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A new discrete distribution arising in a model of DNA replication

Part of: Physiological, cellular and medical topics Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: richardc@maths.usyd.edu.au
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Abstract

During DNA replication, small fragments of DNA are formed. These have been observed experimentally and the mechanism of their formation modelled mathematically. Using the stochastic model of Cowan and Chiu (1992), (1994), we find the probability distribution of the number of fragments. A new discrete distribution arises. The work has interest as an application of the recent theory on quasirenewal equations in Piau (2000).

Keywords

DNA replicationOkazaki fragmentquasirenewal equationsdiscrete distributions

MSC classification

Primary: 60E05: Distributions
Secondary: 60K05: Renewal theory 60K40: Other physical applications of random processes 92C40: Biochemistry, molecular biology 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 754 - 760
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Andrews, G. (1976). The Theory of Partitions (Encyclopedia Math. Appl. 2). Addison-Wesley, Reading, MA.Google Scholar
Cowan, R. (2001). Stochastic models for DNA replication. To appear in Stochastic Processes: Modeling and Simulation (Handbook Statist.), eds Rao, C. R. and Shanbhag, D. N. North-Holland, Amsterdam.Google Scholar
Cowan, R., and Chiu, S. N. (1992). Mathematics of DNA replicating forks. Res. Rept 28, University of Hong Kong.Google Scholar
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Okazaki, R. et al. (1968). In vivo mechanism of DNA chain growth. Cold Spring Harbour Symp. Quant. Biol. 33, 129–143.CrossRefGoogle Scholar
Piau, D. (2000). Quasi-renewal estimates. J. Appl. Prob. 37, 269–275.CrossRefGoogle Scholar