A statistical and mechanistic, model-based analysis of spindle assembly checkpoint signalling

Abstract

The mechanisms that ascertain whether a phase of the cell cycle has been successfully completed and the conditions to proceed to the next phase are fulfilled are called checkpoints. One of them is the spindle assembly checkpoint (SAC), which clears for completion of cell division only if the conditions for a proper partitioning of the genetic material are fulfilled. Despite complete knowledge of its function for decades, the underlying mechanism on themolecular level is still not completely elucidated. We have data at hand that show how persistent the SAC is in individual yeast cells, when the amounts of its signalling components are altered. Since these manipulations are done on the genetic level, the effcacy is the same for each cell of a strain. Therefore, one would expect the SAC to show a homogeneous response in such a clonal population of cells. However, the data reveal that SAC persistence, measured as duration of cell cycle arrest in prometaphase, is highly variable between cells of the same strain. In this thesis we use statistical modelling to quantify the observed cell-to-cell variability and analyse subpopulation structures in clonal populations of yeast cells. The sophisticated statistical analysis is complemented by mechanistic modelling of the molecular mechanism of the SAC on the population level. The statistical analysis of the data is hampered by the fact that the data are censored, i.e. that prometaphase length as the variable of interest is not completely observable in many cells. To account for this in the analysis and to exploit the information which is only accessible by simultaneously analysing the data from multiple stains, we propose a general framework for multi-experiment mixture modelling, named MEMO. Employing this framework, we show that reduction of the amount of individual SAC proteins results in a split of the clonal population of cells into subpopulations with opposing SAC phenotypes. While one subpopulation retains a completely functional SAC, a second subpopulation with an impaired SAC emerges and increases. We quantify the sensitivity of this effect as a function of type and amount of the manipulated protein. Such a quantification allows for the prediction of the subpopulation structure of yet unobserved protein manipulations. The striking observation of phenotypically different subpopulations in a population of genetically identical cells is underscored by the fact that noise in the protein abundances is small. We complement the statistical analysis of the data with mechanistic models of the molecular mechanism of SAC signalling. By exploiting the information contained in the population split, we identify ultrasensitivity and potential bistability to be a property of the dynamical system that forms the SAC. This implies high sensitivity with respect to noise in the abundance of signalling and targeted proteins. Furthermore, we assess the contribution of different SAC components to the observed cell-to-cell variability. While the statistical modelling framework proposed in this thesis can help to prevent misinterpretation of data in the presence of censoring, also in other single-cell data settings, our findings on the properties of the SAC signalling system provide novel insights into this intricate molecular mechanism.