Quantitative Molecular Ensemble Interpretation of NMR Dipolar Couplings without Restraints

The role of structural dynamics in the thermal adaptation of hyperthermophilic enzymes

Proteins from hyperthermophilic organisms are evolutionary optimised to adopt functional structures and dynamics under conditions in which their mesophilic homologues are generally inactive or unfolded. Understanding the nature of such adaptation is of crucial interest to clarify the underlying mechanisms of biological activity in proteins. Here we measured NMR residual dipolar couplings of a hyperthermophilic acylphosphatase enzyme at 80°C and used these data to generate an accurate structural ensemble representative of its native state. The resulting energy landscape was compared to that obtained for a human homologue at 37°C, and additional NMR experiments were carried out to probe fast (¹⁵N relaxation) and slow (H/D exchange) backbone dynamics, collectively sampling fluctuations of the two proteins ranging from the nanosecond to the millisecond timescale. The results identified key differences in the strategies for protein-protein and protein-ligand interactions of the two enzymes at the respective physiological temperatures. These include the dynamical behaviour of a β-strand involved in the protection against aberrant protein aggregation and concerted motions of loops involved in substrate binding and catalysis. Taken together these results elucidate the structure-dynamics-function relationship associated with the strategies of thermal adaptation of protein molecules.

Molecular insights on CALX-CBD12 interdomain dynamics from MD simulations, RDCs, and SAXS

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the translocation of Na⁺ with the transport of Ca²⁺ in the opposite direction. The exchanger is an essential Ca²⁺ extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca²⁺-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca²⁺ sensor called CBD12. Binding of intracellular Ca²⁺ to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca²⁺-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR (¹H-¹⁵N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca²⁺-bound state is less frequently sampled. These results are consistent with the view that Ca²⁺ binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs' allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.

Rapid and accurate determination of atomistic RNA dynamic ensemble models using NMR and structure prediction

Biomolecules form dynamic ensembles of many inter-converting conformations which are key for understanding how they fold and function. However, determining ensembles is challenging because the information required to specify atomic structures for thousands of conformations far exceeds that of experimental measurements. We addressed this data gap and dramatically simplified and accelerated RNA ensemble determination by using structure prediction tools that leverage the growing database of RNA structures to generate a conformation library. Refinement of this library with NMR residual dipolar couplings provided an atomistic ensemble model for HIV-1 TAR, and the model accuracy was independently supported by comparisons to quantum-mechanical calculations of NMR chemical shifts, comparison to a crystal structure of a substate, and through designed ensemble redistribution via atomic mutagenesis. Applications to TAR bulge variants and more complex tertiary RNAs support the generality of this approach and the potential to make the determination of atomic-resolution RNA ensembles routine.

Determining dynamic ensembles of biomolecules is still challenging. Here the authors present an approach for rapid RNA ensemble determination that combines RNA structure prediction tools and NMR residual dipolar coupling data and use it to determine atomistic ensemble models for a variety of RNAs.

Companion Simulations and Modeling to NMR-Based Dynamical Studies of Proteins

NMR-based studies of protein dynamics and molecular simulations have a synergistic relationship. Molecular simulations, in combination with interpretative theoretical models, leverage the dynamical information obtained from NMR. They provide the concrete physical schema underlying the quantities measured by NMR, and help extend the range of applications beyond the strictly dynamic properties. NMR data in turn provide concrete data to test and improve the potential functions used for simulation of dynamics of proteins. The concept of time correlation functions is central to the understanding of many dynamical processes. Their evaluation through atomistic simulations is discussed, with application to different dynamical quantities measured by NMR. While advances in computers have made such atomistic simulations almost routine, the companion use of simple interpretive models is stressed, to provide not just numbers but physical insight.

