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

Part of: Special processes Applications Stochastic processes

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: [email protected].
∗∗ Postal address: School of Natural Sciences, University of California, Merced, USA. Email address: [email protected].
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Abstract

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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 

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