Transport of molecular motors along protein filaments in a half-closedgeometry is a common feature of biologically relevant processes in cellularprotrusions. Using a lattice gas model we study how the interplay betweenactive and diffusive transport and mass conservation leads to localised domainwalls and tip localisation of the motors. We identify a mechanism for tasksharing between the active motors (maintaining a gradient) and the diffusivemotion (transport to the tip), which ensures that energy consumption is low andmotor exchange mostly happens at the tip. These features are attributed tostrong nearest-neighbour correlations that lead to a strong reduction of activecurrents, which we calculate analytically using an exact moment-identity, andmight prove useful for the understanding of correlations and active transportalso in more elaborate systems.
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