### Math Biology Seminar Abstracts

Wednesday February 12, 2003

## Inside the Mind of the Amoeba: Simulation and Analysis of
Biochemical Signal-Transduction Networks.

Peter Thomas

Salk Institute, San Diego

Abstract:
In lieu of nervous systems, single-celled organisms use complex
networks of biochemical reactions to sense the world around them, make
decisions, and take action. A wealth of quantitative biological data
from bioinformatics to fluorescence microscopy has created the
possibility of building biophysically realistic models of the
information processing occurring inside cells, in analogy to models of
biological neural networks. Biochemical networks present several
unique mathematical challenges. Chemical reactants are localized
within subcellular volumes, requiring PDE rather than ODE treatments
of their behavior. Small numbers of interacting molecules make the
typical biochemical network inherently noisy, leading us to consider
approximations to stochastic PDEs. Finally, chemical systems
typically occupy state spaces of large dimension, forcing us to look
for effective means of "coarse-graining" the representation of
chemical states. We have constructed a finite-element model for
solving arbitrary boundary-coupled reaction-diffusion PDEs as a
platform for studying spatially heterogeneous signal-transduction
networks, and used it to develop a model for the orienting response of
a eukaryotic cell during directed cell movement (chemotaxis). We are
building on this finite-element framework to accommodate the effects
of fluctuations as an approach to stochastic PDEs, and as a way of
formalizing dimension-reduction of chemical state spaces.

For more information contact J. Keener, 1-6089

E-mail:
keener@math.utah.edu