Assessing the effect of conformational averaging on the measured values of observables

Reducing the measurement time of exact NOEs by non-uniform sampling

We have previously reported on the measurement of exact NOEs (eNOEs), which yield a wealth of additional information in comparison to conventional NOEs. We have used these eNOEs in a variety of applications, including calculating high-resolution structures of proteins and RNA molecules. The collection of eNOEs is challenging, however, due to the need to measure a NOESY buildup series consisting of typically four NOESY spectra with varying mixing times in a single measurement session. While the 2D version can be completed in a few days, a fully sampled 3D-NOESY buildup series can take 10 days or more to acquire. This can be both expensive as well as problematic in the case of samples that are not stable over such a long period of time. One potential method to significantly decrease the required measurement time of eNOEs is to use non-uniform sampling (NUS) to decrease the number of points measured in the indirect dimensions. The effect of NUS on the extremely tight distance restraints extracted from eNOEs may be very pronounced. Therefore, we investigated the fidelity of eNOEs measured from three test cases at decreasing NUS densities: the 18.4 kDa protein human Pin1, the 4.1 kDa WW domain of Pin1 (both in 3D), and a 4.6 kDa 14mer RNA UUCG tetraloop (2D). Our results show that NUS imparted negligible error on the eNOE distances derived from good quality data down to 10% sampling for all three cases, but there is a noticeable decrease in the eNOE yield that is dependent upon the underlying sparsity, and thus complexity, of the sample. For Pin1, this transition occurred at roughly 40% while for the WW domain and the UUCG tetraloop it occurred at lower NUS densities of 20% and 10%, respectively. We rationalized these numbers through reconstruction simulations under various conditions. The extent of this loss depends upon the number of scans taken as well as the number of peaks to be reconstructed. Based on these findings, we have created guidelines for choosing an optimal NUS density depending on the number of peaks needed to be reconstructed in the densest region of a 2D or 3D NOESY spectrum.

Functional cross-talk between allosteric effects of activating and inhibiting ligands underlies PKM2 regulation

Several enzymes can simultaneously interact with multiple intracellular metabolites, however, how the allosteric effects of distinct ligands are integrated to coordinately control enzymatic activity remains poorly understood. We addressed this question using, as a model system, the glycolytic enzyme pyruvate kinase M2 (PKM2). We show that the PKM2 activator fructose 1,6-bisphosphate (FBP) alone promotes tetramerisation and increases PKM2 activity, but addition of the inhibitor L-phenylalanine (Phe) prevents maximal activation of FBP-bound PKM2 tetramers. We developed a method, AlloHubMat, that uses eigenvalue decomposition of mutual information derived from molecular dynamics trajectories to identify residues that mediate FBP-induced allostery. Experimental mutagenesis of these residues identified PKM2 variants in which activation by FBP remains intact but cannot be attenuated by Phe. Our findings reveal residues involved in FBP-induced allostery that enable the integration of allosteric input from Phe and provide a paradigm for the coordinate regulation of enzymatic activity by simultaneous allosteric inputs.

Mapping Local Conformational Landscapes of Proteins in Solution

The ability of proteins to adopt multiple conformational states is essential to their function, and elucidating the details of such diversity under physiological conditions has been a major challenge. Here we present a generalized method for mapping protein population landscapes by NMR spectroscopy. Experimental NOESY spectra are directly compared with a set of expectation spectra back-calculated across an arbitrary conformational space. Signal decomposition of the experimental spectrum then directly yields the relative populations of local conformational microstates. In this way, averaged descriptions of conformation can be eliminated. As the method quantitatively compares experimental and expectation spectra, it inherently delivers an R factor expressing how well structural models explain the input data. We demonstrate that our method extracts sufficient information from a single 3D NOESY experiment to perform initial model building, refinement, and validation, thus offering a complete de novo structure determination protocol.

