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
4:10p.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 8, 2004.
No seminar.
Wednesday, December 1, 2004.
No seminar.
Wednesday, November 17, 2004.
Daniele Andreucci,
University of Rome, La Sapienza, Italy.
Title: Mathematical models for electrical conduction in
biological tissues.
Abstract:
We compare some mathematical models, based on the theory of
homogenization, for electrical or thermal conduction
in media with a microstructure. Though they essentially originate
from the same setting, before homogenization, the limiting
mathematical schemes deeply differ, due to different
scaling choices in the conditions prescribed on the
interface of the microstructure.
Wednesday, November 10, 2004.
Brett McKinney,
Immunology and Infectious Disease,
Vanderbilt University.
Grammatical evolution for reverse engineering of biochemical pathways
from time-series data.
Abstract: With the development of high throughput technologies,
datasets are becoming available that involve the time-dependent profiles
of biologically important chemicals, such as mRNA levels in gene
expression experiments, protein levels in protein arrays, and
concentrations of chemicals participating in metabolic pathways. The
kinetic profiles of these biochemicals can be accurately predicted by
solving the appropriate system of differential equations, and while
numerical methods have been developed to estimate model parameters from
time-series data, these methods generally assume that the mathematical
model is already known. Unfortunately, for these complex biological
systems, models are at best partially known. In this talk I will
describe a new machine learning method known as Grammatical Evolution
and how we have applied it to the inverse problem of reverse engineering
a coupled system of nonlinear ordinary differential equations from time
series data. This method simultaneously infers the topology of the model
and the model parameters.
Wednesday, November 3, 2004.
Mark Byrne, Department of Pharmacology, Vanderbilt University.
Title: Lipid"omics": Methods and Applications.
Abstract: Mass spectral analysis of lipid extracts from a homogeneous
cell population (~10^6 cells) allows for the identification of more than
450 lipids (including acyl chain composition). In addition,
species-specific lipid changes can be assessed in response to
perturbations of the population by ligand addition or other alterations
of the population. I will discuss data analysis issues, some
applications of lipid-"omics", and attempts to bridge the gap between
experimental results and understanding in the form of phenomenological
models (ODEs) of inter-cellular signaling events.
Wednesday, October 27, 2004.
Lixin Shen, Department of Pharmacology, Vanderbilt University.
Title: Mathematical and Numerical Modeling of Spatio-Temporal
Signaling in Rod Phototransduction.
Abstract: We present a mathematical model for the rod
phototransduction cascade, describing the diffusion of the second
messengers, cGMP and Ca2+ in signaling in the rod outer segment of
vertebrates. Numerical simulations of the response of dark-adapted
Salamander rods to dim light flashes are performed. The results are
consistent with experimental data. The simulations are based on finite
element discretization and implemented in Matlab.
Wednesday, October 20, 2004.
No seminar.
Thursday, October 14, 3:10pm, 1120 Stevenson Center.
Dr. Stephen J. Watson, Engineering Sciences and Applied Mathematics,
Northwestern University.
Title: Coarsening Dynamics of Nano-Faceted Crystalling Surfaces.
Research Interests:
The mathematical theory and modeling of self-assembly and pattern
formation in phase ordering systems that arise in the natural sciences.
My research has been primarily driven in this direction by questions
arising in Nanotechnology, such as the behavior of quantum dot arrays on
silicon surfaces. The world of Biology also offers compelling examples
of such behaviors, such as the phase ordering of membrane proteins on
the lipid bi-layer of a cell; a problem which I plan to attack in the
future.
Wednesday, October 13, 2004.
Joseph McLaughlin,
Department of Pharmacology,
Vanderbilt University.
Title: Mathematical Modeling of Thrombin-Mediated
Vascular Permeability.
Abstract: Endothelial cells line the interior of blood vessels
forming a dynamic layer which acts as a barrier between blood and
interstitial tissues. The ability to dynamically regulate the
permeability of the monolayer is essential to a healthy vasculature.
Barrier dysfunction leads to edema, a devastating component of many
diseases such acute lung injury or adult respiratory distress syndrome
(ARDS) and sepsis. Thrombin is a potent activator of barrier
dysfunction, here we are studying the mechanisms by which thrombin
mediates endothelial permeability changes in human microvascular
endothelial cells (HMEC-1). Thrombin exerts its cellular effects by
interacting with G protein coupled protease-activated receptors (PAR)
thereby activating several classes of G proteins. PARs are unique among
G protein-coupled receptors in that they are activated by thrombin
cleaving the amino-terminal extracellular domain of the receptor,
exposing a new terminus which folds back onto the receptor and activates
it. Peptide analogs of the tethered ligand function as thrombin
receptor agonist peptides (TRAP). We show here that thrombin and TRAP
can differentially regulate different classes of G protein signaling
pathways. We interpret this to mean different conformations of PARs
traffic to different G proteins. This hypothesis would provide a
therapeutic window to search for allosteric modulators of PARs that work
at different sites from the tethered ligand.
