Waiting Cycle Times and Generalized Haldane Equality in the Steady-state Cycle Kinetics of Single Enzymes

Details Waiting Cycle Times and Generalized Haldane Equality in the Steady-state Cycle Kinetics of Single Enzymes Waiting Cycle Times and Generalized Haldane Equality in the Steady-state Cycle Kinetics of Single Enzymes

2009-04-15

arxiv.org/abs/0904.2255v1

Physics

Condensed Matter

Statistical Mechanics

24 pages,4 figures; in Journal of Physical Chemistry 2008

Scientific paper

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 $$, $$, and $$ are the reciprocal of the steady-state cycle flux $J^{ss}$, the forward steady-state cycle flux $J^{ss}_{+}$ and the backward steady-state cycle flux $J^{ss}_{-}$ respectively. We also show that the distribution of $T_{+}$ conditioned on $T_{+}$) and the one of $T_{-}$ conditioned on $T_{-}$) are both just the same as $$. In addition, the forward and backward stepping probabilities $p^{+},p^{-}$ 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 evidences are also included.

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