374

Biochimica et Biophysica Acta, 537 (1978) 374--379 Q Elsevier/North-Holland Biomedical Press

BBA 38059 A CONTRIBUTION TO THE DEBATE ABOUT HYDROPHOBIC EFFECTS

AASE HVIDT Chemistry Laboratory III, H.C. ~)rsted Institute, University of Copenhagen, Copenhagen (Denmark)

(Received June 2nd, 1978)

Summary Based on available measurements of the concentration dependence of the volume and the heat capacity of aqueous solutions of low molecular weight compounds it is suggested t h a t non-polar molecules or non-polar groups in aqueous solution fluctuate between solvated and non-solvated states. The experimental data indicate that the change in standard free energy of the hydrophobic solvation is positive and so large that the solvation is incomplete even in the most dilute solutions studied. It is tentatively suggested that the hydrophobic solvation enhances the solubility in water of non-polar substances, and that the reason why non-polar groups in protein solutions are buried in the interior of the protein conformations is a low degree of solvation of these groups in the solvent exposed state.

Introduction The experimental observation that the changes in standard molar entropy and enthalpy of the transfer (at room temperature) of non-polar substances from non-aqueous to aqueous media are both negative has led to the conception t h a t non-polar molecules (or non-polar groups) in aqueous solution are solvated by structures of water with a lower energy and a lower entropy than pure water (the s o , a i l e d 'ice-like' water structures, or Frank-Evans 'icebergs') [1,2]. The 'ice-like' water structures are assumed to have a larger specific volume than pure water and it has been suggested [3] that the decrease of the apparent molar volume of the solute with increasing concentration {which is characteristic of dilute aqueous solutions of, for example, alcohols [4--9], ketones [6], or alkylamides [6]) is due to an overlapping in the solutions of cospheres of bulky water surrounding the alkyl groups of the solute molecules. In the discussion of recent volumetric investigations [9] it was pointed out, however, that this concentration dependence of the volume is so strong that it can

.375 hardly be explained by overlapping effects. Alternatively, it is suggested that alkyl groups (--R) in aqueous solution fluctuate between solvated and nonsolvated states --R + n H20 ~ - - R ( H 2 0 ) , (AH ° < 0, AS ° < 0, AV ° > 0 ) .

(1)

The volumetric data indicate that the hydrophobic solvation is a highly cooperative reaction (the order of magnitude of n is 10), and that the equilibrium constant of the solvation g -- [--R(H20)n ] [--R] [H:O]"

(2)

is a b o u t 5 5 - " (mol • dm-3) -n. For this value of K the degree of solvation of the alkyl groups [--R(H20),] P = [ - - R ( H 2 0 ) , ] + I--R]

(3)

at the lowest concentrations studied (where [H20] ~ 55 mol • dm -3) is a b o u t one half, and the solvation equilibrium is extremely sensitive to changes in (water) concentration, temperature or pressure [9]. The concentration dependence of the volume and the heat capacity [7] Of dilute aqueous solutions of low molecular weight substances are in accordance with the existence in the solutions of equilibria like formula 1. In the following the implications of such equilibria for the solubility of non-polar substances in water, and for h y d r o p h o b i c interactions in aqueous protein solutions are discussed. T h e s o l u b i l i t y o f n o n - p o l a r s u b s t a n c e s in w a t e r

In pioneer papers on hydrophobic effects [1,2], it was explained that the transfer of non-polar substances from non-aqueous media to water is an exothermic process (AH ° ,: 0). The low affinity of non-polar substances for w a t e r is associated with exceptionally large, negative changes in standard e n t r o p y ( A S ° < 0, so that A G o = A H ° - - T A S e ~ 0), most likely due to structural changes of the water introduced b y the solute. Direct investigations of the conditions in aqueous solutions of purely nonpolar substances (for instance, the alkanes) are hampered b y the low solubility, and studies of the concentration dependence of hydrophobic effects are therefore limited to solutions of substances which contain both polar and non-polar groups. The experiments with such solutions which indicate that the change in standard free energy of the hydrophobic solvation is positive ( A G e ~ n R T In 55 for Eqn. 2), m a y cause a reconsideration of the conditions in solutions of purely non-polar substances. The dissolution of a non-polar molecule, R, in water m a y be considered as a two-step process transfer

R (in non-aqueous m e d i u m ) , -

solvation

~ R (in water) ~

' R(H20)n (in water)

(4) In the reaction scheme above, and in the following, the term 'transfer' refers

376 t o the t r a n s f e r o f a n o n - p o l a r substance f r o m a n o n - a q u e o u s m e d i u m t o a nonsolvated state in water. Due t o the strong association b e t w e e n the molecules in liquid w a t e r the changes in standard e n t h a l p y and free e n e r g y o f the transfer process are positive, i.e., (A/~transfe -

-

r >>

0 , A S t r0a n s f e r

0 TAStransfer

>•

>

0, and

A V t r0a n s f e r

= A/_~transfe r

0) .

