Target finding in fibrous biological environments

We study first-passage time (FPT) distributions of target finding events through complex environments with elongated obstacles distributed with different anisotropies and volume occupation fractions. For isotropic systems and for low densities of aligned obstacles, FPTs are exponentially distributed. At large enough densities of aligned obstructions, elongated channels emerge, gradually reducing the dynamics dimensionality from 3D, to 1D in the case of narrow structures. We analyze how the local structure of the channels, such as geometry and size, modifies the FPT distribution. We find that channel size and geometry determines the shape of the FPT distribution and its mean first-passage time. Moreover, we develop an exactly solvable model for synthetic rectangular channels that captures the effects of the tortuous local structure of the 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. Because of the complex nature of fibrous biological environments in tissues, we suggest that our results shed light on the understanding of the molecular transport occurring between cells.