Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T17:15:18.819Z Has data issue: false hasContentIssue false
  • English
  • Français

A Crump-Mode-Jagers Branching Process Model of Prion Loss in Yeast

Part of: Stochastic processes Special processes Applications

Published online by Cambridge University Press:  19 February 2016

Peter Olofsson  and
Suzanne S. Sindi
Peter Olofsson*
Affiliation:
Trinity University
Suzanne S. Sindi*
Affiliation:
University of California, Merced
*
∗ Postal address: Department of Mathematics, Trinity University, One Trinity Place, San Antonio, TX 78212, USA. Email address: polofsso@trinity.edu.
∗∗ Postal address: School of Natural Sciences, University of California, Merced, USA. Email address: ssindi@ucmerced.edu.
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.

The yeast Saccharomyces cerevisiae has emerged as an ideal model system to study the dynamics of prion proteins which are responsible for a number of fatal neurodegenerative diseases in humans. Within an infected cell, prion proteins aggregate in complexes which may increase in size or be fragmented and are transmitted upon cell division. Recent work in yeast suggests that only aggregates below a critical size are transmitted efficiently. We formulate a continuous-time branching process model of a yeast colony under conditions of prion curing. We generalize previous approaches by providing an explicit formula approximating prion loss as influenced by both aggregate growth and size-dependent transmission.

Keywords

Branching processprionyeast

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 60K99: None of the above, but in this section 62P10: Applications to biology and medical sciences 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 453 - 465
Copyright
© Applied Probability Trust 

References

Bateman, D. A. and Wickner, R. B. (2013). The [{ PSI +] prion exists as a dynamic cloud of variants. PLoS Genetics 9, e1003257.Google Scholar
Byrne, L. J. et al. (2007). Cell division is essential for elimination of the yeast [{PSI +] prion by guanidine hydrochloride. Proc. Nat. Acad. Sci. USA 104, 11688–11693.Google Scholar
Byrne, L. J. et al. (2009). {The number and transmission of [{PSI+] prion seeds (propagons) in the yeast Saccharomyces cerevisiae}. PLoS ONE 4, e4670.Google Scholar
Cole, D. J. et al. (2004). {Estimating the number of prions in yeast cells}. Math. Med. Biol. 21, 369–395.Google Scholar
Collinge, J. (1999). Variant Creutzfeldt–Jakob disease. The Lancet 354, 317–323.Google Scholar
Derdowski, A. et al. (2010). A size threshold limits prion transmission and establishes phenotypic diversity. Science 330, 680–683.Google Scholar
Fowler, D. M. and Kelly, J. W. (2009). Aggregating knowledge about prions and amyloid. Cell 137, 20–22.Google Scholar
Green, P. J. (1981). {Modelling yeast cell growth using stochastic branching processes}. J. Appl. Prob. 18, 799–808.CrossRefGoogle Scholar
Griffith, J. S. (1967). Self-replication and scrapie. Nature 215, 1043–1044.CrossRefGoogle ScholarPubMed
Hartwell, L. H. and Unger, M. W. (1977). {Unequal division in Saccharomyces cerevisiae and its implications for the control of cell division.} J. Cell Biology 75, 422–435.CrossRefGoogle ScholarPubMed
Jagers, P. and Nerman, O. (1984). {The growth and composition of branching populations}. Adv. Appl. Prob. 16, 221–259.Google Scholar
Morgan, B. J., Ridout, M. S. and Ruddock, L. W. (2003). {Models for yeast prions}. Biometrics 59, 562–569.Google Scholar
Olofsson, P. and Bertuch, A. A. (2010). {Modeling growth and telomere dynamics in Saccharomyces cerevisiae}. J. Theoret. Biol. 263, 353–359.Google Scholar
Olofsson, P. and Daileda, R. C. (2011). Budding yeast, branching processes, and generalized Fibonacci numbers. Math. Magazine 84, 163–172.Google Scholar
Palmer, K. J., Ridout, M. S. and Morgan, B. J. T. (2011). Kinetic models of guanidine hydrochloride-induced curing of the yeast [{P}{S}{I}^+] prion. J. Theoret. Biol. 274, 1–11.Google Scholar
Prusiner, S. (1982). Novel proteinaceous infectious particles cause scrapie. Science 216, 136–144.CrossRefGoogle ScholarPubMed
Robert, C. P. and Casella, G. (2009). Introducing Monte Carlo Methods with R. Springer, New York.Google Scholar
Sinclair, D., Mills, K. and Guarente, L. (1998). {Aging in Saccharomyces cerevisiae}. Annual Rev. Microbiol. 52, 533–560.Google Scholar
Sindi, S. S. and Olofsson, P. (2013). A discrete-time branching process model of yeast prion curing curves. Math. Pop. Stud. 20, 1–13.CrossRefGoogle ScholarPubMed
Sindi, S. S. and Serio, T. R. (2009). {Prion dynamics and the quest for the genetic determinant in protein-only inheritance}. Curr. Opinion Microbiol. 12, 623–630.Google Scholar
Tanaka, M., Collins, S. R., Toyama, B. H. and Weissman, J. S. (2006). The physical basis of how prion conformations determine strain phenotypes. Nature 442, 585–589.Google Scholar
Tuite, M. F. and Cox, B. S. (2009). Prions remodel gene expression in yeast. Nature Cell Biol. 11, 241–243.Google Scholar