Hydration of peptides. I. Calculation of accessible surface areas for several conformations of a cyclic dipeptide

J. theor. Biol. (1980) 87,71-84

Hydration of Peptldes. I. Calculation of Accessible Surface Areas for Several Conformations of a Cyclic Dipeptide M. GENEST, F. VOVELLE AND M.PTAK~ Centre de Biophysique Moltkwlaire, C.N.R.S., lA, avenue de la Recherche Scientifique, 45045 Orlkans Cedex, France B. MAIGRETAND

S.PREMILAT

Laboratoire Nancy-

de Biophysique Molkulaire (ERA 828), Giversite’ 1, Case oficielle 140, 54037 Nancy Cedex, France

(Received

22 October 1979, and in revised form 18 March

de

1980)

The concept of “static accessibility” to water has been used to determine the accessible surface area of a cyclic dipeptide: C(L-Thr-~-His). Different calculated and experimental conformations of this model molecule have been examined, which allows us to analyse the variations of accessibility of the hydration sites localized on the peptide backbone and on the polar side chains. The maximum solvation criterion involves a large destabilization of conformations governed by intramolecular interactions. The variations of the amphiphilic character with the conformations are relatively small. Nevertheless, the experimental conformation seems to reflect such a behaviour, especially in the crystal, in which the amphiphilic character is compatible with intermolecular interactions. The accessibility studies must be regarded only as a preliminary step to a more quantitative analysis of peptide hydration.

1. Introduction In an attempt to describe quantitatively the extent to which atoms located on the surface of a solute molecule can form contacts with the solvent, Lee & Richards (197 1) introduced the concept of “static accessibility” describing the relationship of globular proteins to water. A similar concept was introduced by Hermann (1972,1977) in his theory of hydrophobic bonding in which the solubility of hydrocarbons in water was empirically correlated with the solvent cavity surface area. Additional concepts, such as “contact” and “re-entrant” areas and their “sum molecular” area were then introduced by Richards (1977) to estimate the surface roughness. The accessible t From

whom

reprints

must be requested. 71

0022-5193/80/210071+14

$02.00/O

@ 1980 Academic

Press Inc. (London)

Ltd.

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surface area of a protein has been shown to be directly related to hydrophobic energy (Chothia, 1974, 1975), and its relationship with the real volume and the shape of the macrcmolecule has been discussed (Gates, 1979; Greer & Bush, 1978). The first application of the above concepts to small peptides has been done recently by Ponnuswamy & Manavalan (1976) and Manavalan & Ponnuswamy (1977). As pointed out by these authors, the accessibility concept can give only rough information about the possibilities of solutesolvent association, and could be compared with the earlier “hard sphere” calculations describing the allowed conformational space of peptides (Ramachandran & Sasisekaran, 1968). In the course of a general study of peptide hydration, we have examined different aspects of solute-solvent interactions, including the qualitative aspect based on solvent accessibility and a more quantitative one based on calculations of interaction energy. This paper reports the study of accessibility to water of the cyclic dipeptide C(L-Thr-~-His) for which several experimental and theoretical studies have already been presented (Cotrait et al., 1976; Ptak, Dreux & Heitz, 1978; Genest & Ptak, 1976, 1978; Vovelle & Ptak, 1979). This molecule was found to be a suitable model for peptide hydration studies, especially focused on the behaviour of polar side chains. Even for this small molecule, examination of the surface topology for different conformations, and determination of exposure of particular sites to solvent, can give useful information on hydration properties of these side chains. Furthermore, the amphiphilic character of such a molecule, though not very marked, may contribute to determining its stable conformations. 2. Methods

