5.2. Methods for measuring scalar and dipolar couplings in dilute liquid crystal medium

There are three subsequent stages in protein structure determination. (1) Assignment of backbone resonances to the sequentially specific sites. (2) Identification of secondary structure elements. (3) Determination of a protein fold or a complete tertiary structure.

The assignment procedure can be performed, for example, by using HNCACB and HN(CO)CACB experiments (Salzmann et al. 1999) with either protonated or perdeuterated samples. Identification of the protein secondary structure is based on chemical shifts (Wishart & Sykes 1994), J-couplings, secondary structure specific NOE correlations (Wüthrich, 1986), and hydrogen bonds (Dingley & Grzesiek 1998).

Determination of a protein fold relies on long-range distance constraints, which are readily available from NOE intensities. However, the intensity of NOE signals is proportional to the inverse sixth power of the interatomic distance (1/r6 dependence), and it falls off rapidly as the distance between protons increases, limiting its applicability to serving as long-range distance information. As a result, the largest long-distance NOE intensities are usually found between side-chain protons. Unfortunately, these protons are much more tedious to assign than protons in the main-chain. Moreover, owing to the limited range of NOE intensities (< 5-6 Å), it is inevitably difficult to gain information on the relative orientation of domains. Additionally, as perdeuteration is usually preferred for larger proteins, owing to the gain in sensitivity and resolution, it dramatically decreases the available NOE information originating from aliphatic protons. Obviously then, obtaining good quality structure for perdeuterated, yet modular proteins, by using NOE information alone is laborious (Kay & Gardner 1997).

It has been shown recently that other type of structural information obtained from residual dipolar couplings can supplement the NOE information in order to recognize a protein fold (Tjandra et al. 1996; Tjandra et al. 1997b; Bax & Tjandra 1997; Tjandra & Bax 1997; Annila et al. 1999). Usually, for diamagnetic molecules there is hardly any dipolar contribution in scalar couplings in the high-resolution NMR spectrum due to motional averaging. However, when a certain molecule with anisotropic magnetic susceptibility is placed into a very high magnetic field, molecular tumbling is not completely isotropic because the molecule has a preference for a particular orientation. Consequently, a residual dipolar contribution appears. Hence, the measured splitting is caused by both the scalar and residual dipolar couplings (J+D). Although this phenomenon has been used in the NMR of small molecules for several years (Lounila & Jokisaari, 1982), it has been demonstrated on proteins only recently. Tolman and co-workers determined residual dipolar couplings ranging from -1 to 5 Hz for 1H-15N spin pairs at a 17.6 T magnetic field for the paramagnetic protein cyanometmyoglobin (Tolman (et al. 1995). Bax and co-workers measured very small 1H-15N and 1H-13C dipolar couplings (< 0.3 Hz), which were in very good agreement with the crystal structure, for the small diamagnetic protein ubiquitin (Tjandra et al. 1996). Similar results were also obtained for the GATA-1 protein-DNA complex (Tjandra et al. 1997b). Evidently, the method is not particularly suitable for diamagnetic proteins as the induced dipolar contributions are very small. It is applicable for systems with relatively large magnetic susceptibility, e.g. nucleic acids, protein-nucleic acid complexes, and metal binding proteins.

Fortunately, a method was found to induce a weak and tunable alignment while maintaining the high resolution and sensitivity of the normal isotropic spectrum. By dissolving the protein into a dilute nematic liquid crystal medium consisting of oriented phospholipid particles (bicelles), it is possible to induce a weak alignment of the protein (Bax & Tjandra 1997; Tjandra & Bax 1997). This has enabled the measurement of a large number of residual dipolar couplings in the protein backbone, including those between 15N(i)-13C’(i-1) and even 1HN(i)-13Cα(i-1). Unfortunately, proteins exist which interact destructively with bicelles, and consequently with this type of liquid crystal (Clore et al. 1998). Very recently, certain virus particles and membrane fragments have been shown to orientate in the magnetic field, providing an alternative liquid crystal media suitable for many proteins (Clore et al. 1998; Hansen et al. 1998; Koenig et al. 1999).

The dipolar contribution between amide proton and nitrogen will not necessarily provide precise information for structure calculation. If the internuclear bond vector is nearly parallel to the applied magnetic field, small changes in the vector orientation will not markedly affect the size of the dipolar coupling. The situation is very different when the bond-vector is orientated close to the magic angle (54.77º). In this case, small changes in vector orientation will produce significant variation in dipolar couplings. Therefore, it is obvious that error functions are non-linear. It would be beneficial to retrieve dipolar couplings from different orientations, but in practice this is restricted primarily due to a lack of liquid crystals orienting in different directions with respect to the applied magnetic field, and somewhat by the planarity of the peptide bond.

Constructive use of several heteronuclear dipolar couplings measurable in the polypeptide backbone will not only improve the quality of the structure but will also provide also a wealth of information on backbone dynamics. The utilization of tunable alignment via liquid crystal media enables assessment of residual dipolar couplings between 15N(i)-13C"(i-1), 15N(i)-13Cα(i/i-1), 13C"(i-1)-13Cα(i-1), 13Cα(i-1)-13Cβ(i-1), 1HN(i)-13C"(i-1), and 1HN(i)-13Cα(i/i-1), in addition to 1HN-15N. Figure 9 shows the maximal predicted dipolar contributions to different scalar couplings when the dipolar contribution to one-bond 1H-15N splitting is around 25 Hz. As emphasized in Figure 9, up to nine residual couplings are present in the protein main-chain, which can be measured with reasonable precision from perdeuterated samples.

Figure 9. The estimated maximal dipolar contributions to various scalar couplings between different nuclei in the protein main-chain when the maximal contribution to 1JNH is 25 Hz in a dilute liquid crystal.

