Molecular Structure Refinement Based on Residual Dipolar Couplings: A Comparison of the Molecular Rotational-Sampling Method with the Alignment-Tensor Approach.

In NMR experiments, residual dipolar couplings (RDCs) in a molecule can be measured by averaging the dipolar couplings (DCs) over the rotational motion of a molecule in an environment that induces a slight anisotropic orientation distribution of the molecule. Since the shape of the anisotropic distribution cannot be measured, it is standard practice to use a particular orientation distribution of the molecule with respect to the magnetic field, in the form of a so-called alignment tensor (AT), to calculate RDC-values for the molecule. Since the same alignment tensor is commonly used to calculate the different RDCs of a molecule, this approach rests on the assumption that the rotational motion of the molecule is decoupled from its internal motions and that the molecule is rigid. The validity of these two assumptions is investigated for a small, simple molecule, using a relatively rigid atomic interaction function or force field and a more flexible one. By simulating the molecule using an orientation-biasing force an anisotropic rotational distribution can be generated, for which RDCs can be obtained. Using these RDCs as target RDCs when applying one of the two approaches of structure refinement based on RDCs, it can be investigated how well the target RDCs are approximated in the RDC restraining and whether the corresponding nonuniform orientation distribution is reproduced. For the relatively rigid version of the molecule, the AT approach reproduces the target RDC-values, although the nonuniform orientation distribution of the angle θab,H between the vector r⃗ab connecting two atoms a and b in the molecule and the vector representing the direction of the magnetic field H⃗ as generated in the orientation-biasing simulation cannot be reproduced in the AT RDC-restraining simulation. For the relatively flexible version of the molecule, the AT approach fails to reproduce both the target RDC values and the nonuniform orientation distribution. For biomolecules with flexible parts, the application of the AT approach is thus not recommended. Instead, a method based on sampling of the rotational and internal degrees of freedom of the molecule should be applied in molecular structure determination or refinement based on measured RDCs.

Molecular structure refinement based on residual dipolar couplings using magnetic-field rotational sampling.

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using magnetic-field rotational sampling of the rotational degrees of freedom of a molecule in conjunction with molecule-internal configurational sampling. By applying rotational sampling, as is occurring in the experiment, leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and, therefore, the assumptions that the overall rotation of the molecule is decoupled from its internal motions and that the molecule is rigid. Two simple molecules, a relatively rigid and a very flexible cyclo-octane molecule with eight aliphatic side chains containing 24 united atoms, serve as so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility, force-field dominance, and the number of RDC restraints available on the outcome of structure refinement based on RDCs. Magnetic-field rotational sampling is basically equivalent but more efficient than explicitly sampling the rotational degrees of freedom of the molecule. In addition, the performance of the method is less dependent on the number NRDC of measured RDC-values available. The restraining forces bias the overall orientation distribution of the molecule correctly. This study suggests that the information content of RDCs with respect to molecular structure is limited.

Molecular dynamics simulation or structure refinement of proteins: are solvent molecules required? A case study using hen lysozyme.

In protein simulation or structure refinement based on values of observable quantities measured in (aqueous) solution, solvent (water) molecules may be explicitly treated, omitted, or represented by a potential of mean-solvation-force term, depending on protein coordinates only, in the force field used. These three approaches are compared for hen egg white lysozyme (HEWL). This 129-residue non-spherical protein contains a variety of secondary-structure elements, and ample experimental data are available: 1630 atom-atom Nuclear Overhauser Enhancement (NOE) upper distance bounds, 213 3 J-couplings and 200 S2 order parameters. These data are used to compare the performance of the three approaches. It is found that a molecular dynamics (MD) simulation in explicit water approximates the experimental data much better than stochastic dynamics (SD) simulation in vacuo without or with a solvent-accessible-surface-area (SASA) implicit-solvation term added to the force field. This is due to the missing energetic and entropic contributions and hydrogen-bonding capacities of the water molecules and the missing dielectric screening effect of this high-permittivity solvent. Omission of explicit water molecules leads to compaction of the protein, an increased internal strain, distortion of exposed loop and turn regions and excessive intra-protein hydrogen bonding. As a consequence, the conformation and dynamics of groups on the surface of the protein, which may play a key role in protein-protein interactions or ligand or substrate binding, may be incorrectly modelled. It is thus recommended to include water molecules explicitly in structure refinement of proteins in aqueous solution based on nuclear magnetic resonance (NMR) or other experimentally measured data.

Backbone N-Amination Promotes the Folding of ß-Hairpin Peptides via a Network of Hydrogen Bonds.

Molecular dynamics (MD) simulations have been used to characterize the effects of backbone N-amination of residues in a model ß-hairpin peptide. This modification is of considerable interest as N-aminated peptides have been shown to inhibit amyloid-type aggregation. Six derivatives of the ß-hairpin peptide, which contain one, two, or four N-aminated residues, have been studied. For each peptide 100 ns MD simulations starting from the folded ß-hairpin structure were performed. The effects of the N-amination prove to be very sequence dependent. N-Amination of a residue involved in interstrand hydrogen bonding (Val3) leads to unfolding of the ß-hairpin, whereas N-amination of a residue toward the C-terminus (Leu11) gives fraying at the termini of the peptide. In the other derivatives the peptide remains folded, with increasing levels of N-amination reducing the right-handed twist of the ß-hairpin and favoring population of a type II' rather than a type I' ß-turn. MD simulations (100 ns) have also been run for each peptide starting from an unfolded extended chain. Here, the peptide with four N-aminated residues shows the most folding into the ß-hairpin (34%). Analysis of the simulations shows that N-amination favors the population of ß (φ, ψ) conformations by the preceding residue due to, at least in part, a network of weak NH2(i)-CO(i) and NH2(i)-CO(i-2) hydrogen bonds. It also leads to a reduction of misfolding because of changes in the hydrogen-bonding potential. Both of these features help funnel the peptide to the folded ß-hairpin structure. The conformational insights provided through this work give a firm foundation for the design of N-aminated peptide inhibitors for modulating protein-protein interactions and aggregation.

On the use of 3J-coupling NMR data to derive structural information on proteins.

Values of 3J-couplings as obtained from NMR experiments on proteins cannot easily be used to determine protein structure due to the difficulty of accounting for the high sensitivity of intermediate 3J-coupling values (4-8 Hz) to the averaging period that must cover the conformational variability of the torsional angle related to the 3J-coupling, and due to the difficulty of handling the multiple-valued character of the inverse Karplus relation between torsional angle and 3J-coupling. Both problems can be solved by using 3J-coupling time-averaging local-elevation restraining MD simulation. Application to the protein hen egg white lysozyme using 213 backbone and side-chain 3J-coupling restraints shows that a conformational ensemble compatible with the experimental data can be obtained using this technique, and that accounting for averaging and the ability of the algorithm to escape from local minima for the torsional angle induced by the Karplus relation, are essential for a comprehensive use of 3J-coupling data in protein structure determination.

On the Use of Side-Chain NMR Relaxation Data to Derive Structural and Dynamical Information on Proteins: A Case Study Using Hen Lysozyme.

Values of S2CH and S2NH order parameters derived from NMR relaxation measurements on proteins cannot be used straightforwardly to determine protein structure because they cannot be related to a single protein structure, but are defined in terms of an average over a conformational ensemble. Molecular dynamics simulation can generate a conformational ensemble and thus can be used to restrain S2CH and S2NH order parameters towards experimentally derived target values S2CH (exp) and S2NH (exp). Application of S2CH and S2NH order-parameter restraining MD simulation to bond vectors in 63 side chains of the protein hen egg white lysozyme using 51 S2CH (exp) target values and 28 S2NH (exp) target values shows that a conformational ensemble compatible with the experimentally derived data can be obtained by using this technique. It is observed that S2CH order-parameter restraining of C-H bonds in methyl groups is less reliable than S2NH order-parameter restraining because of the possibly less valid assumptions and approximations used to derive experimental S2CH (exp) values from NMR relaxation measurements and the necessity to adopt the assumption of uniform rotational motion of methyl C-H bonds around their symmetry axis and of the independence of these motions from each other. The restrained simulations demonstrate that side chains on the protein surface are highly dynamic. Any hydrogen bonds they form and that appear in any of four different crystal structures, are fluctuating with short lifetimes in solution.

An NMR and MD study of complexes of bacteriophage lambda lysozyme with tetra- and hexa-N-acetylchitohexaose.

The X-ray structure of lysozyme from bacteriophage lambda (λ lysozyme) in complex with the inhibitor hexa-N-acetylchitohexaose (NAG6) (PDB: 3D3D) has been reported previously showing sugar units from two molecules of NAG6 bound in the active site. One NAG6 is bound with four sugar units in the ABCD sites and the other with two sugar units in the E'F' sites potentially representing the cleavage reaction products; each NAG6 cross links two neighboring λ lysozyme molecules. Here we use NMR and MD simulations to study the interaction of λ lysozyme with the inhibitors NAG4 and NAG6 in solution. This allows us to study the interactions within the complex prior to cleavage of the polysaccharide. 1 HN and 15 N chemical shifts of λ lysozyme resonances were followed during NAG4/NAG6 titrations. The chemical shift changes were similar in the two titrations, consistent with sugars binding to the cleft between the upper and lower domains; the NMR data show no evidence for simultaneous binding of a NAG6 to two λ lysozyme molecules. Six 150 ns MD simulations of λ lysozyme in complex with NAG4 or NAG6 were performed starting from different conformations. The simulations with both NAG4 and NAG6 show stable binding of sugars across the D/E active site providing low energy models for the enzyme-inhibitor complexes. The MD simulations identify different binding subsites for the 5th and 6th sugars consistent with the NMR data. The structural information gained from the NMR experiments and MD simulations have been used to model the enzyme-peptidoglycan complex.

Structure of SPH (self-incompatibility protein homologue) proteins: a widespread family of small, highly stable, secreted proteins.

SPH (self-incompatibility protein homologue) proteins are a large family of small, disulfide-bonded, secreted proteins, initially found in the self-incompatibility response in the field poppy (Papaver rhoeas), but now known to be widely distributed in plants, many containing multiple members of this protein family. Using the Origami strain of Escherichia coli, we expressed one member of this family, SPH15 from Arabidopsis thaliana, as a folded thioredoxin fusion protein and purified it from the cytosol. The fusion protein was cleaved and characterised by analytical ultracentrifugation, circular dichroism and nuclear magnetic resonance (NMR) spectroscopy. This showed that SPH15 is monomeric and temperature stable, with a ß-sandwich structure. The four strands in each sheet have the same topology as the unrelated proteins: human transthyretin, bacterial TssJ and pneumolysin, with no discernible sequence similarity. The NMR-derived structure was compared with a de novo model, made using a new deep learning algorithm based on co-evolution/correlated mutations, DeepCDPred, validating the method. The DeepCDPred de novo method and homology modelling to SPH15 were then both used to derive models of the 3D structure of the three known PrsS proteins from P. rhoeas, which have only 15-18% sequence homology to SPH15. The DeepCDPred method gave models with lower discreet optimised protein energy scores than the homology models. Three loops at one end of the poppy structures are postulated to interact with their respective pollen receptors to instigate programmed cell death in pollen tubes.

Structural Aspects of the O-glycosylation Linkage in Glycopeptides via MD Simulations and Comparison with NMR Experiments.

