
for gene regulatory networks which is an extension of the Boolean
modeling approach. This framework incorporates propensity parameters for
activation and degradation and is able to capture the cell-to-cell
variability. It will be presented in the context of finite dynamical
systems, where each gene can take on a finite number of states, and
where time is also a discrete variable. Applications using methods from
control theory for Markov decision processes will be presented for the
purpose of developing optimal intervention strategies. A background to
stochastic modeling will be given and the methods will be applied to the
p53-mdm2 complex.

Thursday, September 12, 2013 - 16:05 ,
Location: Skiles 005 ,
R.Stoop ,
Inst. of Neuroinformatics, ETH, Zurich ,
Organizer:

We study to what extent cortical columns with their particular wiring,
could boost neural computation. Upon a vast survey of columnar networks
performing various real-world cognitive tasks, we detect no signs of the
expected enhancement. It is on a mesoscopic?intercolumnar?scale that
the wiring among the columns, largely irrespective of their inner
organization, enhances the speed of information transfer and minimizes
the total wiring length required to bind distributed columnar
computations towards spatiotemporally coherent results.
We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in
networks with efficiency properties beyond those by scale-free networks
and we exhibit corroborating evidence for this suggestion. Despite the
current emphasis on simpler, e.g., critical, networks, networks with
more than one connectivity decay behavior may be the rule rather than
the exception.
Ref: Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains
Ralph Stoop, Victor Saase, Clemens Wagner, Britta Stoop, and Ruedi Stoop,
PRL 108105 (2013)

Wednesday, August 28, 2013 - 11:05 ,
Location: Skiles Bld Room 005 ,
Mason Porter ,
Oxford, UK ,
Organizer:

I discuss "simple" dynamical systems on networks and examine how
network structure affects dynamics of processes running on top of
networks. I consider results based on "locally tree-like" and/or
mean-field and pair approximations and examine when they seem to work
well, what can cause them to fail, and when they seem to produce accurate
results even though their hypotheses are violated fantastically. I'll
also present a new model for multi-stage complex contagions--in which
fanatics produce greater influence than mere followers--and examine
dynamics on networks with hetergeneous correlations. (This talk discusses
joint work with Davide Cellai, James Gleeson, Sergey Melnik, Peter Mucha, J-P Onnela, Felix Reed-Tsochas, and Jonathan Ward.)

Wednesday, April 24, 2013 - 11:05 ,
Location: Skiles 006 ,
B.W. Rink ,
Vrije Univ. Amsterdam ,
Organizer:

Abstract: Dynamical systems with a coupled cell network structure arise
in applications that range from statistical mechanics and electrical
circuits to neural networks, systems biology, power grids and the world
wide web.
A network structure can have a strong impact on the behaviour of
a dynamical system. For example, it has been observed that networks can
robustly exhibit (partial) synchronisation, multiple eigenvalues and
degenerate bifurcations. In this talk I will explain how semigroups and
their representations can be used to understand and predict these
phenomena. As an application of our theory, I will discuss how a simple
feed-forward motif can act as an amplifier.
This is joint work with Jan Sanders.

Wednesday, April 17, 2013 - 11:05 ,
Location: Skiles Bldg, Room 006 ,
Lev Tsimring ,
UC San Diego, BIOCircuits Inst. ,
Organizer:

In this talk, I will describe our recent experimental and theoretical work
on small synthetic gene networks
exhibiting oscillatory behavior. Most living organisms use internal genetic
"clocks" to govern fundamental
cellular behavior. While the gene networks that produce oscillatory
expression signals are typically quite
complicated, certain recurring network motifs are often found at the core
of these biological clocks. One
common motif which may lead to oscillations is delayed auto-repression. We
constructed a synthetic two-gene
oscillator based on this design principle, and observed robust and tunable
oscillations in bacteria. Computational
modeling and theoretical analysis show that the key mechanism of
oscillations is a small delay in the negative
feedback loop. In a strongly nonlinear regime, this time delay can lead to
long-period oscillations that can be
characterized by "degrade and fire'' dynamics. We also achieved
synchronization of synthetic gene
oscillators across cell population as well as multiple populations using
variants of the same design in which
oscillators are synchronized by chemical signals diffusing through cell
membranes and throughout the
populations.

Wednesday, January 30, 2013 - 11:05 ,
Location: Skiles Bld Room 005 ,
Andrew Vlasic ,
Indiana University ,
Organizer:

For many evolutionary dynamics, within a population there are finitely many types that compete with each other. If we think of a type as a strategy, we may consider this dynamic from a game theoretic perspective. This evolution is frequency dependent, where the fitness of each type is given by the expected payoff for an individual in that subpopulation. Considering the frequencies of the population, the logarithmic growth is given by the difference of the respective fitness and the average fitness of the population as a whole. This dynamic is Darwinian in nature, where Nash Equilibria are fixed points, and Evolutionary Stable Strategies are asymptotically stable. Fudenberg and Harris modified this deterministic dynamic by assuming the fitness of each type are subject to population level shocks, which they model by Brownian motion. The authors characterize the two strategy case, while various other authors considered the arbitrary finite strategy case, as well as different variations of this model. Considering how ecological and social anomalies affect fitness, I expand upon the Fudenberg and Harris model by adding a compensated Poisson term. This type of stochastic differential equation is no longer continuous, which complicates the analysis of the model. We will discuss the approximation of the 2 strategy case, stability of Evolutionary Stable Strategies and extinction of dominated strategies for the arbitrary finite strategy case. Examples of applications are given. Prior knowledge of game theory is not needed for this talk.