Determining stereo-specific 1H nuclear magnetic resonance assignments from distance geometry calculations

Stereo-specific 1H nuclear magnetic resonance assignments can be obtained following distance geometry structure calculations. The key to this method is to allow stereo-related atoms or methyls to float between pro-R and pro-S configurations, the final configuration being determined by the experimental constraints. Resonances from stereo-related pairs are given initial random assignments (either pro-R or pro-S) for identifying nuclear Overhauser effects (NOEs). A list of distance constraints using these assignments is compiled and a series of structures calculated where the chirality of non-C alpha chiral centers is not constrained; no pseudoatom corrections are required. Calculated structures are both locally and globally well-determined since the assignments rely upon the structure determination rather than the structure quality relying upon stereo-specific assignments. The method represents a global approach to determining stereo-specific assignments versus previously reported methods where only intraresidue NOEs and J-coupling information are used.     

Determination of the complete three-dimensional structure of the trypsin inhibitor from squash seeds in aqueous solution by nuclear magnetic resonance and a combination of distance geometry and dynamical simulated annealing

The complete three-dimensional structure of the trypsin inhibitor from seeds of the squash Cucurbita maxima in aqueous solution was determined on the basis of 324 interproton distance constraints, 80 non-nuclear Overhauser effect distances, and 22 hydrogen-bonding constraints, supplemented by 27 phi backbone angle constraints derived from nuclear magnetic resonance measurements. The nuclear magnetic resonance input data were converted to the distance constraints in a semiquantitative manner after a sequence specific assignment of 1H spectra was obtained using two-dimensional nuclear magnetic resonance techniques. Stereospecific assignments were obtained for 17 of the 48 prochiral centers of the squash trypsin inhibitor using the floating chirality assignment introduced at the dynamical simulated annealing stage of the calculations. A total of 34 structures calculated by a hybrid distance geometry-dynamical simulated annealing method exhibit well-defined positions for both backbone and side-chain atoms. The average atomic root-mean-square difference between the individual structures and the minimized mean structure is 0.35(+/- 0.08) A for the backbone atoms and 0.89(+/- 0.17) A for all heavy atoms. The precision of the structure determination is discussed and correlated to the experimental input data.     

Analysis of secondary structure in proteins by chemical cross-linking coupled to MS

Chemical cross-linking is an attractive technique for the study of the structure of protein complexes due to its low sample consumption and short analysis time. Furthermore, distance constraints obtained from the identification of cross-linked peptides by MS can be used to construct and validate protein models. If a sufficient number of distance constraints are obtained, then determining the secondary structure of a protein can allow inference of the protein's fold. In this work, we show how the distance constraints obtained from cross-linking experiments can identify secondary structures within the protein sequence. Molecular modeling of alpha helices and beta sheets reveals that each secondary structure presents different cross-linking possibilities due to the topological distances between reactive residues. Cross-linking experiments performed with amine reactive cross-linkers with model alpha helix containing proteins corroborated the molecular modeling predictions. The cross-linking patterns established here can be extended to other cross-linkers with known lengths for the determination of secondary structures in proteins.     

Energy embedding of trypsin inhibitor

Energy embedding has been shown recently to be a useful extension of the distance geometry approach to conformational calculations in the case of very small molecules and simple energy functions. This paper tests the ability of energy embedding to locate low energy conformations satisfying both weak and strong geometric constraints when the molecule is the small protein, bovine pancreatic trypsin inhibitor, and the energy function is the complicated Oobatake-Crippen residue–residue potential. Using the potential function alone, the algorithm reaches a structure with energy lower than that of the native conformation, but with little resemblance to it. Aided by numerous geometric constraints, such as preformed secondary structure segments, the algorithm again finds a local minimum with energy better than that of the native, and with only 3.3 Å rms deviation from it. This is significantly closer to the native value than can be obtained using standard distance geometry and the geometric constraints alone. Thus, energy embedding using the Oobatake-Crippen potential function is a significant help in finding native conformations of proteins. However, additional trials on a hairpin bend fragment of trypsin inhibitor demonstrate the potential's shortcomings in encouraging proper secondary structure.     

Stereospecific assignments in proteins using exact NOEs

Recently developed methods to measure distances in proteins with high accuracy by “exact” nuclear Overhauser effects (eNOEs) make it possible to determine stereospecific assignments, which are particularly important to fully exploit the accuracy of the eNOE distance measurements. Stereospecific assignments are determined by comparing the eNOE-derived distances to protein structure bundles calculated without stereospecific assignments, or an independently determined crystal structure. The absolute and relative CYANA target function difference upon swapping the stereospecific assignment of a diastereotopic group yields the respective stereospecific assignment. We applied the method to the eNOE data set that has recently been obtained for the third immunoglobulin-binding domain of protein G (GB3). The 884 eNOEs provide relevant data for 47 of the total of 75 diastereotopic groups. Stereospecific assignments could be established for 45 diastereotopic groups (96 %) using the X-ray structure, or for 27 diastereotopic groups (57 %) using structures calculated with the eNOE data set without stereospecific assignments, all of which are in agreement with those determined previously. The latter case is relevant for structure determinations based on eNOEs. The accuracy of the eNOE distance measurements is crucial for making stereospecific assignments because applying the same method to the traditional NOE data set for GB3 with imprecise upper distance bounds yields only 13 correct stereospecific assignments using the X-ray structure or 2 correct stereospecific assignments using NMR structures calculated without stereospecific assignments.     

A Self-Organizing Algorithm for Modeling Protein Loops

Protein loops, the flexible short segments connecting two stable secondary structural units in proteins, play a critical role in protein structure and function. Constructing chemically sensible conformations of protein loops that seamlessly bridge the gap between the anchor points without introducing any steric collisions remains an open challenge. A variety of algorithms have been developed to tackle the loop closure problem, ranging from inverse kinematics to knowledge-based approaches that utilize pre-existing fragments extracted from known protein structures. However, many of these approaches focus on the generation of conformations that mainly satisfy the fixed end point condition, leaving the steric constraints to be resolved in subsequent post-processing steps. In the present work, we describe a simple solution that simultaneously satisfies not only the end point and steric conditions, but also chirality and planarity constraints. Starting from random initial atomic coordinates, each individual conformation is generated independently by using a simple alternating scheme of pairwise distance adjustments of randomly chosen atoms, followed by fast geometric matching of the conformationally rigid components of the constituent amino acids. The method is conceptually simple, numerically stable and computationally efficient. Very importantly, additional constraints, such as those derived from NMR experiments, hydrogen bonds or salt bridges, can be incorporated into the algorithm in a straightforward and inexpensive way, making the method ideal for solving more complex multi-loop problems. The remarkable performance and robustness of the algorithm are demonstrated on a set of protein loops of length 4, 8, and 12 that have been used in previous studies.     

Solution structure of murine epidermal growth factor determined by NMR spectroscopy and refined by energy minimization with restraints.

The solution structure of murine epidermal growth factor (mEGF) at pH 3.1 and a temperature of 28 degrees C has been determined from NMR data, using distance geometry calculations and restrained energy minimization. The structure determination is based on 730 conformational constraints derived from NMR data, including 644 NOE-derived upper bound distance constraints, constraints on the ranges of 32 dihedral angles based on measurements of vicinal coupling constants, and 54 upper and lower bound constraints associated with nine hydrogen bonds and the three disulfide bonds. The distance geometry interpretation of the NMR data is based on previously published sequence-specific 1H resonance assignments [Montelione et al. (1988) Biochemistry 27, 2235-2243], supplemented here with individual assignments for some side-chain amide, methylene, and isopropyl methyl protons. The molecular architecture of mEGF is the same as that described previously [Montelione et al. (1987) Proc. Natl. Acad. Sci. U.S.A. 84, 5226-5230], but the structure is overall more precisely determined by a more extensive set of NMR constraints. Analysis of proton NMR line widths, amide proton exchange rates, and side-chain 3J(H alpha-H beta) coupling constants provides evidence for internal motion in several regions of the mEGF molecule. Because mEGF is one member of a large family of homologous growth factors and protein domains for which X-ray crystal structures are not yet available, the atomic coordinates resulting from the present structure refinement (which we have deposited in the Brookhaven Protein Data Bank) are important data for understanding the structures of EGF-like proteins and for further detailed comparisons of these structures with mEGF.     

Small-angle X-ray scattering constraints and local geometry like secondary structures can construct a coarse-grained protein model at amino acid residue resolution

We have developed a new methodology that determines protein structures using small-angle X-ray scattering (SAXS) data. The current bottlenecks in determining the protein structures require a new strategy using the simple design of an experiment, and SAXS is suitable for this purpose in spite of its low information content. First we demonstrated that SAXS constraints work additively to NMR-derived information in calculating structures. Next, structure calculations for nine proteins taking different folds were performed using the SAXS constraints combined with the NMR-derived distance restraints for local geometry such as secondary structures or those for tertiary structure. The results show that the SAXS constraints complemented the tertiary-structural information for all the proteins, and that accuracy of the structures thus obtained with SAXS constraints and local geometrical restraints ranged from 1.85 to 4.33 Å. Based on these results, we were able to construct a coarse-grained protein model at amino acid residue resolution.     

Protein structure alignment using a genetic algorithm

We have developed a novel, fully automatic method for aligning the three-dimensional structures of two proteins. The basic approach is to first align the proteins' secondary structure elements and then extend the alignment to include any equivalent residues found in loops or turns. The initial secondary structure element alignment is determined by a genetic algorithm. After refinement of the secondary structure element alignment, the protein backbones are superposed and a search is performed to identify any additional equivalent residues in a convergent process. Alignments are evaluated using intramolecular distance matrices. Alignments can be performed with or without sequential connectivity constraints. We have applied the method to proteins from several well-studied families: globins, immunoglobulins, serine proteases, dihydrofolate reductases, and DNA methyltransferases. Agreement with manually curated alignments is excellent. A web-based server and additional supporting information are available at http://engpub1.bu.edu/-josephs.     

Optimal bundling of transmembrane helices using sparse distance constraints

We present a two-step approach to modeling the transmembrane spanning helical bundles of integral membrane proteins using only sparse distance constraints, such as those derived from chemical cross-linking, dipolar EPR and FRET experiments. In Step 1, using an algorithm, we developed, the conformational space of membrane protein folds matching a set of distance constraints is explored to provide initial structures for local conformational searches. In Step 2, these structures refined against a custom penalty function that incorporates both measures derived from statistical analysis of solved membrane protein structures and distance constraints obtained from experiments. We begin by describing the statistical analysis of the solved membrane protein structures from which the theoretical portion of the penalty function was derived. We then describe the penalty function, and, using a set of six test cases, demonstrate that it is capable of distinguishing helical bundles that are close to the native bundle from those that are far from the native bundle. Finally, using a set of only 27 distance constraints extracted from the literature, we show that our method successfully recovers the structure of dark-adapted rhodopsin to within 3.2 A of the crystal structure.     

1H NMR assignments of apo calcyclin and comparative structural analysis with calbindin D9k and S100 beta.

The homodimeric S100 protein calcyclin has been studied in the apo state by two-dimensional 1H NMR spectroscopy. Using a combination of scalar correlation and NOE experiments, sequence-specific 1H NMR assignments were obtained for all but one backbone and > 90% of the side-chain resonances. To our knowledge, the 2 x 90 residue (20 kDa) calcyclin dimer is the largest protein system for which such complete assignments have been made by purely homonuclear methods. Sequential and medium-range NOEs and slowly exchanging backbone amide protons identified directly the four helices and the short antiparallel beta-type interaction between the two binding loops that comprise each subunit of the dimer. Further analysis of NOEs enabled the unambiguous assignment of 556 intrasubunit distance constraints, 24 intrasubunit hydrogen bonding constraints, and 2 x 26 intersubunit distance constraints. The conformation of the monomer subunit was refined by distance geometry and restrained molecular dynamics calculations using the intrasubunit constraints only. Calculation of the dimer structure starting from this conformational ensemble has been reported elsewhere. The extent of structural homology among the apo calcyclin subunit, the monomer subunit of apo S100 beta, and monomeric apo calbindin D9k has been examined in detail by comparing 1H NMR chemical shifts and secondary structures. This analysis was extended to a comprehensive comparison of the three-dimensional structures of the calcyclin monomer subunit and calbindin D9k, which revealed greater similarity in the packing of their hydrophobic cores than was anticipated previously. Together, these results support the hypothesis that all members of the S100 family have similar core structures and similar modes of dimerization. Analysis of the amphiphilicity of Helix IV is used to explain why calbindin D9k is monomeric, but full-length S100 proteins form homodimers.     

Protein NMR structure determination with automated NOE assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA

Combined automated NOE assignment and structure determination module (CANDID) is a new software for efficient NMR structure determination of proteins by automated assignment of the NOESY spectra. CANDID uses an iterative approach with multiple cycles of NOE cross-peak assignment and protein structure calculation using the fast DYANA torsion angle dynamics algorithm, so that the result from each CANDID cycle consists of exhaustive, possibly ambiguous NOE cross-peak assignments in all available spectra and a three-dimensional protein structure represented by a bundle of conformers. The input for the first CANDID cycle consists of the amino acid sequence, the chemical shift list from the sequence-specific resonance assignment, and listings of the cross-peak positions and volumes in one or several two, three or four-dimensional NOESY spectra. The input for the second and subsequent CANDID cycles contains the three-dimensional protein structure from the previous cycle, in addition to the complete input used for the first cycle. CANDID includes two new elements that make it robust with respect to the presence of artifacts in the input data, i.e. network-anchoring and constraint-combination, which have a key role in de novo protein structure determinations for the successful generation of the correct polypeptide fold by the first CANDID cycle. Network-anchoring makes use of the fact that any network of correct NOE cross-peak assignments forms a self-consistent set; the initial, chemical shift-based assignments for each individual NOE cross-peak are therefore weighted by the extent to which they can be embedded into the network formed by all other NOE cross-peak assignments. Constraint-combination reduces the deleterious impact of artifact NOE upper distance constraints in the input for a protein structure calculation by combining the assignments for two or several peaks into a single upper limit distance constraint, which lowers the probability that the presence of an artifact peak will influence the outcome of the structure calculation. CANDID test calculations were performed with NMR data sets of four proteins for which high-quality structures had previously been solved by interactive protocols, and they yielded comparable results to these reference structure determinations with regard to both the residual constraint violations, and the precision and accuracy of the atomic coordinates. The CANDID approach has further been validated by de novo NMR structure determinations of four additional proteins. The experience gained in these calculations shows that once nearly complete sequence-specific resonance assignments are available, the automated CANDID approach results in greatly enhanced efficiency of the NOESY spectral analysis. The fact that the correct fold is obtained in cycle 1 of a de novo structure calculation is the single most important advance achieved with CANDID, when compared with previously proposed automated NOESY assignment methods that do not use network-anchoring and constraint-combination.     

Sequence-specific 1H NMR assignments and determination of the secondary structure for the activation domain isolated from pancreatic procarboxypeptidase B

Nearly complete sequence-specific 1H NMR assignments are presented for amino acid residues 3-81 in the 81-residue globular activation domain of porcine pancreatic procarboxypeptidase B isolated after limited tryptic proteolysis of the zymogen. These resonance assignments are consistent with the chemically determined amino acid sequence. Regular secondary structure elements were identified from nuclear Overhauser effects and the sequence locations of slowly exchanging backbone amide protons. The molecule contains two alpha-helices, including residues 20-30 and approximately residues 58-72, and a three-stranded antiparallel beta-sheet with the individual strands extending approximately from 12 to 17, 50 to 55, and 75 to 77. The identification of these secondary structures and a preliminary analysis of additional long-range NOE distance constraints show that isolated activation domain B forms a stable structure with the typical traits of a globular protein. The data presented here are the basis for the determination of the complete three-dimensional structure of activation domain B, which is currently in progress.     

Solution NMR studies of the integral membrane proteins OmpX and OmpA from Escherichia coli

Membrane proteins are usually solubilized in polar solvents by incorporation into micelles. Even for small membrane proteins these mixed micelles have rather large molecular masses, typically beyond 50000 Da. The NMR technique TROSY (transverse relaxation-optimized spectroscopy) has been developed for studies of structures of this size in solution. In this paper, strategies for the use of TROSY-based NMR experiments with membrane proteins are discussed and illustrated with results obtained with the Escherichia coli integral membrane proteins OmpX and OmpA in mixed micelles with the detergent dihexanoylphosphatidylcholine (DHPC). For OmpX, complete sequence-specific NMR assignments have been obtained for the polypeptide backbone. The 13C chemical shifts and nuclear Overhauser effect data then resulted in the identification of the regular secondary structure elements of OmpX/DHPC in solution, and in the collection of an input of conformational constraints for the computation of the global fold of the protein. For OmpA, the NMR assignments are so far limited to about 80% of the polypeptide chain, indicating different dynamic properties of the reconstituted OmpA beta-barrel from those of OmpX. Overall, the present data demonstrate that relaxation-optimized NMR techniques open novel avenues for studies of structure, function and dynamics of integral membrane proteins.     

Solution conformation of cytochrome c-551 from Pseudomonas stutzeri ZoBell determined by NMR.

1H NMR spectroscopy and solution structure computations have been used to examine ferrocytochrome c-551 from Pseudomonas stutzeri ZoBell (ATCC 14405). Resonance assignments are proposed for all main-chain and most side-chain protons. Stereospecific assignments were also made for some of the beta-methylene protons and valine methyl protons. Distance constraints were determined based upon nuclear Overhauser enhancements between pairs of protons. Dihedral angle constraints were determined from estimates of scalar coupling constants and intra-residue NOEs. Twenty structures were calculated by distance geometry and refined by energy minimization and simulated annealing on the basis of 1012 interproton distance and 74 torsion angle constraints. Both the main-chain and side-chain atoms are well defined except for two terminal residues, and some side-chain atoms located on the molecular surface. The average root mean squared deviation in the position for equivalent atoms between the 20 individual structures and the mean structure obtained by averaging their coordinates is 0.56 +/- 0.10 A for the main-chain atoms, and 0.95 +/- 0.09 A for all nonhydrogen atoms of residue 3 to 80 plus the heme group. The average structure was compared with an analogous protein, cytochrome c-551 from pseudomonas stutzeri. The main-chain folding patterns are very consistent, but there are some differences, some of which can be attributed to the loss of normally conserved aromatic residues in the ZoBell c-551.     

High-resolution solution structure of reduced French bean plastocyanin and comparison with the crystal structure of poplar plastocyanin

The three-dimensional solution structure of reduced (CuI) plastocyanin from French bean leaves has been determined by distance geometry and restrained molecular dynamics methods using constraints obtained from 1H n.m.r. (nuclear magnetic resonance) spectroscopy. A total of 1244 experimental constraints were used, including 1120 distance constraints, 103 dihedral angle constraints and 21 hydrogen bond constraints. Stereospecific assignments were made for 26 methylene groups and the methyls of 11 valines. Additional constraints on copper co-ordination were included in the restrained dynamics calculations. The structures are well defined with average atomic root-mean-square deviations from the mean of 0.45 A for all backbone heavy atoms and 1.08 A for side-chain heavy atoms. French bean plastocyanin adopts a beta-sandwich structure in solution that is similar to the X-ray structure of reduced poplar plastocyanin; the average atomic root-mean-square difference between 16 n.m.r. structures and the X-ray structure is 0.76 A for all backbone heavy atoms. The conformations of the side-chains that constitute the hydrophobic core of French bean plastocyanin are very well defined. Of 47 conserved residues that populate a single chi 1 angle in solution, 43 have the same rotamer in the X-ray structure. Many surface side-chains adopt highly preferred conformations in solution, although the 3J alpha beta coupling constants often indicate some degree of conformational averaging. Some surface side-chains are disordered in both the solution and crystal structures of plastocyanin. There is a striking correlation between measures of side-chain disorder in solution and side-chain temperature factors in the X-ray structure. Side-chains that form a distinctive acidic surface region, believed to be important in binding other electron transfer proteins, appear to be disordered. Fifty backbone amide protons form hydrogen bonds to carbonyls in more than 60% of the n.m.r. structures; 45 of these amide protons exchange slowly with solvent deuterons. Ten hydrogen bonds are formed between side-chain and backbone atoms, eight of which are correlated with decreased proton exchange. Of the 60 hydrogen bonds formed in French bean plastocyanin, 56 occur in the X-ray structure of the poplar protein; two of the missing hydrogen bonds are absent as a result of mutations. It appears that molecular dynamics refinement of highly constrained n.m.r. structures allows accurate prediction of the pattern of hydrogen bonding.     

Functional insights from structural predictions: analysis of the Escherichia coli genome

Fold assignments for proteins from the Escherichia coli genome are carried out using BASIC, a profile-profile alignment algorithm, recently tested on fold recognition benchmarks and on the Mycoplasma genitalium genome and PSI BLAST, the newest generation of the de facto standard in homology search algorithms. The fold assignments are followed by automated modeling and the resulting three-dimensional models are analyzed for possible function prediction. Close to 30% of the proteins encoded in the E. coli genome can be recognized as homologous to a protein family with known structure. Most of these homologies (23% of the entire genome) can be recognized both by PSI BLAST and BASIC algorithms, but the latter recognizes an additional 260 homologies. Previous estimates suggested that only 10-15% of E. coli proteins can be characterized this way. This dramatic increase in the number of recognized homologies between E. coli proteins and structurally characterized protein families is partly due to the rapid increase of the database of known protein structures, but mostly it is due to the significant improvement in prediction algorithms. Knowing protein structure adds a new dimension to our understanding of its function and the predictions presented here can be used to predict function for uncharacterized proteins. Several examples, analyzed in more detail in this paper, include the DPS protein protecting DNA from oxidative damage (predicted to be homologous to ferritin with iron ion acting as a reducing agent) and the ahpC/tsa family of proteins, which provides resistance to various oxidating agents (predicted to be homologous to glutathione peroxidase).     

Estimation of protein secondary structure from circular dichroism spectra: inclusion of denatured proteins with native proteins in the analysis

We have expanded our reference set of proteins used in the estimation of protein secondary structure by CD spectroscopy from 29 to 37 proteins by including 3 additional globular proteins with known X-ray structure and 5 denatured proteins. We have also modified the self-consistent method for analyzing protein CD spectra, SELCON3, by including a new selection criterion developed by W. C. Johnson, Jr. (Proteins Struct. Funct. Genet. 35, 307-312, 1999). The secondary structure corresponding to the denatured proteins was approximated to be 90% unordered, owing to the spectral similarity of the denatured proteins and unordered structures. We examined the thermal denaturation of ribonuclease T1 by CD using both the original and expanded sets of reference proteins and obtained more consistent results with the expanded set. The expanded set of reference proteins will be helpful for the determination of protein secondary structure from protein CD spectra with higher reliability, especially of proteins with significant unordered structure content and/or in the course of denaturation.     

Reliability of exclusively NOESY-based automated resonance assignment and structure determination of proteins

Protein structure determination by NMR can in principle be speeded up both by reducing the measurement time on the NMR spectrometer and by a more efficient analysis of the spectra. Here we study the reliability of protein structure determination based on a single type of spectra, namely nuclear Overhauser effect spectroscopy (NOESY), using a fully automated procedure for the sequence-specific resonance assignment with the recently introduced FLYA algorithm, followed by combined automated NOE distance restraint assignment and structure calculation with CYANA. This NOESY-FLYA method was applied to eight proteins with 63–160 residues for which resonance assignments and solution structures had previously been determined by the Northeast Structural Genomics Consortium (NESG), and unrefined and refined NOESY data sets have been made available for the Critical Assessment of Automated Structure Determination of Proteins by NMR project. Using only peak lists from three-dimensional ¹³C- or ¹⁵N-resolved NOESY spectra as input, the FLYA algorithm yielded for the eight proteins 91–98 % correct backbone and side-chain assignments if manually refined peak lists are used, and 64–96 % correct assignments based on raw peak lists. Subsequent structure calculations with CYANA then produced structures with root-mean-square deviation (RMSD) values to the manually determined reference structures of 0.8–2.0 Å if refined peak lists are used. With raw peak lists, calculations for 4 proteins converged resulting in RMSDs to the reference structure of 0.8–2.8 Å, whereas no convergence was obtained for the four other proteins (two of which did already not converge with the correct manual resonance assignments given as input). These results show that, given high-quality experimental NOESY peak lists, the chemical shift assignments can be uncovered, without any recourse to traditional through-bond type assignment experiments, to an extent that is sufficient for calculating accurate three-dimensional structures.     

Solution structures of the rabbit neutrophil defensin NP-5

Solution structures of the rabbit neutrophil defensin NP-5 have been determined by 1H nuclear magnetic resonance (n.m.r.) spectroscopy and distance geometry techniques. This 33 amino acid peptide is part of the oxygen-independent mammalian defense system against microbial infection. The structures were generated from 107 n.m.r. derived inter-residue proton-proton distance constraints. A distance geometry algorithm was then used to determine the range of structures consistent with these distance constraints. These distance geometry calculations employed an improved algorithm that allowed the chirality constraints to be relaxed on prochiral centers when it was not possible to make stereo-specific assignments of protons on these centers. This procedure gave superior results compared with standard distance geometry methods and also produced structures that were more consistent with the original n.m.r. data. Analysis of the NP-5 structures shows that the overall folding of the peptide backbone is well defined by the n.m.r. distance information but that the side-chain group conformations are generally less well defined.