Use of Circular Statistics To Model αMan-(1→2)-αMan and αMan-(1→3)-α/βMan O-Glycosidic Linkage Conformation in 13C-Labeled Disaccharides and High-Mannose Oligosaccharides

A new experimental method, MA' AT analysis, has been applied to investigate the conformational properties of O-glycosidic linkages in several biologically important mannose-containing di- and oligosaccharides. Methyl α-d-mannopyranosyl-(1→2)-α-d-mannopyranoside (2), methyl α-d-mannopyranosyl-(1→3)-α-d-mannopyranoside (3), and methyl α-d-mannopyranosyl-(1→3)-β-d-mannopyranoside (4) were prepared with selective ¹³C-enrichment to enable the measurement of NMR scalar couplings across their internal O-glycosidic linkages. Density functional theory (DFT) was used to parameterize equations for J_CH and J_CC values in 2-4 that are sensitive to phi (ϕ) and psi (ψ). The experimental J-couplings and parameterized equations were treated using a circular statistics algorithm encoded in the MA' AT program. Conformations about ϕ and ψ treated using single-state von Mises models gave excellent fits to the ensembles of redundant J-couplings. Mean values and circular standard deviations (CSDs) for each linkage torsion angle ϕ (CSD) and ψ (CSD) in 2, -29° (25°) and 20° (22°); in 3, -36° (36°) and 8° (27°); in 4, -37° (34°) and 10° (26°); ϕ = H1'-C1'-O1'-CX and ψ = C1'-O1'-CX-HX (CX = aglycone carbon) were compared to histograms obtained from 1 μs aqueous molecular dynamics (MD) simulations and X-ray database statistical analysis. MA' AT-derived models of ψ were in very good agreement with the MD and X-ray data, but not those of ϕ, suggesting a need for force field revision. The effect of structural context on linkage conformation was also investigated in four selectively ¹³C-labeled homomannose tri- and tetrasaccharides using the MA' AT method. In the cases examined, context effects were found to be small.

Improved NOE fitting for flexible molecules based on molecular mechanics data – a case study with S-adenosylmethionine

Using the important biomolecule S-adenosyl methionine as an exemplar, we provide a new, enhanced approach for fitting MD data to high-accuracy NOE data, providing improvements in structure determination.

eNORA2 Exact NOE Analysis Program

We have recently developed an NMR protocol to extract exact distances between nuclei in proteins from an exact interpretation of NOESY buildup intensities (eNOEs). This enabled us to calculate multistate structural ensembles that exhibit realistic spatial sampling and long-range correlations. Our initial studies were laborious and required a deep understanding of the underlying spin dynamics. Here, we present a MatLab package that integrates all data processing steps required to convert intensities of assigned peaks in NOESY series into upper and lower distance limits for structure calculation. Those steps include organization of the data in object format, extraction of autorelaxation and cross-relaxation rate constants by fitting of diagonal peak decays and cross peak buildups, validation of the data, correction for spin diffusion, graphical display of the results, and generation of distance limits in CYANA compatible format. The analysis may be carried out using a full relaxation matrix or a simplified "divide and conquer" approach that allows for partial deuteration of protons. As the program does not require expertise beyond that of standard resonance assignment/structure calculation, it is suitable for experts and nonexperts alike.

How to tackle protein structural data from solution and solid state: An integrated approach

Long-range NMR restraints, such as diamagnetic residual dipolar couplings and paramagnetic data, can be used to determine 3D structures of macromolecules. They are also used to monitor, and potentially to improve, the accuracy of a macromolecular structure in solution by validating or "correcting" a crystal model. Since crystal structures suffer from crystal packing forces they may not be accurate models for the macromolecular structures in solution. However, the presence of real differences should be tested for by simultaneous refinement of the structure using both crystal and solution NMR data. To achieve this, the program REFMAC5 from CCP4 was modified to allow the simultaneous use of X-ray crystallographic and paramagnetic NMR data and/or diamagnetic residual dipolar couplings. Inconsistencies between crystal structures and solution NMR data, if any, may be due either to structural rearrangements occurring on passing from the solution to solid state, or to a greater degree of conformational heterogeneity in solution with respect to the crystal. In the case of multidomain proteins, paramagnetic restraints can provide the correct mutual orientations and positions of domains in solution, as well as information on the conformational variability experienced by the macromolecule.

