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Stochastic models of yeast kinetochore-microtubule interactions
Our objective is to reveal how kinetochore proteins regulate kinetochore microtubule (kMT) dynamics and along what pathways kinetochore proteins convert chemical and mechanical signals into kMT regulation, taking the budding yeast S. cerevisiae as our model system. We want to achieve this by building a model of the network of functional interactions between kinetochore proteins and devising a biophysical description of how the different kinetochore network states affect kMT dynamics. Model parameters will be estimated using large sets of wildtype and mutant kMT trajectories measured via live-cell light microscopy. Data from wildtype and mutant strains will be used together for model calibration in order to limit the space of possible kinetochore states. Due to the stochasticity of kMT dynamics, simulated and experimental kMT trajectories cannot be compared and matched on a time-point by time-point basis. A method that allows the calibration of probabilistic models using stochastic data is the method of indirect inference. In this approach, the matching between model prediction and experimental observations is achieved at the level of a set of intermediate statistics, or descriptors, that represent the essential features in the data. We have established autoregressive moving average (ARMA) model parameters as a unique and complete set of descriptors of S. cerevisiae kMT dynamics, making them ideal intermediate statistics for model calibration. ARMA models extract the dependence of kMT length on its history and on a related random state fluctuations series which embodies the stochastic nature of kMT dynamics. The comparison of ARMA descriptors is done within a statistical hypothesis testing framework, using the variance-covariance matrices of the descriptors. The p-values from the statistical tests can be used to construct an objective function to match model-generated and experimental kMT trajectories. They can be also used to detect differences between kMT dynamics under different experimental conditions on a continuous scale. This has allowed us to cluster kMT dynamics in different mutants and to identify functional groups among kinetochore proteins. Via ARMA analysis, we found that the regulation of kMT dynamics varies with temperature and cell cycle, but not with the chromosome an MT is attached to. We also found that the essential proteins Okp1p, Ipl1p and Dam1p and the nonessential motor Kip3p play a role in the regulation of kMT dynamics. In particular, the mutants ipl1-321, dam1-1 and kip3Δ exhibit the same misregulation of kMT dynamics, suggesting that the corresponding three proteins form a functional group. These results illustrate that ARMA descriptors are sensitive enough to detect the subtle changes in kMT dynamics resulting from kinetochore protein mutation and that the clustering of kMT dynamics in different kinetochore mutants based on ARMA descriptors reveals functional groups among kinetochore proteins, assisting in the construction of a mechanistic model of kinetochore-kMT interactions.
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