Conditions for Solvability in Chemical Reaction Networks at Quasi-Steady-State
Conditions for Solvability in Chemical Reaction Networks at Quasi-Steady-State
复制标题
准稳态化学反应网络的可解性条件
DOI：
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发表时间：
2017
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通讯作者：
Mark Sweeney
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作者：
Mark Sweeney
准稳态假设（英语：Quasi-stable-state assumption，简称QSSA）是一种广泛应用于化学和化学工程的近似方法，用来简化反应机理。该方法的关键步骤是求多元多项式组的根式。然而，Pantea，Gupta，Rawlings和Craciun表明存在相关多项式不可由根解的机制，因此QSSA的约化是不可能的。然而，在实践中，QSSA的减少总是成功的。为了对这一现象提供一些解释，我们证明了一类常见的化学反应网络是可解的。在建立这一结果的过程中，我们研究的问题，当它是可能的，以确保有许多（准）稳定状态。我们还将我们的结果应用到几个例子中，特别是证明了Pantea，Gupta，Rawlings和Craciun提出的不可解例子的极小性。
The quasi-steady-state assumption (QSSA) is an approximation that is widely used in chemistry and chemical engineering to simplify reaction mechanisms. The key step in the method requires a solution by radicals of a system of multivariate polynomials. However, Pantea, Gupta, Rawlings, and Craciun showed that there exist mechanisms for which the associated polynomials are not solvable by radicals, and hence reduction by QSSA is not possible. In practice, however, reduction by QSSA always succeeds. To provide some explanation for this phenomenon, we prove that solvability is guaranteed for a class of common chemical reaction networks. In the course of establishing this result, we examine the question of when it is possible to ensure that there are finitely many (quasi) steady states. We also apply our results to several examples, in particular demonstrating the minimality of the nonsolvable example presented by Pantea, Gupta, Rawlings, and Craciun.