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
3:10 PM
in 1310 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, April 18,
2:10 PM
(Note: Special Time), SC 1310.
Peter Hinow, Vanderbilt University
Title: A mathematical model separates quantitatively the cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor.
Abstract:
In this talk we report on some recent joint work with Shizhen Emily Wang
(Department of Cancer Biology, Vanderbilt University) and Glenn Webb,
(Department of Mathematics, Vanderbilt University).
Oncogene signaling is known to deregulate cell proliferation resulting in
uncontrolled growth and cellular transformation. Gene amplification and/or
somatic mutations of the HER2/Neu (ErbB2) proto-oncogene occur in
approximately 20% of breast cancers. A therapeutic strategy that has been
used to block HER2 function is the small molecule tyrosine kinase
inhibitor lapatinib. Using human mammary epithelial cells that overexpress
HER2, we determined the anti-proliferative effect of lapatinib through
measuring the total cell number and analyzing the cell cycle distribution.
A mathematical model was used to interpret the experimental data. The
model suggests that lapatinib acts as expected by slowing the transition
through G1 phase. However, the experimental data indicated a previously
unreported late cytotoxic effect, which was incorporated into the model.
Both effects depend on the dosage of the drug and show saturation
kinetics. The model separates quantitatively the cytostatic and cytotoxic
effects of lapatinib and may have implications for preclinical studies
with other anti-oncogene therapies.
Wednesday, April 11, 3:10 PM, SC 1310.
Miriam Kraatz, Vanderbilt University
Title: Correlational equivalence testing.
Wednesday, March 21, 3:10 PM, SC 1310.
Joachim Escher, University of Hannover
Title: Bifurcation Analysis of an Elliptic Free Boundary Problem
Modelling the Growth of Avascular Tumors.
Abstract:
We are concerned with a moving boundary problem modelling the growth
of in vitro tumors. The problem under discussion consists in two elliptic
equations involving surface tension effects on the free boundary.
Besides well-posedness issues we are interested in the stability properties
and bifurcation behaviour of steady state solutions.
Wednesday, February 28, 3:10 PM, SC 1310.
Yosef Cohen, University of Minnesota
Title: Evolutionary distributions: A theoretical framework for evolutionary ecology.
Abstract:
Adaptive traits are inherited with small mutations. They are subject to natural selection. An adaptive space is made of a set of adaptive traits. Within this adaptive space live distributions of the density of phenotypes. The dynamics of this density reflect evolution by natural selection. We call these distributions Evolutionary Distributions (ED). The adaptive space with its ED form the evolutionary space. ED are derived from first principles of population dynamics: birth, death, mutations and selection. This approach leads to a rich behavior of ED with and without stability. With ED, it is easy to understand how we may find phenotypes on a set of adaptive traits. Thus, invasions by mutants represent perturbations to the ED. Stable ED therefore do not allow invasion of mutants and as such, are akin to the concept of evolutionary stable strategies (ESS). We apply the theory to three common coevolutionary interactions: competion, predation and host pathogen. We also apply the theory to (open) ecosystems and illustrate applications in the context of primary producers and primary consumers ecosystems. We also illustrate applications of coevolution in the context of global change. The theory is restricted to (not necessarily continuous) adaptive traits that can be characterized by real numbers.
Wednesday, February 21, 3:10 PM, SC 1310.
Huaizhong Ren, Tennessee State University
Title: Autonomous Stochastic Perturbations of Hamiltonian Systems.
Abstract:
The perturbation of a Hamiltonian system of one degree of freedom by a small
autonomous random field is considered in the simplest nontrivial case, where the
Hamiltonian has at least one saddle critical point. The study focuses on the long
time behavior of a solution under the perturbation. For a special type of perturbing
field with some mild restriction, we show that the Averaging Principle holds and
describe the limit by a random process on a graph, which is homeomorphic to the
space of level sets of the Hamiltonian. This may also help in regularizing some
deterministic perturbations of the Hamiltonian system.
Wednesday, February 14, 3:10 PM, SC 1310.
Heiko Enderling, Center of Cancer Systems Biology, Caritas St. Elizabeth's Medical Center, Tufts University School of Medicine
Title: Mathematical model of breast cancer development, local treatment and recurrence.
Abstract: Cancer development is a stepwise process through which normal somatic cells acquire mutations which enable them to escape their normal function in the tissue and become self-sufficient in survival. We present a simplified differential equation model of carcinogenesis mutation and expansion process, in which we assume that the loss of two tumour suppressor genes is
sufficient to give rise to a cancer cell. Our mathematical model of the stepwise development of breast cancer verifies the idea that the normal mutation rate in genes is only sufficient to give rise to a tumour within a
clinically observable time if a high number of breast stem cells and tumour suppressor genes exist or genetic instability is involved as a driving force of the mutation pathway. Furthermore our model shows that if a mutation occurred in stem cells pre-puberty, and formed a field of cells with this mutation through clonal formation of the breast, it is most likely that a tumour will arise from within this area. We then apply different treatment strategies, namely surgery and different adjuvant adiotherapy protocols, and use the model to identify different sources of local recurrence and analyse their prevention.
Wednesday, February 7, 3:10 PM, SC 1310.
Christoph Walker, Vanderbilt University
Title: Global well-posedness of a haptotaxis model with spatial and age
structure.
Abstract: A system of non-linear partial differential equations modeling
tumor invasion into surrounding healthy tissue is analyzed. The model
focuses on key components involved in tumor cell migration and takes
into account cell motility and haptotaxis, that is, the directed
migratory response of tumor cells to the extracellular environment.
Individual cell processes are modeled according to cell age. Global
existence and uniqueness of non-negative solutions is shown.
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