Shepherding by biased diffusion organizes diffusible proteins on microtubules

Abstract

How microscopic interactions give rise to cellular-scale order in the crowded environment of cells remains an open problem. Far-from-equilibrium mixtures of active and passive molecules self-organize, but the principles remain unclear. Microtubules are cytoskeletal polymers composed of 13 protofilaments bound by mixtures of actively moving motors and passively diffusing microtubule-associated proteins (MAPs), serving as a model system for self-organization on a multi-lane lattice. Here, we combine computational modeling, analytic theory, and in vitro reconstitution to demonstrate that motors can "shepherd" diffusive MAPs by rectifying Brownian motion into net directional drift without motor-MAP binding. Our model reveals that biased movement increases when fewer protofilaments are accessible or when lateral diffusion between protofilaments is limited, identifying local dimensionality and diffusion as key parameters governing spatial patterning. Notably, shepherding depends not on individual motor processivity but on the total number of motors bound to microtubules. We experimentally recapitulate micron-scale shepherding with a kinesin-1 motor (K401) and a diffusive MAP (PRC1), which show no detectable binding. These findings reveal shepherding as an emergent mechanism by which ensembles of motors generate micron-scale spatial patterning and transport of MAPs without direct binding interactions.