The Hydrophobic Effect Enlazul M. Huque Department of Biological Sciences, The University of Calgary. Calgary, AB, Canada T2N IN4 There is certainly no lack of experimental information implicating hydrophobic interactions in a variety of biochemical and biological processes of varying complexities. Interactions between apolar residues attached to a common polymeric backbone can help to promote conformational changes, of which the folding of globular proteins is probably the best example. In a classic publication Bigelow ( I ) reported that a protein must have a certain minimum hydrophobicity to be stable in a globular conformation. He showed that the calculated average hydrophobicity for over 150 proteins lay between 4.5 and 5.0 kJ (mol residue)-'. Configurational entropy tending to destabilize proteins is estimated to be of several hundred kilojoules per mole, whereas experimental stability is close to 10 kJ mol-I (2).Stabilizing interactions, which include hydrogen bonds, van der Waals, coulombic, as well as hydrophohic interactions, are therefore very large compared with the marginal stahility. Hydrophobic interactions are also believed to contrihute to maintenance of ordered macromolecular structures whether they be simple helices, suchas polyglutamic acid, or more complex intramolecular structures such as blood plasma proteins or membrane lipoproteins. Association of insulin monomers and of tobacco mosaic virus subunits, and binding of cbymotrypsin to substate are examples of hydrophobic interactions. Though the existence of hydrophobic substances and organic molecules of a dual nature, with one part soluble (hydrophilic part) and another insoluble in water (hydrophohic part), has heen known for a long time, the physical basis for the hydrophohic effect is not widely understood. Many people talk and think loosely about hydrophobic interactions, particularly in the context of hiopolymer structures. Thermodynamic Background The chemical potential for a hydrocarbon dissolved in water is given by the expression (3)
+ RT ln x, + RT In f,
p, = pwO
(1)
where x , is the concentration of solute in mole fraction units, f , the activity coefficient a t that concentration and pwOthe standard chemical potential (specific part of the chemical potential, called by Gurney (4) the unitary potential). The reference state is the state of infinite dilution. The term RT In f , represents only that part of the chemical potential that arises from interactions of solute molecules with each other and R T ln x , is the purely statistical contribution to the chemical potential that arises from the entropy of mixing solvent and solute molecules. The standard potential p d therefore represents only the internal free energy of solute molecules and the free energy of its interactions with the solvent. There would be a similar factor in the standard chemical potential in a hydrocarbon solvent p~~ = pH:
+ R T h xH, + RT In f H ,
(2)
If mole fraction units are used, and since the internal free energy is the same in both solvents, (~H,O- pwO)represents the difference between the free energy of interactions with the solvent. This is the basis of the standard thermodynamic transfer functions, a popular way of approaching solvation.
The aim is to compare the behavior of a given solute in a number of differen; solvent environments-for illustration. let us consider the standard chemical potential of solute A in solvents 1 and 2 as being p10 and i z o , respectively. The difference between these potentials, A@, known a s the standard chemical potential of transfer corresponds to the cbemical potential involved when 1mol of A is transferred from an infinitelv dilute solution in solvent 1 to solvent 2. The reference state of A can be either pure A in the liquid state or the ideal gas. The solvents can be either pure components or mixtures. In other words, ApO is a measure of the difference in solvation interactions experienced by the probe molecule A in the two different media. If Ap0 < 0, it indicates that the molecule A prefers solvent 2 to solvent 1,and vice versa for ApO> 0. I t is possible to measure enthalpy contributions to ApO, either directly by calorimetry or indirectly by measurements of ApOa t several temperatures. no wing free energy and enthalpy, the corresponding entropy of transfer is then easilv calculated. G o t h e r useful way of representing the thermodynamic behavior of liauid mixture is bv the concept of excess functions. ~ c c o r d i to n ~this concepi, the excesskihbs free energy change of mixing of a binary mixture is defined as (6) GE = Gexpt- Gid
(3)
where Gerpt is the experimentally determined free energy of mixing and Gia is the free energy calculated on the basis of an ideal mixture, i.e. Gid = RT(x, ln x ,
+ x , ln r,)
(4)
where x; is the mole fraction of species i. Therefore. the term GE mekures the contribution of interactions between component 1and 2. Other excess thermodvnamic functions. ex., knthalpy, entropy, heat capacity, and;olume, can he defined in a similar manner. By definition, positive deviations from Raoult's law are equivalent to GE > 0, and negative deviations to GE < 0.
