Südi J
Institut für Toxikologie, Christian Albrechts Universität, Kiel, Germany.
Math Biosci. 1996 Nov;138(1):45-77. doi: 10.1016/s0025-5564(96)00114-9.
A recent report by Brown and Cooper demonstrated the usefulness of calculating "flux control coefficients" for each of the rate constants involved in the assumed kinetic mechanism of a single enzyme. The calculations of Brown and Cooper involved numerical differentiation. The present article substantiates this report by showing that the numerical results of Brown and Cooper can also be obtained in an explicit form. The analytical equations given establish the relationship between rigorously specified overall rate processes and "elementary rate constants," both being defined by the rate equations of classical enzyme kinetics. It is shown that analytical flux control coefficients can be obtained for all types of rate processes considered in classical enzyme kinetics, including, "initial rates," equilibrium exchange reactions, and reactions at limiting levels of substrate (and/or product) saturation. By restricting the discussion to strictly consecutive (ordered, unbranched, linear) mechanisms, the line of reasoning can be presented in a relatively simple form. The main conclusions are the following: (a) It is advantageous to carry out the analysis in terms of paired (conjugated) control coefficients. (b) Flux control analysis of "elementary rate constants" does not require any extra kinetic argument. (c) Neither the immediate aim nor the results of the presented type of analysis are directly relevant to theories of metabolic control. On the contrary, the type of control analysis considered completes classical enzyme kinetics with a new facet. (d) For illustrating its usefulness, the concept of flux control coefficients is applied to the problem of optimization of enzyme activity.
布朗和库珀最近的一份报告证明了，对于单一酶假定动力学机制中涉及的每个速率常数，计算“通量控制系数”是有用的。布朗和库珀的计算涉及数值微分。本文通过表明布朗和库珀的数值结果也可以以显式形式获得，证实了这份报告。给出的解析方程建立了严格指定的总速率过程与“基本速率常数”之间的关系，两者均由经典酶动力学的速率方程定义。结果表明，对于经典酶动力学中考虑的所有类型的速率过程，包括“初始速率”、平衡交换反应以及底物（和/或产物）饱和极限水平下的反应，都可以获得解析通量控制系数。通过将讨论限制在严格连续（有序、无分支、线性）机制上，推理过程可以以相对简单的形式呈现。主要结论如下：（a）用成对（共轭）控制系数进行分析是有利的。（b）对“基本速率常数”的通量控制分析不需要任何额外的动力学论证。（c）所提出的这种分析类型的直接目的和结果都与代谢控制理论没有直接关系。相反，所考虑的这种控制分析类型为经典酶动力学增添了一个新的方面。（d）为了说明其有用性，通量控制系数的概念被应用于酶活性优化问题。
