2016/06/02 by Cesar A. Vargas-García, Vargas-García, César Augusto, Mohammad Soltani +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Cell Behavior (q-bio.CB) #Evolution and Genetic Dynamics #FOS: Biological sciences #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1606.00535
openalex publication_date 2016/06/02 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
A ubiquitous feature of living cells is their growth over time followed by\ndivision into daughter cells. How isogenic cell populations maintain size\nhomeostasis, i.e., a narrow distribution of cell size, is an intriguing\nfundamental problem. We model cell size using a stochastic hybrid system, where\na cell grows exponentially in size (volume) over time and probabilistic\ndivision events are triggered at discrete time intervals. Moreover, whenever\ndivision events occur, size is randomly partitioned among daughter cells. We\nfirst consider a scenario, where a timer (i.e., cell-cycle clock) that measures\nthe time since the last division event regulates both the cellular growth and\ndivision rates. Analysis reveals that such a timer-controlled system cannot\nachieve size homeostasis, in the sense that, the cell-to-cell size variation\ngrows unboundedly with time. To explore biologically meaningful mechanisms for\ncontrolling size we consider two classes of regulation: a size-dependent growth\nrate and a size-dependent division rate. Our results show that these strategies\ncan provide bounded intercellular variation in cell size, and exact\nmathematical conditions on the form of regulation needed for size homeostasis\nare derived. Different known forms of size control strategies, such as, the\nadder and the sizer are shown to be consistent with these results.\nInterestingly, for timer-based division mechanisms, the mean cell size depends\non the noise in the cell-cycle duration but independent of errors incurred in\npartitioning of volume among daughter cells. In contrast, the mean cell size\ndecreases with increasing partitioning errors for size-based division\nmechanisms. Finally, we discuss how organisms ranging from bacteria to\nmammalian cells have adopted different control approaches for maintaining size\nhomeostasis.\n