Hydrophoblc Hydration Hydrocarbons are generally readily soluble in most nonpolar solvents but only sparingly soluhle in water. Table 1 shows changes in the enthalpy and in the unitary free energy (standard chemical potential) and entropy when various simple aliphatic and aromatic hvdrocarbons (prohe molecules) aretransferred from a variety of organiE solvents to water (5,6).Although AGOis found to be positive, the interaction energy (enthalpy) is negative (exothermic transfer) for the aliphatic compounds and zero (nearly athermal) for the aromatic ones. The process is invariably accompanied by avery large decrease in entropy. I t is therefore clear that the low affinitv of these suhstances for water is not caused hv an unfavorable energetic situation. I t is a consequence of negative entronv effect. which overcomes the favorable enthalnv term. ~ h i iarge ; edtropy effect in water is characteristic &t onlv for hvdrocarhons. hut also for manv other molecules containing nonpolar groups attached to polar groups, as may be seen from the following two facts (5): Volume 68 Number 7 July 1989
581
Table 1.
Standard Thermodynamic Tranrler Functions for Some Hydrocarbons and Argon lrom Organlc Solvent (5) to Water (kJ mol-'1' PTocess
Temperature (K)
ArrD
A#
TAP
Methane in benzene to water Memane in ether to water Methane in CCi, to water Methane in cyciahexane to water Methane in 1.4-dioxan to water Methane in methanol to water Methane In ethanol to water Argon in Mexane to water Argon in ethanol to water Argon in ethanediai to water Ethane in benzene lo water Ethane in CCil to water Ethane in ethanol to water Ethylene in benzene to water Acetylene in benzene to water Propane (liquid) to water butane (liquld) to water Benzene (liquid) to water Toluene (liquid) to water Ethylbenzene (liquid)to water m or pXylene (liquid) to water
298 298 298 298 298
10.88 13.81 12.13
-11.72
-22.44 -23.69
298 298 298 298
298
298 298 298 298 298 298 298 291 291
291 291
(1) Mixtures of lower aliphatic alcohols, such as methanol, ethanol, and prapanol with water all show positive deviations from Raoult's law indicating AGQ 0 when the alcohol molecule is transferred from the pure alcohol (less polar) phase to water. The process is found to he exothermic (@ < 0), which means that the unitary entropy decreases on such a transfer (AS' = (@ - AGo)IT< 0). (2) Solubilities of a number of liquid aliphatic derivatives (for example, diethyl ketone, diethyl ether, diethylsulfide,ethyl acetate, n-hutanol, heptanal, ethyl bromide, n- and isopropyl chlorides and bromides) in water decreases as the temnerature is raised. This means, h i Le Chatelirr's principle, that &C < U for the transfer prorewand low solubilitirsat higher temperature*(AG'> 01is due u, the negative entropy of mixma.
