Herding of proteins by the ends of shrinking polymers

The localization of proteins to the ends of biopolymers can facilitate the regulation of polymerization dynamics. Several mechanisms have been proposed to achieve this localization. Here, we show that a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a novel "herding" mechanism. We formalize this using a lattice-gas model and a continuum description, 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.