The Ribbon of Hydrogen Bonds in theThree-Dimensional Structure of Globular ProteinsPart 1. Theory and a Simple Example
DAVID PETERS AND JANE PETERSDepartment of Crystallography, Birkbeck College, University of London, Malet Street, LondonWC1E 7HX, U.K.
Accepted 17 June 1999
Abstract. We report quantum mechanical computations and experimental evidence which suggestthat the backbone conformation of globular proteins depends generally on the conservation of thatpart of the hydrogen bond network or ribbon which is joined, in general, directly to the backboneand is largely independent of the remainder of this whole network of hydrogen bonds. The familiarhydrogen bonds of theα helix and theβ sheet form about one-half of this ribbon of hydrogen bonds.Both water molecules and hydrogen bonding side chain groups are involved in the formation of theribbon. This view of the three-dimensional structure of globular proteins in terms of the ‘molecule’allows us to deal with the non-secondary structure as well as with the familiar secondary structure.It also suggests that the ribbon contains approximately the same number of hydrogen bonds withinall three structures – theα helix, theβ sheet and the coil – and that this is the reason for the easeof interconversion of these three structures. The quantum mechanical computations on hydrogenbonding suggest that delocalised water molecules which have substantial mobility are an essentialpart of the ribbon. This situation arises because the hydrogen bonding groups of the protein moleculeare not free to move to optimise the hydrogen bonding geometries as are the oxygen atoms in thewaters and ices. Such delocalised water molecules either have highB values or are invisible in theX-ray data and yet are able to form a structure which is as strong as a normal hydrogen bond. Theexperimental data on the point mutations of the THRI57 residue of the T4 phage lysome providesan initial test of this model. Both the local backbone conformation and the ribbon of hydrogenbonds are conserved throughout all the mutations of residue 157, providing that the delocalised watermolecules are accepted as a genuine part of the structure. These mutations include the introductionof hydrocarbon side chains at position 157 when water molecules or other side chain groups takeover the formation of the hydrogen bonds. We suggest that, provided steric effects are not important,many point mutations succeed because they leave the ribbon of hydrogen bonds (and so the backboneconformation) largely unchanged.
The importance of globular proteins in science and medicine has led to an in-tensive search for an understanding of the three- dimensional structure of thesemolecules [1–9]. Many different types of theory have been proposed, ranging fromthe largely empirical [1–6] to the formal quantum mechanical [7–9], but none of
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these approaches seems to have gained universal acceptance in everyday work inthe laboratory and we have attempted to find another approach [10] which is partlyformal and partly empirical and is closely connected with both the well establishedorganic chemistry approach to large molecules [11] and also with the computa-tional methods of the quantum mechanical theory of molecular structure [12]. Theformer requirement seems natural since globular proteins are very large organicmolecules and the latter arises from the fact that it is now generally accepted thatthe structure of molecules is best understood through quantum mechanical meth-ods. In this way, we are able to use familiar methods and terminology of organicchemistry and at the same time retain contact with the formal theory of molecularstructure.
With these ideas in mind, we suggested [10, 13, 14] that networks of hydrogenbonds are the major bonding factor in the three-dimensional structure of the pro-teins, following the early conjecture of Pauling and Corey [15] and the work ofRose and his colleagues [16]. Water molecules are often involved to a major extentin the formation of these networks, as are the hydrogen bonding side chains, butthe important element is the network of hydrogen bonds itself rather than the atomswhich form them. We reported some preliminary quantum mechanical computa-tions earlier [10, 14], together with some experimental data on the global aspectsof the hydrogen bonding networks. We also reported some rough estimates of theenergy quantities which are associated with the networks for a number of globularproteins.