The so-called “static accessibility” to the solvent is estimated from the accessible surface area of each atom of the solute molecule settled in a given conformation. The atomic accessible surface area of an atom i is the area of the surface of a sphere of radius Ri on each point of which the centre of a solvent molecule can be placed in contact with this atom, without penetrating any other atoms of the molecule. Ri is given by the sum of the van der Waals radius ri and the radius of the “spherical” solvent molecule r,. In the present calculations, the set of atomic van der Waals radii used is that given by Bondi (1964), i.e. 1.7 8, for carbon, 1.52 8, for oxygen, 1.55 A for nitrogen and 1.20 A for hydrogen atoms. The radius of the envelope sphere of water molecule has been calculated with these van der Waals radii and is r,,, = 1.97 A. This value is greater than those used elsewhere (Lee &

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Richards, 1971; Hermann, 1972; Chothia, 1975; Greer & Bush, 1978; Janin et al., 1978; Finney, 1978), but the results are not significantly modified by such variations in the choice of r, . The atomic accessible surface area associated with each atom of the solute molecule is calculated by spherical trigonometry. The imidazole ring of the His side chain of the solute molecule is taken in its more stable tautomeric configuration (NE-H”). In a first step, a possible correlation between accessibility and hydration sites has been looked for. For this purpose, only four conformations of lowest intramolecular energies were considered among all the stable conformations previously obtained from calculations in vacuum (Genest & Ptak, 1976,1978) (Table 1). In two of them (A and B conformations) the His TABLE

1

Conformations of the four lowest intramolecular energy states (A, B, C, D) (Genest & Ptak, 1976, 1978) (optimized with the use of X-ray data), and of the crystal structure (Cotrait et al., 1976). Rotational x1 angles of the four states I-IV Conformations

of lowest

A Xi

Thr

XT X:

His

;;

B

energy C

Crystal D

structure

59.4” 65.2” 61.1”

62.0’ 297.8” 61.2’

57.9” 177.1” 61.3”

57.0” 175.9” 61.2”

69.6’ 242.0” 60.0”

76.7” 245.5”

38,0° 120.7”

307.0” 336.8”

291.3” 26.9”

305.0” 100~8”

Four I

representative

conformations II

III

!V

XI Thr

60”

300”

300”

60”

x1 His

60”

60”

300”

300”

and Thr side chains are folded above the diketopiperazine (DKP) ring, whereas in the two others (C and D conformations), the His side chain protrudes outside the DKP ring, the Thr side chain remaining in a folded state. These conformations, previously obtained by using standard geometry, were optimized here by using X-ray data for bond angles and bond lengths. In addition to these four forms, the conformations found in the crystal were also considered (Cotrait et al., 1976), as also was a calculated

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form in which a water molecule interacts simultaneously with the two side chains (Vovelle & Ptak, 1979). In a second step, in order to determine the maximum accessibility of each polar group, a larger set of conformations was examined. Therefore, four different representative conformations (Genest & Ptak, 1976, 1978) denoted states I-IV were selected, which combine folded forms (x1 = 60”) and unfolded forms (x2 = 300”) of the Thr and His side chains (Table 1). State IV is close to the crystal structure. The variations of the accessibility of polar atoms were calculated by rotating these side chains around the Cp -Cy bonds (x2 angles) and the corresponding accessibility maps were then drawn. The useful regions of these maps were delimited by enforcing a rule of steric hindrance. Close contacts were found for state I (60”, 60”) (Fig. 1) where the two folded side chains can interact when the x2 angles change, and to a lesser extent for state II (300”, 60”), although all conformations were allowed for states III and IV. Nevertheless, the regions of minimum stability were reported on the accessibility maps (Fig. 2). In a third step, the amphiphilic behaviour of the dipeptide defined by the ratio of the accessible surface areas of the atoms involved respectively in polar and nonpolar groups was analysed for the previous four states. The limitations due to close contacts and the regions of low stability were also reported on the corresponding table (Table 4). 3. Results (A)

ATTEMPT

AT

LOCALIZATION

OF

ACCESSIBILITY

HYDRATION

SITES

FROM

STUDY

Atoms of the solute molecule which interact strongly with water molecules are those establishing hydrogen bonds. In c(L-Thr-L-His), there are four proton acceptor atoms, CQ His, CO Thr, N&His, FH Thr, and four proton donor atoms, NIJ His, NH Thr, N”H” His, OH” Thr. HCCI l-IN*-C

