Generalized ordering parameter S2 for N-H peptide bonding as measure of the conformational flexibility of proteins: comparison of algorithms of S2 calculation from molecular dynamics simulation data

NMR spectroscopy in combination with molecular dynamics (MD) simulation technique is a powerful tool for investigation of biomolecule conformations. In the present study we compare the two algorithms of calculation of the generalized order parameter S2 for the peptide N-H bond from MD simulation data. The program based on this algorithm has been written and the effect of an adjustible parameter on results of calculation was studied. HIV-1 protease MD simulation was performed during 7.36 ns using GROMACS 3.1.4. software package. The calculated order parameter values are in good agreement with those obtained by other authors using NMR.     

Comparison of NMR and MD N–H bond order parameters: example of HIV-1 protease

It has been suggested that the cause of disagreements between molecular dynamics (MD) and NMR N–H bond order parameters is the fact that the NMR order parameter is determined for different amino acid residues at different time intervals, while the MD one is derived for all residues from the same MD trajectory of the same time interval. Therefore, it has been proposed for correct comparison with NMR data to calculate the MD order parameter for different amino acid residues separately for trajectory ranges close to NMR correlation time. The MD simulation of the human immunodeficiency virus type-1 protease (HIV-1 PR) with monoprotonated active centre was performed for verification of the proposition. It has been shown that the protease in aqueous solution adopts a set of conformations, which are intermediate between semiopen and closed ones. The calculated MD N–H bond order parameters are in agreement with literature NMR data in confidence interval limits.     

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.     

Hydrogen bonds in crystal structures of amino acids, peptides and related molecules

The results of a survey of 439 hydrogen bonds in 95 recently determined crystal structures of amino acids, peptides and related molecules suggest that the following generalizations hold true for linear (angle X-H---Y greater than 150 degrees) hydrogen bonds. (1) The charge on the acceptor group does not influence the length of a hydrogen bond. (2) For a given acceptor group, the hydrogen bond lengths increase in the order imidazolium N--H less than ammonium N-H less than guanidinium N-H; this order holds true for oxygen anion acceptor groups. Cl-ions and the uncharged oxygen of water molecules. (3) The uncharged imidazole N-H group forms shorter hydrogen than the amide N-H GROUP. (4) The carboxyl O-H groups form shorter hydrogen bonds than other hydroxyl groups. (5) The hydrogen bonds involving a halogen ion are longer than hydrogen bonds with other acceptors when corrected for their longer van der Walls radii. The observed differences between the lengths of hydrogen bonds formed by different donor and acceptor groups in amino acids and peptides, imply differences in the energetics of their formation.     

Natures of benzene-water and pyrrole-water interactions in the forms of σ and π types: theoretical studies from clusters to liquid mixture

A combined and sequential use of quantum mechanical (QM) calculations and classical molecular dynamics (MD) simulations was made to investigate the σ and π types of hydrogen bond (HB) in benzene-water and pyrrole-water as clusters and as their liquid mixture, respectively. This paper aims at analyzing similarities and differences of these HBs resulted from QM and MD on an equal footing. Based on the optimized geometry at ωb97xD/aug-cc-pVTZ level of theory, the nature and property of σ and π types of HBs are unveiled by means of atoms in molecules (AIM), natural bond orbital (NBO) and energy decomposition analysis (EDA). In light of the above findings, MD simulation with OPLS-AA and SPC model was applied to study the liquid mixture at different temperatures. The MD results further characterize the behavior and structural properties of σ and π types HBs, which are somewhat different but reasonable for the clusters by QM. Finally, we provide a reasonable explanation for the different solubility between benzene/water and pyrrole/water.

