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.

中文翻译：

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化学反应网络中速率无关的图形条件

化学反应网络 (CRN) 提供了一种有用的分子相互作用网络抽象，其中分子结构和质量守恒原理被抽象出来，专注于网络结构的主要动力学特性。在他们对常微分方程的解释中，我们说具有不同输入和输出物种的 CRN 计算了一个正实函数 $f ：R+ $\rightarrow$ R+$，如果对于输入物种的任何初始浓度 x，输出分子种类稳定在浓度 f (x)。通过证明任何可计算的实函数都可以由 CRN 在有限的分子种类集上计算，已经建立了化学模拟计算概念的图灵完备性。与速率无关的 CRN 形成了一类具有高实用价值的受限 CRN，因为它们具有绝对稳健性，即结果完全独立于反应速率并仅取决于输入浓度。由与速率无关的 CRN 计算的函数在数学上被表征为输入物种的分段线性函数集。然而，这并没有提供一种方法来确定给定的 CRN 是否与速率无关。在本文中，我们提供了 CRN 的 Petri 网结构的图形条件，该结构包含所有物种或某些输出物种的速率无关属性。我们表明，在 Biomodels 存储库的策划部分，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无关条件，一些输出物种有 94 个，其中一些非平凡输出物种有 29 个。我们的图形条件基于对位置不变量和虹吸管的 Petri 网概念的非标准使用，这些概念是出于效率原因通过约束编程技术计算的。