How the hydrophobic factor drives protein folding Robert L. Baldwina,1 and George D. Roseb a Department of Biochemistry, Stanford University Medical Center, Beckman Center, School of Medicine, Stanford, CA 94305-5307; and bJenkins Department of Biophysics, The Johns Hopkins University, Baltimore, MD 21218
Contributed by Robert L. Baldwin, September 7, 2016 (sent for review June 29, 2016; reviewed by David S. Eisenberg and Richard Wolfenden)
How hydrophobicity (HY) drives protein folding is studied. The 1971 Nozaki–Tanford method of measuring HY is modified to use gases as solutes, not crystals, and this makes the method easy to use. Alkanes are found to be much more hydrophobic than rare gases, and the two different kinds of HY are termed intrinsic (rare gases) and extrinsic (alkanes). The HY values of rare gases are proportional to solvent-accessible surface area (ASA), whereas the HY values of alkanes depend on special hydration shells. Earlier work showed that hydration shells produce the hydration energetics of alkanes. Evidence is given here that the transfer energetics of alkanes to cyclohexane [Wolfenden R, Lewis CA, Jr, Yuan Y, Carter CW, Jr (2015) Proc Natl Acad Sci USA 112(24):7484– 7488] measure the release of these shells. Alkane shells are stabilized importantly by van der Waals interactions between alkane carbon and water oxygen atoms. Thus, rare gases cannot form this type of shell. The very short (approximately picoseconds) lifetime of the van der Waals interaction probably explains why NMR efforts to detect alkane hydration shells have failed. The close similarity between the sizes of the opposing energetics for forming or releasing alkane shells confirms the presence of these shells on alkanes and supports Kauzmann’s 1959 mechanism of protein folding. A space-filling model is given for the hydration shells on linear alkanes. The model reproduces the n values of Jorgensen et al. [Jorgensen WL, Gao J, Ravimohan C (1985) J Phys Chem 89:3470–3473] for the number of waters in alkane hydration shells. protein folding solvent shells
| hydrophobicity | hydrophobic effect | hydration shells |
W
hen Kauzmann published his classic 1959 paper (1) on a new hydrophobic factor that drives protein folding, he gave examples from the literature (his table 3) of the energetics of transferring alkanes and aromatic hydrocarbons between various organic solvents and water. These examples show that the transfer free energy is favorable and sizable when a hydrocarbon solute is transferred from water to an organic solvent. Finding a favorable transfer free energy from water to an organic solvent prompted Kauzmann (1, 2) to suggest a protein-folding mechanism in which hydrocarbon side chains of the unfolded protein are driven to leave water and enter the folded protein interior because the interior is water free. Tanford (3) in 1962 then showed how the hydrophobic factor can be evaluated quantitatively [as the hydrophobicity (HY)] for amino acid side chains by using their solubilities in ethanol and water. Tanford (3) showed that the transfer free energy from water to ethanol can be found from the solubilities of the solute in water and ethanol, and he pointed out that the required solubility data are given in the book by Cohn and Edsall (4). By making free-energy calculations from these data, Tanford (3) in 1962 began the quantitative study of HY, and he argued that it is the key to understanding how proteins fold. In 1971, Nozaki and Tanford (5) gave the name HY to this type of analysis. The longstanding meaning of the term hydrophobic (water-hating) is that a hydrophobic solute is much more soluble in most organic solvents than in water (6). Nozaki and Tanford (5) used this meaning to develop a method of measuring HY values from the solute’s solubilities in water and ethanol, or other reference solvent. In 1971, they gave their measurements of HY values (5)
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for 12 amino acid side chains and for the peptide unit. Their 1971 HY values agree fairly well with the ones Tanford (3) gave in 1962, based on literature values for the solubilities. The 1971 Nozaki–Tanford paper (5) became an instant classic, and their method of measuring HY values was widely accepted. However, the 1971 Nozaki–Tanford method is difficult to use and was not used after 1971, not even by Tanford. To make the Nozaki–Tanford method of measuring HY values simpler to use, we modified the method to use gases rather than crystalline side chains as solutes. Some of the crystalline amino acids studied in 1971 by Nozaki and Tanford (5) were insoluble in both reference solvents, ethanol and dioxane, used by them. Thus, they had to make solubility measurements in mixtures of water and ethanol (or dioxane) to obtain measurable solubilities, and they needed to make difficult extrapolations to obtain solubility results for 100% ethanol or 100% dioxane. Using the modified method given here, with gases as solutes, there is no similar solubility problem. HY values are measured here for alkanes and rare gases. Alkanes are found to be much more hydrophobic than rare gases; in fact, there are two different kinds of HY. This result was expected from the proposal by Jorgensen et al. (7), who showed that van der Waals (vdW) interactions between alkane carbon and water oxygen atoms tether a fixed number (n) of water molecules to each of the seven alkanes they studied. Moreover, Jorgensen et al. (7) measured the Lennard–Jones potential of the C...O vdW interaction and found that it is quite strong. Jorgensen et al. (7) proposed that these tethered water molecules serve as Kauzmann’s (1, 2) hydration shells, which contribute to the solute’s HY. Thus, alkanes were expected to be more hydrophobic than rare gases because rare gases lack carbon atoms and cannot form these tethered water molecules. A Modified Nozaki–Tanford Method of Measuring HY The solubility (s) of the solute is converted to a change in free energy (ΔG*) by using Eq. 1 below, in which the solubility s is Significance A study of how hydrophobicity (HY) drives protein folding reveals two kinds of HY: intrinsic (proportional to surface area) and extrinsic (augmented by hydration shells). The Nozaki–Tanford method of measuring HY has been modified to use gaseous solutes. Hydration shells on alkanes explain the unusual HY of alkanes. Transfer of alkanes from water to cyclohexane causes release of alkane hydration shells. Comparing the energetics of formation and release shows that hydration shells are clearly present on alkanes and supports Kauzmann’s 1959 mechanism for how the hydrophobic factor drives protein folding. A spacefilling model is given for the hydration shells on linear alkanes. Author contributions: R.L.B. and G.D.R. designed research, performed research, analyzed data, and wrote the paper. Reviewers: D.S.E., University of California, Los Angeles; and R.W., University of North Carolina. The authors declare no conflict of interest. Freely available online through the PNAS open access option. 1
To whom correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1610541113/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1610541113
Fig. 1. Measurement of the HY values of two nonpolar gaseous solutes (n-heptane, strongly hydrophobic, and argon, weakly hydrophobic) is illustrated for a choice of seven possible reference solvents. The HY value (units, kilocalories per mole) is given (Eq. 3) by the difference between the ΔG* values of the solute in water (solvent 8) and in ethanol (solvent 6, used here as the reference solvent). The solvents are as follows: 1, hexane; 2, 1-decanol; 3, 1-octanol; 4, 1-butanol; 5, 2propanol; 6, ethanol; 7, methanol; 8, water. ΔG* values are from Abraham (8).
treated as an equilibrium constant, and ΔG* is termed its standard free energy of solution (8): ΔGp = −RT ln s.