Monomeric Aβ(1-40) and Aβ(1-42) Peptides in Solution Adopt Very Similar Ramachandran Map Distributions That Closely Resemble Random Coil

The pathogenesis of Alzheimer’s disease is characterized by the aggregation and fibrillation of amyloid peptides Aβ^1–40 and Aβ^1–42 into amyloid plaques. Despite strong potential therapeutic interest, the structural pathways associated with the conversion of monomeric Aβ peptides into oligomeric species remain largely unknown. In particular, the higher aggregation propensity and associated toxicity of Aβ^1–42 compared to that of Aβ^1–40 are poorly understood. To explore in detail the structural propensity of the monomeric Aβ^1–40 and Aβ^1–42 peptides in solution, we recorded a large set of nuclear magnetic resonance (NMR) parameters, including chemical shifts, nuclear Overhauser effects (NOEs), and J couplings. Systematic comparisons show that at neutral pH the Aβ^1–40 and Aβ^1–42 peptides populate almost indistinguishable coil-like conformations. Nuclear Overhauser effect spectra collected at very high resolution remove assignment ambiguities and show no long-range NOE contacts. Six sets of backbone J couplings (³J_HNHα, ³J_C′C′, ³J_C′Hα, ¹J_HαCα, ²J_NCα, and ¹J_NCα) recorded for Aβ^1–40 were used as input for the recently developed MERA Ramachandran map analysis, yielding residue-specific backbone ϕ/ψ torsion angle distributions that closely resemble random coil distributions, the absence of a significantly elevated propensity for β-conformations in the C-terminal region of the peptide, and a small but distinct propensity for α_L at K28. Our results suggest that the self-association of Aβ peptides into toxic oligomers is not driven by elevated propensities of the monomeric species to adopt β-strand-like conformations. Instead, the accelerated disappearance of Aβ NMR signals in D₂O over H₂O, particularly pronounced for Aβ^1–42, suggests that intermolecular interactions between the hydrophobic regions of the peptide dominate the aggregation process.

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.

Information content of long-range NMR data for the characterization of conformational heterogeneity

Long-range NMR data, namely residual dipolar couplings (RDCs) from external alignment and paramagnetic data, are becoming increasingly popular for the characterization of conformational heterogeneity of multidomain biomacromolecules and protein complexes. The question addressed here is how much information is contained in these averaged data. We have analyzed and compared the information content of conformationally averaged RDCs caused by steric alignment and of both RDCs and pseudocontact shifts caused by paramagnetic alignment, and found that, despite the substantial differences, they contain a similar amount of information. Furthermore, using several synthetic tests we find that both sets of data are equally good towards recovering the major state(s) in conformational distributions.

Exploring regions of conformational space occupied by two-domain proteins

The presence of heterogeneity in the interdomain arrangement of several biomolecules is required for their function. Here we present a method to obtain crucial clues to distinguish between different kinds of protein conformational distributions based on experimental NMR data. The method explores subregions of the conformational space and provides both upper and lower bounds of probability for the system to be in each subregion.

The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

Application of the maximum entropy principle to determine ensembles of intrinsically disordered proteins from residual dipolar couplings

We present a method based on the maximum entropy principle that can re-weight an ensemble of protein structures based on data from residual dipolar couplings (RDCs).

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.

Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.

Binding of two intrinsically disordered peptides to a multi-specific protein: a combined Monte Carlo and molecular dynamics study

The unique ability of intrinsically disordered proteins (IDPs) to fold upon binding to partner molecules makes them functionally well-suited for cellular communication networks. For example, the folding-binding of different IDP sequences onto the same surface of an ordered protein provides a mechanism for signaling in a many-to-one manner. Here, we study the molecular details of this signaling mechanism by applying both Molecular Dynamics and Monte Carlo methods to S100B, a calcium-modulated homodimeric protein, and two of its IDP targets, p53 and TRTK-12. Despite adopting somewhat different conformations in complex with S100B and showing no apparent sequence similarity, the two IDP targets associate in virtually the same manner. As free chains, both target sequences remain flexible and sample their respective bound, natively -helical states to a small extent. Association occurs through an intermediate state in the periphery of the S100B binding pocket, stabilized by nonnative interactions which are either hydrophobic or electrostatic in nature. Our results highlight the importance of overall physical properties of IDP segments, such as net charge or presence of strongly hydrophobic amino acids, for molecular recognition via coupled folding-binding.

A substantial fraction of our proteins are believed to be partly or completely disordered, meaning that they contain regions that lack a stable folded structure under typical physiological conditions. This is a feature which plays a key role in their functions. For example, it allows them to have many structurally different binding partners which in turn permits the construction of the intricate signaling and regulatory networks necessary to sustain complex biological organisms such as ourselves. Whereas measuring the binding strengths of associations involving disordered proteins is routine, the binding process itself is today still not fully understood. We use two different computational models to study the interactions of a folded protein, S100B, which can bind various disordered peptides. In particular, we compare two peptides whose structures are known when in complex with S100B. Our results suggest that, although the peptides assume different structures in the bound state, there are similarities in how they associate with S100B. The possibility to computationally model the interplay between proteins is an important complement to experiments, by identifying crucial steps in the binding process. This is essential to understand, e.g., how single mutations sometimes lead to serious diseases.