Dipolar couplings can basically be measured using the existing experiments devised for the determination of scalar coupling constants. However, due to a non-existing conformational degree of freedom, many of the one- and two-bond scalar couplings have not earlier attracted much attention. Thus, there is a lack of optimized pulse sequences for the measurement of those couplings that were previously regarded as structurally insignificant. One guideline in this thesis was to devise a set of pulse sequences enabling a convenient measurement of several dipolar couplings from two-dimensional spectra superficially resembling the familiar 15N-HSQC, a spectrum that is usually available at an early stage of the structure determination procedure. Convenience is a desirable feature, especially when several different couplings are to be measured. Accordingly, many of the pulse sequences are designed to utilize spin-state-selective filtering (II-IV), which is advantageous for minimizing spectral crowding due to coupling. However, for large or highly α-helical proteins, the 15N-1H correlation map may be insufficiently resolved, and for that reason spin-state-selective, two-dimensional 13C’-1H and especially three-dimensional 13C’-15N-1H correlation-based methods are also taken into use.

Several spectroscopic reasons in favor of measuring couplings from the 15N, 1H correlation spectra exist. 1) Among the nuclei in the backbone of proteins, amide protons and nitrogens usually provide the best dispersion of chemical shifts, that is, minimal cross-peak overlap. 2) The amide nitrogen and proton relax more slowly in protonated samples than aliphatic carbons and protons do. Furthermore, transverse relaxation optimized spectroscopy (TROSY), which exploits the destructive relaxation interference between 15N chemical shift anisotropy (CSA) and 15N-1H dipolar interaction, offers significant improvement in resolution and sensitivity in high magnetic fields, especially with perdeuterated samples (Pervushin et al. 1997). 3) Heteronuclear polarization transfer steps are more easily and precisely controlled with nitrogen than with carbon because no significant coupling exists between nitrogens in the protein backbone. 4) The water signal can be effectively suppressed without disturbing the 1HN signals of the solute.

There are also practical advantages in measuring couplings from the 15N, 1H correlation spectra. Several dipolar couplings measured conveniently from two-dimensional 15N-1H correlation spectra give insight into conformational changes induced by ligand-binding, in a manner similar to the structure/activity relationship (SAR) by NMR studies in which binding epitopes can be localized from changes in chemical shifts (Shuker et al. 1996; Hajduk et al. 1997). As amide nitrogen and proton chemical shifts are very sensitive to changes in chemical environment and conformation, it is conceivable that changes in residual dipolar couplings induced by ligand-binding could also be observed concomitantly with chemical shift changes to reveal conformational changes.

5.2.1. Pulse sequences for determination of 1JNC’ and 2JHNC’ couplings

The simplest way of determining 1JNC’ and 2JHNC’ coupling constants is to record a two-dimensional 13C’-coupled 15N-HSQC spectrum (Delaglio et al. 1991). Because the backbone 15N nuclei are coupled to three different carbon spins, i.e. 13C’(i-1), 13Cα(i-1), and 13Cα(i), it is necessary to decouple the 13Cα spins to measure the 1JNC’ splitting adequately. Thus, 1JNC’ is measured from the indirectly detected dimension, whereas 2JHNC’ can be measured from the orthogonal, i.e. proton, dimension in a familiar E.COSY fashion provided that the 13C’ spin-state is left untouched between the t1 evolution period and acquisition. When this pulse sequence is combined with the spin-state-selective IPAP-HSQC (Ottiger et al. 1998), three different coupling constants can be measured from the same experiment (Wang et al. 1998). This pulse sequence has good sensitivity and the appearance of a 15N, 1H correlation map, but it creates doublets in the spectrum and thus increases spectral overlap. However, this can be avoided by inserting a spin-state-selective filter, sensitive to the 13C’-spin-state, prior to the t1 evolution period [II, IV]. Figure 10 shows the gradient-selected, sensitivity-enhanced versions of the HN(α/β-NC’-J) and HN(α/β-NC’-J)-TROSY pulse schemes, which enable simultaneous measurement of 1JNC’, 2JHNC’, and 1JNH couplings from a two-dimensional 15N, 1H correlation spectrum superficially resembling 15N-HSQC or TROSY. In this triple-spin-state-selective experiment, the magnetization is initially transferred from the amide proton to its directly bound nitrogen using the familiar INEPT step. Subsequently, with the aid of a spin-state-selective filter element, either antiphase or in-phase 15N magnetization with respect to the 13C’ spin is created. During the following t1 period, the 15N chemical shift is recorded with simultaneous evolution of 15N-13C’ coupling. Ultimately, by inserting a generalized TROSY scheme (Andersson et al. 1998; Weigelt 1998) prior to the acquisition period, the most slowly relaxing 15N and 1HN multiplet components can be selected, thus providing a 15N, 1H correlation spectrum with high sensitivity and resolution.

Figure 10. Pulse schemes of the (A) HN(α/β-NC"-J) and (B) HN(α/β-NC"-J)-TROSY experiments for the measurement of 1JNC" and 2JHNC" couplings from the 15N, 1H correlation spectrum. Narrow and wide bars denote 90º and 180º pulses, respectively, whereas selective 90º pulses for water are denoted by half-ellipses. 13C" 180˚ pulses are applied with a strength of δ/√3, where δ is the frequency between centers of the 13C" and 13Cα regions. Aliphatic carbons are selectively decoupled during t1 with the semi-selective SEDUCE-1 decoupling scheme (McCoy & Mueller 1992). Alternatively, an 180º pulse selective for α-carbons can be used. If the gradient-selected, sensitivity-enhanced HSQC is used, 15N is decoupled during acquisition using the WALTZ-16 decoupling field (Shaka et al. 1983). The delays employed are: Δ = 1/(4JNH); Ta = 1/(4JNC’); δ = gradient duration + recovery delay. (A) Phase cycling for the in-phase experiment: φ1 = x, -x; φ2 = x; φ3 = 2(y), 2(-y); φ4 = x; φrec. = x, -x. For the antiphase experiment, the phases of the φ1 and φ2 pulses are incremented by 90º. Frequency discrimination in F1 is obtained using the PEP sensitivity-enhanced gradient selection (Kay et al. 1992; Schleucher et al. 1993) by inverting the sign of the Gs gradient pulse together with the inversion of φ4. (B) Phase cycling for the in-phase experiment: φ1 = x, -x; φ2 = x; φ3 = y; φ4 = x; φ5 = 2(y), 2(-y); φrec. = x, -x. For the in-phase experiment, φ5 is incremented by 90º. For the axial peak suppression, φ1, φ4, and φ5 are incremented in the usual States-TPPI manner (Marion et al. 1989). Quadrature detection and TROSY selection in F1 is obtained by collecting two data sets, (I): φ2 = y; φ3 = x, (II): φ2 = -y; φ3 = -x, with simultaneous change in the gradient polarity (Weigelt 1998).

