Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T12:35:49.913Z Has data issue: false hasContentIssue false
  • English
  • Français

A stochastic model for the breaking of molecular segments

Published online by Cambridge University Press:  14 July 2016

J. F. Bithell
J. F. Bithell*
Affiliation:
Department of Biomathematics, University of Oxford
Get access Rights & Permissions [Opens in a new window]

Extract

In many chemical and biochemical situations it is of interest to know the distribution that results from the breaking up of long molecules into shorter segments under certain hypotheses. For example, Montroll and Simha (1940) assumed that polymers consist of discrete units—monomers—connected by bonds all of which have an equal chance of breaking in the depolymerization process. Charlesby (1954) used a different approach to essentially the same model and in effect obtained differential equations for the moments of the ensuing distributions. More recently, Daniels (1967) has given a more thorough mathematical exposition, especially with regard to the effect of the initial length distribution, while Blatt (1967) has considered a model in which not all links are susceptible to breakage.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 59 - 73
Copyright
Copyright © Applied Probability Trust 

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

Blatt, J. M. (1967) Enzymatic break-up of polypeptides as a stochastic process. J. Theoret. Biol. 17, 282–303.Google Scholar
Charlesby, A. (1954) Molecular-weight changes in the degradation of long-chain polymers. Proc. Roy. Soc. A 224, 120–128.Google Scholar
Chiang, C. L. (1966) On the expectation of the reciprocal of a random variable. Amer. Statist. 20, No. 4, 28.Google Scholar
Daniels, H. E. (1967) The distribution of molecular chain length subject to a constant probability of bond breakage. Unpublished note. Google Scholar
Feller, W. (1957) An Introduction to Probability Theory and its Applications. Vol. I. Wiley, New York.Google Scholar
Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
Montroll, E. W. and Simha, R. (1940) Theory of depolymerization of long chain molecules. J. Chem. Phys. 8, 721–727.Google Scholar
Peacocke, A. R. and Pritchard, N. J. (1968) The ultrasonic degradation of biological macromolecules under conditions of stable cavitation. II. Degradation of deoxyribonucleic acid. Biopolymers. Biopolymers, 6, 605–623.Google Scholar
Pritchard, N. J., Hughes, D. E. and Peacocke, A. R. (1966) The ultrasonic degradation of biological macromolecules under conditions of stable cavitation. I. Theory, methods and application to deoxyribonucleic acid. Biopolymers 4, 259–273.Google Scholar