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.

An improved structural characterisation of reduced French bean plastocyanin based on NMR data and local-elevation molecular dynamics simulation

Deriving structural information about a protein from NMR experimental data is still a non-trivial challenge to computational biochemistry. This is because of the low ratio of the number of independent observables to the number of molecular degrees of freedom, the approximations involved in the different relationships between particular observable quantities and molecular conformation, and the averaged character of the experimental data. For example, protein (3)J-coupling data are seldom used for structure refinement because of the multiple-valuedness and limited accuracy of the Karplus relationship linking a (3)J-coupling to a torsional angle. Moreover, sampling of the large conformational space is still problematic. Using the 99-residue protein plastocyanin as an example we investigated whether use of a thermodynamically calibrated force field, inclusion of solvent degrees of freedom, and application of adaptive local-elevation sampling that accounts for conformational averaging produces a more realistic representation of the ensemble of protein conformations than standard single-structure refinement in a non-explicit solvent using restraints that do not account for averaging and are partly based on non-observed data. Yielding better agreement with observed experimental data, the protein conformational ensemble is less restricted than when using standard single-structure refinement techniques, which are likely to yield a picture of the protein which is too rigid.

Ensemble fits of restrained peptides' conformational equilibria to NMR data. Dependence on force fields: AMBER/8 ff03 versus ECEPP/3

Two variants of NMR-based conformational analyses of flexible peptides are compared using two examples meeting the formula Tyr-D-Daa-Phe-Daa-NH₂ (Daa=diamino acid): 1 combining D-Dab² (α,γ-diaminobutyryl) with Lys⁴, and 2 -D-Dap² (α,β-diaminopropionyl) with Orn⁴. The ω-amino groups of D-Daa² and Daa⁴ are coupled with C=O into the urea, restraining 1 and 2 with 16- and 14-membered rings and leading to potent and impotent μ/δ opioid peptides, respectively. To the current task, we took from an earlier work (Filip et al, J. Pept. Sci. 11 (2005) 347-352) the NMR NOE- and J-data in H₂O/D₂O; and the selection of the ensembles of 1 and 2, 822 and 788 conformational families, respectively, obtained by using the EDMC/ECEPP3 method. Here, we generated ensembles of 1 and 2 using AMBER molecular dynamics in explicit water to eventually selected 686 and 761 conformers for 1 and 2, respectively. We did numbers of fits for both types of the conformational ensembles of 1 and 2 to their NOE- and J-data using a common method i.e. maximum entropy approach (Groth et al, J. Biomol. NMR 15 (1999) 315-330). Both types of the well structurally diversified ensembles fit to quite different equilibria in regressions to common experimental NOE- and J-restraints using maximum entropy principle, which is a disappointing message. Intriguing is startlingly small standard deviation in J-couplings: σ(JNHαH) ≈ 0.01 Hz for LES-MD/AMBER ensemble, contrary to σ(JNHαH) = 0.8 - 1.1 Hz for the EDMC/ECEPP ensemble, over the wide range of entropy, i.e. relatively insensitive to it. A similar feature is not the case when comparing σ(NOE) in both methods. Hence, at minute entropy contributions, it follows that J does or does not transpose "overfitted" into the final σ(J) in the AMBER or ECEPP ensemble, respectively. Could this be an effect of softness of the AMBER flexible-valence force field compared to ECEPP rigid-geometry, and its effect on ensemble sampling? We do not know an answer.

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16-31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 phi torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular alpha-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured (3)J(H(N)-H(Calpha))-coupling constants, indicating that different conformers of GCN4p16-31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and (3)J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and (3)J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16-31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16-31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.

