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 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.Comment: revtex, 5 pages, 4 figure

Communication : consistent picture of lateral subdiffusion in lipid bilayers : molecular dynamics simulation and exact results

International audienceThis communication presents a molecular dynamics simulation study of a bilayer consisting of 128 dioleoyl-sn-glycero-3-phosphocholine molecules, which focusses on the center-of-mass diffusion of the lipid molecules parallel to the membrane plane. The analysis of the simulation results is performed within the framework of the generalized Langevin equation and leads to a consistent picture of subdiffusion. The mean square displacement of the lipid molecules evolves as ∝ t(α), with α between 0.5 and 0.6, and the fractional diffusion coefficient is close to the experimental value for a similar system obtained by fluorescence correlation spectroscopy. We show that the long-time tails of the lateral velocity autocorrelation function and the associated memory function agree well with exact results which have been recently derived by asymptotic analysis [G. Kneller, J. Chem. Phys. 134, 224106 (2011)]. In this context, we define characteristic time scales for these two quantities