Interpreting dynamically-averaged scalar couplings in proteins

On the Validation of Protein Force Fields Based on Structural Criteria

Molecular dynamics simulations depend critically on the quality of the force field used to describe the interatomic interactions and the extent to which it has been validated for use in a specific application. Using a curated test set of 52 high-resolution structures, 39 derived from X-ray diffraction and 13 solved using NMR, we consider the extent to which different parameter sets of the GROMOS protein force field can be distinguished based on comparing a range of structural criteria, including the number of backbone hydrogen bonds, the number of native hydrogen bonds, polar and nonpolar solvent-accessible surface area, radius of gyration, the prevalence of secondary structure elements, J-coupling constants, nuclear Overhauser effect (NOE) intensities, positional root-mean-square deviations (RMSD), and the distribution of backbone ϕ and ψ dihedral angles. It is shown that while statistically significant differences between the average values of individual metrics could be detected, these were in general small. Furthermore, improvements in agreement in one metric were often offset by loss of agreement in another. The work establishes a framework and test set against which protein force fields can be validated. It also highlights the danger of inferring the relative quality of a given force field based on a small range of structural properties or small number of proteins.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Integrating experimental data with molecular simulations to investigate RNA structural dynamics

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule Förster resonance energy transfer, or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field.

Simulating Polyproline II-Helix-Rich Peptides with the Latest Kirkwood-Buff Force Field: A Direct Comparison with AMBER and CHARMM

We simulated the dynamics of a set of peptides characterized by ensembles rich in PPII-helical content, to assess the ability of the most recent Kirkwood-Buff force field (KBFF20) to sample this conformational peculiarity. KBFF has been previously shown to capably reproduce experimental dimensions of disordered proteins, while being limited in confidently sampling structured proteins. Further development of the force field bridged this gap. It is however still unknown what are the main differences between KBFF and AMBER/CHARMM force fields. A direct comparison is now possible as both AMBER/CHARMM force fields have been used to sample peptides rich in PPII-helical content. We found that KBFF20 samples' PPII-helical content qualitatively matches both AMBER and CHARMM force fields, with the main difference being the KBFF ability to populate the α_R region of the Ramachandran plot in the set of simulated peptides. Overall, KBFF20 is a well-balanced force field, able to sample the dynamics of both structured and unstructured proteins.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

Force Field Effects in Simulations of Flexible Peptides with Varying Polyproline II Propensity

Five peptides previously suggested to possess polyproline II (PPII) structure have here been investigated by using atomistic molecular dynamics simulations to compare how well four different force fields known for simulating intrinsically disordered proteins relatively well (Amber ff99SB-disp, Amber ff99SB-ILDN, CHARM36IDPSFF, and CHARMM36m) can capture this secondary structure element. The results revealed that all force fields sample PPII structures but to different extents and with different propensities toward other secondary structure elements, in particular, the β-sheet and "random coils". A cluster analysis of the simulations of histatin 5 also revealed that the conformational ensembles of the force fields are quite different. We compared the simulations to circular dichroism and nuclear magnetic resonance spectroscopy experiments and conclude that further experiments and methods for interpreting them are needed to assess the accuracy of force fields in determining PPII structure.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

The effect of different cutoff schemes in molecular simulations of proteins

Molecular simulations of nanoscale systems invariably involve assumptions and approximations to describe the electrostatic interactions, which are long-ranged in nature. One approach is the use of cutoff schemes with a reaction-field contribution to account for the medium outside the cutoff scheme. Recent reports show that macroscopic properties may depend on the exact choice of cutoff schemes in modern day simulations. In this work, a systematic analysis of the effects of different cutoff schemes was performed using a set of 52 proteins. We find no statistically significant differences between using a twin-range or a single-range cutoff scheme. Applying the cutoff based on charge groups or based on atomic positions, does lead to significant differences, which is traced to the cutoff noise for energies and forces. While group-based cutoff schemes show increased cutoff noise in the potential energy, applying an atomistic cutoff leads to artificial structure in the solvent at the cutoff distance. Carefully setting the temperature control, or using an atomistic cutoff for the solute and a group-based cutoff for the solvent significantly reduces the effects of the cutoff noise, without introducing structure in the solvent. This study aims to deepen the understanding of the implications different cutoffs have on molecular dynamics simulations.

