K-Neighbourhood Analysis: A Method for Understanding SMLM Images as Compositions of Local Neighbourhoods.

Single molecule localisation microscopy (SMLM) is a powerful tool that has revealed the spatial arrangement of cell surface signalling proteins, producing data of enormous complexity. The complexity is partly driven by the convolution of technical and biological signal components, and partly by the challenge of pooling information across many distinct cells. To address these two particular challenges, we have devised a novel algorithm called K-neighbourhood analysis (KNA), which emphasises the fact that each image can also be viewed as a composition of local neighbourhoods. KNA is based on a novel transformation, spatial neighbourhood principal component analysis (SNPCA), which is defined by the PCA of the normalised -nearest neighbour vectors of a spatially random point pattern. Here, we use KNA to define a novel visualisation of individual images, to compare within and between groups of images and to investigate the preferential patterns of phosphorylation. This methodology is also highly flexible and can be used to augment existing clustering methods by providing clustering diagnostics as well as revealing substructure within microclusters. In summary, we have presented a highly flexible analysis tool that presents new conceptual possibilities in the analysis of SMLM images.