Two Different Kinds of HY Fig. 2 compares the values of (HY/ASA) for alkanes and rare gases, plotted against molecular weight, and confirms that alkanes and rare gases have different kinds of HYs. HY/ASA should be a constant for a given set of gases if HY is proportional to ASA. Chothia’s 1974 paper (9) argues that the Nozaki–Tanford HY values of the amino acid side chains are proportional to their ASA values. (The values of HY and ASA used here are given in Supporting Information; see Table S1.) The ASA values were found by the fast method of Shrake and Rupley (10), which has been tested elsewhere (11). The values of (HY/ASA) in Fig. 2 are seen to be considerably larger for alkanes than for rare gases. Moreover, the (HY/ASA) values are nearly constant within the set of rare gases, whereas the (HY/ASA) values are definitely not constant within the set of alkanes. Thus, Fig. 2 shows two different kinds of HY, one (intrinsic) for rare gases and another (extrinsic) for alkanes. The difference between the (HY/ASA) values of alkanes and rare gases increases with molecular weight (M), as expected if the difference in (HY/ASA) values is caused chiefly by the
[1]
When the solubility s is small, ΔG* is large and positive. The ratio of the solute’s solubilities in two solvents, 1 and 2, is found from the difference between the values of ΔG* in the two solvents, and the free-energy difference between the two solvents gives the transfer free energy between the two solvents. −RT lnðs1 =s2 Þ = ΔGp1 − ΔGp2 .
[2]
Tanford (3) used the transfer free energy of the norleucine side chain from various organic solvents to water (4) to show that this transfer free energy is nearly the same when four common organic solvents (methanol, ethanol, butanol, and acetone) are used as the reference solvent. Tanford (3) then proposed that thermal unfolding of a globular protein in water may likewise be considered as a transfer process from an organic solvent to water, in which the densely packed hydrophobic side chains of the folded protein constitute the reference solvent. The definition of HY given in 1971 by Nozaki and Tanford (5) is the transfer free energy of the solute from an organic solvent (e.g., ethanol) to water: HY = ΔGpw − ΔGpr ,
[3]
where w is water and r is reference solvent. Measuring HY Values of Alkanes and Rare Gases Fig. 1 illustrates how HY is measured by the modified Nozaki– Tanford method. An assortment of seven organic solvents is used as alternative reference solvents, to show that different organic Baldwin and Rose
Fig. 2. Values of (HY/ASA) are plotted against molecular weight (M) for linear alkanes and for rare gases. HY is the hydrophobicity (HY value; units are kilocalories per mole) found by the modified Nozaki–Tanford method described here; ASA is the solvent-accessible surface area; units are square angstroms. See Supporting Information for values of HY and ASA.
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solvents may be used as the reference solvent. The solubilities of numerous gases in these solvents have either been measured by Abraham (8) or else quoted by him from critical reviews. From the measured gas solubilities, ΔG* values can be found by Eq. 1 and HY values can be found by Eq. 3. The choice of the reference solvent is arbitrary. However, the variation in ΔG* among the seven alternative reference solvents in Fig. 1 is small compared with the value of HY for n-heptane, which is given here by the difference between the ΔG* values of n-heptane in water (solvent 8) and in ethanol (solvent 6). Thus, the HY value of n-heptane can be measured straightforwardly, despite the arbitrary choice of a reference solvent. For the weakly hydrophobic solute argon, Fig. 1 shows that HY is again measurable although the HY value of argon is much smaller than that of n-heptane.
Table 1. The energetics of forming (f) and releasing (r) alkane hydration shells (kilocalories per mole at 25 °C) Alkane Propane Butane Isobutane
ΔGo (f)*
T ΔSo (f)*
ΔGo (r)†
T ΔSo (r)†
1.96, 1.96 2.09 2.32
−6.98, −6.79 −7.75 −7.55
−5.56 −5.77 −5.77
7.04 6.80 6.37
Makes vdW contact with its surrounding water ring. *Forming (f) an alkane hydration shell by alkane transfer from vapor to water (12). † Releasing (r) the shell from the alkane by alkane transfer from liquid water to liquid cyclohexane (15) through mixing the aqueous and cyclohexane liquids. Two sets of values are given for propane from two different published datasets (12). Data for vapor to water transfer of alkanes (12) are based on the Ben–Naim standard state, in which alkane transfer occurs between fixed positions in the gas and liquid phases.
