Stochastic modeling of cell growth with symmetric or asymmetric division

Andrew Marantan and Ariel Amir
Phys. Rev. E 94, 012405 – Published 13 July 2016

Abstract

We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

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  • Received 11 February 2016
  • Revised 11 May 2016

DOI:https://doi.org/10.1103/PhysRevE.94.012405

©2016 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living Systems

Authors & Affiliations

Andrew Marantan1 and Ariel Amir2

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 94, Iss. 1 — July 2016

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