Rotational diffusion anisotropy of proteins from simultaneous analysis of 15N and 13Cα nuclear spin relaxation

Current methods of determining the rotational diffusion tensors of proteins in solution byNMR spectroscopy exclusively utilize relaxation rate constants for backbone amide 15N spins.However, the distributions of orientations of N-H bond vectors are not isotropic in manyproteins, and correlations between bond vector orientations reduce the accuracy and precisionof rotational diffusion tensors extracted from 15N spin relaxation data. The inclusion of both13C and 15N spin relaxation rate constants increases the robustness of the diffusiontensor analysis because the orientations of the C-H bond vectors differ from theorientations of the N-H bond vectors. Theoretical and experimental results for calbindin D9k,granulocyte colony stimulating factor, and ubiquitin, three proteins with different distributionsof N-H and C-H bond vectors, are used to illustrate the advantages of thesimultaneous utilization of 13C and 15N relaxation data.     

Correlation between changes in nuclear magnetic resonance order parameters and conformational entropy: molecular dynamics simulations of native and denatured staphylococcal nuclease

Recent work has suggested that changes in NMR order parameters may quantitatively reflect changes in the conformational entropy of a protein ensemble. The extent of the mathematical relationship between local entropy changes as seen by NMR order parameters and the full protein entropy change is a complex issue. As a step towards a fuller understanding of this problem, molecular dynamics calculations of both native and denatured staphylococcal nuclease were performed. The N-H bond vector motion, in both explicit and implicit solvent, was analyzed to estimate local and global entropy changes. The calculated N-H bond vector order parameters from simulation agreed on average with experimental values for both native and denatured structures. However, the inverted-U profile of order parameters versus residue number observed experimentally for denatured nuclease was only partially reproduced by simulation of compact denatured structures. Comparisons made across the full set of simulations revealed a correlation between the N-H order parameter-based conformational entropy change and the total quasiharmonic-based conformational entropy change between the native and denatured structures. The calculations showed that about 25% of the total entropy change was reflected by changes in simulated S2 values. This result suggests that NMR-derived order parameters may be used to provide a reasonable estimate of the total conformational entropy change on protein folding.     

A novel view of domain flexibility in E. coli adenylate kinase based on structural mode-coupling (15)N NMR relaxation.

Adenylate kinase from Escherichia coli (AKeco), consisting of a single 23.6 kDa polypeptide chain folded into domains CORE, AMPbd and LID, catalyzes the reaction AMP+ATP-->2ADP. In the ligand-free enzyme the domains AMPbd and LID execute large-amplitude movements controlling substrate binding and product release during catalysis. Domain flexibility is investigated herein with the slowly relaxing local structure (SRLS) model for (15)N relaxation. SRLS accounts rigorously for coupling between the global and local N-H motions through a local ordering potential exerted by the protein structure at the N-H bond. The latter reorients with respect to its protein surroundings, which reorient on the slower time scale associated with the global protein tumbling. AKeco diffuses globally with correlation time tau(m)=15.1 ns, while locally two different dynamic cases prevail. The domain CORE features ordering about the equilibrium N-H bond orientation with order parameters, S(2), of 0.8-0.9 and local motional correlation times, tau, mainly between 5-130 ps. This represents a conventional rigid protein structure with rapid small-amplitude N-H fluctuations. The domains AMPbd and LID feature small parallel (Z(M)) ordering of S(2)=0.2-0.5 which can be reinterpreted as high perpendicular (Y(M)) ordering. M denotes the local ordering/local diffusion frame. Local motion about Z(M) is given by tau( parallel) approximately 5 ps and local motion of the effective Z(M) axis about Y(M) by tau( perpendicular)=6-11 ns. Z(M) is tilted at approximately 20 degrees from the N-H bond. The orientation of the Y(M) axis may be considered parallel to the C(alpha)(i-1)-C(alpha)(i) axis. The tau( perpendicular) mode reflects collective nanosecond peptide-plane motions, interpretable as domain motion. A powerful new model of protein flexibility/domain motion has been established. Conformational exchange (R(ex)) processes accompany the tau( perpendicular) mode. The SRLS analysis is compared with the conventional model-free analysis.     

