Randomness of spatial distributions of two proteins in the cell nucleus involved in mRNA synthesis and their relationship.

Randomness and relation between point positions play an important role in archeology, cosmology, geography, and biology. An often-discarded effect is the edge effect, the effect that points are bound to a certain region. Without an appropriate correction, the outcome will be wrong. We studied the problem of randomness by comparing the distribution of interpoint distances with what can be expected for randomly distributed points (pair correlation function in statistics), and applied this to two sets of nuclear proteins inside the cell nucleus. The technique comprised labelling the proteins with a fluorescent dye, recording the fluorescent distribution with a 3D confocal microscope, and detecting the positions of the individual fluorescent spots. Results showed that, apart from studying randomness, the method is well equipped to quantitatively analyze a spot detection procedure, as the resolving power and the subvoxel accuracy were clearly visible. Given the results of assessing the randomness of the general transcription factor BRG1 and the RNA synthesizing protein RNA polymerase II (polII) in the cell nucleus, we concluded that the high intensity spots of the BRG1 protein are regularly spaced. The low intensity spots of the BRG1 protein and the low- and high-intensity spots of the polII protein showed more random behavior. The BRG1 and polII proteins showed correlation; unexpectedly, the relation was also found for the low-intensity spots, which were expected to have a more random behavior.