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Stochastic models for bacteriophage

Published online by Cambridge University Press:  14 July 2016

J. Gani
J. Gani*
Affiliation:
University of Sheffield
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Extract

Viruses are small particles of RNA (Ribonucleic Acid) or DNA (DeoxyRibonucleic Acid) wrapped in a protein coat, which can be crystallized into a variety of regular geometric, often polyhedral, shapes. They are much smaller than bacteria, and are capable of passage through filters designed to, arrest these. Among the numerous viruses, bacteriophages (or bacterial viruses), called phages for short, have been the subject of much concentrated study. Over the past twenty years in particular, their structure, parasitic cycle, and most recently part of their genetic mapping, have been elucidated; the isolated DNA strand used by phages as their genetic information carrier, makes them eminently suitable in investigations on the molecular basis of life.

Type
Review Paper
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 225 - 268
Copyright
Copyright © Applied Probability Trust 

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References

References

I. Introduction

Adams, M. H. (1959) Bacteriophages. Interscience, New York.CrossRefGoogle Scholar
Edgar, R. S. and Epstein, R. H. (1965) The genetics of a bacterial virus. Sci. Amer. 212 (2) 70–78.CrossRefGoogle ScholarPubMed
Epstein, R. H. et al. (1963) Physiological studies of conditional lethal mutants of bacteriophage T4D. Cold Spring Harbor Symp. Quant. Biol. 28, 375–394.CrossRefGoogle Scholar
Hershey, A. D. (1958) The production of recombinants in phage crosses. Cold Spring Harbor Symp. Quant. Biol. 23, 19–46.CrossRefGoogle ScholarPubMed
Sanders, F. K. (1961) The life of viruses. Penguin Science Survey 2, 147–159.Google Scholar
Smith, K. M. (1962) Viruses. Cambridge U.P. Google Scholar
Stent, G. S. (1963) Molecular Biology of Bacterial Viruses. W. H. Freeman and Co., San Francisco.Google Scholar
Stent, G. S., (Ed.) (1960) Papers on Bacterial Viruses. Little, Brown, Boston.CrossRefGoogle Scholar
Watson, J. D. and Crick, F. H. C. (1953) The structure of DNA. Cold Spring Harbor Symp. Quant. Biol. 18, 123–131.CrossRefGoogle ScholarPubMed
Weidel, W. (1959) Virus. U. of Michigan Press, Ann Arbor.Google Scholar
Armtage, P. (1952) The statistical theory of bacterial populations subject to mutation. J. R. Statist. Soc. B14, 1–40.Google Scholar
Bartlett, M. S. (1961) Equations for stochastic path integrals. Proc. Camb. Phil. Soc. 57, 568–573 CrossRefGoogle Scholar
Gani, J. (1962) An approximate stochastic model for phage reproduction in a bacterium. J. Aust. Math. Soc. 2, 478–483.CrossRefGoogle Scholar
Gani, J. and Yeo, G. F. (1965) Some birth-death and mutation models for phage reproduction. J. Appl. Prob. 2, 150–161.CrossRefGoogle Scholar
Green, D. M. and Krieg, D. R. (1961) The delayed origin of mutants induced by exposure of extracellular phage T4 to ethyl methane sulfonate. Proc. Nat. Acad. Sci. 47, 64–72.CrossRefGoogle ScholarPubMed
Kendall, D. G. (1948) On the generalized “Birth-and-Death” process. Ann. Math. Statist. 19, 1–15.CrossRefGoogle Scholar
Kimball, A. W. (1965) A model for chemical mutagenesis in bacteriophage. Biometrics (to appear).CrossRefGoogle Scholar
Luria, S. E. (1951) The frequency distribution of spontaneous bacteriophage mutants as evidence for the exponential rate of phage reproduction. Cold Spring Harbor Symp. Quant. Biol. 16, 463–470.CrossRefGoogle ScholarPubMed
Ohlsen, Sally (1963) Further models for phage reproduction in a bacterium. Biometrics 19 441–449.CrossRefGoogle Scholar
