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Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces

机译:广义质量作用系统:化学计量和动力学顺序子空间的复杂平衡平衡和符号向量

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摘要

Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary power-law rate functions and serves as a more realistic model for reaction networks in intracellular environments. In addition to the complexes of a network and the related stoichiometric subspace, we introduce corresponding kinetic complexes, which represent the exponents in the rate functions and determine the kinetic-order subspace. We show that several results of chemical reaction network theory carry over to the case of generalized mass action kinetics. Our main result essentially states that if the sign vectors of the stoichiometric and kinetic-order subspace coincide, there exists a unique complex balancing equilibrium in every stoichiometric compatibility class. However, in contrast to classical mass action systems, multiple complex balancing equilibria in one stoichiometric compatibility class are possible in general.
机译:群众行动系统捕获在均匀和稀溶液中的化学反应网络。我们建议一个广义的质量作用系统的概念,该系统可以接受任意的幂律率函数,并可以作为细胞内环境中反应网络的更实际模型。除了网络和相关的化学计量子空间的络合物之外,我们还引入了相应的动力学络合物,它们代表了速率函数中的指数并确定了动力学级子空间。我们表明,化学反应网络理论的一些结果可以推广到广义质量作用动力学的情况。我们的主要结果基本上表明,如果化学计量和动力学顺序子空间的符号向量重合,则在每个化学计量的相容性类别中都存在唯一的复杂平衡平衡。但是,与经典的质量作用系统相反,一个化学计量的相容性类别中的多个复杂平衡平衡通常是可能的。

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