I t had been shown unequivocally by Butler (7)that this entropy effect is caused by changes in the aqueous phase when nonpolar molecules were added, rather than by changes in the nonpolar phase. The probable origin of the large negative entropy change was first clearly stated by Frank and Evans (8)that the presence of apolar solute molecules caused an increase in the order of the water surrounding the solute. This postulate of increased structure provides a qualitative explanation of the negative AS0. Glew (9) showed the existence of close similarities between the thermodynamic properties of methane clathrate hydrate and those of aoueous methane solutions. Thus. the most satisfactory way o> rationalizing observed thermodynamic results is t o vostulate that introduction of avolar molecules of residues into water leads to a reduction of the degrees of freedomspatial,orientational,dynamirof the neighhoring water molecules, i.e., water becomes more solidlike. The et'fert is now called hydrophohic hydration. There is a class of crystalline hydrates that rlosely resembles this picture of hydrophobic hydration. Thus, if solutionr of rare gases, hydrocarhons. and sliehtlv oolar molecules are cooled. then the solid phask that separates out does not consist of ice but of a socalled clathrate hydrate in which water provides a hydrogenbonded framework that contains holes or cavities that are occupied by solute molecules. The framework resembles ice in the sense that every water molecule is hydrogen bonded to four other water molecules. but the tetrahedral hydrogen bond geometry of ice is somewhat distorted. his-in t i r n gives rise to the types of cavity structures. Depending on the degree of tetrahedral angle distortion, cavities of different diameters can be created, capable of accommodating guest molecules of different dimensions. Guest molecules are not normally bonded to the water lattice but are free to rotate
-
582
. &
Journal of Chemical Education
7.61
6.05 6.68 6.72 6.50 5.03 0.21 15.90 15.487 10.20 12.22 7.82 21.13 24.48 17.03 19.46 23.01 24.27
Table 2.
-10.04 -10.46 -9.95 -11.89 -7.97 -8.18
-14.90
-9.21 -7.11
-24.94 -22.44
-6.74
-18.70 -8.73 -28.68 -28.68 -17.04 -19.48 -23.13 -24.35
-0.80 -7.53 -4.18 0.00 0.00 0.00 0.00
-22.44
-17.56 -17.94 -14.65
Volume Changes In the TraMler 01 Hydrocarbonsfrom Nonpolar Solvents to Water at 25 OCa Process
MBmane in hexane to methane in water Etnane in hexane to ethane m water Propane, pure lquid to propane in water at 10 atm Benzene, pure liquid to benzene in water
AV irnLlmi\ -22.7 -18 1 -21 0
-6.2
.Ref 5.
inside the cavities. Aqueous solutions of clathrate formers thus suggest that the clathrate hydrate is a realistic model for theihenomenon of hydrophbbic hydration. Thus, the negative TAP values (Table 1) arise from reduction in the allowed degrees of freedom of water molecules in the vicinity of the apolar molecule and reduction in the diffusion rates of such water molecules. A negative AVO (Table 2) in the transfer of hydrocarbons from nonpolar solvents to water implies a net volume shrinkage when the solute is added to water. This is due to the considerable emvtv . . mace . that exists in water due to its four coordinated structure. All that is required when thesolute id introduced is a slight reorganization of this free volume to form cavities capahe of accommodating solute molecules. Linear dependence of CpEon the number of CHz groups in solute molecules was found for several homologous series (Fig. 1). Positive sign of CPEsignifies that the specific heat of water in the presence of solute molecules is much higher than the specific heat of ordinary water. This means introduction of the solute into water eives rise to structures that are thermally more labile than is pure water; here again the clathrate model seems to fit the data. I t is to be noted that aromatic hydrocarbons are considerably less hydrophohic than a l i ~ h a t i chvdrocarbons with the same number of carbon aioms (6):~he major factor responsible for the difference must arise from interactions with water, that is, the hydrophobicity is less for aromatic compounds, probably because the r electrons lead to stronaer . van der Waals interactions with water molecules. Hydrophoblc Interactions Since the solution of an apolar group in water is accompanied by an unfavorable entropy change, Kauzmann (5)considered that there would be a tendency for the apolar groups
/-
0 ROH Successive curves om diaploced upwards bv about 8 0 J Imo1.~)-' Figure 2. Excess partial molar volumes of representative solutes In aqueous solutions as function of solute conesn~atian(ref 6).
FOWO 1 Llmklng panlai molar excess heat capacnles of several homologous S e l w as funct'on of the number of carbon atoms in the alryl chain (ref 6 )
Table 3. Thermodynamic Palr lnteradlon Coenlcfents tor Ethanol and Urea In Aqueous Solutions at 25 'C (J mot-' (mol
of the solutes t o come in contact with one another in solutions lessening their area of contact with water. This tendency of apolar groups t o come together in aqueous solutions and t h k rninirniie energetically unfavorable interactions interartion. As such it with water is termed the hydrophobic . . is one of the important factors in micelle formation and in hydrophobic column chromatography, a novel methodology for the purification of a variety of biological and industrial materials. At fairly low temperatures, the strength of the hvdronhobic interactions increase as the temnerature is incieaseb. This is in marked contrast t o the behavior of normal chemical honds. Whereas the phenomenon of hvdroohobic hydration is reflected in the limiting thermodynamic solution pro~erties,the concentration dependence of various thermod-ynami quantities provides iniormation about solute association effects. A general way of formalizing such interactions is by means ofpower series expressions of thermodynamic quantities in terms of solute concentration called the virial expansion (uirialcomes from the Latin word for force). Thus for the free energy A
.
where the virial coefficients g22, g222, . . express the contributions to GE (excess free energy) by pair, triplet, etc., molecular interactions. Similar equations can he written for all other excess nronerties. For dilute solutions onlv the first term contrib&s'significantly to GE.In terms of free energy, introduction of n o n ~ o l a rmolecules into water is a hiehlv unfavorable process. In order to minimize unfavorable water solute interactions. solute molecules interact ~referentiallv. thus reducing the number of their solvent contacts. ~ h u s & ; should be negative. According to this picture second virial coefficients Tszz, hzz, uzz, etc., should all have the opposite signs of those of the corresponding properties associated with hydrophobic hydration. This is found to be the case (Tahle 3) and has given rise to the seemingly obvious conclusion that the hydrophohic interaction is a partial reversal of the entropically unfavorable hydration process. Concentration dependence of VzEallows the differentiation between hydrophobic solutes and solutes that are predominantly polar. For the former class of compounds 6VZE/
-
ka-')-V Coefficient
Ethanol
Urea
62%< 0, whereas for the polar compounds this derivative is positive. This is also the type of behavior one would expect if the hydrophohic interaction were simply a partial reversal of hydrophobic hydration, i.e., solute-solute contacts replacing solute-water contacts. Figure 2 combines the excess data for a variety of solutes in aqueous solutions. These data do not conform t o the reversal model and raise doubts about its validity. Minima in the curves indicate that the negative limiting VzE values become more, not less, pronounced as alcohol concentration increases. i.e.. shrinkage of the mixture per mole of added alcohol becomes great& u p to a point with increasing concentration. In terms of the clathrate hydrate model this means that two adjoining water cavities are more stable than two isolated cavities when both are occupied by a guest molecule. The effect is more pronounced for larger solute molecules. Eventually the sign of 6VzE/6x2reveries and V2E(x2)then approaches zero. Presumably a t some given solute concentration there will no longer he enough water molecules left to provide a fully intact cavity structure. Alcohol molecules will then be able to interact directly, water being "squeezed out" and relaxing to its normal configurational state. Net attractive interactions between solute molecules are also observed in solvents other than water and also for polar solutes in water (6).One can therefore define ageneralsolvophobic interactions the criterion of which is t h a t gzz < 0. Differences between this general effect and the hydrophohic interactions are illustrated in Table 3, which summarizes the various pair interaction parameters. Negative g22 parameters for the two solutes are of the same order of magnitude, Volume 66
Number 7 July 1989
583
