Simulated annealing with restrained molecular dynamics using a flexible restraint potential: theory and evaluation with simulated NMR constraints.

A new functional representation of NMR-derived distance constraints, the flexible restraint potential, has been implemented in the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168) for molecular structure generation. In addition, flat-bottomed restraint potentials for representing dihedral angle and vicinal scalar coupling constraints have been introduced into CONGEN. An effective simulated annealing (SA) protocol that combines both weight annealing and temperature annealing is described. Calculations have been performed using ideal simulated NMR constraints, in order to evaluate the use of restrained molecular dynamics (MD) with these target functions as implemented in CONGEN. In this benchmark study, internuclear distance, dihedral angle, and vicinal coupling constant constraints were calculated from the energy-minimized X-ray crystal structure of the 46-amino acid polypeptide crambin (ICRN). Three-dimensional structures of crambin that satisfy these simulated NMR constraints were generated using restrained MD and SA. Polypeptide structures with extended backbone and side-chain conformations were used as starting conformations. Dynamical annealing calculations using extended starting conformations and assignments of initial velocities taken randomly from a Maxwellian distribution were found to adequately sample the conformational space consistent with the constraints. These calculations also show that loosened internuclear constraints can allow molecules to overcome local minima in the search for a global minimum with respect to both the NMR-derived constraints and conformational energy. This protocol and the modified version of the CONGEN program described here are shown to be reliable and robust, and are applicable generally for protein structure determination by dynamical simulated annealing using NMR data.     

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.     

Multidomain binding of transforming growth factor alpha to the epidermal growth factor receptor.

Solubilized epidermal growth factor receptor (EGF-R) has been used in an extension of the Geysen epitope mapping protocol in order to provide additional insight into the amino acid residues in human transforming growth factor alpha (hTGF alpha) which are critical to recognition and binding. Overlapping heptapeptides which encompassed the 50 amino acid primary sequence of hTGF alpha were synthesized on a polyethylene solid phase, and the amount of detergent-solubilized EGF-R bound to each peptide was measured using ELISA. EGF-R appeared to bind reproducibly to four heptapeptides cognate to sequences in both the N- and C-domains of hTGF alpha (residues 22-28, 28-34, 36-42, and 44-50). Visualization of these four regions on three-dimensional solution phase structures of hTGF alpha, derived from 1H NMR measurements [Kline, T.-P., Brown, F.K., Brown, S.C., Jeffs, P.W., Kopple, K.D., & Mueller, L. (1990) Biochemistry 29, 7805-7813], indicated that the peptide segments are located on a single face of the protein and suggested the presence of a potential receptor binding cavity. If peptide segments within both the N- and C-domains of hTGF alpha are involved in binding to EGF-R, then this has direct consequences for possible molecular mechanisms by which receptor activation might take place. For example, the observed conformational flexibility in the six NMR-derived hTGF alpha structures due to variations in the main-chain torsion angles of Val-33, in combination with the involvement of residues from both domains in the proposed binding cavity, may imply that receptor activation results from interdomain reorientation in the protein ligand.(ABSTRACT TRUNCATED AT 250 WORDS)     

Conformational analysis of protein structures derived from NMR data

A study is presented of the conformational characteristics of NMR-derived protein structures in the Protein Data Bank compared to X-ray structures. Both ensemble and energy-minimized average structures are analyzed. We have addressed the problem using the methods developed for crystal structures by examining the distribution of ?, Ψ, and χ angles as indicators of global conformational irregularity. All these features in NMR structures occur to varying degrees in multiple conformational states. Some measures of local geometry are very tightly constrained by the methods used to generate the structure, e.g., proline ? angles, α-helix ?, Ψ angles, ω angles, and C_α chirality. The more lightly restrained torsion angles do show increasead clustering as the number of overall experimental observations increases. ?, Ψ, and χ₁ angle conformational heterogeneity is strongly correlated with accessibility but shows additional differences which reflect the differing number of observations possible in NMR for the various side chains (e.g., many for Trp, few for Ser). In general, we find that the core is defined to a notional resolution of 2.0 to 2.3 Å. Of real interest is the behavior of surface residues and in particular the side chains where multiple rotameric states in different structures can vary from 10% to 88%. Later generation structures show a much tighter definition which correlates with increasing use of J-coupling information, stereospecific assignments, and heteronumclear techniques. A suite of programs is being developed to address the special needs of NMR-derived structures which will take into account the existence of increased mobility in solution. © 1993 Wiley-Liss, Inc.     

The NMR solution structure of the pheromone Er-11 from the ciliated protozoan Euplotes raikovi.

The NMR solution structure of the pheromone Er-11, a 39-residue protein from the ciliated protozoan Euplotes raikovi, was calculated with the distance geometry program DIANA from 449 NOE upper distance constraints and 97 dihedral angle constraints, and the program OPAL was employed for structure refinement by molecular mechanics energy minimization in a water bath. For a group of 20 conformers used to characterize the solution structure, the average of the pairwise RMS deviations from the mean structure calculated for the backbone heavy atoms N, C alpha, and C' of residues 2-38 was 0.30 A. The molecular architecture is dominated by an up-down-up bundle of three short helices with residues 2-9, 12-19, and 22-32, which is closely similar to the previously determined structures of the homologous pheromones Er-1, Er-2, and Er-10. This finding provides structural evidence for the capability shown by these pheromones to compete with each other in binding reactions to their cell-surface receptors.     

Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH

The structure of the 36 residue villin headpiece subdomain is investigated with the electrostatically driven Monte Carlo method. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) force field, plus two different continuum solvation models, were used to describe the conformational energy of the chain with both blocked and unblocked N and C termini. A statistical analysis of an ensemble of ab initio generated conformations was carried out, based on a comparison with a set of ten native-like structures derived from published experimental data, by using rigid geometry and NMR-derived constraints obtained at pH 3.7. The ten native-like structures satisfy the NMR-derived constraints. The whole ensemble of conformations of the terminally unblocked villin headpiece sub-domain, generated by using ECEPP/3 with a continuum solvation model, were subsequently evaluated at pH 3.7 with a potential function that includes ECEPP/3 combined with a fast multigrid boundary element method. At pH 3.7, the lowest-energy conformation found during the conformational search satisfies approximately 70% of both the distance and the dihedral-angle constraints, and possesses the characteristic packing of three phenylalanine residues that constitute the main part of the hydrophobic core of the molecule. On the other hand, computations at pH 3.7 and pH 7.0 for the ten native-like structures satisfying the NMR-derived constraints indicate a substantial change in the charge distribution for each type of amino acid residue with the change in pH. The results of this study provide a basis to understand the effect of the interactions, such as hydrophobicity, charge-charge interaction and solvent polarization, on the stability of this small alpha-helical protein.     

NMR and molecular modeling characterization of RGD containing peptides.

The tripeptide sequence arginine-glycine-aspartic acid (RGD) has been shown to be the key recognition segment in numerous cell adhesion proteins. The solution conformation and dynamics in DMSO-d6 of the cyclic pentapeptides, [formula: see text], a potent fibrinogen receptor antagonist, and [formula: see text], a weak fibrinogen receptor antagonist, have been characterized by nuclear magnetic resonance (NMR) spectroscopy and molecular modeling. 1H-1H distance constraints derived from two-dimensional NOE spectroscopy and torsional angle constraints obtained from 3JNH-H alpha coupling constants, combined with computer-assisted modeling using conformational searching algorithms and energy minimization have allowed several low energy conformations of the peptides to be determined. Low temperature studies in combination with molecular dynamics simulations suggest that each peptide does not exist in a single, well-defined conformation, but as an equilibrating mixture of conformers in fast exchange on the NMR timescale. The experimental results can be fit by considering pairs of low energy conformers. Despite this inherent flexibility, distinct conformational preferences were found which may be related to the biological activity of the peptides.     

Solution structure of the orphan nuclear receptor rev-erb beta response element by 1H, 31P NMR and molecular simulation*

Rev-erb beta is an orphan receptor that binds as a homodimer or as a monomer to DNA. The solution structure of the non-palindromic 15 bp DNA duplex d(TAGAATGTAGGTCAG), the response element of Rev-erb beta for monomeric binding, was determined by 1H and 31P NMR, energy minimization with NMR-derived restraints for distances and NOE back-calculation methods. The refined final structures have the typical overall features of B-type DNA. However, titration of this 15 bp duplex with ReDBD, the DNA binding domain of Rev-erb beta, showed large shifts of imino protons and 31P signals, suggesting major conformational changes.     

Solution structure of a DNA duplex with a chiral alkyl phosphonate moiety

The solution structures of two DNA decamers of sequence d(CCACCpxGGAAC)·(GTTCCGGTGG) with a chiral alkyl phosphonate moiety (px) have been determined using NMR and restrained molecular dynamics simulations and compared with the solution structure of the unmodified duplex. The ¹H NMR spectra of two samples with pure stereochemistry in the modified phosphate have been assigned. The structures of both diastereoisomers, as well as the unmodified control duplex, have been determined from NMR-derived distance and torsion angle constraints. Accurate distance constraints were obtained from a complete relaxation matrix analysis of the NOE intensities. The structures have been refined with state of the art molecular dynamics methods, including explicit solvent and applying the particle mesh Ewald method to properly evaluate the long-range electrostatic interactions. In both cases, the calculations converge to well-defined structures, with RMSDs of ~1 Å. The resulting structures belong to the general B family of DNA structures, even though the presence of the alkyl phosphonate moiety induces some slight displacement to the A-form in the neighborhood of the modified phosphate. Partial neutralization of this phosphate and the steric effect of the alkyl moiety provoke moderate bending in the DNA. This effect is more pronounced in the S diastereoisomer, where the alkyl group points inwards to the double helix.     

High-resolution three-dimensional structure of reduced recombinant human thioredoxin in solution

The solution structure of recombinant human thioredoxin (105 residues) has been determined by nuclear magnetic resonance (NMR) spectroscopy combined with hybrid distance geometry-dynamical simulated annealing calculations. Approximate interproton distance restraints were derived from nuclear Overhauser effect (NOE) measurements. In addition, a large number of stereospecific assignments for beta-methylene protons and torsion angle restraints for phi, psi, and chi 1 were obtained by using a conformational grid search on the basis of the intraresidue and sequential NOE data in conjunction with 3JHN alpha and 3J alpha beta coupling constants. The structure calculations were based on 1983 approximate interproton distance restraints, 52 hydrogen-bonding restraints for 26 hydrogen bonds, and 98 phi, 71 psi, and 72 chi 1 torsion angle restraints. The 33 final simulated annealing structures obtained had an average atomic rms distribution of the individual structures about the mean coordinate positions of 0.40 +/- 0.06 A for the backbone atoms and 0.78 +/- 0.05 A for all atoms. The solution structure of human thioredoxin consists of a five-stranded beta-sheet surrounded by four alpha-helices, with an active site protrusion containing the two redox-active cysteines. The overall structure is similar to the crystal and NMR structures of oxidized [Katti, S. K., LeMaster, D. M., & Eklund, H. (1990) J. Mol. Biol. 212, 167-184] and reduced [Dyson, J. H., Gippert, G. P., Case, D. A., Holmgren, A., & Wright, P. (1990) Biochemistry 29, 4129-4136] Escherichia coli thioredoxin, respectively, despite the moderate 25% amino acid sequence homology. Several differences, however, can be noted. The human alpha 1 helix is a full turn longer than the corresponding helix in E. coli thioredoxin and is characterized by a more regular helical geometry. The helix labeled alpha 3 in human thioredoxin has its counterpart in the 3(10) helix of the E. coli protein and is also longer in the human protein. In contrast to these structural differences, the conformation of the active site loop in both proteins is very similar, reflecting the perfect sequence identity for a stretch of eight amino acid residues around the redox-active cysteines.     

Systematic solution to homo‐oligomeric structures determined by NMR

Protein structure determination by NMR has predominantly relied on simulated annealing‐based conformational search for a converged fold using primarily distance constraints, including constraints derived from nuclear Overhauser effects, paramagnetic relaxation enhancement, and cysteine crosslinkings. Although there is no guarantee that the converged fold represents the global minimum of the conformational space, it is generally accepted that good convergence is synonymous to the global minimum. Here, we show such a criterion breaks down in the presence of large numbers of ambiguous constraints from NMR experiments on homo‐oligomeric protein complexes. A systematic evaluation of the conformational solutions that satisfy the NMR constraints of a trimeric membrane protein, DAGK, reveals 9 distinct folds, including the reported NMR and crystal structures. This result highlights the fundamental limitation of global fold determination for homo‐oligomeric proteins using ambiguous distance constraints and provides a systematic solution for exhaustive enumeration of all satisfying solutions. Proteins 2015; 83:651–661. © 2015 Wiley Periodicals, Inc.     

Factors influencing accuracy of computer-built models: a study based on leucine zipper GCN4 structure.

A three-dimensional model of the leucine zipper GCN4 built from its amino acid sequence had been reported previously by us. When the two alternative x-ray structures of the GCN4 dimer became available, the root mean square (r.m.s.) shifts between our model and the structures were determined as approximately 2.7 A on all atoms. These values are similar to the r.m.s. shift of 2.8 A between the two GCN4 structures in the different crystal forms (C2 and P2(1)2(1)2(1)). CONGEN conformational searches were run to better understand the conditions that may determine the preference of different conformers in different environments and to test the sensitivity of our current modeling techniques. With a judicious choice of CONGEN search parameters, the backbone r.m.s. deviation improved to 0.8 A and 2.5 A on all atoms. The side-chain conformations of Val and Leu at the helical interface were well reproduced (1.2 A r.m.s.), and the large side-chain misplacements occurred with only a small number of charged amino acids and a tyrosine. Inclusion of the crystal environment (C2 symmetry), as a passive background, into the side-chain conformational search further improved the accuracy of the model to an r.m.s. deviation of 2.1 A. Conformational searches carried out in the two different crystal environments and employing the AMBER protein/DNA forcefield, as implemented in CONGEN, gave the r.m.s. values of 2.2 A (for the C2 symmetry) and 2.5 A (for the P2(1)2(1)2(1) symmetry). In the C2 symmetry crystal, as much as 40% of the surface of each dimer was involved in crystal contacts with other dimers, and the charged residues on the surface often interacted with immobilized water molecules. Thus, occasional large r.m.s. deviations between the model and the x-ray side chains were due to specific conditions that did not occur in solution.     

Solution structure of apamin determined by nuclear magnetic resonance and distance geometry

The solution structure of the bee venom neurotoxin apamin has been determined with a distance geometry program using distance constraints derived from NMR. Twenty embedded structures were generated and refined by using the program DSPACE. After error minimization using both conjugate gradient and dynamics algorithms, six structures had very low residual error. Comparisons of these show that the backbone of the peptide is quite well-defined with the largest rms difference between backbone atoms in these structures of 1.34 A. The side chains have far fewer constraints and show greater variability in their positions. The structure derived here is generally consistent with the qualitative model previously described, with most differences occurring in the loop between the beta-turn (residues 2-5) and the C-terminal alpha-helix (residues 9-17). Comparisons are made with previously derived models from NMR data and other methods.     

The NMR solution structure of the pheromone Er-2 from the ciliated protozoan Euplotes raikovi.

The NMR structure of the pheromone Er-2 from the ciliated protozoan Euplotes raikovi has been determined in aqueous solution. The structure of this 40-residue protein was calculated with the distance geometry program DIANA from 621 distance constraints and 89 dihedral angle constraints; the program OPAL was employed for the energy minimization. For a group of 20 conformers used to characterize the solution structure, the average pairwise RMS deviation from the mean structure calculated for the backbone heavy atoms N, C alpha, and C' of residues 3-37 was 0.31 A. The molecular architecture is dominated by an up-down-up bundle of 3 short helices of residues 5-11, 14-20, and 23-33, which is similar to the structures of the homologous pheromones Er-1 and Er-10. Novel structural features include a well-defined N-cap on the first helix, a 1-residue deletion in the second helix resulting in the formation of a 3(10)-helix rather than an alpha-helix as found in Er-1 and Er-10, and the simultaneous presence of 2 different conformations for the C-terminal tetrapeptide segment, i.e., a major conformation with the Leu 39-Pro 40 peptide bond in the trans form and a minor conformation with this peptide bond in the cis form.     

Application of restrained minimization, simulated annealing and molecular dynamics simulations for the conformational analysis of oligosaccharides.

The purpose of the present study was to determine the confidence with which the small number of 1H NMR nuclear Overhauser effect (NOE) distance constraints measurable across glycosidic linkages in oligosaccharides could be used for solution conformational analysis. This was assessed by use of these constraints in restrained molecular mechanical minimization of the tetrasaccharide Gal beta 1----4(Fuc alpha 1----3)Glc-NAc beta 1----3Gal, a model compound of the Lewis-X antigenic determinant. This presents a particularly severe test case in view of extreme resonance overlap and a dearth of inter-residue distance constraints. It is concluded that these constraints, when used in conventional restrained minimization, result in the generation of 'virtual conformations' and local minima about glycosidic linkages. However, these restraints are nevertheless found to be useful in the initial stages of a conformational analysis strategy involving restrained minimization combined with dynamical simulated annealing to define more accurately the global minimum energy configuration, together with molecular dynamics simulation to explore conformational mobility about this minimum. Theoretical ROE values calculated over the time course of the MD simulation, using a formalism appropriate for the time scale of the internal motion, are compared with those obtained experimentally in the oligosaccharide.     

Conformation of sarafotoxin-6b in aqueous solution determined by NMR spectroscopy and distance geometry

The solution structure of sarafotoxin-6b in water has been determined using high-resolution NMR spectroscopy. 127 proton-proton distance measurements and three phi dihedral angle constraints derived from NMR spectra were used to calculate the solution structure using a combination of distance geometry and restrained molecular dynamics. The major structural feature of the resulting family of five structures was a right-handed alpha-helix extending from K9 to Q17. In contrast, the C-terminal region of the peptide appears not to adopt a preferred conformation in aqueous solution. The present structure is compared with those previously determined for endothelin peptides in non-aqueous solvents.     

Solution structure of the tumor necrosis factor receptor-1 death domain.

Tumor necrosis factor receptor-1 death domain (TNFR-1 DD) is the intracellular functional domain responsible for the receptor signaling activities. The solution structure of the R347K mutant of TNFR-1 DD was solved by NMR spectroscopy. A total of 20 structures were calculated by means of hybrid distance geometry-simulated annealing using a total of 1167 distance constraints and 117 torsion angle constraints. The atomic rms distribution about the mean coordinate positions for the 20 structures for residues composing the secondary structure region is 0.40 A for the backbone atoms and 1.09 A for all atoms. The structure consists of six antiparallel alpha-helices arranged in a similar fashion to the other members of the death domain superfamily. The secondary structure and three-dimensional structure of R347K TNFR1-DD are very similar to the secondary structure and deduced topology of the R347A TNFR1-DD mutant. Mutagenesis studies identified critical residues located in alpha2 and part of alpha3 and alpha4 that are crucial for self-interaction and interaction with TRADD. Structural superposition with previously solved proteins in the death domain superfamily reveals that the major differences between the structures reside in alpha2, alpha3, and alpha4. Interestingly, these regions correspond to the binding sites of TNFR1-DD, providing a structural basis for the specificity of death domain interactions and its subsequent signaling event.