This approach provides obvious advantages: 1) The spectral overlap diminishes. 2) As we separate the α- and β-spin-states of the 1JNC’ doublet into different subspectra, i.e. remove the overlap, the measured coupling is not an underestimate of the true coupling. The above-mentioned statements are valid only if an adequate subspectral editing is obtained, i.e. corresponding α- and β-spin-states are well separated into the two subspectra. As can be seen in Figure 6, good suppression of the undesired multiplet component is achieved for 1JNC’ couplings in the range between 11.5 and 18.5 Hz. Within this range, the principle component is at least 30 times larger than the undesired minor component. We can thus obtain a very good filtering in isotropic phase, where the variation of the 1JNC’ couplings is negligible with respect to the filtering capability. In the anisotropic phase, especially when strongly orienting Pf1 phages (Hansen et al. 1998) are exploited, insufficient subspectral editing is expected for some residues. However, this can easily be avoided by scaling the corresponding in- or antiphase spectra before the reconstruction of subspectra. Figure 11 shows overlaid subspectra recorded using the pulse sequence shown in Figure 10B from the uniformly 15N, 13C labeled human cardiac troponin C (cTnC), which has a molecular weight of 18 kDa (161 residues). Dipolar contribution to 1JHNC’ can clearly be seen in the F2-dimension by observing the direction of the slope connecting the E.COSY multiplets.

Figure 11. Expansion of the HN(α/β-NC’-J) spectrum recorded from U-(15N, 13C) 18 kDa cTnC (0.5 mM) in a dilute liquid crystal at 40ºC, t1,max (t2) = 71 (128) ms, 16 transients. The upfield and downfield multiplet components are shown overlaid. 1(J+D)NC’ and 2(J+D)HNC’ couplings can be measured along the 15N- and 1H-dimensions, respectively. The spectrum was recorded on the Varian Unity 600 NMR spectrometer. The data were zero-filled to 2048x2048 points prior to Fourier transformation, and phase-shifted squared sine-bell window functions were applied in both dimensions.

It is also possible to measure 1JNC’ and 2JHNC’ couplings from a HNCO-type spectrum by utilizing a short filter element matched to the 1JHN coupling. Ottiger (et al. 1998) have devised a pulse sequence in which the 2JHNC’ coupling can be measured from a spin-state-selective two-dimensional H(N)CO spectrum. In their approach, 2JHNC’ is measured from the 13C’-dimension. Advantages of measuring 2JHNC’ from the 13C’ rather than from the proton dimension are more favorable relaxation properties and the absence of large proton-proton dipolar contributions in the anisotropic phase if protonated samples are used. Unfortunately, the 13C’ chemical shift range is rather small (~10 ppm), and owing to its large chemical shift anisotropy, relaxation properties are not optimal at the highest magnetic fields. Kay and co-workers have used TROSY-based accordion spectroscopy (Bodenhausen & Ernst 1981) to measure 1JNC’ and 2JHNC’ from 3D-HNCO spectrum (Yang et al. 1999). In this case, 1JNC’ and 2JHNC’ are determined from the 15N- and 1H-dimensions from the slowly relaxing cross-peak. However, as the 15N-13C’ coupling is not refocused, the couplings are measured from an antiphase splitting, and errors similar to those found in the phase-sensitive COSY are likely to occur in unfavorable cases. In addition, spectral crowding increases since the number of peaks is doubled.

Figure 12 illustrates two-dimensional H(α/β-NC’-J)CO and corresponding 3D-HNCO(α/β-NC’-J) pulse schemes (II; Permi et al. 2000) for determination of 1JNC’ coupling either from spin-state-selective 13C’-1HN or 13C’-15N-1HN correlation spectrum, respectively.

Figure 12. Pulse sequences of the (A) H(α/β-NC"-J)CO and (B) HNCO(α/β-NC"-J) experiments for measuring 1JNC" couplings from the two (three)-dimensional 13C", (15N), 1H correlation spectrum. Narrow and wide bars denote 90º and 180º pulses, respectively, whereas selective 90º pulses for water are denoted by half-ellipses. Aliphatic carbons are selectively decoupled during t1 with the semi-selective SEDUCE-1 decoupling scheme (McCoy & Mueller 1992). Alternatively, a 180º pulse selective for α-carbons can be used. The WALTZ-16 sequence (Shaka et al. 1983) was used to decouple 1H during heteronuclear coherence transfer and 15N during acquisition. 13C 90˚ (180˚) pulses were applied with a strength of δ/√15 (δ/√3), where δ is the frequency between centers of the 13C" and 13Cα regions. All 13C" pulses were applied on-resonance and 13Cα pulses off-resonance with phase modulation by δ. The vertical arrow indicates the position of the off-resonance compensation pulse. The delays employed are: Δ = τ = 1/(4JNH); Ta = 1/(4JNC’); Tb = 1/(4JC"Cα); 0 ≤ κ ≤ Ta’/t1,max; λ ≥ 0; δ = gradient duration + recovery delay. (A) Phase cycling for the in-phase experiment: φ1 = x, -x; φ2 = 2(y), 2(-y); φ3 = 4(x), 4(-x); φrec. = x, 2(-x), x. For the antiphase experiment, the phase of φ2 is incremented by 90º. Frequency discrimination in F1 is achieved by incrementing φ1 according to the States-TPPI protocol (Marion et al. 1989). (B) Phase cycling for the in-phase experiment: : φ1 = y; φ2 = x, -x; φ3 = x; φ4 = 2(y), 2(-y); φ5 = 4(x), 4(-x); φrec. = x, 2(-x), x. For the antiphase experiment, phase of the φ4 pulse is incremented by 90º. Frequency discrimination in F1 is achieved by incrementing φ2 according to the States-TPPI protocol. Frequency discrimination in F2 is obtained using the PEP sensitivity-enhanced gradient selection (Kay et al. 1992). The echo and anti-echo signals are collected separately by inverting the sign of the Gs gradient pulse together with the inversion of φ3. In addition to echo/anti-echo selection, φ1 and φrec. are inverted according to the States-TPPI protocol for axial peak suppression. A 90º pulse on the carbonyl carbon after the t2 period serves as a purge pulse for the undesired dispersive magnetization component arising from the 1/(2JNC") mismatch (III-IV).

