Generalized Euler-Lotka equation for correlated cell divisions

TL;DR

This paper derives a generalized Euler-Lotka equation accounting for correlated cell division times, providing a more accurate prediction of microbial population growth rates in the presence of correlations.

Contribution

It introduces an exact, large deviation theory-based equation that extends the classic Euler-Lotka equation to correlated cell division times.

Findings

The generalized equation closely matches experimental data.

Correlations in cell division times significantly affect growth rate predictions.

The discrepancy between classical and generalized models is measurable.

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.