Proc. Natl. Acad. Sci. USA Vol. 88, pp. 10880-10884, December 1991 Biophysics Contribution of the hydrophobic effect to protein stability: Analysis based on simulations of the Ile-96 -- Ala mutation in barnase MARTINE PREVOST*, SHOSHANA J. WODAK*, BRUCE TIDORtt, AND MARTIN KARPLUSt *Unite de Conformation des Macromolecules Biologiques, Universitd Libre de Bruxelles, Avenue Paul Hdger-CP160, B-1050 Brussels, Belgium; and tDepartment of Chemistry, Harvard University, Cambridge, MA 02138 Contributed by Martin Karplus, April 4, 1991

ABSTRACT Molecular dynamics simulations have been interior corresponds to a nonpolar or a slightly polar liquid used to compute the difference in the unfolding free energy (e.g., alcohol-like) is not clear (17, 21). Because such ques- between wild-type barnase and the mutant in which Ile-96 is tions are difficult to approach experimentally (11), theoretical replaced by alanine. The simulations yield results (-3.42 and analyses based on a detailed microscopic description are -5.21 kcal/mol) that compare favorably with experimental needed to provide fuller understanding. Methods for com- values (-3.3 and -4.0 kcal/mol). The major contributions to puting free energy changes by use ofmolecular dynamics (22) the free energy difference arise from bonding terms involving and Monte Carlo (23, 24) techniques are particularly well degrees of freedom of the mutated side chain and from non- suited for this purpose. Although such calculations are still bonded interactions of that side chain with its environment in not routine (25, 26), they are of considerable utility because the folded protein. By comparison with simulations of an they evaluate thermodynamic quantities that can be com- extended peptide in the absence of solvent, used as a reference pared directly with experiment. More important, a recent state, hydration effects are shown to play a minor role in the formulation of the free energy simulation method (27) makes overall free energy balance for the Ile -* Ala transformation. it possible to decompose the computed values into contribu- The implications of these results for our understanding of the tions from different parts of the system (protein residues hydrophobic effect and its contribution to protein stability are versus solvent), as well as individual energy-such as non- discussed. bonded interactions (van der Waals, electrostatic) and vibra- tional-terms. Hydrophobic interactions are believed to make a major The present study describes the application of the free contribution to stabilizing the native structure of proteins in energy simulation method to the substitution ofisoleucine by an aqueous environment (1-4). According to the classical alanine at position 96 in barnase, an extracellular ribonucle- picture (1) and more recent theoretical analyses (4), the ase from Bacillus amyloliquefaciens. This 110-residue en- hydrophobic effect leads to structures in which many, but not zyme is of particular interest because it is being used as a all, of the nonpolar side chains are packed together in the for and protein interior where they avoid contact with water. Mea- paradigm studying protein stability folding (13, 14). surements of solvation effects have shown that the hydro- The crystal structure is known to 2.0-A resolution (28). The phobic effect is largely entropic in origin at room temperature enzyme is a one-domain protein that undergoes reversible (5). The unfavorable entropy of solvation is ascribed to the thermal and urea-induced denaturation closely approximat- entropy decrease of water surrounding the nonpolar groups ing a two-state equilibrium (29). The protein contains signif- (6, 7); this is in accord with simulation studies ofhydrophobic icant secondary structure, including a }-sheet in which solutes (8, 9) and peptides in water (10). position 96 occupied by isoleucine is situated (see Fig. 1). Although the general role of the hydrophobic effect in This residue is fully buried and participates in a closely protein folding is understood, a more detailed quantitative packed hydrophobic interface with an a-helix. description of its contributions to protein stability is essen- We report the results and analysis of simulations of the tial. Site-directed mutagenesis experiments combined with "alchemical" transformations (27) ofIle-96 into alanine in the thermal and spectroscopic stability measurements are now native solvated protein and in an extended conformation used being used to dissect the contributions of individual amino as a model for the denatured state in water. For comparison acids (11). Substitutions of buried or partly buried nonpolar the same transformation with the extended model was sim- residues in several proteins (12-15) have shown that the ulated in the absence of solvent. The implications of the change in thermodynamic stability between the wild type and results for our understanding of the hydrophobic effect and mutant can be related to the free energies of transfer (16-18) its contribution to protein stability are outlined. and/or the accessible surface areas (19) of the individual substituted residues. Although there is a good overall corre- lation when a wide range of substitutions are considered (12), METHOD the variation seen among the hydrophobic aliphatic side The free energy difference, AG, between two states A and B chains does not show any simple relation with transfer free representing, respectively, wild-type and mutant proteins, is energies. Moreover, the interpretation is somewhat confused calculated by "computer alchemy", in which one amino acid by the use of transfer free energy values from different is transformed into another (27). This operation is achieved solvents or from the gas phase to water for analyzing the by using a hybrid potential function V(rN, A) = (1 - A)VA(rN) experimental data (12, 14). There are also more basic ques- + AVB(rN) where A is a coupling parameter varied from 0 to tions concerning the effect of hydrophobic solvation of 1, VA(rN) and VB(rN) are the empirical potentials describing individual nonpolar groups and its relationship to their bulk the wild-type and mutant protein, respectively. The symbol properties in the protein interior (20). Whether the protein Abbreviations:'EF, exponential formula; TI, thermodynamic integra- The publication costs of this article were defrayed in part by page charge tion. payment. This article must therefore be hereby marked "advertisement" tPresent address: Whitehead Institute for Biomedical Research, in accordance with 18 U.S.C. §1734 solely to indicate this fact. Nine Cambridge Center, Cambridge, MA 02142.

