Target finding in fibrous biological environments

We use a lattice model to study first-passage time distributions of target finding events through complex environments with elongated fibers distributed with different anisotropies and volume occupation fractions. For isotropic systems and for low densities of aligned fibers, the three-dimensional search is a Poisson process with the first-passage time exponentially distributed with the most probable finding time at zero. At high enough densities of aligned fibers, elongated channels emerge, reducing the dynamics dimensionality to one dimension. We show how the shape and size of the channels modify the behavior of the first-passage time distribution and its short, intermediate, and long time scales. We develop an exactly solvable model for synthetic rectangular channels, which captures the effects of the tortuous local structure of the elongated channels that naturally emerge in our system. For arbitrary values of the nematic order parameter of fiber orientations, we develop a mapping to the simpler situation of fully aligned fibers at some other effective volume occupation fraction. Our results shed light on the molecular transport of biomolecules between biological cells in complex fibrous environments.