MD simulations reveal alternate conformations of the oxyanion hole in the Zika virus NS2B/NS3 protease

Recent crystallography studies have shown that the binding site oxyanion hole plays an important role in inhibitor binding, but can exist in two conformations (active/inactive). We have undertaken molecular dynamics (MD) calculations to better understand oxyanion hole dynamics and thermodynamics. We find that the Zika virus (ZIKV) NS2B/NS3 protease maintains a stable closed conformation over multiple 100-ns conventional MD simulations in both the presence and absence of inhibitors. The S1, S2, and S3 pockets are stable as well. However, in two of eight simulations, the A132-G133 peptide bond in the binding pocket of S1' spontaneously flips to form a 3₁₀-helix that corresponds to the inactive conformation of the oxyanion hole, and then maintains this conformation until the end of the 100-ns conventional MD simulations without inversion of the flip. This conformational change affects the S1' pocket in ZIKV NS2B/NS3 protease active site, which is important for small molecule binding. The simulation results provide evidence at the atomic level that the inactive conformation of the oxyanion hole is more favored energetically when no specific interactions are formed between substrate/inhibitor and oxyanion hole residues. Interestingly, however, transition between the active and inactive conformation of the oxyanion hole can be observed by boosting the valley potential in accelerated MD simulations. This supports a proposed induced-fit mechanism of ZIKV NS2B/NS3 protease from computational methods and provides useful direction to enhance inhibitor binding predictions in structure-based drug design.     

Simulation of interactions between nucleic acid bases by refined atom-atom potential functions

Energy of interaction between nitrogen bases of nucleic acid has been calculated as a function of parameters determining the mutual position of two bases. Refined atom-atom potential functions are suggested. These functions contain terms proportional to the first (electrostatics), sixth (or tenth for the atoms forming a hydrogen bond) and twelfth (repulsion of all atoms) powers of interatomic distance. Calculations have shown that there are two groups of minima of the base interaction energy. The minima of the first group correspond to coplanar arrangement of the base pairs and hydrogen bond formation. The minima of the second group correspond to the position of bases one above the other in almost parallel planes. There are 28 energy minima corresponding to the formation of coplanar pairs with two (three for the G:C pair) almost linear N-H . . . O and (or) N-H . . . N hydrogen bonds. The position of nitrogen bases paired by two such H-bonds in any crystal of nucleic acid component in polynucleotide complexes and in tRNA is close to the position in one of these minima. Besides, for each pair there are energy minima corresponding to the formation of a single N-H . . . O or N-H . . . N and one C-H . . . O or C-H . . . N hydrogen bond. The form of potential surface in the vicinity of minima has been characterized. The results of calculations agree with the experimental data and with more rigorous calculations based on quantum-mechanical approach.     

Interaction of the peptide bond with solvent water: a vapor phase analysis

A dynamic technique, using radioactivity as a means of detection, makes it possible to measure the partial pressures of highly polar compounds in dilute aqueous solution. The results can be expressed in terms of the dimensionless distribution coefficient for transfer of a compound from dilute aqueous solution to the vapor phase. For acetic acid this coefficient is 1.1 X 10(-5), for acetamide 7.6 X 10(-8), for N-methylacetamide 4.1 X 10(-8), and for N,N-dimethylacetamide 5.4 X 10(-7). Thus acetamide is much more strongly solvated than the uncharged acetic acid molecule. The results suggest: (1) that the peptide bond represents an extreme among uncharged functional groups in the degree to which it is stabilized by solvent water; (2) that the very great hydrophilic character of the peptide bond may be associated mainly with hydrogen bonding of the solvent to the carbonyl oxygen atom (rather than the N-H group); and (3) that the observed equilibria of biosynthesis and hydrolysis of peptide bonds in aqueous solution are largely determined by differences between reactants and products in their free energies of solvation. It is anticipated that where "bound" water is found in proteins, it will often be found to be associated with peptide bonds, and will tend to be associated with the C-O group rather than with the N-H group.     

