质量作用动力学翻译后修饰反应网络中的变量消除
Variable elimination in post-translational modification reaction networks with mass-action kinetics
摘要：
我们定义了化学反应网络的一个子类，称为翻译后修饰系统。这类系统的重要生物学实例包括MAPK级联和双组分系统，它们在实验和理论上都得到了充分研究。这样一个系统的稳定状态是一个多项式方程组的解，该方程组的变量与方程组一样多。即使对于小型系统，寻找解决方案的任务也是令人望而生畏的。我们开发了一个数学框架的基础上的概念，削减，它提供了一个线性消除过程，以减少系统中的变量的数量。稳态由一组“核心”变量代数参数化，并且非负稳态对应于核心变量的非负值。此外，最小割是物种图中的连通分量，并提供守恒律。给出了一组独立的守恒律何时可以由割导出的判据。
英文摘要：
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.
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