标题： 翻译结果：在具有质量作用动力学的翻译后修饰反应网络中的变量消去 显示英文标题

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

摘要： 我们定义了一类称为翻译后修饰系统的化学反应网络子类。 这种系统的重要生物学例子包括MAPK级联和双组分系统，它们在实验和理论上都得到了广泛研究。 此类系统的稳态是具有与方程数量相同变量的多项式方程组的解。 即使对于小系统，寻找这些解的任务也令人望而生畏。 我们开发了一个基于切割概念的数学框架，该框架提供了一种线性消去过程，以减少系统中的变量数量。 稳态通过一组“核心”变量进行代数参数化，非负稳态对应于核心变量的非负值。 此外，最小切割是物种图中的连通组件，并提供了守恒定律。 给出了何时可以从切割中推导出一组独立的守恒定律的标准。 显示英文摘要

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.