Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph
Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph
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DOI：
10.1137/050634177
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发表时间：
2006-01-01
影响因子：
1.9
通讯作者：
Feinberg, Martin
中科院分区：
文献类型：
--
作者：
Craciun, Gheorghe;Feinberg, Martin
对于质量作用动力学，等温均匀连续流搅拌釜式反应器中多重平衡的容量由化学反应的底层网络结构决定。我们提出了一种新的图论方法来区分复杂的反应网络，可以承认多个平衡和那些不能。特别是，我们与每个网络的物种反应图，这是类似的反应网络表示所绘制的生物化学家，我们表明，如果该图满足一定的弱条件，对应于网络的微分方程不能承认多个平衡，无论什么值的速率常数。因为这些条件非常温和，它们相当于强大的（而且相当微妙的）必要条件，如果网络要有能力产生多重均衡，它就必须满足这些条件。这类广泛的定性结果特别适用，因为对于复杂的反应网络，单个反应速率常数很少完全已知（如果它们是已知的话）。一些结论性意见涉及与生物学的联系。
For mass action kinetics, the capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the structure of the underlying network of chemical reactions. We suggest a new graph-theoretical method for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot. In particular, we associate with each network a species-reaction graph, which is similar to reaction network representations drawn by biochemists, and we show that, if the graph satisfies certain weak conditions, the differential equations corresponding to the network cannot admit multiple equilibria no matter what values the rate constants take. Because these conditions are very mild, they amount to powerful (and quite delicate) necessary conditions that a network must satisfy if it is to have the capacity to engender multiple equilibria. Broad qualitative results of this kind are especially apt, for individual reaction rate constants are rarely known fully for complex reaction networks (if they are known at all). Some concluding remarks address connections to biology.