Cluster Analysis of Protein Point Pattern Sets using Minkowski Functionals

Point patterns arise in many different areas of physical and applied research, often resulting in sets of patterns that may or may not be fundamenally different. We introduce here a numerical taxonomy procedure for clustering point pattern sets using their approximated Minkowski functionals. We demonstrate that this procedure is robust in distinguishing different spatial processes, even when the number of points in the patterns are small, vary wildly from pattern to pattern, or when the patterns are drawn from very similar processes. We then place this routine in a quantitative biology context by analyzing two point pattern sets of fluorescently labeled inter-cellular proteins, LAT and TAC, that have been acquired from experiments with immune cells. Overall, we find that this routine is a robust method for distinguishing point pattern sets, and provides meaningful insight regarding the homogeneity of a spatial process.