Predictions from a stochastic polymer model for the MinDE dynamics in E.coli

TL;DR

This paper extends a deterministic polymer model of Min protein oscillations in E. coli to a stochastic version, providing analytical predictions for oscillation characteristics that match experimental observations.

Contribution

It introduces a stochastic formulation of a polymer model for Min protein dynamics, enabling analytical predictions of oscillation distributions.

Findings

Predicts distributions of MinD zone lengths and oscillation periods.

Provides a tractable example of a stochastic hybrid system.

Matches experimental measurements of Min protein oscillations.

Abstract

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations -- both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.