# Variable elimination in post-translational modification reaction networks with mass-action kinetics

Source: [Variable elimination in post-translational modification reaction networks with mass-action kinetics](<https://www.sota2.com/research/paper/68fa4f361e209131ce961b7b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:11:47.713Z

Authors: Elisenda Feliu, Carsten Wiuf

Published: 2011-07-18T19:26:04.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1107.3531>)

[PDF](<https://arxiv.org/pdf/1107.3531.pdf>)