Structural Chemistry Using NMR Spectroscopy, Peptides*

Structural Chemistry Using NMR Spectroscopy, Peptides Martin Huenges and Horst Kessler, Technische Universita¨t Mu¨nchen, Garching, Germany & 1999 Elsevier Ltd. All rights reserved. This article is reproduced from the previous edition, volume 3, pp 2246–2260, & 1999, Elsevier Ltd.

Symbols A B J Pi Rij r u2, u0

W 2, W 0

c r s1, s2 sc sm /, w, x v x0

cross peak intensity magnetic flux density coupling constant population of rotamer i relaxation rate between spins i and j internuclear distance probability of double- and zero-quantum transitions, respectively, in the rotating frame transition probability for doubleand zero-quantum transitions, respectively gyromagnetic ratio cross-relaxation rate correlation times correlation time mixing time peptide backbone angles bond angles of peptide sidechains Larmor frequency

Introduction The majority of biological processes depend directly on peptides and proteins. The sequence of most peptides and all proteins are encoded genetically and the polypeptides are post-translationally modified, processed and transported to their specific location in the cell. The wide range of possible chemical structures (owing to the combination of functional groups of their amino acid residues), especially in their three-dimensional dynamic conformation, allows peptides and proteins to play many different roles in biological processes, such as hormone/ receptor interactions, cellular adhesion and cellular recognition, transport mechanisms between cell compartments or through membranes, and the processing of almost all chemical compounds, including peptides and proteins, to name only a few. Although the conformation and dynamics of peptides and proteins are encoded in their sequence, they are not

2730

yet reliably predictable based on it. The determination of the dynamic 3D structure therefore was, and still is, of utmost importance for the interpretation and artificial modulation of their functions. The challenges posed by peptides and proteins have strongly stimulated the development of modern NMR spectroscopy. Most of the multidimensional NMR techniques now available were designed and applied initially to peptides and proteins. We will discuss in this article first some general problems which arise in the NMR spectroscopy of peptides. Then, NMR techniques for signal assignment and extraction of conformational parameters will be described, followed by a short excursion into structure determination using NMR parameters. The final part will include the analysis of peptide dynamics based on NMR data.

General Problems with Peptides Peptides are composed of a linear, branched or cyclic array of amino acid residues (Figure 1). The peptide chain is defined and numbered from the N to the C terminus. The a carbon atoms of the amino acids are linked by peptide bonds. The bonds to the a carbon atom are described by their bond angles f(N–Ca), c(Ca–CO) and w1(Ca–Cb). The usually planar peptide bonds prefer the trans-configuration (o ¼ 1801) as shown in Figure 1 for the Phe-Gly and Gly-Val bonds. Only in the case of Xaa-Pro pairs are cis- and TRANS- conformations of similar energy. In Figure 1 the Val–Pro bond is in the cis-configuration. The barrier between cis and trans peptide bonds is between 16 and 20 kcal mol1 which leads to a slow exchange between the conformations on the NMR time-scale at room temperature. At higher temperature the exchange between the two states occurs at an increased rate, leading to a coalescence of the two signal sets in NMR spectra. Rotations around f, c and w1 are fast on the NMR time-scale. As a result it is not straightforward to distinguish between a single preferred conformation and a rapid equilibrium between several conformations (see below). Linear peptides, approximately up to dodecamers, are normally very flexible and do not exist in or prefer a single conformation, although

Structural Chemistry Using NMR Spectroscopy, Peptides

Figure 1

2731

Schematic representation of the tetrapeptide sequence – FVGP – used to illustrate the nomenclature.

sometimes a slight preference for a distinct set of structures is observed. However, cyclization and/or sterically demanding substitution restrain the conformational space and often allow the identification of a preferred conformation. The equilibrium between the different conformations of a peptide can be very sensitive to the environment. Hence, different conformations can be found in a single unit cell of a crystal, between different crystals, between crystal and solution as well as between ‘free’ and receptor bound peptides. ‘Free’ conformations are embedded in the solvent whose chemical and physical properties can induce drastic changes when different solvents are used. The evidence for such conformational changes often is indirect (solvent induced signal shifts), but a careful analysis of the whole 3D structure can also lead to the detection of such exchange processes (see e.g. antamanide). Direct observation of solvent-induced conformational shifts is possible in the case of the cis/trans isomerization of an alkylated peptide bond, since rotation around this bond is slow enough to be resolved on the NMR time-scale. For example, when cyclosporin A is dissolved in CDCl3, benzene or THF one strongly dominating conformation is observed that contains a NMeVal9-NMeVal10cis amide bond. The corresponding conformation with the same amide in the trans-conformation is populated at less than 5%. In more polar solvents, such as CD3CN and MeOH, a number of coexisting conformations are found, whereas a single but very different conformation is found when the peptide is bound to the receptor. However, in cases of peptides with unmodified CONH peptide bonds cis-conformations are only very rarely observed. Generally, it is recommended that proof of conformational homogeneity, i.e. the dominance of a single or a few conformation(s) under given conditions, be

obtained before beginning a detailed NMR analysis. Criteria for preferred conformations are: Large chemical shift dispersion within the set of H • and H signals. Large between diastereotopic protons • such asshiftH difference protons of Gly, or of H protons in the

N

a

a

• • •

b

side-chains of Phe, Tyr, His, Trp, Ser, Cys and the two b methyl groups of Val, for example. Strong differences in HN–Ha coupling constants of different residues and Ha–HbproR/Ha–HbproS coupling constants in each side-chain. Pronounced differences in NOE intensities. Appearance of long-range NOEs between protons of non-neighboured residues.

Only if these criteria are met is it worthwhile initiating a careful conformational analysis. In general, conformational restraints, such as cyclization, binding to a receptor or complexation with metal ions, are necessary to fulfil these conditions. If the NMR data indicate a flexible structure, a structural discussion is not meaningful since the bioactive conformation of interest, i.e. the conformation of the peptide bound at the receptor, is selected out of a large ensemble of alternative conformations.

