Solution conformations of human growth hormone releasing factor: comparison of the restrained molecular dynamics and distance geometry methods for a system without long-range distance data

A series of three-dimensional structures of the 1-29 fragment of human growth hormone releasing factor in trifluoroethanol have been determined by molecular dynamics and distance geometry methods. The resulting structures satisfy information from nuclear Overhauser effect (NOE) distance data and an empirical potential energy function. Although the polypeptide was found to have an ordered structure in all simulations, the NOE data were not sufficient for global convergence to a unique three-dimensional geometry. Several satisfactory structures have been determined, all of which are extended conformations consisting of a short beta-strand and two alpha-helices (residues 6-13 and residues 16-29) connected by short segments of less well defined secondary structure. Because of the lack of NOE data connecting the helix segments, their relative orientation is not uniquely determined.     

Determination of three-dimensional structures of proteins from interproton distance data by hybrid distance geometry-dynamical simulated annealing calculations

A new hybrid distance space-real space method for determining three-dimensional structures of proteins on the basis of interproton distance restraints is presented. It involves the following steps: (i) the approximate polypeptide fold is obtained by generating a set of substructures comprising only a small subset of atoms by projection from multi-dimensional distance space into three-dimensional cartesian coordinate space using a procedure known as 'embedding'; (ii) all remaining atoms are then added by best fitting extended amino acids one residue at a time to the substructures; (iii) the resulting structures are used as the starting point for real space dynamical simulated annealing calculations. The latter involve heating the system to a high temperature followed by slow cooling in order to overcome potential barriers along the pathway towards the global minimum region. This is carried out by solving Newton's equations of motion. Unlike conventional restrained molecular dynamics, however, the non-bonded interactions are represented by a simple van der Waals repulsion term. The method is illustrated by calculations on crambin (46 residues) and the globular domain of histone H5 (79 residues). It is shown that the hybrid method is more efficient computationally and samples a larger region of conformational space consistent with the experimental data than full metric matrix distance geometry calculations alone, particularly for large systems.     

Analysis of the relative contributions of the nuclear Overhauser interproton distance restraints and the empirical energy function in the calculation of oligonucleotide structures using restrained molecular dynamics

The relative contributions of the interproton distance restraints derived from nuclear Overhauser enhancement measurements and of the empirical energy function in the determination of oligonucleotide structures by restrained molecular dynamics are investigated. The calculations are based on 102 intraresidue and 126 interresidue interproton distance restraints derived from short mixing time two-dimensional nuclear Overhauser enhancement data on the dodecamer 5'd(CGCGPATTCGCG)2 [Clore, G.M., Oschkinat, H., McLaughlin, L.W., Benseler, F., Scalfi Happ, C., Happ, E., & Gronenborn, A.M. (1988) Biochemistry 27, 4185-4197]. Eight interproton distance restraint lists were made up with errors ranging from -0.1/+0.2 to -1.2/+1.3 A for r less than 2.5 A and from -0.2/+0.3 to -1.3/+1.4 A for r greater than or equal to 2.5 A. These restraints were incorporated into the total energy function of the system in the form of square-well potentials with force constants set sufficiently high to ensure that the deviations between calculated distances and experimental restraints were very small (average interproton distance rms deviation of less than 0.06 A). For each data set, six calculations were carried out, three starting from classical A-DNA and three from classical B-DNA. The results show that structural changes occurring during the course of restrained molecular dynamics and the degree of structural convergence are determined by the interproton distance restraints. All the structures display similar small deviations from idealized geometry and have the same values for the nonbonding energy terms comprising van der Waals, electrostatic, and hydrogen-bonding components. Thus, the function of the empirical energy function is to maintain near perfect stereochemistry and nonbonded interactions.(ABSTRACT TRUNCATED AT 250 WORDS)     

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 determination of the three-dimensional structure of barley serine proteinase inhibitor 2 by nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The solution structure of the 64 residue structured domain (residues 20-83) of barley serine proteinase inhibitor 2 (BSPI-2) is determined on the basis of 403 interproton distance, 34 phi backbone torsion angle and 26 hydrogen bonding restraints derived from n.m.r. measurements. A total of 11 converged structures were computed using a metric matrix distance geometry algorithm and refined by restrained molecular dynamics. The average rms difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.2 A for the backbone atoms and 2.1 +/- 0.1 A for all atoms. The overall structure, which is almost identical to that found by X-ray crystallography, is disc shaped and consists of a central four component mixed parallel and antiparallel beta-sheet flanked by a 13 residue alpha-helix on one side and the reactive site loop on the other.     