Evaluating amber force fields using computed NMR chemical shifts

NMR chemical shifts can be computed from molecular dynamics (MD) simulations using a template matching approach and a library of conformers containing chemical shifts generated from ab initio quantum calculations. This approach has potential utility for evaluating the force fields that underlie these simulations. Imperfections in force fields generate flawed atomic coordinates. Chemical shifts obtained from flawed coordinates have errors that can be traced back to these imperfections. We use this approach to evaluate a series of AMBER force fields that have been refined over the course of two decades (ff94, ff96, ff99SB, ff14SB, ff14ipq, and ff15ipq). For each force field a series of MD simulations are carried out for eight model proteins. The calculated chemical shifts for the ¹ H, ¹⁵ N, and ¹³ C^a atoms are compared with experimental values. Initial evaluations are based on root mean squared (RMS) errors at the protein level. These results are further refined based on secondary structure and the types of atoms involved in nonbonded interactions. The best chemical shift for identifying force field differences is the shift associated with peptide protons. Examination of the model proteins on a residue by residue basis reveals that force field performance is highly dependent on residue position. Examination of the time course of nonbonded interactions at these sites provides explanations for chemical shift differences at the atomic coordinate level. Results show that the newer ff14ipq and ff15ipq force fields developed with the implicitly polarized charge method perform better than the older force fields.

Error assessment in molecular dynamics trajectories using computed NMR chemical shifts

Accurate chemical shifts for the atoms in molecular mechanics (MD) trajectories can be obtained from quantum mechanical (QM) calculations that depend solely on the coordinates of the atoms in the localized regions surrounding atoms of interest. If these coordinates are correct and the sample size is adequate, the ensemble average of these chemical shifts should be equal to the chemical shifts obtained from NMR spectroscopy. If this is not the case, the coordinates must be incorrect. We have utilized this fact to quantify the errors associated with the backbone atoms in MD simulations of proteins. A library of regional conformers containing 169,499 members was constructed from 6 model proteins. The chemical shifts associated with the backbone atoms in each of these conformers was obtained from QM calculations using density functional theory at the B3LYP level with a 6-311+G(2d,p) basis set. Chemical shifts were assigned to each backbone atom in each MD simulation frame using a template matching approach. The ensemble average of these chemical shifts was compared to chemical shifts from NMR spectroscopy. A large systematic error was identified that affected the ¹H atoms of the peptide bonds involved in hydrogen bonding with water molecules or peptide backbone atoms. This error was highly sensitive to changes in electrostatic parameters. Smaller errors affecting the ¹³C^a and ¹⁵N atoms were also detected. We believe these errors could be useful as metrics for comparing the force-fields and parameter sets used in MD simulation because they are directly tied to errors in atomic coordinates.

Finding Our Way in the Dark Proteome

The traditional structure-function paradigm has provided significant insights for well-folded proteins in which structures can be easily and rapidly revealed by X-ray crystallography beamlines. However, approximately one-third of the human proteome is comprised of intrinsically disordered proteins and regions (IDPs/IDRs) that do not adopt a dominant well-folded structure, and therefore remain "unseen" by traditional structural biology methods. This Perspective considers the challenges raised by the "Dark Proteome", in which determining the diverse conformational substates of IDPs in their free states, in encounter complexes of bound states, and in complexes retaining significant disorder requires an unprecedented level of integration of multiple and complementary solution-based experiments that are analyzed with state-of-the art molecular simulation, Bayesian probabilistic models, and high-throughput computation. We envision how these diverse experimental and computational tools can work together through formation of a "computational beamline" that will allow key functional features to be identified in IDP structural ensembles.

Capturing a Dynamic Chaperone-Substrate Interaction Using NMR-Informed Molecular Modeling

Chaperones maintain a healthy proteome by preventing aggregation and by aiding in protein folding. Precisely how chaperones influence the conformational properties of their substrates, however, remains unclear. To achieve a detailed description of dynamic chaperone-substrate interactions, we fused site-specific NMR information with coarse-grained simulations. Our model system is the binding and folding of a chaperone substrate, immunity protein 7 (Im7), with the chaperone Spy. We first used an automated procedure in which NMR chemical shifts inform the construction of system-specific force fields that describe each partner individually. The models of the two binding partners are then combined to perform simulations on the chaperone-substrate complex. The binding simulations show excellent agreement with experimental data from multiple biophysical measurements. Upon binding, Im7 interacts with a mixture of hydrophobic and hydrophilic residues on Spy's surface, causing conformational exchange within Im7 to slow down as Im7 folds. Meanwhile, the motion of Spy's flexible loop region increases, allowing for better interaction with different substrate conformations, and helping offset losses in Im7 conformational dynamics that occur upon binding and folding. Spy then preferentially releases Im7 into a well-folded state. Our strategy has enabled a residue-level description of a dynamic chaperone-substrate interaction, improving our understanding of how chaperones facilitate substrate folding. More broadly, we validate our approach using two other binding partners, showing that this approach provides a general platform from which to investigate other flexible biomolecular complexes through the integration of NMR data with efficient computational models.