A powerful conformational searching and enhanced sampling simulation method, and unbiased molecular dynamics simulations have been used along with NMR spectroscopic observables to provide a detailed structural view of O-glycosylation. For four model systems, the force-field parameters can accurately predict experimental NMR observables (J couplings and NOE's). This enables us to derive conclusions based on the generated ensembles, in which O-glycosylation affects the peptide backbone conformation by forcing it towards to an extended conformation. An exception is described for ß-GalNAc-Thr where the α content is increased and stabilized via hydrogen bonding between the sugar and the peptide backbone, which was not observed in the rest of the studied systems. These observations might offer an explanation for the evolutionary preference of α-linked GalNAc glycosylation instead of a ß link.

Validation of Molecular Simulation: An Overview of Issues.

Computer simulation of molecular systems enables structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic, or supra-molecular level. To interpret results of such simulations appropriately, the quality of the calculated properties must be evaluated. This depends on the way the simulations are performed and on the way they are validated by comparison to values Qexp of experimentally observable quantities Q. One must consider 1) the accuracy of Qexp , 2) the accuracy of the function Q(rN ) used to calculate a Q-value based on a molecular configuration rN of N particles, 3) the sensitivity of the function Q(rN ) to the configuration rN , 4) the relative time scales of the simulation and experiment, 5) the degree to which the calculated and experimental properties are equivalent, and 6) the degree to which the system simulated matches the experimental conditions. Experimental data is limited in scope and generally corresponds to averages over both time and space. A critical analysis of the various factors influencing the apparent degree of (dis)agreement between simulations and experiment is presented and illustrated using examples from the literature. What can be done to enhance the validation of molecular simulation is also discussed.

Interpretation of Seemingly Contradictory Data: Low NMR S2 Order Parameters Observed in Helices and High NMR S2 Order Parameters in Disordered Loops of the Protein hGH at Low pH.

At low pH, human growth hormone (hGH) adopts a partially folded state, in which the native helices are maintained, but the long loop regions and side-chain packing become disordered. Some of the S2 order parameters for backbone N-H vectors derived from NMR relaxation measurements on hGH at low pH initially seem contradictory. Three isolated residues (15, 20, and 171) in helices A and D exhibit low order parameter values (<0.5) indicating flexibility, whereas residue 143 in the centre of a long flexible loop region has a high order parameter (0.82). Using S2 order parameter restraining MD simulations, this paradox has been resolved. Low S2 values in helices are due to the presence of a mixture of 310 -helical and α-helical hydrogen bonds. High S2 values in relatively disordered parts of a protein may be due to fluctuating networks of hydrogen bonds between the backbone and the side chains, which restrict the motion of N-H bond vectors.

On the use of time-averaging restraints when deriving biomolecular structure from ³J -coupling values obtained from NMR experiments.

Deriving molecular structure from [Formula: see text]-couplings obtained from NMR experiments is a challenge due to (1) the uncertainty in the Karplus relation [Formula: see text] connecting a [Formula: see text]-coupling value to a torsional angle [Formula: see text], (2) the need to account for the averaging inherent to the measurement of [Formula: see text]-couplings, and (3) the sampling road blocks that may emerge due to the multiple-valuedness of the inverse function [Formula: see text] of the function [Formula: see text]. Ways to properly handle these issues in structure refinement of biomolecules are discussed and illustrated using the protein hen egg white lysozyme as example.

A molecular dynamics simulation investigation of the relative stability of the cyclic peptide octreotide and its deprotonated and its (CF3)-Trp substituted analogs in different solvents.

The cyclic octa-peptide octreotide and its derivatives are used as diagnostics and therapeutics in relation to particular types of cancers. This led to investigations of their conformational properties using spectroscopic, NMR and CD, methods. A CF3-substituted derivative, that was designed to stabilize the dominant octreotide conformer responsible for receptor binding, turned out to have a lower affinity. The obtained spectroscopic data were interpreted as to show an increased flexibility of the CF3 derivative compared to the unsubstituted octreotide, which could then explain the lower affinity. In this article, we use MD simulation without and with time-averaged NOE distance and time-averaged local-elevation 3J-coupling restraining representing experimental NMR data to determine the conformational properties of the different peptides in the different solvents for which experimental data are available, that are compatible with the NOE atom-atom distance bounds and the 3JHNHα-couplings as derived from the NMR measurements. The conformational ensembles show that the CF3 substitution in combination with the change of solvent from water to methanol leads to a decrease in flexibility and a shift in the populations of the dominant conformers that are compatible with the experimental data.

