A stochastic model for error correction of kinetochore-microtubule attachments in budding yeast.

To divide replicated chromosomes equally between daughter cells, kinetochores must attach to microtubules emanating from opposite poles of the mitotic spindle (biorientation). An error correction mechanism facilitates this process by destabilizing erroneous kinetochore-microtubule attachments. Here we present a stochastic model of kinetochore-microtubule attachments, via an essential protein Ndc80 in budding yeast, Saccharomyces cerevisiae. Using the model, we calculate the stochastic dynamics of a pair of sister kinetochores as they transition among different attachment states. First of all, we determine the kinase-to-phosphatase balance point that maximizes the probability of biorientation, while starting from an erroneous attachment state. We find that the balance point is sensitive to the rates of microtubule-Ndc80 dissociation and derive an approximate analytical formula that defines the balance point. Secondly, we determine the probability of transition from low-tension amphitelic to monotelic attachment and find that, despite this probability being approximately 33%, biorientation can be achieved with high probability. Thirdly, we calculate the contribution of the geometrical orientation of sister kinetochores to the probability of biorientation and show that, in the absence of geometrical orientation, the biorientation error rate is much larger than that observed in experiments. Finally, we study the coupling of the error correction mechanism to the spindle assembly checkpoint by calculating the average binding of checkpoint-related proteins to the kinetochore during the error correction process.