Julian Weichsel and Ulrich S. Schwarz

Two competing orientation patterns explain experimentally observed anomalies in growing actin networks

PNAS published online before print March 22, 2010, doi: 10.1073/pnas.0913730107 

The lamellipodium of migrating animal cells protrudes by directed
polymerization of a branched actin network. The underlying mechanisms
of filament growth, branching, and capping can be studied in in vitro
assays. However, conflicting results have been reported for the
force–velocity relation of such actin networks, namely both convex and
concave shapes as well as history dependencies. Here we model
branching as a reaction that is independent of the number of existing
filaments, in contrast to capping, which is assumed to be proportional
to the number of existing filaments. Using both stochastic network
simulations and deterministic rate equations, we show that such a
description naturally leads to the stability of two qualitatively
different stationary states of the system, namely a ± 35° and a
+70/0/-70° orientation pattern. Changes in network growth velocity
induce a transition between these two patterns. For sufficiently
different protrusion efficiency of the two network architectures, this
leads to hysteresis in the growth velocity of actin networks under
force. Dependent on the history of the system, convex and concave
regimes are obtained for the force–velocity relation. Thus a simple
generic model can explain the experimentally observed anomalies, with
far reaching consequences for cell migration.