indicating that in solutions there is a net attraction between pair of solute molecules. The net attraction arises from a very different origin, with urea behaving in the normal, expected way, while ethanol exhibits the symptoms of hydronhobic interaction. Computer experiments, together with the ah initio molecular orbital (MO) calculations have been carried out both for pure water and an infinitely dilute aqueous solutions of methanol and tertiary butanol a t 25 O C (10). A number of configurations have been used to obtain average quantities for enerm and various distribution functions. I t is found that withintroduction of one alcohol molecule, the potential energy and structure of water tend t o stabilize as a whole. Such stabilization in energy and structure show angular dependence, owing t o anisotropic nature of the alcohol-water interactions. Calculations for several reeions classified according to the direction from the alcohol&olecule have been attempted t o examine the contribution of hydrophilic and hydrophobic regions to the total hydration structure. The hvdronhilic region as a whole does not show a large energetic s~abil~zation, though pair distribution function closely indicates larger hydrogen-bonding interactions for some water molecules in this region. In contrast to this, the hydrophobic region is characterized by large overall energy stabilization as a result of the sum of a large number of smaller interactions. Strong hydrogen bondings in the hydrophilic region seem to act coo~erativelvwith the structure stabilization in the hydrophobic region-to form a fairly stable hydration structure around alcohols. Hvdronhohic hvdration of tertia. . ry butanol is found to he far more prono&ced than that of methanol, perhaps because the tertiary hutanol molecule is bulky and the three-dimensional hydration shell around i t can be more stable hv fixing nearby water molecules firmly with hydrogen bandito tertiary butanol. The position and orientation of a water molecule may be specified in terms of the coordinates of the mass center (component of a vector) and three Euler angles. The position and orientation ofone such molecule relative wanother may he similarly descrihed in terms of a vector joining the twu mass centers and differences in the Euler angles. The nair distribution function fl10for pure water is a measure of the orobnhilitv that two molecules will simultaneouslv take uo particulapspatial positions and orientations. he effect df introducing solute molecules must then be expressed in terms of three pair distribution functions, fll (water water), f12 (water solute), and f22 (solute solute). For very dilute solutions fzp is negligible. Therefore, for structure making potential of a solute: (6) fd. = fu + fi2 Thus as the solute is added, the shape of f1lo can be changed t o fll. Simultaneously apeak will probably develop in ftz and in ...~. f.,. If ...~ f.,~, narrows with concentration this indicates structure promotion. Hydrophobic hydration will always he associated with a narrowing of the f,, and a well developed f12 maxima. Hydrophobicinteract& would involve t h e emergence of a new fzp peak and a broadening of fll and flz, and it is t o be exnected. therefore. that f . ~ .would undereo a broadening. ~ h k r eeksts, however, 'gother possibihy, namelv that hvdro~hobicinteractions take d a c e with f i l remaining either &hanged or actually exhibiting a further narrowing. However, fll and any changes in fil due to the presence of a solute molecule can be monitored by the diffusional motions of the two species in solutions by the NMR (nuclear magnetic resonance) techniques. The criterion of "structure promotion" in the solvent relates fls to Dl (diffusion coefficient) and the correlation time 71 (average time between collisions for translational motion and the average time for rotation by 1rad for rotational motion; correlati& times depend on factors such as temperature, size of molecule, shape of molecule, and the viscosity of the solution). Structure promotion changes the shape andlor peak posi584
Journal of Chemical Education
Figure 3. RDtational conelationtimes r of 'H and "0 in water and acetone (as indicated)as function ol acetone concentration. Broken lines refer to 5 ' C and drawn lines to 25 'C. Concentration C' corresponds to lhe acetone clalhrate hydrate stoichiornnry (ref 6).
