Effects of limited input distance constraints upon the distance geometry algorithm.

In this paper we examine the distance geometry (DG) algorithm in the form used to determine the structure of proteins. We focus on three aspects of the algorithm: bound smoothing with the triangle inequality, the random selection of distances within the bounds, and the number of distances needed to specify a structure. Computational experiments are performed using simulated and real data for basic pancreatic trypsin inhibitor (BPTI) from nmr and crystallographic measurements. We find that the upper bounds determined by bound smoothing to be a linear function of the true crystal distance. A simple model that describes the results obtained with randomly selected trial distances is proposed. Using this representation of the trial distances, we show that BPTI DG structures are more compact than the true crystal structure. We also show that the DG-generated structures no longer resemble test structures when the number of these interresidue distance constraints is less than the number of degrees of freedom of the protein backbone. While the actual model will be sensitive the way distances are chosen, our conclusions are likely to apply to other versions of the DG algorithm.     

An evaluation of the combined use of nuclear magnetic resonance and distance geometry for the determination of protein conformations in solution

An evaluation of the potential of nuclear magnetic resonance (n.m.r.) as a means of determining polypeptide conformation in solution is performed with the aid of a new distance geometry program which is capable of computing complete spatial structures for small proteins from n.m.r. data. Ten sets of geometric constraints which simulate the results available from n.m.r. experiments of varying precision and completeness were extracted from the crystal structure of the basic pancreatic trypsin inhibitor, and conformers consistent with these constraints were computed. Comparison of these computed structures with each other and with the original crystal structure shows that it is possible to determine the global conformation of a polypeptide chain from the distance constraints which are available from n.m.r. experiments. The results obtained with the different data sets also provide a standard by which the quality of protein structures computed from n.m.r. data can be evaluated when no crystal structure is available, and indicate directions in which n.m.r. experiments for protein structure determination could be further improved.     

Limited sampling of conformational space by the distance geometry algorithm: implications for structures generated from NMR data

Calculations with a metric matrix distance geometry algorithm were performed that show that the standard implementation of the algorithm generally samples a very limited region of conformational space. This problem is most severe when only a small amount of distance information is used as input for the algorithm. Control calculations were performed on linear peptides, disulfide-linked peptides, and a double-stranded DNA decamer where only distances defining the covalent structures of the molecules (as well as the hydrogen bonds for the base pairs in the DNA) were included as input. Since the distance geometry algorithm is commonly used to generate structures of biopolymers from distance data obtained from NMR experiments, simulations were performed on the small globular protein basic pancreatic trypsin inhibitor (BPTI) that mimic calculations performed with actual NMR data. The results on BPTI and on the control peptides indicate that the standard implementation of the algorithm has two main problems: first, that it generates extended structures; second, that it has a tendency to consistently produce similar structures instead of sampling all structures consistent with the input distance information. These results also show that use of a simple root-mean-square deviation for evaluating the quality of the structures generated from NMR data may not be generally appropriate. The main sources of these problems are identified, and our results indicate that the problems are not a fundamental property of the distance geometry algorithm but arise from the implementations presently used to generate structures from NMR data. Several possible methods for alleviating these problems are discussed.     

Determination of a high-quality nuclear magnetic resonance solution structure of the bovine pancreatic trypsin inhibitor and comparison with three crystal structures.

A high-quality three-dimensional structure of the bovine pancreatic trypsin inhibitor (BPTI) in aqueous solution was determined by 1H nuclear magnetic resonance (n.m.r.) spectroscopy and compared to the three available high-resolution X-ray crystal structures. A newly collected input of 642 distance constraints derived from nuclear Overhauser effects and 115 dihedral angle constraints was used for the structure calculations with the program DIANA, followed by restrained energy minimization with the program AMBER. The BPTI solution structure is represented by a group of 20 conformers with an average root-mean-square deviation (RMSD) relative to the mean solution structure of 0.43 A for backbone atoms and 0.92 A for all heavy atoms of residues 2 to 56. The pairwise RMSD values of the three crystal structures relative to the mean solution structure are 0.76 to 0.85 A for the backbone atoms and 1.24 to 1.33 A for all heavy atoms of residues 2 to 56. Small local differences in backbone atom positions between the solution structure and the X-ray structures near residues 9, 25 to 27, 46 to 48 and 52 to 58, and conformational differences for individual amino acid side-chains were analyzed for possible correlations with intermolecular protein-protein contacts in the crystal lattices, using the pairwise RMSD values among the three crystal structures as a reference.     

Solution conformation of proteinase inhibitor IIA from bull seminal plasma by 1H nuclear magnetic resonance and distance geometry

A determination of the solution conformation of the proteinase inhibitor IIA from bull seminal plasma (BUSI IIA) is described. Two-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) was used to obtain a list of 202 distance constraints between individually assigned hydrogen atoms of the polypeptide chain, to identify the positions of the three disulfide bridges, and to locate the single cis peptide bond. Supplementary geometric constraints were derived from the vicinal spin-spin couplings and the locations of certain hydrogen bonds, as determined by nuclear magnetic resonance (n.m.r.). Using a new distance geometry program (DISGEO) which is capable of computing all-atom structures for proteins the size of BUSI IIA, five conformers were computed from the NOE distance constraints alone, and another five were computed with the supplementary constraints included. Comparison of the different structures computed from the n.m.r. data among themselves and with the crystal structures of two homologous proteins shows that the global features of the conformation of BUSI IIA (i.e. the overall dimensions of the molecule and the threading of the polypeptide chain) were well-defined by the available n.m.r. data. In the Appendix, we describe a preliminary energy refinement of the structure, which showed that the constraints derived from the n.m.r. data are compatible with a low energy spatial structure.     

The polypeptide fold of the globular domain of histone H5 in solution. A study using nuclear magnetic resonance, distance geometry and restrained molecular dynamics.

The polypeptide fold of the 79-residue globular domain of chicken histone H5 (GH5) in solution has been determined by the combined use of distance geometry and restrained molecular dynamics calculations. The structure determination is based on 307 approximate interproton distance restraints derived from n.m.r. measurements. The structure is composed of a core made up of residues 3-18, 23-34, 37-60 and 71-79, and two loops comprising residues 19-22 and 61-70. The structure of the core is well defined with an average backbone atomic r.m.s. difference of 2.3 +/- 0.3 A between the final eight converged restrained dynamics structures and the mean structure obtained by averaging their coordinates best fitted to the core residues. The two loops are also well defined locally but their orientation with respect to the core could not be determined as no long range ([i-j[ greater than 5) proton-proton contacts could be observed between the loop and core residues in the two-dimensional nuclear Overhauser enhancement spectra. The structure of the core is dominated by three helices and has a similar fold to the C-terminal DNA binding domain of the cAMP receptor protein.     

A distance geometry program for determining the structures of small proteins and other macromolecules from nuclear magnetic resonance measurements of intramolecular1H−1H proximities in solution

DISGEO is a new implementation of a distance geometry algorithm which has been specialized for the calculation of macromolecular conformation from distance measurements obtained by two-dimensional nuclear Overhauser enhancement spectroscopy. The improvements include (1) a decomposition of the complete embedding process into two successive, more tractable calculations by the use of “substructures”, (2) a compact data structure for storing incomplete distance information on a structure, (3) a more efficient shortest-path algorithm for computing the triangle inequality limits on all distances from this information, (4) a new algorithm for selecting random metric spaces from within these limits, (5) the use of chirality constraints to obtain good covalent geometry without the use ofad hoc weights or excessive optimization. The utility of the resultant program with nuclear magnetic resonance data is demonstrated by embedding complete spatial structures for the protein basic pancreatic trypsin inhibitor vs all 508 intramolecular, interresidue proton-proton contacts shorter than 4.0 Å that were present in its crystal structure. The crystal structure could be reproduced from this data set to within 1.3 Å minimum root mean square coordinate difference between the backbone atoms. We conclude that the information potentially available from nuclear magnetic resonance experiments in solution is sufficient to define the spatial structure of small proteins.     

GENFOLD: a genetic algorithm for folding protein structures using NMR restraints.

We report the development and validation of the program GENFOLD, a genetic algorithm that calculates protein structures using restraints obtained from NMR, such as distances derived from nuclear Overhauser effects, and dihedral angles derived from coupling constants. The program has been tested on three proteins: the POU domain (a small three-helix DNA-binding protein), bovine pancreatic trypsin inhibitor (BPTI), and the starch-binding domain from Aspergillus niger glucoamylase I, a 108-residue beta-sheet protein. Structures were calculated for each protein using published NMR restraints. In addition, structures were calculated for BPTI using artificial restraints generated from a high-resolution crystal structure. In all cases the fittest calculated structures were close to the target structure, and could be refined to structures indistinguishable from the target structures by means of a low-temperature simulated annealing refinement. The effectiveness of the program is similar to that of distance geometry and simulated annealing methods, and it is capable of using a very wide range of restraints as input. It can thus be readily extended to the calculation of structures of large proteins, for which few NOE restraints may be available.     

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.     

Application of molecular dynamics with interproton distance restraints to three-dimensional protein structure determination. A model study of crambin

The applicability of restrained molecular dynamics for the determination of three-dimensional protein structures on the basis of short interproton distances (less than 4 A) that can be realistically determined from nuclear magnetic resonance measurements in solution is assessed. The model system used is the 1.2 A resolution crystal structure of the 46 residue protein crambin, from which a set of 240 approximate distance restraints, divided into three ranges (2.5 +/- 0.5, 3.0+0.5(-1.0) and 4 +/- 1 A), is derived. This interproton distance set comprises 159 short-range ([i-j] less than or equal to 5) and 56 ([i-j] greater than 5) long-range inter-residue distances and 25 intra-residue distances. Restrained molecular dynamics are carried out using a number of different protocols starting from two initial structures: a completely extended beta-strand; and an extended structure with two alpha-helices in the same positions as in the crystal structure (residues 7 to 19, and 23 to 30) and all other residues in the form of extended beta-strands. The root-mean-square (r.m.s.) atomic differences between these two initial structures and the crystal structure are 43 A and 23 A, respectively. It is shown that, provided protocols are used that permit the secondary structure elements to form at least partially prior to folding into a tertiary structure, convergence to the correct final structure, both globally and locally, is achieved. The r.m.s. atomic differences between the converged restrained dynamics structures and the crystal structure range from 1.5 to 2.2 A for the backbone atoms and from 2.0 to 2.8 A for all atoms. The r.m.s. atomic difference between the X-ray structure and the structure obtained by first averaging the co-ordinates of the converged restrained dynamics structures is even smaller: 1.0 A for the backbone atoms and 1.6 A for all atoms. These results provide a measure with which to judge future experimental results on proteins whose crystal structures are unknown. In addition, from an examination of the dynamics trajectories, it is shown that the convergence pathways followed by the various simulations are different.     

The conformations of hirudin in solution: a study using nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The solution conformations of the protein hirudin have been investigated by the combined use of distance geometry and restained molecular dynamics calculations. The basis for the structure determination comprised 359 approximate inter-proton distance restrains and 10 phi backbone torsion angle restrains derived from n.m.r. measurements. It is shown that hirudin is composed of three domains: a central core made up of residues 3-30, 37-46 and 56-57; a protruding 'finger' (residues 31-36) consisting of the tip of an antiparallel beta sheet, and an exposed loop (residues 47-55). The structure of each individual domain is relatively well defined with average backbone atomic r.m.s. differences of <2 A between the final seven converged restrained dynamic structures and the mean structure obtained by averaging their coordinates. The orientation of the two minor domains relative to the central core, however, could not be determined as no long-range (i-h >5) interdomain proton-proton contacts could be observed in the two-dimensional nuclear Overhauser enhancement spectra. From the restrained molecular dynamics calculations it appears that the two minor domains exhibit large rigid-body motions relative to the central core.     

Efficient computation of three-dimensional protein structures in solution from nuclear magnetic resonance data using the program DIANA and the supporting programs CALIBA, HABAS and GLOMSA.

A novel procedure for efficient computation of three-dimensional protein structures from nuclear magnetic resonance (n.m.r.) data in solution is described, which is based on using the program DIANA in combination with the supporting programs CALIBA, HABAS and GLOMSA. The first part of this paper describes the new programs DIANA. CALIBA and GLOMSA. DIANA is a new, fully vectorized implementation of the variable target function algorithm for the computation of protein structures from n.m.r. data. Its main advantages, when compared to previously available programs using the variable target function algorithm, are a significant reduction of the computation time, and a novel treatment of experimental distance constraints involving diastereotopic groups of hydrogen atoms that were not individually assigned. CALIBA converts the measured nuclear Overhauser effects into upper distance limits and thus prepares the input for the previously described program HABAS and for DIANA. GLOMSA is used for obtaining individual assignments for pairs of diastereotopic substituents by comparison of the experimental constraints with preliminary results of the structure calculations. With its general outlay, the presently used combination of the four programs is particularly user-friendly. In the second part of the paper, initial results are presented on the influence of the novel DIANA treatment of diastereotopic protons on the quality of the structures obtained, and a systematic study of the central processing unit times needed for the same protein structure calculation on a range of different, commonly available computers is described.     

Conformational changes of the chaperone SecB upon binding to a model substrate--bovine pancreatic trypsin inhibitor (BPTI)

SecB is a homotetrameric cytosolic chaperone that forms part of the protein translocation machinery in E. coli. Due to SecB, nascent polypeptides are maintained in an unfolded translocation-competent state devoid of tertiary structure and thus are guided to the translocon. In vitro SecB rapidly binds to a variety of ligands in a non-native state. We have previously investigated the bound state conformation of the model substrate bovine pancreatic trypsin inhibitor (BPTI) as well as the conformation of SecB itself by using proximity relationships based on site-directed spin labeling and pyrene fluorescence methods. It was shown that SecB undergoes a conformational change during the process of substrate binding. Here, we generated SecB mutants containing but a single cysteine per subunit or an exposed highly reactive new cysteine after removal of the nearby intrinsic cysteines. Quantitative spin labeling was achieved with the methanethiosulfonate spin label (MTS) at positions C97 or E90C, respectively. Highfield (W-band) electron paramagnetic resonance (EPR) measurements revealed that with BPTI present the spin labels are exposed to a more polar/hydrophilic environment. Nanoscale distance measurements with double electron-electron resonance (DEER) were in excellent agreement with distances obtained by molecular modeling. Binding of BPTI also led to a slight change in distances between labels at C97 but not at E90C. While the shorter distance in the tetramer increased, the larger diagonal distance decreased. These findings can be explained by a widening of the tetrameric structure upon substrate binding much like the opening of two pairs of scissors.     

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.     

Polypeptide fold in the two metal clusters of metallothionein-2 by nuclear magnetic resonance in solution

The solution conformation of rabbit liver Cd27+-metallothionein-2 was determined by nuclear magnetic resonance (n.m.r.) and distance geometry. The n.m.r. data are based on complete sequence-specific resonance assignments for the polypeptide chain. This letter describes the global arrangement of the polypeptide chain, which forms two distinct domains containing metal clusters of three and four Cd ions, respectively.     

Human interleukin 4. The solution structure of a four-helix bundle protein.

Heteronuclear 13C and 15N three-dimensional nuclear magnetic resonance (n.m.r.) techniques have been used to determine the solution structure of human interleukin 4, a four-helix bundle protein. A dynamical simulated annealing protocol was used to calculate an ensemble of structures from an n.m.r. data set of 1735 distance restraints, 101 phi angle restraints and 27 pairs of hydrogen bond restraints. The protein structure has a left-handed up-up-down-down topology for the four helices with the two long overhand loops in the structure being connected by a short section of irregular antiparallel beta-sheet. Analysis of the side-chains in the protein shows a clustering of hydrophobic residues, particularly leucines, in the core of the bundle with the side-chains of charged residues being located on the protein surface. The solution structure has been compared with a recent structure prediction for human interleukin 4 and with crystal structures of other helix bundle proteins.     

Determination of local conformation of proteins from 1H-NMR spectroscopy data

A method is proposed to determine conformations of amino acid residues of the protein and effective correlation time tau c from cross-peak intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra. The method consists in fitting complete relaxation matrix of dipeptide unit protons to experimental cross-peak intensities by varying phi, psi, chi torsional angles and tau c. To verify the method, NOESY spectra of basic pancreatic trypsin inhibitor (BPTI) were theoretically generated at mixing times tau m = 25-300 ms and tau c = 4 ns and used for local structure determination. The method works well with optimum for measurement of NOE intensities tau m 100-200 ms. As a result, the backbone phi, psi torsion angles were unambiguously determined at tau m = 100 ms for all but Gly residues of BPTI, and chi 1 angles were determined for the majority of side chains. The obtained dipeptide unit conformations are very close to the BPTI crystallographic structure: root mean square deviation (RMSD) of interproton distances within dipeptide units, on the average, is 0.08 A (maximal deviation 0.44 A), and RMSD of phi and psi angles are 18 and 9 degrees, respectively (maximal deviations are 44 and 22 degrees).     

Detection of local structures in reduced unfolded bovine pancreatic trypsin inhibitor.

The structure of BPTI and reduced BPTI in concentrated guanidinium HCl (GUHCl) in the presence of glycerol has been probed by measurements of dynamic nonradiative excitation energy transfer between probes attached to its amino groups. Interprobe distance distributions were obtained from analysis of donor fluorescence decay curves and used to characterize local structures in unordered states of the protein. Site specifically fluorescently labeled BPTI derivatives (1-n)BPTI (n = 15, 20, 41, 46) were used, each carrying a 2-methoxy-naphthyl-1-methylenyl group (MNA) at the N-terminal amino group of arg1 and 7-(dimethylamino)-coumarin-4-yl-acetyl residue (DA-coum) at one of its epsilon-NH2 groups of the lysine side chains. Analysis of donor fluorescence decay kinetics gave the interprobe distance distributions in the native and denatured states. The N-terminal-segment, residues 1-15, is in an extended conformation (with an average interprobe distance of 34 +/- 2 A) in the native state. Upon unfolding by reduction with DTT or beta-mercapto ethanol in 6 M GUHCl/glycerol mixture, the conformation of this segment relaxed to a state characterized by a reduced average interprobe distance and a larger width of the distances distribution. The average distance between residues 1 and 26, i.e., between the N-terminus and the turn of the twisted beta sheet element (residues 18-35), increased upon unfolding. At -30 degrees C in the above solvent, the distribution between these two sites was probably composed of two conformational subpopulations. About 45 +/- 20% of the molecules were characterized by a short interprobe distance (like the native state) representing a compact conformation, and 55 +/- 20% of the molecules showed large interprobe distances representing an expanded (unfolded) conformation. Thus local structures seem to exist in reduced denatured BPTI even under denaturing conditions in 6 M GUHCl/glycerol mixtures. Some of those structures are unstable in guanidinium isothiocyanate (GUSCN). The method introduced here is suitable for probing local structures and very long range interactions in unfolded proteins and for search for folding initiation sites (FISs) and early folding intermediates.     

Combined use of proton-proton Overhauser enhancements and a distance geometry algorithm for determination of polypeptide conformations. Application to micelle-bound glucagon

In a new approach for the determination of polypeptide conformation, experimental data on intramolecular distances between pairs of hydrogen atoms obtained from nuclear Overhauser enhancement studies are used as input for a distance geometry algorithm. The algorithm determines the limits of the conformation space occupied by the polypeptide chain. The experimental data are used in such a way that the real conformation should in all cases be within these limits. Two important features of the method are that the results do not depend critically on the accuracy of the distance measurements by nuclear Overhauser enhancement studies and that internal mobility of the polypeptide conformation is explicitly taken into consideration. The use of this new procedure is illustrated with a structural study of the region 19-27 of glucagon bound to perdeuterated dodecylphosphocholine micelles.     

Computation of relaxation matrix elements from incomplete NOESY data sets

Summary The structural determination of biological molecules in solution by NMR relies on the determination of a set of interatomic distances obtained by measurement of intramolecular nuclear Overhauser effects (NOE). It is shown in this paper that it is possible to obtain the accurate relaxation rate (and hence the interatomic distance) from the direct measurement of a single NOE signal. The precise analysis of a NOESY peak evolution with respect to the mixing time allows the evaluation of the relaxation parameters for the pair of spins under consideration. This is done without any assumption on the relaxation of unmeasured spins, or on the movement of the molecule. The theoretical basis of this method is presented. In order to evaluate the proposed method, a simulated case on the protein BPTI is studied, which shows that the method performs very well even in the case of noisy data sets.