The three-dimensional structure of alpha1-purothionin in solution: combined use of nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The determination of the three-dimensional solution structure of α1-purothionin using a combination of metric matrix distance geometry and restrained molecular dynamics calculations based on n.m.r. data is presented. The experimental data comprise complete sequence-specific proton resonance assignments, a set of 310 approximate interproton distance restraints derived from nuclear Overhauser effects, 27 Ø backbone torsion angle restraints derived from vicinal coupling constants, 4 distance restraints from hydrogen bonds and 12 distance restraints from disulphide bridges. The average atomic rms difference between the final nine converged structures and the mean structure obtained by averaging their coordinates is 1.5 ± 0.1 å for the backbone atoms and 2.0 ± 0.1 å for all atoms. The overall shape of α1-purothionin is that of the capital letter L, similar to that of crambin, with the longer arm comprising two approximately parallel α-helices and the shorter arm a strand and a mini anti-parallel β sheet.     

Solution structure of human calcitonin gene-related peptide by 1H NMR and distance geometry with restrained molecular dynamics

The structure of human calcitonin gene-related peptide 1 (hCGRP-1) has been determined by 1H NMR in a mixed-solvent system of 50% trifluoroethanol/50% H2O at pH 3.7 and 27 degrees C. Complete resonance assignment was achieved by using two-dimensional methods. Distance restraints for structure calculations were obtained by semiquantitative analysis of intra- and interresidue nuclear Overhauser effects; in addition, stereospecific or X1 rotamer assignments were obtained for certain side chains. Structures were generated from the distance restraints by distance geometry, followed by refinement using molecular dynamics, and were compared with experimental NH-C alpha H coupling constants and amide hydrogen exchange data. The structure of hCGRP-1 in this solvent comprises an amino-terminal disulfide-bonded loop (residues 2-7) leading into a well-defined alpha-helix between residues 8 and 18; thereafter, the structure is predominantly disordered, although there are indications of a preference for a turn-type conformation between residues 19 and 21. Comparison of spectra for the homologous hCGRP-2 with those of hCGRP-1 indicates that the conformations of these two forms are essentially identical.     

The combined use of NMR, distance geometry, and restrained molecular dynamics for the conformational study of a cyclic somatostatin analogue

A cyclic peptide analogue of somatostatin, including the o-aminomethylphenylacetic acid spacer, was studied by the combined use of two-dimensional nmr spectroscopy, distance geometry, and restrained molecular dynamics. Analysis of distances determined from nuclear Overhauser effect (NOE) buildup rates revealed that these were inconsistent with a unique backbone conformation near the spacer. Assuming that the conformational heterogeneity is localized to the spacer, the NOE distances measured for the remaining part of the molecule were used to generate a large number of structures with the distance geometry algorithm, which were then refined by restrained energy minimization. Four classes of structures emerged, which together account for all observed NOEs. A representative structure of each class was further refined with the restrained molecular dynamics technique, and shown to be stable on a 20-ps time scale. The flexibility of the spacer was examined by simulating interconversions induced by an appropriate restraining potential. As a result, the explanation for the lack of somatostatin activity of the analogue studied was reconsidered.     

Conformational study of cyclolinopeptide A. A distance geometry and molecular dynamics approach

The conformation of cyclolinopeptide A, c(Pro-Pro-Phe-Phe-Leu-Ile-Ile-Leu-Val), a naturally occurring peptide with remarkable cytoprotective activity, has been investigated by means of distance geometry calculations and molecular dynamics simulations. The starting points for all the calculations were an X-ray structure and other structures obtained from distance geometry calculations based on NMR data. Restrained and unrestrained molecular dynamics simulations are reported in vacuo and in CCl4. Structural and dynamic properties are investigated and compared with those experimentally determined. The conformation obtained from the MD simulations which best reproduces the NMR parameters is at the same time one of the most stable ones and is also fairly similar to the crystal structure. An explanation for the occurrence of multiple conformations in solution at room temperature is given.     

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.     