We now go on to study the hydrogen bonding networks in greater detail andthe local structure of the networks in particular. We treat the conformation of thebackbone as the major problem and leave aside for the present the question ofthe conformations of the side chains. The reason for so doing is that there is anatural distinction between the two, in the sense that the backbone is comparat-ively rigid while the side chains are generally more mobile than the backbone. Wemust establish which parts of the network are directly involved with the backboneconformation of the molecule and which parts are not so involved. The methodused was suggested in the first instance by some results of quantum mechanicalcomputations on small model molecules formed by peptides and water moleculesand then by studying the networks which are found in homologous pairs of proteinswhose backbone conformations are essentially the same. The results of these stud-ies clearly suggested that only that part of the network which is directly involvedwith the backbone via hydrogen bonds plays a major role in the conformation ofthe backbone. We refer to this part of the network as the ribbon of hydrogen bonds.The main reason for this conclusion is that the ribbon is broadly conserved betweenhomologous molecules while the outlying parts of the networks are often quitedifferent between homologous molecules [17]. The conserved waters in legumelectin crystals suggest the same conclusion [18]. This ribbon extends over thewhole backbone with only minor breaks so that with it we are able to study the
HYDROGEN BONDS IN STRUCTURE OF GLOBULAR PROTEINS 347
whole of the molecule and not just that part which forms theα helices and theβsheets. These results will be presented in Part 2.
In this paper we concentrate on the simplest possible example of this model,the single point mutation in a residue in a small section of the ribbon where nosteric complications arise and where ample experimental data is available. We arefortunate in having this remarkable collection of data on T4 phage lysozyme whichwas assembled by B. W. Matthews and colleagues [19]. We have examined some50 of these mutations and the simplest case for present purposes is the THR157data where 17 mutations of this residue and closely related residues have beenreported [20]. In all cases, the conformation of the backbone is unchanged fromthat of the wild type molecule. We now show how the experimental and theoreticalresults fit together for this simple case.
The main difficulty in this work derives from the the familiar problem of locat-ing water molecules in the X-ray data for the globular proteins. One of the theoret-ical results reported below suggests that this is not simply an experimental artifactbut is a direct result of the basic properties of hydrogen bonding itself which resultsin water molecules being exceptionally mobile in certain circumstances.
The results of the exploratory quantum mechanical computations are repor-ted in the next paragraph and the relevant results for the THR157 mutations arereported in the following section. Then the comparison between the two sets ofresults is analysed. Finally, the broader aspects of the work and its connection withhomology problems is summarised
2. Quantum Mechanical Results and the Structure of the Ribbon
The following two points in this section show some of the quantum mechanicalresults which first suggested the present interpretation of the three-dimensionalstructure of globular proteins.
2.0.1. The Potential Energy Curve of the Hydrogen Bond
This potential energy curve [21, 22] (the upper curves of Figure 1) apparentlyreproduces the length and strength of the hydrogen bond well despite the modestquality of the abinitio wave function used here [23]. And since it seems likely ongeneral grounds that a type of Morse function will represent the stretching of thehydrogen bond, a curve of this general kind is probably correct.
The result which we need for present purposes is that the hydrogen bond maybe stretched by about 0.5 Å while retaining some 50% (about 2 kcal mol−1) of itsbond energy.
2.0.2. Hydrogen Bonding and Delocalised Water Molecules
Studies of the experimental data on the hydrogen bond networks in globular pro-teins led us to investigate the possibility that while some of the water molecules
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Figure 1. Potential energy diagram for the mobile water structure.Note:. Thex axis showsthe distance of the oxygen of the water molecule from the oxygen of the carbonyl group.The upper pair of curves are the potential energy curve for the stretching of a single hydrogenbond. The solid lower curve is the sum of the two upper curve and the doted curve is a quantummechanical computation of the structure shown above at the 316G level of the Gaussian 90package.
are fixed and have lowB values (10–20 Å2), others are mobile or delocalised andeither have very largeB values (greater than 50 Å2) or are invisible in the X-rayexperiment. Examples are quoted in the following section on experimental data.
The phenomenon may arise as in the following simplified example. If the watermolecule is interposed between two hydrogen bonding protein atoms which areabout 6 Å apart, then two normal co-operatively coupled hydrogen bonds [24–25]are formed with normal lengths. The total energy of this structure will be slightlygreater than that of two separated hydrogen bonds (8–9 kcal mol−1). This is the
HYDROGEN BONDS IN STRUCTURE OF GLOBULAR PROTEINS 349
optimum situation in energetic terms and will lead to a stable water molecule whoseposition cannot be changed greatly without encountering the very steep repulsivepart of the potential energy curves. In other words, in this one-dimensional ex-ample, the water molecule is fixed in space and so has a lowB value (cf. W170 inthe following section).
