Mathematical Modeling of Heterogeneous Bio-Switches

Document Type

Presentation Abstract

Presentation Date

9-30-2004

Abstract

Various biological systems that exhibit transitions between different possible stable steady states under influence of internal and/or external perturbations are usually modeled in terms of nonlinear differential equations with multiple equilibria. Ordinary differential equation models describe cases where fast mixing of isolated species (biological, chemical, etc.) occurs so that spatial dependence of species population/concentration changing in time can be neglected. In these systems perturbation of species population/concentration above a certain threshold level leads to a transition from one spatially uniform steady state to a new spatially uniform state. Such systems can be interpreted as homogeneous (spatially independent) bio-switches. When spatial dependence in the models is important we arrive at heterogeneous switches where the initiation of a transition from one stable equilibrium to another will depend on the type of boundary conditions imposed on a system (no flux conditions vs. fixed species population/concentration conditions), on the presence/absence of convection, as well as on the shape of the initial perturbation. The ideas behind mathematical modeling of heterogeneous bio-switches (i.e., the discussion of why transitions between various steady states occur, how the transitions are initiated, how the tune-ups of switches can be done to change the transition threshold values and to make transitions asymmetric, etc.) are going to be addressed in the presentation.

Additional Details

This talk is a part of the UM-Toyo U Symposium on Bio-Nano Technology & Sciences.

Thursday, 30 September 2004
3:50 p.m. in UC Theatre

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