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Differences Between Pair and Bulk Hydrophobic Interactions Proc. Natl. Acad. Sci. USA Vol. 87, pp. 946-949, February 1990 Biochemistry Differences between pair and bulk hydrophobic interactions ROBERT H. WOODt AND PETER T. THOMPSONt tDepartment of Chemistry, University of Delaware, Newark, DE 19716; and tDepartment of Chemistry, Swarthmore College, Swarthmore, PA 19081 Communicated by Robert L. Baldwin, September 28, 1989 ABSTRACT It is now well known that the pair interaction bic groups between water and hydrophobic medium is illus- between two hydrocarbon molecules in water has distinctly trated by the following thermodynamic cycle. different properties from the bulk hydrophobic interaction familiar to the biochemist, which is modeled by the transfer of nR(g, c@) AG,(g, Ce) IR (g co) a hydrocarbon from aqueous solutions to pure liquid hydro- carbon. We consider experimental data for pair interactions, which have been fitted by a simple empirical potential function, and point out some of their properties. (i) Surface free energy I I AGs and cosphere overlap models, ofthe type considered until now, cannot reproduce correctly both the pair and bulk hydrophobic interactions. (ii) Pair interactions though still attractive are strikingly weaker in aqueous solution than in the gas phase, in c contrast to the usual view ofhydrophobic interactions. (iii) For nR(aq, c@) - R,(aq, co) pair interactions in water, the solvent-separated configuration is less important than the contact configuration if the hydro- Here R is a hydrophobic molecule and co is the chosen carbon has more than two carbon atoms. standard state concentration (co = 1 mol/dm3). For n = 2, AG2(g) = -RT In K2(g) is a measure of the association of a Hydrophobic "bonding" involves the association of nonpo- pair ofgas-phase molecules, while the corresponding AG2(aq) lar groups in an aqueous environment. Kozak et al. (1) have and equilibrium constant, K2(aq), is a measure of the asso- drawn the distinction between bulk hydrophobic interac- ciation of a pair of hydrophobic molecules in water. tions-that is, "interactions involving large clusters of non- For the bulk interaction, the four-sided cycle collapses to polar groups as may, for instance, be found in the interior of a triangular one because the thermodynamic properties of a protein molecule"-and interactions between small num- R,(g) become equal to those of R,(aq) in the limit of large n; bers of nonpolar groups as may, for instance, be found at the a large enough n-mer is a liquid drop of R. The bulk surface of a protein molecule. These qualitatively different interaction familiar to the biochemist is characterized by interactions are generally lumped together in the analysis of (1/n)AG"(aq, c@), which is the Gibbs energy change for biochemical systems. For macromolecules, models of bulk transfer of a hydrocarbon from aqueous solution to pure hydrophobic interactions are appropriate for the buried mo- liquid hydrocarbon when n is large. As proposed originally by lecular interior, while models for pair hydrophobic interac- Kauzmann (2), this process can be used to model the transfer tions are probably more appropriate at the molecular surface of a hydrocarbon side chain, exposed to aqueous solution in where there are many neighboring water molecules present. the unfolded protein, to the interior of the protein as folding The distinction between these two kinds of interactions is occurs. [Note that there is a different bulk interaction in the important because they can be quite different in magnitude. gas phase, characterized by (1/n)AG"(g, c@).] This free en- As described below, the relative effect of water, in general, ergy of transfer from an aqueous phase to a hydrocarbon is to increase the bulk interaction and decrease the pair phase is a measure of bulk hydrophobic interactions. The interaction for saturated hydrocarbons, although both are corresponding reaction for n = 2 is a measure of the pairwise decreased for benzene. The macroscopic features of both hydrophobic interaction, and both of these reactions can be bulk and pair hydrophobic interactions have been extensively compared with the corresponding reactions in the gas phase studied and much is known about them (2-23). At the [at the same concentration to avoid standard-state problems molecular scale a knowledge of aqueous hydrophobic inter- (24, 25)]. This comparison allows the effect of the aqueous actions implies a knowledge ofthe potentials ofaverage force environment on pair and bulk interactions to be measured. A between the hydrophobic species, and many questions about more fundamental comparison is ofthe osmotic second virial these potentials remain unanswered. For a complete under- coefficients, B2(aq) (26), with the corresponding gas-phase standing of these interactions in biochemical processes, we virial coefficients, B2(g), since the virial coefficients are need a detailed knowledge of the forces involved. This