Theory of the statistics of kinetic transitions with application to single-molecule enzyme catalysis

被引:147
|
作者
Gopich, IV [1 ]
Szabo, A [1 ]
机构
[1] NIDDK, Chem Phys Lab, NIH, Bethesda, MD 20892 USA
来源
JOURNAL OF CHEMICAL PHYSICS | 2006年 / 124卷 / 15期
关键词
D O I
10.1063/1.2180770
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Single-molecule spectroscopy can monitor transitions between two microscopic states when these transitions are associated with the emission of photons. A general formalism is developed for obtaining the statistics of such transitions from a microscopic model when the dynamics is described by master or rate equations or their continuum analog, multidimensional reaction-diffusion equations. The focus is on the distribution of the number of transitions during a fixed observation time, the distribution of times between transitions, and the corresponding correlation functions. It is shown how these quantities are related to each other and how they can be explicitly calculated in a straightforward way for both immobile and diffusing molecules. Our formalism reduces to renewal theory when the monitored transitions either go to or originate from a single state. The influence of dynamics slow compared with the time between monitored transitions is treated in a simple way, and the probability distributions are expressed in terms of Mandel-type formulas. The formalism is illustrated by a detailed analysis of the statistics of catalytic turnovers of enzymes. When the rates of conformational changes are slower than the catalytic rates which are in turn slower than the binding relaxation rate, (1) the mean number of turnovers is shown to have the classical Michaelis-Menten form, (2) the correlation function of the number of turnovers is a direct measure of the time scale of catalytic rate fluctuations, and (3) the distribution of the time between consecutive turnovers is determined by the steady-state distribution.
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页数:21
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