Monodisperse domains by proteolytic control of the coarsening instability

TL;DR

This paper demonstrates that proteolytic degradation can stabilize cluster sizes in biological systems, leading to monodisperse domains by balancing coarsening dynamics.

Contribution

It introduces a novel size-control mechanism via proteolytic degradation that stabilizes cluster sizes, supported by theoretical analysis and biological relevance.

Findings

Proteolysis leads to a fixed-point cluster size.

Size distribution width depends on fluxes and proteolytic rate.

Mechanism explains bacterial pseudo-pilus length control.

Abstract

The coarsening instability typically disrupts steady-state cluster-size distributions. We show that degradation coupled to the cluster size, such as arising from biological proteolysis, leads to a novel fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the fixed-point size distribution. At the fixed-point, we show how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism is consistent with the phenomenology of pseudo-pilus length control in the general secretion pathway of bacteria.