Abstract
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.
Highlights
Over the last decades our knowledge on the composition and functioning of the cellular organelles has increased considerably [1], but understanding how cells self-organize and make their molecular components self-assemble into cellular compartments and structures is still a major challenge in cellular biology [2, 3]
partially asymmetric simple exclusion process (PASEP) on networks leads to stationary regimes which have their direct equivalent in totally asymmetric simple exclusion process (TASEP): regular networks feature lowdensity phase (LD), LD − high-density phase (HD) and HD regimes, while irregular networks are dominated by the LD/HD regime
We have found that the heterogeneous LD/HD network regime present in TASEP disappears beyond some critical exchange between network and reservoir, see figure 20
Summary
Over the last decades our knowledge on the composition and functioning of the cellular organelles has increased considerably [1], but understanding how cells self-organize and make their molecular components self-assemble into cellular compartments and structures is still a major challenge in cellular biology [2, 3]. The role of heterogeneities has emerged from our previous studies as an important feature: since exclusion models in one dimension display a boundary-induced first-order phase transition in the particle density [54, 55], transport through complex networks leads to various regimes of density heterogeneities at different spatial scales [52, 53], which depend on the network topology. We rationalize these phenomena starting from the transport characteristics of a single segment between two particle reservoirs. In the conclusions we summarize how this classification allows to present in a compact way how spatial density heterogeneities appear in active transport on networks through an interplay between network topology, disorder, bi-directionality and finite particle processivity
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