Simulation of Interactions between Nucleic Acid Bases by Refined Atom-Atom Potential Functions

Abstract

Energy of interaction between nitrogen bases of nucleic acids has been calculated as a function of parameters determining the mutual position of two bases. Refined atom-atom potential functions are suggested. These functions contain terms proportional to the first (electrostatics), sixth (or tenth for the atoms forming a hydrogen bond) and twelfth (repulsion of all atoms) powers of interatomic distance. Calculations have shown that there are two groups of minima of the base interaction energy. The minima of the first group correspond to coplanar arrangement of the base pairs and hydrogen bond formation. The minima of the second group correspond to the position of bases one above the other in almost parallel planes. There are 28 energy minima corresponding to the formation of coplanar pairs with two (three for the G:C pair) almost linear N-H … O and (or) N-H … N hydrogen bonds. The position of nitrogen bases paired by two such H-bonds in any crystal of nucleic acid component, in polynucleotide complexes and in tRNA is close to the position in one of these minima. Besides, for each pair there are energy minima corresponding to the formation of a single N-H … O or N-H … N and one C-H … O or C-H … N hydrogen bond. The form of potential surface in the vicinity of minima has been characterized. The results of calculations agree with the experimental data and with more rigorous calculations based on quantum- mechanical approach.     

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.     

Accuracy and precision of NMR relaxation experiments and MD simulations for characterizing protein dynamics

Model-free parameters obtained from nuclear magnetic resonance (NMR) relaxation experiments and molecular dynamics (MD) simulations commonly are used to describe the intramolecular dynamical properties of proteins. To assess the relative accuracy and precision of experimental and simulated model-free parameters, three independent data sets derived from backbone ¹⁵N NMR relaxation experiments and two independent data sets derived from MD simulations of Escherichia coli ribonuclease HI are compared. The widths of the distributions of the differences between the order parameters for pairs of NMR data sets are congruent with the uncertainties derived from statistical analyses of individual data sets; thus, current protocols for analyzing NMR data encapsulate random uncertainties appropriately. Large differences in order parameters for certain residues are attributed to systematic differences between samples for intralaboratory comparisons and unknown, possibly magnetic field-dependent, experimental effects for interlaboratory comparisons. The widths of distributions of the differences between the order parameters for two NMR sets are similar to widths of distributions for an NMR and an MD set or for two MD sets. The linear correlations between the order parameters for an MD set and an NMR set are within the range of correlations observed between pairs of NMR sets. These comparisons suggest that the NMR and MD generalized order parameters for the backbone amide N—H bond vectors are of comparable accuracy for residues exhibiting motions on a fast time scale (<100 ps). Large discrepancies between NMR and MD order parameters for certain residues are attributed to the occurrence of “rare” motional events over the simulation trajectories, the disruption of an element of secondary structure in one of the simulations, and lack of consensus among the experimental data sets. Consequently, (easily detectable) severe distortions of local protein structure and infrequent motional events in MD simulations appear to be the most serious artifacts affecting the accuracy and precision, respectively, of MD order parameters relative to NMR values. In addition, MD order parameters for motions on a fast (<100 ps) timescale are more precisely determined than their NMR counterparts, thereby permitting more detailed dynamic characterization of biologically important residues by MD simulation than is sometimes possible by experimental methods. Proteins 28:481–493, 1997. © 1997 Wiley-Liss, Inc.     

Structure and dynamics of Mycobacterium tuberculosis truncated hemoglobin N: insights from NMR spectroscopy and molecular dynamics simulations

