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Noncovalent binding provides an invisible wiring diagram for biomolecular pathways and is the essence of host-guest and supramolecular chemistry. Decades of theoretical and experimental studies provide insight into the determinants of binding affinity and specificity. The many practical applications of targeted molecules have also motivated the development of computational tools for molecular design aimed at drug-discovery1 and, to a lesser extent, the design of low molecular weight receptors.2–6 Nonetheless, there remain unresolved questions and challenges. The rules of thumb for maximizing binding affinity are unreliable, and there is still a need for accurate methods of predicting binding affinities for a range of systems.  Many researchers are now renewing progress in this area by delving deeper into the physical chemistry and modeling of noncovalent binding.1,7 Important themes today include the use of more refined models of interatomic energies,8–12 computational13–23 and experimental24–34 characterization of configurational entropy changes on binding, enhanced techniques for sampling molecular conformations and extracting free energies from simulations,35–43 and the exploitation of advances in computer hardware.44–53  Such efforts require both a quantitative understanding of interactions at the atomic level and a means of mapping of these interactions to macroscopically observable binding affinities. Statistical thermodynamics provides the required mapping, and the theoretical underpinnings of binding thermodynamics appear to be well established.14,54–56 Nonetheless, analyses of binding, both experimental and theoretical, still frequently employ non-rigorous frameworks which can lead to puzzling or contradictory results. This holds especially in relation to entropy changes on binding, which can be both subtle and controversial. For example, although the change in translational entropy when biomolecules associate has been discussed in the literature for over 50 years, it remains a subject of active discussion.15,18,56–71  This review of the theory of free energy and entropy in noncovalent binding aims to support the development of well-founded models of binding and the meaningful interpretation of experimental data. We begin with a rigorous but hopefully accessible discussion of the statistical thermodynamics of binding, taking an approach that differs from and elaborates on prior presentations; background material and detailed derivations are provided in Supporting Information. Then we use this framework to provide new analyses of topics of long-standing interest and current relevance. These include the changes in translational and other entropy components on binding; the implications of correlation for entropy; multivalency (avidity) and the relationship between bimolecular and intramolecular binding; and the applicability of additivity in the interpretation of binding free energies.  Several caveats should be noted. First, we focus on general concepts rather than specific systems or computational methods, the latter having been recently reviewed.1,7 Second, our formulation of binding thermodynamics is based on classical statistical mechanics, although occasional reference is made to quantum mechanics when the connection is of particular interest. Finally, we have not attempted to be exhaustive in citing the literature but hope to have provided enough references to offer a useful entry.

Theory of Free Energy and Entropy in Noncovalent Binding