- 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. USA 105:16148, 2008), we demonstrate the power of our predictions.