Three-dimensional structure of potato carboxypeptidase inhibitor in solution. A study using nuclear magnetic resonance, distance geometry, and restrained molecular dynamics

The solution conformation of potato carboxypeptidase inhibitor (CPI) has been investigated by 1H NMR spectroscopy. The spectrum is assigned in a sequential manner by using two-dimensional NMR techniques to identify through-bond and through-space (less than 5 A) connectivities. A set of 309 approximate interproton distance restraints is derived from the two-dimensional nuclear Overhauser enhancement spectra and used as the basis of a three-dimensional structure determination by a combination of metric matrix distance geometry and restrained molecular dynamics calculations. A total of 11 converged distance geometry structures were computed and refined by using restrained molecular dynamics. The average atomic root mean square (rms) difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.3 A for residues 2-39 and 0.9 +/- 0.2 A for residues 5-37. The corresponding values for all atoms are 1.9 +/- 0.3 and 1.4 +/- 0.2 A, respectively. The larger values for residues 2-38 relative to those for residues 5-37 arise from the fact that the positions of the N- (residues 1-4) and C- (residues 38-39) terminal tails are rather poorly determined, whereas those of the core of the protein (residues 5-37) are well determined by the experimental interproton distance data. The computed structures are very close to the X-ray structure of CPI in its complex with carboxypeptidase, and the backbone atomic rms difference between the mean of the computed structures and the X-ray structure is only 1.2 A. Nevertheless, there are some real differences present which are evidenced by significant deviations between the experimental upper interproton distance limits and the corresponding interproton distances derived from the X-ray structure. These principally occur in two regions, residues 18-20 and residues 28-30, the latter comprising part of the region of secondary contacts between CPI and carboxypeptidase in the X-ray structure.     

Solution three-dimensional structure of surfactin: A cyclic lipopeptide studied by 1H-nmr,distance geometry,and molecular dynamics

The solution three-dimensional structure of the protonated [Leu7]-surfactin, an hepta-peptide extracted from Bacillus subtilis, has been determined from two-dimensional ¹Hnmr performed in ²H₆-dimethylsulfoxide and combined with molecular modeling. Experimental data included 9 coupling constants, 61 nuclear Overhauser effect derived distances, NH temperature coefficients, and ¹³C relaxation times. Two distance geometry (DISMAN) protocols converged toward models of the structure and the best of them were refined by restrained and unrestrained molecular dynamics (GROMOS). Two structures in accord with the set of experimental constraints are presented. Both are characterized by a “horse saddle” topology for ring atoms on which are attached the two polar Glu and Asp side chains showing an orientation clearly opposite to that of the C_11–13 aliphatic chain. Amphipathic and surface properties of surfactin are certainly related to the existence of such minor polar and a major hydrophobic domains. The particular “claw” configuration of acidic residues observed in surfactin gives important clues for the understanding of its cation binding and transporting ability. © 1994 John Wiley & Sons, Inc.     

Solution structure of neurotoxin I from the sea anemone Stichodactyla helianthus. A nuclear magnetic resonance, distance geometry, and restrained molecular dynamics study

The three-dimensional structure of the sea anemone polypeptide Stichodactyla helianthus neurotoxin I in aqueous solution has been determined using distance geometry and restrained molecular dynamics simulations based on NMR data acquired at 500 MHz. A set of 470 nuclear Overhauser enhancement values was measured, of which 216 were used as distance restraints in the structure determination along with 15 dihedral angles derived from coupling constants. After restrained molecular dynamics refinement, the eight structures that best fit the input data form a closely related family. They describe a structure that consists of a core of twisted, four-stranded, antiparallel beta-sheet encompassing residues 1-3, 19-24, 29-34, and 40-47, joined by three loops, two of which are well defined by the NMR data. The third loop, encompassing residues 7-16, is poorly defined by the data and is assumed to undergo conformational averaging in solution. Pairwise root mean square displacement values for the backbone heavy atoms of the eight best structures are 1.3 +/- 0.2A when the poorly defined loop is excluded and 3.6 +/- 1.0A for all backbone atoms. Refinement using restrained molecular dynamics improved the quality of the structures generated by distance geometry calculations with respect to the number of nuclear Overhauser enhancements violated, the size of the total distance violations and the total potential energies of the structures. The family of structures for S. heliathus neurotoxin I is compared with structures of related sea anemone proteins that also bind to the voltage-gated sodium channel.     

Three-dimensional structure of bradykinin in SDS micelles. Study using nuclear magnetic resonance, distance geometry, and restrained molecular mechanics and dynamics

The conformational properties of bradykinin in five molar excess sodium dodecyl sulfate (SDS) micelles have been examined by two-dimensional nuclear magnetic resonance (NMR) techniques at 500 MHz. Detailed structural information for bradykinin in SDS was obtained from quantitative 2-D nuclear Overhauser enhancement (n.O.e.) analyses, distance geometry, and restrained molecular mechanics and dynamics calculations. The conformation of bradykinin in SDS micelles, as determined by these methods, is characterized by a beta-turn-like structure at residues 6-9. A detailed comparison of the structures derived from distance geometry and restrained molecular mechanics and dynamics is also presented.     

