Generalized Euler-Lotka equation for correlated cell divisions

Abstract

Cell division times in microbial populations display significant fluctuations, that impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can be significantly correlated, due to physical properties of cells that are passed through generations. In this paper, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division in E.coli and to experimental data. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable by our approach.

arXiv comment6 pages, 5 figures, combined Main Text + SI. Accepted as a Letter in Physical Review E

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• Analytical cell size distribution: lineage-population bias and parameter inference
• Exponential rate of epidemic spreading on complex networks
• Asymptotic decoupling of population growth rate and cell size distribution
• From noisy cell size control to population growth: when variability can be beneficial
• Cell lineage statistics with incomplete population trees
• Diagrammatic expressions for steady-state distribution and static responses in population dynamics