Elucidating the energetic contributions to the binding free energy.

New exact equations are derived for the terms contributing to the binding free energy (ΔG) of a ligand-receptor pair using our recently introduced formalism which we here call perturbation-divergence formalism (PDF). Specifically, ΔG equals the sum of the average of the perturbation (pertaining to new interactions) and additional dissipative terms. The average of the perturbation includes the sum of the average receptor-ligand interactions and the average of the change of solvation energies upon association. The Kullback-Leibler (KL) divergence quantifies the energetically dissipative terms, which are due to the configurational changes and, using the chain rule of KL divergence, can be decomposed into (i) dissipation due to limiting the external liberation (translation and rotation) of the ligand relative to the receptor and (ii) dissipation due to conformational (internal) changes inside the receptor and the ligand. We also identify all exactly canceling energetic terms which do not contribute to ΔG. Furthermore, the PDF provides a new approach towards dimensionality reduction in the representation of the association process and towards relating the dynamic (high dimensional) with the thermodynamic (one-dimensional) changes.