Unifying autocatalytic and zeroth order branching models for growing actin networks

TL;DR

This paper presents a unified model of actin network growth that bridges the gap between autocatalytic and zeroth order branching models, explaining how cells can maintain stable actin networks across various conditions.

Contribution

It introduces a unifying framework that shows how autocatalytic and zeroth order models are limiting cases, providing a comprehensive understanding of actin network dynamics.

Findings

A smooth transition between the two models at intermediate conditions.

A threshold capping rate determines the dominant growth regime.

Cells can sustain stable actin networks over diverse conditions.

Abstract

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions.