  Understanding design principles of biomolecular recognition is a key question
of molecular biology. Yet the enormous complexity and diversity of biological
molecules hamper the efforts to gain a predictive ability for the free energy
of protein-protein, protein-DNA, and protein-RNA binding. Here, using a variant
of the Derrida model, we predict that for a large class of biomolecular
interactions, it is possible to accurately estimate the relative free energy of
binding based on the fluctuation properties of their energy spectra, even if a
finite number of the energy levels is known. We show that the free energy of
the system possessing a wider binding energy spectrum is almost surely lower
compared with the system possessing a narrower energy spectrum. Our predictions
imply that low-affinity binding scores, usually wasted in protein-protein and
protein-DNA docking algorithms, can be efficiently utilized to compute the free
energy. Using the results of Rosetta docking simulations of protein-protein
interactions from Andre et al., Proc. Natl. Acad. Sci. U.S.A. 105, 16148
(2008), we demonstrate the power of our predictions.
