Conformational averaging in structural biology: issues, challenges and computational solutions

Structural, Spectroscopic, and Computational Insights from Canavanine-Bound and Two Catalytically Compromised Variants of the Ethylene-Forming Enzyme

The ethylene-forming enzyme (EFE) is an Fe(II), 2-oxoglutarate (2OG), and l-arginine (l-Arg)-dependent oxygenase that either forms ethylene and three CO2/bicarbonate from 2OG or couples the decarboxylation of 2OG to C5 hydroxylation of l-Arg. l-Arg binds with C5 toward the metal center, causing 2OG to change from monodentate to chelate metal interaction and OD1 to OD2 switch of D191 metal coordination. We applied anaerobic UV-visible spectroscopy, X-ray crystallography, and computational approaches to three EFE systems with high-resolution structures. The ineffective l-Arg analogue l-canavanine binds to the EFE with O5 pointing away from the metal center while promoting chelate formation by 2OG but fails to switch the D191 metal coordination from OD1 to OD2. Substituting alanine for R171 that interacts with 2OG and l-Arg inactivates the protein, prevents metal chelation by 2OG, and weakens l-Arg binding. The R171A EFE had electron density at the 2OG binding site that was identified by mass spectrometry as benzoic acid. The substitution by alanine of Y306 in the EFE, a residue 12 Å away from the catalytic metal center, generates an interior cavity that leads to multiple local and distal structural changes that reduce l-Arg binding and significantly reduce the enzyme activity. Flexibility analyses revealed correlated and anticorrelated motions in each system, with important distinctions from the wild-type enzyme. In combination, the results are congruent with the currently proposed enzyme mechanism, reinforce the importance of metal coordination by OD2 of D191, and highlight the importance of the second coordination sphere and longer range interactions in promoting EFE activity.

YfeX - A New Platform for Carbene Transferase Development with High Intrinsic Reactivity

Carbene transfer biocatalysis has evolved from basic science to an area with vast potential for the development of new industrial processes. In this study, we show that YfeX, naturally a peroxidase, has great potential for the development of new carbene transferases, due to its high intrinsic reactivity, especially for the N-H insertion reaction of aromatic and aliphatic primary and secondary amines. YfeX shows high stability against organic solvents (methanol and DMSO), greatly improving turnover of hydrophobic substrates. Interestingly, in styrene cyclopropanation, WT YfeX naturally shows high enantioselectivity, generating the trans product with 87 % selectivity for the (R,R) enantiomer. WT YfeX also catalyzes the Si-H insertion efficiently. Steric effects in the active site were further explored using the R232A variant. Quantum Mechanics/Molecular Mechanics (QM/MM) calculations reveal details on the mechanism of Si-H insertion. YfeX, and potentially other peroxidases, are exciting new targets for the development of improved carbene transferases.

Exploring the Molecular Conformation Space by Soft Molecule-Surface Collision

Biomolecules function by adopting multiple conformations. Such dynamics are governed by the conformation landscape whose study requires characterization of the ground and excited conformation states. Here, the conformational landscape of a molecule is sampled by exciting an initial gas-phase molecular conformer into diverse conformation states, using soft molecule-surface collision (0.5-5.0 eV). The resulting ground and excited molecular conformations, adsorbed on the surface, are imaged at the single-molecule level. This technique permits the exploration of oligosaccharide conformations, until now, limited by the high flexibility of oligosaccharides and ensemble-averaged analytical methods. As a model for cellulose, cellohexaose chains are observed in two conformational extremes, the typical "extended" chain and the atypical "coiled" chain-the latter identified as the gas-phase conformer preserved on the surface. Observing conformations between these two extremes reveals the physical properties of cellohexaose, behaving as a rigid ribbon that becomes flexible when twisted. The conformation space of any molecule that can be electrosprayed can now be explored.

Pump-Probe Time-Resolved Serial Femtosecond Crystallography at X-Ray Free Electron Lasers

With time-resolved crystallography (TRX), it is possible to follow the reaction dynamics in biological macromolecules by investigating the structure of transient states along the reaction coordinate. X-ray free electron lasers (XFELs) have enabled TRX experiments on previously uncharted femtosecond timescales. Here, we review the recent developments, opportunities, and challenges of pump-probe TRX at XFELs.

Molecular dynamics simulation of the heart type fatty acid binding protein in a crystal environment

Crystallographic data comes from a space-time average over all the unit cells within the crystal, so dynamic phenomena do not contribute significantly to the diffraction data. Many efforts have been made to reconstitute the movement of the macromolecules and explore the microstates that the confined proteins can adopt in the crystalline network. We explored different strategies to simulate a heart fatty acid binding protein (H-FABP) crystal by means of Molecular Dynamics (MD) simulations. We evaluate the effect of introducing restraints according to experimental isotropic B-factors and we analyzed the H-FABP motions in the crystal using Principal Component Analysis (PCA), isotropic and anisotropic B-factors. We compared the behavior of the protein simulated in the crystal confinement versus in solution, and we observed the effect of that confinement in the mobility of the protein residues. Restraining one-third of Cα atoms based on experimental B-factors produce lower B-factors than simulations without restraints, showing that the position restraint of the atoms with the lowest experimental B-factor is a good strategy to maintain the geometry of the crystal with an obvious decrease in the degrees of motion of the protein. PCA shows that, as position restraint reduces the conformational space explored by the system, the motion of the crystal is better recovered, for an essential subspace of the same size, in the simulations without restraints. Restraining only one Cα seems to be a good balance between giving flexibility to the system and preserving its structure. Communicated by Ramaswamy H. Sarma.

Residual Structures and Transient Long-Range Interactions of p53 Transactivation Domain: Assessment of Explicit Solvent Protein Force Fields

Molecular dynamics simulations using physics-based atomistic force fields have been increasingly used to characterize the heterogeneous structural ensembles of intrinsically disordered proteins (IDPs). To evaluate the accuracy of the latest atomistic explicit-solvent force fields in modeling larger IDPs with nontrivial structural features, we focus on the 61-residue N-terminal transactivation domain (TAD) of tumor suppressor p53, an important protein in cancer biology that has been extensively studied, and abundant experimental data is available for evaluation of simulated ensembles. We performed extensive replica exchange with solute tempering simulations, in excess of 1.0 μs/replica, to generate disordered structural ensembles of p53-TAD using six latest explicit solvent protein force fields. Multiple local and long-range structural properties, including chain dimension, residual secondary structures, and transient long-range contacts, were analyzed and compared against available experimental data. The results show that IDPs such as p53-TAD remain highly challenging for atomistic simulations due to conformational complexity and difficulty in achieving adequate convergence. Structural ensembles of p53-TAD generated using various force fields differ significantly from each other. The a99SB-disp force field demonstrates the best agreement with experimental data at all levels and proves to be suitable for simulating unbound p53-TAD and how its conformational properties may be modulated by phosphorylation and other cellular signals or cancer-associated mutations. Feasibility of such detailed structural characterization is a key step toward establishing the sequence-disordered ensemble-function-disease relationship of p53 and other biologically important IDPs.

Glucose Concentration Affects Fibrin Clot Structure and Morphology as Evidenced by Fluorescence Imaging and Molecular Simulations

Although in vivo studies have been conducted in the past to determine hyperglycemic effects and influence on clotting risk in patients with diabetes, the true extent of hyperglycemia on unstable and spontaneous clot formation remains highly debated. Factors such as increased glycation, elevated fibrinogen concentration, elevated prothrombin levels, and decreased plasminogen are known to influence fibrin conversion, clot morphology, and thrombus formation in these individuals. In this regard, the isolated effects of hyperglycemia on irregular fibrin clot formation were investigated in a controlled fibrinogen system. In this study, fibrin clot characteristic differences at 3 glucose concentrations were analyzed to determine the effects of glucose concentration on fibrinogen glycation and fibrin clot morphology using confocal microscopy, glycation quantification, molecular simulations, and image processing methods. Algorithms coupled with statistical analysis support in vivo findings that hyperglycemia increases fibrinogen glycation, with ensuing altered fibrin clot structure characteristics. Our experimental and molecular simulation results consistently show an increased glucose adsorption by fibrinogen with increased glucose concentration. Significant differences in clot structure characteristics were observed, and the results of this work can be used to further develop diagnostic tools for evaluating clotting risk in individuals with hypercoagulable and hyperglycemic conditions.