Developing a molecular dynamics force field for both folded and disordered protein states

Many proteins that perform important biological functions are completely or partially disordered under physiological conditions. Molecular dynamics simulations could be a powerful tool for the structural characterization of such proteins, but it has been unclear whether the physical models (force fields) used in simulations are sufficiently accurate. Here, we systematically compare the accuracy of a number of different force fields in simulations of both ordered and disordered proteins, finding that each force field has strengths and limitations. We then describe a force field that substantially improves on the state-of-the-art accuracy for simulations of disordered proteins without sacrificing accuracy for folded proteins, thus broadening the range of biological systems amenable to molecular dynamics simulations.

Molecular dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any physical model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the-art force fields, and compare the results to over 9,000 available experimental data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with experiment for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biological systems amenable to MD simulation. A similar approach could be taken to improve other force fields.

The Exact NOE as an Alternative in Ensemble Structure Determination

The structure-function paradigm is increasingly replaced by the structure-dynamics-function paradigm. All protein activity is steered by the interplay between enthalpy and entropy. Conformational dynamics serves as a proxy of conformational entropy. Therefore, it is essential to study not only the average conformation but also the spatial sampling of a protein on all timescales. To this purpose, we have established a protocol for determining multiple-state ensembles of proteins based on exact nuclear Overhauser effects (eNOEs). We have recently extended our previously reported eNOE data set for the protein GB3 by a very large set of backbone and side-chain residual dipolar couplings and three-bond J couplings. Here, we demonstrate that at least four structural states are required to represent the complete data set by dissecting the contributions to the CYANA target function, which quantifies restraint violations in structure calculation. We present a four-state ensemble of GB3, which largely preserves the characteristics obtained from eNOEs only. Due to the abundance of the input data, the ensemble and χ(1) angles in particular are well suited for cross-validation of the input data and comparison to x-ray structures. Principal component analysis is used to automatically identify and validate relevant states of the ensembles. Overall, our findings suggest that eNOEs are a valuable alternative to traditional NMR probes in spatial elucidation of proteins.

The Dynamic Basis for Signal Propagation in Human Pin1-WW

Allostery is the structural manifestation of information transduction in biomolecules. Its hallmark is conformational change induced by perturbations at a distal site. An increasing body of evidence demonstrates the presence of allostery in very flexible and even disordered proteins, encouraging a thermodynamic description of this phenomenon. Still, resolving such processes at atomic resolution is difficult. Here we establish a protocol to determine atomistic thermodynamic models of such systems using high-resolution solution state nuclear magnetic resonance data and extensive molecular simulations. Using this methodology, we study information transduction in the WW domain of a key cell-cycle regulator Pin1. Pin1 binds promiscuously to phospho-Ser/Thr-Pro motifs, however, disparate structural and dynamic responses have been reported upon binding different ligands. Our model consists of two topologically distinct states whose relative population may be specifically skewed by an incoming ligand. This model provides a canonical basis for the understanding of multi-functionality in Pin1.

