Lolkema J S
Department of Microbiology, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Haren, The Netherlands.
Biochim Biophys Acta. 1995 Oct 25;1252(2):284-94. doi: 10.1016/0167-4838(95)00112-8.
Friction analysis is proposed as the application of general control analysis to single enzymes to describe the control of elementary kinetic steps on the overall catalytic rate. For each transition, a friction coefficient is defined that measures the sensitivity of the turnover rate to the free energy of the transition state complex of the transition. The latter is captured in a single property of the transition, termed friction, as the geometrical mean of the inverse of the forward and backward rate constants. By definition, the friction coefficient measures the relative change in the turnover rate in response to a small change in the friction. The friction coefficient is the sum of the flux control coefficients of the forward and backward rate constants from general control theory and measures the extent to which an elementary step is rate determining. Two basic rules apply to the friction coefficients: (i) the summation theorem states that summation of the friction coefficients over all the steps in a scheme results in a value of 1, and (ii) the group rule states that grouping of rate constants of similar transitions results in a friction coefficient for the group that is the sum of the friction coefficients of the individual steps in the group. The friction coefficients are derived for a number a kinetic schemes taking the rate equations as the starting point and both rules are demonstrated. In fully coupled systems the friction coefficients of individual steps lie between 0 and 1. In partially uncoupled systems the summation theorem applies to all the rates in the system, however, the summation of subsets of friction coefficients may exceed the value of one, implying negative values for other steps in the scheme. The values of individual friction coefficients lie between -1 and 1. The friction coefficient is redefined in a numerical treatment of the steady state of more complex enzymatic schemes.
摩擦分析被提议作为将通用控制分析应用于单一酶，以描述基本动力学步骤对整体催化速率的控制。对于每个转变，定义一个摩擦系数，该系数测量周转速率对转变过渡态复合物自由能的敏感性。后者在转变的一个单一属性中体现，称为摩擦，它是正向和反向速率常数倒数的几何平均值。根据定义，摩擦系数测量周转速率响应摩擦的微小变化时的相对变化。摩擦系数是通用控制理论中正向和反向速率常数的通量控制系数之和，它衡量一个基本步骤成为速率决定步骤的程度。摩擦系数适用两条基本规则：(i) 求和定理指出，对一个反应机制中所有步骤的摩擦系数求和，结果为1；(ii) 分组规则指出，将相似转变的速率常数分组，会得到该组的一个摩擦系数，它是该组中各个步骤摩擦系数之和。以速率方程为起点，针对一些动力学反应机制推导了摩擦系数，并证明了这两条规则。在完全耦合系统中，各个步骤的摩擦系数介于0和1之间。在部分解耦系统中，求和定理适用于系统中的所有速率，然而，摩擦系数子集的求和可能超过1，这意味着反应机制中其他步骤的摩擦系数为负值。各个摩擦系数的值介于 -1和1之间。在对更复杂酶促反应机制的稳态进行数值处理时，对摩擦系数进行了重新定义。