tion of some of the pair distribution functions in such a manner that there is a net narrowing in f,,l,. This in turn would lead t o a decrease in Dl and to a lengthening of rl. Aqueous solutions of acetone, methanol, ethanol and pyridine showed their hydrophohic character in NMR studies (6). Figure 3 provides an example of this approach for the system water acetone. The two upper curves describe rl of 'H of water only. The lower three curves show the rotational diffusion behavior of the acetone molecule, measured both by 'H and ' 7 0 NMR relaxation. Five important conclusions can be drawn from the results: Initial addition of acetone to water leads to a slowing down of rotational diffusion of the water molecules, hut, as acetone concentration is increased. the effect eraduallv.dissooears. .. (2) This inhibition of the rotational motion of water is very sensitive to temperature. (3) Hardly any correspondingslowingdown of the acetone molecule is observed, in fact, acetone, despite its larger size, rotates more rapidly than do water molecules. (4) Only a very slight temperature effect is observed for the rotational correlation time of acetone. (5) The similaritv of values for 'H and 170maenetic relaxation rates " in acetone suggest that the acetone molcculr in aqueous sohtimx performs isotropic tumhling motions. (1)
The picture that emerges is this: when acetone is added to wate;, the diffusional motions of the water molecules are inhibited, but there is no corresponding inhibition to the motions of acetone. The activation energy for rotational diffusion of water is large, hut that of acetone is close to zero. The values for acetone diffusion lie close to values associated with the diffusion of acetone in the dilute vapor state or as a guest molecule in the crystalline clathrate hydrate. All these findings are completely compatible with the cavity model of the hydrophobic effect. The composition denoted by C* and the arrow in the figure corresponds to the stoichiometric composition of the acetone clathrate hydrate. This suggests that the actual "structures" in aqueous solutions of hydrophobic solute species are fairly rudimentary and incompleteiy formed, some of them requiring a smalle; number ofwater molecules than does the stoichiometric crystalline clnthrate. This conclusion is consistent with the computer simulation study of hydrophobic interactions.
Figure 4. Diagrammatic representation of (a)hydrophobic hydration and (b-e) hydrophobic interactions; (b) Kauzmann-Nemethy-Scheraga contact interactions. (c) globular protein folding. (d) proposed iongrange interactions, and (e) possible stabilization of helix by interactions as in (d) (ref 1fl.
Concluding Remarks I n this article I discussed t h e physical basis a n d current understanding of t h e hydrophohic effects. Though t h e model described above explains many observations reasonably well. t h e oriein a n d t h e details of t h e effect a r e n o t universally a i c e p t e d r ~ h e r ea r e many questions left for t h e researchers t o address i n t h e future. Amone manv existine controversies, a few a r e a s follows:
-
(1) Statistical mechanical studies, computer simulation experiments, and the thermodynamic excess functions, both at infinite dilutions and a t finite concentrations, suggest that the twin phenomena of hydrophobic hydration and hydrophobic interactions reflect structural changes in water induced by chemical groups that
are unable to participate in hydrogen bonding, although its dependence on concentration is not yet well understood. Once the importance of hydrophohie association to protein stability and other phenomena were realized, the natural way of specifying such an interaetion was to consider it a partial reversal of the solution process. At high concentrations in substantially nanaqueous environments, such as exist in mieelles, lipid hilayers, or the interior of globular proteins (Fig. 4), this model no doubt accounts well enough for observed behavior, but in predominantly aqueous environments, where it is suggested that hydrophobic groups are stabilized not by contact interactions, but by long-range interactions (water acting as a cement). Such a model of long-range hydrophobic interactions might well be able to account for helical structures of certain homopoiypeptides in aqueous solutions, the existence of which is still somewhat of a puzzle. (2) AGO for n-hutanol and tetrahydrofuran is 9.83 and 7.17 kJ/ mol a t 25 'C (11). The difference is due not so much to the lower AS0 of tetrahydrofuran as to its much more negative @.Various investigations of the role played by differences in the configurational entropy of cyclic and normal compounds are on record, hut the matter remains to be clarified. (3) Concentration dependence of some thermodynamic properties of some simple dilute aqueous solutions does not appear to be compatible with the model for solute association of hydrophobic interactions. At higher concentrations, the higher order terms of virial coefficients are important, and the minima in the VSE(x2) curves are hard to interpret. If the temperature dependence of VzE(xz) are examined, these are found to be extremely complex and difficult to exnlain. (4) Statistical mechanical studies of alkane solubilities in HzO and D20 indicate that hydrophobic interactions in H20 are stroneer. althoueh the reverse is the case far benzene. Both @and ASO arefound & he oositive in all cases. and the matter remains to he explained. It is aiso n