In both schemes, the magnetization is transferred from 1HN to 13C’ via directly bound 15N, and overall sensitivity is improved by employing proton decoupling during the 15N-13C’ INEPT steps (Figure 12). Subsequently, proton single-quantum coherence is excited and edited with respect to 15N. Editing is based on the large and uniform 1JHN coupling, providing an excellent subspectral editing with respect to the J-mismatch (Figure 6). Thus, at the beginning of the t1 period, magnetization is in the form of 4HNzNzC’y in one experiment, whereas it is in the form of 2HNzC’y in the other. After labeling the 13C’ chemical shift and 1JNC’ coupling frequencies during the t1 evolution period, the magnetization is transferred back to the amide proton. In the 3D-HNCO(α/β-NC’-J) scheme (Permi et al. 2000; Figure 12B), the 15N chemical shift is detected during 13C’-15N back-transfer in the usual constant-time manner, utilizing the gradient-selected sensitivity-enhancement scheme. Eventually, after a post-acquisitional addition and subtraction of the corresponding in- and antiphase data sets, the cross-peaks appear at ωC"(i-1) + πJC"N, ωHN(i) and ωC"(i-1) - πJC"N, ωHN(i) in 2D, and ωC"(i-1) + πJC"N, ωN(i), ωHN(i) and ωC"(i-1) - πJC"N, ωN(i), ωHN(i) in 3D data sets, respectively. The separation of cross-peak placements in the F1-dimension between the two subspectra yields the 1JNC" couplings.

The improvement over the pulse sequence presented by Kay and co-workers is the spin-state-selective filtering utilized in the 13C’-dimension. Hence, overlapping 15N-13C’ doublet components are separated into two subspectra. Although transverse relaxation of 13C’ is faster than that of 15N in larger proteins, α/β-filtering establishes the use of a shorter acquisition time in the 13C’-domain. It is also beneficial to scale 1JNC’ coupling up with respect to the 13C’ chemical shift in order to reduce the experimental time (at the cost of transverse relaxation, of course). Therefore, the number of t1 increments can be reduced in the 3D version of the experiment. This also enables a more precise measurement of variations in 1JNC’, and reduces random measurement errors since the measured coupling is divided by 1+κ. For large, perdeuterated proteins, the measurement of 1JNC" is better carried out using the 3D HNCO(α/β-NC’-J)-TROSY scheme (Permi et al. 2000).

5.2.2. Determination of 1JC’Cα coupling

Relatively large dipolar contributions, i.e. 5-6 Hz, can be expected for one-bond scalar coupling between 13C’(i-1) and 13Cα(i-1) in the protein backbone. The scalar coupling varies between 51-55 Hz, but to the best of our knowledge, no dependence on backbone local conformation has been reported. The most obvious way of measuring this coupling is to record a 13C-HSQC spectrum, in which the coupling between 13Cα and 13C’ is allowed to evolve during the t1 evolution period. This evolution period is usually implemented as a constant-time to decouple the relatively large couplings between aliphatic 13Cα and 13Cβ. This is not very suitable for larger protonated protein samples due to the rapid relaxation of the 13Cα spins and the constant-time nature of the experiment. Clearly, neither is the method applicable to perdeuterated samples. Alternatively, starting from the 1HN magnetization, one could record a two-dimensional 13C’-1H correlation spectrum, in which the 1JC’Cα coupling evolves concomitantly with the 13C’ chemical shift during t1. However, as the dispersion of resonances in the 13C’-dimension is rather limited, the resulting 2D-spectrum may have severely overlapping signals.

As already mentioned, a 15N, 1H correlation map usually gives best results when considering minimum overlap in a two-dimensional spectrum. Thus, it is advantageous to record the 15N, 1H correlation spectrum, in which one is able to measure the 1JC’Cα coupling from cross-peak displacements in the F1-dimension. Several slightly different approaches can be used, one of which is illustrated in Figure 13. In a simple HN(α/β-COCA-J) experiment (III; Figure 13A), the 1HN magnetization is first transferred to its preceding 13C’ spin. At this point, the half-filter sensitive to the 13Cα spin-state is inserted into the pulse sequence to create either NzC’y or NzC’xCαz coherence for the in-phase and antiphase experiment, respectively. Subsequently, a mixed DQ/ZQ coherence between 15N and the preceding 13C’ is created by applying a 90° pulse for 15N (time point a in Figure 13A). During the following t1 evolution period, the 15N chemical shift evolves concomitantly with the 1JC’Cα coupling. Ultimately, the magnetization is transferred back to 15N single-quantum coherence and is brought back to the amide proton. Eventually, after addition and subtraction of the in-phase and antiphase data sets and their corresponding quadrature counterparts, correlations at ωN(i) + πJC"Cα, ωHN(i) and ωN(i) - πJC"Cα, ωHN(i) appear. It is then obvious that 1JC’Cα can be measured from the cross-peak displacement in the F1-dimension between the two subspectra.

