Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T20:02:26.066Z Has data issue: false hasContentIssue false

On the interpretation of random fluctuations in competing chemical systems

Published online by Cambridge University Press:  14 July 2016

Peter Hall*
Affiliation:
The Australian National University
*
Postal address: Department of Statistics, The Faculties, The Australian National University, P.O. Box 4, Canberra, ACT 2600, Australia.

Abstract

Several stochastic models have been proposed to describe the kinetic theory of reversible chemical reactions. However, in macroscopic systems the effects of stochastic variability are often outweighed by mean effects. In the present paper we show that some observed phenomena can be explained quite adequately by a stochastic model in which the stochastic variability is not negligible in comparison with mean effects. Our argument involves approximations to a stochastic model for competing chemical reactions.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartholomay, A. F. (1958) Stochastic models for chemical reactions. I. Theory of the unimolecular reaction process. Bull. Math. Biophys. 20, 175190.CrossRefGoogle Scholar
Darvey, I. G., Ninham, B. W. and Staff, P. J. (1966) Stochastic models for second-order chemical reaction kinetics. The equilibrium state. J. Chem. Phys. 45, 21452155.Google Scholar
Dunstan, F. D. J. and Reynolds, J. F. (1981) Normal approximation for distributions arising in the stochastic approach to chemical reaction kinetics. J. Appl. Prob. 18, 263267.CrossRefGoogle Scholar
Gani, J. and Saunders, I. (1978) Nucleolar aggregation: Modelling and simulation. J. Theoret. Biol. 72, 8190.CrossRefGoogle ScholarPubMed
Hall, P. (1983) On the roles of the Bessel and Poisson distributions in chemical kinetics. J. Appl. Prob. 20, 585599.CrossRefGoogle Scholar
Heyde, C. C. and Heyde, E. (1971) Stochastic fluctuations in a one substrate one product enzyme system: are they ever relevant? J. Theoret. Biol. 30, 395404.Google Scholar
Orriss, J. (1969) Equilibrium distributions for systems of chemical reactions with applications to the theory of molecular adsorption. J. Appl. Prob. 6, 505515.CrossRefGoogle Scholar
Tallis, G. M. and Leslie, R. T. (1969) General models for r-molecular reactions. J. Appl. Prob. 6, 7487.Google Scholar