Seminars are listed in reverse chronological order. The
top of the list is subject to change, since more seminars
are still being planned. All seminars are held at
3:10p.m.
in 1432 Stevenson Center
unless otherwise noted. For further
information on events in the department, you may also
consult the
colloquia schedule, the
weekly
calendar and past
calendars.
Wednesday, December 10th, 2003.
Scott Gruver, of the
Department of Pharmacology,
Vanderbilt University.
Modeling Chemotaxis in Dictyostelium.
Abstract: For proper function, eukaryotic cells must be able to sense
and respond to both spatial and temporal information present in their
environment. Chemotaxis is the cellular process whereby a cell senses
spatial information in the form of a chemical concentration gradient and
responds by moving up the gradient in a directed manner. For the soil-
inhabiting Dictyostelium chemotaxis is a mechanism not only used to
locate bacterial food sources but also in their astonishing survival
mechanism where ~106 individual cells aggregate to form one
multicellular reproductive body. Our abstractions of the biochemical and
biophysical mechanisms implicated in Dictyostelium chemotaxis lead to a
hybrid model focusing on two central aspects of chemotactic cells: a
continuous reaction-diffusion system describing the ability of the cell
to sense concentration gradients which will then serve as input for a
cellular automata model of the kinetic and mechanical properties of the
cytoskeleton, the complex molecular machine responsible for cell
motility and morphology. Preliminary results will be discussed.
Wednesday, December 3rd, 2003.
Darren R. Oldson, of the
Department of Mathematics,
Vanderbilt University.
Dynamics of Feedback--Regulated Flow in the Nephrons of the Kidney:
Perturbations, Oscillations, and Compensation.
Abstract: A mathematical model previously formulated by Layton et al.
predicts that limit-cycle oscillations (LCO) in nephron flow are mediated
by tubuloglomerular feedback (TGF) and that the LCO arise from a
bifurcation that depends heavily on the feedback gain magnitude
\gamma. We will use this model to show how sustained perturbations
in proximal tubule flow, a common experimental maneuver, can initiate
or terminate LCO by changing the value of \gamma. This result may
help explain experiments in which intratubular pressure oscillations
were initiated by the sustained introduction or removal of fluid from
the proximal tubule. In addition, this model predicts that sustained
perturbations that initiate or terminate LCO can yield substantial and
abrupt changes in both distal NaCl delivery and NaCl delivery
compensation, changes that may play an important role in the response
to physiological challenge. The linear stability analysis for an
ordinary differential equation will be compared with the linear
stability analysis for the delay partial differential equation that
arises in this model for TGF.
Wednesday, November 19th, 2003.
Laurent Pujo-Menjouet, of the
Department of Mathematics,
Vanderbilt University.
Long Period Oscillations in a G0 Model of Hematopoietic
Stem Cells.
Abstract: This paper analyzes the dynamics of a Go cell cycle model of
pluripotential stem cells to understand the origin of the long period
oscillations observed in periodic chronic myelogenousleukemia (PCML). The
model dynamics are described by a system of two delayed differential
equations. We give conditions for the local stability of the non-trivial
steady state. We use this conditions to study when stability is lost and
oscillations occur, and how various parameters modify the period of these
oscillations. We modify the original model in order to compute an
explicit solution and give an exact form of the period and the amplitude
of oscillations. We illustrate these results numerically and show that
the main parameters controlling the period are the cellular loss rates.
Wednesday, October 15th, 2003.
Tim Schulze, of the
Department of Mathematics,
University of Tennessee.
The Many Facets of Thin Film Growth.
Abstract: Thin layers of crystalline material are often deposited onto
a substrate to produce coating surfaces and micro-electronic materials.
These "epitaxial" thin films are studied and modeled over an enormous
range of length scales. I will review some of the common approaches
to modeling this problem and present a hybrid method for simulating
epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations
with the Burton-Cabrera-Frank model for crystal growth. This involves
partitioning the computational domain into KMC regions and regions
where one time-steps a discretized diffusion equation. Computational
speed and accuracy are discussed. The method is significantly faster
than KMC while accounting for many effects due to stochastic
fluctuations. I will illustrate this approach with simulations of
a two-dimensional "step-flow" instability.
Wednesday, October 1st, 2003.
David Chopp, of
Engineering Sciences and
Applied Mathematics,
Northwestern University.
Modeling Quorum Sensing in Bacterial Biofilms.
Abstract: Bacterial biofilms may be the most common form of life on the
planet. Neary all fluid/solid interfaces host some form of biofilm. Some
biofilms are beneficial, and others are destructive. There is much yet
to be learned about the aggregation of cells, and their subsequent
differentiation into structured biofilms. Some biofilms are able to
monitor their localpopulation density, and control their group behavior
through the use of signal molecules. When a threshold concentration of
the signal in the biofilm is reached (called quorum sensing), the
population may change behavior in a fundamental way. In this talk, we
will explore a mathematical description of quorum sensin. The model will
be tied to experiments on the bacterium P. aeruginosa, which is the most
common form of infection for people with cystic fibrosis. We will use
the model to predict the onset of quorum sensing, which is the trigger
for P. aeruginosa to become virulent.
Monday, September 29th, 2003.
Angela Stevens, of
the Max Planck Institute for
Mathematics in the Sciences, Leipzig, Germany.
Structure and Function: Interacting Cell Systems.
Abstract: Cell systems, which build up defined structures, as in
tissues,
organs and in self-organizing microbiological populations, do so
by a complex interplay of several mechanisms. Among them are,
cell signaling, cell growth, cell death, and cell motion, whose
specific functioning and malfunctioning often results in clearly
distinguishable patterns on the population level.
A major question in this context is, how can the underlying
functioning of the respective cell system be deduced from
this macroscopic information observed by experimentalists?
Examples will be presented for the analysis of such kind of
"inverse" questions for signal dependent motion in interacting
cell systems. Kinetic and parabolic models for chemosensitive
movement will be discussed.
Wednesday, September 24th, 2003.
G. Bard Ermentrout, of the
Department of Mathematics,
University of Pittsburgh.
Flash and Turn: Self-Organization in Ants and Fireflies.
In this talk, I will describe analogies between self-organization
between communicating insects and similar behavior observed in networks
of neurons. I will first explore models of synchronous flashing of
fireflies. Firelies communicate with flashes of light and in parts of
southeast Asia, thousands congregate and rhythmically flash in unison.
Certain species are able to slowly adjust their intrinsic properties in
orde to phase-lock with essentially no phaselag. Others behave as
conventional coupled oscillators. The second part of the talk describes
communication through odor between ants. I describe models for learning
trails that behave much like winner-take-all algorithms in neural
networks. I then describe the behavior of rotating ant mills in which
groups of ants produce essentially a rotating wave of activity.
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