Deriving Structural Information from Experimentally Measured Data on Biomolecules.

During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Qexp of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Qexp , 2) inaccuracies in the function Q(r→) used to relate the quantity Q to structure r→ , 3) how to account for the averaging inherent in the measurement of Qexp , 4) how to handle the possible multiple-valuedness of the inverse r→(Q) of the function Q(r→) , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X-ray and neutron diffraction, small-angle and wide-angle X-ray scattering, free-electron laser imaging, cryo-electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion-mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non-experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.

Comparison of the backbone dynamics of wild-type Hydrogenobacter thermophilus cytochrome c(552) and its b-type variant.

Cytochrome c552 from the thermophilic bacterium Hydrogenobacter thermophilus is a typical c-type cytochrome which binds heme covalently via two thioether bonds between the two heme vinyl groups and two cysteine thiol groups in a CXXCH sequence motif. This protein was converted to a b-type cytochrome by substitution of the two cysteine residues by alanines (Tomlinson and Ferguson in Proc Natl Acad Sci USA 97:5156-5160, 2000a). To probe the significance of the covalent attachment of the heme in the c-type protein, (15)N relaxation and hydrogen exchange studies have been performed for the wild-type and b-type proteins. The two variants share very similar backbone dynamic properties, both proteins showing high (15)N order parameters in the four main helices, with reduced values in an exposed loop region (residues 18-21), and at the C-terminal residue Lys80. Some subtle changes in chemical shift and hydrogen exchange protection are seen between the wild-type and b-type variant proteins, not only for residues at and neighbouring the mutation sites, but also for some residues in the heme binding pocket. Overall, the results suggest that the main role of the covalent linkages between the heme group and the protein chain must be to increase the stability of the protein.

Characterization of the flexible lip regions in bacteriophage lambda lysozyme using MD simulations.

The upper and lower lip regions in lysozyme from bacteriophage lambda (λ-lysozyme) are flexible in solution and exhibit two different conformations in crystal structures of the protein. MD simulations have been used to characterize the structure and dynamics of these lip regions, which surround the active site. Ten different simulations have been run including those with restraining to experimental NOE distance and (1)H-(15)N order parameter data. The simulations show that the lower lip region, although undergoing considerable backbone fluctuations, contains two persistent ß-strands. In the upper lip region, a wide range of conformations are populated and it is not clear from the available data whether some helical secondary structure is present. The work provides a clear example of the advantages of combining MD simulations with experimental data to obtain a structural interpretation of the latter. In this case, time-averaged order parameter restraining has played an essential role in enabling convergence between two different starting structures and identifying the extent to which flexible regions in solution can contain persistent secondary structure.

Molecular dynamics simulations of barley and maize lipid transfer proteins show different ligand binding preferences in agreement with experimental data.

Experimental studies of barley and maize lipid transfer proteins (LTPs) show that the two proteins bind the ligand palmitate in opposite orientations in their internal cavities. Moreover, maize LTP is reported to bind the ligand caprate in the internal cavity in a mixture of two orientations with approximately equal occupancy. Six 30 ns molecular dynamics (MD) simulations of maize and barley LTP with ligands bound in two orientations (modes M and B) have been used to understand the different ligand binding preferences. The simulations show that both maize and barley LTP could bind palmitate in the orientation observed experimentally for maize LTP (mode M), with the predominant interaction being a salt bridge between the ligand carboxylate headgroup and a conserved arginine side chain. However, the simulation of barley LTP with palmitate in the mode B orientation shows the most favorable protein-ligand interaction energy. In contrast, the simulations of maize LTP with palmitate and with caprate in the mode B orientation show no persistent ligand binding, the ligands leaving the cavity during the simulations. Sequence differences between maize and barley LTP in the AB loop region, in residues at the base of the hydrophobic cavity, and in the helix A region are identified as contributing to the different behavior. The simulations reproduce well the experimentally observed binding preferences for palmitate and suggest that the experimental data for maize LTP with caprate reflect ligand mobility in binding mode M rather than the population of binding modes M and B.