N’ ~ \B ,C H

CO-NH Hz-C’H( NH-CO’

\

CH3 C’H -C’H’

\

OyHy

The atomic accessibilities are given in Table 2. A maximum accessible surface area of 50 A’ is found for the two CO atoms. The folding of the His side chains reduces the accessibility of the CO His for the A conformation and that of the CH Thr for the B conformation. As expected, the accessibility of the NH Thr does not depend on the position of the His side chain,

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2 Atomic accessible surface areas (A 2, of the four selected conformations (A, B, C, D) and of the crystal structure of c(L-Thr-L-His) TABLE

Accessible Stable Atoms C” C 0 N H C” CO H” C’ 0 N H H” C6 ,“: ,“s ;; CY CS HS N’ H’ C’ H’ NS ,“p”

Residue

Thr His His His His His His His Thr Thr ‘Thr Thr ‘Thr ‘Thr Thr rhr Thr Thr Thr His His His His His His His His His His

1 1 : 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2

surface

area (A’)

conformation A

, A

B

C

D

Crystal

0.14 4.27 49.91 2.51 26.02 0.32 0.81 24.57 4.31 41.76 2.16 15.74 18.90 0.00 5.71 3.07 14.53 29,25 31.61 7.09 16.94 2.79 8.57 14.41 3.54 35.16 11.35 40.80 20.53 24.41 21.62

0.14 4.27 46.12 2.51 19.96 0.32 0.86 24.08 4.31 49.80 2.16 16.96 19.21 0.00 2.20 1.57 18.93 29.13 34.02 7.33 16.84 2.53 8.59 16.45 3.54 40.12 11.58 41.18 21.02 15.81 28.18

0.14 4.44 51.21 2.51 10.85 0.32 0.35 18.68 4.57 50.83 2.16 17.48 18.72 0.00 31.08 9.13 20.76 29.21 30.30 7.30 15.93 1.88 15.89 34.76 7.08 43.78 18.98 41.90 11.91 6.76 20.87

0.14 4.50 51.23 2.61 11.45 0.32 0.64 19.84 4.65 50.50 2.16 17.59 18.61 0.00 31.18 11.03 20.82 29.31 30.34 7.32 15.75 2.67 17.92 35.07 7.08 43.78 22.27 41.90 6.78 10.05 14.08

0.14 4.21 50.19 2.51 13.78 0.32 1.41 16.62 4.41 50.68 2.16 16.40 20.11 0.00 20.18 15.88 17.62 28.94 31.98 7.11 18.77 3.14 12.78 31.71 6.87 43.78 18.91 41.90 16.06 8.46 17.80

whereas the accessibility of the NH His is maximum (26 A2) for the A conformation and minimum (10-l lx”) for the C and D conformations. The C conformation leads to a N”---H-N His interaction which explains this weak value (Genest & Ptak, 1976, 1978). In the folded A and B states, the accessibility of the Q”H Thr atom is strongly reduced because of the screening effect of the His side chain. A similar screening effect is observed for the OH” Thr in A and B conformations. It may be noted that, for the crystal form, the accessible surface area of 0” atom is 16 A’.

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For the His side chain, the accessibility of N&H’ does not mainly depend on the conformations, whereas that of NS His% reduced in the C and D conformations. This first analysis reveals two important features: (a) the accessibility of the polar atoms of the DKP ring is generally large and is only slightly influenced by the conformations of the more mobile His side chain; (b) the accessibility of the polar atoms of the two side chains strongly depends on their conformational state, except for the NEBE atom of the imidazole ring. (B)

CALCULATION

OF

THE

MAXIMUM

ACCESSIBLE

SURFACE

AREAS

For states I-IV, the values of maximum surface areas of the polar atoms determined by varying both x2 angles are reported in Table 3. The accesTABLE

Maximum

3

accessible surface areas of the polar atoms of c(L-Thr-L-His)

