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

Julian Weichsel, Krzysztof Baczynski, and Ulrich S. Schwarz

Phys. Rev. E 87, 040701(R) (2013)

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.