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First-order stochastic chemical reactions and oscillations in the variance

Published online by Cambridge University Press:  14 July 2016

Richard C. Hertzberg  and
Vincent F. Gallucci
Richard C. Hertzberg*
Affiliation:
University of Washington
Vincent F. Gallucci*
Affiliation:
University of Washington
*
∗Postal address: Center for Quantitative Science in Forestry, Fisheries and Wildlife, University of Washington, 3737 15th Ave. N.E., Seattle, WA 98105, U.S.A.
∗Postal address: Center for Quantitative Science in Forestry, Fisheries and Wildlife, University of Washington, 3737 15th Ave. N.E., Seattle, WA 98105, U.S.A.
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Abstract

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

Keywords

MARKOV PROCESSKINETICSFIRST-ORDER REACTIONSOSCILLATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1087 - 1093
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Some of the results are from a dissertation by R. Hertzberg in partial fulfillment of the requirements for a Ph.D. from the Biomathematics Group, University of Washington, Seattle, 1977. This research was partially supported by NIH Training Grant No. 67–0488.

References

Bartholomay, A. F. (1958) Stochastic models for chemical reactions. I. Theory of the unimolecular reaction process. Bull. Math. Biophys. 20, 175–190.Google Scholar
Bartholomay, A. F. (1960) Molecular set theory: a mathematical representation for chemical reaction mechanisms. Bull. Math. Biophys. 22, 285–307.Google Scholar
Cornish-Bowden, A. (1976) Principles of Enzyme Kinetics. Butterworths, London.Google Scholar
Darvey, I. G. and Staff, P. J. (1966) Stochastic approach to first-order chemical reaction kinetics. J. Chem. Phys. 44, 990–997.Google Scholar
Fredrickson, A. G. (1966) Stochastic triangular reactions. Chem. Eng. Sci. 21, 687–691.Google Scholar
Hertzberg, R. (1980) Stochastic chemical kinetics and consistency in the mean.Google Scholar
Heyde, C. C. and Heyde, E. (1969) A stochastic approach to a one substrate, one product enzyme reaction in the initial velocity phase. J. Theoret. Biol. 25, 159–167.Google Scholar
Landahl, H. D. (1955) Note on the periodic properties of biochemical systems represented by linear equations. Bull. Math. Biophys. 17, 127–140.Google Scholar