The solvation is assumed to o c c u r in equilibria like f o r m u l a 1, i.e.

Ags0olvation < 0, ASs°olvation < O, and AG°olvation ~ n R T In 55 ~ 10 n kJ • tool -1 at r o o m t e m p e r a t u r e . T h e value 55 in the e x p r e s s i o n o f AG o m u s t n o t be t a k e n t o o literally; it is n o m o r e t h a n an a p p r o x i m a t e value o f t h e m o l a r c o n c e n t r a t i o n o f w a t e r in v e r y dilute a q u e o u s solutions. Fig. 1 illustrates the degree o f solvation, p , as a f u n c t i o n o f the w a t e r conc e n t r a t i o n , calculated a c c o r d i n g t o f o r m u l a 3 for n = 10. T h e equilibrium (1), u n d e r l y i n g the calculation o f p , is u n d o u b t e d l y an oversimplification o f the solvation process. T h e solvation does p r o c e e d as a series o f stepwise additions o f w a t e r m o l e c u l e s t o the solute, and h y d r a t e s with d i f f e r e n t values o f n are p r e s e n t in the solutions. T h e f o r m u l a t i o n (1) f o r n = 10 and K ~ 5 5 - " ( m o l • dm-3) - n , h o w e v e r , emphasizes t w o characteristic features o f the h y d r o p h o b i c solvation: (1) t h e h y d r o p h o b i c solvation process is a highly c o o p e r a t i v e react i o n b e t w e e n m a n y w a t e r m o l e c u l e s , and (2), the c o n c e n t r a t i o n d e p e n d e n c e o f the solvation is e x t r e m e l y strong at low solute c o n c e n t r a t i o n s , i.e. at w a t e r c o n c e n t r a t i o n s o f a p p r o x . 55 m o l • d m -3 * T h e solubility, S, o f the substance R in w a t e r is the sum o f the c o n c e n t r a t i o n o f solvated and non-solvated R m o l e c u l e s in the s o l u t i o n u n d e r c o n d i t i o n s w h e r e the n o n - s o l v a t e d m o l e c u l e s are in equilibrium with R in the pure state. A t s a t u r a t i o n we have [a]saturatio

n = M

exp(--AG°transfer/RT)

w h e r e AGtransfer 0 is the d i f f e r e n c e b e t w e e n the chemical p o t e n t i a l o f (nonsolvated) R in the s t a n d a r d state in the s o l u t i o n and in t h e p u r e state. M is the sum o f the m o l a r c o n c e n t r a t i o n s o f all species in the solution. It follows f r o m Eqn. 3 t h a t [ R ( H 2 0 ) , , ] = JR]

P 1--p

so the solubility m a y be expressed as M S = [R]saturatio

n + [R(H2O)]saturation-=

1-__ p:at~rr:ti~

n

exp(--AG°transfcr/RT)

(5) •- ~ t m a y he n o t e d t h a t the shape of curves r e p r e s e n t i n g p as a f u n c t i o n of l n [ H 2 O], c a l c u l a t e d a c c o r d i n g t o Eqn. 3, d e p e n d s o n the value of n, o n l y , d p / d l n [ H 2 0 ] = n p ( 1 - - p ) . S o l v a t i o n curves c o r r e s p o n d i n g to t h e s a m e value of n, b u t d i f f e r e n t values of K are parallel. The c o n c e n t r a t i o n of w a t e r at the ' t r a n s i t i o n p o i n t ' , w h e r e p = 1 is [ H 2 0 ] = ~¢r~-

377

0.8 n=lO 0.6

0./*

0.2

0.0

I

I

-0.6 3O

-0.4 I

35

-0.2 I

40

I

/.5

0 I

I

02

0./,

0.6 LnlN20] + [l/n]l~"K

I

50 55 (60)

[H20] I mol,drn -3

F i g . I . T h e degree o f s o l v a t i o n , p , c a l c u l a t e d according to E q n . 3 f o r n = I 0 . The l o w e r scale o f the abscissa specifies the c o n c e n t r a t i o n o f water for K = 5 5 "--n ( m o l • d m - 3 ) - n , n = 1 0 ,

The solvated R molecules are presumably highly soluble in water, so the solubility is determined b y the value of A G t0r a n s f e z , and by the degree of solvation in the saturated solution, Psaturation. The larger the degree of solvation ( A/-~transfer. The degree of solvation, however, decreases with increasing temperature (dp/dT < 0, since ~olvation < 0) SO the sign of the heat of dissolution may become positive at higher temperatures, as is actually found to be the case for saturated solutions of the butanols [10].

Hydrophobic effects in protein solutions The role of hydrophobic interactions in protein conformations is reviewed b y Kauzmann [2]. In this review the transfer of low molecular weight alkanes from organic solvents to water is tentatively suggested as a model of the transfer of non-polar groups from the interior of globular proteins (in the native state) to contact with water (in the denatured state). The limitations of this model are discussed in ref. 2 and in many following papers on the thermodynamics of protein solutions, particularly in discussions of pressure-volume effects [11--15]. In a macromolecular solution a constituent group of a macromolecule shall always be in the neighbourhood of other groups of its own molecule, so the local concentration of solvent molecules around the group is lower than the concentration of solvent molecules in dilute solutions of low molecular weight model compounds. This fundamental difference between macromolecules and

378 low molecular weight models is particularly pertinent to aqueous solutions of substances which contain alkyl groups [13]. When the change in standard free energy of a highly cooperative solvation process is large and positive, such as seems to be the case for the hydrophobic solvation, the solvation phenomena are restricted to dilute systems, and the degree of solvation of the solute depends markedly on the solvent concentration (Fig. 1). It is difficult to estimate the effective water concentration (strictly, the activity of water) near an alkyl group of a macromolecule, except that it is much lower than the water concentration in aqueous solutions of low molecular weight alkanes, and it is, therefore, difficult to exploit data on solutions of low molecular weight compounds to predict the contribution from hydrophobic effects to the stability of protein conformations. In a discussion of the utility of the concept of water structure in the rationalization of the properties of aqueous solutions of proteins and small molecules [16] it was emphasized that although there is experimental evidence in favour of the existence of Frank-Evans 'icebergs' around non-polar molecules in aqueous solution it is an open question to what extent solvent rearrangement dominates the thermodynamic properties of aqueous solutions. It is the aim of the present paper, in continuation of the argumentation in ref. 16 to call attention to available measurements of the concentration dependence of the volume and the heat capacity of aqueous solutions of low molecular weight compounds. The experimental data indicate that the extent of hydrophobic solvation depends markedly on the water concentration and on the temperature. The domination of hydrophobic effects appears to be restricted to dilute solutions, and to decrease with increasing temperature. The negative change in enthalpy and entropy of the dissolution of alkanes in water at room temperature are most likely due to solvation effects, but the state of an alkane molecule in water is n o t representative of the state of an alkyl group in a protein molecule. The reason why most non-polar groups in protein solutions at room temperature are buried in interior regions of the protein conformation can hardly be that these groups introduce entropy-low structures in water when exposed to the solvent. As an alternative explanation it is tentatively suggested that the affinity for water of the alkyl groups in protein molecules is low because of the low probability of hydrophobic solvation (due to the low local concentration of water around the alkyl groups), and because the change in enthalpy of the transfer to a non-solvated state in water is positive. References 1 2 3 4 5 6 7 8 9 10

F r a n k , H.S. a n d Evans, M.J. ( 1 9 4 5 ) J. C h e m . Phys. 13, 5 0 7 - - 5 3 1 K a u z m a n n , W. ( 1 9 5 9 ) A d v . P r o t e i n C h e m . 14, 1 - - 6 3 F r i e d m a n , H.L. a n d K r i s h n a n , C.V. ( 1 9 7 2 ) J. S o l u t i o n C h e m . 2, 1 1 9 - - 1 4 0 F r a n k s , F. a n d S m i t h , H . T . ( 1 9 6 8 ) T r a n s . F a r a d a y Soc. 6 4 , 2 9 6 2 - - 2 9 7 2 F r a n k s , F. a n d S m i t h , H . T . ( 1 9 6 8 ) J. C h e m . Eng. D a t a 13, 5 3 8 - - 5 4 1 B~je, L. a n d H v i d t , Aa. ( 1 9 7 1 ) J. C h e m . T h e r m o d y n . 3 , 6 6 3 - - 6 7 3 deVisser, C., P e r r o n , G. a n d D e s n o y e r s , J.E. ( 1 9 7 7 ) Can. J. C h e m . 55, 8 5 6 - - 8 6 2 B r u u n , S.G. a n d H v i d t , Aa. ( 1 9 7 7 ) Ber. B u n s e n g e s . P h y s . C h e m . 8 1 , 9 3 0 - - 9 3 3 H v i d t , Aa., Moss, R. and N i e l s e n , G. ( 1 9 7 8 ) A c t a C h e m . S e a n d . B 32, 2 7 4 - - 2 8 0 Hill, A.E. a n d Malisoff, W.M. ( 1 9 2 6 ) J. A m . C h e m . Soc. 4 8 , 9 1 8 - - 9 2 7

379 11 12 13 14 15 16

Brandts, J.F., Oliveira, R.J. and Westort, C. (1970) Biochemistry 9, 1038--1047 Hawley, S.A. (1971) Biochemistry 10, 2436--2442 B~je, L. and Hvidt, Aa. (1972) Biopolymers 11, 2357--2364 Zipp, A. and Kauzmann, W. (1973) Biochemistry 12, 4217---4227 Hvidt, Aa. (1975) J. Theor. Biol. 50, 245--252 Holtzer, A. and Emerson, M.F. (1969) J. Phys. Chem. 73, 26--33