How do we estimate, from thermodynamic measurements, the number of water molecules adsorbed or released from biomolecules as a result of a biochemical process such as binding and allosteric effects? Volumetric and osmotic stress analyses are established methods for estimating water numbers; however, these techniques often yield conflicting results. In contrast, Kirkwood–Buff theory offers a novel way to calculate excess hydration number from volumetric data, provides a quantitative condition to gauge the accuracy of osmotic stress analysis, and clarifies the relationship between osmotic and volumetric analyses. I have applied Kirkwood–Buff theory to calculate water numbers for two processes: ( i ) the allosteric transition of hemoglobin and ( ii ) the binding of camphor to cytochrome P450. I show that osmotic stress analysis may overestimate hydration number changes for these processes.

Protein stability is enhanced by the addition of osmolytes, such as sugars and polyols and inert crowders, such as polyethylene glycols. This stability enhancement has been quantified by the preferential hydration parameter which can be determined by experiments. To understand the mechanism of protein stability enhancement, we present a statistical mechanical analysis of the preferential hydration parameter based upon Kirkwood–Buff theory. Previously, the preferential hydration parameter was interpreted in terms of the number of hydration waters, as well as the cosolvent exclusion volume. It was not clear how accurate these interpretations were, nor what the relationship is between the two. By using the Kirkwood–Buff theory and experimental data, we conclude that the contribution from the cosolvent exclusion dominantly determines the preferential hydration parameters for crowders. For osmolytes, although the cosolvent exclusion largely determines the preferential hydration parameters, the contribution from hydration may not be negligible.

Cosolvents added to aqueous solutions of biomolecules profoundly affect protein stability, as well as biochemical equilibria. Some cosolvents, such as urea and guanidine hydrochloride, denature proteins, whereas others, such as osmolytes and crowders, stabilize the native structures of proteins. The way cosolvents interact with biomolecules is crucial information required to understand the cosolvent effect at a molecular level. We present a statistical mechanical framework based upon Kirkwood–Buff theory, which enables one to extract this picture from experimental data. The combination of two experimental results, namely, the cosolvent-induced equilibrium shift and the partial molar volume change upon the reaction, supplimented by the structural change, is shown to yield the number of water and cosolvent molecules bound or released during a reaction. Previously, denaturation experiments (e.g., m-value analysis) were analyzed by empirical and stoichiometric solvent-binding models, while the effects of osmolytes and crowders were analyzed by the approximate molecular crowding approach for low cosolvent concentration. Here we synthesize these previous approaches in a rigorous statistical mechanical treatment, which is applicable at any cosolvent concentration. The usefulness and accuracy of previous approaches was also evaluated.