Determination of ensemble-average pairwise root mean-square deviation from experimental B-factors

Root mean-square deviation (RMSD) after roto-translational least-squares fitting is a measure of global structural similarity of macromolecules used commonly. On the other hand, experimental x-ray B-factors are used frequently to study local structural heterogeneity and dynamics in macromolecules by providing direct information about root mean-square fluctuations (RMSF) that can also be calculated from molecular dynamics simulations. We provide a mathematical derivation showing that, given a set of conservative assumptions, a root mean-square ensemble-average of an all-against-all distribution of pairwise RMSD for a single molecular species, <RMSD(2)>(1/2), is directly related to average B-factors (<B>) and <RMSF(2)>(1/2). We show this relationship and explore its limits of validity on a heterogeneous ensemble of structures taken from molecular dynamics simulations of villin headpiece generated using distributed-computing techniques and the Folding@Home cluster. Our results provide a basis for quantifying global structural diversity of macromolecules in crystals directly from x-ray experiments, and we show this on a large set of structures taken from the Protein Data Bank. In particular, we show that the ensemble-average pairwise backbone RMSD for a microscopic ensemble underlying a typical protein x-ray structure is approximately 1.1 A, under the assumption that the principal contribution to experimental B-factors is conformational variability.

Determination of the free energy landscape of alpha-synuclein using spin label nuclear magnetic resonance measurements

Natively unfolded proteins present a challenge for structure determination because they populate highly heterogeneous ensembles of conformations. A useful source of structural information about these states is provided by paramagnetic relaxation enhancement measurements by nuclear magnetic resonance spectroscopy, from which long-range interatomic distances can be estimated. Here we describe a method for using such distances as restraints in molecular dynamics simulations to obtain a mapping of the free energy landscapes of natively unfolded proteins. We demonstrate the method in the case of alpha-synuclein and validate the results by a comparison with electron transfer measurements. Our findings indicate that our procedure provides an accurate estimate of the relative statistical weights of the different conformations populated by alpha-synuclein in its natively unfolded state.

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.

Protein NMR chemical shift calculations based on the automated fragmentation QM/MM approach

An automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach has been developed to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field (SCF) calculations of the NMR chemical shieldings for the mini-protein Trp cage. The root-mean-square errors (RMSEs) for 1H, 13C, and 15N NMR chemical shieldings are equal to or less than 0.09, 0.32, and 0.78 ppm, respectively, for all Hartree-Fock (HF) and density functional theory (DFT) calculations reported in this work. The environmental electrostatic potential is necessary to accurately reproduce the NMR chemical shieldings using the AF-QM/MM approach. The point-charge models provided by AMBER, AM1/CM2, PM3/CM1, and PM3/CM2 all effectively model the electrostatic field. The latter three point-charge models are generated via semiempirical linear-scaling SCF calculations of the entire protein system. The correlations between experimental 1H NMR chemical shifts and theoretical predictions are >0.95 for AF-QM/MM calculations using B3LYP with the 6-31G**, 6-311G**, and 6-311++G** basis sets. Our study, not unexpectedly, finds that conformational changes within a protein structure play an important role in the accurate prediction of experimental NMR chemical shifts from theory.

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.

A coupled equilibrium shift mechanism in calmodulin-mediated signal transduction

We used nuclear magnetic resonance data to determine ensembles of conformations representing the structure and dynamics of calmodulin (CaM) in the calcium-bound state (Ca(2+)-CaM) and in the state bound to myosin light chain kinase (CaM-MLCK). These ensembles reveal that the Ca(2+)-CaM state includes a range of structures similar to those present when CaM is bound to MLCK. Detailed analysis of the ensembles demonstrates that correlated motions within the Ca(2+)-CaM state direct the structural fluctuations toward complex-like substates. This phenomenon enables initial ligation of MLCK at the C-terminal domain of CaM and induces a population shift among the substates accessible to the N-terminal domain, thus giving rise to the cooperativity associated with binding. Based on these results and the combination of modern free energy landscape theory with classical allostery models, we suggest that a coupled equilibrium shift mechanism controls the efficient binding of CaM to a wide range of ligands.

The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.

Determination of conformationally heterogeneous states of proteins

Although conformationally heterogeneous states of proteins are involved in a range of important biological processes, including protein folding and misfolding, and signal transduction, detailed knowledge of their structure and dynamics is still largely missing. Proteins in many of these states are constantly changing shape, such that they are better described as ensembles of conformations rather than in terms of well-defined structures, as is normally the case for native states. Methods in which molecular simulations are combined with experimental measurements are emerging as a powerful route to the accurate determination of the conformational properties of these states of proteins.

