Diffusive Transport on Directed Random Networks

We study diffusive motion of non-interacting particles on directed random networks, motivated by the structural polarity of cytoskeletal filamentous structures in biological systems. We consider a complex network consisting of directed intersecting filaments. The network structure can be characterized by the distribution of the segment length between two neighboring intersections and the distribution of the angle between two intersecting filaments. The transport problem is studied by introducing a master equation for the probability of arriving at the vicinity of a given position along a certain direction. Using an analytical Fourier–Z-transform technique, we present expressions for the mean square displacement and the diffusion coefficient in terms of the microscopic geometrical properties of the structure and the persistency of the walker. The method enables us to investigate the influence of structural inhomogeneity and anisotropy of the network on the transport properties.