Herding of proteins by the ends of shrinking polymers

The control of biopolymer length is mediated by proteins that localize to polymer ends and regulate polymer-ization dynamics. Several mechanisms have been proposed to achieve end localization. Here, we propose a novel mechanism by which a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a "herding" effect. We formalize this process using both lattice-gas and continuum descriptions, and we present experimental evidence that the microtubule regulator spastin employs this mechanism. Our findings extend to more general problems involving diffusion within shrinking domains.