Using default constraints of the spindle assembly checkpoint to estimate the associated chemical rates

To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.A fundamental step in cell division consists in the alignment of each pair of chromosomes. This process occurs during metaphase, where centrosome nucleated microtubules interact with the chromosomes kinetochores to build the mitotic spindle. Only after all chromosomes have become aligned at the metaphase plate and when every kinetochore is properly attached to a bundle of microtubules, the cell enters anaphase. To prevent premature progression to anaphase, even if all-but-one of the kinetochores have been attached and the chromosomes are aligned, unattached or improperly attached kinetochores generate a signal inhibiting the anaphase activators. This process is called the spindle assembly checkpoint (SAC).Although the exact mechanisms of the SAC and anaphase processes are still unclear, several key steps have been identified. Sister chromatids are initially bound by proteins such as cohesin. During anaphase onset, separase protein cleaves cohesin, thus allowing the sister chromatids to separate [1]. Usually, separase is prevented from cleaving cohesin through its association with another protein called securin. Securin can be ubiqitylated by the activated Cdc20-anaphase promoting complex/cyclosome (Cdc20-APC/C) at the kinetochores [2]. However, when the kinetochores are not all properly attached, the SAC enables the ubiquitylation and inhibition of Cdc20 binding with APC/C [2,3]. The mechanisms leading to Cdc20 ubiquitylation involve several proteins such as Mad2, BubR1, Bub3 [4]. Current models [5-