Proc. Natl. Acad. Sci. USA Vol. 83, pp. 8069-8072, November 1986 Biochemistry Temperature dependence of the hydrophobic interaction in protein folding (hydrocarbon model) ROBERT L. BALDWIN Department of Biochemistry, Stanford University Medical Center, Stanford, CA 94305 Contributed by Robert L. Baldwin, July 21, 1986 ABSTRACT Accurate calorimetric data for the thermo- (4) observed that the transfer of a nonpolar compound from dynamics of transfer of six liquid hydrocarbons to water have an organic medium to H20 is characterized by a large positive been combined with solubility data to provide a model for the value of ACp. The nature of the large enthalpy change in temperature dependence of the hydrophobic interaction in unfolding at high temperatures is unknown. The reason for protein folding. The model applies at temperatures for which the intersection near 1100C in plots of the specific enthalpy the change in heat capacity (ACp) is constant. The extrapolated and entropy of unfolding is also not known. Privalov (1) value of the temperature (T) at which the entropy of transfer suggested that it must result from the properties of the (AS') reaches zero is strikingly similar (T, = 112.8°C ± 2.2C) hydrophobic interaction. for the six hydrocarbons. This rmding provides an interpreta- The purpose of this article is to show that data for the tion for the empirical relation discovered by Sturtevant: the thermodynamics of solution of liquid hydrocarbons in H20 ratio AS°/ACp measured at 25C is constant for the transfer of provide a model for the temperature dependence of the nonpolar substances from nonaqueous media to water. Con- hydrophobic interaction in protein folding. Accurate calori- stancy ofthis ratio is equivalent to Ts = constant. When applied metric data are available for the heat of solution in H20 of to protein folding, the hydrocarbon model gives estimates ofthe seven liquid hydrocarbons in the range 15'C-350C (5). The contributions ofthe hydrophobic interaction to the entropy and seven hydrocarbons show quite uniform behavior, and an enthalpy changes on unfolding and, by difference, estimates of equation of state has been given (6) that describes their the residual contributions from other sources. The major share thermodynamic properties as functions of a single variable, of the large enthalpy change observed on unfolding at high nH, the number of H atoms per molecule. I show here that a temperatures comes from the hydrophobic interaction. The hydrocarbon model based on these data provides explana- hydrophobic interaction changes from being entropy-driven at tions for some of the thermodynamic properties of protein 22°C to being enthalpy-driven at 113°C. Finally, the hydro- unfolding reactions. In particular, the hydrocarbon model carbon model predicts that plots ofthe specific entropy change predicts that the major share of the large enthalpy change on unfolding versus temperature should nearly intersect close observed on protein unfolding at high temperatures comes to 113°C, as observed by Privalov. from the hydrophobic interaction. As defined here, "hydrophobic interaction" refers to the The thermodynamic properties of the unfolding reactions of process in which a hydrophobic side chain of an unfolded globular proteins are now known accurately as a function of protein is taken out of H20 and is buried in the interior of a temperature through calorimetric studies. Many ofthese data protein through folding. When this definition is used, the have been obtained by Privalov and co-workers, and they are hydrophobic interaction can be modeled by solvent transfer summarized and analyzed by him (1). The unfolding reactions experiments, as shown originally by Kauzmann (7), and of different proteins display certain common properties. The developed by Tanford (8-11) and other workers (12, 13). The enthalpy of unfolding depends on the temperature at which solvent transfer model is open to criticism, particularly unfolding occurs, which can be varied by adjusting pH or because the interior of a protein differs in obvious respects guanidine hydrochloride concentration. The unfolding from an organic liquid (14-17). Nevertheless, following an enthalpy is small at room temperature but increases rapidly earlier analysis (18), Rose et al. (19) find a close correlation with temperature, becoming large at high temperatures. ACp, between the average extent of burial of an amino acid side the difference in heat capacity between the native and chain and its hydrophobicity on the scale of Nozaki and in the Tanford (10). The liquid transfer process is used here as a unfolded forms, is independent of temperature range semi-quantitative model for the burial of hydrophobic side studied (up to 80°C). Plots of the specific enthalpy of chains during folding, and criticisms of the model are dis- unfolding (enthalpy per g) versus temperature intersect at a cussed later. common high temperature for several globular proteins [at Transfer of a hydrocarbon from the pure liquid to H20 can 110°C, see figure 24 ofPrivalov's review (1)]. The slope ofthe be divided into two steps: (l) transfer from the liquid hydro- plot, which is ACp per g of protein, is linearly related to the carbon into the vapor phase and (ii) transfer from the vapor fraction of hydrophobic residues. These proteins also show phase into H20. Data for the second step of the transfer an approximate intersection point near 110°C when the process have been given for compounds that serve as models specific entropy of unfolding is plotted against temperature for amino acid side chains (20). When the overall process is (see figure 26 in ref. 1). analyzed theoretically (21-26), it is necessary to consider Some of these properties are understood but others are each step separately. Experimentally, the overall transfer obscure. The large and positive value of ACp is commonly process can be modeled by a single experiment, either by a attributed to the hydrophobic interaction, although other liquid partition experiment or by a solubility experiment. The factors may contribute to ACp (2, 3). As early as 1935, Edsall Abbreviations: T., temperature at which AS' = 0; Th, temperature at The publication costs ofthis article were defrayed in part by page charge which AR"= 0. (AS0 and AJ? refer to the standard-state entropy and payment. This article must therefore be hereby marked "advertisement" enthalpy changes for transfer of a hydrocarbon from the liquid in accordance with 18 U.S.C. §1734 solely to indicate this fact. hydrocarbon to H20.) 8069 Downloaded by guest on September 26, 2021 8070 Biochemistry: Baldwin Proc. Natl. Acad. Sci. USA 83 (1986) equations used to analyze these experiments are presented by which AS0 goes to zero. If T2 is taken to be Ts, the temperature Tanford (11). at which AS0 is zero, then Eq. 4 becomes Properties of the Liquid Hydrocarbon Model -A50/ACp = ln(Ts/T). [5] Thus, if T, is constant, the ratio AS/ACp is constant. The The standard Gibbs energy of transfer (per mol), AG, is temperatures at which AS0 and AR' go to zero are denoted related to the solubility X by here as T, and Th, following the notation used by Becktel and Schellman to describe the thermodynamics of folding of T4 AG' = -RT In X, [1] lysozyme mutants (J. A. Schellman, personal communica- tion). The values ofAS0, ACp, and T. are given in Table 1. The where X is the mol fraction ofhydrocarbon dissolved in H20. six liquid hydrocarbons show closely similar values of T,: The purpose of using the mol fraction scale is to avoid 386.0 K or 112.80C ± 2.40C. From Sturtevant's relation (2), including in AG' a term involving the entropy of mixing (7, obtained from data for a wide range of nonpolar compounds, 11). It has been argued that a number density scale such as one finds T, = 387.8 K or 114.60C ± 18TC. the molar scale should be used instead (27, 28). For consist- Eq. 5 can be tested with data taken at different tempera- ency with earlier work in the literature, I use the mol fraction tures. Table 2 provides such a test for benzene in H20, for scale here. Numerical examples of the change in AG' caused which the necessary solubility data (30) and calorimetric data by shifting to Ben-Naim's concentration scale have been (5) are available in the range 15'C-350C. Table 2 shows that given (26). The standard-state entropy of transfer, AS', is the same value of T, for benzene is found from data taken at obtained from different temperatures. This is not surprising, because ACp is known to be constant in this range and Eq. 5 assumes only A5 = A /T + R In X, [2] that ACp is constant. What is the meaning of a constant value of T, found for where AH? is the standard enthalpy of transfer. Data for AS0, different nonpolar substances? When AS0 is zero, the solution All0, and X at 250C are given in Table 1 for the six liquid shows ideal entropy of mixing by definition. T. is the hydrocarbons considered. [Propylbenzene, which also was temperature at which an aqueous solution of a nonpolar studied (5) is omitted here for lack of solubility data.] substance becomes a regular solution, with AS0 = 0 but with Data for seven liquid hydrocarbons show A11' to be a linear All nonzero [cf. Shinoda and Fujihira (31)]. There are function oftemperature in the range studied, 15'C-350C, with reasons for suspecting that ACp decreases at high tempera- ACp constant (5): tures (see below). In this case, T, is a hypothetical temper- ature. (In any case, T, is above the boiling point of H20.) If AI(T2) = AI(T1) + ACp(T2 - T1). [31 ACp decreases at high temperatures, then T, is the temper- ature at which AS0 would go to zero ifthe solution obeyed the When ACp is nonzero, AS0 like ARmust be a function of ACp same rules at high temperatures as in the range for which ACp and temperature.