J. Mol. Biol. (1991) 217, 731-736

Accurate Measurements of Coupling Constants from Two-dimensional Nuclear Magnetic Resonance Spectra of Proteins and Determination of +-Angles Svend Ludvigsen, Kim V. Andersen and Flemming M. Poulsen’f Department of Chemistry, Gamle Car&berg Vej 10, DK-2500 (Received 9 July

Carlsberg Laboratory Valby, Copenhagen, Denmark

1990; accepted 23 October 1990)

A new and simple method to measure 3J nNHacoupling constants of proteins by adding and subtracting traces from corresponding two-dimensional nuclear Overhauser enhanced spectroscopy and two-dimensional correlated spectroscopy cross peaks after scaling is proposed. The optimal scaling for the addition and the subtraction of the two traces is obt,ained by minimizing an error function. The method was proven to give accurate and precise measurements of coupling constants when tested with a series of simulated spectra. The accuracy of the method was better than 0.1 Hz for all test cases including the limiting case of J = 2.0 Hz and line-width = 11.0 Hz. The 3JHNHzcoupling constants were measured in two-dimensional nuclear magnetic resonance spectra of the two proteins barley serine proteinase inhibitor (CI-2) and the bacterial ribonuclease (barnase) of Bacillus amyloliquefaciens. The experimentally measured coupling constants were used to calculate the constants in a Karplus equation to be:

3JHNHa= 6.7 cos2(&60)

- 1.3 cos(+-60) + 15.

These constants are in good accordance with those obtained for basic pancreatic trypsin inhibitor (BPTI). In addition, special emphasis is given to the measurements of positive &angles, and to the contribution of molecular dynamics on the apparent coupling constants.

1. Introduction

and accurate determination of these. Although coupling constants are easily measured in phasesensitive COSY spectra when the line-width is small compared to the coupling of interest, the main problem of coupling constant measurements in spectra of relatively large proteins is the broad resonances that hamper a correct measurement of the coupling constant as the distance between the two components of the antiphase doublet (Neuhaus et al., 1985). Several methods have been proposed that overcome this problem; some rely on mathematical manipulations carried out on cross sections of COSY cross peaks (Oschkinat & Freeman, 1984; Kessler et al., 1985; Kim & Prestegard, 1989) or fitting spectral parameters to appropriate cross peaks (Widmer & Wiithrich, 1987; Hyberts et al., 1987; Madi & Ernst, 1988). In proteins where the determination of 3JHNHais of particular interest, “N labeling of recombinant proteins or of proteins of microbial origin, can serve to measure 3JHNH.(Kay et al., 1989; Neri et al., 1990). The application of such methods are, however, limited to proteins of this origin. Therefore in the present paper we propose a

It is well established that two-dimensional ‘H n.m.r.2 spectroscopy can provide detailed structural information of proteins in solution (Wiithrich, 1986). The main source of structural information is derived from careful interpretation of cross peak intensities in NOESY spectra, and equally useful are measurements of coupling constants which can provide the important structural information about dihedral angles in proteins through the Karplus equation (Karplus, 1959; Bystrov, 1976; Pardi et al., 1984). A prerequisite for a correct interpretation of coupling constants in structural studies is a precise 7 Author to whom correspondence should be addressed. $ Abbreviations used: n.m.r., nuclear magnetic resonance; NOESY, 2-dimensional nuclear Overhauser enhanced spectroscopy; COSY, 2-dimensional correlated spectroscopy; 2&F, double-quantum filtered; CI-2, barley serine proteinase inhibitor 2 (chymotrypsin inhibitor 2); barnase, bacterial ribonuclease of Bacillus amyloliquefaciens; FID, free induction decay.

731 0022-2836/91/040731&06



1991 Academic

Press Limited

S. Ludvigsen


In a NOESY spectrum we consider a cross peak at the position of nucleus A along o2 (not necessarily at Ok along the w1 dimension) and this cross peak in terms of product operators is given as:

method by which coupling constants can be measured by generating the sum and the difference of traces of cross peaks in COSY and NOESY spectra, a method that has some resemblance to the DISCO procedure (Kessler et aZ., 1985). This coupling constant measurement method, however, will only extract the active coupling constant, and furthermore it is independent of the line-shape of the peaks used in the analysis. This method, which should be particularly well suited for measurements of coupling constants in proteins, has been applied to two-dimensional ‘H n.m.r. spectra of two proteins for which high-resolution crystal structures are available, the serine proteinase inhibitor (CI-2) from barley (McPhalen & James, 1987) and the bacterial ribonuclease (barnase) from Bacillus amyloliquefaciens (Mauguen et al., 1982). n.m.r. spectra of the two proteins have been extensively investigated and virtually complete assignments are available of both (Kjaer et al., 1987; Byeroft et al.: 1990). Comparisons of predicted and measured coupling constants as well as a qualitative comparison of the structures in crystal and solution were possible based on the analysis of the data.

