Analysis of spatial dependencies of endocytic proteins based on temporal random sets

Statistical image analysis has emerged as a basic methodology in the study of many real phenomena, which can be represented by sequences of binary images. Recent techniques, such as total internal reflection fluorescent microscopy, allow us to image simultaneously two fluorescent-tagged proteins which are relevant in important cellular processes, such as endocytosis. Here, we model these biological pairs of image sequences as realizations of a 3D non-isotropic bivariate random set, in which one dimension corresponds to time. We analyze their second-order properties by means of the cross-covariance and the pair correlation function in order to study colocalization between proteins. Results show the proposed methodology allows us to study spatial dependencies in a formal and robust way.