Dynamic instability, in which abrupt transitions occur between growing and shrinking states, is an intrinsic property of microtubules that is regulated by both mechanics and specialized proteins. We discuss a model of dynamic instability based on the popular idea that growth is maintained by a cap at the tip of the fiber. The loss of this cap is thought to trigger the transition from growth to shrinkage, called a catastrophe. The model includes longitudinal interactions between the terminal tubulins of each protofilament, and ``gating rescues'' between neighboring protofilaments. These interactions allow individual protofilaments to transiently shorten in a phase of overall microtubule growth. The model reproduces the reported dependency of the catastrophe rate on tubulin concentration, the time between tubulin dilution and catastrophe, and the induction of microtubule catastrophes by walking depolymerases. The model also reproduces the comet tail distribution that is characteristic of proteins that bind to the tips of growing microtubules.