Combined procedure of distance geometry and restrained molecular dynamics techniques for protein structure determination from nuclear magnetic resonance data: application to the DNA binding domain of lac repressor from Escherichia coli

The technique of two-dimensional nuclear magnetic resonance (2D-NMR) has recently assumed an active role in obtaining information on structures of polypeptides, small proteins, sugars, and DNA fragments in solution. In order to generate spatial structures from the atom-atom distance information obtained by the NMR method, different procedures have been developed. Here we introduce a combined procedure of distance geometry (DG) and molecular dynamics (MD) calculations for generating 3D structures that are consistent with the NMR data set and have reasonable internal energies. We report the application of the combined procedure on the lac repressor DNA binding domain (headpiece) using a set of 169 NOE and 17 "hydrogen bond" distance constraints. Eight of ten structures generated by the distance geometry algorithm were refined within 10 ps MD simulation time to structures with low internal energies that satisfied the distance constraints. Although the combination of DG and MD was designed to combine the good sampling properties of the DG algorithm with an efficient method of lowering the internal energy of the molecule, we found that the MD algorithm contributes significantly to the sampling as well.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

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.     

Practical applications of time-averaged restrained molecular dynamics to ligand-receptor systems: FK506 bound to the Q50R,A95H,K98I triple mutant of FKBP-13

Summary The ability of time-averaged restrained molecular dynamics (TARMD) to escape local low-energy conformations and explore conformational space is compared with conventional simulated-annealing methods. Practical suggestions are offered for performing TARMD calculations with ligand-receptor systems, and are illustrated for the complex of the immunosuppressant FK506 bound to Q50R,A95H,K98I triple mutant FKBP-13. The structure of ¹³C-labeled FK506 bound to triple-mutant FKBP-13 was determined using a set of 87 NOE distance restraints derived from HSQC-NOESY experiments. TARMD was found to be superior to conventional simulated-annealing methods, and produced structures that were conformationally similar to FK506 bound to wild-type FKBP-12. The individual and combined effects of varying the NOE restraint force constant, using an explicit model for the protein binding pocket, and starting the calculations from different ligand conformations were explored in detail.Abbreviations DG distance geometry - dmFKBP-12 double-mutant (R42K,H87V) FKBP-12 - FKBP-12 FK506-binding protein (12 kDa) - FKBP-13 FK506-binding protein (13 kDa) - HSQC heteronuclear single-quantum coherence - K_NOE force constant (penalty) for NOE-derived distance restraints - MD molecular dynamics - NOE nuclear Overhauser effect - SA simulated annealing - TARMD molecular dynamics with time-averaged restraints - tmFKBP-13 triple-mutant (Q50R,A95H,K98I) FKBP-13 - wtFKBP-12 wild-type FKBP-12     

Molecular dynamics re-refinement of two different small RNA loop structures using the original NMR data suggest a common structure

Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility-using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions-by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to "update" older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias (such as small angle deviations with the current AMBER force fields), and a proper balance between the various restraint weights.     

The solution structure of a monomeric insulin. A two-dimensional 1H-NMR study of des-(B26-B30)-insulin in combination with distance geometry and restrained molecular dynamics.

The solution conformation of des-(B26-B30)-insulin (DPI) has been investigated by 1H-NMR spectroscopy. A set of 250 approximate interproton distance restraints, derived from two-dimensional nuclear Overhauser enhancement spectra, were used as the basis of a structure determination using distance geometry (DG) and distance-bound driven dynamics (DDD). Sixteen DG structures were optimized using energy minimization (EM) and submitted to short 5-ps restrained molecular dynamics (RMD) simulations. A further refinement of the DDD structure with the lowest distance errors was done by energy minimization, a prolonged RMD simulation in vacuo and a time-averaged RMD simulation. An average structure was obtained from a trajectory generated during 20-ps RMD. The final structure was compared with the des-(B26-B30)-insulin crystal structure refined by molecular dynamics and the 2-Zn crystal structure of porcine insulin. This comparison shows that the overall structure of des-(B26-B30)-insulin is retained in solution with respect to the crystal structures with a high flexibility at the N-terminal part of the A chain and at the N-terminal and C-terminal parts of the B chain. In the RMD run a high mobility of Gly A1, Asn A21 and of the side chain of Phe B25 is noticed. One of the conformations adopted by des-(B26-B30)-insulin in solution is similar to that of molecule 1 (Chinese nomenclature) in the crystal structure of porcine insulin.     

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.     

Conformational sampling by NMR solution structures calculated with the program DIANA evaluated by comparison with long-time molecular dynamics calculations in explicit water

The NMR solution structure of bovine pancreatic trypsin inhibitor (BPTI) obtained by distance geometry calculations with the program DIANA is compared with groups of conformers generated by molecular dynamics (MD) simulations in explicit water at ambient temperature and pressure. The MD simulations started from a single conformer and were free or restrained either by the experimental NOE distance restraints or by time-averaged restraints; the groups of conformers were collected either in 10 ps intervals during 200 ps periods of simulation, or in 50 ps intervals during a 1 ns period of simulation. Overall, these comparisons show that the standard protein structure determination protocol with the program DIANA provides a picture of the protein structure that is in agreement with MD simulations using “realistic” potential functions over a nanosecond timescale. For well-constrained molecular regions there is a trend in the free MD simulation of duration 1 ns that the sampling of the conformation space is slightly increased relative to the DIANA calculations. In contrast, for surface-exposed side-chains that are less extensively constrained by the NMR data, the DIANA conformers tend to sample larger regions of conformational space than conformers selected from any of the MD trajectories. Additional insights into the behavior of surface side-chains come from comparison of the MD runs of 200 ps or 1 ns duration. In this time range the sampling of conformation space by the protein surface depends strongly on the length of the simulation, which indicates that significant side-chain transitions occur on the nanosecond timescale and that much longer simulations will be needed to obtain statistically significant data on side-chain dynamics.     

Atomic-level protein structure refinement using fragment-guided molecular dynamics conformation sampling

One of critical difficulties of molecular dynamics (MD)?simulations in protein structure refinement is that the?physics-based energy landscape lacks?a middle-range funnel to guide nonnative conformations toward near-native states. We propose to use the target model as a probe to identify fragmental analogs from PDB. The distance maps are then used to reshape the MD energy funnel. The protocol was tested on 181 benchmarking and 26 CASP targets. It was found that structure models of correct folds with TM-score >0.5 can be often pulled closer to native with higher GDT-HA score, but improvement for the models of incorrect folds (TM-score <0.5) are much less pronounced. These data indicate that template-based fragmental distance maps essentially reshaped the MD energy landscape from golf-course-like to funnel-like ones in the successfully refined targets with a radius of TM-score ～0.5. These results demonstrate a new avenue to improve high-resolution structures by combining knowledge-based template information with physics-based MD simulations.     

NMR three-dimensional solution structure of the serine protease inhibitor cyclotheonamide A

The nmr solution conformation of cyclotheonamide A (CtA) was determined in aqueous media. The data produced 15 distance and 10 torsional constraints which were used to generate conformations using restrained simulated annealing (SA) and distance geometry/simulated annealing (DG/SA) calculations. Two different calculation protocols were performed to ensure proper sampling of conformational space and even though the torsional restraints were input differently, both calculation methods yielded the same conformation of CtA. In the structure calculations, all solutions of the Karplus equation were sampled simultaneously using the restrained SA protocol and large ranges were used for the dihedral restraints in the DG/SA protocol because all solutions to the Karplus equation could not be sampled simultaneously. The solution conformation was also compared to the solid state x-ray conformations of CtA bound to thrombin and trypsin. The conformation of the residues important for active site binding (d -Phe, h-Arg, and Pro) are nearly identical in aqueous solution and solid state with largest differences at the a-Ala and v-Tyr residues. CtA appears to be preordered in structure and does not undergo a significant conformational change upon binding to the enzyme active site. © 1997 John Wiley & Sons, Inc.     

