Biology – Quantitative Biology – Molecular Networks
Scientific paper
2011-07-18
Biology
Quantitative Biology
Molecular Networks
Scientific paper
We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well as theoretically. The steady states of such a system are solutions to a system of polynomial equations with as many variables as equations. Even for small systems the task of finding the solutions is daunting. We develop a mathematical framework based on the notion of a cut, which provides a linear elimination procedure to reduce the number of variables in the system. The steady states are parameterized algebraically by a set of "core" variables, and the non-negative steady states correspond to non-negative values of the core variables. Further, minimal cuts are the connected components in the species graph and provide conservation laws. A criterion for when a set of independent conservation laws can be derived from cuts is given.
Feliu Elisenda
Wiuf Carsten
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