Active Diffusion\nof Self-Propelled Particles in Semiflexible\nPolymer Networks

Mesh-like structures, such as mucus gels or cytoskeleton\nnetworks,\nare ubiquitous in biological systems. These intricate structures are\ncomposed of cross-linked, semiflexible biofilaments, crucial to numerous\nbiological processes. In many biological systems, active self-propelled\nparticles like motor proteins or bacteria navigate these intricate\npolymer networks. In this study, we develop a computational model\nof three-dimensional cubic-topological, swollen polymer networks of\nsemiflexible filaments. We perform Langevin dynamics simulations to\ninvestigate the diffusion of active tracer particles navigating through\nthese networks. By analyzing various physical observables, we investigate\nthe effects of mesh-to-particle size ratio, Péclet number of\nactive particles, and bending stiffness of the polymer networks upon\nactive trapped-and-hopping diffusion of the tracer. When the tracer\nsize is equal to or larger than the mesh size, the polymer stiffness\nsubstantially enhances trapping while suppressing the hopping process.\nNotably, the mean trapped time exhibits an exponential growth law\nto the bending stiffness with an activity-dependent slope. An analytic\ntheory based on the mean first-passage time of active particles in\na harmonic potential is developed. Our findings deepen the comprehension\nof the intricate interplay between the polymer’s bending stiffness,\ntracer size, and the activity of tracer particles. This knowledge\ncan shed light on important biological processes, such as motor-driven\ncargo transport or drug delivery, which hinge on the behavior of active\nparticles within biological gels.