10880 Downloaded by guest on September 28, 2021 Biophysics: Prevost et al. Proc. Natl. Acad. Sci. USA 88 (1991) 10881 summation of contributions involving the interactions of the mutated side chain (27, 32); e.g., one can separate the contributions of the solvent and the protein or can determine the contributions of different types of terms in the energy function. In the present study, which concerns the mutation Ile-96 -> Ala, it is convenient to write AG as a sum of four terms, AG = AGc, + AGnb. + AGci + AGnbi, each of which arises from specific contributions to AV. The first two "side-chain" terms represent contributions that depend solely on atoms of the mutated side chain. The other two terms represent "interaction" terms ofthe side chain with its environment. The potential energy contributions included in the four terms and the specific atoms involved are illustrated in Fig. 2. Previous studies have shown that the method described is adequate for treating charged to nonpolar [e.g., Asp -3 Ala (27)] and charged to charged [e.g., Argo- His (32)] mutations. In the present application, which involves a nonpolar-to- nonpolar mutation, a somewhat more elaborate procedure was used. Six intermediate states were defined along a pathway from A (wild type) to B (mutant). The states were generated by successively modifying van der Waals param- eters and bond lengths of the relevant side chains in the

FIG. 1. Environment of Ile-% in the crystal structure ofbarnase. A ribbon tracing of the backbone of barnase is shown in yellow, and the residues included in the molecular dynamics simulation zone are shown in magenta, except for Ile-96 shown in red; sequence num- bering is as follows: 7-12, 14, 15, 63, 71, 88-91, 93-98, 107-110. Residues subjected to Langevin dynamics (displayed in bluegreen) are as follows: 6, 9, 13, 16, 18, 20, 64, 69-70, 72-74, 76, 87, 92, 99, 106-107. Twenty-one water molecules included in the simulations are displayed in light blue. The unfolded system (data not shown) includes residues 94-99 in an extended conformation and 145 water molecules.

