  Biopolymer networks having a meshwork topology, e.g., extracellular matrix
and mucus gels, are ubiquitous. It is an open question to understand how
self-propelled agents such as Janus colloidal particles diffuse through such a
biopolymer network. Here, we computationally explore this issue in-depth by
explicitly modeling three-dimensional biopolymer networks and performing
Langevin dynamics simulations of active diffusion of the self-propelled tracers
therein. We show that the active tracer performs distinct diffusion dynamics
depending on the mesh-to-particle size and P\'eclet number (Pe). When the
particle is smaller than the mesh size, it moves as if in free space with a
decreased mobility depending on the polymer occupation density and Pe. However,
when the particle size is increased to be comparable to the mesh size, the
active particles explore the polymer network using the trapped-and-hopping
mechanism. We study the trapped time distribution, flight length distribution,
the mean-squared displacement, and the long-time diffusivity at varying Pe. If
the particle is larger than the mesh, it captures the collective viscoelastic
dynamics from the polymer network at short times and the simple diffusion of
the total system at large times. Finally, we discuss the scaling behavior of
the long-time diffusivity with Pe, where we find a range of Pe that yields a
nontrivial power law. The latter turns out to arise from a large fluctuation of
trapped, activated tracers in conjugation with responsive polymer networks.

Soft Condensed Matter;Biological Physics