Spatial organization of assemblies of protein complexes by colocalization analysis

The precise localization of multiple species of proteins and protein complexes organized in nanodomains and large, non-periodic protein assemblies has been shown to be important for cellular function. Cryo-electron tomography is uniquely suited to visualize such assemblies in situ, with single nanometer precision, together with their cellular environment. Here we present in detail and characterize a parameter-free, second order point pattern analysis method that is applicable to cellular cryo-electron tomograms, and provides quantitative and statistical characterization of the colocalization between two or more distinct groups of complexes, such as those that comprise protein assemblies. By numerical and analytical calculations, we show that this colocalization method can correctly detect and distinguish different forms of point pattern interactions between complexes, and therefore identify specific types of spatial distribution of complexes, which result from multiple biochemical interactions and diffusion in cellular environments. We also present image processing tasks that precede the colocalization to facilitate its applications to cellular junctions and other biological systems.