arXiv 1207.34532012-07-14q-bio.MNmath.DS

生化网络的复线性不变量

Complex-linear invariants of biochemical networks

R. L. Karp, M. Pérez Millán, T. Dasgupta, A. Dickenstein, J. Gunawardena

备注：: 36 pages, 6 figures

摘要：

在分子网络中发现的非线性通常妨碍了对网络行为的数学分析，而这在很大程度上是通过数值模拟来研究的。这可能导致参数确定的困难问题。然而，分子网络通过质量作用动力学产生多项式动力学系统，其稳态是一组多项式方程的零点。这些方程可以用代数方法分析，其中参数被视为符号表达式，其数值不必事先知道。例如，网络的“不变量”是选定状态变量的多项式表达式，在任何稳定状态下都为零。已经发现了编码关键网络属性并区分不同网络结构的不变量。虽然不变量可以通过计算代数方法计算，例如Gröbner基，但这些对于生物现实网络来说在计算上是不可行的。在这里，我们利用化学反应网络理论（CRNT）开发了一个有效的程序来计算不变量，是“复合物”的线性组合，或单项式来自质量作用。我们展示了如何使用这个过程来证明霍恩和杰克逊和Shinar和Feinberg的网络不足最早的结果。然后，我们将我们的方法应用于酶的双功能性，包括细菌EnvZ/OmpR渗透压调节剂和哺乳动物6-磷酸果糖-2-激酶/果糖-2，6-二磷酸酶糖酵解调节剂，其网络有不足之处多达四个。我们表明，双功能导致不同形式的浓度控制，是强大的初始条件或总量的变化。最后，我们概述了一个系统的程序，使用复杂的线性不变量来分析任何缺陷的分子网络。

英文摘要：

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gröbner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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