(A ‘)

States I

II

III

IV

Polar atoms of the side chains

NS His QYH Thr OHY Thr NT@ His

25.2 2.5 10.7 41.8

28 34.5 27.5 43

28.1 37.7 30.7 43.7

28 32.5 33.0 43.8

Polar atoms of the DKP ring

CO NH CQ NH

47 25 SO.5 16.5

49 26.6 37.7 21.7

50.7 14.5 37.7 22.0

50.7 14.5 51.2 17.2

His His Thr Thr

sibility maps are obtained by drawing the iso-accessible surface area curves by 1 A2 steps, the maximum being taken as the origin. The maps corresponding to NS His, Q”H Thr, OH7 Thr and N”B’ His atoms are represented in Fig. 1, for state I. For this state, the theoretical maximum values of accessibility are on the outside of the sterically allowed region. Similar maps are given in Fig. 2 for the NS His, Q”H Thr and OH’ Thr atoms of the dipeptide in state IV. For this state, there is no sterichindrance; a region of less favourable intramolecular energy coincides with a region of maximum accessibility of the N8 atom. Some common features emerge from these two sets of maps. The accessibility of the Q”H Thr and OH’ Thr atoms vary in opposite directions when the x2 Thr angle is changed (Figs 1 and 2),

HYDRATION

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(a)

(b)

0

240

300

360

60 His

120

180

240 X,” His

0

60

P’H

Xg His

0 N*tj’

I

300

360

0

60 05’

120

0

Thr

Thr

240

300

360

300

360

X; His

120

180

240 XG His

FIG. 1. Accessibility maps (x2 His, xz Thr) of polar atoms associated with state I. (a) NS His. (b) QYH Thr. (c) N’H” His. (d) OH7 Thr. The bifolded conformation A has been localized on the maps. The iso-accessible surface area contours are drawn by 1 A* steps from the maximum value (X) taken as the origin. The iso-accessible surface area contour (- - - -) equal to 12 A2 is also represented (see discussion). Only the regions located between F 4 are sterically allowed.

likewise the accessibilities of the N’ His and N’K His atoms when the x2 His angle is changed (Fig. 1). Theoretically, the allowed conformations offering the best accessibility of the solvent for all the polar groups should be localized in a region determined by the overlapping of the individual regions of maximum accessibility. It is obvious that one cannot find a conformation which accounts for a simultaneous maximum accessible area for all hydration sites. The better compromise is found for the semi-folded state IV by combining the optimum accessibilities of the N” His and OH_’ Thr atoms (Fig. 2).

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. ._ ----.- ..__ 1 ~____._____... --'_'..-.- .'. ...._ -_,--,,..... '.

240

---c

180 t D

Q7H Thr

-:

Xg His

The accessible surface area of the N’ !-j‘ His atom IS constant

240

01 0

60 O@Thr

120

I 180

240

300

I 360

Xs His

FIG. 2. Accessibility maps (xl His, ,ya Thr) of polar atoms associated with state IV. (a) NS His. (b) 07H Thr. (c) NW His. (d) OH_T Thr. The semi-folded conformations C and D have been localized on the maps, as the crystal one (0) and the most stable calculated conformation of the hydrated di eptide (m) (Vovelle & Ptak, 1979). The iso-accessible surface area contours are drawn by 1 A II steps from the maximum value (x) taken as the origin. The iso-accessible surface area contour (- - - -) equal to 12 A2 is also represented (see discussion). The region of maximum intramolecular energy is indicated by a.

(C)

AMPHIPHILIC

PROPERTIES

A criterion for the maximum solvation of polar groups is certainly not sufficient to determine the conformations which could exist in water. Indeed, other groups of the molecule, like CH, CH2 and CH3 groups, may interact with the solvent, inducing so-called hydrophobic effects. The amphiphilic character of the dipeptide will then be defined by the overall hydrophilichydrophobic balance expressed, for example, by the ratio of the accessible

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surface areas of the atoms contained respectively in polar and nonpolar groups. The tables of the accessible surface areas of all the atoms of the molecule are determined by varying the x2 Thr and x2 His rotational angles, and the ratios between the accessible surface areas of polar and nonpolar atoms are thus calculated. The results are presented in Table 4. The value of the maximum ratio (1.13) is weak for the folded state I, compared with that obtained when the two side chains are in an open state III (1~54). When the Thr side chain is not folded over the DKP ring (state II), the maximum value of the ratio (1.50) occurs for x2 His = 300” and ,y2 Thr = 210-270”. The most interesting case is state IV for which the maximum occurs when x2 His = 120-150”, x2 Thr = 150-240” with a ratio equal to 1.41, It is quite clear that the study of the amphiphilic character of the molecule allows determination of conformational regions other than those previously found from the maximum solvation study. The crystal structure, reported on the hydrophilic-hydrophobic map, shows that it corresponds to a region of maximum ratio. Then, for the solid state, it seems that the molecule has a conformation consistent with its amphiphilic character and allowing optimal intermolecular interactions. 4. Discussion The determination of accessibility gives only a qualitative view of the different possibilities of the solvation of the molecule. Roughly, there are various competitive processes which determine the hydrated solute conformation. (a) Optimization of short intramolecular interactions, as calculated for an isolated molecule in vacuum. Such a process stabilizes compact conformations (bifolded conformations) or those involving hydrogen bonds (semi-folded conformations). (b) Maximum solvation of polar groups, as determined previously. (c) Optimization of the amphiphilic character which partly includes organization of solvent around the solute molecule. The occurrence of the second process is well illustrated by a comparison of the stable conformations in vacuum and those offering the best accessibility to the solvent. According to the results reported in Table 3, the unfolding of the His side chain strongly increases the accessibility of both side chains. A maximum of accessibility is reached when the Thr side chain is also unfolded (state III). The intramolecular interactions favour a bifolded conformation (x1 Thr = 60”, x1 His = 60”) while the interactions with the solvent are

Thr

II

0”

60”

120”

180”

240”

300”

360”

Sme

0”

60”

120”

180”

240”

300”

360”

StareI

x2

4

I 0”

60”

120”

180”

,y2 His

Ratios between the sum of the accessible surface areas of the hydrophilic

TABLE

240”

and hydrophobic

1.44 1.47 1.49 1.50 1.50 n 1.50 1.48 l-46 1.45 1.44 1.43 1.43 1.44

300”

1 1 1 1 1 1 1 1 1 1 1 1 1

atoms for states I-IV

1 3 5 6 5 5 3 2 1 1 0 9 1

360”

t \

1.23 1.25 1.27 1.29 1.30 1.30 1.30 1.30 1.29 1.27 1.25 1.24 1.23

1.32 1.35 1.37 1.37 1‘37 1.37 1.38 1.38 1,37 1.35 1.32 1.31 1.32

1.20 1.21 1.23 1.26 1.27 1.26 $27 1.27 1.26 1.23 1.21 1.20 1.20

1.29 1.32 1.34 1.34 1.34 1.34 1.35 1.35 1.34 1.32 1.29 1.28 1.29

1.24 1.25 1.27 1.29 1,30 1.30 1.30 1.30 1.28 1.26 1.24 1.24 1.24

1.35 1.37 1.39 1.40 1.39 1.40 1.40 1.41 1.40 1.37 1.35 1.33 1.35

1.29 1.30 1.33. 1.35 1.36. 1.36 1.36 1.36 1.34 1.31 1.29 1.29 1.29

1.42 1.45 1.47 1.47 1.47 1.47 1.48 1.48 1.48 1.45 1.42 1.41 1.42

1.39 1.36 1.34 1.34 1.34

1.34 1.35 1.38 1.40

R 1.50 1.47 1.46 1.47

1.47 1.50 1.52 1.53 1.53 1.53 1.53

1.39 1.36 1.34 1.33 1.33

1.33 1.35 1.37 1.39

1.51 1.50 1.48 1.45 1.43 1.45

1.45 1.48 1.50 1.50 1.50 1.50 1.51

1.25 1.27 1.29 1.31 1.32 1.32 1.32 1.32 1.31 1.29 1.27 1.26 1.25

0 2 4 6 7 7 7 7 6 4 2 1 0

1.23 1.24 1.26 1.28 1.30 1.29 1.30 1.30 1.28 1.25 1.23 1.23 1.23

1.35 1.37 1.39 1.40 1.40 1.40 1.40 1.41 1.40 1.37 1.35 1.33 1.35

1.27 1.29 1.31 1.33 1.34 1.34 1.34 1.34 1.32 1.29 1.27 1.27 1.27

1.43 1.45 1.47 1.48 1.48 1.48 1.48 1.49 1.48 1.45 1.43 1.41 1.43

1.30 1.31 1.34 1.36 1.37 1.37 1.37 1.37 1.35 1.32 1.30 1.30 1.30

1.45 1.48 1.50 1.50 1.50 1.50 1.51 1.51 1.50 1.48 1.45 1.44 1.45

1.29 I.31 1.33 1.35 1.36 1.36 1.37c 1.37 1.35 1.33 1.31 1.30 1.29

1.41 1.43 1.45 1.46 1.45 1.46 1.46 1.47 1.46 1.43 1.40 1.39 1.41

1.23 1.25 1.27 1.29 1.30 1.30 1.30 1.30 1.29 1.27 1.25 1.24 1.23

1.32 1.35 1.37 1.37 1.37 1.37 1.38 1.38 1.37 1.35 1.32 1.31 1.32

t The most stable conformations calculated in vacuum A, C, D, the most stable conformation of the hydrated cyclic dipeptide (m) [Thr OH . . Hz0 . . . Imidazole His (Vovelle & Ptak, 1979)] and the crystal structure (0) are reported on the maps. For states I and II, the hatched regions are sterically forbidden. For states III and IV, the hatched regions correspond to the higher values of the intramolecular energy. They are determined by the xz angle values (200-220” for state III, 200” for state IV).

0”

60”

120”

180”

240”

300”

360”

State IV

O0

60”

120”

180”

240”

300”

360”

State III

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maximum for the extended conformations (x1 Thr = 60” or 300”, xl His = 300”). An optimization of the accessible surface area of the side chains’ polar groups can also require variations of the x2 angles. For the bifolded conformation A, the accessible surface area of the N’ His and CH atoms are relatively high (Fig. 1). On the other hand, the best exposure of the NeHE atom requires a large x2 rotation of the His side chain. The semi-folded conformations C and D, as well as the conformation found in the crystal, are far from the maximum accessible surface area regions of the N” His and QYH Thr atoms (Fig. 2). Following the hydration mode of both side chains, large x2 rotations can occur which destabilize the C and D conformations. As previously said, the amphiphilic character of the dipeptide determines other conformational regions than those required for a maximum of accessible surface areas. Experimental conformations account partly for the different types of solute-solvent interactions. The crystal structure corresponds to a conformation of intermediate accessibility for which N” His and Q”H Thr atoms have about 16 A’ of accessible surface area. Note that this value is in the same order of magnitude as the approximate minimum value corresponding to a contact between the hydration sphere and an atom (about 12 A’). The insertion of a water molecule between the two side chains is compatible with accessibilities of N’ His and CH Thr only slightly larger than this minimum. That suggests a well optimized packing of atoms in the crystal. In the crystal, as well as in aqueous solution, the Thr side chain is folded k1 -60-70”) (Cotrait et al., 1976; Ptak, Dreux & Heitz, 1978). Such a conformation was found as the most stable one by minimizing the intramolecular energy (Genest & Ptak, 1976). The hydration of the OH group and the interactions of the hydrophobic CH3 group with water as well as the intermolecular interactions occurring in the crystalline lattice are then compatible with such a folding. In solution, the His side chain is partly unfolded because of the hydration of the N6 and NdHe atoms. This unfolding, not complete, accounts for the competition between various processes: maximum solvation, folding governed by intramolecular interactions, bridging of the two side chains through a water molecule, optimization of the hydrophilic-hydrophobic balance. In the crystal, these two last processes are compatible with the formation of a regular lattice. All the previous criteria determining solute-solvent interactions are qualitative and do not allow prediction of the right structure of the global system. An approach would be to account for the energy of these interactions by considering especially the length and the directivity of the hydrogen bonds.