rN represents atomic coordinates of the system composed of parts of the protein and solvating waters. The free energy difference AG between the two states A (wild type) and B (mutant) can be obtained from either oftwo formally exact expressions. The first is called the "exponen- tial formula" (EF) (30) and has the form V(rN, A,+1) - V(rN, A,) AG = -kBT In (e kBT )

AVAAi = -kT>EIn (ee kBT A.' [1] FIG. 2. Terms included in different free energy components. where AV = VB(rN) - VA(rN), AAi = Ai+1 - Ai, kB the Different contributions to these terms are depicted by arrows. (a and Boltzmann constant and T the absolute temperature; the b) Terms that depend only on the isoleucine side chain and involve exclusively atoms Cp, Cyl, Cv2, and C81. (a) Contributions to AG_, angle brackets represent an ensemble average obtained with that comprise covalent terms consisting ofbond stretching and angle the potential V(rNA,), to represent the system. An equivalent bending. The entire contribution comes from Ile-96 because the C; formulation, called thermodynamic integration (TI), yields atom of alanine has no self-energy component in the potential owing the following expression (31): to the fact that aliphatic groups are treated as extended atoms (33). (b) Contributions to AGnb,, the intra-side-chain nonbonded term, which are limited to van der Waals interaction between C81 and Cy2 AG = F (aV/aA)A dA - (AV)A.k AA, [2] atoms. (c and d) Contributions concerning interactions of atoms Jo belonging to the isoleucine side chain with atoms ofthe remainder of protein and/or solvent. (c) Terms included in AGcj; these comprise covalent components-bond stretching and valence angle bend- where the canonical average (dV/aA)A is equal to (AV)A when ing-as well as torsional terms. (d) Nonbonded terms that contribute the hybrid potential energy function V(rN, Ai) is linear in A. to AGnbi, which are limited to van der Waals interaction. Equivalent An important advantage of Eq. 2, relative to Eq. 1, is that drawings could be made for the alanine side chain with the exclusion the total free energy change can be represented as an exact of a and b. Downloaded by guest on September 28, 2021 10882 Biophysics: Prevost et al. Proc. Natl. Acad. Sci. USA 88 (1991)

direction of the transformation. The overall free energy AGr-*f difference was computed as the sum of the individual free I I protein Ef E energy differences AGj between these successive states, E, reference yielding AG(A -- B) = 7_,1 AGj. Individual AGj values were AGf u water AGsoiv computed from Eqs. 1 and 2 with three intermediate values of A: 1/6, 3/6, and 5/6. This protocol corresponds to taking AGu'->A 1->AA discrete points along a nonlinear pathway between states A <>A AGr and B and interpolating linearly between these points. This approach was chosen to improve convergence of the rela- tively small energy difference dominated by van der Waals terms (25) while preserving the possibility of decomposing i A AGf ->u waAer AGsoiv A the results into individual contributions. protein Ef - Eu I Er reference The ensemble averages over configuration space required

for Eqs. 1 and 2 were obtained for both the folded and unfolded _~ states, by stochastic boundary molecular dynamics simula- AG, tions at 300 K (34) within an 11-A sphere having a 2-A FIG. 3. Thermodynamic cycles used to describe AAG in calcu- boundary region, using the CHARMM program (33). The sim- lations and experiments. The vertical direction concerns alchemical

ulations were done on the folded state starting with the processes corresponding to the Ile -. Ala transformation; the hori- high-resolution crystallographic coordinates of barnase (28). zontal direction concerns chemical steps ofthe unfolding or solvation The unfolded state was modeled from a heptapeptide com- reactions. The thermodynamic cycle, on the left, refers to the prising the protein fragment centered on residue 96. The unfolding process of barnase. The left-hand side concerns the peptide was taken to be in an extended conformation. transformation in the folded protein (Ef). The right-hand side con- cerns the transformation in the unfolded state (E.). Unfolding of the wild-type protein in the presence of isoleucine is shown at top, and RESULTS unfolding of the alanine-containing mutant is shown at bottom. The thermodynamic cycle on the right refers to the solvation process of The simulations yield values of the alchemical free energy the unfolded protein-i.e., transfer from the reference phase (gas differences for the transformation of Ile -- Ala in the solvated phase) to water. On the right side of the cycle, the transformation native protein (AGfA), in the solvated unfolded state occurs in the gas phase (E,). The process of transferring the iso- (AGI MA), and the unsolvated reference state (AGh MA); see