Distance geometry and related methods for protein structure determination from NMR data

An automatic search for similar spatial arrangements of alpha-helices and beta-strands in globular proteins

A fast search algorithm to reveal similar polypeptide backbone structural motifs in proteins is proposed. It is based on the vector representation of a polypeptide chain fold in which the elements of regular secondary structures are approximated by linear segments (Abagyan and Maiorov, J. Biomol. Struct. Dyn. 5, 1267-1279 (1988)). The algorithm permits insertions and deletions in the polypeptide chain fragments to be compared. The fast search algorithm implemented in FASEAR program is used for collecting beta alpha beta supersecondary structure units in a number of alpha/beta proteins of Brookhaven Data Bank. Variation of geometrical parameters specifying backbone chain fold is estimated. It appears that the conformation of the majority of the fragments, although almost all of them are right-handed, is quite different from that of standard beta alpha beta units. Apart from searching for specific type of secondary structure motif, the algorithm allows automatically to identify new recurrent folding patterns in proteins. It may be of particular interest for the development of tertiary template approach for prediction of protein three-dimensional structure as well for constructing artificial polypeptides with goal-oriented conformation.

Solution of the phase problem in the X-ray diffraction method for proteins with the nuclear magnetic resonance solution structure as initial model. Patterson search and refinement for the alpha-amylase inhibitor tendamistat

Patterson search calculations using the three-dimensional structure of the alpha-amylase inhibitor from Streptomyces tendae obtained from experimental nuclear magnetic resonance (n.m.r.) data were performed to study the possibility of solving the phase problem in the X-ray diffraction method with protein structures determined by n.m.r. Using all heavy atoms (C, N, O, S) of the residues 5 to 73 in the best n.m.r. structure of the alpha-amylase inhibitor (520 out of the 558 heavy atoms in the complete polypeptide chain), the maximum of the rotation function corresponded to the correct solution obtained by the previous independent determination of the crystal structure. However, additional local maxima, which are not significantly lower than the global maximum, also showed up. Performing the Patterson search with a model containing the backbone atoms and the heavy atoms of only the interior side-chains (399 atoms), which are much better defined by the n.m.r. data, the correct maximum was significantly higher than all other maxima. A translation search for the best orientation of the latter model yielded the correct solution. The energy-restrained crystallographic refinement was performed with this model to an R-factor of 26%. This corresponds approximately to the R-factor calculated for the X-ray crystal structure previously determined using the isomorphous replacement technique, if the residues 1 to 4 and 74 and all localized solvent molecules were removed from this structure. During the refinement the root-mean-square deviation between the two structures decreased from 1.03 A to 0.26 A for the polypeptide backbone and from 1.64 A to 0.73 A for all heavy atoms. There are no major local conformational differences between the two structures, with the single exception of the side-chain of Gln52.

Comparison of the high-resolution structures of the alpha-amylase inhibitor tendamistat determined by nuclear magnetic resonance in solution and by X-ray diffraction in single crystals

The three-dimensional structure of the alpha-amylase inhibitor Tendamistat determined by nuclear magnetic resonance in aqueous solution is compared with the Tendamistat crystal structure refined at 2.0 A resolution. Between the two independently obtained structures the root-mean-square distances are 1.05 A for the backbone atoms N, C alpha and C', 1.25 A for the backbone and the interior side-chains, and 1.84 A for all heavy atoms. These numbers show that the interior of the molecule is nearly identical in the two states. Near the protein surface a small number of local differences between the two structures were identified. In most surface areas the solution structure appears more disordered than the crystal structure, with the exception of Tyr15, which was not observed in the X-ray diffraction.

A combined 2D-NMR and molecular dynamics analysis of the structure of the actinomycin D: d(ATGCAT)2 complex

We present a comparative analysis of an NMR experiment and molecular and harmonic dynamics simulations of an actinomycin D: d(ATGCAT)2 complex. A comparison of NOE measurements and 1/R6 weighted proton-proton distances confirm the general correctness of the Actinomycin D-DNA model proposed by Sobell. There are, however, some substantial differences between the proton-proton distances inferred from the NOE results and the molecular and harmonic dynamics simulations. The remaining discrepancies could either come from contributions of other conformations to the average properties of the complex or from uncertainties in the NMR distance analysis. An analysis of the molecular dynamics helix properties, sugar puckers, hydrogen bonding, rms fluctuations and torsional properties are qualitatively consistent with those from previous simulations, but the presence of an intercalated drug leads to some new structural and dynamical features.