Figure 13. Pulse sequences of the (A) HN(α/β-C"Cα-J), (B) HN(α/β-C"Cα-J)-TROSY, and (C) HNCO(α/β-C"Cα-J) experiments for the measurement of 1JC"Cα couplings from the two (three)-dimensional (13C"), 15N, 1H correlation spectra. Narrow and wide bars denote 90˚ and 180˚ pulses, respectively, whereas selective 90˚ pulses for water are denoted by half-ellipses. 13C 90˚ (180˚) pulses are applied with a strength of δ/√15 (δ/√3), where δ is the frequency between centers of the 13C" and 13Cα regions. All 13C" pulses are applied on-resonance and 13Cα pulses off-resonance with phase modulation by δ. The vertical arrow indicates the position of the off-resonance compensation pulses. The WALTZ-16 sequence (Shaka et al. 1983) is used to decouple 1H during heteronuclear transfer and 15N during acquisition in non-TROSY experiments. The delays employed are: Δ = 1/(4JNH); Ta = 1/(4JNC’); Tb = 1/(4JC"Cα). (A) Phase cycling scheme for the in-phase experiment is φ1 = x, -x; φ2 = 2(x), 2(-x); φ3 = x; φ4 = x; φ5 = 4(x), 4(-x); φrec. = x, 2(-x), x. For the antiphase experiment, φ2 and φ3 are incremented by 90˚. Frequency discrimination in F1 is obtained using the PEP sensitivity-enhanced gradient selection (Kay et al. 1992). The echo and anti-echo signals are collected separately by inverting the sign of Gs gradient pulse together with inversion of φ4. (B) Phase cycling for the in-phase spectrum: φ1 = y; φ2 = x; φ3 = y; φ4 = x, -x; φ5= 4(x), 4(-x); φ6 = 2(x), 2(-x); φrec. = x, 2(-x), x. ). For the antiphase experiment, φ1 and φ6 are incremented by 90˚. Delays as in (A) except for Ta = 1/(4JNC’) + Tb/2 – Δ/2 - κ*t1/4; T’a = 1/(4JNC’) - Tb/2 - Δ/2 + κ*t1/4. 0 ≤ κ ≤ Ta/t1,max; δ = gradient duration + recovery delay. Frequency discrimination in F1 is obtained using the sensitivity-enhanced TROSY scheme with gradient selection (Weigelt 1998). The echo and anti-echo signals are collected separately by inverting the sign of Gs gradient pulse together with inversion of φ2 and φ3. (C) The phase cycling scheme for cos(πJC"Cαt1) cos(ωC"t1) modulated data is φ1 = x; φ2 = x, -x; φ3 = 2(x), 2(-x); φ4 = 4(x), 4(-x); φ5 = x; φrec. = x, 2(-x), x. For sin(πJC"Cαt1) sin(ωC"t1) modulated data, φ3 is incremented by 90˚. Frequency discrimination in F1 is achieved by incrementing φ2 according to the States-TPPI protocol (Marion et al. 1989). Frequency discrimination in F2 is obtained using the PEP sensitivity-enhanced gradient selection. The echo and anti-echo signals are collected separately by inverting the sign of Gs gradient pulse together with inversion of φ5.

An alternative approach is to utilize the double-semi-constant-time scheme (DSCT) to evolve part of the 15N chemical shift during the 15N-13C’ out- and 13C’-15N back-transfer steps. By combining this approach with the sensitivity-enhanced TROSY scheme, more sensitive spectra for larger proteins can be obtained (IV). Alternatively, one could first record the coupling between 13C’ and 13Cα under 13C’ single-quantum coherence and monitor the 15N chemical shift under 15N single quantum coherence during the 13C’-15N back-transfer step, by employing the semi-constant-time TROSY scheme in order to obtain sufficient resolution in the 15N dimension. Additional sensitivity improvement is obtained by concatenating the first 15N, 1H spin-state-selective filter element in the TROSY scheme with the 13C’-15N back-INEPT step (Salzmann et al. 1999; Permi et al. 2000; Figure 13B). Regrettably, use of both out- and back- 15N-13C’ INEPT steps for 15N shift evolution results in concomitant downscaling of 1JC’Cα and increases the error in the measured coupling. However, improvement in overall sensitivity may compete with the downscaling of apparent splitting and thus, no clear distinction between the accuracy of the two experiments can be made. One interesting aspect is the function of the last 90° pulse on 13C’ following the 13C’-15N back-INEPT step. This pulse purges the undesired dispersive magnetization components arising from the J-mismatch of delay 2Ta, used to refocus 1JNC’ (III, IV). In most cases, due to relaxation, the delay 2Ta is set shorter than 1/(2JNC’), and as a result, the dispersive antiphase term also contributes to the detected signal. Therefore, it is essential to use a purge pulse on 13C’ to yield an absorptive line shape. It may also be advantageous to apply selective decoupling of either the 13Cα and/or 13C’ spins during acquisition (Yang & Kay 1999). This is because two- and three-bond dipolar contributions between 1HN(i) and 13Cα(i/i-1)/13C’(i) spins can be quite large in the anisotropic medium, and decoupling of these spins may improve the sensitivity of the experiments, even with larger proteins.

When considering large or highly alpha-helical proteins where resonance overlap is likely to occur more frequently, the need for a three-dimensional experiment is inevitable. The most obvious way to achieve sufficient resonance dispersion is then to record a HNCO-type experiment where 13C’ is allowed to couple to its preceding 13Cα during t1. Kay and co-workers have successfully applied this approach with a TROSY implementation for two large, perdeuterated proteins (Yang et al. 1999). However, analogously to their HNCO-TROSY scheme for the measurement of 1JNC’ and 2JHNC’ couplings, the 13Cα coupled HNCO-TROSY experiment creates doublets in the spectrum, which may degrade a number of adequately separated cross-peaks. Thus, to achieve a minimum resonance overlap, it is advantageous to record an α/β-filtered HNCO-experiment (III; Permi et al. 2000; Figure 13C). Analogously to the 3D-HNCO(α/β-NC’-J) scheme, post-acquisitional addition and subtraction of the in- and antiphase data sets result in two spectra with correlations at ωC"(i-1) + πJC"Cα, ωN(i), ωHN(i) and ωC"(i-1) - πJC"Cα, ωN(i), ωHN(i), respectively. This ensures a minimum resonance overlap and allows direct extraction of 13C"-13Cα coupling constants by subtracting cross-peak frequencies in the F1-dimension in the two subspectra. Since the 13C"-13Cα coupling is large (~53 Hz) and the spin-state-selective filtering is utilized, t1,max can be sufficiently short, i.e. 20 ms. Without spin-state separation, a limited acquisition time for the 1JC"Cα coupling would result in 13C"-13Cα doublets, which are not resolved to the baseline. Consequently, the separation of doublet components would underestimate the true coupling values.