Backbone dynamics of human parathyroid hormone (1-34): flexibility of the central region under different environmental conditions

The presence of a stable tertiary structure in the bioactive N-terminal portion of parathyroid hormone (PTH), a major hormone in the maintenance of extracellular calcium homeostasis, is still debated. In this work, 15N relaxation parameters of the 33 backbone amides of human PTH(1-34) were determined in phosphate-buffered saline solution (PBS) and in the presence of dodecylphosphocholine (DPC) micelles. The relaxation parameters were analyzed using both the model-free formalism (G. Lipari and A. Szabo, Journal of the American Chemical Society, 1982, Vol. 104, pp. 4546-4549) and the reduced spectral density functions approach (J.-F. Lefevre, K. T. Dayie, J. W. Peng, and G. Wagner, Biochemistry, 1996, Vol. 35, pp. 2674-2686). In PBS, the region around Gly12 possesses a high degree of flexibility and the C-terminal helix is less flexible than the N-terminal one. In the presence of DPC micelles, the mobility of the entire molecule is reduced, but the stability of the N-terminal helix increases relative to the C-terminal one. A point of relatively higher mobility at residue Gly12 is still present and a new site of local mobility at residues 16-17 is generated. These results justify the lack of experimental nuclear Overhauser effect (NOE) restraints with lack of tertiary structure and support the hypothesis that, in the absence of the receptor, the relative spatial orientation of the two N- and C-terminal helices is undefined. The flexibility in the midregion of PTH(1-34), maintained in the presence of the membrane-mimetic environment, may enable the correct relative disposition of the two helices, favoring a productive interaction with the receptor.

Comparing atomistic simulation data with the NMR experiment: how much can NOEs actually tell us?

Simulated molecular dynamics trajectories of proteins and nucleic acids are often compared with nuclear magnetic resonance (NMR) data for the purposes of assessing the quality of the force field used or, equally important, trying to interpret ambiguous experimental data. In particular, nuclear Overhauser enhancement (NOE) intensities or atom-atom distances derived from them are frequently calculated from the simulated ensembles because the distance restraints derived from NOEs are the key ingredient in NMR-based protein structure determination. In this study, we ask how diverse and nonnative-like an ensemble of structures can be and still match the experimental NOE distance upper bounds well. We present two examples in which simulated ensembles of highly nonnative polypeptide structures (an unfolded state ensemble of the villin headpiece and a high-temperature denatured ensemble of lysozyme) are shown to match fairly well the experimental NOE distance upper bounds from which the corresponding native structures were derived. For example, the unfolded ensemble of villin headpiece, which is on average 0.90 +/- 0.13 nm root-mean-square deviation away from the native NMR structure, deviates from the experimental restraints by only 0.027 nm on average. However, this artificially good agreement is largely a consequence of 1) the highly nonlinear effects of r(-6) (or r(-3)) averaging and 2) focusing only on the experimentally observed set of NOE bounds. Namely, in addition to the experimentally observed NOEs, both simulated ensembles (especially the villin ensemble) also predict a large number of NOEs, which are not seen in the experiment. If these are taken into account, the agreement between simulation and experiment gets markedly worse, as it should, given the nonnative nature of the underlying simulated ensembles. In light of the examples given, we conclude that comparing experimental NOE distance restraints with large simulated ensembles provides just by itself only limited information about the quality of simulation.

Interpreting NMR Data for β-Peptides Using Molecular Dynamics Simulations

NMR is one of the most used techniques to resolve structure of proteins and peptides in solution. However, inconsistencies may occur due to the fact that a polypeptide may adopt more than one conformation. Since the NOE distance bounds and (3)J-values used in such structure determination represent a nonlinear average over the total ensemble of conformers, imposition of NOE or (3)J-value restraints to obtain one unique conformation is not an appropriate procedure in such cases. Here, we show that unrestrained MD simulation of a solute in solution using a high-quality force field yields a conformational ensemble that is largely compatible with the experimental NMR data on the solute. Four 100 ns MD simulations of two forms of a nine-residue beta-peptide in methanol at two temperatures produced conformational ensembles that were used to interpret the NMR data on this molecule and resolve inconsistencies between the experimental NOEs. The protected and unprotected forms of the beta-peptide adopt predominantly a 12/10-helix in agreement with the qualitative interpretation of the NMR data. However, a particular NOE was not compatible with this helix indicating the presence of other conformations. The simulations showed that 3(14)()-helical structures were present in the ensemble of the unprotected form and that their presence correlates with the fulfillment of the particular NOE. Additionally, all inter-hydrogen distances were calculated to compare NOEs predicted by the simulations to the ones observed experimentally. The MD conformational ensembles allowed for a detailed and consistent interpretation of the experimental data and showed the small but specific conformational differences between the protected and unprotected forms of the peptide.