hydration shells on alkanes. The number of waters (n value) of an alkane hydration shell is known to be proportional to the ASA of the alkane (12), so the difference between alkanes and rare gases in (HY/ASA) is expected to increase with M. Why should a hydrophobic solute be much more soluble in most organic solvents than in water? The answer given here is that Sceats and Rice (13) were correct in arguing that liquid water (25 °C) is fully H bonded. The H-bonded structure of liquid water tends to exclude all solutes. Sharp and Madan (14) have analyzed how the Sceats and Rice model treats the interactions between hydrophobic, nonpolar solutes and the H-bonded structure of liquid water. Both the 1971 Nozaki–Tanford (5) method and the modified method given here use solubilities found with saturated solutions, as discussed by Tanford in 1962 (3). A saturated liquid solution has different solute concentrations depending on whether the saturating phase is a solid (as in the 1971 method) or a gas (as here). A valuable alternative way of measuring HY values is by physical mixing of two solutions, to transfer the solute from water into cyclohexane; this method was introduced recently by Wolfenden et al. (15). Water and cyclohexane are almost immiscible: the concentration of water in wet cyclohexane at 20 °C is only 2.5 × 10−3 M (16). According to the equations given here and by Nozaki and Tanford (5), solubilities found by using saturated solutions should be used to find the HY value of the solute. Possible Relation Between the Very Short (Approximately Picoseconds) Lifetime of the C...O vdW Interaction and the Failure of NMR Studies to Detect Alkane Hydration Shells Kauzmann (1, 2) expected hydration shells on hydrocarbon solutes to be the key to understanding how the hydrophobic factor drives protein folding. In 1987, looking back on subsequent efforts to test his 1959 hypothesis about protein folding, he said, “I still believe that the Frank & Evans ’iceberg’ model of 40 years ago is correct: when it is transferred into water the nonpolar hydrocarbon molecule induces, in the layer of water immediately surrounding it, a cage of more or less fully hydrogen-bonded water molecules (the ’iceberg’)” (2). Kauzmann (2) discussed the surprising properties of hydrocarbons in water and argued that they must reflect the presence of hydration shells. He implied that when these shells are found and studied, their role in driving folding will become obvious. Qvist and Halle (17) in 2008 looked for water cages by NMR. They expected H-bonded water cages to be semirigid and found that instead water molecules adjacent to nonpolar groups rotate rapidly, like bulk water molecules. One of the four partly hydrophobic solutes studied by Qvist and Halle (17) was N-acetyl-leucine-N-methylamide, which should have an alkane-like hydration shell. See also the recent NMR study of protein hydration shells by Zhong and coworkers (18). 12464 | www.pnas.org/cgi/doi/10.1073/pnas.1610541113
We suggest that the rapid rotations of water molecules in alkane hydration shells (17) can be explained by the very short (approximately picoseconds) lifetimes of C...O vdW interactions, because hydration shells that are stabilized importantly by these vdW interactions must be continually broken down and remade on a very fast timescale. The evidence for C...O vdW interactions stabilizing alkane hydration shells is given above and can be summarized as follows. In 1985, Jorgensen et al. (7) measured the number (n) of water molecules tethered by C...O vdW interactions to each alkane. In 2014, the hydration energetics of the alkanes were found to be proportional to the n values of these tethered water molecules (12). Thus, the observed hydration energetics show that the alkane hydration shells are stabilized importantly by C...O vdW interactions. Other interactions, such as H bonding of the water molecules, may also be important in stabilizing these shells. Comparing the Energetics of Forming and Releasing Dynamic Hydration Shells There is a large unfavorable entropy change when an alkane becomes hydrated, and the entire hydration energetics, including the entropy change, are known to be caused by forming a hydration shell (12). Table 1 shows that the entropy change is approximately reversed when the hydration shell is removed from an alkane by transfer from water to cyclohexane. This comparison is shown in Table 1 for each of the three alkanes studied by Wolfenden et al. (15). The result is an important test of Kauzmann’s 1959 hydration shell mechanism (1, 2) for driving protein folding, which says that hydration shells play a key role in the mechanism. Note that the entropy change upon release of the shells is accompanied by a sizable change in free energy, like Kauzmann’s observations in 1959 (1). The alkane hydration shells have complex structures in the model given below, and this complexity readily explains the large entropy changes upon forming or releasing the shells. When the shells are released into cyclohexane, which is nearly water-free, they appear to break
Fig. 3. A space-filling model is illustrated for alkane hydration shells on linear alkanes, beginning here with methane. See also Figs. S1 and S2. Each hydration shell is anchored to its alkane by vdW attraction between solute carbon and water oxygen atoms. The Lennard–Jones potential of the C...O vdW attraction was evaluated by Jorgensen et al. (7). The alkane shown here is methane, whose H atoms are light green and have a vdW radius of 1.0 Å. Methane is enclosed by an icosahedral shell of 20 hydration waters (red spheres), each of which has a vdW radius of 1.4 Å. A top layer of five water molecules has been removed for viewing clarity. Each water makes vdW contact with its immediate water neighbors and also with the vdW surface of methane.
Baldwin and Rose
Fig. 4. Comparison between the number of waters (n) in the hydration shells of linear alkanes found in the simulation analysis by Jorgensen et al. (7) and in the space-filling model for hydration shells of linear alkanes given here.
down, which explains why the entropy change for transfer into cyclohexane is nearly the reverse of the entropy change for forming the shell (Table 1).
HY as a Driving Force in Protein Folding Three recent papers suggest that progress in understanding the protein-folding problem is limited by our inability to predict how hydrophobic residues interact with water and with each other to yield free-energy values that can drive the folding process. For example, a mutational study by Bachmann et al. (22) of how unfolded S peptide combines with folded S protein to form folded and enzymatically active ribonuclease S indicates that HY (especially at two residue positions in S peptide) is the key energetic variable in the combination reaction. It is a very intriguing result, because it suggests that interactions between hydrophobic residues are probably important in determining the folding pathway of a globular protein. The second example is a commentary by Eisenberg and Sawaya (23) on what two recent determinations of high-resolution structures of amyloid-β fibrils mean for understanding Alzheimer’s disease. One goal of determining amyloid fibril structures is to understand how amyloid-β fibrils spread throughout the brain; hydrophobic interactions between fibril structural elements are likely to be important (23). However, we lack methods of locating and estimating the strengths of such hydrophobic interactions. A third, quite different, example concerns the theoretical prediction of how HY participates in driving protein folding. Perunov and England (24) study the problem with computer simulations. They conclude that not knowing enough about HY is a key factor that limits our ability to predict rapidly 3D structures (approximately accurate) of folded monomeric proteins.
Space-Filling Model for C...O Hydration Shells on Linear Alkanes A space-filling model for C...O vdW hydration shells on linear alkanes is given here, beginning with methane, the shortest alkane. Both experiment (19) and simulation (7) have shown that the hydration shell of methane in water has 20 waters. Fig. 3 shows that 20 is also the value of n needed to form a closed, confluent, vdW shell of water molecules around methane. In the space-filling model given here, linear alkanes longer than methane can have C...O vdW hydration shells by adding vdW rings of four waters each, two staggered rings for every pair of additional carbons in the chain. The solvent shell for methane can be subdivided into two caps of eight waters each plus an interior ring of four waters. An additional ring of four waters can then be added for each successive alkane carbon in the chain (Figs. S1 and S2). The n values (the number of waters in a hydration shell) given by the space-filling model agree well with the n values measured by Jorgensen et al. (7), as shown in Fig. 4. The alkane hydration shell may also be H bonded, as well as being anchored by vdW interactions, and we do not attempt to
ACKNOWLEDGMENTS. R.L.B. thanks David Chandler for urging him to find out how much the hydration shell of a hydrocarbon contributes to its HY, and he thanks Matt Footer, Bill Jorgensen, Peter Kim, and Jack Kyte for discussion. G.D.R. gratefully acknowledges support from the National Science Foundation.
1. Kauzmann W (1959) Some factors in the interpretation of protein denaturation. Adv Protein Chem 14:1–63. 2. Kauzmann W (1987) Thermodynamics of unfolding. Nature 325:763–764. 3. Tanford C (1962) Contribution of hydrophobic interactions to the stability of the globular conformation of proteins. J Am Chem Soc 84:4240–4247. 4. Cohn EJ, Edsall JT (1943) Proteins, Amino Acids and Peptides (Reinhold Publishing, New York), pp 196–216. 5. Nozaki Y, Tanford C (1971) The solubility of amino acids and two glycine peptides in aqueous ethanol and dioxane solutions. Establishment of a hydrophobicity scale. J Biol Chem 246(7):2211–2217. 6. Tanford C (1978) The hydrophobic effect and the organization of living matter. Science 200(4345):1012–1018.
7. Jorgensen WL, Gao J, Ravimohan C (1985) Monte Carlo simulations of alkanes in water: Hydration numbers and the hydrophobic effect. J Phys Chem 89: 3470–3473. 8. Abraham MH (1982) Free energies, enthalpies, and entropies of solution of gaseous nonpolar nonelectrolytes in water and nonaqueous solvents. The hydrophobic effect. J Am Chem Soc 104:2085–2094. 9. Chothia C (1974) Hydrophobic bonding and accessible surface area in proteins. Nature 248(446):338–339. 10. Shrake A, Rupley JA (1973) Environment and exposure to solvent of protein atoms. Lysozyme and insulin. J Mol Biol 79(2):351–371. 11. Zehfus MH, Seltzer JP, Rose GD (1985) Fast approximations for accessible surface area and molecular volume of protein segments. Biopolymers 24(12):2511–2519.
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model the H bonding here. An accurate X-ray structure is known of type I water clathrate (20), in which the water molecules are H bonded to each other. Type I is a frequently occurring water clathrate that encloses different nonpolar ligands in various host–guest compounds. Having H-bonded water molecules and being crystalline does not necessarily make type I structures stable. Fire ice (21), which is a type I water clathrate that encloses methane and which covers the ocean floor, is a good example. Although it is crystalline and stabilized by water H bonds, it is also stabilized by the high pressures found at the ocean floor and it melts rapidly when brought to the ocean surface. The hydration shells on alkanes longer than methane resemble capped tubes. The interactions made by water molecules in the caps are different from the interactions made by waters in the tube sections. According to the space-filling model given here, the mass of an alkane hydration shell is typically much larger than the mass of the alkane itself. The n value of the methane hydration shell is 20 waters and so the mass of the shell is 20 × 18 = 360, whereas the mass of CH4 is 16. The n value of the butane shell is 29.9 waters (7) and the mass of the shell is 538, whereas the butane mass is 56. Thus, the presence of such large hydration shells on alkanes plausibly explains the big differences seen in Fig. 2 between the HY/ASA values of alkanes and rare gases.
12. Baldwin RL (2014) Dynamic hydration shell restores Kauzmann’s 1959 explanation of how the hydrophobic factor drives protein folding. Proc Natl Acad Sci USA 111(36):13052–13056. 13. Sceats MG, Rice SA (1980) A random network model calculation of the free energy of liquid water. J Chem Phys 72:6183–6191. 14. Sharp KA, Madan B (1997) Hydrophobic effect, water structure, and heat capacity changes. J Phys Chem B 101:4343–4348. 15. Wolfenden R, Lewis CA, Jr, Yuan Y, Carter CW, Jr (2015) Temperature dependence of amino acid hydrophobicities. Proc Natl Acad Sci USA 112(24):7484–7488. 16. Radzicka A, Wolfenden R (1988) Comparing the polarities of the amino acids: Sidechain distribution coefficients between the vapor phase, cyclohexane, 1-octanol, and neutral aqueous solution. Biochemistry 27:1664–1670. 17. Qvist J, Halle B (2008) Thermal signature of hydrophobic hydration dynamics. J Am Chem Soc 130(31):10345–10353. 18. Qin Y, Wang L, Zhong D (2016) Dynamics and mechanism of ultrafast water-protein interactions. Proc Natl Acad Sci USA 113(30):8424–8429.
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19. Dec SF, Bowler KE, Stadterman LL, Koh CA, Sloan ED, Jr (2006) Direct measure of the hydration number of aqueous methane. J Am Chem Soc 128(2):414–415. 20. McMullan RK, Jeffrey GA (1965) Polyhedral clathrate hydrates. IX. Structure of ethyleneoxide hydrate. J Chem Phys 42:2725–2732. 21. Sloan ED, Jr, Koh CA (2008) Clathrate Hydrates of Natural Gases (Dekker, New York), 3rd Ed, pp 189–256. 22. Bachmann A, Wildemann D, Praetorius F, Fischer G, Kiefhaber T (2011) Mapping backbone and side-chain interactions in the transition state of a coupled protein folding and binding reaction. Proc Natl Acad Sci USA 108(10):3952–3957. 23. Eisenberg D, Sawaya MR (2016) Implications for Alzheimer’s disease of an atomic resolution structure of amyloid-β(1–42) fibrils. Proc Natl Acad Sci USA 113(34): 9398–400. 24. Perunov N, England JL (2014) Quantitative theory of hydrophobic effect as a driving force of protein structure. Protein Sci 23(4):387–399.
Baldwin and Rose
Contributed by Robert L. Baldwin, September 7, 2016 (sent for review June 29, 2016; reviewed by David S. Eisenberg and Richard Wolfenden)
How hydrophobicity (HY) drives protein folding is studied. The 1971 Nozaki–Tanford method of measuring HY is modified to use gases as solutes, not crystals, and this makes the method easy to use. Alkanes are found to be much more hydrophobic than rare gases, and the two different kinds of HY are termed intrinsic (rare gases) and extrinsic (alkanes). The HY values of rare gases are proportional to solvent-accessible surface area (ASA), whereas the HY values of alkanes depend on special hydration shells. Earlier work showed that hydration shells produce the hydration energetics of alkanes. Evidence is given here that the transfer energetics of alkanes to cyclohexane [Wolfenden R, Lewis CA, Jr, Yuan Y, Carter CW, Jr (2015) Proc Natl Acad Sci USA 112(24):7484– 7488] measure the release of these shells. Alkane shells are stabilized importantly by van der Waals interactions between alkane carbon and water oxygen atoms. Thus, rare gases cannot form this type of shell. The very short (approximately picoseconds) lifetime of the van der Waals interaction probably explains why NMR efforts to detect alkane hydration shells have failed. The close similarity between the sizes of the opposing energetics for forming or releasing alkane shells confirms the presence of these shells on alkanes and supports Kauzmann’s 1959 mechanism of protein folding. A space-filling model is given for the hydration shells on linear alkanes. The model reproduces the n values of Jorgensen et al. [Jorgensen WL, Gao J, Ravimohan C (1985) J Phys Chem 89:3470–3473] for the number of waters in alkane hydration shells. protein folding solvent shells
| hydrophobicity | hydrophobic effect | hydration shells |
W
hen Kauzmann published his classic 1959 paper (1) on a new hydrophobic factor that drives protein folding, he gave examples from the literature (his table 3) of the energetics of transferring alkanes and aromatic hydrocarbons between various organic solvents and water. These examples show that the transfer free energy is favorable and sizable when a hydrocarbon solute is transferred from water to an organic solvent. Finding a favorable transfer free energy from water to an organic solvent prompted Kauzmann (1, 2) to suggest a protein-folding mechanism in which hydrocarbon side chains of the unfolded protein are driven to leave water and enter the folded protein interior because the interior is water free. Tanford (3) in 1962 then showed how the hydrophobic factor can be evaluated quantitatively [as the hydrophobicity (HY)] for amino acid side chains by using their solubilities in ethanol and water. Tanford (3) showed that the transfer free energy from water to ethanol can be found from the solubilities of the solute in water and ethanol, and he pointed out that the required solubility data are given in the book by Cohn and Edsall (4). By making free-energy calculations from these data, Tanford (3) in 1962 began the quantitative study of HY, and he argued that it is the key to understanding how proteins fold. In 1971, Nozaki and Tanford (5) gave the name HY to this type of analysis. The longstanding meaning of the term hydrophobic (water-hating) is that a hydrophobic solute is much more soluble in most organic solvents than in water (6). Nozaki and Tanford (5) used this meaning to develop a method of measuring HY values from the solute’s solubilities in water and ethanol, or other reference solvent. In 1971, they gave their measurements of HY values (5)
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for 12 amino acid side chains and for the peptide unit. Their 1971 HY values agree fairly well with the ones Tanford (3) gave in 1962, based on literature values for the solubilities. The 1971 Nozaki–Tanford paper (5) became an instant classic, and their method of measuring HY values was widely accepted. However, the 1971 Nozaki–Tanford method is difficult to use and was not used after 1971, not even by Tanford. To make the Nozaki–Tanford method of measuring HY values simpler to use, we modified the method to use gases rather than crystalline side chains as solutes. Some of the crystalline amino acids studied in 1971 by Nozaki and Tanford (5) were insoluble in both reference solvents, ethanol and dioxane, used by them. Thus, they had to make solubility measurements in mixtures of water and ethanol (or dioxane) to obtain measurable solubilities, and they needed to make difficult extrapolations to obtain solubility results for 100% ethanol or 100% dioxane. Using the modified method given here, with gases as solutes, there is no similar solubility problem. HY values are measured here for alkanes and rare gases. Alkanes are found to be much more hydrophobic than rare gases; in fact, there are two different kinds of HY. This result was expected from the proposal by Jorgensen et al. (7), who showed that van der Waals (vdW) interactions between alkane carbon and water oxygen atoms tether a fixed number (n) of water molecules to each of the seven alkanes they studied. Moreover, Jorgensen et al. (7) measured the Lennard–Jones potential of the C...O vdW interaction and found that it is quite strong. Jorgensen et al. (7) proposed that these tethered water molecules serve as Kauzmann’s (1, 2) hydration shells, which contribute to the solute’s HY. Thus, alkanes were expected to be more hydrophobic than rare gases because rare gases lack carbon atoms and cannot form these tethered water molecules. A Modified Nozaki–Tanford Method of Measuring HY The solubility (s) of the solute is converted to a change in free energy (ΔG*) by using Eq. 1 below, in which the solubility s is Significance A study of how hydrophobicity (HY) drives protein folding reveals two kinds of HY: intrinsic (proportional to surface area) and extrinsic (augmented by hydration shells). The Nozaki–Tanford method of measuring HY has been modified to use gaseous solutes. Hydration shells on alkanes explain the unusual HY of alkanes. Transfer of alkanes from water to cyclohexane causes release of alkane hydration shells. Comparing the energetics of formation and release shows that hydration shells are clearly present on alkanes and supports Kauzmann’s 1959 mechanism for how the hydrophobic factor drives protein folding. A spacefilling model is given for the hydration shells on linear alkanes. Author contributions: R.L.B. and G.D.R. designed research, performed research, analyzed data, and wrote the paper. Reviewers: D.S.E., University of California, Los Angeles; and R.W., University of North Carolina. The authors declare no conflict of interest. Freely available online through the PNAS open access option. 1
To whom correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1610541113/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1610541113
Fig. 1. Measurement of the HY values of two nonpolar gaseous solutes (n-heptane, strongly hydrophobic, and argon, weakly hydrophobic) is illustrated for a choice of seven possible reference solvents. The HY value (units, kilocalories per mole) is given (Eq. 3) by the difference between the ΔG* values of the solute in water (solvent 8) and in ethanol (solvent 6, used here as the reference solvent). The solvents are as follows: 1, hexane; 2, 1-decanol; 3, 1-octanol; 4, 1-butanol; 5, 2propanol; 6, ethanol; 7, methanol; 8, water. ΔG* values are from Abraham (8).
treated as an equilibrium constant, and ΔG* is termed its standard free energy of solution (8): ΔGp = −RT ln s.