Figure 14. A representative 2D-plane from the HNCO(α/β-C"Cα-J)-TROSY spectrum recorded from the 30.4 kDa protein E2. The corresponding upfield and downfield 1JC"Cα multiplet components are shown overlaid. A 1D trace is taken at the 13C’ chemical shift of 176.0 ppm. The spectrum was recorded on the Varian Unity INOVA 600 NMR spectrometer using 4 transients per FID from 1.0 mM U-(15N, 13C) and 80% 2H-labeled E2, 95%/5% H2O/D2O, 40 ºC, t1,max, t2,max, (t3) = 17, 18, (64) ms. Resolution in the F1-domain was doubled using forward linear prediction. Data were zero-filled to 128x512x512 data matrices and apodized with shifted squared sine-bell functions in all dimensions.

For larger proteins, measurement of 1JC"Cα is best carried out by using the transverse-relaxation-optimized HNCO(α/β-C’Cα-J)-TROSY scheme (Permi et al. 2000). The TROSY version is essentially similar to the non-TROSY version, excluding a few modifications. In this case, the time period for 15N frequency labeling is implemented in a manner similar to the semi-constant-time (SCT) TROSY evolution (IV). The 13C’-15N back-INEPT step and the first spin-state-selective filter element of the generalized TROSY scheme are concatenated to obtain an optimum sensitivity (Permi et al. 2000). In addition, for the selection of the most slowly relaxing 15N-1H multiplet component, it is possible to take advantage of the gradient- and sensitivity-enhanced TROSY implementation (Weigelt 1998). This enables minimal phase cycling needed for the coherence selection, and also provides for excellent water suppression.

The corresponding cross-peaks in the HNCO(α/β-C’Cα-J)-TROSY experiment, after addition and subtraction, appear at ωC’(i-1) + πJC’Cα, ωN(i) - πJNH, ωHN(i) + πJNH and ωC’(i-1) – πJC’Cα, ωN(i) - πJNH, ωHN(i) + πJNH, respectively. Therefore, 1JC’Cα couplings can be measured analogously to the HNCO(α/β-C’Cα-J) experiment, but from the most slowly relaxing 15N-1H multiplet component. A three-dimensional HNCO(α/β-C’Cα-J)-TROSY spectrum recorded from the 30.4 kDa (286 amino acid residues), uniformly 15N/13C and 80% 2H-labeled protein, E2, is shown in Figure 14. The in- and antiphase data sets were recorded in an interleaved manner over 18 hours at a 600 MHz 1H frequency.

5.2.3. Access to 1JNCα, 2JHNCα, 2JNCα, and 3JHNCα

Determination of 1JNCα and 2JNCα from proteins is a difficult task because both intra- and interresidual couplings between the amide nitrogen and 13Cα are comparable, and rather small in magnitude. The intraresidual coupling varies between 7 and 12 Hz, whereas interresidual 2JNCα shows a discrepancy between 4 and 9 Hz (Bystrov 1976). If a 15N-HSQC spectrum without 13Cα decoupling during the t1 evolution period (Delaglio et al. 1991) is recorded, the cross-peaks split into a doublet of doublets in the 15N-dimension. This is due to the coupling of 15N(i) to both the 13Cα(i) and 13Cα(i-1) spins. Analogously to the case of 1JNC’, it is necessary to decouple the 13C’ spins from 15N during t1 in order to maintain the simplified multiplet structure. In addition, if the spin-state of 13Cα is not perturbed, the 15N, 1H cross-peaks show a tilted E.COSY pattern because both the intra- and interresidual 13Cαs act as passive spins during the t1 and t2 periods. In practice, a triplet-like cross-peak is found due to the overlapping α- and β-states of the corresponding doublet of doublets. Even in small proteins, it is difficult to resolve the two center lines of the multiplet. Recording the corresponding TROSY spectrum, with the most slowly relaxing multiplet component, provides narrower line widths, but adequate separation of the multiplet components is still difficult in most cases, as can be seen in Figure 15, illustrating the 15N, 1H cross-peak from Lys63 in ubiquitin (IV).

Figure 15. Expansion of the Lys63 15N, 1H cross-peak recorded using the {13Cα}-15N-TROSY experiment. The spectrum was recorded on the Varian Unity 600 NMR spectrometer from 1.0 mM U-(15N, 13C) ubiquitin, 90/10% H2O/D2O, 25ºC, t1,max (t2) = 222 (128) ms. Data were zero-filled to 4kx4k data matrices and apodized with shifted squared sine-bell functions in both dimensions. The data were processed using a squared cosine bell weighting functions in both dimensions.

One possibility is to make use of accordion-style J-multiplication, as illustrated in Figure 16. The pulse sequence is a simple modification of the {13Cα}-15N-TROSY. In this case, the 15N chemical shift is recorded during the t1 period, whereas the coupling between 13Cα and 15N evolves simultaneously for κ*t1, where κ is the multiplication coefficient. This approach necessitates, however, that the 15N spin relaxes at a favorable rate due to the long period of time during which the 15N spin is in the transverse plane.