Wednesday, October 6, 2004.
Daniel Hahs, Center for Human Genectics Research,
Vanderbilt Medical Center.
Title: Real-time parameter estimation problems in
biotechnology.
Abstract: The purpose of this talk is to describe some problems
in the biotechnology area where real-time parameter estimation is
required and demonstrate implementations of Kalman filtering to provide
it. Five sample problems include estimation of: 1) enzyme kinetics, 2)
fermentation system model parameters, 3) chemical reaction order and
Arrhenius constants, 4) cellular response parameters for cell layer
n rate in an
age-structured population.
diffused with toxin, and 5) cellular product generation rate
in an age-structured population.
Wednesday, September 29, 2004.
Philip Crooke ,
Department of Mathematics,
Vanderbilt University.
Title: Mathematical Modeling in a Clinical Science: Pulmonary and
Critical Care Medicine.
Abstract: Mathematical modeling has been used effectively in the basic
sciences of biomedical research. I believe that it can be used also in
more applied areas of medicine, namely, the clinical sciences. In this
talk, we examine some simple mathematical models that may aid clinicians
in providing more effective and safer patient care. The main focus of
the talk is the modeling of mechanical ventilation with the central goal
of providing information to the clinician that minimizes lung injury.
Using very elementary approaches, we construct models that provide
information about tidal volumes, mean alveolar pressures, and
end-expiratory pressures, given the physiologic parameters of the
patient and the clinical-set parameters of the ventilator. We look at
lung recruitment using variable compliance models, non-invasive
ventilation and its instabilities, and the Ranieri stress index as a
measure of tidal recruitment and hyperinflation.
Wednesday, September 22, 2004.
No seminar
Wednesday, September 15, 2004.
Laurent Pujo-Menjouet ,
Department of Mathematcis,
Vanderbilt University.
Analysis of Cell Kinetics Using a Cell Division Marker:
Mathematical Modeling of Experimental Data.
Abstract :
We consider an age-maturity structured model arising from a blood cell
proliferation problem. This model is ``hybrid" i.e., continuous in
time and age but the maturity variable is discrete. This is due to the
fact that we include the cell division marker CarboxyFluorescein
diacetate Succinimidyl Ester (CFSE). We use our mathematical analysis
in conjunction with experimental data taken from the division analysis
of primitive murine bone marrow cells to characterize the
maturation/proliferation process. Cell cycle parameters such as
proliferative rate $\beta$, cell cycle duration $\tau$, apoptosis rate
$\gamma$ and loss rate $\mu$ can be evaluated from CFSE+ cell tracking
experiments.
Wednesday, September 8, 2004.
Doug Hardin ,
Department of Mathematics,
Vanderbilt University.
Properties of minimum Riesz energy point sets on rectifiable manifolds.
Abstract: For a compact set $A\subset {\bf R}^{d'}$, we consider
minimal $s$-energy arrangements of $N$ points
that interact through a power law (Riesz) potential $V=1/r^{s}$,
where $s>0$ and $r$ is Euclidean distance in ${\bf R}^{d'}$.
For example, this is the classical Thomson problem of distributing
electrons on a sphere in the case
$A$ is the unit sphere in ${\bf R}^3$, and $s=1$.
In applications one is often interested in determining when such point
sets
are ``uniformly'' distributed on
$A$ for large $N$. Physicists are also interested in ``universal''
(i.e. independent of $s$)
properties of such configurations.
In this talk I will present recent results
characterizing asymptotic (as $N\to \infty$) properties of $s$-energy
optimal
$N$-point configurations for a class of rectifiable $d$-dimensional
manifolds and $s\ge d$. This is joint work with E.B. Saff.
Wednesday, September 1, 2004.
Juergen Saal,
Department of Mathematics,
Vanderbilt University.
An Analytical Approach to the Ekman Boundary Layer Problem
Abstract: Boundary layers appear in a natural way in geophysical fluid
dynamics. The boundary layer in the theory of rotating fluids, known as
the Ekman layer, is between a uniform geostrophic flow and a solid
boundary at which the no slip condition applies. The observed effect
inside the layer, i.e. close to the boundary, is that the flow vector
behaves as a growing spiral, the Ekman spiral, converging to the
geostrophic flow while increasing the distance to the boundary.
Mathematically this situation is modeled by the Navier-Stokes equations
with Coriolis force in a half-space. The Ekman spiral solution is an
exact solution of this system. We will discuss existence and uniqueness
of (time-) local strong solutions of the problem for a certain class of
initial data including the Ekman spiral solution. The method is to apply
a standard iteration procedure to the nonlinear Navier-Stokes equations.
The main difficulties arising in this approach are caused by the
particular class of initial data. Since the Ekman spiral solution
depends on the normal component only, we have to deal with spaces of
initial data nondecreasing at infinity.
Previous semesters:
