Statistically enhanced self-attraction of random patterns

In this work we develop a theory of interaction of randomly patterned surfaces as a generic prototype model of protein-protein interactions. The theory predicts that pairs of randomly superimposed identical (homodimeric) random patterns have always twice as large magnitude of the energy fluctuations with respect to their mutual orientation, as compared with pairs of different (heterodimeric) random patterns. The amplitude of the energy fluctuations is proportional to the square of the average pattern density, to the square of the amplitude of the potential and its characteristic length, and scales linearly with the area of surfaces. The greater dispersion of interaction energies in the ensemble of homodimers implies that strongly attractive complexes of random surfaces are much more likely to be homodimers, rather than heterodimers. Our findings suggest a plausible physical reason for the anomalously high fraction of homodimers observed in real protein interaction networks.