Two Different Kinds of HY Fig. 2 compares the values of (HY/ASA) for alkanes and rare gases, plotted against molecular weight, and confirms that alkanes and rare gases have different kinds of HYs. HY/ASA should be a constant for a given set of gases if HY is proportional to ASA. Chothia’s 1974 paper (9) argues that the Nozaki–Tanford HY values of the amino acid side chains are proportional to their ASA values. (The values of HY and ASA used here are given in Supporting Information; see Table S1.) The ASA values were found by the fast method of Shrake and Rupley (10), which has been tested elsewhere (11). The values of (HY/ASA) in Fig. 2 are seen to be considerably larger for alkanes than for rare gases. Moreover, the (HY/ASA) values are nearly constant within the set of rare gases, whereas the (HY/ASA) values are definitely not constant within the set of alkanes. Thus, Fig. 2 shows two different kinds of HY, one (intrinsic) for rare gases and another (extrinsic) for alkanes. The difference between the (HY/ASA) values of alkanes and rare gases increases with molecular weight (M), as expected if the difference in (HY/ASA) values is caused chiefly by the
[1]
When the solubility s is small, ΔG* is large and positive. The ratio of the solute’s solubilities in two solvents, 1 and 2, is found from the difference between the values of ΔG* in the two solvents, and the free-energy difference between the two solvents gives the transfer free energy between the two solvents. −RT lnðs1 =s2 Þ = ΔGp1 − ΔGp2 .
[2]
Tanford (3) used the transfer free energy of the norleucine side chain from various organic solvents to water (4) to show that this transfer free energy is nearly the same when four common organic solvents (methanol, ethanol, butanol, and acetone) are used as the reference solvent. Tanford (3) then proposed that thermal unfolding of a globular protein in water may likewise be considered as a transfer process from an organic solvent to water, in which the densely packed hydrophobic side chains of the folded protein constitute the reference solvent. The definition of HY given in 1971 by Nozaki and Tanford (5) is the transfer free energy of the solute from an organic solvent (e.g., ethanol) to water: HY = ΔGpw − ΔGpr ,
[3]
where w is water and r is reference solvent. Measuring HY Values of Alkanes and Rare Gases Fig. 1 illustrates how HY is measured by the modified Nozaki– Tanford method. An assortment of seven organic solvents is used as alternative reference solvents, to show that different organic Baldwin and Rose
Fig. 2. Values of (HY/ASA) are plotted against molecular weight (M) for linear alkanes and for rare gases. HY is the hydrophobicity (HY value; units are kilocalories per mole) found by the modified Nozaki–Tanford method described here; ASA is the solvent-accessible surface area; units are square angstroms. See Supporting Information for values of HY and ASA.
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solvents may be used as the reference solvent. The solubilities of numerous gases in these solvents have either been measured by Abraham (8) or else quoted by him from critical reviews. From the measured gas solubilities, ΔG* values can be found by Eq. 1 and HY values can be found by Eq. 3. The choice of the reference solvent is arbitrary. However, the variation in ΔG* among the seven alternative reference solvents in Fig. 1 is small compared with the value of HY for n-heptane, which is given here by the difference between the ΔG* values of n-heptane in water (solvent 8) and in ethanol (solvent 6). Thus, the HY value of n-heptane can be measured straightforwardly, despite the arbitrary choice of a reference solvent. For the weakly hydrophobic solute argon, Fig. 1 shows that HY is again measurable although the HY value of argon is much smaller than that of n-heptane.
Table 1. The energetics of forming (f) and releasing (r) alkane hydration shells (kilocalories per mole at 25 °C) Alkane Propane Butane Isobutane
ΔGo (f)*
T ΔSo (f)*
ΔGo (r)†
T ΔSo (r)†
1.96, 1.96 2.09 2.32
−6.98, −6.79 −7.75 −7.55
−5.56 −5.77 −5.77
7.04 6.80 6.37
Makes vdW contact with its surrounding water ring. *Forming (f) an alkane hydration shell by alkane transfer from vapor to water (12). † Releasing (r) the shell from the alkane by alkane transfer from liquid water to liquid cyclohexane (15) through mixing the aqueous and cyclohexane liquids. Two sets of values are given for propane from two different published datasets (12). Data for vapor to water transfer of alkanes (12) are based on the Ben–Naim standard state, in which alkane transfer occurs between fixed positions in the gas and liquid phases.
