Tension-Dependent Dynamic Microtubule Model for Metaphase and Anaphase Phenomena

Abstract

We present a theoretical model describing metaphase chromosome oscillations, microtubule (MT) attachment error correction, and anaphase chromosome separation. During metaphase, chromosome pairs align near the center of a bipolar MT spindle and oscillate as the MTs attaching them to the cell poles polymerize and depolymerize. Simultaneously, the cell fixes misaligned chromosome pairs by some tension-dependent mechanism. In anaphase, chromosome pairs separate as depolymerizing MTs pull each chromosome toward its respective cell pole. Instead of including all known components to develop a comprehensive, species-specific description, we introduce a minimal model based on fundamental properties of MT kinetics. We use the tension-dependence of single MT polymerization/depolymerization kinetics measured by Akiyoshi et al. [1] and assume the same functional dependence for compressed MTs. We apply these to a many MT model, and solve this stochastic model numerically and by a master equation approach. We find that the tension dependence of rates enhances the speed of single chromosome pulling by MTs during anaphase- or error-correction-like behavior. Additionally, the force-velocity curve for a single chromosome attached to dynamic MTs exhibits bi-stability: at high loads, large tension fluctuations induce MTs to spontaneously switch from a depolymerizing state into a polymerizing state. The system is hysteretic; to recover depolymerization from the polymerizing state, the load must be decreased to a far smaller value than that required to initially induce polymerization. This behavior leads to the chromosome oscillations we observe in the two-chromosome system. Interestingly, we observe breathing oscillations, which are not captured by any other chromosome oscillation model. Our minimal model reflects general features of the underlying mechanisms of these phenomena, and reveals how different components control chromosome dynamics through the rate constants.[1] Akiyoshi et al. (2010) Nature 468, 576-579.