Proton nuclear magnetic resonance studies on the variant-3 neurotoxin from Centruroides sculpturatus Ewing: sequential assignment of resonances

We report the sequential assignment of resonances to specific residues in the proton nuclear magnetic resonance spectrum of the variant-3 neurotoxin from the scorpion Centruroides sculpturatus Ewing (range southwestern U.S.A.). A combination of two-dimensional NMR experiments such as 2D-COSY, 2D-NOESY, and single- and double-RELAY coherence transfer spectroscopy has been employed on samples of the protein dissolved in D2O and in H2O for assignment purposes. These studies provide a basis for the determination of the solution-phase conformation of this protein and for undertaking detailed structure-function studies of these neurotoxins that modulate the flow of sodium current by binding to the sodium channels of excitable membranes.

New methodology for computer-aided modelling of biomolecular structure and dynamics. 1. Non-cyclic structures

A general methodology is proposed for the conformational modelling of biomolecular systems. The approach allows one: (i) to describe the system under investigation by an arbitrary set of internal variables, i.e., torsion angles, bond angles, and bond lengths; it offers a possibility to pass from the free structure to a completely fixed one with the number of variables from 3N to zero, respectively, where N is the number of atoms; (ii) to consider both, a single molecule and a complex of many molecules, (e.g., proteins, water, ligands, etc.) in terms of one universal model; (iii) to study the dynamics of the system using explicit analytical Lagrangian equations of motion, thus opening up possibilities for investigations of slow concerted motions such as domain oscillations in proteins etc.; (iv) to calculate the partial derivatives of various functions of conformation, e.g., the conformational energy or external constraints imposed, using a standard efficient procedure regardless of the variables and the structure of the system. The approach is meant to be used in various investigations concerning the conformations and dynamics of biomacromolecules.

Protein structure determination in solution by nuclear magnetic resonance spectroscopy

Knowledge of three-dimensional protein structures is one of the foundations of protein design and protein engineering. Nuclear magnetic resonance spectroscopy was recently introduced as a second method for protein structure determination, in addition to the well-established diffraction techniques with protein single crystals. This new approach enables one to carry out detailed structural studies of proteins in solution and other noncrystalline states, which may be similar or identical to the physiological environment, and promises new insights into the dynamics of protein molecules and the protein-folding problem.

Improved strategies for the determination of protein structures from NMR data: the solution structure of acyl carrier protein

The hybrid method that combines the early stages of a distance geometry program with simulated annealing in the presence of NMR constraints was optimized to obtain structures fully consistent with the observed NMR data. This was achieved by using more restrictive bounds of the NOE constraints than those usually used in the literature and by grouping the NOEs into classes dependent on the quality of the experimental NOE data. The 'floating' stereospecific assignment introduced at the simulated annealing stage of the calculations further improved the definition of the local conformation. An improved sampling and convergence property of the hybrid method was obtained by means of fitting the substructure obtained from the distance geometry program to different conformations. Compared to the standard hybrid methods, this procedure gave superior structures for a 77 amino acid protein, acyl carrier protein from Escherichia coli.

Computer-assisted resonance assignments

Investigation of NMR spectra by automatic procedures began only a few years ago. Many projects are still in progress and results have not been published; completed projects, with published results, have not yet found their final form. Other approaches might be incorporated. One example is the simulation of cross-peaks. These calculations explicitly take into account spectral parameters set for data acquisition and processing. They thus allow realistic simulations of expected peak patterns. Comparison of experimentally obtained peaks with a collection of simulated peaks helps characterize the spin system and determine coupling constants, especially in strongly coupled systems. Whereas automatic assignment procedures will require improvement for quite some time, it seems that useful and time-saving software tools complementing pure computer graphics will be available in the very near future.

