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We consider a class of biologically-motivated stochastic processes in which aunicellular organism divides its resources (volume or damaged proteins, inparticular) symmetrically or asymmetrically between its progeny. Assuming thefinal amount of the resource is controlled by a growth policy and subject toadditive and multiplicative noise, we derive the "master equation" describinghow the resource distribution evolves over subsequent generations and use it tostudy the properties of stable resource distributions. We find conditions underwhich a unique stable resource distribution exists and calculate its momentsfor the class of affine linear growth policies. Moreover, we apply anasymptotic analysis to elucidate the conditions under which the stabledistribution (when it exists) has a power-law tail. Finally, we use the resultsof this asymptotic analysis along with the moment equations to draw a stabilityphase diagram for the system that reveals the counterintuitive result thatasymmetry serves to increase stability while at the same time widening thestable distribution. We also briefly discuss how cells can divide damagedproteins asymmetrically between their progeny as a form of damage control. Inthe appendix, motivated by the asymmetric division of cell volume inSaccharomyces cerevisiae, we extend our results to the case wherein mother anddaughter cells follow different growth policies.

Stochastic modeling of cell growth with symmetric or asymmetric division