Steinberg, C. and Stahl, F. (1961) The clone-size distribution of mutants arising from a steady-state pool of vegetative phage. J. Theoret. Biol. 1, 488–497.Google Scholar
Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge.Google Scholar
Bartlett, M. S. and Kendall, D. G. (1951) On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biology. Proc. Camb. Phil. Soc. 46, 65–76.CrossRefGoogle Scholar
Davis, A. W. (1964a) On the characteristic functional for a replacement model. J. Aust. Math. Soc. 4, 233–243.CrossRefGoogle Scholar
Davis, A. W. (1964b) A note on the characteristic functional for a replacement process of Gani. J. Appl. Prob. 1, 157–160.CrossRefGoogle Scholar
Gani, J. and Yeo, G. F. (1962) On the age distribution of n ranked elements after several replacements. Aust. J. Statist. 4, 55–60.CrossRefGoogle Scholar
Gani, J. (1962) On the age distribution of replaceable ranked elements. ICM Abstracts of Short Communications, 160, Stockholm. (1965) J. Math. Anal. Applications 10, 587–597.CrossRefGoogle Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Ver lag, Berlin.CrossRefGoogle Scholar
Kendall, D. G. (1950) Random fluctuations in the age-distribution of a population whose development is controlled by the simple “Birth-and-Death” process. J. R. Statist. Soc. B 12 278–285.Google Scholar
David, F. N. and Barton, D. E. (1962) Combinatorial Chance. Griffin, London.CrossRefGoogle Scholar
Gani, J. (1962) A simple population model for phage reproduction. Bull. Math. Statist. 10, 1–3.CrossRefGoogle Scholar
Gani, J. (1962a) The extinction of a bacterial colony by phages: a branching process with deterministic removals. Biometrika 49, 272–276.CrossRefGoogle Scholar
Gani, J. (1963) Models for a bacterial growth process with removals. J. R. Statist. Soc. B 25, 140–149.Google Scholar
Kelly, C. D. and Rahn, O. (1932) The growth rates of individual bacterial cells. J. Bact. 23, 147–153.CrossRefGoogle Scholar
Kendall, D. G. (1952) On the choice of a mathematical model to represent normal bacterial growth. J. R. Statist. Soc. B 14, 41–44.Google Scholar
Powell, E. O. (1955) Some features of the generation times of individual bacteria. Biometrika 42, 16–44.CrossRefGoogle Scholar
Tobias, C. A. (1960) Quantitative approaches to the cell division process. Proc. 4th Berkeley Symp. 4, 369–385.Google Scholar
Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
Brenner, S. (1955) The adsorption of bacteriophage by sensitive and resistant cells of Escherichia coli strain B. Proc. Roy. Soc. B 144, 93–99.Google ScholarPubMed
Gani, J. and Nagai, T. (1964) A model for phage attachment to bacteria with death and reproduction. Ann. Math. Statist. 35, 1835 (Abstract). To appear.Google Scholar
Gani, J. (1965) Stochastic phage attachment to bacteria. Biometrics 21, 134–139.CrossRefGoogle Scholar
Kendall, D. G. (1949) Stochastic processes and population growth. J. R. Statist. Soc. B 11, 230–264.Google Scholar
Moran, P. A. P. and Fazekas De St. Groth, S. (1962) Random circles on a sphere. Biometrika 49, 384–396.CrossRefGoogle Scholar
Ruben, H. (1963) The estimation of a fundamental interaction parameter in an emigrationimmigration process. Ann. Math. Statist. 84, 238–259.CrossRefGoogle Scholar
Srivastava, R. C. (1965) Estimation of the parameter in the stochastic model for phage attachment to bacteria. Ph. D. thesis, Michigan State University. Ann. Math. Statist. 36, 729 (Abstract).Google Scholar
Stevens, W. L. (1939) Solution to a geometrical problem in probability. Ann. Eugen. Lond. 9, 315–320.CrossRefGoogle Scholar
Valentine, R. C. and Strand, M. (1965) Complexes of F-pili and RNA bacteriophage. Science 148, (No. 3669) 511–513.CrossRefGoogle ScholarPubMed
Yassky, D. (1962) A model for the kinetics of phage attachment to bacteria in suspension. Biometrics 18, 185–191.CrossRefGoogle Scholar