化学反应网络中速率独立性的图解条件
Graphical Conditions for Rate Independence in Chemical Reaction Networks
摘要：
化学反应网络（CRN）提供了分子相互作用网络的有用抽象，其中分子结构以及质量守恒原理被抽象出来，以专注于网络结构的主要动力学性质。在通过常微分方程的解释中，我们说具有不同输入和输出物质的CRN计算正实函数$f : R+ $ \rightarrow $ R+$，如果对于任何输入物质的初始浓度x，输出分子物质的浓度稳定在浓度f（x）。图灵完备性的概念化学模拟计算已经建立了证明，任何可计算的实函数可以计算的CRN在一组有限的分子物种。速率无关CRN形成具有高实用价值的受限类别的CRN，因为它们在结果完全独立于反应速率并且仅取决于输入浓度的意义上享有绝对鲁棒性的形式。由速率无关CRN计算的函数在数学上被表征为来自输入物种的分段线性函数的集合。然而，这并没有提供一种方法来决定给定的CRN是否是速率无关的。在本文中，我们提供了图形条件的Petri网结构的CRN，需要率独立性的财产，无论是对所有物种或某些输出物种。我们发现，在Biomodels存储库的精选部分中，在测试的590个反应模型中，发现2个反应图满足我们对所有物种的速率独立条件，94个反应图满足某些输出物种的速率独立条件，其中29个反应图满足某些非平凡输出物种的速率独立条件。我们的图形条件是基于一个非标准的使用的Petri网概念的地方不变和虹吸管计算的约束编程技术的效率的原因。
英文摘要：
Chemical Reaction Networks (CRNs) provide a useful abstraction of molecular interaction networks in which molecular structures as well as mass conservation principles are abstracted away to focus on the main dynamical properties of the network structure. In their interpretation by ordinary differential equations, we say that a CRN with distinguished input and output species computes a positive real function $f : R+ $\rightarrow$ R+$, if for any initial concentration x of the input species, the concentration of the output molecular species stabilizes at concentration f (x). The Turing-completeness of that notion of chemical analog computation has been established by proving that any computable real function can be computed by a CRN over a finite set of molecular species. Rate-independent CRNs form a restricted class of CRNs of high practical value since they enjoy a form of absolute robustness in the sense that the result is completely independent of the reaction rates and depends solely on the input concentrations. The functions computed by rate-independent CRNs have been characterized mathematically as the set of piecewise linear functions from input species. However, this does not provide a mean to decide whether a given CRN is rate-independent. In this paper, we provide graphical conditions on the Petri Net structure of a CRN which entail the rate-independence property either for all species or for some output species. We show that in the curated part of the Biomodels repository, among the 590 reaction models tested, 2 reaction graphs were found to satisfy our rate-independence conditions for all species, 94 for some output species, among which 29 for some non-trivial output species. Our graphical conditions are based on a non-standard use of the Petri net notions of place-invariants and siphons which are computed by constraint programming techniques for efficiency reasons.
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