Structural Insights from Molecular Dynamics Simulations of Tryptophan 7-Halogenase and Tryptophan 5-Halogenase

Many natural organic compounds with pharmaceutical applications, including antibiotics (chlortetracycline and vancomycin), antifungal compounds (pyrrolnitrin), and chemotherapeutics (salinosporamide A and rebeccamycin) are chlorinated. Halogenating enzymes like tryptophan 7-halogenase (PrnA) and tryptophan 5-halogenase (PyrH) perform regioselective halogenation of tryptophan. In this study, the conformational dynamics of two flavin-dependent tryptophan halogenases-PrnA and PyrH-was investigated through molecular dynamics simulations, which are in agreement with the crystallographic and kinetic experimental studies of both enzymes and provide further explanation of the experimental data at an atomistic level of accuracy. They show that the binding sites of the cofactor-flavin adenine dinucleotide and the substrate do not come into close proximity during the simulations, thus supporting an enzymatic mechanism without a direct contact between them. Two catalytically important active site residues, glutamate (E346/E354) and lysine (K79/K75) in PrnA and PyrH, respectively, were found to play a key role in positioning the proposed chlorinating agent, hypochlorous acid. The changes in the regioselectivity between PrnA and PyrH arise as a consequence of differences in the orientation of substrate in its binding site.

HyRes: a coarse-grained model for multi-scale enhanced sampling of disordered protein conformations

Efficient coarse-grained (CG) models can be coupled with atomistic force fields to accelerate the sampling of atomistic energy landscapes in the multi-scale enhanced sampling (MSES) framework. This approach may be particularly suitable for generating atomistic conformational ensembles of intrinsically disordered proteins (IDPs). While MSES is relatively robust to inherent CG artifacts, achieving optimal sampling efficiency requires CG modeling to generate the local and long-range fluctuations that are largely consistent with those at the atomistic level. Here, we describe a new hybrid resolution CG model (HyRes) for MSES simulations of disordered protein states, which is specifically designed to provide semi-quantitative secondary structure propensities together with a qualitative description of long-range nonspecific interactions. The HyRes model contains an atomistic description of the backbone with intermediate resolution side chains. The secondary structure propensities are tuned by adjusting the backbone hydrogen-bonding strength and the ϕ/ψ torsion profile. The sizes and covalent geometries of the side chains are parameterized to reproduce distributions derived from atomistic simulations. Lennard-Jones parameters for sidechain beads are assigned to reproduce statistical potentials derived from the protein structural database, and then globally parameterized with nonspecific electrostatic interactions to reproduce the free energy profiles of pair wise interactions and the key conformational properties of model peptides. Application of HyRes to MSES simulations of small IDPs suggests that it is capable of driving faster structural transitions at the atomistic level and increasing the convergence rate compared to the Cα-only Gō-like models previously utilized. With further optimization, we believe that the new CG model could greatly improve the efficiency of MSES simulations of the larger and more complex IDPs frequently involved in cellular signalling and regulation.

Molecular Docking, Molecular Dynamics, and Structure-Activity Relationship Explorations of 14-Oxygenated N-Methylmorphinan-6-ones as Potent μ-Opioid Receptor Agonists

Among opioids, morphinans are of major importance as the most effective analgesic drugs acting primarily via μ-opioid receptor (μ-OR) activation. Our long-standing efforts in the field of opioid analgesics from the class of morphinans led to N-methylmorphinan-6-ones differently substituted at positions 5 and 14 as μ-OR agonists inducing potent analgesia and fewer undesirable effects. Herein we present the first thorough molecular modeling study and structure–activity relationship (SAR) explorations aided by docking and molecular dynamics (MD) simulations of 14-oxygenated N-methylmorphinan-6-ones to gain insights into their mode of binding to the μ-OR and interaction mechanisms. The structure of activated μ-OR provides an essential model for how ligand/μ-OR binding is encoded within small chemical differences in otherwise structurally similar morphinans. We reveal important molecular interactions that these μ-agonists share and distinguish them. The molecular docking outcomes indicate the crucial role of the relative orientation of the ligand in the μ-OR binding site, influencing the propensity of critical non-covalent interactions that are required to facilitate ligand/μ-OR interactions and receptor activation. The MD simulations point out minor differences in the tendency to form hydrogen bonds by the 4,5α-epoxy group, along with the tendency to affect the 3–7 lock switch. The emerged SARs reveal the subtle interplay between the substituents at positions 5 and 14 in the morphinan scaffold by enabling the identification of key structural elements that determine the distinct pharmacological profiles. This study provides a significant structural basis for understanding ligand binding and μ-OR activation by the 14-oxygenated N-methylmorphinan-6-ones, which should be useful for guiding drug design.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

Dimerization and ligand binding in tyrosylprotein sulfotransferase-2 are influenced by molecular motions

Tyrosylprotein sulfotransferase-2 catalyses important, but a less explored posttranslational modification of proteins.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

Are current atomistic force fields accurate enough to study proteins in crowded environments?

The high concentration of macromolecules in the crowded cellular interior influences different thermodynamic and kinetic properties of proteins, including their structural stabilities, intermolecular binding affinities and enzymatic rates. Moreover, various structural biology methods, such as NMR or different spectroscopies, typically involve samples with relatively high protein concentration. Due to large sampling requirements, however, the accuracy of classical molecular dynamics (MD) simulations in capturing protein behavior at high concentration still remains largely untested. Here, we use explicit-solvent MD simulations and a total of 6.4 µs of simulated time to study wild-type (folded) and oxidatively damaged (unfolded) forms of villin headpiece at 6 mM and 9.2 mM protein concentration. We first perform an exhaustive set of simulations with multiple protein molecules in the simulation box using GROMOS 45a3 and 54a7 force fields together with different types of electrostatics treatment and solution ionic strengths. Surprisingly, the two villin headpiece variants exhibit similar aggregation behavior, despite the fact that their estimated aggregation propensities markedly differ. Importantly, regardless of the simulation protocol applied, wild-type villin headpiece consistently aggregates even under conditions at which it is experimentally known to be soluble. We demonstrate that aggregation is accompanied by a large decrease in the total potential energy, with not only hydrophobic, but also polar residues and backbone contributing substantially. The same effect is directly observed for two other major atomistic force fields (AMBER99SB-ILDN and CHARMM22-CMAP) as well as indirectly shown for additional two (AMBER94, OPLS-AAL), and is possibly due to a general overestimation of the potential energy of protein-protein interactions at the expense of water-water and water-protein interactions. Overall, our results suggest that current MD force fields may distort the picture of protein behavior in biologically relevant crowded environments.

Protein behavior is strongly affected by highly crowded and interaction-rich environments, i.e., typical conditions in both biologically relevant systems, such as the cellular interior, and solution-based structural experiments, including NMR and different spectroscopies. On the other hand, primarily because of limited computational power, molecular dynamics (MD) simulations, a premier high-resolution method for analyzing structure, dynamics and interactions of proteins, have been predominantly used to study individual proteins at infinite dilution. To fill this gap, we use MD simulations to study the behavior of wild-type (aggregation-resistant) and oxidatively damaged (aggregation-prone) forms of villin headpiece at high concentration, and reveal unexpected limitations and inaccuracies of modern-day MD force fields when it comes to modeling proteins at physiologically or experimentally relevant concentrations.

