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Analyzing the morphological appearance and the spatial distribution of large dense-core vesicles (granules) in the cell cytoplasm is central to the understanding of regulated exocytosis. This paper is concerned with the automatic detection of granules and the statistical analysis of their spatial locations in different cell groups. We model the locations of granules of a given cell as a realization of a finite spatial point process and the point patterns associated with the cell groups as replicated point patterns of different spatial point processes. First, an algorithm to segment the granules using electron microscopy images is proposed. Second, the relative locations of the granules with respect to the plasma membrane are characterized by two functional descriptors: the empirical cumulative distribution function of the distances from the granules to the plasma membrane and the density of granules within a given distance to the plasma membrane. The descriptors of the different cells for each group are compared using bootstrap procedures. Our results show that these descriptors and the testing procedure allow discriminating between control and treated cells. The application of these novel tools to studies of secretion should help in the analysis of diseases associated with dysfunctional secretion, such as diabetes.