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Hybrid systems approach to modeling stochastic dynamics of cell size

Cesar Augusto Vargas-Garcia, Abhyudai Singh
doi: https://doi.org/10.1101/044131
Cesar Augusto Vargas-Garcia
1C. Vargas is with Department of Electrical and Computer Engineering, University of Delaware, Newark, DE USA 19716.
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  • For correspondence: cavargar@udel.edu
Abhyudai Singh
2A. Singh is with the Department of Electrical and Computer Engineering, Biomedical Engineering, Mathematical Sciences, Center for Bioinformatics and Computational Biology, University of Delaware, Newark, DE USA 19716.
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  • For correspondence: absingh@udel.edu
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Abstract

A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider three different classes of models: i) a size-dependent growth rate and timer-dependent division rate; ii) a constant growth rate and size-dependent division rate and iii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

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Posted March 16, 2016.
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Hybrid systems approach to modeling stochastic dynamics of cell size
Cesar Augusto Vargas-Garcia, Abhyudai Singh
bioRxiv 044131; doi: https://doi.org/10.1101/044131
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Hybrid systems approach to modeling stochastic dynamics of cell size
Cesar Augusto Vargas-Garcia, Abhyudai Singh
bioRxiv 044131; doi: https://doi.org/10.1101/044131

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