Figure 16. The J-multiplied {13Cα}-15N-TROSY experiment for the measurement of 1JNCα, 2JNCα, 2JHNCα, and 3JHNCα couplings in 15N, 13C, (2H)-labeled proteins. Narrow and wide bars denote 90˚ and 180˚ pulses, respectively, whereas selective 90˚ pulses for water are denoted by half-ellipses. 13C" 180˚ pulses were applied with a strength of δ/√3, where δ is the frequency between centers of the 13C" and 13Cα regions. Aliphatic carbons are selectively decoupled during t1 with the semi-selective SEDUCE-1 decoupling scheme (McCoy & Mueller 1992). Alternatively, a 180˚ pulse selective for α-carbons can be used. The delays employed are: Δ = 1/(4JNH); δ = gradient duration + recovery delay; κ ≥ 0. Phase cycling: φ1 = x, -x; φ2 = x; φ3 = y; φrec. = x, -x. Quadrature detection and TROSY selection in F1 is obtained by collecting two data sets, (I): φ2 = x; φ3 = y, (II): φ2 = -x; φ3 = -y, with simultaneous change in the gradient polarity (Weigelt 1998).

It is obvious that the multiplet pattern could be simplified if one of the 13Cα spins coupled to the 15N spin could be selectively decoupled. This approach is not suitable for proteins due to numerous 13Cα spins, therefore, an alternative method is required to obtain a simplified multiplet pattern. We have used the HN(α/β-NCα-J)-TROSY experiment (IV; Figure 17), allowing exploitation of spin-state-selective filtering sensitive to the 13Cα(i-1) spin-state. The pulse sequence in Figure 17 has been modified similar to the one presented in Figure 13B to obtain higher sensitivity.

Figure 17. The pulse scheme of the HN(α/β-NCα-J)-TROSY experiment for determination of 1JNCα, 2JNCα, 2JHNCα, and 3JHNCα couplings in 15N/13C/(2H)-labeled protein samples. The delays employed are: Δ = 1/(4JNH); Ta = 1/(4JNC"); T’a = 1/(4JNC") - Δ; Tb = 1/(4JC"Cα); 0 ≤ κ ≤ T’a/t1,max. Phase cycling for the in-phase spectrum: φ1 = x, -x; φ2 = x; φ3 = y; φ4 = 2(x), 2(-x); φ5 = 4(x), 4(-x); φrec. = x, 2(-x), x; for the antiphase spectrum, φ4 is incremented by 90˚. The arrow indicates the position of the Bloch-Siegert compensation pulse in the antiphase filter. Frequency discrimination in F1 is obtained using the sensitivity-enhanced TROSY scheme with gradient selection. The echo and anti-echo signals are collected separately by inverting the sign of Gs gradient pulse together with inversion of φ2 and φ3. Resolution in the 15N-dimension is improved by implementing an evolution period for the 15N chemical shift and the 15N-13Cα couplings in a semi-constant time manner. Narrow and wide bars denote 90˚ and 180˚ pulses, respectively, whereas selective 90˚ pulses for water are denoted by half-ellipses. 13C 90˚ (180˚) pulses are applied with a strength of δ/√15 (δ/√3), where δ is the frequency between centers of 13C" and 13Cα regions. All 13C" pulses are applied on-resonance and 13Cα pulses off-resonance with phase modulation by δ.

Initially, magnetization is transferred from the 1HN spin to 13C’, as in the TROSY-type HNCO scheme. The subsequent spin-state-selective filter element is employed to edit the 13Cα(i-1) spin-state in order to create 4HNzNzC’z coherence in the in-phase experiment and 8HNzNzC’zCαz coherence in the corresponding antiphase experiment (time point a). During the following 13C’-15N back-INEPT step, which is implemented as a semi-constant time, the 15N chemical shift evolves simultaneously with couplings to 13Cα(i) and 13Cα(i-1) on the most slowly relaxing 15N-1H multiplet component. Post-acquisitional addition and subtraction yields two subspectra, in which the centers of visible doublets are separated by 2JNCα. The individual doublet components in either subspectrum are separated by 1JNCα. Figure 18 clearly illustrates this spectral simplification, showing previously overlapping doublet components overlaid with thick and thin contours. Two additional couplings, namely 3JHNCα and 2JHNCα, are readily available from this HN(α/β-NCα-J) experiment in the 1H dimension. A familiar E.COSY pattern emerges since the 13Cα spin acts as a common passive spin to both the 15N and 1HN spins during the t1 and acquisition periods, respectively. Thus, 3JHNCα can be determined from cross-peak displacement in the F1-dimension between two subspectra, whereas 2JHNCα can be measured from the tilt between doublet components in the F2-dimension within each subspectrum. Analogously to the former HN(α/β-C’Cα-J) schemes, to preserve the purely absorptive line shape in F1 and F2, an additional 90° pulse on 13C’ is applied prior to the acquisition period.

Figure 18. A selected F2-F3 plane from the 3D-HNCO(α/β-NCα-J)-TROSY experiment recorded from the 30.4 kDa, uniformly 15N/13C and 80% 2H-labeled protein, E2. The spectrum was recorded on the Varian Unity INOVA 600 NMR spectrometer using 8 transients per FID from 1.0 mM U-(15N, 13C) and 80% 2H-labeled E2, 95%/5% H2O/D2O, 40 ºC, t1,max, t2,max, (t3) = 12, 35, (56) ms. Resolution in the F1-domain was doubled using forward linear prediction. Data were zero-filled to 128x1kx1k data matrices and apodized with shifted squared sine-bell functions in all dimensions. The upfield and downfield 1JNCα multiplet components are shown overlaid. The visible splittings for the 1JNCα and 2JNCα couplings were multiplied by a factor of 4.

