Homotopy methods for counting reaction network equilibria

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, non-linear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases...

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Bibliographic Details
Published in:Mathematical biosciences 2008-12, Vol.216 (2), p.140-149
Main Authors: Craciun, Gheorghe, Helton, J. William, Williams, Ruth J.
Format: Article
Language:English
Subjects:
Biochemical reaction networks
Homotopy
Kinetics
Models, Biological
Models, Chemical
Multiple equilibria
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Summary:Dynamical system models of complex biochemical reaction networks are usually high-dimensional, non-linear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2008.09.001