where z is the mixing time for the NOESY experiment. fN(tl) involves the chemical shift’ evolution under t, of the other nucleus in the NOESY cross peak. After Fourier transformation of the COSY spectrum and the NOESY spectrum traces of the two cross peaks after proper scaling (which is considered lat’er) are added and subtracted to yield C and A, where:

and A = -21A/,z+I,x






= -1,z(1-2I&


The frequency difference between t,he multiplets in C and A is precisely J,,, the active coupling. Not,e that if JAM is small compared to the line-width the difference between the center frequencies of C and A is still JAM. This manipulation of traces is close to the idea of the DISCO method where traces from different cross peaks in COSY spectra were added and subtracted to yield the passive coupling. The trace of a cross peak can be extracted as a sum of the traces that form the cross peak. In this manner the S/N ratio is increased significantly. F(w,, w2) is the surface of t’he spectrum and F can be decomposed into E”(w,, wz) = F1(w,)F,(w,), where F,(w,) and Fz(wz) are the Fourier transforms of the t, and t,-dependent terms of the two-dimensional FID, respectively. Thus, the trace of interest G(w,) contains the t,-dependent contributions of equations (1) and (2), which is the information

In the following we consider an AMX spin system with the emphasis on extracting the coupling constant JAM. It is assumed that no strong coupling effects are present. At the beginning of the t, period (acquisition) the COSY cross peak considered at (w,, 02) = (w,, wA) is in terms of product operators (Sorensen et al., 1983) given by the following expression: cos(nJMXtl) = [email protected])~


~*,[email protected]~

2. Theory

21AxIMz eeiUMtl sin(xJA,t,)

et al














Figure 1. The PU’OESY ( + ) and COSY trace (M) before addition and subtraction. The )3 trace (0) and the A trace (A) are separated by the true coupling constant, if the scale factor, according to eqns (6) and (7); is chosen correctly. In (a) the scale factor is 60, which is too large, and thus the C and A trace are not symmetric around their individual centers. In (b) the scale factor is 2.0, which is too small. The simulated coupling is 4.0 Hz and the full line-width at half height is Il.0 Hz; the correct scale factor in this case (c) is 40.

Coupling Constants Measurements and @Angles







7.7 (b)


Figure 2. Baseline-corrected

COSY and NOESY cross peaks of Ala35 in CI-2 are shown in (a) and (b), respectively. Continuous lines are positive contours, broken lines are negative. The NOESY cross peak represents a sequential NOE effect between Glu34 HN and Ala35 HN. (c) The extracted traces (COSY (w) and NOESY trace (+)) and the Z (0) and A (A) trace which are separated by 3.7 Hz, the actual 3Ju~H. value. necessary


for further =


spectral resolution. The principle of these measurements is shown in Figure 1, where the COSY and NOESY traces are shown with the differences and sums appropriately scaled. In the evaluation of spectral values between two spectral points the interpolated value based on a second-order polynomial fit to three neighboring points was used.



01 =a


o,, 0s are the limits enclosing the cross peak. As previously mentioned the trace of a COSY cross peak and a NOESY cross peak needs proper scaling before addition and subtraction. The trace of the COSY cross peak is denoted G,-(0,) and that of NOESY GN(02), thus the scale factor X can be defined as: W4 4~4

= G&d = -G&J,)

+ +

mW&W) max(GN(oi)) max(Qd4)) max(G,(w’,))

G (c’, )S N ’ ’




The optimal S factor is obtained when all negative contributions from the antiphase component have disappeared (Fig. 1). It should be noted that the results of this method are independent of the use of any window functions, provided that the same window function is used for both the COSY and the NOESY FIDs along t,. In order to cal\ulate the optimal scaling factor we used a symmetry-based error function, r~ (eqn (S)), to measure the suchess of the used scale factor. When the antiphase component has disappeared in the C and the A trace the remaining two components, which are both absorptive, will be symmetric around the center frequency. Thus, the center frequency obtained for the X and the A trace are exactly separated by JAM. The optimal scaling factor is reached where the symmetry-based error function c has minimum:

Wcenter 4s)= c (~(W)--(O+2(w-ocenter)))2, W=W*,AW


where cod is the outer border for the region of interest, Ocenter the center of the C trace and Ao the

3. Methods To test the described method spectra were simulated at conditions normally met within spectra of proteins. One set of cross peaks was simulated with pairs of NOESY and COSY cross peaks based on a simple AX spin system Line-widths were simulated at 5.0, 8.0 and 11.0 Hz, coupling constants at 2.0, 3.0, 40; 5.0, 7.0 and 9.0 Hz giving at set of 18 pairs of NOESY and COSY cross peaks. A COSY cross peak between the amide proton in the o2 direction and the H” in the o1 direction respectively, exhibit an antiphase doublet pattern along w2. However, the passive 4 bond couplings 4JHNHB which can contribute with couplings up to 05 Hz have to be accounted for in the measurements. Therefore, the same set as described above was used in a second simulation with an additional passive coupling of 65 Hz for all cross peaks in order to test the ability of the method to eliminate the effects from small passive couplings. In order to test the influence of noise a set of spectra was simulated with the addition of different levels of random noise. A home-written program (M. Kjaer, unpublished results) was used to create cross peaks. The spectral resolution was 091 Hz/point in w2, and 3.65 Hz/point in oi. In the simulations the acquisition times were 0274 s in t,, and 0.0681 s in t,, thus zero-filling was made in t, from 512 to 2048 points and in t, from 128 to 512 points to give the above-mentioned resolution. In order to test the influence of the application of window functions the simulations were performed using, respectively, a number of different window functions, or none, prior to Fourier transformation. Cross peaks with systematic noise artifacts normally show a missing or abnormal convergence for the error function CT. In such cases visual inspection rather than automatic detection of such behavior is preferable, because this can provide an additional criterion for proper analysis of the Z and A traces.

S. Ludvigsen


et al.

Table 1 Coupling


in the simuEated spectra


Simulated line-widths? Simulated coupling constants WI 2.0

50 Hz J measured$ 204/2.06 2.99/3.00 402/403 &97/497 699/s-99 S.99/8~99

3.0 4-O 50 7.0 PO

SeparationS 3.7313.77 411/4,15 4.74j4.77 X14/556 7.1q7.19 9.17/9.17

8.0 Hz JmeasuredS

11.0 Hz



%04/C 10 541j5.45 5-871590 6.4716.50 7-86/7.87 954/955

2.9q2.99 403/404 soa/ 7.01/7.01 900/!+00



1.9sj1.97 3.00/3.00 4~00/4aO 5~00/5~01 7.01:7.01 8.98/8.98

6,67/6TO C96j7.00 7.3217.35 7.7317.76 8+7/8+39 [email protected]/10.28

t The line-width is defined as the full width at half height. $ The first value is the measurement. in simulations without the additional pa.ssive coupling. second value stems from simulations with the additional passive coupling (see the text).

The proposed method was applied to genuine protein Z-dimensional n.m.r. data. Measurements were performed on cross peaks in NOESY spectra (mixing t,ime 0.150 s) and COSY spectra between HN and H” in 2 proteins, CI-2 and ba.rnase. For both proteins the crystal and the solution structures are known (McPhalen & James, 1987; Clore et al., 1987; S, Ludvigsen, H. Shen, M. Kjaer & F. M. Pouisen, unpublished results; Mauguen et al.; 1982; M. Bycroft, S. Ludvigsen, A. R. Fersht & F. M. Poulsen, unpublished results). NOESY (Jeener et al.; 1979; Anil-Kumar et al., 1980, 1981; States et al., 1982) and 2QF-COSY (Piantini et al., 1982; Rance et al., 1983) were recorded at 500 MHz on a Bruker AM500 n.m.r. speetrometer equipped with an Aspect 3000 computer. The recorded n.m.r. data were transferred to, a Stardent 1500 or VAX 1 l/750 computer where all further processing was performed using a home-made n.m.r. software package. In all cases the spectra were recorded and transformed using the hyper-complex 2-dimensional Fourier transform yielding quadrat,ure detection and pure phase (Bachmann et al., 1977; States et al., 1982). All spect~ra of these 2 proteins were resolution-enhanced by sine-bells shifted x/5 in both dimensions. The experimental details concerning t,hese n.m.r. experiments were as described (Kjaer et al., 1987).