From a structural average to the conformational ensemble of a DNA bulge

Direct experimental measurements of conformational ensembles are critical for understanding macromolecular function, but traditional biophysical methods do not directly report the solution ensemble of a macromolecule. Small-angle X-ray scattering interferometry has the potential to overcome this limitation by providing the instantaneous distance distribution between pairs of gold-nanocrystal probes conjugated to a macromolecule in solution. Our X-ray interferometry experiments reveal an increasing bend angle of DNA duplexes with bulges of one, three, and five adenosine residues, consistent with previous FRET measurements, and further reveal an increasingly broad conformational ensemble with increasing bulge length. The distance distributions for the AAA bulge duplex (3A-DNA) with six different Au-Au pairs provide strong evidence against a simple elastic model in which fluctuations occur about a single conformational state. Instead, the measured distance distributions suggest a 3A-DNA ensemble with multiple conformational states predominantly across a region of conformational space with bend angles between 24 and 85 degrees and characteristic bend directions and helical twists and displacements. Additional X-ray interferometry experiments revealed perturbations to the ensemble from changes in ionic conditions and the bulge sequence, effects that can be understood in terms of electrostatic and stacking contributions to the ensemble and that demonstrate the sensitivity of X-ray interferometry. Combining X-ray interferometry ensemble data with molecular dynamics simulations gave atomic-level models of representative conformational states and of the molecular interactions that may shape the ensemble, and fluorescence measurements with 2-aminopurine-substituted 3A-DNA provided initial tests of these atomistic models. More generally, X-ray interferometry will provide powerful benchmarks for testing and developing computational methods.

How does conformational flexibility influence key structural features involved in activation of anaplastic lymphoma kinase?

Anaplastic Lymphoma Kinase (ALK) plays a major role in developing tumor processes and therefore has emerged as a validated therapeutic target. Applying atomistic molecular dynamics simulations on the wild type enzyme and the nine most frequently occurring and clinically important activation mutants we revealed important conformational effects on key interactions responsible for the activation of the enzyme.

Epigenetic molecular recognition: a biomolecular modeling perspective

The abnormal regulation of epigenetic protein families is associated with the onset and progression of various human diseases. However, epigenetic processes remain relatively obscure at the molecular level, thus preventing the rational design of chemical therapeutics. An array of robust computational and modeling approaches can complement experiments to shed light on the complex mechanisms of epigenetic molecular recognition and can guide medicinal chemists in designing selective and potent drug molecules. Herein we present a review of studies focused on epigenetic molecular recognition from a biomolecular modeling viewpoint. Although the known epigenetic targets are numerous, this review focuses on the more limited protein families on which computational modeling has been successfully applied. Therefore, we review three main topics: 1) histone deacetylases, 2) histone demethylases, and 3) histone tail dynamics. A brief review of the biological background and biomedical relevance is presented for each topic, followed by a detailed discussion of the computational studies and their relevance.

A systematic framework for molecular dynamics simulations of protein post-translational modifications

By directly affecting structure, dynamics and interaction networks of their targets, post-translational modifications (PTMs) of proteins play a key role in different cellular processes ranging from enzymatic activation to regulation of signal transduction to cell-cycle control. Despite the great importance of understanding how PTMs affect proteins at the atomistic level, a systematic framework for treating post-translationally modified amino acids by molecular dynamics (MD) simulations, a premier high-resolution computational biology tool, has never been developed. Here, we report and validate force field parameters (GROMOS 45a3 and 54a7) required to run and analyze MD simulations of more than 250 different types of enzymatic and non-enzymatic PTMs. The newly developed GROMOS 54a7 parameters in particular exhibit near chemical accuracy in matching experimentally measured hydration free energies (RMSE = 4.2 kJ/mol over the validation set). Using this tool, we quantitatively show that the majority of PTMs greatly alter the hydrophobicity and other physico-chemical properties of target amino acids, with the extent of change in many cases being comparable to the complete range spanned by native amino acids.

Post-translational modifications, i.e. chemical changes of protein amino acids, play a key role in different cellular processes, ranging from enzymatic activation to transcription and translation regulation to disease development and aging. However, our understanding of their effects on protein structure, dynamics and interaction networks at the atomistic level is still largely incomplete. In particular, molecular dynamics simulations, despite their power to provide a high-resolution insight into biomolecular function and underlying mechanisms, have been limited to unmodified, native proteins due to a surprising deficiency of suitable tools and systematically developed parameters for treating modified proteins. To fill this gap, we develop and validate force field parameters, an essential part of the molecular dynamics method, for more than 250 different types of enzymatic and non-enzymatic post-translational modifications. Additionally, using this tool, we quantitatively show that microscopic properties of target amino acids, such as hydrophobicity, are greatly affected by the majority of modifications. The parameters presented in this study greatly expand the range of applicability of computational methods, and in particular molecular dynamics simulations, to a large set of new systems with utmost biological and biomedical importance.

