Quantitative methods for diffusion measurements in fluorescence microscopy

Doctoral thesis, 2019

In this work, statistical methods are developed for mapping mass transport locally based on images collected using a confocal laser scanning microscope. Besides presenting raster image correlation spectroscopy as an established method in fluorescence microscopy, we introduce a single particle tracking method which takes advantage of the raster scanning of the image in a confocal microscope. In single particle tracking, particles are identified and followed in consecutive frames of a video to measure their diffusive mobility. Both a maximum likelihood and a centroid-based method have been developed to locate the particles and hence to estimate the diffusion coefficient. The method is generalized to analyse mixtures of particles having different diffusion coefficients. The proposed method allows us to study the entire distribution of diffusion coefficients, enabling the characterization of heterogeneous systems. Motivated by experiments with particle mixtures, we investigate the use of cross-validation to perform model selection, i.e. to select the number of mixture components, and compare it to some existing model selection criteria. In the specific case of normal mixtures, we prove a bound on the error between the cross-validated conditional risk and an oracle benchmark conditional risk, which assumes the knowledge of the true density generating the data. Furthermore, a detailed statistical analysis of the raster image correlation spectroscopy method is presented, uncovering the relationship between molecular and experimental parameters and the estimated diffusion coefficient. We propose a statistical method to compare different experimental conditions and apply it to find the optimal parameters to perform an experiment. The methods and models investigated and developed in this thesis are of general interest. In particular, the quantitative methods considered to study confocal images can be used in a wide range of applications, while the use of crossvalidation to perform model selection of mixture models is a valuable contribution to the statistical literature.