Topological edge currents promote exploratory chromosome capture in microtubule dynamic instability

Microtubules capture chromosomes during mitosis by stochastically switching between growth and shrinkage at catastrophe events. They display strikingly rich biochemistry and dynamics, regulated by a stabilizing cap with distinct conformational states. Microtubule lengths at catastrophe are observed to follow a peaked distribution, while their growth “stutters” briefly before catastrophe. Such complexity makes it hard to capture all these observations without a large number of tunable parameters. Here, we introduce a topological model of the microtubule cap that reproduces the features above through dynamical edge states, that provides a minimal description with just two free parameters. Our approach further provides an analytical description of catastrophes and allows the same features to persist over a wide range of tubulin concentration, consistent with experimental observations.