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Biophysical Chemistry
Volumes 101-102, 10 December 2002, Pages 565-576
 
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doi:10.1016/S0301-4622(02)00145-X    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2002 Elsevier Science B.V. All rights reserved.

Single-molecule enzymology: stochastic Michaelis–Menten kinetics

Hong Qiana and Elliot L. ElsonCorresponding Author Contact Information, E-mail The Corresponding Author, b

a Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA b Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 660 South Euclid Ave. Box 8231, St. Louis, MO 63110, USA

Received 23 January 2002; 
accepted 8 April 2002. ;
Available online 11 December 2002.

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Abstract

We provide a stochastic analysis of single-molecule enzymatic reactions that follow Michaelis–Menten kinetics. We show that this system can exhibit oscillatory behavior in the non-equilibrium steady-state at appropriate substrate concentrations. The stochastic model includes both enzyme dynamics and substrate turnover kinetics. The relationship between the probability of substrate survival and the time-correlation of enzyme conformation trajectories is discussed. Deterministic kinetics at large substrate concentrations are obtained as a limit of the stochastic model. We suggest that in addition to fluctuating enzyme conformation, the stochastic nature of substrate concentration fluctuations is another possible source of the complex behavior of single-molecule enzyme kinetics.

Author Keywords: Stochastic analysis; Oscillatory behaviour; Non-equilibrium; Enzyme dynamics; Deterministic kinetics

Article Outline

1. Introduction
2. Non-equilibrium steady-state enzyme turnover
2.1. Steady-state probability
2.2. Transition probability
2.3. Time correlation functions
3. Stochastic substrate kinetics
3.1. A relation between cyclic enzyme dynamics and substrate kinetics
4. Discussion
Appendix A. Higher-order correlation functions for two-state kinetics
Appendix B. Real eigenvalues in equilibrium
Appendix C. Distribution and moments of substrate fluctuation
Appendix D. Duality between mean arrival time and steady-state cyclic flux
References



Biophysical Chemistry
Volumes 101-102, 10 December 2002, Pages 565-576
 
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