The potent nitric oxide dioxygenase (NOD) activity (trHbN-Fe2?-O? + (?)NO → trHbN-Fe3?-OH? + NO??) of Mycobacterium tuberculosis truncated hemoglobin N (trHbN) protects aerobic respiration from inhibition by (?)NO. The high activity of trHbN has been attributed in part to the presence of numerous short-lived hydrophobic cavities that allow partition and diffusion of the gaseous substrates (?)NO and O? to the active site. We investigated the relation between these cavities and the dynamics of the protein using solution NMR spectroscopy and molecular dynamics (MD). Results from both approaches indicate that the protein is mainly rigid with very limited motions of the backbone N-H bond vectors on the picoseconds-nanoseconds time scale, indicating that substrate diffusion and partition within trHbN may be controlled by side-chains movements. Model-free analysis also revealed the presence of slow motions (microseconds-milliseconds), not observed in MD simulations, for many residues located in helices B and G including the distal heme pocket Tyr33(B10). All currently known crystal structures and molecular dynamics data of truncated hemoglobins with the so-called pre-A N-terminal extension suggest a stable α-helical conformation that extends in solution. Moreover, a recent study attributed a crucial role to the pre-A helix for NOD activity. However, solution NMR data clearly show that in near-physiological conditions these residues do not adopt an α-helical conformation and are significantly disordered and that the helical conformation seen in crystal structures is likely induced by crystal contacts. Although this lack of order for the pre-A does not disagree with an important functional role for these residues, our data show that one should not assume an helical conformation for these residues in any functional interpretation. Moreover, future molecular dynamics simulations should not use an initial α-helical conformation for these residues in order to avoid a bias based on an erroneous initial structure for the N-termini residues. This work constitutes the first study of a truncated hemoglobin dynamics performed by solution heteronuclear relaxation NMR spectroscopy.     

Non-aromatic stabilised form of 3,4-difluoropyrrole at triosmium clusters: N-H and C-H versus C-F activation

Reaction of 3,4-difluoropyrrole with the labile triosmium cluster [Os₃(CO)₁₀(CH₃CN)₂] affords products in which C-H, N-H and C-F bonds are cleaved under mild conditions. C-H and N-H bonds are cleaved to give [Os₃H(NCCFCFCH₂)(CO)₁₀] (1) a non-aromatic stabilised form of 3,4-difluoropyrrole. Thermolysis of 1 affords in moderate yields the compounds [Os₃H₂(CCCFCHNH)(CO)₉] (2) and [Os₃H₂(NCHCFCFC)(CO)₉] (3). For compound 3, C-H and N-H bonds are cleaved with concomitant migration of H atoms to the metal framework. In contrast, for compound 2 activation of C-H and C-F bonds leads to coordination of the ligand through the carbon atoms, acting as a four-electron donating species.     

N-H...O, O-H...O, and C-H...O hydrogen bonds in protein-ligand complexes: strong and weak interactions in molecular recognition

The characteristics of N-H...O, O-H...O, and C-H...O hydrogen bonds are examined in a group of 28 high-resolution crystal structures of protein-ligand complexes from the Protein Data Bank and compared with interactions found in small-molecule crystal structures from the Cambridge Structural Database. It is found that both strong and weak hydrogen bonds are involved in ligand binding. Because of the prevalence of multifurcation, the restrictive geometrical criteria set up for hydrogen bonds in small-molecule crystal structures may need to be relaxed in macromolecular structures. For example, there are definite deviations from linearity for the hydrogen bonds in protein-ligand complexes. The formation of C-H...O hydrogen bonds is influenced by the activation of the C(alpha)-H atoms and by the flexibility of the side-chain atoms. In contrast to small-molecule structures, anticooperative geometries are common in the macromolecular structures studied here, and there is a gradual lengthening as the extent of furcation increases. C-H...O bonds formed by Gly, Phe, and Tyr residues are noteworthy. The numbers of hydrogen bond donors and acceptors agree with Lipinski's "rule of five" that predicts drug-like properties. Hydrogen bonds formed by water are also seen to be relevant in ligand binding. Ligand C-H...O(w) interactions are abundant when compared to N-H...O(w) and O-H...O(w). This suggests that ligands prefer to use their stronger hydrogen bond capabilities for use with the protein residues, leaving the weaker interactions to bind with water. In summary, the interplay between strong and weak interactions in ligand binding possibly leads to a satisfactory enthalpy-entropy balance. The implications of these results to crystallographic refinement and molecular dynamics software are discussed.