The role of localization in the operation of the mitotic spindle assembly checkpoint.

The mitotic spindle assembly checkpoint (MSAC) is an important regulatory mechanism of the cell cycle, ensuring proper chromosome segregation in mitosis. It delays the transition to anaphase until all chromosomes are properly attached to the mitotic spindle by emitting a diffusible "wait anaphase"-signal from unattached kinetochores. Current models of the checkpoint disregard important spatial properties like localization, diffusion and realistic numbers of kinetochores. To allow for in silico studies of the dynamics of these models in a more realistic environment, we introduce a mathematical framework for quasi-spatial simulation of localized biochemical processes that are typically observed during checkpoint activation and maintenance. The "emitted inhibition" model of the MSAC by Doncic et al. (Proc Natl Acad Sci USA 2005; 102:6332-7) assumes instantaneous activation of the diffusible "wait anaphase"-signal upon kinetochore encounter. We modify this model to account for binding kinetics with finite rates and use the developed framework to determine the feasible range of the binding parameters. We find that for proper activation, the binding rate constant has to be fast and above a critical value. Furthermore, this critical value depends significantly on the amount of local binding sites at each kinetochore. The critical values lie in a physiological realistic regime (10(4)-10(6) M(-1)s(-1)). We also determine the feasible parameter range for fast checkpoint activation of the "Mad2 template" model, for which the kinetic parameters have recently been studied in vitro by Simonetta et al. (PLoS Biology 2009; 7:1000010). We find critical values for binding and catalysis rate constants, both significantly higher than the measured values. Our results suggest that yet unknown mechanisms at the kinetochores facilitate binding and catalysis in vivo. We conclude that quantitative models of the MSAC have to account for the limited availability of binding sites at kinetochores.