Restrained molecular dynamics simulations of HIV-1 protease: the first step in validating a new target for drug design

To test the anticorrelated relationship that was recently displayed in conventional molecular dynamics (MD) simulations, several different restrained MD simulations on a wild type and on the V82F/I84V drug-resistant mutant of HIV-1 protease were performed. This anticorrelated relationship refers to the observation that compression of the peripheral ear-to-cheek region of HIV protease (i.e., the elbow of the flap to the fulcrum and the cantilever) occurred as the active site flaps were opening, and, conversely, expansion of that ear-to-cheek region occurred as both flaps were closing. An additional examination of this anticorrelated relationship was necessary to determine whether it can be harnessed in a useful manner. Consequently, six different MD experiments were performed that incorporated pairwise distance restraints in that ear-to-cheek region (i.e., the distance between the alpha-carbons of Gly40 and Gln61 was restrained to either 7.7 or 10.5 A, in both monomers). Pushing the backbones of the ear and the cheek regions away from each other slightly did force the flaps that guard the active site to remain closed in both the wild type and the mutant systems-even though there were no ligands in the active sites. Thus, these restrained MD simulations provided evidence that the anticorrelated relationship can be exploited to affect the dynamic behavior of the flaps that guard the active site of HIV-1 protease. These simulations supported our hypothesis of the mechanism governing flap motion, and they are the first step towards validating that peripheral surface as a new target for drug design.     

Secondary structure inducing potential of beta-amino acids: torsion angle clustering facilitates comparison and analysis of the conformation during MD trajectories

While numerous examples of beta-peptides--exclusively composed of beta-amino acids--have been investigated during the past decade, there are only few reports on the conformational preference of a single beta-amino acid when incorporated into a cyclopeptide. The conformational bias of beta-amino acids on the secondary structure of cyclopeptides has been investigated by NMR spectroscopy in combination with distance geometry (DG) and molecular dynamics (MD) calculations using experimental constraints. The atomic coordinate RMSD criterion usually employed for clustering of conformations after DG and MD calculations does not necessarily group similar peptide conformations, as there is an insufficient correlation between atomic coordinates and torsion angles. To improve on this shortcoming and to eliminate any arbitrary decisions during this process, a torsion angle clustering procedure has been implemented. For the cyclic pentapeptides cyclo-(-Val-beta-Hala-Phe-Leu-Ile-) 1 and cyclo-(-Ser-Pro-Leu-beta-Hasn-Asp-) 3, the beta-amino acid is found in the central position of an extended gamma-turn (pseudo gamma-turn, Psigamma-turn), while the beta-Hpro residue in the cyclic hexapeptide cyclo-(-Ser-beta-Hpro-Leu-Asn-Ile-Asp-) 5 preferentially occupies position i+1 of a pseudo beta-turn (Psibeta-turn). These results further corroborate the hypothesis of beta-amino acids being reliable inducers of secondary structure in cyclic penta- and hexapeptides. They can be employed in the de novo design of biologically active cyclopeptides in pharmaceutical research, since the three-dimensional presentation of pharmacophoric groups in the side chains can be tailored by incorporation of beta-amino acids in strategic sequential positions.     

High resolution 1H NMR study of the solution structure of the S4 segment of the sodium channel protein

A peptide (S4) of the rat brain sodium channel has been synthesized, studied by high-resolution NMR and its secondary structure modelled by distance geometry and restrained molecular dynamics techniques.     

Structure determination of [Arg8]vasopressin methylenedithioether in dimethylsulfoxide using NMR.

