Relevant parameters in models of cell division control.

A recent burst of dynamic single-cell data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different models were used to propose specific mechanisms, but the links between them are poorly explored. The lack of comparative studies makes it difficult to appreciate how well any particular mechanism is supported by the data. Here, we describe a simple and generic framework in which two common formalisms can be used interchangeably: (i) a continuous-time division process described by a hazard function and (ii) a discrete-time equation describing cell size across generations (where the unit of time is a cell cycle). In our framework, this second process is a discrete-time Langevin equation with simple physical analogues. By perturbative expansion around the mean initial size (or interdivision time), we show how this framework describes a wide range of division control mechanisms, including combinations of time and size control, as well as the constant added size mechanism recently found to capture several aspects of the cell division behavior of different bacteria. As we show by analytical estimates and numerical simulations, the available data are described precisely by the first-order approximation of this expansion, i.e., by a "linear response" regime for the correction of size fluctuations. Hence, a single dimensionless parameter defines the strength and action of the division control against cell-to-cell variability (quantified by a single "noise" parameter). However, the same strength of linear response may emerge from several mechanisms, which are distinguished only by higher-order terms in the perturbative expansion. Our analytical estimate of the sample size needed to distinguish between second-order effects shows that this value is close to but larger than the values of the current datasets. These results provide a unified framework for future studies and clarify the relevant parameters at play in the control of cell division.

[1]  S. Jun,et al.  Cell-size maintenance: universal strategy revealed. , 2015, Trends in microbiology.

[2]  J. Skotheim,et al.  Dilution of the cell cycle inhibitor Whi5 controls budding yeast cell size , 2015, Nature.

[3]  K. Kaneko,et al.  Noise-driven growth rate gain in clonal cellular populations , 2016, Proceedings of the National Academy of Sciences.

[4]  P. Painter,et al.  Mathematics of microbial populations. , 1968, Annual review of microbiology.

[5]  Yu Tanouchi,et al.  A noisy linear map underlies oscillations in cell size and gene expression in bacteria , 2015, Nature.

[6]  O. Neijssel,et al.  Generality of the growth kinetics of the average individual cell in different bacterial populations , 1982, Journal of bacteriology.

[7]  G. Crooks,et al.  Scaling laws governing stochastic growth and division of single bacterial cells , 2014, Proceedings of the National Academy of Sciences.

[8]  Andrea Rinaldo,et al.  Scaling body size fluctuations , 2013, Proceedings of the National Academy of Sciences.

[9]  Julie A. Theriot,et al.  Relative Rates of Surface and Volume Synthesis Set Bacterial Cell Size , 2016, Cell.

[10]  Ariel Amir,et al.  Cell size regulation in bacteria , 2013, bioRxiv.

[11]  Andrew Wright,et al.  Robust Growth of Escherichia coli , 2010, Current Biology.

[12]  Philippe Nghe,et al.  Individuality and universality in the growth-division laws of single E. coli cells. , 2014, Physical review. E.

[13]  J. Xavier,et al.  Cell-Size Homeostasis and the Incremental Rule in a Bacterial Pathogen. , 2015, Biophysical journal.

[14]  Setsu Kato,et al.  A Constant Size Extension Drives Bacterial Cell Size Homeostasis , 2014, Cell.

[15]  Marco Cosentino Lagomarsino,et al.  Concerted control of Escherichia coli cell division , 2014, Proceedings of the National Academy of Sciences.

[16]  M. Hoffmann,et al.  Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism , 2014, BMC Biology.

[17]  John T. Sauls,et al.  Cell-Size Control and Homeostasis in Bacteria , 2015, Current Biology.

[18]  G. Crooks,et al.  Universality in stochastic exponential growth. , 2014, Physical review letters.

[19]  Ariel Amir,et al.  Single-Cell Analysis of Growth in Budding Yeast and Bacteria Reveals a Common Size Regulation Strategy , 2014, Current Biology.