It may happen, however, that the two parts of the protein molecule are held apartby other and larger energy requirements such as those from theφ, ψ diagram. Ifthis is so and the two protein atoms are held at a distance of say 7 Å apart, as inFigure 1, then it might seem that the water molecule would be forced to chooseone or the other protein atom with which to form its hydrogen bond. This wouldleave the other part of the protein molecule disconnected as far as the hydrogenbonding structure is concerned. If, however, we position the water molecule in themiddle, it is apparently capable of forming two ‘half hydrogen bonds’, as shownin Figure 1. The total energy of the whole structure is then about the same asthat of one fully developed hydrogen bond. Moreover, the two parts of the proteinmolecule are held together by such a structure. This follows (Figure 1) either bysimply superimposing two potential energy curves of the single hydrogen bond(solid line) or by direct computation of the total energy of the structure using thequantum mechanical methods as for a single hydrogen bond (dotted line).
As a result of this situation, the water molecule may move over a distance ofabout 1 Å without appreciable change in the total energy of the system. Moreover,its electron density is spread out, perhaps to the point of making the water moleculeinvisible in the X-ray experiment. This phenomenum of very highB values orinvisibility of water molecules seems to occur widely in the globular proteins (cf.W543 in the following section).
The computations leading to the results shown in Figure 1 are preliminary anddetailed computations on problems in two or three dimensions are required, but thesimple one-dimensional case illustrates the point clearly. It may happen, of course,that two or more water molecule are involved in more complicated problems of thisgeneral kind so that they move inside a larger cavity.
It should be appreciated that there is no connection between the delocalisedwater molecule described here and the effect which is observed [26] under highpressure with waters and ices. In the latter situation, the OH bond itself is changedmaterially as the hydrogen atom assumes a symmetrical position between the twooxygen atoms and this is a higher energy process than that which we discuss here.
3. Experimental Results for Threonine 157 in T4 Phage Lysozyme
This example is the simplest and most complete case of which we are aware con-cerning point mutations in globular proteins. It forms part of a very large set ofX-ray structural data published by Matthews and colleagues on T4 phage lysozyme[27]. This is the simplest possible example of the present theory, concerning only
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Table I. Mutations of residue 157 in the lysozyme of bacteriophage T4
1See Figure 2 for the hydrogen bonding pattern. All mutations are of residue 157 unless other-wise specified.2A + sign means that the group or water molecule is present unchanged in the mutant. A−sign means that it is absent.3The numerical values in column 1 are in Å. They are the standard deviations between the wildtype molecule and the mutants over some ten residues around residue 157. TheB values incolumns 4 and 5 are in Å2.4All the more remote hydrogen bonding remains essentially unchanged throughout the series.
one side chain group which projects outwards from the molecule. Such mutationscause little or no change in the steric situation of the organic part of the structure.
Residue 157 has been successfully mutated 14 times, as shown in Table I. Threeother closely related examples are also shown in the table. This residue is locatedoff the end of the 144–153α helix but is not involved with the helix hydrogen bond-ing. The conformation of the backbone in the native molecule is well conserved inall 17 mutations throughout the section of interest (cf. see table). The diagram ofthe hydrogen bonding in the wild type is shown in Figure 2. This diagram is a directtracing from the graphics display, apart from minor changes to eliminate eclipsingof atoms and bonds.
The central group of seven hydrogen bonds, whose total bond energy is some 30to 35 kcal mol−1 (allowing 4–5 kcal mol−1 per hydrogen bond) is a well developedstructure which, with some reservations, is conserved throughout all mutations.Experience with estimates of conformational energy quantities [10] suggests that
HYDROGEN BONDS IN STRUCTURE OF GLOBULAR PROTEINS 351
Figure 2. The hydrogen bonding in the vicinity of residue 157.Note: The drawing is a directtrace from the graphics display, with minor modifications to remove eclipsing of atoms andbonds.
such energy quantities may well be sufficient to hold the backbone in the observedconformation.
The water molecule 170 is conserved throughout all 17 mutations and relatedchanges of residue 157 and itsB value is exceptionally low (cf. see Table I). Thisis an example of the immobile water molecule discussed in the preceding section.The OH group of the residue 155 is similarly conserved in position and hydrogenbonding.
The water molecule 543 is the interesting case with a highB value (Table I)when visible and, in many mutations, effectively invisible in the X-ray experiment.We suggest that this is a case of the delocalised water molecule as discussed in theprevious section. The present situation is of course more complicated than the one-dimensional example but a similar result seems plausible in the present context ofwater 543.
The conservation of the hydrogen bonds themselves rather than the conservationof the atoms forming them was reported [28] earlier in the context of the compar-ison of the homologous molecules papain and actinidin and it is illustrated here bythe replacing of the OH group of threonine 157 by a water molecule in cases D1and G or by the carboxylate or amide side chain in cases D2 and N (table). Thereare scattered references to this phenomenon throughout the literature on the three-
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dimensional structure of globular proteins, particularly for the replacement of theammonium ion of lysine with a water molecule [17].
It seems that, taken overall, these experimental results are consistent with theconcept of a ribbon of hydrogen bonds whose exact structure is not clear as yet,which has sufficient binding energy in its hydrogen bonds to account for the ob-served conformation of the backbone of a globular protein.
4. Summary
The central idea of this search for a simple understanding of the three-dimensionalstructure of globular proteins is that we consider the protein molecule plus thewaters of the ribbon as the basic ‘molecule’ rather than the protein molecule alone.The main reason for so doing is that, providing that the energy of the chemicalbonds themselves remains largely unchanged during changes in conformation ofthe protein molecule, then the hydrogen bonding of this ribbon controls the positiveattractive conformational energy of the molecule. We do not imply that the longcontroversy concerning hydrogen bonding versus hydrocarbon interactions as thedeterminant of protein conformation is solved: only that we should first establishfrom both experiment and theory whether hydrogen bonding alone can providea useful working model for many problems which involve the three-dimensionalstructure of globular proteins.
In their original publication, Alber, Matthews et al. [20] reported small de-creases in free energy (0–2.9 kcal mol−1) across the set of mutants of threonine157 and they commented that these reductions in stability of the mutants are sur-prisingly small as compared with the wild type molecule. This result is consistentwith the present view of the structure of the molecules and, indeed, in a first approx-imation we would expect that all the molecules, wild type and mutants, would havethe same energy. The small differences in energy which are observed, then, mayhave their origins in second-order changes in the structure and energy of the ribbonwhich we cannot interpret at this stage. Such secondary effects will presumablyexist in the real molecules, coming perhaps from within the molecule in the formof long range effects which we neglect in the first stage of development of themethod.
It is assumed, of course, that the space filling requirements of all groups as inthe φ, ψ diagram are satisfied and that other attractive and repulsive forces arerelatively unimportant in context, provided that a qualitative or semiquantitativepicture is the first objective of the work. The latter forces may of course be incor-porated into the picture via the quantum mechanical computations at a later stage,as it proves necessary to do so in order to convert the qualitative picture into a morequantitative one.
The immediate application of this view of the structure of globular proteinsis to point mutations in the non-secondary structure of the molecule as with thethreonine 157 case. The conservation of the ribbon of hydrogen bonds in this
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region is then the key to the conservation of the backbone conformation in theregion, although small modifications of the latter’s conformation will be accept-able in most cases. Moreover, there may well be other requirements to be satisfiedbefore a successful mutation is achieved – particularly those involving solubility,aggregation and chemical reactivity together with folding mechanisms.
It is well known that in many instances we may exchange hydrocarbon andhydrogen bonding side chains in a successful mutation and this may have suggestedthat hydrogen bonding is less important than other effects, such as hydrocarbon-to-hydrocarbon interactions in the structure of the molecule. The natural explanationwithin the present view of the structure of the proteins is that the hydrogen bonds ofsuch side chains make noirreplaceablecontribution to the ribbon itself. The muta-tions in the lower half of Table I exemplify the point in the case of the threonine157 side chain. There is the interesting possibility of the introduction of a newhydrogen bonding side chain group, which may be able to disrupt the originalribbon of hydrogen bonds and so change the conformation of the backbone, but wehave found no clear example of this as yet. The introduction of an ionic side chaingroup – such as aspartic acid – is the most likely candidate for such behaviour.
The normal secondary structure of theα helices andβ sheets is part of theribbon of hydrogen bonds. We find in general [17] that theα helix is concernedonly with its internal hydrogen bonding and is not involved to any great extentwith hydrogen bonding to side chains and water molecules in so far as the sidesof the helix are concerned. The helix ends are quite different in structure [16]. Inthe case of theβ sheet, there seems to be more involvement of the backbone withside chains and waters while with the non-secondary structure there is extensivehydrogen bonding to both waters and side chains.
Ionic side chain groups form hydrogen bonds which are almost as strong asweak chemical bonds [33] and so may have longer range influence on structure.Some quantum mechanical results suggest that this is so in the present contextand such ions as the ammonium ion of the lysine cation may be able to affect theconformation of the backbone through more than one hydrogen bond. We havefound no clear experimental example of this point as yet.
There remain of course a number of major questions to be settled with thepresent approach. One such is how the nature of the individual side chains affectsthe geometry and energy of the ribbon of hydrogen bonds and leads to the greatvariety of backbone conformations which is observed in globular proteins [1–6].Another is the question of the role of the non-ribbon part of the complete hydro-gen bond network in tertiary and quarternary structures. The resolution of theseproblems seems feasible and would leave us with a complete understanding of thethree-dimensional structure of these important molecules.
We have chosen to study the backbone conformation separately from that of theside chains in this work since it seems that the former is more fundamental than thelatter. Mobility of side chains without changes in the backbone conformation seemsto be a commonplace phenomenon [34] and presumably involves relatively small
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energy changes as compared with changes in the conformation of the backbone.This model is closely related to the concept of molten globules [35] in which theconformation of the backbone of the protein is conserved while the side chainconformations and the tertiary structure are lost.
An exchange of one hydrocarbon side chain group for another may well ex-ert an influence on the structure of the ribbon of hydrogen bonds via the spacefilling requirements of the atoms of the two groups. For example, an exchange ofglycine and valine [36] may seem innocuous in hydrogen bonding terms but thebulky valine side chain with two methyl groups close to the backbone may leadto a secondary change in the ribbon of hydrogen bonds and so to a change in theconformation of the backbone. The more extensive change of Y35G in trypsin [37]which leads to a drastic change in the conformation of the molecule may arise fromthe disruptive effect of the benzene ring on the water structure within the ribbon.The present example of threonine 157 does not involve space filling problems sincethe various side chains are not involved with the bulk of the molecule.
The point mentioned in the last paragraph that the heat of folding of the globularproteins is small in relation to the conformational energy itself clearly implies thatthe energy differences betweenα helices,β sheets and coil structures are small.This point alone may suggest that all three types of structure are controlled bya single main force. Were this not so then a complicated balancing of variousdifferent forces would be required to achieve this result. At first sight, this situationis difficult to explain in hydrogen bonding terms since, as mentioned above, theα
helix has a large amount of backbone to backbone hydrogen bonding, theβ sheethas rather less and the coil has very little such hydrogen bonding. This difficultyonly arises, however, if all hydrogen bonding to water is ignored. If we include suchhydrogen bonding, as we do in the present approach, then this difficulty disappearsbecause there is extensive hydrogen bonding to water in the coil, less in theβ
sheet and almost none in theα helix (apart from the ends of the helix). If it provespossible to quantify this result in the future, then we will have an understanding ofthe ease with which globular proteins change their conformation.
One point concerning the two lower curves of Figure 1 should be noted. If ac-curate computations of these curves show that they are asymmetric with a shallowminimum to the left or right hand side, then freezing of the sample in the X-rayexperiment may have the effect of fixing the water molecule in this minimum andthus make the water molecule’sB value appear much smaller. It would also detachthe water molecule from the other atom and so change the pattern of hydrogenbonding in this region. And similarly for more complicated examples of this deloc-alisation phenomenon. If this does occur in practice, then such experiments wouldgive us a picture of the details of the structure of the protein molecule which couldbe slightly false.
HYDROGEN BONDS IN STRUCTURE OF GLOBULAR PROTEINS 355
Acknowledgements
We are indebted to T. L. Blundell, for extensive support of this work, to Dr. I. J.Tickle and R. Westlake of Birkbeck College, to Dr. R. W. Baker and A. Hume of theUniversity of London Computer Centre for help with the computational and graph-ics work, to Dr. R. E. Hubbard for supplying the original programs from which theNETWORK package was developed. The advice of many crystallographers hasalso been invaluable.
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