Structure of hen egg-white lysozyme solvated in TFE/water: a molecular dynamics simulation study based on NMR data.

Various experimental studies of hen egg white lysozyme (HEWL) in water and TFE/water clearly indicate structural differences between the native state and TFE state of HEWL, e.g. the helical content of the protein in the TFE state is much higher than in the native state. However, the available detailed NMR studies were not sufficient to determine fully a structure of HEWL in the TFE state. Different molecular dynamics (MD) simulations, i.e. at room temperature, at increased temperature and using proton-proton distance restraints derived from NMR NOE data, have been used to generate configurational ensembles corresponding to the TFE state of HEWL. The configurational ensemble obtained at room temperature using atom-atom distance restraints measured for HEWL in TFE/water solution satisfies the experimental data and has the lowest protein energy. In this ensemble residues 50-58, which are part of the ß-sheet in native HEWL, adopt fluctuating α-helical secondary structure.

The dynamics of lysozyme from bacteriophage lambda in solution probed by NMR and MD simulations.

(15) N NMR relaxation studies, analyses of NMR data to include chemical shifts, residual dipolar couplings (RDC), NOEs and H(N) -H(α) coupling constants, and molecular dynamics (MD) simulations have been used to characterise the behaviour of lysozyme from bacteriophage lambda (λ lysozyme) in solution. The lower and upper lip regions in λ lysozyme (residues 51-60 and 128-141, respectively) show reduced (1) H-(15) N order parameters indicating mobility on a picosecond timescale. In addition, residues in the lower and upper lips also show exchange contributions to T2 indicative of slower timescale motions. The chemical shift, RDC, coupling constant and NOE data for λ lysozyme indicate that two fluctuating ß-strands (ß3 and ß4) are populated in the lower lip region while the N terminus of helix α6 (residues 136-139) forms dynamic helical turns in the upper lip region. This behaviour is confirmed by MD simulations that show hydrogen bonds, indicative of the ß-sheet and helical secondary structure in the lip regions, with populations of 40-60 %. Thus in solution λ lysozyme adopts a conformational ensemble that will contain both the open and closed forms observed in the crystal structures of the protein.

Characterization of an alternative low energy fold for bovine α-lactalbumin formed by disulfide bond shuffling.

Bovine α-lactalbumin (αLA) forms a misfolded disulfide bond shuffled isomer, X-αLA. This X-αLA isomer contains two native disulfide bridges (Cys 6-Cys 120 and Cys 28-Cys 111) and two non-native disulfide bridges (Cys 61-Cys 73 and Cys 77-Cys 91). MD simulations have been used to characterize the X-αLA isomer and its formation via disulfide bond shuffling and to compare it with the native fold of αLA. In the simulations of the X-αLA isomer the structure of the α-domain of native αLA is largely retained in agreement with experimental data. However, there are significant rearrangements in the ß-domain, including the loss of the native ß-sheet and calcium binding site. Interestingly, the energies of X-αLA and native αLA in simulations in the absence of calcium are closely similar. Thus, the X-αLA isomer represents a different low energy fold for the protein. Calcium binding to native αLA is shown to help preserve the structure of the ß-domain of the protein limiting possibilities for disulfide bond shuffling. Hence, binding calcium plays an important role in both maintaining the native structure of αLA and providing a mechanism for distinguishing between folded and misfolded species.