Vienna-PTM web server: a toolkit for MD simulations of protein post-translational modifications

Post-translational modifications (PTMs) play a key role in numerous cellular processes by directly affecting structure, dynamics and interaction networks of target proteins. Despite their importance, our understanding of protein PTMs at the atomistic level is still largely incomplete. Molecular dynamics (MD) simulations, which provide high-resolution insight into biomolecular function and underlying mechanisms, are in principle ideally suited to tackle this problem. However, because of the challenges associated with the development of novel MD parameters and a general lack of suitable computational tools for incorporating PTMs in target protein structures, MD simulations of post-translationally modified proteins have historically lagged significantly behind the studies of unmodified proteins. Here, we present Vienna-PTM web server (http://vienna-ptm.univie.ac.at), a platform for automated introduction of PTMs of choice to protein 3D structures (PDB files) in a user-friendly visual environment. With 256 different enzymatic and non-enzymatic PTMs available, the server performs geometrically realistic introduction of modifications at sites of interests, as well as subsequent energy minimization. Finally, the server makes available force field parameters and input files needed to run MD simulations of modified proteins within the framework of the widely used GROMOS 54A7 and 45A3 force fields and GROMACS simulation package.

Peptide crystal simulations reveal hidden dynamics

Molecular dynamics simulations of biomolecular crystals at atomic resolution have the potential to recover information on dynamics and heterogeneity hidden in X-ray diffraction data. We present here 9.6 μs of dynamics in a small helical peptide crystal with 36 independent copies of the unit cell. The average simulation structure agrees with experiment to within 0.28 Å backbone and 0.42 Å all-atom RMSD; a model refined against the average simulation density agrees with the experimental structure to within 0.20 Å backbone and 0.33 Å all-atom RMSD. The R-factor between the experimental structure factors and those derived from this unrestrained simulation is 23% to 1.0 Å resolution. The B-factors for most heavy atoms agree well with experiment (Pearson correlation of 0.90), but B-factors obtained by refinement against the average simulation density underestimate the coordinate fluctuations in the underlying simulation where the simulation samples alternate conformations. A dynamic flow of water molecules through channels within the crystal lattice is observed, yet the average water density is in remarkable agreement with experiment. A minor population of unit cells is characterized by reduced water content, 310 helical propensity and a gauche(-) side-chain rotamer for one of the valine residues. Careful examination of the experimental data suggests that transitions of the helices are a simulation artifact, although there is indeed evidence for alternate valine conformers and variable water content. This study highlights the potential for crystal simulations to detect dynamics and heterogeneity in experimental diffraction data as well as to validate computational chemistry methods.

Structural ensemble and microscopic elasticity of freely diffusing DNA by direct measurement of fluctuations

Precisely measuring the ensemble of conformers that a macromolecule populates in solution is highly challenging. Thus, it has been difficult to confirm or falsify the predictions of nanometer-scale dynamical modeling. Here, we apply an X-ray interferometry technique to probe the solution structure and fluctuations of B-form DNA on a length scale comparable to a protein-binding site. We determine an extensive set of intrahelix distance distributions between pairs of probes placed at distinct points on the surface of the DNA duplex. The distributions of measured distances reveal the nature and extent of the thermally driven mechanical deformations of the helix. We describe these deformations in terms of elastic constants, as is common for DNA and other polymers. The average solution structure and microscopic elasticity measured by X-ray interferometry are in striking agreement with values derived from DNA-protein crystal structures and measured by force spectroscopy, with one exception. The observed microscopic torsional rigidity of DNA is much lower than is measured by single-molecule twisting experiments, suggesting that torsional rigidity increases when DNA is stretched. Looking forward, molecular-level interferometry can provide a general tool for characterizing solution-phase structural ensembles.

Synergistic applications of MD and NMR for the study of biological systems

Modern biological sciences are becoming more and more multidisciplinary. At the same time, theoretical and computational approaches gain in reliability and their field of application widens. In this short paper, we discuss recent advances in the areas of solution nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations that were made possible by the combination of both methods, that is, through their synergistic use. We present the main NMR observables and parameters that can be computed from simulations, and how they are used in a variety of complementary applications, including dynamics studies, model-free analysis, force field validation, and structural studies.

