Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-02T01:49:13.424Z Has data issue: false hasContentIssue false
  • English
  • Français

A Stochastic Model for Virus Growth in a Cell Population

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

J. E. Björnberg ,
T. Britton ,
E. I. Broman  and
E. Natan
J. E. Björnberg*
Affiliation:
Uppsala University
T. Britton*
Affiliation:
Stockholm University
E. I. Broman*
Affiliation:
Uppsala University
E. Natan*
Affiliation:
University of Cambridge
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden.
∗∗ Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden.
∗∗∗∗ Postal address: MRC Laboratory of Molecular Biology, University of Cambridge, Francis Crick Avenue, Cambridge CB2 0QH, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.

Keywords

Branching processinteracting branching processmodel for virus growth

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces 92D15: Problems related to evolution
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 599 - 612
Copyright
© Applied Probability Trust 

References

Ackers, G. K., Johnson, A. D. and Shea, M. A. (1982). Quantitative model for gene regulation by lambda phage repressor. Proc. Nat. Acad. Sci. USA 79, 1129–1133.CrossRefGoogle ScholarPubMed
Arkin, A., Ross, J. and McAdams, H. H. (1998). Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells. Genetics 149, 1633–1648.CrossRefGoogle ScholarPubMed
Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.CrossRefGoogle Scholar
Aurell, E. and Sneppen, K. (2002). Epigenetics as a first exit problem. Phys. Rev. Lett. 88, 048101.CrossRefGoogle ScholarPubMed
Björnberg, J. E. and Broman, E. I. (2014). Coexistence and noncoexistence of Markovian viruses and their hosts. J. Appl. Prob. 51, 191–208.CrossRefGoogle Scholar
Haccou, P., Jagers, P. and Vatutin, V. A. (2007). Branching Processes: Variation, Growth, and Extinction of Populations. Cambridge University Press.Google Scholar
Harris, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
Joh, R. I. and Weitz, J. S. (2011). To lyse or not to lyse: transient-mediated stochastic fate determination in cells infected by bacteriophages. PLoS Comput. Biol. 7, 1002006.CrossRefGoogle ScholarPubMed
Johnson, A. D. et al. (1981). λ repressor and cro-components of an efficient molecular switch. Nature 294, 217–223.CrossRefGoogle ScholarPubMed
Kendall, W. S. and Saunders, I. W. (1983). Epidemics in competition II: the general epidemic. J. R. Statist. Soc. B 45, 238–244.Google Scholar
Lieb, M. (1953). The establishment of lysogenicity in. J. Bacteriology 65, 642–651.CrossRefGoogle Scholar
Little, J. W., Shepley, D. P. and Wert, D. W. (1999). Robustness of a gene regulatory circuit. EMBO J. 18, 4299–4307.CrossRefGoogle ScholarPubMed
Lwoff, A. (1953). Lysogeny. Bacteriological Rev. 17, 269–337.CrossRefGoogle ScholarPubMed
McAdams, H. H. and Shapiro, L. (1995). Circuit simulation of genetic networks. Science 269, 650–656.CrossRefGoogle ScholarPubMed
Nowak, M. A. and May, R. M. (2000). Virus Dynamics. Mathematical Principles of Immunology and Virology. Oxford University Press.CrossRefGoogle Scholar
Oppenheim, A. B. et al. (2005). Switches in bacteriophage lambda development. Ann. Rev. Genetics 39, 409–429.CrossRefGoogle ScholarPubMed
Reinitz, J. and Vaisnys, J. R. (1990). Theoretical and experimental analysis of the phage lambda genetic switch implies missing levels of co-operativity. J. Theoret. Biol. 145, 295–318.CrossRefGoogle ScholarPubMed
Renshaw, E. (1991). Modelling Biological Populations in Space and Time. Cambridge University Press.CrossRefGoogle Scholar
Santillán, M. and Mackey, M. C. (2004). Why the lysogenic state of phage λ is so stable: a mathematical modeling approach. Biophysical J. 86, 75–84.CrossRefGoogle Scholar
Shea, M. A. and Ackers, G. K. (1985). The OR control system of bacteriophage lambda: a physical-chemical model for gene regulation. J. Molec. Biol. 181, 211–230.CrossRefGoogle ScholarPubMed
St-Perre, F. and Endy, D. (2008). Determination of cell fate selection during phage lambda infection. Proc. Nat. Acad. Sci. USA 105, 20705–20710.CrossRefGoogle Scholar
Zeng, L. et al. (2010). Decision making at a subcellular level determines the outcome of bacteriophage infection. Cell 141, 682–691.CrossRefGoogle Scholar