hydration shells on alkanes. The number of waters (n value) of an alkane hydration shell is known to be proportional to the ASA of the alkane (12), so the difference between alkanes and rare gases in (HY/ASA) is expected to increase with M. Why should a hydrophobic solute be much more soluble in most organic solvents than in water? The answer given here is that Sceats and Rice (13) were correct in arguing that liquid water (25 °C) is fully H bonded. The H-bonded structure of liquid water tends to exclude all solutes. Sharp and Madan (14) have analyzed how the Sceats and Rice model treats the interactions between hydrophobic, nonpolar solutes and the H-bonded structure of liquid water. Both the 1971 Nozaki–Tanford (5) method and the modified method given here use solubilities found with saturated solutions, as discussed by Tanford in 1962 (3). A saturated liquid solution has different solute concentrations depending on whether the saturating phase is a solid (as in the 1971 method) or a gas (as here). A valuable alternative way of measuring HY values is by physical mixing of two solutions, to transfer the solute from water into cyclohexane; this method was introduced recently by Wolfenden et al. (15). Water and cyclohexane are almost immiscible: the concentration of water in wet cyclohexane at 20 °C is only 2.5 × 10−3 M (16). According to the equations given here and by Nozaki and Tanford (5), solubilities found by using saturated solutions should be used to find the HY value of the solute. Possible Relation Between the Very Short (Approximately Picoseconds) Lifetime of the C...O vdW Interaction and the Failure of NMR Studies to Detect Alkane Hydration Shells Kauzmann (1, 2) expected hydration shells on hydrocarbon solutes to be the key to understanding how the hydrophobic factor drives protein folding. In 1987, looking back on subsequent efforts to test his 1959 hypothesis about protein folding, he said, “I still believe that the Frank & Evans ’iceberg’ model of 40 years ago is correct: when it is transferred into water the nonpolar hydrocarbon molecule induces, in the layer of water immediately surrounding it, a cage of more or less fully hydrogen-bonded water molecules (the ’iceberg’)” (2). Kauzmann (2) discussed the surprising properties of hydrocarbons in water and argued that they must reflect the presence of hydration shells. He implied that when these shells are found and studied, their role in driving folding will become obvious. Qvist and Halle (17) in 2008 looked for water cages by NMR. They expected H-bonded water cages to be semirigid and found that instead water molecules adjacent to nonpolar groups rotate rapidly, like bulk water molecules. One of the four partly hydrophobic solutes studied by Qvist and Halle (17) was N-acetyl-leucine-N-methylamide, which should have an alkane-like hydration shell. See also the recent NMR study of protein hydration shells by Zhong and coworkers (18). 12464 | www.pnas.org/cgi/doi/10.1073/pnas.1610541113
We suggest that the rapid rotations of water molecules in alkane hydration shells (17) can be explained by the very short (approximately picoseconds) lifetimes of C...O vdW interactions, because hydration shells that are stabilized importantly by these vdW interactions must be continually broken down and remade on a very fast timescale. The evidence for C...O vdW interactions stabilizing alkane hydration shells is given above and can be summarized as follows. In 1985, Jorgensen et al. (7) measured the number (n) of water molecules tethered by C...O vdW interactions to each alkane. In 2014, the hydration energetics of the alkanes were found to be proportional to the n values of these tethered water molecules (12). Thus, the observed hydration energetics show that the alkane hydration shells are stabilized importantly by C...O vdW interactions. Other interactions, such as H bonding of the water molecules, may also be important in stabilizing these shells. Comparing the Energetics of Forming and Releasing Dynamic Hydration Shells There is a large unfavorable entropy change when an alkane becomes hydrated, and the entire hydration energetics, including the entropy change, are known to be caused by forming a hydration shell (12). Table 1 shows that the entropy change is approximately reversed when the hydration shell is removed from an alkane by transfer from water to cyclohexane. This comparison is shown in Table 1 for each of the three alkanes studied by Wolfenden et al. (15). The result is an important test of Kauzmann’s 1959 hydration shell mechanism (1, 2) for driving protein folding, which says that hydration shells play a key role in the mechanism. Note that the entropy change upon release of the shells is accompanied by a sizable change in free energy, like Kauzmann’s observations in 1959 (1). The alkane hydration shells have complex structures in the model given below, and this complexity readily explains the large entropy changes upon forming or releasing the shells. When the shells are released into cyclohexane, which is nearly water-free, they appear to break
Fig. 3. A space-filling model is illustrated for alkane hydration shells on linear alkanes, beginning here with methane. See also Figs. S1 and S2. Each hydration shell is anchored to its alkane by vdW attraction between solute carbon and water oxygen atoms. The Lennard–Jones potential of the C...O vdW attraction was evaluated by Jorgensen et al. (7). The alkane shown here is methane, whose H atoms are light green and have a vdW radius of 1.0 Å. Methane is enclosed by an icosahedral shell of 20 hydration waters (red spheres), each of which has a vdW radius of 1.4 Å. A top layer of five water molecules has been removed for viewing clarity. Each water makes vdW contact with its immediate water neighbors and also with the vdW surface of methane.
Baldwin and Rose
Fig. 4. Comparison between the number of waters (n) in the hydration shells of linear alkanes found in the simulation analysis by Jorgensen et al. (7) and in the space-filling model for hydration shells of linear alkanes given here.
down, which explains why the entropy change for transfer into cyclohexane is nearly the reverse of the entropy change for forming the shell (Table 1).
HY as a Driving Force in Protein Folding Three recent papers suggest that progress in understanding the protein-folding problem is limited by our inability to predict how hydrophobic residues interact with water and with each other to yield free-energy values that can drive the folding process. For example, a mutational study by Bachmann et al. (22) of how unfolded S peptide combines with folded S protein to form folded and enzymatically active ribonuclease S indicates that HY (especially at two residue positions in S peptide) is the key energetic variable in the combination reaction. It is a very intriguing result, because it suggests that interactions between hydrophobic residues are probably important in determining the folding pathway of a globular protein. The second example is a commentary by Eisenberg and Sawaya (23) on what two recent determinations of high-resolution structures of amyloid-β fibrils mean for understanding Alzheimer’s disease. One goal of determining amyloid fibril structures is to understand how amyloid-β fibrils spread throughout the brain; hydrophobic interactions between fibril structural elements are likely to be important (23). However, we lack methods of locating and estimating the strengths of such hydrophobic interactions. A third, quite different, example concerns the theoretical prediction of how HY participates in driving protein folding. Perunov and England (24) study the problem with computer simulations. They conclude that not knowing enough about HY is a key factor that limits our ability to predict rapidly 3D structures (approximately accurate) of folded monomeric proteins.