The structure of [Arg8]vasopressin methylenedithioether ([AVP]CH2) has been determined in dimethylsulfoxide-d6. Two-dimensional DQF-COSY and NOESY spectra were measured and used to derive angle and distance constraints for restrained molecular dynamics (MD) calculations. In the MD trajectory, two types of beta-turn structure were found in the region from Tyr2 to Asn5, suggesting an equilibrium between type-I and type-II' beta-turn structures. When Halpha chemical shifts were used as an additional constraint, the type-I turn was favoured. To validate this result, an independent energy minimization procedure was used, using differences between calculated and observed chemical shifts. The two approaches gave essentially identical results. It is therefore concluded that the type-I turn predominates in solution. Analysis of calculated chemical shift contributions suggests that the beta-turn structure found in AVP is well preserved in [AVP]CH2, although the pressin ring size is expanded.     

Biomolecular structure refinement based on adaptive restraints using local-elevation simulation

Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, ³ J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values ϕ correspond to the same ³ J-coupling constant and high-energy barriers are separating those, restraining ³ J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to ³ J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental ³ J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom–atom distance upper bounds. Afterwards the torsional angles ϕ are kept restrained by the built-up local-elevation potential energies.     

Determination of protein structures from nuclear magnetic resonance data using a restrained molecular dynamics approach: the lac repressor DNA binding domain

A procedure is described to determine from NMR data the three-dimensional structure of biomolecules. This procedure combines model building with a restrained Molecular Dynamics algorithm, in which distance information from NOEs is incorporated in the form of pseudo potentials. The method has been applied to the N-terminal DNA-binding domain or "headpiece" (amino acids 1-51) of the lac repressor from E. coli, for which no crystal structure is available. The spatial structure of the headpiece is discussed in terms of known physical and biochemical data and of its DNA binding properties.     

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.     

The structure of ColE1 rop in solution

Summary The structure of the ColE1 repressor of primer (rop) protein in solution was determined from the proton nuclear magnetic resonance data by a combined use of distance geometry and restrained molecular dynamics calculations. A set of structures was determined with low internal energy and virtually no violations of the experimental distance restraints. Rop forms homodimers: Two helical hairpins are arranged as an antiparallel four helix bundle with a left-handed rope-like twist of the helix axes and with left-handed bundle topology. The very compact packing of the side chains in the helix interfaces of the rop coiled-coil structure may well account for its high stability. Overall, the solution structure is highly similar to the recently determined X-ray structure (Banner, D.W., Kokkinidis, M. and Tsernoglou, D. (1987)J. Mol. Biol.,196, 657–675), although there are minor differences in regions where packing forces appear to influence the crystal structure.Abbreviations rop repressor of primer - NMR nuclear magnetic resonance - NOE nuclear Overhauser enhancement - NOESY NOE spectroscopy - RAN Set Structures generated from random choice of the dihedrai angles - HEL Set Structures generated from random choice of the dihedral angles restricted to ranges allowed for helices - MD molecular dynamics - EM energy minimization - RMSD root-mean-square deviation of atomic positions     

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.     

Conformational analysis of cyclic peptides in solution

The strategy and tactics of conformational analysis of cyclic peptides in solution is demonstrated by the example of cyclo(-D-Pro-Phe-Thr-Phe-Trp-Phe-). Spin-locked experiments like rotating frame nuclear Overhauser enhancement spectroscopy (ROESY), ROTO, and TOCSY are successfully applied to assign all proton signals and to obtain distance information. A crude conformational model was built using the nmr data. This starting model was refined by restrained molecular dynamics (MD) calculations using ROE derived distances and fixed bond angles as determined from homo- and heteronuclear coupling constants. To mimic the solvent and to reduce artifacts in an in vacuo calculation the charges of the solvent-exposed NH protons were gradually reduced according to the temperature gradients. The thus obtained "conformation" (mean of a 40 ps MD trajectory) shows very close similarity to x-ray structures in an orthorhombic and in two monoclinic crystal modifications of the same compound. The main difference is the breaking of an intermolecular hydrogen bond of the threonine hydroxyl group on dissolution of the crystal and forming an intramolecular hydrogen bond in solution.