4. Results The correlation between the measured coupling constants, and the corresponding parameters with and without small passive couplings in the simulations,



a remarkably



function is applied that increases the S/X ratio at the expense of line-broadening (for instance Gaussian multiplication), the measurements of even small couplings of resonances with broad lines is made possible; thus, apodization can be preferable in such cases. Working with recorded spectra (Fig. 2) it was observed that the method was sensitive to small shifts in the spectrum offsets or small resonance frequency differences between the corresponding peaks in the COW and the NOESY spectra. It is therefore recommended to record the two spectra under similar experimental conditions. Furthermore, it was noticed that the use of baseline corrections enhanced the success rate of the convergence of the scaling procedure for certain sets of cross peaks. The results obtained with the present met,hod f’ar the measurements of 3JHNHe in CI-2 and barnase were compared to those predicted on the basis of dihedral angles from the crystal structures using the Karplus equation with the parameters found by Pardi (Pardi et al., 1984). This comparison is shown in Figure 3. Given that the Pardi parameters have been established on the basis of data fr’om only one protein we have used the present data set of I!2

and in

of the method to eliminate contributions from small passive couplings was demonstrated (Table 1). These measurements of coupling constants in spectra without any noise were almost independent of t,he used window function (exponential, sine-bell or Gaussian). The sensitivity of the method was further examined by measuring coupling constant,s in spectra with random noise, and it was found that even at S/N ratios of 6 : 1 the accuracy of the measurements were still within 0.5 Hz in the range of coupling constants and line-width outlined. Thus, for ratios of S/N above 10 : 1, the method must be considered both precise and accurate for coupling constant measurements. If, aIternatively, an apodization



the a.bility

8 J

6 4 2 -180

I -120

I -60

/ 0

I 60


I 180


Figure 3. Plot of measured 3JHNH, in CI-2 (+) and barnase (H) as a function of the dihedral angle 4 found in the crystal structures. The continuous curve show-s the best-fitted Karplus equation to the measured couplings, which is quite similar to the broken curve based on the constants found by Pardi (Pardi et al., 1984).

Coupling Constants Measurements and @-Angles


Table 2 coupling constants to the Karplus equation Number of couplings

CI-2 Barnase All BPTI




r.m.s.7 1.16 0.89






66 6.7 64

-1.4 -1.3 -1.4

1.6 1.5

112 36


1.01 0.87

UPTI, basic pancreatic trypsin inhibitor. t r.m.s. is the root-mean-square deviation between the fitted values and the measured coupling constants (Pardi et al.; 1984).

measurements to obtain a new set of constants for the Karplus equation for a comparisonj’. Our results (Table 2) give a Karplus equation: 3JHNH” = 6.7 cos2($-60)-

1.3 cos(+60)

+ 1.5,

which deviates only a little from the equation found by Pardi (Table 2). The root-mean-square deviation between the measured couplings and those derived from the Karplus curve is 1.01 Hz.

5. Discussion The present study has focused attention on the finding of a sample of residues in the two proteins (CI-2 and barnase) that have positive &angles, typical for the type II turns (Wiithrich, 1986). Except for one of the residues (His18 in barnase, constants were all 3JHNH. = 5.8 Hz) these coupling measured to be 6*8( kO.3) Hz. Furthermore, it was found that the size of the HN-H” NOES for these residues, as expected, is considerably larger than for reflecting that the HNpH” any other &angles, distance is 2.2 A for &angles of +60” and 2.7 A for $-angles of - 57” typical of a-helices (1 A = 0.1 nm). For example, the average intensity of the HN-H” NOES was seen to be 2.7( f 0%) times larger than the average intensity of HN-H” NOES of residues in 2.5 and 4.5 Hz. helices with 3JH~Hz between Therefore, the identification of residues in proteins that have positive @-angles near +60” can be made unambiguously on the basis of these two sets of measurements. The results of the determination of the Karplus parameters (Table 2) for Cl-2 show a large rootmean-square deviation compared to those of the two other proteins. A comparison between the measured 3JHNH. and the predicted ones for CI-2 shows large differences for residues 55, 56, 59 and 60, which are located in the subtilisin binding loop Interpretation of measured coupling region. constants as structural parameters have been examined (Hoch et al., 1985; Kessler et aZ., 1988), and it has been shown using molecular dynamics simula-

t The full list of measured coupling constants used in Fig. 3 can be obtained, on request, to the authors. The data will be submitted to the protein n.m.r. database, c/o Professor John L. Markley (Ulrich et al. (1989).


tions that the time-averaged coupling constants are close to the coupling constants predicted by X-ray crystallography using the Karplus equation when the mobility is low. On the backbone of the protein one can normally expect little mobility, and thus 3JHNHacan be related directly through a Karplus equation to the dihedral angle 4. In contrast, for many side-chains near the surface of the protein where the mobility is higher, the measured coupling constants can not be related to predicted couplings on the basis of a crystal structure. A relatively higher mobility is a reasonable explanation for the incorrect predicted sizes of coupling constants of the four mentioned residues in the loop region of CI-2. Leaving out those four measurements of coupling constants lowers the root-mean-square deviation for the Karplus fit (Table 2) from 1.16 Hz to 0.85 Hz, and the constants fitted change only slightly (Table 2: A = 7.3, B = - 1.0, C = 0.9). Even though this coupling constant measurement method is used to extract 3JH1HNH. couplings in proteins in this case; it can also be used to extract other coupling constants. The method can for example, in combination with the DISCO method (Kessler et al., 1985), be a powerful tool to measure other coupling constants in protein n.m.r. spectra. The authors thank Fersht for samples

Dr Mark Bycroft and Professor Alan of barnase and Professor R. W.

Dodson for the crystal structure

co-ordinates of barnase.

Cand. Scient. Jens Christian Madsen and Cand. Scient. Mogens Kjaer are thanked for fruitful discussions and advice. MS Pia Mikkelsen is thanked for skilled preparation of samples of CI-2.

References Anil-Kumar, Ernst, R. R. & Wiithrich, K. (1980). A Two-dimensional Nuclear Overhauser Enhancement (2D NOE) Experiment for the Elucidation of Complete Proton-Proton Cross-relaxation Networks in Biological Macromolecules. Biochem. Biophys. Res. Commun. 95, l-6. Anil-Kumar, Wagner, G., Ernst, R. R. & Wiithrich, K. (1981). Buildup Rates of the Nuclear Overhauser Effect Measured by Two-dimensional Proton Magnetic Resonance Spectroscopy: Implications for J. Amer. Chem. Sot. Studies of Protein Conformation.

103, 3654-3658. Bachmann, P., Aue, W. P., Miiller, L. & Ernst, R. R. (1977). Phase Separation in Two-dimensional Spectroscopy. J. Magn. Reson. 28, 29-39. Bycroft, M.; Sheppard, R. N., Lau, S. T. K. & Fersht, A. R. (1990). Sequential Assignment of the ‘H Nuclear Magnetic Resonance Spectrum of Barnase.

Biochemistry, Bystrov, V. F. Conformational

29, 7425-7432.

(1976). Spin-Spin Coupling and the States of Peptide Systems. Progr. NMR Xpectrosc. 10, 41-81. Clore, G. M., Gronenborn, A. M., Kjaer, M. & Poulsen, F. M. (1987). The Determination of the Three-dimensional Structure of Barley Serine Proteinase Inhibitor 2 by Nuclear Magnetic Resonance, Distance Geometry and Restrained Molecular Dynamics. Protein Eng. 1, 305-311.


S. Ludvigsen

Hoch, J. C., Dobson, C. M. & Karplus, M. (1985). Vicinal Coupling Constants and Protein Dynamics. Biochemistry, 24, 3831-3841. Hyberts, S. G., Marki, W. & Wagner, G. (1987). Stereo-specific Assignments of Side-chain Protons and Characterization of Torsion Angles in Eglin c. Eur. J. Riochem. 164, 625-635. Jeener, J., Meier, B. H., Bachmann, P. & Ernst, R. R. (1979). Investigation of Exchange Processes by Two-dimensional NMR spectroscopy. J. Chem. Phys. 71> 4546-4553. Karplus, M. (1959). Contact Electron-spin Coupling of Nuclear Magnetic Moments. J. Phys. Chem. 30, 11-15. Kay, L. E., Brooks, B., Sparks, S. W., Torchia, D. A. & Bax, A. (1989). Measurement of NH-CaH Coupling Staphylococcal Nuclease by Constants in Two-dimensional NMR and Comparison with X-ray Crystallographic Results. J. Amer. Chem. Sot. 111, 5488-5490. Kim, Y. & Prestegard, J. H. (1989). Measurement of Vicinal Couplings from Cross Peaks in COSY Spectra. J. Magn. Reson. 84, 9-13. Kessler, H., Miiller, A. & Oschkinat, H. (1985). Differences and Sums of Traces within COSY Spectra (DISCO) for the Extraction of Coupling Constants: ‘Decoupling’ After the Measurement. Magn. Reson. Chem. 23, 844-852. Kessler, H.; Griesinger, C., Lautz, J., Miiller, A., van Gunsteren, W. F. 6 Berendsen, H. J. C. (1988). Conformational Dynamics Detected by Nuclear Magnetic Resonance NOE Values and J Coupling Constants. J. Amer. Chem. Sot. 110, 3393-3396. Kjaer, M., Ludvigsen, S., Sorensen, 0. W., Denys, L. A., Kindtler; J. & Poulsen, F. M. (1987). Sequence Specific Assignment of the Proton Nuclear Magnetic Resonance Spectrum of Barley Serine Proteinase Inhibitor 2. Carlsberg Res. Commun. 52, 327-354. Madi, Z. L. & Ernst, R. R. (1988). Compmer Analysis of Two-dimensional NMR Spectra. Estimation of Parameters by Least-squares Spectral Approximation. J. Magn. Reson. 79, 513-527. Mauguen, Y.; Hartley, R. W., Dodson, E. J., Dodson, G. G., Bricogne, G., Chothia, C. & Jack, A. (1982). Molecular Structure of a New Family of Ribonucleases. Nature (London), 297, 162164. McPhalen, C. A. & James, M. N. G. (1987). Crystal and Molecular Structure of the Serine Proteinase Edited

et al. Inhibitor CI-2 from Barley See&. Biochemistry, 26; 261-269. Neri, D., Qtting, G. & Wiithrich, K. (1990). New Nuclear Magnetic Resonanee Experiment for Measurements of the Vicinal Coupling Constants 3JHNz in Proteins. J. Amer. Chem. Sot. 112, 3663-3665. Neuhaus; D., Wagner, G., Vasak, M., KSigi, H. R. $ Wiithrich, K. (1985). Systematic Application for High-resolution, Phase-sensitive Two-dimensional ‘H-NMR Techniques for the Identification of the Amino-acid-proton Spin Systems in Proteins. Rabbit Metallothionein-2. Eur. J. Bioehem. 151, 257-273. Oschkinat, H. & Freeman, R,. (1984). Fine Structure in Two-dimensional NMR Correlation Spectroscopy. J. Magn. Reson. 60, 164-169. Pardi, A., Billeter, M. & Wiithrich, K. (1984). Calibration of the Angular Dependence of the Amide Proton-C” Proton Coupling Constants, ‘JwN,, in a Globular Protein. J. Mol. Biol. 180. 741-751. Piantini, U., Sorensen, 0. W. & Ernst, R. R. (1982). Multiple Quantum Filters for Elucidating NMR Coupling Networks. J. Amer. Chem. Sot. 104, 6800-6801. Rance, M., Sorensen, 0. W., Bodenhausen, G., Wagner, G., Ernst, R. R. & Wiithrich, K. (1983). Improved Spectral Resolution in COSY ‘H NMR Spectra. of Proteins via Double Quantum Filtering. Rio&em. Biophys. Res. Commun. 117, 479-485. States, D. J., Haberkorn, R. A. & Ruben, D. J. (1982). A Two-dimensional Nuclear Overhauser Experiment with Pure Absorption Phase in Four Qua,drants. J. Magn. Reson. 48, 286-292. Scrrensen; 0. W., Eich, 6. W., Levitt, M. H.: Bodenhausen, G. & Ernst, R. R. (1983). Product Operator Formalism for the Description of NMR Pulse Experiments. Prog. NMR Spectrosc. 16, 1633192. Ulrich, E. L.: Markley, J. L. & Kyogoku, Y. (1989). Creation of a Nuclear Magnetic Resonance Data Repository and Literature Database. Protein Seq. Data Anal. 2, 23. Widmer, H. & Wiithrich, K. (1987). Simulated Two-dimensional NMR Cross-peak Fine Structures Spin Systems in Polypeptides and for “H Polydeoxynucleotides. J. Magn. Reson. 74, 316-336. Wiithrich, K. (1986). NMR of Proteins and Nucleic Acids, Wiley-Interscience, New York.

by P. Wright

Accurate measurements of coupling constants from two-dimensional nuclear magnetic resonance spectra of proteins and determination of phi-angles.

A new and simple method to measure 3JHNH alpha coupling constants of proteins by adding and subtracting traces from corresponding two-dimensional nucl...
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