NMR structural refinement of an extrahelical adenosine tridecamer d(CGCAGAATTCGCG)2 via a hybrid relaxation matrix procedure

Until very recently interproton distances from NOESY experiments have been derived solely from the two-spin approximation method. Unfortunately, even at short mixing times, there is a significant error in many of these distances. A complete relaxation matrix approach employing a matrix eigenvalue/eigenvector solution to the Bloch equations avoids the approximation of the two-spin method. We have calculated the structure of an extrahelical adenosine tridecamer oligodeoxyribonucleotide duplex, d(CGCAGAATTCGCG)2, by an iterative refinement approach using a hybrid relaxation matrix method combined with restrained molecular dynamics calculations. Distances from the 2D NOESY spectra have been calculated from the relaxation rate matrix which has been evaluated from a hybrid NOESY volume matrix comprising elements from the experiment and those calculated from an initial structure. The hybrid matrix derived distances have then been used in a restrained molecular dynamics procedure to obtain a new structure that better approximates the NOESY spectra. The resulting partially refined structure is then used to calculate an improved theoretical NOESY volume matrix which is once again merged with the experimental matrix until refinement is complete. Although the crystal structure of the tridecamer clearly shows the extrahelical adenosine looped out way from the duplex, the NOESY distance restrained hybrid matrix/molecular dynamics structural refinement establishes that the extrahelical adenosine stacks into the duplex.     

Two-dimensional 1H and 31P NMR spectra and restrained molecular dynamics structure of a covalent CPI-CDPI2-oligodeoxyribonucleotide decamer complex

CPI-CDPI2 is a synthetic analogue of CC-1065, which is a naturally occurring antitumor antibiotic. Assignment of the 1H NMR spectra of a CPI-CDPI2-oligodeoxyribonucleotide decamer, d-(CGCTTAAGCG)2, complex has been made by two-dimensional 1H/1H spectroscopy. The solution structure of the complex was calculated by an iterative hybrid relaxation matrix method combined with NOESY distance restrained molecular dynamics. Refinement proceeded in two steps in which the decamer was initially refined alone and then CPI-CDPI2 was added to the structure to allow initial estimates of drug-DNA contacts. A hybrid matrix/MD refinement was used to better take into account problems associated with spin diffusion. Thus the distances from the 2D NOESY spectra were calculated from the relaxation rate matrix which were evaluated from a hybrid NOESY volume matrix comprising elements from the experimental spectrum and those calculated from an initial structure. The hybrid matrix derived distances were then used in a restrained molecular dynamics procedure to obtain a new structure that better approximates the NOESY spectra. The resulting partially refined structure was then used to calculate an improved theoretical NOESY volume matrix which is once again merged with the experimental matrix until refinement is complete. The efficacy of CC-1065 has been attributed to its minor groove binding and alkylation to the N3 position of adenosine. CPI-CDPI2 appears to bind to the decamer in a similar manner. The effect of CPI-CDPI2 on the decamer's 1H and 31P spectrum was consistent with a minor groove binding motif with the drug alkylating at A17 with the CDPI rings oriented toward the 5'-end of the alkylated strand. In addition, the NMR data support one major adduct but also indicate the presence of a minor adduct. The latter could represent a drug alkylation of the DNA at a secondary site (or alternative orientation of the rings).     

Solution structure of the EcoRI DNA sequence: refinement of NMR-derived distance geometry structures by NOESY spectrum back-calculations

The solution structure of the self-complementary DNA duplex [d(CGCGAATTCGCG)]2, which contains the EcoRI restriction site sequence GAATTC at the center, has been studied by two-dimensional nuclear magnetic resonance spectroscopy. Time-dependent nuclear Overhauser effect spectra were used to obtain the initial cross-relaxation rates between 155 pairs of protons. These initial cross-relaxation rates were converted into interproton distances and entered into a distance (bounds) matrix. A distance geometry algorithm (DSPACE) was used to create embedded starting structures and to refine these structures until they showed good agreement with the distance matrix; symmetry constraints were included in the refinement procedure, making the two strands in the refined distance geometry structures virtually identical and significantly improving the agreement with the distance matrix. The NOESY spectrum for one of these distance geometry structures was then calculated from the explicit coordinates by numerically integrating all the z-magnetization transfer pathways among neighboring protons within a specified radius. Distances in this distance geometry structure that did not agree with the experimental NOESY time course were then adjusted accordingly. This process was iterated until a good agreement between calculated and experimental NOESY spectra was reached. The final structure, which generates good agreement with the experimental NOESY spectrum, displays kinks at the C3-G4 base step and at the A6-T7 base step that appear to be similar to those reported for the EcoRI restriction site DNA bound to its endonuclease. The solution structure is not the same as the crystal structure of this DNA duplex.     

How accurately can oligonucleotide structures be determined from the hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics approach?

The accuracy and precision of structures derived from a combined hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics methodology were examined with simulations that included typical experimental errors. NOESY data were simulated for a DNA dodecamer duplex, d-(CGCGAATTCGCG)2, with added volume error of approximately 20% and low-level thermal noise. Distances derived from a hybrid relaxation matrix analysis of the NOE data were used as constraints in molecular dynamics driven structural refinements of several initial model geometries. The final structures were compared against results obtained from the traditional isolated two-spin approximation treatment of these NOESY volumes and also against refined structures that employed error-free data. Results show that the structures derived from the relaxation rate matrix analysis of the NOESY data are more accurate than those derived from a simple two-spin approximation analysis and it is possible to achieve refinement to the level of simulated experimental error. Results may be significantly improved with the use of either more accurately measured NOESY volumes or additional matrix-derived constraints. Many of the helical parameters and backbone torsional angles may be accurately reproduced by the hybrid matrix methodology.     

A Renaissance Man: In Memoriam of Jon Widom (1955–2011)

Abstract

Assignment of the ¹H and ³¹P resonances of a decamer DNA duplex, d(CGCTTAAGCG)₂ was determined by two-dimensional COSY, NOESY and ¹H- ³¹P Pure Absorption phase Constant time (PAC) heteronuclear correlation spectroscopy. The solution structure of the decamer was calculated by an iterative hybrid relaxation matrix method combined with NOESY-distance restrained molecular dynamics. The distances from the 2D NOESY spectra were calculated from the relaxation rate matrix which were evaluated from a hybrid NOESY volume matrix comprising elements from the experiment and those calculated from an initial structure. The hybrid matrix-derived distances were then used in a restrained molecular dynamics procedure to obtain a new structure that better approximates the NOESY spectra. The resulting partially refined structure was then used to calculate an improved theoretical NOESY volume matrix which is once again merged with the experimental matrix until refinement is complete. J_H3′-P coupling constants for each of the phosphates of the decamer were obtained from ¹H-³¹P J-resolved selective proton flip 2D spectra. By using a modified Karplus relationship the C4′-C3′-03′-P torsional angles (?) were obtained. Comparison of the ³¹P chemical shifts and J_H3′-P coupling constants of this sequence has allowed a greater insight into the various factors responsible for ³¹P chemical shift variations in oligonucleotides. It also provides an important probe of the sequence-dependent structural variation of the deoxyribose phosphate backbone of DNA in solution. These correlations are consistent with the hypothesis that changes in local helical structure perturb the deoxyribose phosphate backbone. The variation of the ³¹P chemical shift, and the degree of this variation from one base step to the next is proposed as a potential probe of local helical conformation within the DNA double helix. The pattern of calculated ? and ζ torsional angles from the restrained molecular dynamics refinement agrees quite well with the measured J_H3′-P coupling constants. Thus, the local helical parameters determine the length of the phosphodiester backbone which in turn constrains the phosphate in various allowed conformations.     

2'-deoxyribonolactone lesion in DNA: refined solution structure determined by nuclear magnetic resonance and molecular modeling

The solution conformation of the DNA duplex d(C1G2C3A4C5L6C7A8C9G10C11).d(G12C13G14T15G16T17G18T19G20C21G22 ) containing the 2'-deoxyribonolactone lesion (L6) in the middle of the sequence has been investigated by NMR spectroscopy and restrained molecular dynamics calculations. Interproton distances have been obtained by complete relaxation matrix analysis of the NOESY cross-peak intensities. These distances, along with torsion angles for sugar rings and additional data derived from canonical A- and B-DNA, have been used for structure refinement by restrained molecular dynamics (rMD). Six rMD simulations have been carried out starting from both regular A- and B-DNA forms. The pairwise rms deviations calculated for each refined structure are <1 A, indicating convergence to essentially the same geometry. The accuracy of the rMD structures has been assessed by complete relaxation matrix back-calculation. The average sixth-root residual index (Rx = 0.052 +/- 0.003) indicated that a good fit between experimental and calculated NOESY spectra has been achieved. Detailed analysis revealed a right-handed DNA conformation for the duplex in which both the T17 nucleotide opposite the abasic site and the lactone ring are located inside the helix. No kinking is observed for this molecule, even at the abasic site step. This structure is compared to that of the oligonucleotide with the identical sequence containing the stable tetrahydrofuran abasic site analogue that we reported previously [Coppel, Y., Berthet, N., Coulombeau, C., Coulombeau, Ce., Garcia, J., and Lhomme, J. (1997) Biochemistry 36, 4817-4830].     

Relaxation matrix analysis of two-dimensional nuclear Overhauser effect spectra

The large number of interproton distances extracted from two-dimensional nuclear Overhauser effect spectra has enabled determination of biomolecular structures in solution. The accuracy of those distances is increased substantially and the number of distances increased significantly by analysis of the experimental peak intensities using a complete relaxation matrix approach. More distances and more accurate distances both lead to a higher resolution structure. A complete relaxation matrix analysis also enables simulation of peak intensities for any postulated structure; comparison of these intensities with experimental intensities can provide a guide for structure refinement as well as a measure of the quality of the structure derived.     

Simulation of NOESY spectra of DNA segments: A new scaling procedure for iterative comparison of calculated and experimental NOE intensities

Summary A new algorithm for simulation of two-dimensional NOESY spectra of DNA segments has been developed. For any given structure, NOE intensities are calculated using the relaxation matrix approach and a new realistic procedure is suggested for 1:1 comparison of calculated and experimental intensities. The procedure involves a novel method for scaling of calculated NOE intensities to represent volumes of digitised cross peaks in NOESY spectra. A data base of fine structures of all the relevant cross peaks with Lorentzian line shapes and in-phase components, is generated in a digitised manner by two-dimensional Fourier transformation of simulated time domain data, assuming a total intensity of 1.0 for each of the cross peaks. With this procedure, it is shown that the integrated volumes of these digitised cross peaks above any given threshold scale exactly as the total intensity of the respective peaks. This procedure eliminates the repetitive generation of digitised cross peaks by two-dimensional Fourier transformation during the iterative process of structure alteration and NOE intensity calculation and thus enhances the speed of DNA structure optimization. Illustrative fits of experimental and calculated spectra obtained using the new procedure are shown.[/p]     

Effects of Experimentally Achievable Improvements in the Quality of NMR Distance Constraints on the Accuracy of Calculated Protein Structures

New methods for collecting cross-relaxation data from proteins and nucleic acids make it possible to improve the accuracy and precision of interproton distance measurements used as input for NMR solution structure determinations. It thus is of interest to determine whether such experimentally achievable improvements in input distance constraints have significant effects on the precision and accuracy of the resulting structures. To answer this question, we have turned to a computational procedure involving the use of data simulated from a known structure, in order to allow unambiguous assessments of accuracy. The approach to improved distances evaluated here is that afforded by magnetization exchange network editing (MENE); MENE pulse sequences break the network of cross-relaxation interactions into regions that are manipulated so as to defeat certain spin-diffusion terms. A target structure was prepared from the X-ray structure of a small protein, turkey ovomucoid third domain (OMTKY3). A normal NOESY spectrum and two varieties of MENE spectra, BD-NOESY and CBD-NOESY, were simulated by means of complete relaxation matrix analysis. These results were used to create different input data sets with the same number of constraints (perfectly accurate distances derived from the target structure, more accurate distances derived from the MENE simulations, and less accurate distances derived from the NOESY simulation), and these, interpreted at different levels of precision, were used as input for solution structure calculations. The results showed that the use of more precise input data measurably improves the local precision and accuracy of calculated structures, but only if the more precise data include the actual target distance. Incorporation of the experimentally achievable, accurate distances with higher precision afforded by the MENE pulse sequences into the set of input distances was found to improve the accuracy of the resulting structures, particularly in terms of side-chain conformation.     

A variable target intensity-restrained global optimization (VARTIGO) procedure for determining three-dimensional structures of polypeptides from NOESY data: Application to gramicidin-S

Summary A global optimization method for intensity-restrained structure refinement, based on variable target function (VTF) analysis, is illustrated using experimental data on a model peptide, gramicidin-S (GS) dissolved in DMSO. The method (referred to as VARTIGO for variable target intensity-restrained global optimization) involves minimization of a target function in which the range of NOE contacts is gradually increased in successive cycles of optimization in dihedral angle space. Several different starting conformations (including all-trans) have been tested to establish the validity of the method. Not all optimizations were successful, but these were readily identifiable from their large NOE R-factors. We also show that it is possible to simultaneously optimize the rotational correlation time along with the dihedral angles. The structural features of GS thus obtained from the successful optimizations are in excellent agreement with the available experimental data. A comparison is made with structures generated from an intensity-restrained single target function (STF) analysis. The results on GS suggest that VARTIGO refinement is capable of yielding better quality structures. Our work also underscores the need for a simultaneous analysis of different NOE R-factors in judging the quality of optimized structures. The NOESY data on GS in DMSO appear to provide evidence for the presence of two orientations for the ornithine side chain, in fast exchange. The NOESY spectra for this case were analyzed using a relaxation rate matrix which is a weighted average of the relaxation rate matrices for the individual conformations.     

NMR solution structure of an oxaliplatin 1,2-d(GG) intrastrand cross-link in a DNA dodecamer duplex

We have determined, at high resolution, the NMR solution structure of an oxaliplatin-GG DNA dodecamer in the AGGC sequence context by 2D NMR studies. Homonuclear assignment strategies resulted in unambiguous assignment of 203 out of 249 protons, which corresponds to assignment of approximately 81% of the protons. Assignments of H5' and H5" protons were tentative due to resonance overlap. The structure of the oxaliplatin duplex was calculated using the program CNS with a simulated annealing protocol. A total of 510 experimental restraints were employed in the structure calculation. Of 20 calculated structures, the 15 with the lowest energy were accepted as a family. The RMSD of the 15 lowest energy structures was 0.68 A, indicating good structural convergence. The theoretical NOESY spectrum obtained by back-calculation from the final average structure showed excellent agreement with the experimental data, indicating that the final structure was in good agreement with the experimental NMR data. Significant conformational differences were observed between the oxaliplatin-GG 12-mer DNA we studied and all previous solution structures of cisplatin-GG DNA duplexes. For example, the oxaliplatin-GG adduct shows much less distortion at the AG base-pair step than the cisplatin-GG adducts. In addition, the oxaliplatin-GG structure also has a narrow minor groove and an overall axis bend of about 31 degrees, both of which are very different from the recent NMR structures for the cisplatin-GG adducts. These structural differences may explain some of the biological differences between oxaliplatin- and cisplatin-GG adducts.     

Structure determination of [d(ATATATAUAT)]2 via two-dimensional NOE spectroscopy and molecular dynamics calculations

Proton homonuclear two-dimensional (2D) NOE spectra were obtained for the decamer [d(ATATATAUAT)]2 as a function of mixing time, and proton resonance assignments were made. Quantitative assessment of the 2D NOE cross-peak intensities was used in conjunction with the program MARDIGRAS, which entails a complete relaxation matrix analysis of the 2D NOE peak intensities, to obtain a set of upper and lower bound interproton distance constraints. The analysis with MARDIGRAS was carried out using three initial models: A-DNA, B-DNA and Z-DNA. The distance constraints determined were essentially the same regardless of initial structure. These experimental structural constraints were used with restrained molecular dynamics calculations to determine the solution structure of the decamer. The molecular dynamics program AMBER was run using A-DNA or B-DNA as starting model. The root-mean-square (rms) difference between these two starting models is 0.504 nm. The two starting models were subjected to 22.5 ps of restrained molecular dynamics calculations. The coordinates of the last 10.5 ps of the molecular dynamics runs were averaged to give two final structures. MDA and MDB. The rms difference between these two structures is 0.09 nm, implying convergence of the two molecular dynamics runs. The 2D NOE spectral intensities calculated for the derived structures are in good agreement with experimental spectra, based on sixth-root residual index analysis of intensities. A detailed examination of the structural features suggests that while the decamer is in the B-family of DNA structures, many torsion angle and helical parameters alternate from purine to pyrimidine, with kinks occurring at the U-A steps.     

Error distribution derived NOE distance restraints

Errors and imprecisions in distance restraints derived from NOESY peak volumes are usually accounted for by generous lower and upper bounds on the distances. In this paper, we propose a new form of distance restraints, replacing the subjective bounds by a potential function obtained from the error distribution of the distances. We derived the shape of the potential from molecular dynamics calculations and by comparison of NMR data with X-ray crystal structures. We used complete cross-validation to derive the optimal weight for the data in the calculation. In a model system with synthetic restraints, the accuracy of the structures improved significantly compared to calculations with the usual form of restraints. For experimental data sets, the structures systematically approach the X-ray crystal structures of the same protein. Also standard quality indicators improve compared to standard calculations. The results did not depend critically on the exact shape of the potential. The new approach is less subjective and uses fewer assumptions in the interpretation of NOESY peak volumes as distance restraints than the usual approach. Figures of merit for the structures, such as the RMS difference from the average structure or the RMS difference from the data, are therefore less biased and more meaningful measures of structure quality than with the usual form of restraints.     

Quantitative internuclear distancesvia two-dimensional nuclear magnetic resonance spectra: A test case and a DNA octamer duplex

Two-dimensional proton nuclear magnetic resonance nuclear Overhauser effect experiments have been performed at a series of mixing times on proflavine and on a DNA octamer duplex [d-(GGAATTCC)]₂ in solution. Using the complete matrix approach recently explored theoretically (Keepers and James, 1984), proton-proton internuclear distances were determined quantitatively for proflavine from the two-dimensional nuclear Overhauser effect results. Since proflavine is a rigid molecule with X-ray crystal structure determined, interproton distances obtained from the two-dimensional nuclear Overhauser effect experiments in solution can be compared with those for the crystalline compound agreement is better than 10 %. Experimental two-dimensional nuclear Overhauser effect spectral data for [d-(GGAATTCC)]₂ were analyzed by comparison with theoretical two-dimensional nuclear Overhauser effect spectra at each mixing time calculated using the complete 70 × 70 relaxation matrix. The theoretical spectra were calculated using two structures: a standard B-form DNA structure and an energy-minimized structure based on similarity of the octamer's six internal residues with those of [d-(CGCGAATTCGCG)]₂, for which the crystal structure has been determined. Neither the standard B-DNA nor the energy-minimized structure yield theoretical two-dimensional nuclear Overhauser effect spectra which accurately reproduce all experimental peak intensities. But many aspects of the experimental spectra can be represented by both the B-DNA and the energy-minimized structure. In general, the energy-minimized structure yields theoretical two-dimensional nuclear Overhauser effect spectra which mimic many, if not all, features of the experimental, spectra including structural characteristics at the purine-pyrimidine junction.     

Three-dimensional solution structure of the HIV-1 protease complexed with DMP323, a novel cyclic urea-type inhibitor, determined by nuclear magnetic resonance spectroscopy.

The three-dimensional solution structure of the HIV-1 protease homodimer, MW 22.2 kDa, complexed to a potent, cyclic urea-based inhibitor, DMP323, is reported. This is the first solution structure of an HIV protease/inhibitor complex that has been elucidated. Multidimensional heteronuclear NMR spectra were used to assemble more than 4,200 distance and angle constraints. Using the constraints, together with a hybrid distance geometry/simulated annealing protocol, an ensemble of 28 NMR structures was calculated having no distance or angle violations greater than 0.3 A or 5 degrees, respectively. Neglecting residues in disordered loops, the RMS deviation (RMSD) for backbone atoms in the family of structures was 0.60 A relative to the average structure. The individual NMR structures had excellent covalent geometry and stereochemistry, as did the restrained minimized average structure. The latter structure is similar to the 1.8-A X-ray structure of the protease/DMP323 complex (Chang CH et al., 1995, Protein Science, submitted); the pairwise backbone RMSD calculated for the two structures is 1.22 A. As expected, the mismatch between the structures is greatest in the loops that are disordered and/or flexible. The flexibility of residues 37-42 and 50-51 may be important in facilitating substrate binding and product release, because these residues make up the respective hinges and tips of the protease flaps. Flexibility of residues 4-8 may play a role in protease regulation by facilitating autolysis.     

Improved simulation of NOESY spectra by RELAX-JT2 including effects of J-coupling, transverse relaxation and chemical shift anisotropy

RELAX-JT2 is an extension of RELAX, a program for the simulation of 1H 2D NOESY spectra and (15)N or (13)C edited 3D NOESY-HSQC spectra of biological macromolecules. In addition to the already existing NOE-simulation it allows the proper simulation of line shapes by the integrated calculation of T(2) times and multiplet structures caused by J-couplings. Additionally the effects of relaxation mediated by chemical shift anisotropy are taken into account. The new routines have been implemented in the program AUREMOL, which aims at the automated NMR structure determination of proteins in solution. For a manual or automatic assignment of experimental spectra that is based on the comparison with the corresponding simulated spectra, the additional line shape information now available is a valuable aid. The new features have been successfully tested with the histidine-containing phosphocarrier protein HPr from Staphylococcus carnosus.     

Principles of quantitative analysis of two-dimensional spectra of nuclear Overhauser effect in evaluation of protein and peptide conformation

To elucidate potentialities of two-dimensional homonuclear Overhauser effect (NOESY) spectra of peptides and proteins for their spatial structure determination, impact of experimental parameters and intrinsic properties of the investigated molecule on proton cross-peak volumes in NOESY spectra was analysed. Recommendations which could increase accuracy of cross-peak volume measurements were suggested. Influence of intrinsic properties of a molecule (spin-lattice relaxation times T1, correlation time tau C and surrounding protons) on the volume of cross-peak for particular protons was analyzed using a complete relaxation matrix of the (formula; see text) helix of gramicidin A. Nonselective relaxation time T1 of the protons was found to affect only slightly the results of cross-peak volumes computer simulation, whereas correlation time tau C and surrounding protons seriously influenced cross-peak volumes. Nevertheless, cross-peak volumes between NH, C alpha H and C beta H protons of a dipeptide fragment of the entire molecule could be accurately simulated using the relaxation matrix of the individual dipeptide. Thus local conformations (torsion angles phi, psi and chi 1) of amino acid residues could be deduced independently of one another and prior to the complete analysis of a molecular structure. The result can be obtained even in the presence of spin-diffusion at mixing times providing maximal volumes of cross-peaks in NOESY spectra.     

NMR study of self-paired parallel duplex of d(AAAAACCCCC) in solution.

The oligonucleotide d(A5C5) in solution forms a parallel self-duplex at neutral and low pH values. H2O NMR spectra at pH 5.1 indicate the presence of five imino resonances at lower temperatures; and the structure is stable up to 60 degrees C. These signals can arise only from the hemiprotonated C+.C pairs [Westhof, E. and Sundaralingham, M. (1980) Biochemistry 77, 1852-1856; Westhof, E. and Sundaralingham, M. (1980) J. Mol. Biol. 142, 331-361] and constitute the first direct observation of C+.C hemiprotonated pairs in solution. The cross peaks from H1's and more than five distinct AH8's in 500 MHz 1H 2D-NOESY spectra indicate that there are two conformationally different and energetically similar A-tracts. There is good qualitative agreement between NOESY data and two theoretically derived structures in which A-tracts are reverse Watson-Crick and reverse Hoogsteen base-paired, respectively.     

Reconstruction of NOESY maps. A requirement for a reliable conformational analysis of biomolecules using 2D NMR

The modelling of the conformation of a biomolecule in solution is based mainly on the internuclear distances deduced from measurements of nuclear Overhauser effects (nOe) in NOESY correlation maps. The distances are then used as restraints in the energy minimization procedure, which leads to one or several optimized conformations. A general and safe technique for validating these structures with respect to the experimental data is here proposed: from the internuclear distances, the relaxation matrix can be computed under the assumption of a unique rotational correlation time. By stepwise integration of these relaxation equations, the NOESY maps can be accurately reconstructed for any mixing time. Because multi-spin effects are correctly taken into account, any difference between the experimental and theoretical maps can be easily interpreted in terms of conformation, and possible inconsistencies due to conformational averaging can be pointed out. The technique is illustrated for a bacterial lipopeptide, mycosubtilin, the spectrum of which is completely assigned.     

Comparison of experimentally determined protein structures by solution of Bloch equations

Nuclear Overhauser enhancement (NOESY) spectra were theoretically generated by solving the generalized Bloch equations with the appropriate initial conditions. The input to the equations were the coordinates of the protons of two similar crystal structures of basic pancreatic trypsin inhibitor. The two NOESY spectra obtained were compared to published experimental spectra of the protein in solution. It was found that the two crystal structures of basic pancreatic trypsin inhibitor give different theoretical spectra. The solution of the Bloch equations is very sensitive to small variations in the distance between protons (approx. 0.2 A), and to differences in the surrounding configurations. The method allows a detailed comparison of the crystal and solution structures of proteins. The structure of the trypsin inhibitor in solution was found to be similar to either one or the other crystal forms in different regions of the molecule.