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

Source: [Waiting Cycle Times and Generalized Haldane Equality in the Steady-state Cycle Kinetics of Single Enzymes](<https://www.sota2.com/research/paper/68fa237b2c2a37601939859d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:32.348Z

Authors: Hao Ge

Published: 2009-04-15T07:51:42.000Z

## Abstract

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 $J^{ss}$, 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 $T\_{+}\<T\_{-}$ is identical to the distribution of $T\_{-}$ conditioned on $T\_{-}\<T\_{+}$, which is referred as 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 $p^{+},p^{-}$ 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0904.2255>)

[PDF](<https://arxiv.org/pdf/0904.2255.pdf>)