| Abstract: | Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events. |