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83

5. Conclusions The so-called “static accessibility” concept applied to small molecules confirms the conclusion given by Ponnuswamy: the method allows prediction in a qualitative manner of the hydration scheme of a molecule, as the “hard sphere” model can predict the sterically allowed conformations. In the particular case of c(L-Thr-L-His) for which we have a set of different conformations (calculated conformations in vacuum, calculated conformations including internal water molecules, experimental conformations observed in solid state and in solution), the study of accessibility to the solvent allows us to understand the various processes occurring for the solvation of a molecule. The maximum hydration of polar groups generally requires an important destabilization of the conformations determined by intramolecular interactions. This process seems to be attenuated when the amphiphilic character of the solute molecule is taken into account. Nevertheless the amphiphilic criterion must be used with precaution. Indeed, for a small molecule, the hydrophilic-hydrophobic balance is only slightly influenced by the conformational changes. Furthermore, for a larger molecule, the correlation between the accessible surface area and the free energy of the solvent has been subject to criticism (Hildebrand, 1979). Another approach, more quantitative, is presented in the following paper, in which the stability of the various hydration sites are determined (Vovelle ef al., 1980). REFERENCES BONDI, A. (1964). J. phys. Chem. 68,441. CHOTHIA, C. (1974). Nature 248,338. CHOTHIA, C. (1975). Nature 254,304. CHOTHIA, C. & JANIN, J. (1975). Nature 256,705. COTRAIT, M., PTAK, M., BUSEITA, B. & HEITZ, A. (1976). I. Amer. Chem. Sot. 98,1073. RNNEY, J. L. (1978). J. mol. Biol. 119,415. GATES, R. E. (1979). J. mol. Biol. 127,345. GENES-I’, M. & PTAK, M. (1976). Biocbem. biophys. Res. Commun. 68, 1174. GENEST, M. & PTAK, M. (1978). Int. J, Peptide Protein Res. 11, 194. GREER. J. 8~ BUSH, B. L. (1978). Pmt. nad. Acad. Sci. U.S.A. 75,303. HERMANN, R. B. (1972). J. phys. C&em. 76,2754. HERMANN, R. B. (1977). Proc. mtn. Acad. Sci. U.S.A. 74,4144. HILDEBRAND, J. H. (1979). Proc. nati. Acad. Sci. U.S.A. 76, 194. JANIN, J. & CHOTHIA, C. (1978). Biochemistry 17,2943. JANIN, J., WODAK, S., LEVITT, M. & MAIGRET, B. (1978). J. mol. Biol. 125,357. LEE, B. & RICHARDS, F. M. (1971).J. mol. Biof. 55,379. MANAVALAN, P. & PONNUSWAMY, P. K. (1977). Biochem. J. 167,171. PONNUSWAMY, P. K. & MANAVALAN, P. (1976). J. theor. Biol. 60,481. F’TAK, M., DREUX, M. & HEITZ, A. (1978). Biopolymers 17, 1129.

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RAMACHANDRAN,G.N.& SASISEKARAN,~.(~~~~). Adv.Protein Chem.23,283. RICHARDS, F. M. (1977). Ann. Rev. Biophys. Bioeng. 6, 151. VOVELLE,F.,GENEST,M.,PTAK,M.,MAIGRET,B.& PREMILAT, S(198Ob.J. theor. Biol. 87,

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VOVELLE, F. & PTAK, M. (1979).

Int. J. Peptide

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Res. 13,435.