Ge Hao
School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China.
J Phys Chem B. 2008 Jan 10;112(1):61-70. doi: 10.1021/jp0729967. Epub 2007 Dec 11.
Enzyme kinetics are cyclic. A more realistic reversible three-step mechanism of the Michaelis-Menten kinetics is investigated in detail, and three kinds of waiting cycle times T, T+, T- are defined. It is shown that the mean waiting cycle times T, T+, and T- are the reciprocal of the steady-state cycle flux Jss, the forward steady-state cycle flux Jss+ and the backward steady-state cycle flux Jss, respectively. We also show that the distribution of T+ conditioned on T+<T- is identical to the distribution of T- conditioned on T-< T+, which is referred to as the generalized Haldane equality. Consequently, the mean waiting cycle time of T+ conditioned on T+<T- (T+|T+<T-) and the one of T- conditioned on T-<T+ (T-|T-<T+) are both just the same as T. In addition, the forward and backward stepping probabilities p+ and p- are also defined and discussed, especially their relationship with the cycle fluxes and waiting cycle times. Furthermore, we extend the same results to the n-step cycle, and finally, experimental and theoretically based evidence are also included.
酶动力学是循环的。详细研究了米氏动力学更现实的可逆三步机制，并定义了三种等待循环时间T、T+、T-。结果表明，平均等待循环时间T、T+和T-分别是稳态循环通量Jss、正向稳态循环通量Jss+和反向稳态循环通量Jss的倒数。我们还表明，在T+<T-条件下T+的分布与在T-<T+条件下T-的分布相同，这被称为广义哈代等式。因此，在T+<T-条件下T+的平均等待循环时间（T+|T+<T-）和在T-<T+条件下T-的平均等待循环时间（T-|T-<T+）都与T相同。此外，还定义并讨论了正向和反向步移概率p+和p-，特别是它们与循环通量和等待循环时间的关系。此外，我们将相同的结果扩展到n步循环，最后还包括了基于实验和理论的证据。
