Different anomalous diffusion regimes measured in the dynamics of tracer particles in actin networks

It was previously believed that diffusion of a tracer particle in a viscoelastic material should be of the fractional Brownian motion (fBm) type. This is due to the long-term memory in the response of such materials to mechanical perturbations. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk (CTRW) type in one study that focused on the ensemble average characteristics. Here, we analyze the dynamics of two differently sized tracer particles in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion the particle performs. We find that the tracer particle diffusion has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the tracer particle's motion in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with occasional caging events with power-law-distributed escape times.