leucine-containing unfolded protein from the gas phase to water is Table 1. By use of the thermodynamic cycle (Fig. 3), the shown on top. The solvation process for the alanine-containing corresponding difference in unfolding free energy, AAGf mu unfolded protein is shown on bottom. The outer thermodynamic cycle brings the unfolded protein in the reference (gas phase) to the can be obtained from the following expression (36): AAGf mu folded state in solution. The process of transferring the isoleucine- = AGhIPA - AGh PA = AGQ.u - AGf mu. The computed value containing unfolded protein from the gas phase to the isoleucine- for AAGf mu is -3.42 and -5.21 kcal/mol, when calculated by containing folded state is shown on top. The same process in the the EF and the TI methods, respectively. This result is to be presence of alanine is shown on bottom. compared with the experimental values of -3.3 and -4.0 kcal/mol, obtained from slightly different analyses of the energy change in going from the gas phase to the folded same experimental data (13, 14). Correspondingly, the sol- protein by use of the relation, AAGf = AGhA - AGIhPA. vation free energy difference AAG is given as follows: The resulting values are + 3.17 and +4.06 kcal/mol from the AAGru = AGhIA - AGrhA = AG ,1v - AG,1o, where AGOlv EF and TI methods, respectively. No direct measurement of is the measured solvation free energy corresponding to the this quantity is available from experiment, although it can be transfer from the gas phase to aqueous solution. The calcu- obtained by difference from the other experimental results lated values are -0.25 and -1.15 kcal/mol from the EF and given in Table 1; the estimated values of +3.1 and +3.8 TI methods, respectively; the experimental estimate for the kcal/mol correspond to the two different measured values of difference in solvation energies of isoleucine versus alanine AAGf .u. Thus, the simulation and experiment agree that the is -0.21 kcal/mol (16). Finally, we can calculate the free essential effect of the mutation is the difference in the Table 1. Computed free energy changes (in kcal/mol) for Ile -* Ala mutation in barnase /aGf--AA~~hA ~AGhAY-OG A AGhAYOI-A &v-+fV~ AUAvl-vu Contribution* protein water reference AAGfou AAGrb.u AAGrf protein water cs -3.28 -4.73 -3.18 -1.45 -1.55 -0.10 -1.88 -1.63 ci -1.40 -3.09 -5.07 -1.69 1.98 3.67 -1.80 -1.60 nbs -0.97 -0.79 -0.24 0.18 -0.55 -0.71 -1.12 -0.51 nbi 2.56 0.31 1.35 -2.25 -1.04 1.21 7.7 8.0 TI (total) -3.09 -8.3 -7.15 -5.21 -1.15 4.06 2.90 4.26 EF -3.39 -6.81 -6.56 -3.42 -0.25 3.17 EXP -3.3t; -4.0t -0.21§ AGf, AGu, and AGr are free energies for alchemical transformation Ile -. Ala, in folded state (protein), unfolded state (water), and unfolded state in gas phase (reference), respectively. A&AGf, taG,., and vAGr f are as explained in text. EXP, experimental results. Different free energy contributions considered (see text and Fig. 2) are listed in column 1. The next to last column lists values of AV and its components evaluated using ensemble averages computed for the folded protein at states A, (close to isoleucine) and A,, (close to alanine) by the formula: AV"A = (VAia exp(-AVAA)/kT)A, /(exp(-AVAk)/kT)A, - (VIje exp(-AVAA)/kT)Ak/(exp(-AVAA)/kT)A,, where Vile and VAa are the appropriate contributions to the potential energy of the side chain, and ,Ak = 0.17. A corresponding expression is used for the unfolded state (last column). All calculations were done with the CHARMM program (33) using parameters and described procedures (32). Calculations of AG for a given A consist of an equilibration simulation of 5 ps followed by an averaging period of 10 ps. All computations were done on a Cyber 205 computer at the former John von Neuman Center. *For definitions, see text and Fig. 2. tData from ref. 14. tData from ref. 13. §Data from ref. 16. Downloaded by guest on September 28, 2021 Biophysics: Prevost et al. Proc. Natl. Acad. Sci. USA 88 (1991) 10883 stability of the folded state rather than the differential sol- may result from the fact that, in the absence of solvent, atoms vation of isoleucine and alanine in the unfolded state. of the isoleucine side chain interact exclusively with the In view of the sensitivity of free energy values to the heptapeptide, particularly with those in the main chain at- convergence of simulations (37), it is important to assess the oms. statistical precision of the results. The computations have It is of interest to compare the above results with the been performed with two formally equivalent procedures (the decomposition of the average potential energy at the end EF and TI methods) that would give identical results if full points of the Ile -. Ala transformation pathway, listed in the convergence had been achieved. The discrepancy between last two columns of Table 1. Although