Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws.
Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws.
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具有双线性速率定律的化学反应网络稳态方程的解析解。
DOI：
10.1109/tcbb.2013.41
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Edwards,JeremyS
中科院分区：
文献类型：
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作者：
Halász,AdámM;Lai,Hong-Jian;McCabePryor,Meghan;Radhakrishnan,Krishnan;Edwards,JeremyS
真正的稳态是一个罕见的发生在活的有机体，但他们的知识是必不可少的准稳态近似，多稳态分析，和其他重要的工具，在化学反应网络（CRN）的调查，用于描述分子过程的细胞水平。在这里，我们提出了一种方法，可以提供封闭形式的稳态解决方案，复杂的系统，从CRN与二元反应和质量作用速率定律。我们将寻找稳定状态的非线性代数问题映射到高维空间中的线性问题上。我们表明，线性化版本的稳态方程服从线性守恒定律的原始CRN。我们确定了两类问题，其中完整的，最小参数化的解决方案，可以只使用机器的线性系统和一个明智的选择作为自由参数的变量。我们在CRN上举例说明了我们的方法，提供了明确的公式，描述了两种重要类型的RTK受体-配体系统（VEGF和EGF-ErbB 1）的信号启动。
True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.