Unifying autocatalytic and zeroth-order branching models for growing actin networks

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 numbers. 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, these mechanisms allow cells to grow stable actin networks over a large range of different conditions.