DNA loci colocalization is the result of a thermodynamic phase transition. We show this through the plots of the normalized mean square distance (, (a)) and of the fraction of paired DNA loci (, (b)) at equilibrium, as functions of , the interaction energy between the molecular factors (MFs) and the DNA binding sites (BSs). As increases, and , from values typical of Brownian diffusion ( and , orange horizontal lines), rapidly saturate to values which signal DNA loci full colocalization (, , blue horizontal lines), after a threshold value (defined by the criterion ). Superimposed fits for both and are power-law functions (gray dashed lines). In (c) the characteristic time scale needed to reach thermodynamic equilibrium is illustrated, as function of . turned out to be an increasing function, as the stronger MF-BS bonds make the DNA loci diffusion more difficult. A “jump” is observed at , when the phase transition takes place. The superimposed fits are power-law functions. We took an MF concentration and a DNA BS number .
