Dynamics of actin monomers assembled into long filaments

We investigate the dynamics of actin monomers that are assembled into long filaments via the particle-based Brownian dynamics simulations. In order to study the dynamics of long filaments containing up to several hundred protomers, a coarse-grained model for actin polymerization involving several simplifications is used. In order to overcome the large separation of time scales between the diffusive motion of the free monomers and the relatively slow polymerized and depolymerized processes at the two ends of the filaments, all polymerized and depolymerized rates are rescaled by a dimensionless parameter. Actin protomers within a filament generally possess three nucleotide states corresponding to a bound adenosine triphosphate (ATP), adenosine diphosphate with inorganic phosphate (ADP. Pi), and ADP molecules in the presence of ATP hydrolysis. Here in this paper, single nucleotide state and two nucleotide states of actin protomers are described by the simplified theoretical model, giving the dependence of the growth rate on actin concentration. The simplest case where all protomers are identical, is provided by the assembly of ADP-actins. In the simulations, the growth rate is found to increase linearly with free monomer concentration, which agrees quantitatively with in vitro experimental result. These surprised phenomena observed in the experiments, such as treadmilling processes and length diffusion of actin filaments at the steady state, are presented in detail by Brownian dynamics simulations. For free actin concentrations close to the critical concentration, cT ccr, T, the filaments undergo treadmilling, that is, they grow at the barbed end and shrink at the pointed end, leading to the directed translational motion of the filament. In the absence of ATP hydrolysis, the functional dependence of a length diffusion constant on ADP-actin monomer concentration implies that a length diffusion constant is found to increase linearly with ADP-actin monomer concentration. With the coupling of ATP hydrolysis, a peak of the filament length diffusion as a function of ATP-actin monomer concentration is observed i. e. , the length diffusion coefficient is peaked near to 35 mon2/s below the critical concentration and recovers to the expected estimate of 1 mon2/s above the critical concentration. These obtained results are well consistent with the experimental results and stochastic theoretical analysis. Furthermore, several other quantities and relations that are difficult to study experimentally but provide nontrivial crosschecks on the consistency of our simulations, are investigated in the particle-based simulations. The particle-based simulations developed in our studies would easily extend to study a variety of more complex systems, such as the assembly process of other dynamic cytoskeletons