Waiting cycle times and generalized Haldane equality in the steady-state cycle kinetics of single enzymes.

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.