Further along the Road Less Traveled: AMBER ff15ipq, an Original Protein Force Field Built on a Self-Consistent Physical Model

We present the AMBER ff15ipq force field for proteins, the second-generation force field developed using the Implicitly Polarized Q (IPolQ) scheme for deriving implicitly polarized atomic charges in the presence of explicit solvent. The ff15ipq force field is a complete rederivation including more than 300 unique atomic charges, 900 unique torsion terms, 60 new angle parameters, and new atomic radii for polar hydrogens. The atomic charges were derived in the context of the SPC/E_b water model, which yields more-accurate rotational diffusion of proteins and enables direct calculation of nuclear magnetic resonance (NMR) relaxation parameters from molecular dynamics simulations. The atomic radii improve the accuracy of modeling salt bridge interactions relative to contemporary fixed-charge force fields, rectifying a limitation of ff14ipq that resulted from its use of pair-specific Lennard-Jones radii. In addition, ff15ipq reproduces penta-alanine J-coupling constants exceptionally well, gives reasonable agreement with NMR relaxation rates, and maintains the expected conformational propensities of structured proteins/peptides, as well as disordered peptides—all on the microsecond (μs) time scale, which is a critical regime for drug design applications. These encouraging results demonstrate the power and robustness of our automated methods for deriving new force fields. All parameters described here and the mdgx program used to fit them are included in the AmberTools16 distribution.

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.

Pushing the limits of signal resolution to make coupling measurement easier

Novel band selective decoupled pure shift selective refocusing experiments allowed simplification of the measurement of all δ¹H, and J_HH couplings with an ultrahigh spectral resolution in peptides.

Ensemble-based interpretations of NMR structural data to describe protein internal dynamics

NMR spectroscopy is the leading technique to characterize protein internal dynamics at the atomic level and on multiple time scales. However, the structural interpretation of the observables obtained by various measurements is not always straightforward and in many cases dynamics-related parameters are only used to “decorate” static structural models without offering explicit description of conformational heterogeneity. To overcome such limitations, several computational techniques have been developed to generate ensemble-based representations of protein structure and dynamics with the use of NMR-derived data. An important common aspect of the methods is that NMR observables and derived parameters are interpreted as properties of the ensemble instead of individual conformers. The resulting ensembles reflect the experimentally determined internal mobility of proteins at a given time scale and can be used to understand the role of internal motions in biological processes at atomic detail. In this review we provide an overview of the calculation methods currently available and examples of biological insights obtained by the ensemble-based models of the proteins investigated.

On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method

An issue of general interest in computer simulations is to incorporate information from experiments into a structural model. An important caveat in pursuing this goal is to avoid corrupting the resulting model with spurious and arbitrary biases. While the problem of biasing thermodynamic ensembles can be formulated rigorously using the maximum entropy method introduced by Jaynes, the approach can be cumbersome in practical applications with the need to determine multiple unknown coefficients iteratively. A popular alternative strategy to incorporate the information from experiments is to rely on restrained-ensemble molecular dynamics simulations. However, the fundamental validity of this computational strategy remains in question. Here, it is demonstrated that the statistical distribution produced by restrained-ensemble simulations is formally consistent with the maximum entropy method of Jaynes. This clarifies the underlying conditions under which restrained-ensemble simulations will yield results that are consistent with the maximum entropy method.

Structural refinement from restrained-ensemble simulations based on EPR/DEER data: application to T4 lysozyme

DEER (double electron-electron resonance) is a powerful pulsed ESR (electron spin resonance) technique allowing the determination of distance histograms between pairs of nitroxide spin-labels linked to a protein in a native-like solution environment. However, exploiting the huge amount of information provided by ESR/DEER histograms to refine structural models is extremely challenging. In this study, a restrained ensemble (RE) molecular dynamics (MD) simulation methodology is developed to address this issue. In RE simulation, the spin-spin distance distribution histograms calculated from a multiple-copy MD simulation are enforced, via a global ensemble-based energy restraint, to match those obtained from ESR/DEER experiments. The RE simulation is applied to 51 ESR/DEER distance histogram data from spin-labels inserted at 37 different positions in T4 lysozyme (T4L). The rotamer population distribution along the five dihedral angles connecting the nitroxide ring to the protein backbone is determined and shown to be consistent with available information from X-ray crystallography. For the purpose of structural refinement, the concept of a simplified nitroxide dummy spin-label is designed and parametrized on the basis of these all-atom RE simulations with explicit solvent. It is demonstrated that RE simulations with the dummy nitroxide spin-labels imposing the ESR/DEER experimental distance distribution data are able to systematically correct and refine a series of distorted T4L structures, while simple harmonic distance restraints are unsuccessful. This computationally efficient approach allows experimental restraints from DEER experiments to be incorporated into RE simulations for efficient structural refinement.

