Non-homogeneous temporal Boolean models to study endocytosis

Many medical and biological problems require the analysis of large sequences of microscope images, these images capture phenomena of interest and it is essential to characterize their spatial and temporal properties. The purpose of this paper is to show a new statistical methodology for estimating these parameters of interest in image sequences obtained in the observation of endocytosis. Endocytosis is a process by which cells traffic molecules from the extracellular space into different intracellular compartments. These images are obtained using a very specialized microscopy technique called Total Internal Reflecting (TIRFM). The Homogeneous Temporal Boolean Model (HTBM) has been recently used to analyze these type of sequences of images. By using a HTBM, spatial homogeneity of events in the cell membrane must be assumed but this is an open question in the biological understanding of the endocytic process. Our aim in this paper is to generalize this methodology to overcome this drawback. In the methodological aspect this work has a threefold aim: to broaden the notion of HTBM by introducing the concept of Non-Homogeneous Temporal Boolean Model; to introduce a hypothesis testing procedure to check the spatial homogeneity assumption; and finally, to reformulate the existing methodology to work with underlying non-homogeneous point processes. We check the goodness of our methodology on a simulated data set and compare our results with those provided by visual inspection and by assuming spatial homogeneity. The accuracy of the results obtained with simulated data ensures the validity of our methodology. Finally we apply it, as an illustration, to three sequences of a particular type of endocytosis images. The spatial homogeneity test confirms that spatial homogeneity cannot be assumed. As a result, our methodology provides more accurate estimations for the duration of the events and, information about areas of the membrane with higher accumulation of them.