paper integrals of the direct or vacuum potential U [for B2(g)] and presents some conclusions about the effects of water on bulk of the potential of mean force U* [for B2(aq)]. Thus, and pair interactions of hydrophobic molecules and suggests some tests of molecular scale models of these interactions. B2(g) = -2 {exp(U/kT) - 1} 4irr2dr, [1] Pair Versus Bulk Interactions and B2(aq) is the same integral with U* substituted for U. The relationships between pair interactions, bulk interac- Returning to the diagram AG', is the free energy of solva- tions, hydrophobic solvation, and the transfer of hydropho- tion from the gas phase into water of an n-mer. The thermo- dynamic cycle gives the relationship between hydrophobic The publication costs of this article were defrayed in part by page charge interactions and the free energies of solvation of the n-mer payment. This article must therefore be hereby marked "advertisement" and the monomer. A knowledge of any three of the above in accordance with 18 U.S.C. §1734 solely to indicate this fact. processes allows one to calculate the fourth process. 946 Downloaded by guest on September 29, 2021 Biochemistry: Wood and Thompson Proc. Natl. Acad. Sci. USA 87 (1990) 947 A variety of methods for estimating bulk hydrophobic Table 1. Comparison of gas phase [BAB(g)] and osmotic interactions exist, most of which involve the partitioning of [BAB(aq)] second virial coefficients for cyclohexane, nonpolar compounds between water and either the gas phase cyclohexanol, and benzene or nonpolar solvents or the partitioning of hydrophobic BAB(aq),*BAB(g), groups between the surface and interior of proteins (2-14, A B cm3 mol' cm3 mol1 27-30). It is well known that the bulk hydrophobic interaction C6H,10H C6H,10H -209* for saturated hydrocarbons is much more attractive in water C6H1jOH C6H12 -368t than in the gas phase (3), and this is easily demonstrated from C6H12 C6H12 -527,t -487§ -17341 the thermodynamic cycle described above. If the AGs is -410,11 -402** positive, as it is for saturated hydrocarbons,§ then for large -596tt n, AGn(aq)/n must be more negative than AGl(g)/n, since C6H6 C6H6 -388t -14801 AG1/n, being primarily a surface effect, must approach zero *From ref. 34. as n becomes large. (The free energy of immersing a large tFrom ref. 35. aggregate in water, AGs, is proportional to n2/3 for a reason- tEstimated by a linear extrapolation of the data in this table versus ably shaped aggregate and the limit,. AGl/n = 0.) This number of OH groups. analysis of bulk interactions for hydrophobic solutes leads to §Estimated from BAB(aq) for C6H11OH - C6H12 corrected for the Stryer's (32) statement that "water accentuates the interac- CH2-OH interactions using the group additivity principle (21, 22). tion of nonpolar molecules." From ref. 36. Estimates of pairwise interactions of two nonpolar solutes 11 Estimated from BAB(aq) for C6HjjOH - C6HjjOH corrected for the are obtained from osmotic second virial coefficients in aque- CH2-OH and OH-OH interactions using the group additivity prin- ous solutions, BAB(aq), which are a measure of the tendency ciple (21, 22). two to associate above and the associ- **Estimated from the group additivity principle (21, 22). of molecules beyond ttEstimated from a site-interaction model that fits BAB(aq) for eight ation that would be present in a random solution of A and B alcohols (26). in water (1, 15-22). For strongly associating species BAA(aq) becomes equal to minus the ordinary thermodynamic asso- virial coefficient [BAB(g)] of cyclohexane with itself. From ciation constant [-K2(aq)].¶ Franks has reviewed early ev- the aqueous solution data we can estimate the BAB(aq) for idence for the differences between pair and bulk interactions cyclohexane with itselfin a variety ofways (26) (see Table 1). (23). Recently, Watanabe and Andersen (33) have shown that These estimates involve (i) the extrapolation ofBAB(aq) as a hydrophobic solvation does not necessarily imply the exis- function of the number of hydroxyl groups on the molecules, tence of hydrophobic association. In their simulation of a (ii) the correction of BAB(aq) for the effect of the OH group model for krypton dissolved in water, they found that the interactions, using a group additivity principle (21, 22), and krypton molecules exhibited typical hydrophobic solvation (iii) the direct group additivity prediction ofBAB(aq) (21, 22). (AG' positive) but had net repulsive interactions between agreement and each other in water [positive BAB(aq)] and, thus, no tendency All of these estimates are in reasonable show to associate in an aqueous solution. Thus, neither hydropho- clearly that the osmotic second virial coefficient in water, bic hydration nor attractive bulk interactions have to be BAB(aq), is less than one-third of the gas-phase osmotic associated with attractive pairwise hydrophobic interactions. second virial coefficient, BAB(g), and, thus, that the tendency Clark et al.
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