Quantifying Colocalization: Thresholding, Void Voxels and the H(coef)

A critical step in the analysis of images is identifying the area of interest e.g. nuclei. When the nuclei are brighter than the remainder of the image an intensity can be chosen to identify the nuclei. Intensity thresholding is complicated by variations in the intensity of individual nuclei and their intensity relative to their surroundings. To compensate thresholds can be based on local rather than global intensities. By testing local thresholding methods we found that the local mean performed poorly while the Phansalkar method and a new method based on identifying the local background were superior. A new colocalization coefficient, the H(coef), highlights a number of controversial issues. (i) Are molecular interactions measurable (ii) whether to include voxels without fluorophores in calculations, and (iii) the meaning of negative correlations. Negative correlations can arise biologically (a) because the two fluorophores are in different places or (b) when high intensities of one fluorophore coincide with low intensities of a second. The cases are distinct and we argue that it is only relevant to measure correlation using pixels that contain both fluorophores and, when the fluorophores are in different places, to just report the lack of co-occurrence and omit these uninformative negative correlation. The H(coef) could report molecular interactions in a homogenous medium. But biology is not homogenous and distributions also reflect physico-chemical properties, targeted delivery and retention. The H(coef) actually measures a mix of correlation and co-occurrence, which makes its interpretation problematic and in the absence of a convincing demonstration we advise caution, favouring separate measurements of correlation and of co-occurrence.