PARTITIONING OF FREE-ENERGY CONTRIBUTIONS IN THE ESTIMATION OF BINDING CONSTANTS - RESIDUAL MOTIONS AND CONSEQUENCES FOR AMIDE-AMIDE HYDROGEN-BOND STRENGTHS

Any bimolecular association is entropically unfavorable because of degrees of freedom of translation and rotation lost when two molecules come together to form a complex. For a ligand Of molecular weight 200, the formation of a ''rigid'' dimer (one in which there is no residual relative motion of the associating components A and B in the complex A.B) opposes binding by ca. 10(-9) to 10(-10) M-1 in binding constant. If relative motions (including new soft vibrations) in the complex are then credited to the functional group interactions then the amide-amide hydrogen bonds, for example, those involved in the reported formation of lactam dimers in solution, are concluded to promote dimerization by ca. 10(4) per hydrogen bond (Doig, A. J.; Williams, D. H. J. Am. Chem. Soc. 1992, 114, 338). An alternative approach is to regard residual relative motions remaining in the complex as constituting translational and rotational entropy of A and B that was not lost. In this paper and in the preceding paper we have attempted to quantitate the contribution of residual motions in weakly bound complexes from literature data on the fusion, sublimation, and dissolution of model compounds. If the entropic advantage of the residual motions is removed as entropy that is not lost in the bimolecular association, then free energies for amide-amide hydrogen bond formation are obtained that are not significantly different from the conventional view of these bonds of between -2 and -8 kJ mol-1. The same conclusion is reached in ligand extension studies for the binding of peptide cell wall analogues to the antibiotics vancomycin and ristocetin A if credit for residual motions is removed, and allowance is made for a larger hydrophobic effect than originally envisioned (Williams, D. H., et al. J. Am. Chem, Soc. 1991, 113, 7020).