Although the statistical thermodynamics of noncovalent binding has been considered in a number of theoretical papers, few methods of computing binding affinities are derived explicitly from this underlying theory. This has contributed to uncertainty and controversy in certain areas. This article therefore reviews and extends the connections of some important computational methods with the underlying statistical thermodynamics. A derivation of the standard free energy of binding forms the basis of this review. This derivation should be useful in formulating novel computational methods for predicting binding affinities. It also permits several important points to be established. For example, it is found that the double-annihilation method of computing binding energy does not yield the standard free energy of binding, but can be modified to yield this quantity. The derivation also makes it possible to define clearly the changes in translational, rotational, configurational, and solvent entropy upon binding. It is argued that molecular mass has a negligible effect upon the standard free energy of binding for biomolecular systems, and that the cratic entropy defined by Gurney is not a useful concept. In addition, the use of continuum models of the solvent in binding calculations is reviewed, and a formalism is presented for incorporating a limited number of solvent molecules explicitly.

It is pointed out that the Ornstein–Zernike equations recently used by Madden in treating quenched-annealed mixtures are approximate. The exact equations are given and briefly discussed.

We describe a novel, two-step method for directly computing the conformational free energy of a molecule. In the first step, a finite set of low-energy conformations is identified, and its contribution to the configuration integral is evaluated by a straightforward Monte Carlo technique. The method of finding energy minima incorporates certain features of the global-underestimator method and of a genetic algorithm. In the second step, the contribution to the configuration integral due to conformations not included in the initial integration is determined by Metropolis Monte Carlo sampling. Applications to alanine oligopeptides and to three cyclic urea inhibitors of HIV protease are presented.

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