Bayesian analysis of data from segmented super-resolution images for quantifying protein clustering

Abstract: Super-resolution imaging techniques have largely improved our capabilities to visualize nanometric structures in biological systems. Their application further enables one to potentially quantitate relevant parameters to determine the molecular organization and stoichiometry in cells. However, the inherently stochastic nature of the fluorescence emission and labeling strategies imposes the use of dedicated methods to accurately measure these parameters. Here, we describe a Bayesian approach to precisely quantitate the relative abundance of molecular oligomers from segmented images. The distribution of proxies for the number of molecules in a cluster -- such as the number of localizations or the fluorescence intensity -- is fitted via a nested sampling algorithm to compare mixture models of increasing complexity and determine the optimal number of mixture components and their weights. We test the performance of the algorithm on {\it in silico} data as a function of the number of data points, threshold, and distribution shape. We compare these results to those obtained with other statistical methods, showing the improved performance of our approach. Our method provides a robust tool for model selection in fitting data extracted from fluorescence imaging, thus improving the precision of parameter determination. Importantly, the largest benefit of this method occurs for small-statistics or incomplete datasets, enabling accurate analysis at the single image level. We further present the results of its application to experimental data obtained from the super-resolution imaging of dynein in HeLa cells, confirming the presence of a mixed population of cytoplasmatic single motors and higher-order structures.