Wednesday February 12, 2003
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.
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