Restrained-ensemble molecular dynamics simulations based on distance histograms from double electron-electron resonance spectroscopy

DEER (double electron-electron resonance) spectroscopy is a powerful pulsed ESR (electron spin resonance) technique allowing the determination of spin-spin distance histograms between site-directed nitroxide label sites on a protein in their native environment. However, incorporating ESR/DEER data in structural refinement is challenging because the information from the large number of distance histograms is complex and highly coupled. Here, a novel restrained-ensemble molecular dynamics simulation method is developed to incorporate the information from multiple ESR/DEER distance histograms simultaneously. Illustrative tests on three coupled spin-labels inserted in T4 lysozyme show that the method efficiently imposes the experimental distance distribution in this system. Different rotameric states of the χ1 and χ2 dihedrals in the spin-labels are also explored by restrained ensemble simulations. Using this method, it is hoped that experimental restraints from ESR/DEER experiments can be used to refine structural properties of biological systems.

PPM: a side-chain and backbone chemical shift predictor for the assessment of protein conformational ensembles

The combination of the wide availability of protein backbone and side-chain NMR chemical shifts with advances in understanding of their relationship to protein structure makes these parameters useful for the assessment of structural-dynamic protein models. A new chemical shift predictor (PPM) is introduced, which is solely based on physical-chemical contributions to the chemical shifts for both the protein backbone and methyl-bearing amino-acid side chains. To explicitly account for the effects of protein dynamics on chemical shifts, PPM was directly refined against 100 ns long molecular dynamics (MD) simulations of 35 proteins with known experimental NMR chemical shifts. It is found that the prediction of methyl-proton chemical shifts by PPM from MD ensembles is improved over other methods, while backbone Cα, Cβ, C', N, and H(N) chemical shifts are predicted at an accuracy comparable to the latest generation of chemical shift prediction programs. PPM is particularly suitable for the rapid evaluation of large protein conformational ensembles on their consistency with experimental NMR data and the possible improvement of protein force fields from chemical shifts.

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.

On the calculation of ³Jαβ-coupling constants for side chains in proteins

Structural knowledge about proteins is mainly derived from values of observables, measurable in NMR spectroscopic or X-ray diffraction experiments, i.e. absorbed or scattered intensities, through theoretically derived relationships between structural quantities such as atom positions or torsional angles on the one hand and observable quantities such as squared structure factor amplitudes, NOE intensities or (3) J-coupling constants on the other. The standardly used relation connecting (3) J-couplings to torsional angles is the Karplus relation, which is used in protein structure refinement as well as in the evaluation of simulated properties of proteins. The accuracy of the simple and generalised Karplus relations is investigated using side-chain structural and (3) J (αβ)-coupling data for three different proteins, Plastocyanin, Lysozyme, and FKBP, for which such data are available. The results show that the widely used Karplus relations are only a rough estimate for the relation between (3) J (αβ)-couplings and the corresponding χ(1)-angle in proteins.