the signs for the AVf the free energy differences for isoleucine and alanine ob- and A1Vu values are the same as the corresponding AG values, tained by these methods is 1.8 kcal/mol for denaturation and the magnitudes are very different. In particular the "nbi" 0.9 kcal/mol for solvation. The two calculations show very term is =8 kcal/mol for both folded and unfolded states. This consistent behavior, as the largest difference between indi- result agrees well with the computed interaction energy ofthe vidual AGj values obtained with the EF and TI procedures isoleucine side chain (C3 excluded) with the rest of the does not exceed 0.6 kcal/mol. Computations based on the protein in the crystal conformation (=7 kcal/mol). That the standard deviation of individual AGj free energy values computed free energy changes (+2.56 and +0.31 for folded obtained by the TI procedure estimate the precision of the and unfolded states, respectively; see Table 1) are much overall free energy difference to be -1 kcal/mol. smaller than these values suggests that other effects are To obtain insight into the origin ofthe free energy changes, involved. Because the present simulations are not precise the thermodynamic integration procedure given in Eq. 2 was enough to evaluate the entropic and energetic contributions used. The calculated free energies for the folded protein, the to the free energy, other aspects ofthe simulations have been unfolded protein in solution, and the reference state are analyzed in an attempt to gain further insight. In doing so, the decomposed into four distinct contributions listed in Table 1; structure of the alanine mutant has been assumed to differ for definitions, see Fig. 2. little from wild type. This assumption is in agreement with Most of the computed free energy difference of unfolding, evidence from NMR measurements (14) and with the com- AAGf..,, arises from three terms: the nonbonded interaction putations, which indicate that rms deviations between wild- of the mutated side chain with the rest of the system (AAGnbi type and alanine mutant structures are <1 A when all atoms = -2.25 kcal/mol), the covalent interactions ofthe side chain are considered. Atomic volume calculations done by using with the rest ofthe system (AAGci = -1.69 kcal/mol), and the coordinates from end points of the simulation pathway (38) intra-side-chain covalent term (AAGCS = -1.45 kcal/mol). suggest that the packing around residue 96 is looser in the The contribution from nonbonded intra-side-chain interac- alanine-containing mutant than in the wild type. This should tions is negligible for this case (AAGnbs = 0.18 kcal/mol). lead to favorable entropic contributions in the mutant pro- The computed contributions of the nonbonded interaction tein. To examine this conjecture, rms atomic fluctuations term, AGnbi, which in this case is entirely due to van der from several independent 30-ps vacuum molecular dynamics Waals interactions, are unfavorable for alanine relative to trajectories of the wild-type and the mutant proteins were isoleucine in both the folded and unfolded states (columns 2 compared. Although these were found to be similar on and 3 in Table 1), but the unfavorable effect in the unfolded average, fluctuations of main-chain and C3 atoms of residue state is marginal, leading to an overall negative contribution 96 were about twice as large in the alanine mutant, suggesting to AAGnbi. that the latter is indeed more mobile, in agreement with a The free energy changes from side-chain covalent terms stabilizing entropic contribution. A corresponding analysis (AGcs) are large and favor alanine in both the folded and was not made for the unfolded structure. The standard unfolded states. This is expected because the covalent mo- picture of the hydrophobic effect would suggest an increase tional contributions are always positive (destabilizing), and in the entropy of the unfolded state of alanine relative to only isoleucine has covalent interactions within the side isoleucine, as increased water structure is expected in the chain. To interpret their origin, an estimate was made of the presence of the larger hydrophobic isoleucine side chain. expected internal free energy with a classical harmonic model for 1-butane, taken as a model for an isoleucine side chain; the value for the single atom representing the alanine side DISCUSSION chain is zero. It yields a value of -3.66 kcal/mol, most of In what follows, we address two questions: the first concerns which comes from the vibrational enthalpy ofthe six classical the analysis by Kellis et al. (13, 14) of several apolar side- internal degrees of freedom. This value compares favorably chain mutations in barnase, and the second deals with the with the simulation results for the sum of AGs and AGnbS in more general question