First passage of molecular motors on networks of cytoskeletal filaments

Molecular motors facilitate intracellular transport through a combination of passive motion in the cytoplasm and active transport along cytoskeletal filaments. Although the motion of motors on individual filaments is often well characterized, it remains a challenge to understand their transport on networks of filaments. Here we use computer simulations of a stochastic jump process to determine first-passage times (FPTs) of a molecular motor traversing an interval containing randomly distributed filaments of fixed length. We characterize the mean first-passage time (MFPT) as a function of the number and length of filaments. Intervals containing moderate numbers of long filaments lead to the largest MFPTs with the largest relative standard deviation; in this regime, some filament configurations lead to anomalously large FPTs due to spatial regions where motors become trapped for long times. For specific filament configurations, we systematically reverse the directionality of single filaments and determine the MFPT of the perturbed configuration. Surprisingly, altering a single filament can dramatically impact the MFPT, and filaments leading to the largest changes are commonly found in different regions than the traps. We conclude by analyzing the mean square displacement of motors in unconfined systems with a large density of filaments and show that they behave diffusively at times substantially less than the MFPT to traverse the interval. However, the effective diffusion coefficient underestimates the MFPT across the bounded interval, emphasizing the importance of local configurations of filaments on first-passage properties.