Systematic validation of protein force fields against experimental data

Molecular dynamics simulations provide a vehicle for capturing the structures, motions, and interactions of biological macromolecules in full atomic detail. The accuracy of such simulations, however, is critically dependent on the force field—the mathematical model used to approximate the atomic-level forces acting on the simulated molecular system. Here we present a systematic and extensive evaluation of eight different protein force fields based on comparisons of experimental data with molecular dynamics simulations that reach a previously inaccessible timescale. First, through extensive comparisons with experimental NMR data, we examined the force fields' abilities to describe the structure and fluctuations of folded proteins. Second, we quantified potential biases towards different secondary structure types by comparing experimental and simulation data for small peptides that preferentially populate either helical or sheet-like structures. Third, we tested the force fields' abilities to fold two small proteins—one α-helical, the other with β-sheet structure. The results suggest that force fields have improved over time, and that the most recent versions, while not perfect, provide an accurate description of many structural and dynamical properties of proteins.

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.

A method to explore protein side chain conformational variability using experimental data

Experimentally measured values of molecular properties or observables of biomolecules such as proteins are generally averages over time and space, which do not contain sufficient information to determine the underlying conformational distribution of the molecules in solution. The relationship between experimentally measured NMR (3)J-coupling values and the corresponding dihedral angle values is a particularly complicated case due to its nonlinear, multiple-valued nature. Molecular dynamics (MD) simulations at constant temperature can generate Boltzmann ensembles of molecular structures that are free from a priori assumptions about the nature of the underlying conformational distribution. They suffer, however, from limited sampling with respect to time and conformational space. Moreover, the quality of the obtained structures is dependent on the choice of force field and solvation model. A recently proposed method that uses time-averaging with local-elevation (LE) biasing of the conformational search provides an elegant means of overcoming these three problems. Using a set of side chain (3)J-coupling values for the FK506 binding protein (FKBP), we first investigate the uncertainty in the angle values predicted theoretically. We then propose a simple MD-based technique to detect inconsistencies within an experimental data set and identify degrees of freedom for which conformational averaging takes place or for which force field parameters may be deficient. Finally, we show that LE MD is the best method for producing ensembles of structures that, on average, fit the experimental data.

Analysis of sub-tauc and supra-tauc motions in protein Gbeta1 using molecular dynamics simulations

The functions of proteins depend on the dynamical behavior of their native states on a wide range of timescales. To investigate these dynamics in the case of the small protein Gbeta1, we analyzed molecular dynamics simulations with the model-free approach of nuclear magnetic relaxation. We found amplitudes of fast timescale motions (sub-tau(c), where tau(c) is the rotational correlation time) consistent with S(2) obtained from spin relaxation measurements as well as amplitudes of slow timescale motions (supra-tau(c)) in quantitative agreement with S(2) order parameters derived from residual dipolar coupling measurements. The slow timescale motions are associated with the large variations of the (3)J couplings that follow transitions between different conformational substates. These results provide further characterization of the large structural fluctuations in the native states of proteins that occur on timescales longer than the rotational correlation time.

Observing biological dynamics at atomic resolution using NMR

Biological macromolecules are highly flexible and continually undergo conformational fluctuations on a broad spectrum of timescales. It has long been recognized that dynamics have an important role in the action of these molecules. However, the relationship between molecular function and motion is extremely challenging to delineate, because the conformational space available to macromolecules is vast and the relevant excursions can be infrequent and short-lived. Recent advances in solution nuclear magnetic resonance (NMR) spectroscopy permit biomolecular dynamics to be observed with unprecedented detail. Applications of these new NMR techniques to the study of fundamental processes such as binding and catalysis have provided new insights into how living systems operate at an atomic level.

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

Most experimental methods in structural biology provide time- and ensemble-averaged signals and, consequently, molecular structures based on such signals often exhibit only idealized, average features. Second, most experimental signals are only indirectly related to real, molecular geometries, and solving a structure typically involves a complicated procedure, which may not always result in a unique solution. To what extent do such conformationally-averaged, non-linear experimental signals and structural models derived from them accurately represent the underlying microscopic reality? Are there some structural motifs that are actually artificially more likely to be "seen" in an experiment simply due to the averaging artifact? Finally, what are the practical consequences of ignoring the averaging effects when it comes to functional and mechanistic implications that we try to glean from experimentally-based structural models? In this review, we critically address the work that has been aimed at studying such questions. We summarize the details of experimental methods typically used in structural biology (most notably nuclear magnetic resonance, X-ray crystallography and different types of spectroscopy), discuss their individual susceptibility to conformational (motional) averaging, and review several theoretical approaches, most importantly molecular dynamics simulations that are increasingly being used to aid experimentalists in interpreting structural biology experiments.

