Analysis of a stochastic model for bacterial growth and the lognormality of the cell-size distribution

TL;DR

This paper analyzes a stochastic model of bacterial growth, demonstrating that cell size distribution closely follows a lognormal distribution under realistic parameters, supported by numerical and experimental data.

Contribution

It provides a theoretical framework linking bacterial growth dynamics with the lognormal distribution of cell sizes, highlighting the conditions for this approximation.

Findings

Cell size can be expressed as a sum of independent lognormal variables.

The lognormal approximation quality depends on growth rate and cell cycle distributions.

Experimental parameters align with conditions that produce a good lognormal fit.

Abstract

This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We find that the cell size is expressed as a sum of independent lognormal variables. We show numerically that the quality of the lognormal approximation greatly depends on the distributions of the growth rate and cell cycle. Furthermore, we show that actual parameters of the growth rate and cell cycle take values that give a good lognormal approximation; thus, the experimental cell-size distribution is in good agreement with a lognormal distribution.