  The control of biopolymer length is mediated by proteins that localize to
polymer ends and regulate polymerization 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 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.