Structure and dynamics of the Abeta(21-30) peptide from the interplay of NMR experiments and molecular simulations

We combine molecular dynamics simulations and new high-field NMR experiments to describe the solution structure of the Abeta(21-30) peptide fragment that may be relevant for understanding structural mechanisms related to Alzheimer's disease. By using two different empirical force-field combinations, we provide predictions of the three-bond scalar coupling constants ((3)J(H(N)H(alpha))), chemical-shift values, (13)C relaxation parameters, and rotating-frame nuclear Overhauser effect spectroscopy (ROESY) crosspeaks that can then be compared directly to the same observables measured in the corresponding NMR experiment of Abeta(21-30). We find robust prediction of the (13)C relaxation parameters and medium-range ROESY crosspeaks by using new generation TIP4P-Ew water and Amber ff99SB protein force fields, in which the NMR validates that the simulation yields both a structurally and dynamically correct ensemble over the entire Abeta(21-30) peptide. Analysis of the simulated ensemble shows that all medium-range ROE restraints are not satisfied simultaneously and demonstrates the structural diversity of the Abeta(21-30) conformations more completely than when determined from the experimental medium-range ROE restraints alone. We find that the structural ensemble of the Abeta(21-30) peptide involves a majority population (approximately 60%) of unstructured conformers, lacking any secondary structure or persistent hydrogen-bonding networks. However, the remaining minority population contains a substantial percentage of conformers with a beta-turn centered at Val24 and Gly25, as well as evidence of the Asp23 to Lys28 salt bridge important to the fibril structure. This study sets the stage for robust theoretical work on Abeta(1-40) and Abeta(1-42), for which collection of detailed NMR data on the monomer will be more challenging because of aggregation and fibril formation on experimental timescales at physiological conditions. In addition, we believe that the interplay of modern molecular simulation and high-quality NMR experiments has reached a fruitful stage for characterizing structural ensembles of disordered peptides and proteins in general.

Deciphering protein dynamics from NMR data using explicit structure sampling and selection

Perhaps one of the most prominent realizations of recent years is the critical role that protein dynamics plays in many facets of cellular function. While characterization of protein dynamics is fundamental to our understanding of protein function, the ability to explicitly detect an ensemble of protein conformations from dynamics data is a paramount challenge in structural biology. Here, we report a new computational method, Sample and Select, for determining the ensemble of protein conformations consistent with NMR dynamics data. This method can be generalized and extended to different sources of dynamics data, enabling broad applicability in deciphering protein dynamics at different timescales. The structural ensemble derived from Sample and Select will provide structural and dynamic information that should aid us in understanding and manipulating protein function.

Relation between native ensembles and experimental structures of proteins

Different experimental structures of the same protein or of proteins with high sequence similarity contain many small variations. Here we construct ensembles of "high-sequence similarity Protein Data Bank" (HSP) structures and consider the extent to which such ensembles represent the structural heterogeneity of the native state in solution. We find that different NMR measurements probing structure and dynamics of given proteins in solution, including order parameters, scalar couplings, and residual dipolar couplings, are remarkably well reproduced by their respective high-sequence similarity Protein Data Bank ensembles; moreover, we show that the effects of uncertainties in structure determination are insufficient to explain the results. These results highlight the importance of accounting for native-state protein dynamics in making comparisons with ensemble-averaged experimental data and suggest that even a modest number of structures of a protein determined under different conditions, or with small variations in sequence, capture a representative subset of the true native-state ensemble.