The HN(α/β-NCα-J)-TROSY scheme can be modified to obtain the three-dimensional HNCO(α/β-NCα-J)-TROSY experiment (Permi et al. 2000), which provides improved resolution necessary for highly α-helical proteins. In this case, the 13C’ chemical shift is recorded during the t1 period. The α/β-filter is inserted after the t1 evolution period and for the in-phase (antiphase) experiment, the 4HNzNzC’z (8HNzNzC’zCαz) coherence is created before the t2 evolution period, which is again implemented in a semi-constant-time TROSY manner. However, due to the relatively small size of the 1JNCα coupling, an additional spin-echo period must be inserted for the 15N-13Cα coupling evolution to reduce the number of increments needed in the F2-dimension. Hence, the 1JNCα and 2JNCα couplings scale up by 1+λ (λ ≥ 0) with respect to the 15N chemical shift. After addition and subtraction of the in- and antiphase data sets and their corresponding quadrature counterparts, cross-peaks are found at ωC’(i-1), ωN(i) - πJNH + (1+λ)π2JNCα ± (1+λ)π1JNCα, ωHN(i) + πJNH + π3JHNCα ± π2JHNCα and ωC’(i-1), ωN(i) - πJNH - (1+λ)π2JNCα ± (1+λ)π1JNCα, ωHN(i) + πJNH - π3JHNCα ± π2JHNCα, for the two- and three-dimensional subspectra, respectively.

5.2.4. Insight to side-chains, 1JCαCβ

Up to this point, we have obtained a wealth of data from which the orientation of several internuclear vectors in the protein backbone can be derived. It is obvious that it is crucial to gain information on the orientation of side-chains, as well. A logical approach is to measure the one-bond couplings between the 13Cα and 13Cβ spins. This is readily available from a 13C-HSQC spectrum. However, several reasons limit the applicability of a 13C-HSQC method to larger proteins. First, the high transverse relaxation rates of the 13Cα and 1Hα spins dramatically reduce the intensity and resolution of the 13C-HSQC spectrum. Second, the 1Hα spins resonate close to the water signal, which hampers the interpretation of data. Third, if perdeuterated samples are used, it is clear that this method cannot be used. We can alleviate these problems with a HNCO -based TROSY-type experiment, as shown in Figure 19 (Permi et al. 2000).

Figure 19. The pulse sequence of the HNCO(CαCβ-J)-TROSY experiment for the measurement of 1JCαCβ couplings in 15N/13C/(2H)-labeled proteins. The delays employed are: Δ = 1/(4JNH); Ta = 1/(4JNC"); T’a = 1/(4JNC") - Δ; Tb = 1/(4JC"Cα); 0 ≤ κ ≤ Ta/t2,max; λ ≥ 0; 0 ≤ µ ≤ Tb/t1,max. Phase cycle: φ1 = y; φ2 = x; φ3 = y; φ4 = 2(x), 2(-x); φ5 = x, -x; φ6 = 4(x), 4(-x); φrec. = x, 2(-x), x. The arrow indicates the position of the Bloch-Siegert compensation pulse in the antiphase filter. Frequency discrimination in F1 is obtained using the sensitivity-enhanced TROSY scheme with gradient selection. The echo and anti-echo signals are collected separately by inverting the sign of Gs gradient pulse together with inversion of φ2 and φ3. The resolution in the 15N-dimension is improved by implementing an evolution period for the 15N chemical shift and 15N-13Cα couplings in a semi-constant time manner. Narrow and wide bars denote 90˚ and 180˚ pulses, respectively, whereas selective 90˚ pulses for water are denoted by half-ellipses. 13C 90˚ (180˚) pulses are applied with a strength of δ/√15 (δ/√3), where δ is the frequency between centers of the 13C’ and 13Cα regions. All 13C pulses are applied on-resonance and 13Cα pulses off-resonance with phase modulation by δ.

Initially, magnetization is transferred from the 1HN spin to the preceding 13Cα spin. Depending on the sample, we can use two different schemes to record 1JCαCβ. Consider first a protonated sample. During the following t1 evolution period, 1JCαCβ evolution is allowed to take place, while the large 1JCαHα and the chemical shift of 13Cα are refocused by inserting a 180° (13Cα/Cβ) pulse in the middle of λt1. Instead of 13Cα, we record the 13C’ chemical shift during the following 1JC’Cα refocusing delay. This period is implemented in a semi-constant time manner in order to obtain sufficient resolution in the F1-dimension. Eventually, the 15N chemical shift is incremented during the t2 evolution period by using the semi-constant-time TROSY scheme (IV; Permi et al. 2000). It should be noted that, by using this approach, the 180° (1H) pulse during the t1 time for 1JCαHα refocusing can be omitted. As this pulse would interchange the fast and slow relaxing 15N-1H multiplet components, the presented scheme is preferred. On the other hand, the 13Cα chemical shift can be recorded without mixing the 15N-1H spin-states if we apply during t1 a semi-selective 1Hα decoupling or, alternatively, a spin-locking. Finally, the 13C’, 15N, 1HN correlation map results, where the multiplets in the F1-dimension are resolved by λ* 1JCαCβ, as illustrated in Figure 20 (Permi et al. 2000).

Figure 20. A representative portion of the HNCO(CαCβ-J)-TROSY spectrum of ubiquitin. Cross-peaks are shown for K6, I13, L67, and V70 residues at the 15N cross-section of I13. The cross-peaks are split by apparent 2*1JCαCβ in the F1-dimension (λ = 2). The spectrum was recorded on the Varian Unity INOVA 500 NMR spectrometer using 24 transients per FID from 1.0 mM U-(15N, 13C) ubiquitin, 90%/10% H2O/D2O, 30ºC, t1,max, t2,max, (t3) = 37.6, 18.8, (64) ms. The data were post-processed to a 1024x128x1024 matrix prior to Fourier transformation, and phase-shifted squared sine-bell window functions were applied in all dimensions.

For perdeuterated samples, a scheme in which the 13Cα chemical shift is recorded simultaneously with 1JCαCβ, is preferred. In this case, it is also possible to use J-scaling by inserting an additional spin-echo period for the 1JCαCβ evolution. As the relaxation rate of the 13Cα spin is rather long in perdeuterated samples, this implementation improves the accuracy in data analysis, thanks to the properly resolved coupling. Additionally, since the measured coupling is divided by 1+λ, more precise values with respect to random measurement error can be obtained. Subsequently, magnetization is transferred back to 15N via the 13C’ spin, and the 15N chemical shift is recorded during the SCT TROSY period.