| Summary: | We present a study of exclusion processes on networks as models for complex transport phenomena, and in particular for active transport of motor proteins along the cytoskeleton. Specifically, we focus on the totally asymmetric simple exclusion process (TASEP) as well as its generalizations including backstepping (partially asymmetric simple exclusion process (PASEP)) and exchange with a bulk concentration (TASEP with Langmuir kinetics (TASEP-LK)). We build on the previously used effective rate approach to establish a general methodology in terms of effective rate diagrams, which allows for a simple classification of the stationary transport state of the total network. This approach is general and reveals generic features of exclusion processes on networks. Based on the three examples considered here, we show that the classification can be made in terms of three qualitative different network regimes: a homogeneous regime, a heterogeneous network regime and a heterogeneous segment regime. Using parameters representative of real motor proteins, we show how the transitions between these regimes can be regulated through a variety of multi-scale factors, such as the interplay of exclusion interactions, the non-equilibrium nature of the transport process, motor processivity and the network topology. Using the equilibrium limits of PASEP and TASEP-LK, we also shed further light on the emergence of density heterogeneities in active transport phenomena.
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