2011/07/18 by Elisenda Feliu, Feliu, Elisenda, Carsten Wiuf +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Computational Drug Discovery Methods #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Molecular Networks (q-bio.MN) #math.DS #q-bio.MN
paper · pdf · doi:10.48550/arxiv.1107.3531
arxiv created 2011/07/18 · openalex publication_date 2011/07/18 · arxiv updated 2011/07/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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.