arXiv2005
Polymerization of actin proteins into dynamic structures is essential to eukaryotic cell life. This has motivated a large body of in vitro experiments measuring polymerization kinetics of individual filaments. Here we model these kinetics, accounting for all relevant steps revealed by experiment: polymerization, depolymerization, random ATP hydrolysis and release of phosphate (Pi). We relate filament growth rates to the dynamics of ATP-actin and ADP-Pi-actin caps which develop at filament ends. At the critical concentration of the barbed end, c_crit, we find a short ATP cap and a long fluctuation-stabilized ADP-Pi cap. We show that growth rates and the critical concentration at the barbed end are intimately related to cap structure and dynamics. Fluctuations in filament lengths are described by the length diffusion coefficient, D. Recently Fujiwara et al. [Nature Cell Biol. (2002) 4, 666] and Kuhn and Pollard [Biohys. J. (2005) 88, 1387] observed large length fluctuations slightly above c_crit, provoking speculation that growth may proceed by oligomeric rather than monomeric on-off events. For the single monomer growth process we find that $D$ exhibits a pronounced peak below c_crit}, due to filaments alternating between capped and uncapped states, a mild version of the dynamic instability of microtubules. Fluctuations just above c_crit are enhanced but much smaller than those reported experimentally. Future measurements of D as a function of concentration can help identify the origin of the observed fluctuations.