of the role ofthe hydrophobic effect in the gas-phase reference state (-3.42 kcal/mol), indicating protein stability. that the intrinsic vibrational properties of the isoleucine side Kellis et al. (13) used a thermodynamic cycle very similar chain are unperturbed in the gas-phase-extended heptapep- to Fig. 3 and considered both alchemical processes (Ile -+ Ala tide. In both the folded and solvated unfolded states the transformations) and chemical processes (the unfolding re- values are somewhat more negative. The origin of these action in the presence of isoleucine or alanine). They as- differences, which make significant contributions to AAGf..u sumed that AGci, AG,,, and AGnb, have the same value in the (see Table 1) is not clear. folded and unfolded state and so do not contribute to AAGfu.. The free energy contributions from the covalent interaction The present analysis shows that the nonbonded side-chain term (AGj1) are favorable to alanine in the unfolded and folded contribution, AAGnbb, is indeed small for this case but that states. However, the favorable effect is smaller in the folded both of the other neglected terms are significant. In consid- state, leading to a negative contribution to the wild-type/ ering the covalent term, Kellis et al. (14) focused on the effect mutant free energy difference. The destabilizing effect of due to the change in the number of atoms. Clearly, any isoleucine in the unfolded state may be due to strain intro- contribution due simply to the imbalance of the chemical duced by the surrounding water molecules, whose H bonds equation must cancel out when the chemical processes are with other water molecules and the neighboring main chain considered or when a reference state is introduced for the are adjusted to accommodate the larger nonpolar group. That alchemical process. However, this does not mean that there AGi computed in the unsolvated reference state is very is no covalent contribution to AAGf.but The side-chain term, destabilizing for isoleucine is somewhat surprising. The dom- AGc, consists only ofcontributions from isoleucine, but they inant contribution comes from bond-angle distortions that are different in the folded and unfolded states, which repre- Downloaded by guest on September 28, 2021 10884 Biophysics: Prevost et al. Proc. Natl. Acad. Sci. USA 88 (1991)

sent significantly different environments and so are a non- The present theoretical study thus provides valuable new negligible part of AAGf,. The total covalent contribution insights into the origin of the hydrophobic effect and its role consisting of the sum of AAGCS and AAGci is -3.14 kcal/mol. in the thermodynamics of protein folding. In the future, It does represent a sizable fraction of the total value of improvements ofthe force field and longer simulations should AAGfM (-5.21 kcal/mol). The quantitative values obtained lead to fuller convergence of the ensemble averages and in the present simulation may, of course, be in error, but the permit decomposition of the free energy into the enthalpic conceptual conclusion is unlikely to be wrong. and entropic terms (23). With the available methods, inter- Most of the remaining contribution to AAGf M, arises from actions within the environment, either the protein (other than the free energy term, AAGnbi, corresponding to nonbonded the mutated side chain) or the surrounding solvent, contrib- van der Waals interactions of the side chain with its envi- ute to the calculated free energy difference only through the ronment. This is the term emphasized by Kellis et al. (13), Boltzmann weighting factor inherent in the molecular dy- who concluded furthermore that the nonbonded contribution namics trajectories (39). It would be useful to evaluate the from the alchemical transformation in the folded protein is effect of these contributions, particularly for the present the dominant term, whereas that from the alchemical trans- problem because the solvent and protein matrix are invoked in most descriptions of the role of the hydrophobic effect on formation in the unfolded state is negligible. The calculations protein stability. also show the importance of the nonbonded terms in the folded state. They suggest, however, that only about one half M.P. and S.J.W. acknowledge support from the European Com- of &AGf .u arises from nonbonded interactions and that the munities Biotechnology Action Program (Contract 0319-B) and thank remainder is due to the difference in covalent terms between the Fonds National de la Recherche Scientifique for a grant to one the folded and unfolded states. of us (M.P.). M.K. and B.T. acknowledge partial support from the Studies of amino acid substitutions in several proteins National Science Foundation, the National Institutes of Health, and (12-15) show that the difference in stability of the wild-type the Department of Energy. and mutant proteins is roughly proportional to the free energy 1. Kauzmann, W. (1959) Adv. Protein Chem. 14, 1-63. oftransfer ofthe individual substituted residues from organic 2. Privalov, P. L. (1979) Adv. Protein Chem. 33, 167-241. solvent to water. For Ile -. Ala mutations, the difference in 3. Baldwin, R. L. (1986) Proc. Natl. Acad. Sci. USA 83, 8069-8072. the transfer free energies ranges from 1.5 to 3.11 kcal/mol, 4. Dill, K. A. (1990) Biochemistry 29, 7133-7155. 