Space-Filling Model for C...O Hydration Shells on Linear Alkanes A space-filling model for C...O vdW hydration shells on linear alkanes is given here, beginning with methane, the shortest alkane. Both experiment (19) and simulation (7) have shown that the hydration shell of methane in water has 20 waters. Fig. 3 shows that 20 is also the value of n needed to form a closed, confluent, vdW shell of water molecules around methane. In the space-filling model given here, linear alkanes longer than methane can have C...O vdW hydration shells by adding vdW rings of four waters each, two staggered rings for every pair of additional carbons in the chain. The solvent shell for methane can be subdivided into two caps of eight waters each plus an interior ring of four waters. An additional ring of four waters can then be added for each successive alkane carbon in the chain (Figs. S1 and S2). The n values (the number of waters in a hydration shell) given by the space-filling model agree well with the n values measured by Jorgensen et al. (7), as shown in Fig. 4. The alkane hydration shell may also be H bonded, as well as being anchored by vdW interactions, and we do not attempt to
ACKNOWLEDGMENTS. R.L.B. thanks David Chandler for urging him to find out how much the hydration shell of a hydrocarbon contributes to its HY, and he thanks Matt Footer, Bill Jorgensen, Peter Kim, and Jack Kyte for discussion. G.D.R. gratefully acknowledges support from the National Science Foundation.
1. Kauzmann W (1959) Some factors in the interpretation of protein denaturation. Adv Protein Chem 14:1–63. 2. Kauzmann W (1987) Thermodynamics of unfolding. Nature 325:763–764. 3. Tanford C (1962) Contribution of hydrophobic interactions to the stability of the globular conformation of proteins. J Am Chem Soc 84:4240–4247. 4. Cohn EJ, Edsall JT (1943) Proteins, Amino Acids and Peptides (Reinhold Publishing, New York), pp 196–216. 5. Nozaki Y, Tanford C (1971) The solubility of amino acids and two glycine peptides in aqueous ethanol and dioxane solutions. Establishment of a hydrophobicity scale. J Biol Chem 246(7):2211–2217. 6. Tanford C (1978) The hydrophobic effect and the organization of living matter. Science 200(4345):1012–1018.
7. Jorgensen WL, Gao J, Ravimohan C (1985) Monte Carlo simulations of alkanes in water: Hydration numbers and the hydrophobic effect. J Phys Chem 89: 3470–3473. 8. Abraham MH (1982) Free energies, enthalpies, and entropies of solution of gaseous nonpolar nonelectrolytes in water and nonaqueous solvents. The hydrophobic effect. J Am Chem Soc 104:2085–2094. 9. Chothia C (1974) Hydrophobic bonding and accessible surface area in proteins. Nature 248(446):338–339. 10. Shrake A, Rupley JA (1973) Environment and exposure to solvent of protein atoms. Lysozyme and insulin. J Mol Biol 79(2):351–371. 11. Zehfus MH, Seltzer JP, Rose GD (1985) Fast approximations for accessible surface area and molecular volume of protein segments. Biopolymers 24(12):2511–2519.
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model the H bonding here. An accurate X-ray structure is known of type I water clathrate (20), in which the water molecules are H bonded to each other. Type I is a frequently occurring water clathrate that encloses different nonpolar ligands in various host–guest compounds. Having H-bonded water molecules and being crystalline does not necessarily make type I structures stable. Fire ice (21), which is a type I water clathrate that encloses methane and which covers the ocean floor, is a good example. Although it is crystalline and stabilized by water H bonds, it is also stabilized by the high pressures found at the ocean floor and it melts rapidly when brought to the ocean surface. The hydration shells on alkanes longer than methane resemble capped tubes. The interactions made by water molecules in the caps are different from the interactions made by waters in the tube sections. According to the space-filling model given here, the mass of an alkane hydration shell is typically much larger than the mass of the alkane itself. The n value of the methane hydration shell is 20 waters and so the mass of the shell is 20 × 18 = 360, whereas the mass of CH4 is 16. The n value of the butane shell is 29.9 waters (7) and the mass of the shell is 538, whereas the butane mass is 56. Thus, the presence of such large hydration shells on alkanes plausibly explains the big differences seen in Fig. 2 between the HY/ASA values of alkanes and rare gases.
12. Baldwin RL (2014) Dynamic hydration shell restores Kauzmann’s 1959 explanation of how the hydrophobic factor drives protein folding. Proc Natl Acad Sci USA 111(36):13052–13056. 13. Sceats MG, Rice SA (1980) A random network model calculation of the free energy of liquid water. J Chem Phys 72:6183–6191. 14. Sharp KA, Madan B (1997) Hydrophobic effect, water structure, and heat capacity changes. J Phys Chem B 101:4343–4348. 15. Wolfenden R, Lewis CA, Jr, Yuan Y, Carter CW, Jr (2015) Temperature dependence of amino acid hydrophobicities. Proc Natl Acad Sci USA 112(24):7484–7488. 16. Radzicka A, Wolfenden R (1988) Comparing the polarities of the amino acids: Sidechain distribution coefficients between the vapor phase, cyclohexane, 1-octanol, and neutral aqueous solution. Biochemistry 27:1664–1670. 17. Qvist J, Halle B (2008) Thermal signature of hydrophobic hydration dynamics. J Am Chem Soc 130(31):10345–10353. 18. Qin Y, Wang L, Zhong D (2016) Dynamics and mechanism of ultrafast water-protein interactions. Proc Natl Acad Sci USA 113(30):8424–8429.
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19. Dec SF, Bowler KE, Stadterman LL, Koh CA, Sloan ED, Jr (2006) Direct measure of the hydration number of aqueous methane. J Am Chem Soc 128(2):414–415. 20. McMullan RK, Jeffrey GA (1965) Polyhedral clathrate hydrates. IX. Structure of ethyleneoxide hydrate. J Chem Phys 42:2725–2732. 21. Sloan ED, Jr, Koh CA (2008) Clathrate Hydrates of Natural Gases (Dekker, New York), 3rd Ed, pp 189–256. 22. Bachmann A, Wildemann D, Praetorius F, Fischer G, Kiefhaber T (2011) Mapping backbone and side-chain interactions in the transition state of a coupled protein folding and binding reaction. Proc Natl Acad Sci USA 108(10):3952–3957. 23. Eisenberg D, Sawaya MR (2016) Implications for Alzheimer’s disease of an atomic resolution structure of amyloid-β(1–42) fibrils. Proc Natl Acad Sci USA 113(34): 9398–400. 24. Perunov N, England JL (2014) Quantitative theory of hydrophobic effect as a driving force of protein structure. Protein Sci 23(4):387–399.
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