Toward the semiquantitative estimation of binding constants. Guides for peptide-peptide binding in aqueous solution

An expression is presented for the estimation of approximate binding constants for bimolecular associations in solution. The consequences of the approach have been examined for the bimolecular association of two peptide components in aqueous solution: specifically for the binding of two vancomycin group antibiotics, vancomycin itself and ristocetin A, to the peptide cell wall analogue ^V-Ac-D-AIa-D-AIa and related ligands. Uncertainties in the treatment are relatively large, but the physical insights gained into the binding process (in part with the aid of calorimetric data obtained by others) are enlightening. We conclude that for amide-amide hydrogen bond formation in aqueous solution at room temperature, the intrinsic binding energy is ca. 24 kJ mol"1 (an intrinsic binding constant of ca. 104); this process is almost completely driven by a favorable entropy change associated with the release of water molecules from the amide NH and CO groups involved in hydrogen bond formation. The bimolecular association of N-Ac-D-AIa-D-Ala with ristocetin A has a remarkably small entropy change at 298 K (TAS = 3 ± 1.5 kJ mol"1)- We conclude that the release of water from polar and hydrocarbon groups involved in the binding almost exactly compensates for (i) the unfavorable entropy change due to the freezing out of four rotors of /V-Ac-D-AIa-D-AIa upon binding and (ii) the unfavorable entropy change of a bimolecular association. A crude quantitation of these effects is presented. We also present an estimate of the increase in translational plus rotational free energy, as a function of the ligand mass, occurring when a ligand binds to a larger receptor. This quantity, fundamental to all binding processes, is relatively insensitive to the shape of the ligand. Extension of the approach will allow, in those cases where there is good complementarity between ligand and receptor, the prediction of approximate peptide-peptide binding constants in aqueous solution.