Monte Carlo simulations of rigid biopolymer growth processes

Abstract

Rigid biopolymers, such as actin filaments, microtubules, and intermediate filaments, are vital components of the cytoskeleton and the cellular environment. Understanding biopolymer growth dynamics is essential for the description of the mechanisms and principles of cellular functions. These biopolymers are composed of N parallel protofilaments which are aligned with arbitrary but fixed relative displacements, thus giving rise to complex end structures. We have investigated rigid biopolymer growth processes by Monte Carlo simulations by taking into account the effects of such "end" properties and lateral interactions. Our simulations reproduce analytical results for the case of N = 2, which is biologically relevant for actin filaments. For the case of N = 13, which applies to microtubules, the simulations produced results qualitatively similar to the N = 2 case. The simulation results indicate that polymerization events are evenly distributed among the N protofilaments, which imply that both end-structure effects and lateral interactions are significant. The effect of different splittings in activation energy has been investigated for the case of N = 2. The effects of activation energy coefficients on the specific polymerization and depolymerization processes were found to be unsubstantial. By expanding the model, we have also obtained a force-velocity relationship of microtubules as observed in experiments. In addition, a range of lateral free-energy parameters was found that yields growth velocities in accordance with experimental observations and previous simulation estimates for the case of N = 13.