Three-dimensional structure of the neurotoxin ATX Ia from Anemonia sulcata in aqueous solution determined by nuclear magnetic resonance spectroscopy

With the aid of 1H nuclear magnetic resonance (NMR) spectroscopy, the three-dimensional structure in aqueous solution was determined for ATX Ia, which is a 46 residue polypeptide neurotoxin of the sea anemone Anemonia sulcata. The input for the structure calculations consisted of 263 distance constraints from nuclear Overhauser effects (NOE) and 76 vicinal coupling constants. For the structure calculation several new or ammended programs were used in a revised strategy consisting of five successive computational steps. First, the program HABAS was used for a complete search of all backbone and chi 1 conformations that are compatible with the intraresidual and sequential NMR constraints. Second, using the program DISMAN, we extended this approach to pentapeptides by extensive sampling of all conformations that are consistent with the local and medium-range NMR constraints. Both steps resulted in the definition of additional dihedral angle constraints and in stereospecific assignments for a number of beta-methylene groups. In the next two steps DISMAN was used to obtain a group of eight conformers that contain no significant residual violations of the NMR constraints or van der Waals contacts. Finally, these structures were subjected to restrained energy refinement with a modified version of the molecular mechanics module of AMBER, which in addition to the energy force field includes potentials for the NOE distance constraints and the dihedral angle constraints. The average of the pairwise minimal RMS distances between the resulting refined conformers calculated for the well defined molecular core, which contains the backbone atoms of 35 residues and 20 interior side chains, is 1.5 +/- 0.3 A. This core is formed by a four-stranded beta-sheet connected by two well-defined loops, and there is an additional flexible loop consisting of the eleven residues 8-18. The core of the protein is stabilized by three disulfide bridges, which are surrounded by hydrophobic residues and shielded on one side by hydrophilic residues.

Computational experience with an algorithm for tetrangle inequality bound smoothing

An important component of computer programs for determining the solution conformation of proteins and other flexible molecules from nuclear magnetic resonance data are the so-called "bound smoothing algorithms", which compute lower and upper limits on the values of all the interatomic distances from the relatively sparse set which can usually be measured experimentally. To date, the only methods efficient enough for use in large problems take account of only the triangle inequality, but an appreciable improvement in the precision of the limits is possible if the algebraic relations between the distances among each quadruple of atoms are also considered. The goal of this paper is to use a recently improved algorithm for computing these "tetrangle inequality limits" to determine just how much improvement really is possible, given the types of experimental data that are usually available.

Determination of three-dimensional structures of proteins and nucleic acids in solution by nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy has evolved over the last decade into a powerful method for determining three-dimensional structures of biological macromolecules in solution. Key advances have been the introduction of two-dimensional experiments, high-field superconducting magnets, and computational procedures for converting the NMR-derived interproton distances and torsion angles into three-dimensional structures. This article outlines the methodology employed, describes the major NMR experiments necessary for the spectral analysis of macromolecules, and discusses the computational approaches employed to date. The present state of the art is illustrated using a variety of examples, and future developments are indicated.

Determination of the complete three-dimensional structure of the alpha-amylase inhibitor tendamistat in aqueous solution by nuclear magnetic resonance and distance geometry

The complete three-dimensional structure of the alpha-amylase inhibitor Tendamistat in aqueous solution was determined by 1H nuclear magnetic resonance and distance geometry calculations using the program DISMAN. Compared to an earlier, preliminary determination of the polypeptide backbone conformation, stereo-specific assignments were obtained for 41 of the 89 prochiral groups in the protein, and a much more extensive set of experimental constraints was collected, including 842 distance constraints from nuclear Overhauser effects and over 100 supplementary constraints from spin-spin coupling constants and the identification of intramolecular hydrogen bonds. The complete protein molecule, including the amino acid side-chains is characterized by a group of nine structures corresponding to the results of the nine DISMAN calculations with minimal residual error functions. The average of the pairwise minimal root-mean-square distances among these nine structures is 0.85 A for the polypeptide backbone, and 1.52 A for all the heavy atoms. The procedures used for the structure determination are described and a detailed analysis is presented of correlations between the experimental input data and the precision of the structure determination.

Two-dimensional NMR as a probe of structural similarity applied to mutants of cytochrome c

Using site-directed mutagenesis, it is possible to prepare many mutants of a protein in a short time, and to uncover differences in function. To understand the changes in function, it is essential to understand the effect(s) of the mutation in terms of structural and dynamic changes. It is particularly important to establish a rapid method for comparing the structure of the mutants with that of the wild-type protein. We propose that a combination of overlayed and difference two-dimensional NOE spectra between the wild-type and mutant protein provide a rapid method for determination of structural similarity. The observation of differences other than those due directly to the field effects of the exchanged side chain allow both local and distant conformational changes to be assessed. Here we compare NOESY spectra from a mutant of yeast iso-1-ferrocytochrome c in which the invariant residue Phe-82 has been changed to a Tyr. We conclude that NMR can show subtle changes in protein structure. Specifically, we show the change must involve the reorientation of the side chain of Leu-85 which is proximal to the mutation. The dynamics of the aromatic side chain at position 82 are shown not to give rise to measurable differences between the wild-type and mutant protein. Structural changes are not propagated to a measurable degree in other parts of the protein.

Three-dimensional structure of rabbit liver [Cd7]metallothionein-2a in aqueous solution determined by nuclear magnetic resonance

In previous work the metal-polypeptide co-ordinative bonds in the major protein species of a reconstituted [113Cd7]metallothionein-2 preparation from rabbit liver in aqueous solution were determined, the secondary polypeptide structure was found to contain several half-turns and 3(10)-helical segments, and a preliminary characterization of the overall polypeptide backbone fold in the beta-domain containing the three-metal cluster, and the alpha-domain containing the four-metal cluster, was obtained. Using a new, more extensive set of nuclear magnetic resonance data these earlier structures were improved by new structure calculations. The new experimental data consist of distance constraints from measurements of nuclear Overhauser effects, and dihedral angle constraints derived from both coupling constants and nuclear Overhauser effects. The structure calculations were performed with the program DISMAN. Since no information on the orientation of the two domains relative to each other could be obtained, the structure calculations were performed separately for the alpha-domain and the beta-domain. The average of the pairwise root-mean-square distances among the 20 structures with the least residual violations of input constraints was 2.9 A for the beta-domain and 1.4 A for the alpha-domain (1 A = 0.1 nm). The overall chirality of the polypeptide fold is right-handed for the beta-domain and left-handed for the alpha-domain. For each of the seven metal ions the local chirality of the co-ordination of the four cysteinyl Sy atoms is clearly defined. The improved structures of both domains show the previously noted differences relative to the recently published crystal structure of metallothionein-2a from rat liver.

A simple qualitative representation of polypeptide chain folds: comparison of protein tertiary structures

A new simple quantitative representation of three-dimensional structure of globular proteins is proposed which is useful for comparison of distantly related problems, computer sorting of large sets of conformations, and search of structurally similar domains in protein data base. The folding course of the polypeptide backbone is approximated by a set of successive vectors corresponding to the elements of regular secondary structure (e.g. alpha-helices, strands of beta-sheets) and non-regular segments. The parameters specifying the spatial organization of segments in this vector model are internal coordinates, namely, lengths of the vectors, planar and dihedral angles. Quantitative representation proposed allows to circumvent the problem of insertions/deletions and to avoid the stage of best superposition during protein comparison. An application was made to the comparison of three-dimensional structures of scorpion toxins Centruroides sculpturatus Ewing v-3, Buthus eupeus M9 and I5A, which have different chain lengths and low sequence similarity.

The structure of melittin. A 1H-NMR study in methanol

The conformation of the 26-residue polypeptide melittin has been studied using 1H-NMR spectroscopy in methanolic solution. The 1H-NMR spectrum of melittin has been assigned using two-dimensional NMR techniques and the secondary structure has been calculated from nuclear Overhauser enhancement data using distance geometry and restrained molecular dynamics analyses. The structure is found to be mainly helical, and similar to that found in crystals from diffraction data: residues 2-11 and 13-26 form regular alpha-helices joined by a 'hinge' between residues 11-12. The structure in this hinge region is shown to be significantly different from that in the crystal structure, leading to a smaller angle between the two helices. The possible significance of the proline residues in this and similar membrane-spanning peptides is discussed.