The effects of rigid motions on elastic network model force constants

Elastic network models provide an efficient way to quickly calculate protein global dynamics from experimentally determined structures. The model's single parameter, its force constant, determines the physical extent of equilibrium fluctuations. The values of force constants can be calculated by fitting to experimental data, but the results depend on the type of experimental data used. Here, we investigate the differences between calculated values of force constants and data from NMR and X-ray structures. We find that X-ray B factors carry the signature of rigid-body motions, to the extent that B factors can be almost entirely accounted for by rigid motions alone. When fitting to more refined anisotropic temperature factors, the contributions of rigid motions are significantly reduced, indicating that the large contribution of rigid motions to B factors is a result of over-fitting. No correlation is found between force constants fit to NMR data and those fit to X-ray data, possibly due to the inability of NMR data to accurately capture protein dynamics.

Dynamics may significantly influence the estimation of interatomic distances in biomolecular X-ray structures

Atomic positions obtained by X-ray crystallography are time and space averages over many molecules in the crystal. Importantly, interatomic distances, calculated between such average positions and frequently used in structural and mechanistic analyses, can be substantially different from the more appropriate time-average and ensemble-average interatomic distances. Using crystallographic B-factors, one can deduce corrections, which have so far been applied exclusively to small molecules, to obtain correct average distances as a function of the type of atomic motion. Here, using 4774 high-quality protein X-ray structures, we study the significance of such corrections for different types of atomic motion. Importantly, we show that for distances shorter than 5 Å, corrections greater than 0.5 Å may apply, especially for noncorrelated or anticorrelated motion. For example, 14% of the studied structures have at least one pair of atoms with a correction of ≥ 0.5 Å in the case of noncorrelated motion. Using molecular dynamics simulations of villin headpiece, ubiquitin, and SH3 domain unit cells, we demonstrate that the majority of average interatomic distances in these proteins agree with noncorrelated corrections, suggesting that such deviations may be truly relevant. Importantly, we demonstrate that the corrections do not significantly affect stereochemistry and the overall quality of final refined X-ray structures, but can provide marked improvements in starting unrefined models obtained from low-resolution X-ray data. Finally, we illustrate the potential mechanistic and biological significance of the calculated corrections for KcsA ion channel and show that they provide indirect evidence that motions in its selectivity filter are highly correlated.

Using entropy maximization to understand the determinants of structural dynamics beyond native contact topology

Comparison of elastic network model predictions with experimental data has provided important insights on the dominant role of the network of inter-residue contacts in defining the global dynamics of proteins. Most of these studies have focused on interpreting the mean-square fluctuations of residues, or deriving the most collective, or softest, modes of motions that are known to be insensitive to structural and energetic details. However, with increasing structural data, we are in a position to perform a more critical assessment of the structure-dynamics relations in proteins, and gain a deeper understanding of the major determinants of not only the mean-square fluctuations and lowest frequency modes, but the covariance or the cross-correlations between residue fluctuations and the shapes of higher modes. A systematic study of a large set of NMR-determined proteins is analyzed using a novel method based on entropy maximization to demonstrate that the next level of refinement in the elastic network model description of proteins ought to take into consideration properties such as contact order (or sequential separation between contacting residues) and the secondary structure types of the interacting residues, whereas the types of amino acids do not play a critical role. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as opposed to exclusively stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics. This study provides us with a deeper understanding of the structural basis of experimentally observed behavior, and opens the way to the development of more accurate models for exploring protein dynamics.

As more protein structures are solved, we are able to perform a more critical assessment of the relationship between protein structure and dynamics, and to gain a deeper understanding of the major determinants of structural dynamics. Here we perform a systematic study on a set of proteins structurally determined by NMR spectroscopy. The dynamics are analyzed using elastic network models and a novel method based on entropy maximization to demonstrate that properties such as contact order and secondary structure do play a role in defining the experimentally observed covariance data. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as well as stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics.