INT. J. QUANTUM CHEM.: QUANTUM BIOLOGY SYMP. NO. 1. 21-32 (19741

Quantum-Mechanical Studies of Environmental Effects on Biomolecules.

III. Ab Initio Model Studies of the Hydration of Peptides and Proteins

Abstract

Ah initio SCF calculations on the hydration of the peptide linkage and of the hydrophilic amino acid side chains of proteins are used to cvaluate the binding energies and the most likely positions of the water molccules of the lirst hydration shell. The results are compared with the very scarce available experimental data.

Introduction

As part of a systematic series of theoretical investigations of solvation phenomena. we report here the results of ab initio calculations pertinent to the hydration of proteins and their constituents. Other papers in this series have considered the peptide unit itself [ I , 21 and the nucleic acid bases [3].

The hydration of amino acids and peptides is of obvious importance in relation to the structure and properties of proteins and enzymes. Experimental information about the interaction of water with polypeptides has been obtained recently from water absorption isotherms [4]. deuteron magnetic relaxation [ 5 ] , and nuclear magnetic resonance studies of “unfreezable water” in proteins [6 ] . These experiments are generally interpreted to give a figure for the average number of water molecules associated with each amino acid residue in the polypeptide. The deductions from these different methods are not always in agreement, however. and do not reveal either how the water molecules are disposed. A related question of interest, to which no answer seems available, is the relative importance of the peptide linkages and the hydrophilic side chains in the overall hydration process.

In this paper we present theoretical computations of the interaction energies between water and the most favored hydration sites of (a) the peptide linkage itself, and (b) the hydrophilic amino acid side chains most commonly occurring in poly- peptides.

0 1974 by John Wiley & Sons. Inc. 21

22 PORT AND PULLMAN

Method Since most of the amino acids represent systems too large for a rigorous ab initio

quantum-mechanical study of their hydration, we resort to model systems in an exploratory investigation of polypeptide-water interactions.

Thus to study the hydration of the peptide linkage we take the formamide dimer as a model. The antiparallel dimer of formamide has the two peptide units hydrogen bonded in the same fashion as in an r-helical or P-sheet protein structure. The only significant difference is the replacement of the c( carbon atoms in the polypeptide by hydrogen atoms in the formamide dimer. Since it has been shown [2] that the essential characteristics of the hydrates of formamide itself are maintained in N - methylacetamide, the model used here appears justified. The side chain groups in amino acids will similarly be mimicked by smaller molecules containing the same essential functional groups.

Ab initio calculation of such model systems, apart from its immediate relevance to the model compounds themselves, provides a basis for prediction of hydration characteristics of polypeptides in the absence of particular steric effects.

The interaction energies are calculated by comparing the energies of the “super- molecule” (model compound plus water) with the sum of those of the isolated com- ponents. The calculations are performed in the standard ab initio SCF procedure using the program Gaussian 70’ utilized with a “foreign basis,” namely, the (7s 3p/3s) Gaussian basis contracted to a minimal set which has been used in or previous studies of formamide [l, 8-10]. It must be kept in mind that this basis set over- estimates hydrogen-bond and electrostatic interaction energies relative to the most accurate ab initio calculations. (For the hydrogen-bond energy in water-water interaction the overestimation factor is about 4/3 [l]). In this work, however, we are essentially concerned not with the absolute values of these energies, but with the comparison bet ween different sites and modes of hydration and these relative energies we expect to be reliable.

The bond lengths and angles used in the calculations are taken from standard compilations of x-ray structures [l 11.

Results and Discussion

A. The Peptide Linkage The dimer of formamide representative of the hydrogen-

bonded peptide linkage in proteins is the “linear” dimer in which the carbonyl oxygen of the first molecule is hydrogen bonded to the NH bond tmrts to the carbonyl group of the second as in Structure I. The configuration represented corresponds ideally to the relative disposition of two antiparallel chains of a P-pleated sheet structure, the relative disposition of two parallel chains being deduced from Structure I by a 180’ rotation of the second formamide around the CO.. . . .HN axis. In fact, in the real structures a slight tilting of the two planes occurs. On the other hand the configuration corresponding to the z helix is obtained by an intermediate rotation of about 120’.

(a) The jbrmamide dimer.

HYDRATION OF PEPTIDES AND PROTEINS

H H

/ H-N C- 0

23

\ H

I

A detailed SCF study of the antiparallel dimer I has previously been performed in our laboratory using a small Gaussian basis set [12]. Since we utilize in the present investigation a more extended basis, we have recomputed the quantities relevant to our problem and summarize briefly the essential data. For a linear arrangement of the four C, 0, H, N atoms, the maximum computed hydrogen-bond energy is - 6.4 kcal/mole at an 0-N separation of 2.91 A. In fact, this is not the most favorable arrangement for a formamide dimer. By rotating the second monomer in the plane of the first around the oxygen atom, a maximum of the interaction energy is reached at - 8 kcal/mole for a clockwise rotation of 88' (Figure 1). A rotation in the opposite direction does not yield any other maximum. due presumably to the greater steric crowding involved. However, as in the early computation [12] the energy variations remain small over a very wide angular range, and in particular the neighborhood of the linear arrangement corresponds to a rather flat plateau on the energy surface. Furthermore in this arrangement the energy of the hydrogen bond is practically insensitive to the mutual orientation of the two peptide planes [9]. It is thus not surprising that the linear or nearly linear configuration is the most widely encountered in proteins where a compromise must be reached between a number of factors con-

A € (kcal /mole)

t I 8

I

0 30 60 90 *

Figure 1 . Variation in energy of interaction of two formamide monomers with angle of rotation.

24 PORT AND PULLMAN

tributing to the overall stability, although this would not be the configuration prefer- red by an isolated formamide dimer.

(b) Hj.dratioii of’the hjdrogeiz-bonded carbonyl group. According to the preceding discussion we started with the linear dimer I at an 0.. . .N separation of 2.91 and searched for possible hydration sites by moving a water molecule around the dimer.

Taking as a guide the results obtained in our former work on formamide itself [l], we have explored in detail the possibility of water binding on both sides of the already present 0. . . .HN bond. The equilibrium positions found for the monomer hydrates were chosen as starting points. A first exploration showed the unlikelihood of water acting as proton acceptor to the already bound NH group. (Binding to the other NH is irrelevant to the situation in proteins.) Binding to the carbonyl appeared possible and a detailed search for the most stable positions of water was performed, starting with the equilibrium 0. . . .O distance and polar angles found in the monomer hydrates. The search included variation in the polar angle, with optimization of the 0.. .O distance in the region of the best angular position, as well as a rotation of the water about the H-bond axis. (Small departures from 0.. .HO collinearity have not been explored as they were shown in [ 13 to yield only small energy gains unim- portant in our present problem.) The previous computations had shown a very small likelihood for the oxygen atom of water to lie out of the molecular plane of the formamide molecule to which it is bound, but in the intermediate region crowding might have favored an out-of-plane fixation. This possibility was tested but was found unfavorable.

As a final result of the search, two stable positions (Figure 2) were found in which the water molecule acts as a proton donor to the already hydrogen-bonded carbonyl oxygen. In the most favorable one ( A E = - 7.1 kcal/mole, C-6-H = 90 , 0-0 = 2.85 A), on the more open side of the dimer, the water molecule is coplanar with the proton acceptor (a result also found in other studies [ 1,3]), but a rotation of its nonhydrogen-bonded hydrogen can occur relatively easily. In fact, a secondary energy minimum ( - 5.7 kcal/mole) exists on the energy surface for a COH angle of 80- at the same distance and with the second hydrogen of water rotated by 90 out of the plane. On the other side of the carbonyl oxygen, steric crowding from the rest of the

/ H

\ H

Figure 2. Linear antiparallel dimer of formamide showing the most favorable hydration sites with their calculated interaction energies (kcalimole).

HYDRATION OF PEPTIDES A N D PROTEINS 25

molecule forces the water to lie perpendicular to the plane of the dimer, minimizing the nonbonded hydrogen-hydrogen repulsions. The optimum position occurs again for a C-0---H angle of 90 and a calculated hydrogen-bond length of 2.85 A. Its energy is - 5.8 kcal/mole.

Thus the calculations show that a water molecule can still form reasonably strong hydrogen bonds with the carbonyl group already involved in the hydrogen bond of a formamide dimer, the supplementary binding energy being of the same order of magnitude as that of the dimer in the linear configuration.

The positions of the two hydration sites found for the dimer are very similar to those found previously for the formamide monomer [l] (see Table I). The presence of the second monomer manifests itself in (i) decreasing the hydration energy, (iii) increasing the hydrogen-bond length, (iii) modifying slightly the COH angles.

Effects (i) and (ii) are those expected for a branched trimer where two proton donors are attached to the same proton acceptor [see Section A (c)].

As mentioned previously, in the ct helix of proteins the two peptide units are in fact not coplanar as we have considered but at about 60' from each other (Figure 3). It seems unlikely that this modification would significantly alter the above con- clusions. In fact, due to a reduction of nonbonded interactions one might expect a slight increase of H-bond energy relative to the planar case. This is confirmed by calculation; the H-bond energy for the more stable position of the water molecule

TABLE 1. Characteristics of the hydration sites of a formamide dimer compared to the corresponding ones in a monomer.

0 AE(kcal/mole)

M 2.82 88 -9.G a

m 1 D(in) 2.e5 90 -7.1

D( end) - 2.85 80 4 . 5 a

M 2.82 72 4 . 5 a co I1

D 2.85 90 b

-5.6

M 2.85 - -7.1 NH( trans)

D( end) - 2.85 4 .1

D - dimer [(in)--hydration on the inner carbonyl group. (end)-hydration on the end carbonyl or NH group]; M-monomer; R-distance 0-0: 0-rotation around the carbonyl oxygen starting from the linear arrangement (I-clockwise rotation: 11 --counterclockwise rotation): AE-stabilization by hydration.

"HOH in the formamide plane. 'HOH perpendicular to the formamide plane (see text). ' HOH perpendicular to the formamide plane and bisected by NH.

26 PORT AND PULLMAN

I HCR

I I

Figure 3. The relative positions of the peptidc planes in an r helix.

shown in Figure 2 increases to - 7.4 kcal/mole in the twisted dimer. Note that in the I-helix the second position of Figure 2 cannot be occupied by water for steric reasons.

The calculations predict therefore that an a-helical polypeptide with no hydro- philic side chains may nevertheless have associated with it a "background" level of water bonded to the peptide units. This is supported by experimental measurements [13, 141, although the nature of the interaction was not clearly understood (see, e.g.. [4, p. 1301). It can now be simply ascribed to hydrogen bonds between water and the carbonyl oxygen of the peptide unit. A recent confirmation of the ability of an already hydrogen-bonded peptide carbonyl to further hydrogen bond water can be found in the crystal structure of o bromo carbobenzoxy-glycine-L-proline-L-leucine- glycine-L-proline ethylacetate monohydrate [ 151, where the water is seen to act as a double proton donor to two carbonyl oxygens, one of which is hydrogen bonded to an NH group.

At each terminal of an r-helical structure three peptide units are hydrogen bonded on one side only by their CO or their NH group so that they are available for hydration on their free side. (The same situation exists for the last polypeptide chain in a pleated sheet structure.) We have thus also considered the possibilities of fixation of a water molecule at either end of dimer I. It was found that the NH (trnns to CO) end hydration brings about a stabilization of - 8.1 kcal! mole while CO end hydration yields a stabilization of - 8.5 kcal/mole (only the most stable configuration was studied). The carbonyl end hydration remains nearly the same as in the monomer and appreciably larger than the corresponding inner hydration, whereas the NH end hydration is easier than in the monomer. These results (summarized in Table I) indicate that in these compounds dimerization makes further H bonding more favorable on the proton donor side but not on the proton acceptor side, contrary to the situation observed for simpler molecules like (H,O), [ 161. It may be observed that considerations based on global charge displacements upon dimerization would lead to incorrect prediction on this cooperativity. Thus the oxygens of both the inner carbonyl and the outer carbonyl groups in the form- amide dimer show a global gain in electron with respect to the monomer (0.408. 0.403, and 0.383 excess of electron charge, respectively) which might lead to expect

(c) End hj.dration.

HYDRATION OF PEPTIDES AND PROTEINS 27

both oxygens of the dimer to be better proton acceptors than that of the moncjmer, contrary to reality. In fact, the global gain in charge is not the appropriate quantity to consider in these compounds where the decisive role in the binding is played by the cr electrons of the oxygens [12]. The cr net charges are 0.068, 0.089, and 0.089 respectively, thus showing no gain on the end oxygen and a loss on the inner one in keeping with the fact that the end oxygen shows no enhancement of binding, and the inner one shows a decrease of it. At the NH end, no such interplay of o and 71 charges occurs and the positive charge on the hydrogen. larger in the dimer (0.333) than in the monomer (0.321), acts here fully to enhance H bonding.

B. A d Side Chriiris-H!.riratioii of’ Fornzic Acid aiid of the Formate Ion.

Formic acid was used as a model for the hydration of union- ized carboxyl side chains. The four most favorable modes of interaction with water are shown in Figure 4. By far the most advantageous situation corresponds to water acting as a proton acceptor in forming a hydrogen bond with the hydroxyl group. The in-plane symmetrical approach of water along the line of the hydroxyl group gives a minimum in the total energy of the complex at an 0-0 separation of 2.65 A where the calculated interaction energy is - 11.2 kcal/mole. In the present basis at least, tilting the water molecule to align a lone pair with the direction of the hydro- gen bond does not improve the energy, as the increase in nuclear repulsion is greater than the gain in electronic energy.

As in the case of formamide there are two hydration positions on the carbonyl group with water acting as a proton donor. On the more open side a maximum inter- action energy of -6.1 kcal/mole is calculated when the 0-0 distance is 2.85 A and the C-0-H angle 90 . On the other side of the carbonyl group some H-H repulsion is evident, as the maximum energy is reduced to - 4.9 kca1,’mole and the C-0-H angle increased to 110-, again, at 2.85 A. Finally with water as proton donor to the hydroxyl oxygen the weakest interaction ( - 4.1 kcal/mole) occurs at a C--0-H angle of 90 and for the 0-0 distance of 2.85 A.

(a) Unionizeri Licid.

L - 4.1

-11.2 L

Figure 4. Hydration sites in formic acid with their calculated energies of interaction (kcal mole).

28 PORT AND PULLMAN

On the whole, the hydration of the carbonyl group is less favorable in formic acid than in formamide, whether isolated or dimeric. But the end OH group is a much better proton donor to water than the NH of formamide. These features would most likely be retained in a real carboxylic side chain (-CHI),-COOH, compared to a real peptide bond. Thus comparison of N-methylacetamide to form- amide [ 2 ] has shown that the effect of the methyl groups is essentially to decrease the binding energy to water in all positions and to repel the water molecules closer to the CO axis. A similar although snialler effect may be expected for the binding to the CO group of a (CHz),--COOH side chain, whereas little effect should be felt on the most favorable OH binding.

The formate ion may be expected, on account of its charge, to interact much more strongly with water than does the unionized formic acid. The three possible hydration sites are shown in Figure 5 and the calculated energies also given there bear out this expectation. There are two equivalent sites on the carbonyl groups at the exterior of the molecule. The calculated minima occur with very short hydrogen-bond lengths of 2.65 A. and with ( 2 4 . . .H angles of 1 1 0 , giving an interaction energy of - 22 kcal/mole in each case. This is a strong increase over the energy found for the corresponding interactions with an uncharged carbonyl group. Moreover, at the interior of the molecule one water molecule can form a bridge between the two oxygen atoms and this gives an interaction energy of - 25 kcal/ mole. Here again the presence of a (CH,), substituent instead of the formate hydrogen may decrease the binding in the first two positions and perhaps decrease the COH angle, but is unlikely to affect the bridged position.

The calculations thus predict a carboxylate ion to be much more energetically favorable to hydration than a neutral carboxyl group. There is a quantitative spreading among the available experimental results, but the trend is clearly indicated: Breuer and Kennerley [4] and Kuntz [6 ] agree on two molecules of water per residue for polyglutamic acid. Allowing one water molecule for the peptide linkage (as found in polyglycine) this leaves one water molecule for complexing with a COOH group. In the ionized species Watt and Leeder [17] suggest that COO- complexes two water molecules and Kennerley and Breuer’s results for polysodium glutamate also imply two water molecules on the COO- group. Kuntz, on the other hand, indicates 7.5 water molecules per residue of glutamate, again allowing one for the peptide

(b) Ionized acid.

H

Figure 5. Hydration sites in the formate ion with their calculated energies of interaction (kcalimole).

HYDRATION OF PEPTIDES AND PROTEINS 29

Figure 6 . Hydration sites in ethylamine with their calculated energies of interaction (kcal, mole).

link. This suggests COO- complexed with six or seven water molecules. The very strong interactions predicted by our calculations suggest that the formate ion might influence a second shell of water molecules, and this might perhaps explain the high number found by Kuntz.

C . Basic Side C1iuiii.s- Hydration of' Ethylamiize aid Ethj*lommonium loit

Water can approach ethylamine either as a proton donor on the lone-pair side of the amine nitrogen, or as a proton acceptor toward the NH. A search for the most stable positions has led us to the results summarized in Figure 6. Only a small stabilization energy of - 3.3 kcal/mole at a N - 0 distance of 3.15 hi is found for the approach to NH, but a larger stabilization energy of - 6.3 kcal/ mole occurs on the lone-pair side for N-0 = 2.85 hi. Similar results were obtained for ammonia-water hydrogen bonding [ 181. Clearly aliphatic amines make stronger hydrogen bonds with water through their nitrogen lone pair than through their NH bonds. This is confirmed, for example, by crystal data analysis. In ammonia hydrate [19] and hydrazine hydrate [20] short (2.8 A) hydrogen bonds to water are seen on the lone-pair side of the nitrogens and long ones (3.15-3.2 A) on the NH side.

Note that this behavior is opposite to that of a planar conjugated amine group where the 71 hydrogen bonding of water to the nitrogen lone pair has been found negligible compared to the water binding to the NH bond [ 11.

(b) Charged species. The hydration of ethylammonium ion has a significance reaching beyond the chemistry of proteins since many important families of drug molecules (e.g., the histaminic,. cholinergic, and adrenergic series) contain the ethyl- ammonium group, In an - - ( N H , ) + "cationic head" the positive charge is mainly on the NH protons (+ 0.45 a.u. in ethylammonium) and this gives rise to strong direct interaction with the oxygen of water along the NH bond. Our computations (Figure 7) yield a maximum energy of - 27.8 kcal/mole for the N-H.. .OH, hydrogen bond with a rather short N-0 separation, 2.60 A at the minimum.* Tilting the water

(a) U/iclirrrgnl species.

-.

*Aside from the direct N H binding of water. Figure 7 shows the binding energies in the "axial" and "bisecting" positions corresponding to the hydration sites found in alkylanimonium ions [22]. Although nonnegligible. these ionic interactions are less favorable than direct hydrogen bonding.

30 PORT A N D PULLMAN

-14.4/--

Figure 7. Hydration sites in ethylammonium ion with their calculated energies of inter- action (kcal mole).

molecule so as to direct a water lone pair in the line of the hydrogen bond brings no improvement in the energy. With three nearly equivalent sites of this kind an ethyl ammonium head would appear as an exceptionally hydrophilic group. The formation of three strong hydrogen bonds by the ammonium groups is in fact in agreement with the interpretation of their nuclear magnetic resonance spectra given by Fraenkel and Kim [21].

It appears thus surprising that in their measurement of water binding to proteins, neither Breuer and Kennerley nor Kuntz found a significant difference in hydration between polylysine and polylysine hydrobromide, implying that three water molecules are associated with an amine side chain indifferently to whether it is charged and quaternary or not.

We have explored the possibility that the single effective hydrogen bond formed by ethylamine acting as a proton acceptor on its nitrogen lone pair may cause a sufficient transfer of charge to sensitize the molecule to further hydrogen-bond formation. Calculations do in fact confirm that the ethylamine-water complex in which the water donates a proton to the lone pair forms a subsequent hydrogen bond more easily than the isolated ethylamine molecule (4.1 kcal/mole instead of 3.3). The difference is, however. still not enough to make what would be considered as a hydrogen bond of an average strength.

D. Alipliatic m d Aromatic H.1~lrox.1~1 Groups- Hydration of'Ethcino1 and p-Cresol

Ethanol affords a good model for the serine side chains. It behaves toward water similarly to ethylamine, except that being a stronger acid and a weaker base it is more effective as a proton donor and less effective as a proton acceptor. Thus, as summarized in Figure 8, water acting as proton acceptor forms a fairly strong hydro- gen bond of - 7.3 kcal/mole at an 0-0 distance of 2.85 A (compared with - 3.3 kcal/mole for ethylamine). As a proton donor to the oxygen lone pair water forms a weak hydrogen bond of - 4.8 kcal/mole at 2.85 A (compared with - 6.3 kcal/mole in ethylamine).

p-Cresol. which was adopted as a model for tyrosine, has an oxygen with a 7c lone pair in conjugation with the benzene ring. It forms both proton donor and proton acceptor hydrogen bonds more strongly than does ethanol (see Figure 9).

HYDRATION OF PEPTIDES AND PROTEINS 31

H

H P 7

Figure 8. Hydration sites in ethanol uith their calculated energies of interaction (kcal mole).

0-H

CH3 Figure 9. Hydration sites in p-cresol with their calculated energies of interaction (kcali mole).

/CH

-1 0.0 \

Thus water as a proton acceptor in the direction of the phenolic OH bond has an interaction energy of - 10.0 kcal/mole at an 0 4 separation of 2.75 8. As a proton donor it has an interaction energy of - 6.2 kcal/mole with a C 4 - H angle of 110' (see formic acid) and an 0-0 bond length of 2.85 A.

Thus we predict aromatic -OH groups to be more hydrated than aliphatic ones. This is in accord with the results of Watt and Leeder which indicates that serine complexes one water molecule while tyrosine complexes two.

Conclusion

The intrinsic affinities for water of the various groups considered in this paper are summarized in Table 11. As has been discussed in detail, these values provide an acceptable basis for the evaluation of the number of water molecules susceptible to form the first hydration shell around these groups. In proteins, both the peptide linkages and the hydrophilic side chains represent active hydration sites.

32 PORT A N D PULLMAN

TABLE 11. Cdlcuhted equilibrium distances and energies of interaction of water with various amino acid side chain groups.

030- N I L L O &@ UH OH OH NH2 a i i p h n t i c amioe amide acid acid d1i;lhatic drornetic

Mter B - 25 2Z6 2ad 6.3 1.8 9 . 2 ; ~ 6 . 1 ; ~ 4.1 4.E G.2 6.5

pr-ton donor b - 2-55 2.85 3.35 2.Eii;Z.W 2.E5i2.85 2.85 2.85 2.85

mtrr 2 28 3.3 7.7;7.1 - 11.2 7.3 10.0 as

p r c t m a c c w t o r t 2.60 3.15 2..53;2.E5 - 2.65 2.E5 2.75

"Binding energy (kcallmole). *Equilibrium distance. NO or 00 (A). Bridge.

"Carbonyl. "Reference [ I ] (without taking into account small refinements due to nonlinearity of

A-B.. .H-C. for consistcncy with the present study).

Acknowledgment

This work was supported by the C.N.R.S., A.T.P. A655-2303.

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[lo] A. Pullman, Chem. Phys. Lett. 20. 29 (1973). [ I I] L. E. Sutton. "Interatomic Distances." Spec. Publ. Chem. SOC. I I (1958): 18 (1965). [I21 M. Dreyfus and A. Pullman. Theor. Chim. Acta 19, 20 (1970). [I31 E. F. Mellon. A. H. Korn. and S. R. Hoover. J. Amer. Chem. SOC. 70. 3040 (1948). [I41 M. M. Breuer. J. Phys. Chem. 68,2067 (1964). [I51 T. Ueki. S. Bando, T. Ashida. and M. Kakudo. Acta Cryst. B 28,2219 (1971). [I61 D. Hankins, J. Moskowitz. and F. Stillinger. Chem. Phys. Lett. 4, 527 (1970). [I71 1. C. Watt and J . D. Leeder. J. Text. Ins. 59, 353 (1968). [I81 P. A. Kollman and L. C. Allen. J. Amer. Chem. SOC. 93,4991 (1971). [I91 I. Olovsson and D. H. Templeton. Acta Cryst. 12, 827 (1959). [20] R. Liminga and 1. Olovsson. Acta Cryst. 17, 1523 (1964). [?I] G . Fraenkel and J. P. Kim. J. Amer. Chem. SOC. 88,4203 (1966). [22] G. N. J. Port and A. Pullman. Theor. Chim. Acta 31, 231 (1973).