A composite approach towards a complete model of the myosin rod

Sarcomeric myosins have the remarkable ability to form regular bipolar thick filaments that, together with actin thin filaments, constitute the fundamental contractile unit of skeletal and cardiac muscle. This has been established for over 50 years and yet a molecular model for the thick filament has not been attained. In part this is due to the lack of a detailed molecular model for the coiled-coil that constitutes the myosin rod. The ability to self-assemble resides in the C-terminal section of myosin known as light meromyosin (LMM) which exhibits strong salt-dependent aggregation that has inhibited structural studies. Here we evaluate the feasibility of generating a complete model for the myosin rod by combining overlapping structures of five sections of coiled-coil covering 164 amino acid residues which constitute 20% of LMM. Each section contains ∼ 7-9 heptads of myosin. The problem of aggregation was overcome by incorporating the globular folding domains, Gp7 and Xrcc4 which enhance crystallization. The effect of these domains on the stability and conformation of the myosin rod was examined through biophysical studies and overlapping structures. In addition, a computational approach was developed to combine the sections into a contiguous model. The structures were aligned, trimmed to form a contiguous model, and simulated for >700 ns to remove the discontinuities and achieve an equilibrated conformation that represents the native state. This experimental and computational strategy lays the foundation for building a model for the entire myosin rod.

Protocol To Make Protein NMR Structures Amenable to Stable Long Time Scale Molecular Dynamics Simulations

A robust protocol for the treatment of NMR protein structures is presented that makes them amenable to long time scale molecular dynamics (MD) simulations that are stable. The protocol embeds an NMR structure in a native low energy region of the recently developed ff99SB_φψ(g24;CS) molecular mechanics force field. Extended MD trajectories that start from these structures show good consistency with proton-proton nuclear Overhauser effect data, and they reproduce NMR chemical shift data better than the original NMR structures as is demonstrated for four protein systems. Moreover, for all proteins studied here the simulations spontaneously approach the X-ray crystal structures, thereby improving the effective resolution of the initial structural models.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

Molecular Dynamics: New Frontier in Personalized Medicine

The field of drug discovery has witnessed infinite development over the last decade with the demand for discovery of novel efficient lead compounds. Although the development of novel compounds in this field has seen large failure, a breakthrough in this area might be the establishment of personalized medicine. The trend of personalized medicine has shown stupendous growth being a hot topic after the successful completion of Human Genome Project and 1000 genomes pilot project. Genomic variant such as SNPs play a vital role with respect to inter individual's disease susceptibility and drug response. Hence, identification of such genetic variants has to be performed before administration of a drug. This process requires high-end techniques to understand the complexity of the molecules which might bring an insight to understand the compounds at their molecular level. To sustenance this, field of bioinformatics plays a crucial role in revealing the molecular mechanism of the mutation and thereby designing a drug for an individual in fast and affordable manner. High-end computational methods, such as molecular dynamics (MD) simulation has proved to be a constitutive approach to detecting the minor changes associated with an SNP for better understanding of the structural and functional relationship. The parameters used in molecular dynamic simulation elucidate different properties of a macromolecule, such as protein stability and flexibility. MD along with docking analysis can reveal the synergetic effect of an SNP in protein-ligand interaction and provides a foundation for designing a particular drug molecule for an individual. This compelling application of computational power and the advent of other technologies have paved a promising way toward personalized medicine. In this in-depth review, we tried to highlight the different wings of MD toward personalized medicine.

Negative Regulation of Peptidyl-Prolyl Isomerase Activity by Interdomain Contact in Human Pin1

Pin1 is a modular peptidyl-prolyl isomerase specific for phosphorylated Ser/Thr-Pro (pS/T-P) motifs, typically within intrinsically disordered regions of signaling proteins. Pin1 consists of two flexibly linked domains: an N-terminal WW domain for substrate binding and a larger C-terminal peptidyl-prolyl isomerase (PPIase) domain. Previous studies showed that binding of phosphopeptide substrates to Pin1 could alter Pin1 interdomain contact, strengthening or weakening it depending on the substrate sequence. Thus, substrate-induced changes in interdomain contact may act as a trigger within the Pin1 mechanism. Here, we investigate this possibility via nuclear magnetic resonance studies of several Pin1 mutants. Our findings provide new mechanistic insights for those substrates that reduce interdomain contact. Specifically, the reduced interdomain contact can allosterically enhance PPIase activity relative to that when the contact is sustained. These findings suggest Pin1 interdomain contact can negatively regulate its activity.

Modulating RNA Alignment Using Directional Dynamic Kinks: Application in Determining an Atomic-Resolution Ensemble for a Hairpin using NMR Residual Dipolar Couplings

Approaches that combine experimental data and computational molecular dynamics (MD) to determine atomic resolution ensembles of biomolecules require the measurement of abundant experimental data. NMR residual dipolar couplings (RDCs) carry rich dynamics information, however, difficulties in modulating overall alignment of nucleic acids have limited the ability to fully extract this information. We present a strategy for modulating RNA alignment that is based on introducing variable dynamic kinks in terminal helices. With this strategy, we measured seven sets of RDCs in a cUUCGg apical loop and used this rich data set to test the accuracy of an 0.8 μs MD simulation computed using the Amber ff10 force field as well as to determine an atomic resolution ensemble. The MD-generated ensemble quantitatively reproduces the measured RDCs, but selection of a sub-ensemble was required to satisfy the RDCs within error. The largest discrepancies between the RDC-selected and MD-generated ensembles are observed for the most flexible loop residues and backbone angles connecting the loop to the helix, with the RDC-selected ensemble resulting in more uniform dynamics. Comparison of the RDC-selected ensemble with NMR spin relaxation data suggests that the dynamics occurs on the ps-ns time scales as verified by measurements of R(1ρ) relaxation-dispersion data. The RDC-satisfying ensemble samples many conformations adopted by the hairpin in crystal structures indicating that intrinsic plasticity may play important roles in conformational adaptation. The approach presented here can be applied to test nucleic acid force fields and to characterize dynamics in diverse RNA motifs at atomic resolution.

A community resource of experimental data for NMR / X-ray crystal structure pairs

We have developed an online NMR / X-ray Structure Pair Data Repository. The NIGMS Protein Structure Initiative (PSI) has provided many valuable reagents, 3D structures, and technologies for structural biology. The Northeast Structural Genomics Consortium was one of several PSI centers. NESG used both X-ray crystallography and NMR spectroscopy for protein structure determination. A key goal of the PSI was to provide experimental structures for at least one representative of each of hundreds of targeted protein domain families. In some cases, structures for identical (or nearly identical) constructs were determined by both NMR and X-ray crystallography. NMR spectroscopy and X-ray diffraction data for 41 of these "NMR / X-ray" structure pairs determined using conventional triple-resonance NMR methods with extensive sidechain resonance assignments have been organized in an online NMR / X-ray Structure Pair Data Repository. In addition, several NMR data sets for perdeuterated, methyl-protonated protein samples are included in this repository. As an example of the utility of this repository, these data were used to revisit questions about the precision and accuracy of protein NMR structures first outlined by Levy and coworkers several years ago (Andrec et al., Proteins 2007;69:449-465). These results demonstrate that the agreement between NMR and X-ray crystal structures is improved using modern methods of protein NMR spectroscopy. The NMR / X-ray Structure Pair Data Repository will provide a valuable resource for new computational NMR methods development.

Molecular Dynamics of Biomolecules through Direct Analysis of Dipolar Couplings

Residual dipolar couplings (RDCs) are important probes in structural biology, but their analysis is often complicated by the determination of an alignment tensor or its associated assumptions. We here apply the maximum entropy principle to derive a tensor-free formalism which allows for direct, dynamic analysis of RDCs and holds the classic tensor formalism as a special case. Specifically, the framework enables us to robustly analyze data regardless of whether a clear separation of internal and overall dynamics is possible. Such a separation is often difficult in the core subjects of current structural biology, which include multidomain and intrinsically disordered proteins as well as nucleic acids. We demonstrate the method is tractable and self-consistent and generalizes to data sets comprised of observations from multiple different alignment conditions.

Recovering a representative conformational ensemble from underdetermined macromolecular structural data

Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed the Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked diubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked diubiquitin, and revealed lesser-populated conformations that are preorganized for binding known diubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

A tensor-free method for the structural and dynamical refinement of proteins using residual dipolar couplings

Residual dipolar couplings (RDCs) are parameters measured in nuclear magnetic resonance spectroscopy that can provide exquisitely detailed information about the structure and dynamics of biological macromolecules. We describe here a method of using RDCs for the structural and dynamical refinement of proteins that is based on the observation that the RDC between two atomic nuclei depends directly on the angle ϑ between the internuclear vector and the external magnetic field. For every pair of nuclei for which an RDC is available experimentally, we introduce a structural restraint to minimize the deviation from the value of the angle ϑ derived from the measured RDC and that calculated in the refinement protocol. As each restraint involves only the calculation of the angle ϑ of the corresponding internuclear vector, the method does not require the definition of an overall alignment tensor to describe the preferred orientation of the protein with respect to the alignment medium. Application to the case of ubiquitin demonstrates that this method enables an accurate refinement of the structure and dynamics of this protein to be obtained.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

New opportunities for tensor-free calculations of residual dipolar couplings for the study of protein dynamics

Residual dipolar couplings (RDCs) can provide exquisitely detailed information about the structure and dynamics of proteins. It is challenging, however, to extract such information from RDC measurements in conformationally heterogeneous states of proteins because of the complex relationship between RDCs and protein structures. To obtain new insights into this problem, we discuss methods of calculating the RDCs that do not require the definition of an alignment tensor. These methods can help in particular in the search of effective ways to use RDCs to characterise disordered or partially disordered states of proteins.

Perturbations of the straight transmembrane α-helical structure of the amyloid precursor protein affect its processing by γ-secretase

The amyloid precursor protein (APP) is a widely expressed type I transmembrane (TM) glycoprotein present at the neuronal synapse. The proteolytic cleavage by γ-secretase of its C-terminal fragment produces amyloid-β (Aβ) peptides of different lengths, the deposition of which is an early indicator of Alzheimer disease. At present, there is no consensus on the conformation of the APP-TM domain at the biological membrane. Although structures have been determined by NMR in detergent micelles, their conformation is markedly different. Here we show by using molecular simulations that the APP-TM region systematically prefers a straight α-helical conformation once embedded in a membrane bilayer. However, APP-TM is highly flexible, and its secondary structure is strongly influenced by the surrounding lipid environment, as when enclosed in detergent micelles. This behavior is confirmed when analyzing in silico the atomistic APP-TM population observed by residual dipolar couplings and double electron-electron resonance spectroscopy. These structural and dynamic features are critical in the proteolytic processing of APP by the γ-secretase enzyme, as suggested by a series of Gly(700) mutants. Affecting the hydration and flexibility of APP-TM, these mutants invariantly show an increase in the production of Aβ38 compared with Aβ40 peptides, which is reminiscent of the effect of γ-secretase modulators inhibitors.

Comparison of structure determination methods for intrinsically disordered amyloid-β peptides

Intrinsically disordered proteins (IDPs) represent a new frontier in structural biology since the primary characteristic of IDPs is that structures need to be characterized as diverse ensembles of conformational substates. We compare two general but very different ways of combining NMR spectroscopy with theoretical methods to derive structural ensembles for the disease IDPs amyloid-β 1-40 and amyloid-β 1-42, which are associated with Alzheimer's Disease. We analyze the performance of de novo molecular dynamics and knowledge-based approaches for generating structural ensembles by assessing their ability to reproduce a range of NMR experimental observables. In addition to the comparison of computational methods, we also evaluate the relative value of different types of NMR data for refining or validating the IDP structural ensembles for these important disease peptides.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

Characterization of the interdomain motions in hen lysozyme using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations

Hen lysozyme is an enzyme characterized by the presence of two domains whose relative motions are involved in the mechanism of binding and release of the substrates. By using residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations, we characterize the breathing motions describing the interdomain fluctuations of this protein. We found that the ensemble of conformations that we determined spans the entire range of structures of hen lysozyme deposited in the Protein Data Bank, including both the free and bound states, suggesting that the thermal motions in the free state provide access to the structures populated upon binding. The approach that we present illustrates how the use of residual dipolar couplings as replica-averaged structural restraints in molecular dynamics simulations makes it possible to explore conformational fluctuations of a relatively large amplitude in proteins.

Identification of small-molecule binding pockets in the soluble monomeric form of the Aβ42 peptide

The aggregation of intrinsically disordered peptides and proteins is associated with a wide range of highly debilitating neurological and systemic disorders. In this work we explored the potential of a structure-based drug discovery procedure to target one such system, the soluble monomeric form of the Aβ42 peptide. We utilised for this purpose a set of structures of the Aβ42 peptide selected from clusters of conformations within an ensemble generated by molecular dynamics simulations. Using these structures we carried out fragment mapping calculations to identify binding "hot spots" on the monomeric form of the Aβ42 peptide. This procedure provided a set of hot spots with ligand efficiencies comparable to those observed for structured proteins, and clustered into binding pockets. Such binding pockets exhibited a propensity to bind small molecules known to interact with the Aβ42 peptide. Taken together these results provide an initial indication that fragment-based drug discovery may represent a potential therapeutic strategy for diseases associated with the aggregation of intrinsically disordered proteins.

CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side-chain amino- and methyl-containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ1 and χ2 dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs.

Improved Generalized Born Solvent Model Parameters for Protein Simulations

The generalized Born (GB) model is one of the fastest implicit solvent models and it has become widely adopted for Molecular Dynamics (MD) simulations. This speed comes with tradeoffs, and many reports in the literature have pointed out weaknesses with GB models. Because the quality of a GB model is heavily affected by empirical parameters used in calculating solvation energy, in this work we have refit these parameters for GB-Neck, a recently developed GB model, in order to improve the accuracy of both the solvation energy and effective radii calculations. The data sets used for fitting are significantly larger than those used in the past. Comparing to other pairwise GB models like GB-OBC and the original GB-Neck, the new GB model (GB-Neck2) has better agreement to Poisson-Boltzmann (PB) in terms of reproducing solvation energies for a variety of systems ranging from peptides to proteins. Secondary structure preferences are also in much better agreement with those obtained from explicit solvent MD simulations. We also obtain near-quantitative reproduction of experimental structure and thermal stability profiles for several model peptides with varying secondary structure motifs. Extension to non-protein systems will be explored in the future.

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.

Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.

Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings

Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born

We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.

Toward a predictive understanding of slow methyl group dynamics in proteins

The development of the most recent generation of molecular mechanics force fields promises an increasingly predictive understanding of the protein dynamics-function relationship. Based on extensive validation against various types of experimental data, the AMBER force field ff99SB was benchmarked in recent years as a favorable force field for protein simulations. Recent improvements of the side chain and backbone potentials, made by different groups, led to the ff99SB-ILDN and ff99SBnmr1 force fields, respectively. The combination of these potentials into a unified force field, termed ff99SBnmr1-ILDN, was used in this study to perform a microsecond time scale molecular dynamics simulation of free ubiquitin in explicit solvent for validation against an extensive set of experimental NMR methyl group residual dipolar couplings. Our results show a high level of consistency between the experimental data and the values predicted from the molecular dynamics trajectory reflecting a systematically improved performance of ff99SBnmr1-ILDN over the original ff99SB force field. Moreover, the unconstrained ff99SBnmr1-ILDN MD ensemble achieves a similar level of agreement as the recently introduced EROS ensemble, which was constructed based on a large body of NMR data as constraints, including the methyl residual dipolar couplings. This suggests that ff99SBnmr1-ILDN provides a high-quality representation of the motions of methyl-bearing protein side chains, which are sensitive probes of protein-protein and protein-ligand interactions.

Understanding biomolecular motion, recognition, and allostery by use of conformational ensembles

We review the role conformational ensembles can play in the analysis of biomolecular dynamics, molecular recognition, and allostery. We introduce currently available methods for generating ensembles of biomolecules and illustrate their application with relevant examples from the literature. We show how, for binding, conformational ensembles provide a way of distinguishing the competing models of induced fit and conformational selection. For allostery we review the classic models and show how conformational ensembles can play a role in unravelling the intricate pathways of communication that enable allostery to occur. Finally, we discuss the limitations of conformational ensembles and highlight some potential applications for the future.

Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings

In order to carry out their functions, proteins often undergo significant conformational fluctuations that enable them to interact with their partners. The accurate characterization of these motions is key in order to understand the mechanisms by which macromolecular recognition events take place. Nuclear magnetic resonance spectroscopy offers a variety of powerful methods to achieve this result. We discuss a method of using residual dipolar couplings as replica-averaged restraints in molecular dynamics simulations to determine large amplitude motions of proteins, including those involved in the conformational equilibria that are established through interconversions between different states. By applying this method to ribonuclease A, we show that it enables one to characterize the ample fluctuations in interdomain orientations expected to play an important functional role.