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

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

Structural refinement of membrane proteins by restrained molecular dynamics and solvent accessibility data

We present an approach for incorporating solvent accessibility data from electron paramagnetic resonance experiments in the structural refinement of membrane proteins through restrained molecular dynamics simulations. The restraints have been parameterized from oxygen (ΠO₂) and nickel-ethylenediaminediacetic acid (ΠNiEdda) collision frequencies, as indicators of lipid or aqueous exposed spin-label sites. These are enforced through interactions between a pseudoatom representation of the covalently attached Nitroxide spin-label and virtual “solvent” particles corresponding to O₂ and NiEdda in the surrounding environment. Interactions were computed using an empirical potential function, where the parameters have been optimized to account for the different accessibilities of the spin-label pseudoatoms to the surrounding environment. This approach, “pseudoatom-driven solvent accessibility refinement”, was validated by refolding distorted conformations of the Streptomyces lividans potassium channel (KcsA), corresponding to a range of 2-30 Å root mean-square deviations away from the native structure. Molecular dynamics simulations based on up to 58 electron paramagnetic resonance restraints derived from spin-label mutants were able to converge toward the native structure within 1-3 Å root mean-square deviations with minimal computational cost. The use of energy-based ranking and structure similarity clustering as selection criteria helped in the convergence and identification of correctly folded structures from a large number of simulations. This approach can be applied to a variety of integral membrane protein systems, regardless of oligomeric state, and should be particularly useful in calculating conformational changes from a known reference crystal structure.     

Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. Application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2

An automated method, based on the principle of simulated annealing, is presented for determining the three-dimensional structures of proteins on the basis of short (less than 5 A) interproton distance data derived from nuclear Overhauser enhancement (NOE) measurements. The method makes use of Newton's equations of motion to increase temporarily the temperature of the system in order to search for the global minimum region of a target function comprising purely geometric restraints. These consist of interproton distances supplemented by bond lengths, bond angles, planes and soft van der Waals repulsion terms. The latter replace the dihedral, van der Waals, electrostatic and hydrogen-bonding potentials of the empirical energy function used in molecular dynamics simulations. The method presented involves the implementation of a number of innovations over our previous restrained molecular dynamics approach [Clore, G.M., Brünger, A.T., Karplus, M. and Gronenborn, A.M. (1986) J. Mol. Biol., 191, 523-551]. These include the development of a new effective potential for the interproton distance restraints whose functional form is dependent on the magnitude of the difference between calculated and target values, and the design and implementation of robust and fully automatic protocol. The method is tested on three systems: the model system crambin (46 residues) using X-ray structure derived interproton distance restraints, and potato carboxypeptidase inhibitor (CPI; 39 residues) and barley serine proteinase inhibitor 2 (BSPI-2; 64 residues) using experimentally derived interproton distance restraints. Calculations were carried out starting from the extended strands which had atomic r.m.s. differences of 57, 38 and 33 A with respect to the crystal structures of BSPI-2, crambin and CPI respectively. Unbiased sampling of the conformational space consistent with the restraints was achieved by varying the random number seed used to assign the initial velocities. This ensures that the different trajectories diverge during the early stages of the simulations and only converge later as more and more interproton distance restraints are satisfied. The average backbone atomic r.m.s. difference between the converged structures is 2.2 +/- 0.3 A for crambin (nine structures), 2.4 +/- 0.3 A for CPI (eight structures) and 2.5 +/- 0.2 A for BSPI-2 (five structures). The backbone atomic r.m.s. difference between the mean structures derived by averaging the coordinates of the converged structures and the corresponding X-ray structures is 1.2 A for crambin, 1.6 A for CPI and 1.7 A for BSPI-2.     

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.     

Determination of three-dimensional structures of proteins from interproton distance data by dynamical simulated annealing from a random array of atoms. Circumventing problems associated with folding

A new real space method, based on the principles of simulated annealing, is presented for determining protein structures on the basis of interproton distance restraints derived from NMR data. The method circumvents the folding problem associated with all real space methods described to date, by starting from a completely random array of atoms and introducing the force constants for the covalent, interproton distance and repulsive van der Waals terms in the target function appropriately. The system is simulated at high temperature by solving Newton's equations of motion. As the values of all force constants are very low during the early stages of the simulation, energy barriers between different folds of the protein can be overcome, and the global minimum of the target function is reliably located. Further, because the atoms are initially only weakly coupled, they can move essentially independently to satisfy the restraints. The method is illustrated using two examples of small proteins, namely crambin (46 residues) and potato carboxypeptidase inhibitor (39 residues).