Banaji Murad, Craciun Gheorghe
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK and Department of Biological Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK.
Adv Appl Math. 2010 Feb 1;44(2):168-184. doi: 10.1016/j.aam.2009.07.003.
In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinetics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.
在本文中，我们讨论了如何判定一个一般的化学反应体系在不考虑诸如反应速率常数等参数值，以及不考虑诸如质量作用动力学、米氏动力学等化学动力学类型的情况下，是否无法存在多个平衡态的问题。我们的结果关联了先前描述的化学反应体系单射性的线性代数和图论条件。在建立了这两种形式体系之间的转换关系后，我们表明，之前在质量作用动力学体系背景下开发的一种图论测试方法，可以应用于具有任意动力学的反应体系。该测试方法易于通过算法实现，并且通常无需任何计算就能判定，它排除了所讨论体系存在多个平衡态的可能性。