5. Abraham, M. (1982) J. Am. Chem. Soc. 104, 2085-2094. measured for octanol and cyclohexane, respectively (18, 21). 6. Frank, H. S. & Evans, M. W. (1945) J. Chem. Phys. 13, 507-532. These values are of the same order as the computed or 7. Tanford, C. (1980) The Hydrophobic Effect: Formation of Micelles and experimental unfolding free energy differences. The differ- Biological Membranes (Wiley, New York). ence in the gas phase to water solvation free energies 8. Pangali, C., Rao, M. & Berne, B. J. (1979)J. Chem. Phys. 71, 2982-2990. of 9. Jorgensen, W. L., Gao, J. & Ravimohan, C. (1985) J. Phys. Chem. 89, isoleucine versus alanine is significantly smaller (16). 3470-3473. To understand the origins of these observations it is useful 10. Rossky, P. J. & Karplus, M. (1979) J. Am. Chem. Soc. 101, 1913-1937. to decompose the transfer process from water to the protein 11. Alber, T. (1989) Annu. Rev. Biochem. 58, 765-798. 12. Matsumura, M., Becktel, W. J. & Matthews, B. W. (1988) Nature interior into two separate solvation processes: (i) transfer of (London) 334, 406-410. the side chain from the gas phase to the protein interior and 13. Kellis, J. T., Jr., Nyberg, K., Sali, D. & Fersht, A. R. (1988) Nature (ii) transfer of the side chain from the gas phase to water (London) 333, 784-786. 14. Kellis, J. T., Jr., Nyberg, K. & Fersht, A. R. (1989) Biochemistry 28, (columns 6 and 7 of Table 1). The total free energy difference 4914-4922. between isoleucine and alanine in the gas phase to protein 15. Sandberg, W. S. & Terwilliger, T. C. (1989) Science 245, 54-57. transfer (AAGf) is significantly larger than the correspond- 16. Wolfenden, R., Andersson, L., Cullis, P. M. & Southgate, C. C. B. ing difference in solvation free energies (AAG,,,). This (1981) Biochemistry 20, 849-855. suggests that although 17. McAuliffe, C. (1966) J. Phys. Chem. 70, 1267-1275. hydration effects provide important 18. Fauchere, J. L. & Pliska, V. (1983) Eur. J. Med. Chem. Chim. Ther. 18, contributions to the free energy of transfer of the individual 369-375. side chains from water to the protein interior, they make only 19. Richards, F. M. (1977) Annu. Rev. Biophys. Bioeng. 6, 151-176. a minor contribution to the difference in 20. Wood, R. H. & Thompson, P. T. (1990) Proc. Natl. Acad. Sci. USA 87, stabilization free 946-949. energy between the isoleucine and alanine side chains. As 21. Radzicka, A. & Wolfenden, R. (1988) Biochemistry 27, 1664-1670. already mentioned, important contributions to this free en- 22. Tembe, B. L. & McCammon, J. A. (1984) Comput. 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For other types of mutations, particularly those in- & Jack, A. (1982) Nature (London) 297, 162-164. volving polar or charged groups, the difference in water 29. Hartley, R. W. (1968) Biochemistry 7, 2401-2408. solvation would probably be larger than that for solvation in 30. Zwanzig, R. W. (1954) J. Chem. Phys. 22, 1420-1426. 31. Kirkwood, J. G. (1935) J. Chem. Phys. 3, 300-313. an organic phase. These considerations suggest that transfer 32. Tidor, B. & Karplus, M. (1991) Biochemistry 30, 3217-3228. free energies of amino acids and the various hydrophobicity 33. Brooks, B. R., Bruccoleri, R. E., Olafson, D., States, D., Swaminathan, scales derived from them may include contributions, other S. & Karplus, M. (1983) J. Comp. Chem. 4, 187-217. than pure hydration effects. From the present results, there 34. Brunger, A. T., Brooks, C. L., III, & Karplus, M. (1985) Proc. Natl. can be contributions Acad. Sci. USA 82, 8458-8462. from changes in nonbonded interactions 35. Valleau, J. P. & Torrie, G. M. (1977) in Statistical Mechanics, ed. Berne, of the side chains with the organic phase and from changes in J. (Plenum, New York), Part A, pp. 169-194. covalent side-chain terms. In particular, the suggestion that 36. Mazor, M. & Pettitt, B. M. (1991) Mol. Simulations 6, 1-4. internal degrees of freedom of the solute also contribute to 37. Beveridge, D. L. & DiCapua, F. M. (1989) Annu. Rev. Biophys. Chem. what is commonly 18, 431-492. described as hydrophobicity is an impor- 38. Alard, P. (1991) Ph.D. thesis (Universite Libre de Bruxelles, Brussels). tant result of the analysis. 39. Yu, H.-A. & Karplus, M. (1988) 1. Chem. Phys. 89, 2366-2379. Downloaded by guest on September 28, 2021