We theoretically study the transport properties of self-propelled particleson complex structures, such as motor proteins on filament networks. A generalmaster equation formalism is developed to investigate the persistent motion ofindividual random walkers, which enables us to identify the contributions ofkey parameters: the motor processivity, and the anisotropy and heterogeneity ofthe underlying network. We prove the existence of different dynamical regimesof anomalous motion, and that the crossover times between these regimes as wellas the asymptotic diffusion coefficient can be increased by several orders ofmagnitude within biologically relevant control parameter ranges. In terms ofmotion in continuous space, the interplay between stepping strategy andpersistency of the walker is established as a source of anomalous diffusion atshort and intermediate time scales.
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