The effect of branching on the critical concentration and average filament length of actin

The dependences of the steady-state critical concentration and average filament length of actin solutions, on the filament branching and capping rates, are calculated using a rate methodology based on the total number of actin filaments. The methodology generalizes calculations of the " treadmilling" actin concentration at which an average filament has net zero growth rate. The predictions of the rate methodology are validated by comparison with stochastic-growth simulations that track the positions of all filament subunits over time. For side branching, the critical concentration drops proportionally to the square root of the branching rate; for end branching the drop is linear. The polymerization response to branching has a maximum as a function of the capping-protein concentration. The average filament length drops with increasing branching, because the critical concentration drops. Even small rates of filament uncapping have a large impact on the average filament length in vitro. The potential significance of these phenomena for cell behavior is evaluated.