Towards a robust description of intrinsic protein disorder using nuclear magnetic resonance spectroscopy

In order to understand the conformational behaviour of Intrinsically Disordered Proteins (IDPs), it is essential to develop a molecular representation of the partially folded state. Due to the very large number of degrees of conformational freedom available to such a disordered system, this problem is highly underdetermined. Characterisation therefore requires extensive experimental data, and novel analytical tools are required to exploit the specific conformational sensitivity of different experimental parameters. In this review we concentrate on the use of nuclear magnetic resonance (NMR) spectroscopy for the study of conformational behaviour of IDPs at atomic resolution. Each experimental NMR parameter is sensitive to different aspects of the structural and dynamic behaviour of the disordered state and requires specific consideration of the relevant averaging properties of the physical interaction. In this review we present recent advances in the description of disordered proteins and the selection of representative ensembles on the basis of experimental data using statistical coil sampling from flexible-meccano and ensemble selection using ASTEROIDS. Using these tools we aim to develop a unified molecular representation of the disordered state, combining complementary data sets to extract a meaningful description of the conformational behaviour of the protein.

Gramicidin A backbone and side chain dynamics evaluated by molecular dynamics simulations and nuclear magnetic resonance experiments. I: molecular dynamics simulations

Gramicidin A (gA) channels provide an ideal system to test molecular dynamics (MD) simulations of membrane proteins. The peptide backbone lines a cation-selective pore, and due to the small channel size, the average structure and extent of fluctuations of all atoms in the peptide will influence ion permeation. This raises the question of how well molecular mechanical force fields used in MD simulations and potential of mean force (PMF) calculations can predict structure and dynamics as well as ion permeation. To address this question, we undertook a comparative study of nuclear magnetic resonance (NMR) observables predicted by fully atomistic MD simulations on a gA dimer embedded in a sodium dodecyl sulfate (SDS) micelle with measurements of the gA dimer backbone and tryptophan side chain dynamics using solution-state (15)N NMR on gA dimers in SDS micelles (Vostrikov, V. V.; Gu, H.; Ingólfsson, H. I.; Hinton, J. F.; Andersen, O. S.; Roux, B.; Koeppe, R. E., II. J. Phys. Chem. B2011, DOI 10.1021/jp200906y , accompanying article). This comparison enables us to examine the robustness of the MD simulations done using different force fields as well as their ability to predict important features of the gA channel. We find that MD is able to predict NMR observables, including the generalized order parameters (S(2)), the (15)N spin-lattice (T(1)) and spin-spin (T(2)) relaxation times, and the (1)H-(15)N nuclear Overhauser effect (NOE), with remarkable accuracy. To examine further how differences in the force fields can affect the channel conductance, we calculated the PMF for K(+) and Na(+) permeation through a gA channel in a dimyristoylphosphatidylcholine (DMPC) bilayer. In this case, we find that MD is less successful in quantitatively predicting the single-channel conductance.

Iterative Optimization of Molecular Mechanics Force Fields from NMR Data of Full-Length Proteins

High quality molecular mechanics force fields of proteins are key for the quantitative interpretation of experimental data and the predictive understanding of protein function based on computer simulations. A strategy is presented for the optimization of protein force fields based on full-length proteins in their native environment that is guided by experimental NMR chemical shifts and residual dipolar couplings (RDCs). An energy-based reweighting approach is applied to a long molecular dynamics trajectory, performed with a parent force field, to efficiently screen a large number of trial force fields. The force field that yields the best agreement with the experimental data is then used as the new parent force field, and the procedure is repeated until no further improvement is obtained. This method is demonstrated for the optimization of the backbone φ,ψ dihedral angle potential of the Amber ff99SB force field using six trial proteins and another 17 proteins for cross-validation using (13)C chemical shifts with and without backbone RDCs. The φ,ψ dihedral angle potential is systematically improved by the inclusion of correlation effects through the addition of up to 24 bivariate Gaussian functions of variable height, width, and tilt angle. The resulting force fields, termed ff99SB_φψ(g24;CS) and ff99SB_φψ(g8;CS,RDC), perform significantly better than their parent force field in terms of both NMR data reproduction and Cartesian coordinate root-mean-square deviations between the MD trajectories and the X-ray crystal structures. The strategy introduced here represents a powerful addition to force field optimization approaches by overcoming shortcomings of methods that are solely based on quantum-chemical calculations of small molecules and protein fragments in the gas phase.