Assignment of Signals A prerequisite for the extraction of conformational parameters is the assignment of each signal in the spectrum to a specific spin system, and the assignment of these spin systems to specific residues in the peptide chain. The pulse sequences discussed here are shown in Figure 2.

2732

Structural Chemistry Using NMR Spectroscopy, Peptides

Figure 2 Pulse sequences used in this article. All experiments can be acquired in the phase-sensitive mode, using either TPPI or the States method. Sequences 12 and 13 are best displayed in the magnitude mode because of phase modulation owing to homonuclear couplings in F2. All inverse correlations, except for sequences 12 and 13, can be preceded by a BIRD (bilinear rotating decoupling) pulse sandwich to allow for a fast repetition rate of scans. For simplicity gradients are not given here in most cases.

Assignment of Spin Systems The COSY (correlation spectroscopy) experiment yields information about connectivity between nuclei. COSY cross peaks can be expected for each resolved scalar coupling between nuclei that are connected by two or three bonds. An unambiguous identification of individual amino acid spin systems can be complicated by the overlap of signals in the vicinity of the diagonal of the spectrum, overlap of cross peaks for the long side-chains of Arg, Lys, Pro and Leu and the frequently insufficient signal intensities of resonances that are coupled to many neighbouring nuclei (e.g. Hg of Leu couples to eight vicinal neighbours). A list of other pulse techniques used in structural studies of peptides is given in Table 1. The TOCSY experiment is the most efficient way to obtain complete assignments of spin systems (Figure 3). TOCSY is sometimes called HOHAHA. The duration of the mixing period determines the efficiency of transfer. If a sufficiently long mixing time is

chosen, correlations of the whole proton spin systems are found. TOCSY experiments with short mixing times reveal mainly correlations between directly coupled nuclei. The spin systems of the naturally occurring amino acid residues can be divided into two groups. While the side-chains of Ala, Arg, Gln, Glu, Gly, Ile, Leu, Lys, Met, Thr and Val exhibit unique spin systems and therefore can be identified with relative ease, the residues in the second group, including Asn, Asp, Cys, His, Phe, Ser, Trp and Tyr, all have similar AMXY proton spin systems. Nevertheless, the aromatic residues of the second group can be unambiguously assigned using Hb–H (ring) NOE cross peaks, whereas the Ser-spin system can be easily distinguished from all other possible AMXY spin systems 0 in COSY experiments because of its weak Hb–Hb coupling. Trp is easy to identify via a heteronuclear HMQC experiment owing to its characteristic downfield shift of the b carbon signal.

Structural Chemistry Using NMR Spectroscopy, Peptides Table 1 peptides

Pulse techniques necessary for structural studies of

Technique

Purpose

P.E.COSY

COSY with simplified multiplet structure. P.E.COSY allows for the accurate measurements of homonuclear coupling constants

TOCSY ¼ HOHAHA

Assignment of spin systems. If a long mixing time is used, TOCSY gives total correlation between all nuclei in a spin system

z-filtered TOCSY

TOCSY sequence that leads to cross peaks with pure phases. z-filtered TOCSY needs long measurement times owing to the random variation of the z-filter in 6 to 12 steps between 110 ms and 20 ms

NOESY

NOESY gives distance information about nuclei that are separated by less than 500 pm in space

ROESY

ROESY is ideally suited for the observation of nuclear Overhauser effects for medium-sized peptides at low field strengths

HMQC

HMQC correlates the shifts of protons with a directly bound heteronucleus. Very sensitive

HMQC-TOCSY

HMQC with subsequent TOCSY transfer to coupled protons

DEPT-HMQC

DEPT-edited HMQC, which allows for the distinction of CH, CH2 and CH3 groups. Exclusive selection of these multiplicities is possible with the related HDQC, HTQC and HQQC techniques

o1-filtered TOCSY ¼ HETLOC

Extraction of coupling constants to proton-bearing heteronuclei. Because magnetization is distributed among a large number of spins, this method is rather insensitive

HQQC

Assignment of methyl groups in crowded spectra, when folding is not feasible

HMBC

Assignment of carbons and protons and determination of long-range coupling constants

Selective HMBC

Useful variation of HMBC. For peptides, the selective pulse is usually applied to the carbonyl carbons

2733

Heteronuclear spectroscopy also reduces problems with signal overlap because of the large chemical shift dispersion of 13C nuclei. The most popular heteronuclear correlation experiments for this purpose are HMQC and HMQC-TOCSY experiments (e.g. Figure 4). The latter contains information similar to the homonuclear 1HTOCSY, but, as for all heteronuclear experiments, its sensitivity is lower owing to the lower gyromagnetic ratio and low natural abundance of the 13C nucleus. HMQC sequences can be combined with DEPT editing, allowing for the editing of multiplicities in heteronuclear correlations. The resulting experiments, such as HDQC (heteronuclear double quantum correlation), HTQC (heteronuclear triple quantum correlation) and HQQC (heteronuclear quadruple quantum correlation, make it possible to exclusively excite CH, CH2 or CH3 groups. This results in a simplified assignment procedure. An alternative way of overcoming problems with overlapping resonances in crowded spectral regions is to apply band-selective excitations. Band-selective pulses can be used to selectively excite a desired spectral region in one or more dimensions. The reduction of spectral width in one or more dimensions improves the digital resolution attainable in the chosen dimension, and thus helps to reduce ambiguities in the resonance assignment procedure. As a welcome side-effect it also shortens the measuring time of the experiment. Resolution can further be improved substantially by semi-selective homonuclear decoupling during both the acquisition and the evolution dimensions. This can be achieved in the acquisition dimension by use of homonuclear shaped pulse decoupling in combination with the time-shared decoupling mode during data acquisition and in the evolution dimension by application of a semi-selective refocusing pulse together with a nonselective refocusing pulse in the centre of the evolution period. An example of an experiment implementing these techniques is the BASHD- (band selective homonuclear decoupled) TOCSY experiment. Band selection in the evolution dimension is achieved by the excitation sculpting method. The key element of this method is a double pulse field gradient spin echo (DPFGSE) that leads to pure phase spectra with flat baselines. This cluster of pulses rephases only the selected magnetization affected by the 1801 pulses and avoids any evolution of the J-coupling during this period. The combination of selective pulses and pulse field gradients to select the desired coherence pathway results in pure phase spectra largely devoid of artefacts. This principle can also be extended to any existing homonuclear and heteronuclear selective NMR experiment, as demonstrated by semiselective 2D TOCSY, ROESY, HSQC and HSQCTOCSY experiments.

2734

Structural Chemistry Using NMR Spectroscopy, Peptides

Figure 3 (a) 500 MHz TOCSY spectrum of 20-mmol-L1cyclo(-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-) in DMSO at 300 K with TPPI applied in the F1 dimension. Mixing time was 80 ms. A number of relayed connectivities can be observed. This spectrum is typical for small cyclic peptides. Linear peptides of this size would exhibit much less chemical shift dispersion of HN and Ha protons. The indicated part of the spectrum is expanded in (b) which is the fingerprint region (F2: amide protons, F1: aliphatic protons); coupled nuclei are connected by dashed lines and assigned to the respective residues. (c) Sequence of cyclo (-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-). Tetrahydroisochinolin (Tic) is an unnatural proline like amino acid which lacks the amide proton.

Sequential Assignment Sequential assignment of residues in a peptide chain requires correlation across the peptide bond that separates the proton spin systems of adjacent residues. This sequential information can be provided by dipolar couplings using NOESY or ROESY experiments, or by heteronuclear scalar couplings using HMBC experiments. When only homonuclear proton experiments can be used (e.g. for reasons of sensitivity), NOESY or ROESY experiments are necessarily the method of choice. Shortrange NOE signals, such as those observed between amide and aliphatic protons, are usually also observed for sequentially adjacent residues. Among these the

N a N HN i –Hiþ1 and Hi –Hiþ1 connectivities are especially important for establishment of the sequence (see Figure 5). In practice, however, ambiguities can be encountered in the sequential assignment step owing to overlap of cross peaks, particularly if the peptide contains multiple residues of one type, or if long-range NOE signals are also found in the Ha–HN region of the NOESY or ROESY spectrum, as in the case of folded peptides and small proteins. Sequential assignment of these molecules therefore can be ambiguous and requires a tedious and time-consuming analysis of the NOESY or ROESY spectra. In those cases, a significantly increased resolution in the Ha–HN region of the ROESY spectrum can be

Structural Chemistry Using NMR Spectroscopy, Peptides

2735

Figure 4 500 MHz HMQC–TOCSY spectrum of cyclo (-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-) in DMSO at 300 K. Mixing time was 80 ms. In addition to the directly bound protons the entire spin system can be observed. Coupled nuclei are connected by dashed lines and assigned to their respective residues.

Figure 5 Part of the 500 MHz ROESY spectrum of cyclo (-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-) in DMSO at 300 K. Correlations between the amide protons and Ha protons of one residue and the Ha protons of the preceding residue are essential for the sequential assignment. Cross peaks between neighbouring amide protons are an important source of sequential information. Cross peaks not assigned belong to aromatic protons.

achieved with a BASHD-ROESY pulse sequence, incorporating band selection and homonuclear decoupling in the Ha region of the spectra. Band selection in the evolution dimension is performed with the DPFGSE technique as described above. This NOE-based approach requires previous knowledge of the peptide sequence. The known sequential position of a residue with a unique or characteristic spin system can be used as a first ‘anchor point’, from which sequencing in both directions can be carried out. In cases where the sequence is unknown, a different strategy must be used. In this case, each spin system must be assigned individually to its type of amino acid before a sequential assignment can be achieved. Obviously this approach is restricted to relatively small molecules (up to 30 residues). It is also possible to determine the sequence of a peptide using scalar coupling to the carbonyl carbon. This is best done with standard or selective HMBC experiments, where only carbonyl carbons are excited and indirectly detected during t1. The sequential assignment is then unambiguous and does not require any knowledge about the conformation of the peptide (Figure 6). A clear distinction between the proof of the complete assignment and the conformational analysis is then possible. Such

2736

Structural Chemistry Using NMR Spectroscopy, Peptides

between the two nuclei that contribute to the cross peak. It can be shown that the cross-relaxation rate s that determines the NOE transfer is obtained from eqn [1]. s ¼ W2  W0 ¼

Figure 6 Polypeptide segment with the possible interresidue connectivities between spin systems. (a) Sequential short distance NOEs for peptides. (b) Observable through-bond couplings, useful for the sequencing of peptides.

a sequential assignment might also be used as an independent proof of the existence of a specific peptide bond, as for example formed by cyclization. A complete assignment also includes the stereospecific assignment of diastereotopic groups such as methylene protons or geminal methyl groups in Val or Leu. Such additional information can significantly increase the quality of a 3D structure, which is especially important in the case of small peptides, where typically only a small number of long-range NOEs is available for the conformational analysis. Diastereotopic assignment will be discussed in more depth below.

Extraction of Conformationally Relevant Parameters NOE Effects Nuclear cross relaxation in liquids is caused by mutual spin flips in pairs of dipolar-coupled spins, induced by motional processes. Cross-relaxation efficiency depends on the spatial distances between the relaxing nuclei and leads to a transfer of magnetization between the spins. It causes intensity changes known as nuclear Overhauser effects (NOE). NOEs, as well as ROEs, can only be observed between nuclei that are separated in space by less than 500 pm. The NOE can be rationalized as heat flow from a non-equilibrium state to another neighbouring spin. In the NOE (or ROE) experiment such deviation from the Boltzmann equilibrium of spin states is created via specific pulsing and the efficiency of the heat flow to neighbouring nuclei (NOE build-up) is measured via the induced intensity changes of their NMR signals. The efficiency of dipolar relaxation is a function of the field strength (represented by o0) and the motion (rate of relaxation referred to the external magnetic field) of the molecule, described by the molecular correlation time tc. The intensity of a cross peak appearing in a NOESY spectrum contains information about the relative distances

  g 4h 2t c 6  1 4p 2 10r 6 1 þ 4o 2 t2c

½1

where r is the internuclear distance and W2 and W0 are the transition probabilities for the double-quantum and zeroquantum transition respectively. At a given o the variables that determine the size of s are the correlation time tc and the interproton distance r6ij. It should be noted that for specific combinations of tc and o the second term becomes zero or negative. The build-up of cross peak intensity in a multispin system is given by A(tm) ¼ exp {  Rtm}: Aij ðtm Þ ¼

  1X Rik Rij t2m þ y Aii ð0Þ Rij tm þ 2

½2

where A(tm) is the cross peak intensity as a function of the mixing time tm, R the relaxation matrix and Rij the relaxation rate between spins i and j. For sufficiently short mixing times the quadratic term and those of higher order in tm can be ignored. The cross peak intensity is then directly proportional to the cross-relaxation rate and thus to the inverse sixth power of the distance between the nuclei (when the molecule behaves as a rigid body, tc ¼ constant): ANOE p sij p

1 r ij6

½3

The intensities of NOE effects depend on the size of W2 and W0. As can be seen for eqn [1] the NOE vanishes when W2 ¼ W0, which occurs approximately when the inverse correlation time t1 is of the order of the Larmor frec quency o0. Similar relationships can be derived for ROESY. In this case, the cross peaks are generated by cross relaxation of transverse magnetization. In the rotating frame, s is given by eqn [4]   g 4h 2t 3 s ¼ u2  u0 ¼ 2 þ2 4p 10r 6 1 þ 4o 2 t 2

½4

where u2 and u0 are the transition probabilities for the double-quantum and zero-quantum transitions in the rotating frame, respectively. It is important to note that ROE effects, in contrast to NOE effects, are always positive and never vanish. NOESY as well as ROESY experiments can both provide distance information. However, there are some important differences in their application and in the evaluation of the resulting spectra. The usefulness of either of these techniques depends strongly on the time-scale of the motional processes that cause the cross relaxation. We have to distinguish three

Structural Chemistry Using NMR Spectroscopy, Peptides

Figure 7 Dependence of the maximum NOE and ROE cross peak intensities Ik,max (standardized on a diagonal signal I0) on o and tc for very short mixing times.

cases: (a) the fast-motion limit (extreme narrowing limit) with a short correlation time tc{o1 0 (positive NOEs) (Figure 7). This applies for small molecules in non-viscous solutions. (b) The slow-motion limit (spin-diffusion limit) with a long correlation time tcco1 (negative 0 NOEs) which applies to large macromolecules such as proteins at the maximum currently used magnetic field strengths. (c) For intermediate sized molecules only small, or even no NOE, effects at all are observed. This is the case for peptides with a relative molecular mass of 500 to 1000 Da at resonance frequencies o0 of 300 MHz. Differences of internal mobility, for example via the rotation of side-chains, can then lead to the appearance of both positive and negative NOEs in the same NOESY spectrum, making it impossible to evaluate molecular distances from these data. If only small NOE effects are observed, the ROESY techniques should be used. Two problems have to be considered in the evaluation of ROESY spectra. First, the offset dependence of the spin-lock field introduces intensity variations into the spectrum. Peak intensities will have to be corrected to take this effect into account when distances are to be calculated. The cross peak intensity as a function of offset from the transmitter (when NOE effects are neglected) is given by eqn [5]. AðgB1 Þ ¼ A sin2 yk sin2 yl

½5

where yk,l ¼ arctan (gBl/Ok,l) and Okl, are the offsets of spins k and l from the transmitter. The use of the compensated ROESY sequence leads to a higher intensity for peaks at the edge of the spectrum compared with the standard ROESY. In this case the peak intensity is given by eqn [6]. AðgB1 Þ ¼ A sin yk sin yl

½6

Second, undesired TOCSY peaks appear because some nuclei that are spin coupled experience similar fields during the application of the spin-lock and fulfil the Hartmann–Hahn condition. Since the TOCSY peaks are

2737

phase shifted by 1801 with respect to the ROESY peaks, they can easily be recognized. However, the superposition of contributions from direct and indirect transfer results in a decrease of cross peak intensity and therefore in distances which are too long. When only lower boundaries are used as restraints in MD calculations this would lead to lower restraints and a less well-defined structure but would not induce wrong results. In addition, different internal correlation times, such as the above-mentioned different flexibility of the molecule, have a smaller influence in ROESY than in NOESY spectra. NOESY spectra are preferred in the slow-motion limit but never near the transition from positive to negative NOEs (W2EW0, s-0) because the different internal mobility induces larger errors in distances. In such cases, lowering the temperature (to slow down molecular rotation) is recommended.

Evaluation of NOESY and ROESY Spectra Dipolar cross-relaxation rates, and thus distances, can be determined through NOESY or ROESY experiments using various approaches. The measurement of build-up rates involves the recording of several NOESY spectra with different mixing times. To ensure equal conditions, the measurements should be made in succession. The integrals of cross peaks are determined, and the volumes are plotted as a function of mixing time: Aðtm Þ ¼ 1  expðstm Þ

½7

The derivative of eqn [7] at an extrapolated mixing time of zero yields the rate of build-up of the cross peak. This initial build-up rate is directly proportional to the crossrelaxation rate. dA

ðtm ¼ 0Þ ¼s dtm

½8

The simplest and most common approach is the measurement of a single NOESY or ROESY spectrum with a short mixing time. At short mixing times the NOE buildup is in the linear range. Under this condition, it can be assumed that only direct enhancements sij contribute to the cross peak intensity aij(tm). The evaluation of a single NOESY spectrum can be done by either integration of the cross peaks or in a more qualitative manner by visual inspection of the spectrum. The second approach is often used in the case of NOESY spectra of proteins where an insufficient signal-to-noise ratio and extensive overlap prevent the accurate integration of cross peaks. In large molecules ‘spin diffusion’, i.e. a rapid flow of magnetization from one nucleus via another nucleus to a third one, is the most severe problem. Only very short mixing

2738

Structural Chemistry Using NMR Spectroscopy, Peptides

times can be used and a complete treatment of the relaxation matrices is recommended. In the first approximation the NOEs are only used qualitatively in proteins: cross peaks are then classified according to several semiquantitative categories – usually strong, medium, weak – which correspond to distance ranges. This approach is not recommended for peptides since the integration of cross peaks should lead to considerably more accurate distances and spin diffusion is not so efficient in peptides as it is in large molecules. The so-called ISPA (isolated spin pair approximation) is closer to reality for molecules which are close to the tcEo0 condition. Owing to the fact that absolute values of correlation times are usually not available, interproton distances cannot be directly calculated. Distances are instead obtained by calibration of the cross peak intensities against an internal distance standard, usually the distance between diastereotopic geminal protons (178 pm) or aromatic protons of Tyr (242 pm). Assuming isotropic tumbling and rigid-body model for all parts of the molecule, eqn [9] is then used to calculate all interproton distances: r ij ¼ r ref

 6 aref aij

½9

Usually, the NOE enhancements for the structural and conformational analysis of peptides are extracted from 2D NOESY spectra. The GOESY experiment, a 1D version of the NOESY experiment, uses selective excitation of separated signals and yields accurate measurements even for tiny enhancements. The DPFGSE NOE technique (see above) achieves better sensitivity by not discarding one of the coherence transfer pathways (in contrast to the GOESY technique), while spectra have the same characteristics as GOESY spectra. Therefore, the DPFGSE NOE technique is to be preferred. Determination of Coupling Constants Many J-coupling constants illustrate a clear dependency on dihedral angles and therefore are an important source of conformational information. This relationship is particularly distinct for 3J-couplings. The model for the relationship between bond angles and the coupling constant most often used is that proposed by Karplus (Figure 8). 3

J ¼ A cos 2 y þ B cos y þ C

½10

The equation holds for almost all coupling constants (Table 2). Only the coefficients A, B and C have to be adjusted, depending on the type of the two coupled nuclei and their environment. However, even if the coefficients have been determined, the multiple angles that fulfil eqn [10] (up to four values can be obtained) remain a problem.

Figure 8 The Karplus curve for four coupling constants about the f dihedral angle of an L-amino acid. There are four possible dihedral angles for a given coupling constant. Utilizing a combination of all four coupling constants it is usually possible to narrow down the choice to a single angle. Reproduced with permission of Wiley-VCH from Eberstadt et al. (1995) Angewandte Chemie, International Edition in English 34: 1671–1695.

Table 2 Coupling constants used to determine f, c and w1 angles in peptides Angle

Coupling constant

f c f and c w1

3

JHN,H a, 3JCb,HN 3JHa,CO(i  1) JHN(Ii 1)a 1 JC,aHa 3 JHa,Hb, JCO,H b, JN,H b 3

Despite these problems, the application of coupling constants, in addition to proton–proton distances, in modern conformational analysis of peptides is indispensable. In principle, the coupling constants shown in Table 2 can be used to determine the f, c and w1 angles. For the determination of homonuclear or heteronuclear three-bond coupling constants, three fundamentally different approaches are used: (1) direct measurements of splittings caused by J-couplings, (2) the so-called E.COSY-signal patterns in which the splittings can be measured as shift differences of signals and (3) special experiments which lead to modulation of signal intensities via J (Table 3). A frequent requirement for the latter is a 15N-enriched sample, e.g. for the Jmodulated (15N, 1H)-COSY experiment or the HNHA experiment. Whereas labelled compounds are routinely used for proteins and nucleic acids they are expensive for peptides and therefore rarely used. Determination of Coupling Constants from The Shape of The Signal

All these techniques have to correct or compensate for the partial overlap of multiplet lines by either using

Structural Chemistry Using NMR Spectroscopy, Peptides

additional parameters which depend on the shape of the signals or by fitting a model to the overlapped experimental signal However, this procedure requires that the line width is still smaller than the coupling constant, and furthermore that the signals have a good signal-to-noise ratio. The determination of coupling constants from an antiphase (e.g. COSY) cross peak yields values which are inherently too large owing to the reciprocal signal cancellation of the antiphase pattern. Kim and Prestegard have described an especially simple method for the determination of coupling constants for AX spectra. The splitting of the maxima in the absorptive and in the dispersive signal is measured and the J-coupling is calculated via an extensive cubic equation (Figure 9). Only two calculations are required for the COSY spectra in which the phase are 90 1 shifted. This procedure is especially useful for the determination of coupling constants that cannot easily be extracted from peaks in E.COSY spectra (see below), e.g. for HN–Ha cross peaks. No additional spectrum has to be recorded.

Table 3 Experiments that are used for determining the most important coupling constants in peptides Coupling N

H –H

a

Ha–Hb Couplings within the proline pyrrolidine ring 13 CO–Hb HN–Cb

Technique Direct reading or Kim– Prestegard method E.COSY techniques E.COSY techniques

2739

The simulation of the line shape using a linear combination of reference signals is based on the simulation of a complex nonresolved multiplet, starting out from a library of experimental multiplets. This technique has found widespread application in the determination of heteronuclear long-range coupling constants from HMBC cross peaks of peptide samples with 13C in natural abundance. The major advantage is the relatively high sensitivity of the HMBC experiment because of inverse detection, as well as the fact that the identity of heteronuclear couplings directly ensues from the assignment of the 2D cross signals. In principle, long-range coupling constants can be determined directly from the cross peaks which represent the active coupling. However, since the long-range heteronuclear coupling constants are approximately of the same magnitude as 2JH,H and 3JH,H coupling constants (1–10 Hz), the rather small heteronuclear antiphase coupling constant nJC,H cannot be read directly because of overlapping and reciprocal cancellation of the numerous multiplet lines. Keeler et al. have developed an elegant procedure which allows the determination of the heteronuclear long-range coupling constant from the line shape even in such cases (Figure 10). The difference between a cross section in an HMBC spectrum and the corresponding, reconstructed proton multiplet (e.g. from a 1D spectrum) is the heteronuclear coupling constant of interest. In practice, the proton multiplet will show some overlap in the 1D

HMBC (qualitative), Keeler method HETLOC

Figure 9 Determination of the separation of the signal maxima of an antiphase doublet for the absorptive (na) and dispersive (nd) component. Based on these two parameters the coupling constant J can be calculated. Reproduced with permission of Wiley-VCH from Eberstadt et al. (1995) Angewandte Chemie, International Edition in English 34: 1671–1695.

Figure 10 Schematic of the Titman–Keeler method for the evaluation of heteronuclear coupling constants from HMBC spectra. The synthetic spectrum is computed from the homonuclear reference spectrum and a chosen heteronuclear coupling constant Jtrial. This spectrum is then compared with the actual HMBC spectrum and Jtrial is iteratively varied until a good fit is obtained. Reproduced with permission of Wiley-VCH from Kessler H and Seip S (1994) In: Croasmun WR and Carlson RMK (eds.) Two-Dimensional NMR Spectroscopy, pp. 619–654.

2740

Structural Chemistry Using NMR Spectroscopy, Peptides

spectrum, and therefore a TOCSY spectrum with a pure phase (e.g. with a z-filter) has to be recorded. The homonuclear reference multiplet now differs from the HMBC multiplet only by the absence of the heteronuclear antiphase coupling and the signal amplitude. This can be simulated by scaling of the reference signal in the time domain with the term sin(pJtrialt). The amplitude and Jtrial can now be varied by a nonlinear optimization until the deviation between the two spectra reaches a minimum. At this point Jtrial should be equal to the coupling constant of interest. This method has the advantage that a large number of coupling constants can be determined from a single HMBC spectrum, which usually contains a large number of long-range correlations. However, the quality of the heteronuclear spectrum and especially the signal-tonoise ratio is of crucial importance for the convergence of the optimization. Therefore, the method is time consuming with respect to both recording of the spectra as well as their processing, but it yields accurate values for the coupling constants between heteronuclei. Assuming that the staggered rotamers are predominantly populated (Figure 11), qualitative considerations together with accurately determined homonuclear coupling constants are often sufficient for the diastereotopic assignment of methylene protons. The w1 angle 0 can be set to  601 if the two 3JHa,Hb and 3JHa,Hb coupling constants are small (both B3 Hz). If one strong

Figure 11

and one weak coupling are observed, w1 can be either 60 or 1801. To differentiate these two cases, stereospecific assignment of the Hb protons is required. This is possible with the aid of qualitative heteronuclear J-couplings (e.g. between 13CO and Hb or 15N and Hb) and NOE or ROE cross peak intensities to the different Hb protons. Determination of Coupling Constants by The E.COSY Principle

The E.COSY (exclusive correlation spectroscopy) principle yields a simplified cross peak multiplet, since only the ‘connected transitions’ are excited. This means that the signal intensity in an A, M cross peak from a three-spin system AMX can only be found in those parts of the multiplet pattern where the spin states of the third nucleus X have been conserved. To obtain such an E.COSY pattern, a mixing of spin states of the X nucleus (e.g. by the application of a non-sensitive 901 pulse) must be avoided. The coupling between M and X can then be extracted from the passive coupling of the A, M cross peak as the shift of two in-phase multiplets, which are separated in the indirect dimension and, therefore, have no interfering influence on each other. The only requirement is that the splitting in F1 (the coupling between A and M) must be larger than the line width (Figure 12). The E.COSY technique with the highest sensitivity is P.E.COSY (primitive E.COSY), where the retention of the spin states of the passive spin is achieved using a

The three staggered conformers about the w1 angle of residues with b-methylene protons (see text for details).

Structural Chemistry Using NMR Spectroscopy, Peptides

Figure 12 Ha, Hb region of the 500 MHz P.E.COSY spectrum of cyclo(-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-) in DMSO at 300 K. The enlarged view is of the Phe3 Ha, Hb cross peaks. The displacement of the multiplet patterns can be used to determine the passive couplings with high accuracy. Hbl means the low field b proton and Hbh the high field proton.

small flip angle of the mixing pulse and subtraction of the dispersive diagonal via a reference spectrum. The resulting cross peaks contain strong signal intensities for connected transitions but vanishing intensities for nonconnected transitions. In heteronuclear spectroscopy E.COSY patterns can be easily obtained if no 901 pulse is applied to the heteronucleus (i.e. the states a and b are not mixed). o1-Hetero-filtered (HETLOC) experiments are the method of choice for the determination of long-range coupling constants between protons and 13C or 15N nuclei in natural abundance that carry a directly connected proton (Figure 13). For the determination of the w1 angle the coupling 3JHb can be determined by using a heteronuclear o1-half-filter (X-half-filter) at the beginning of a NOESY or TOCSY experiment (before the t1 delay). Only protons which are directly coupled to the magnetically active heteronucleus (13C or 15N) are selected, while 12CH or 14NH protons are suppressed. Obviously, no heteronuclear decoupling can be performed during the acquisition. The delay D is adjusted according to the value of the heteronuclear coupling constant for the o1half-filter ðD ¼ 12J H ;X Þ resulting in in-phase magnetization at the end of the two delays. The subsequent TOCSY sequence affects only the 13C-coupled protons and transfers the magnetization through the entire spin system. In o1 the signals are split by the large value of the 1 JX,H coupling (e.g. 1JN,H ¼ 90 Hz) in o2 by the desired long-range heteronuclear coupling constant. However, by this method heteronuclear nJH,X couplings can only be determined for heteroatoms which bear a directly bound

2741

Figure 13 Part of the 500 MHz HETLOC (o1-filtered TOCSY) spectrum of cyclo(-Tic-Pro-Phe-Gly-Pro-Pro-Thr-Leu-) in DMSO at 300 K. The enlarged view is of the Thr7 H N, Hb cross peak. The coupling constant is extracted from the separation of the cross peak components in the better resolved acquisition dimension (F 2).

proton. The latter causes the required large splitting in o1 via 1JX,H. Fortunately, using the sensitivity of an inverse detection experiment many heteronuclear coupling constants can be determined from a single spectrum for molecules in natural isotopic abundances.

Structure Determination of Peptides The utilization of NMR data for the determination of the three-dimensional structure of peptides involves the use of computer simulations. The methods can be broken down into two general categories: molecular mechanics/ dynamics (MM or MD) and distance geometry (DG) calculations. MM and MD use a force field to describe the molecule and estimate the potential energy of the given conformation. The standard force field contains a term for distortion of bond lengths, bond angles and dihedral angles plus non-bonded terms for Coulombic interactions and a Lennard-Jones description of the attraction/repulsion of atoms. The application of experimental restraints is achieved by simply introducing an additional term, a socalled penalty function. This penalty function serves to minimize the differences between the calculated values and experimental data. The second general approach, DG calculations, utilizes a description of a molecule based solely on distances. Bond lengths, bond angles and torsion angles are converted into ranges of allowed distances according to the molecular constitution. Distances which satisfy these ranges are chosen randomly to create a distance matrix.

2742

Structural Chemistry Using NMR Spectroscopy, Peptides

The diagonalization of this matrix then produces Cartesian coordinates. The experimental distances are compared with the distances generated from DG calculations based on the covalent structure; if the experimental distances are tighter, they replace those on the consideration of the covalent geometry. The most important parameters for the determination of a three-dimensional structure are NOE-derived distances, bond angles derived from J-coupling constants and temperature dependences of HN proton chemical shifts. Distances from NOESY or ROESY spectra are directly used as restraints for the calculations. Recently, coupling constants have also been used in computational structure refinement. The penalty function employed in this case is directly based on the Karplus equation. If more than one coupling for a single dihedral angle is available, the restraints from coupling constants are quite useful at the level of structure refinement. A limited number of experimental NOE values for peptides normally requires special care. In small peptides more or less all of the protons are on the surface, in contact with the solvent, and thus there are only distances to one side whereas in proteins there are many protons in the core region that are completely surrounded by other protons. Hence, for peptides it is indispensable to collect as much experimental data as possible. This means that accurate, quantitative NOE data as well as correct treatment of J-coupling constants are required. The direct application of the temperature coefficients in structure refinement is problematic, since, while a temperature coefficient may indicate that an HN proton is shielded from the solvent (for example by being involved in a hydrogen bond), it does not allow for identification of the acceptor of that hydrogen bond. Therefore, temperature coefficients, unfortunately, are frequently used only to confirm the final structure. The analysis of the radial distribution function (rdf) of the solvent around an amide proton shows, in our experience, distinct peaks when this proton is solvent exposed. The size and sharpness of these rdfs correlate directly with the size of the temperature gradient. Conformational analysis of a peptide normally begins with the simple assumption of only a single dominating conformation using restrained MD under vacuum, beginning with various starting structures (to prevent structural bias, it is, however, recommended to begin with DG calculations to create the first crude starting structures for the MD). The resulting MD structure is further refined by recalculations of the molecule within an explicit solvent box. This can contain H2O, DMSO, CHCl3, CH3OH or others, depending on the solvent used for the measurement. The best procedure uses a truncated octahedron to allow periodic boundary conditions for an almost spherical box but also cubic boxes may be used. The quality of the final structure is finally checked by

a long trajectory MD calculation (100 ps or more), without all experimental restraints but within the solvent. If all restraints are fulfilled (within about 10 pm), and the same result is always obtained regardless of the selected starting structure, it can be concluded that a ‘single’ satisfying conformation exists (a ‘single conformation’ may still include some flexibility, of the order of 7201 for torsions). There might be other conformations which also fulfil the experimental data, especially when the system is underdetermined owing to an insufficient number of constraints, but this should be apparent if different starting structures lead to different results. If one part of the molecule turns out to be well defined while another part shows larger deviations from the experimental constraints, it can be assumed that the latter part is undergoing intramolecular motion that is fast on the chemical shift time-scale. Short distances r contribute most strongly to the observed NOE intensities (because of the r6 dependence), and hence not all distance constraints derived from NOEs can be fulfilled at the same time if an equilibrium among several conformations exists. Given that there is a sufficient number of restraining parameters one can try to analyse this equilibrium by using timedependent NOEs and/or time-dependent coupling constants, making the assumption that the constraints are not fulfilled at each simulation step, but rather only over a whole trajectory. This allows for analysis not only of the flexibility but also of the detailed nature of the molecular processes involved. In addition, ensemble calculations may be used to analyse flexible structures. However, these calculations are time consuming, difficult to analyse and cannot directly include solvents. Hence, this procedure is only used in rare cases. Side-chain mobility is analysed mainly by assuming a rapid equilibrium between three staggered conformations. The populations of the conformations can then be derived from the homonuclear and heteronuclear coupling constants using Pachler’s equation. The observed coupling Jobs then results as the average over all three rotamers, Ji, weighted with their respective population Pi. J obs ¼

X

Pi J i ði ¼ 123Þ

½11

P½1 ¼

J ðH a ; H bproR Þ  J sc J ap  J sc

½12

P½2 ¼

J ðH bproR ; COÞ  J sc J ap  J sc

½13

P½2 ¼

J ðH a ; H bproS Þ  J sc J ap  J sc

½14

P½3 ¼

J ðH bproS ; COÞ  J sc J ap  J sc

½15

i

Structural Chemistry Using NMR Spectroscopy, Peptides

For homonuclear couplings, the antiperiplanar coupling Jap is 13.6 Hz and the synclinal coupling Jsc is 2.6 Hz while for heteronuclear 1H–13C couplings Jap is 8.5 Hz and Jsc is 1.4 Hz. It should be noted that homonuclear coupling constants and NOE effects alone do not always yield an unambiguous diastereotopic assignment of the b-methylene protons. This means that incorrect values for the dominant bond angle (w1) may be obtained. This is especially the case if MD calculations are performed only under vacuum. In such cases, a globular structure is often predicted for the molecule, which only opens into a realistic conformation when the solvent is explicitly included in the calculations. Especially as peptides have a large surface which can interact with the solvent, it is essential to perform MD calculations in explicit solvents.

Relaxation Parameters and Molecular Dynamics NMR spectroscopy is uniquely capable of comprehensively characterizing the internal motions of peptides in solution at the atomic level over time-scales ranging from picoseconds to hours. NMR techniques used for the study of dynamics include relaxation rate measurements, dynamic NMR and line shape analysis, magnetization transfer experiments, NOESY and ROSEY and amide proton exchange measurements. For diamagnetic peptides in isotropic solvents, the primary mechanism of nuclear magnetic relaxation of protonated 13C nuclei and of 15N nuclei at natural abundance is the dipolar interaction with the directly bound protons. At high magnetic fields, chemical shift anisotropy (CSA) also contributes to the relaxation of the heteronuclei. The rates of these relaxation processes are governed by both the internal motions and the overall rotational motion of the molecule. Consequently, characterization of 13C and 15N heteronuclear relaxation can provide information about internal dynamics of peptides on time-scales faster than the rotational correlation time. The T1r times of protons have been measured to study conformational exchange on the microsecond to millisecond time-scale. However, the complex interaction with surrounding protons, which is strongly dependent on the molecular geometry, may lead to artefacts in the interpretation of the data. The overall tumbling rate, an important parameter for NMR spectroscopy, can best be determined by measuring T1 relaxation times. To determine the overall correlation time tc at least two different field strengths are required. In most cases, the function (T1 versus tc) allows for two possible values of tc. Usually the true tc can be selected based either on reasonable estimates as a function of relative molecular masses or after consideration of

2743

Figure 14 Dependence of T1 on tc at two different field strengths. The different T1 times [T1(1) and T1(2)] clearly correspond to tc(1); the alternative values for tc can be ruled out.

additional relaxation rates such as T2 relaxation times or heteronuclear NOEs (Figure 14). Specific models for internal motions can be used to interpret heteronuclear relaxation, such as restricted diffusion and site-jump models. However, model-free formal methods are preferable, at least for the initial analysis, since available experimental data generally are insufficient to completely characterize complex internal motions or to uniquely determine a specific motional model. The model-free approach of Lipari and Szabo for the analysis of relaxation data has been used for proteins and even for peptides. It attempts to reproduce relaxation rates by a weighted product of spectral density functions with different correlation times ti. The weighting factors are identified as order parameters S2i for the molecular rotational correlation time tc and optional further local correlation times ti. The term (1  S2i ) would then be proportional to the amplitude of the corresponding internal motion. However, the Lipari–Szabo approach is based on the assumption that molecular and local correlation times are not coupled, i.e. they should be distinct enough (e.g. differing by at least a factor of 10 in time) to allow for this separation. However, in small molecules the rates of these different processes are of the same order of magnitude, and the requirements of the Lipari–Szabo approach may not be fulfilled. Molecular dynamics simulation provides a complementary approach for the interpretation of relaxation measurements. See also: NMR Pulse Sequences, Nuclear Overhauser Effect, Solvent Supression Methods in NMR Spectroscopy, Structural Chemistry Using NMR Spectroscopy, Inorganic Molecules, Structural Chemistry Using NMR Spectroscopy, Pharmaceuticals, TwoDimensional NMR.

Further Reading Eberstadt M, Gemmecker G, Mierke DF, and Kessler H (1995) Scalar coupling constants – their analysis and their application for the

2744

Structural Chemistry Using NMR Spectroscopy, Peptides

elucidation of structures. Angewandte Chemie, International Edition in English 34: 1671--1695. Evans JNS (1995) Biomolecular NMR Spectroscopy. Oxford: Oxford University Press. Kessler H and Seip S (1994) NMR of Peptides. In: Croasmun WR and Carlson RMK (eds.) Two-Dimensional NMR Spectroscopy, pp. 619--654. Weinheim: VCH. Kessler H and Schmitt W (1996) Peptides and polypeptides. In: Grant DM and Harris RK (eds.) Encyclopedia of Nuclear Magnetic Resonance, pp. 3527--3537. Chichester: John Wiley & Sons. Lipari G and Szabo A (1982) Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. Journal of the American Chemical Society 104: 4546--4559.

Neuhaus D and Williamson MP (1989) The Nuclear Overhauser Effect in Structural and Conformational Analysis. Weinheim: VCH. Parella T (1996) High quality 1D spectra by implementing pulsed-field gradients as the coherence pathway selection procedure. Magnetic, Resonance in Chemistry 34: 329--347. van Gunsteren WF and Berendsen HJ (1990) Computer simulation of molecular dynamics: Methodology, applications and perspectives in chemistry. Angewandte Chemie, International Edition in English 29: 992. Wu¨thrich K (1986) NMR of Proteins and Nucleic Acids. New York: Wiley.