Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T04:01:51.407Z Has data issue: false hasContentIssue false
  • English
  • Français

The linear cell-size-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Peter Clifford  and
Aidan Sudbury
Peter Clifford
Affiliation:
University of Bristol
Aidan Sudbury
Affiliation:
University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper is developed a theory of branching processes in which the division probability and rate of growth of cells depend only on their ‘size’ and in which ‘size’ is shared between daughters. Specific results are obtained in a linear case including the calculation of the correlation coefficient for the life spans of sisters.

Keywords

BRANCHING PROCESSESCELL-SIZE-DEPENDENTSIZE-DEPENDENTSISTER CORRELATIONGROWTH OF CELL POPULATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 687 - 696
Copyright
Copyright © Applied Probability Trust 1972 

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

[1] Bell, G. I. and Anderson, E. C. (1967) Cell growth and division. I. Biophys. J. 7, 329–351.Google Scholar
[2] Beyer, W. A. (1970) Solution to a mathematical model of cell growth, division and death. Math. Biosci. 6, 431–436.Google Scholar
[3] Fredrickson, A. G. et al. (1967) Statistics and dynamics of procaryotic cell populations. Math. Biosci. 1, 327–374.Google Scholar
[4] Powell, E. (1955) Some features of the generation times of individual bacteria. Biometrika 42, 16–44.Google Scholar
[5] Harris, T. (1963) The Theory of Branching Processes. Prentice Hall Inc., Englewood Cliffs, N.J. Google Scholar
[6] Crump, K. S. and Mode, C. J. (1969) An age-dependent branching process with correlations among sister cells. J. Appl. Prob. 6, 205–210.Google Scholar
[7] Kubitschek, H. E. (1968) Constancy of uptake during the cell cycle of E. Coli. Biophys. J. 8, 1401–12.Google Scholar
[8] Puri, P. S. (1966) A class of stochastic models of response after infection in the absence of defense mechanism. Proc. Fifth Berkeley Symposium on Math. Stat. and Probability, 511–527.Google Scholar
[9] Kendall, D. G. (1948) On the role of variable generation time in the development of a stochastic birth-process. Biometrika 35, 316–330.CrossRefGoogle Scholar
[10] Williams, T. (1969) The distribution of inanimate marks over a non-homogeneous birth-death process. Biometrika 56, 225–227.CrossRefGoogle Scholar
[11] Greig, M. (1972) Ph.D. thesis, University of California, Berkeley.Google Scholar
[12] Sudbury, A. and Clifford, P. Manuscript in preparation.Google Scholar