A Simple Model of Cell Proliferation of Bacteria Using Min Oscillation

TL;DR

This paper presents a simplified mathematical model of Min oscillation in E. coli to explain cell growth and division, demonstrating how oscillatory behavior influences cell cycle variability and spatial organization in cell assemblies.

Contribution

It introduces a new simple model linking Min oscillation to bacterial cell growth and division, capturing oscillatory dynamics and spatial distribution effects.

Findings

Oscillatory state and hysteresis explained with simple differential equations

Cell cycle exhibits fluctuations in the deterministic model

Cell assemblies tend to become more circular over time

Abstract

A mathematical model of Min oscillation in Escherichia coli is numerically studied. The oscillatory state and hysteretic transition are explained with simpler coupled differential equations. Next, we propose a simple model of cell growth and division using the Min oscillation. The cell cycle is not constant but exhibits fluctuation in the deterministic model. Finally, we perform direct numerical simulation of cell assemblies composed of many cells obeying the simple growth and division model. As the cell number increases with time, the spatial distribution of cell assembly becomes more circular, although the cells are aligned almost in the x-direction.