Multiple Loop Conformations of Peptides Predicted by Molecular Dynamics Simulations Are Compatible with Nuclear Magnetic Resonance†

The affinity and selectivity of protein-protein interactions can be fine-tuned by varying the size, flexibility, and amino acid composition of involved surface loops. As a model for such surface loops, we study the conformational landscape of an octapeptide, whose flexibility is chemically steered by a covalent ring closure integrating an azobenzene dye into and by a disulfide bridge additionally constraining the peptide backbone. Because the covalently integrated azobenzene dyes can be switched by light between a bent cis state and an elongated trans state, six cyclic peptide models of strongly different flexibilities are obtained. The conformational states of these peptide models are sampled by NMR and by unconstrained molecular dynamics (MD) simulations. Prototypical conformations and the free-energy landscapes in the high-dimensional space spanned by the phi/psi angles at the peptide backbone are obtained by clustering techniques from the MD trajectories. Multiple open-loop conformations are shown to be predicted by MD particularly in the very flexible cases and are shown to comply with the NMR data despite the fact that such open-loop conformations are missing in the refined NMR structures.

Supramolecular Amyloid-like Assembly of the Polypeptide Sequence Coded by Exon 30 of Human Tropoelastin

Elastin is known to self-aggregate in twisted-rope filaments. However, an ultrastructural organization different from the fibrils typical of elastin, but rather similar to those shown by amyloid networks, is shown by the polypeptide sequence encoded by exon 30 of human tropoelastin. To better understand the molecular properties of this sequence to give amyloid fibers, we used CD, NMR, and FTIR (Fourier transform infrared spectroscopy) to identify the structural characteristics of the peptide. In this study, we have demonstrated, by FTIR, that antiparallel beta-sheet conformation is predominant in the exon 30 fibers. These physical-chemical studies were combined with transmission electron microscopy and atomic force microscopy to analyze the supramolecular structure of the self-assembled aggregate. These studies show the presence of fibrils that interact side-by-side probably originating from an extensive self-interaction of elemental cross beta-structures. Similar sequences, of the general type XGGZG(X, Z = V, L, A, I), are widely found in many proteins such as collagens IV and XVII, major prion protein precursor, amyloid beta A4 precursor protein-binding family, etc., thus suggesting that this sequence could be involved in contributing to the self-assembly of amyloid fibers even in other proteins.

Dissection of human tropoelastin: exon-by-exon chemical synthesis and related conformational studies

Polypeptide sequences encoding the single exons of human tropoelastin were synthesized and their conformations were studied in different solvents and at different temperatures by CD and (1)H NMR. The results demonstrated the presence of labile conformations such as poly-proline II helix (PPII) and beta-turns whose stability is strongly dependent on the microenvironment. Stable, periodic structures, such as alpha-helices, are only present in the poly-alanine cross-linking domains. These findings give a strong experimental basis to the understanding of the molecular mechanism of elasticity of elastin. In particular, they strongly support the description of the native relaxed state of the protein in terms of trans-conformational equilibria between extended and folded structures as previously proposed [Debelle, L., and Tamburro, A. M. (1999) Int. J. Biochem. Cell. Biol. 31, 261-272].

Expected and unexpected results from combined β-hairpin design elements

A model beta-hairpin dodecapeptide [EFGWVpGKWTIK] was designed by including a favorable D-ProGly Type II' beta-turn sequence and a Trp-zip interaction, while also incorporating a beta-strand unfavorable glycine residue in the N-terminal strand. This peptide is highly folded and monomeric in aqueous solution as determined by combined analysis with circular dichroism and 1H NMR spectroscopy. A peptide representing the folded conformation of the model beta-hairpin [cyclic(EFGWVpGKWTIKpG)] and a linear peptide representing the unfolded conformation [EFGWVPGKWTIK] yield unexpected relative deviations between the CD and 1H NMR spectroscopic results that are attributed to variations in the packing interactions of the aromatic side chains. Mutational analysis of the model beta-hairpin indicates that the Trp-zip interaction favors folding and stability relative to an alternate hydrophobic cluster between Trp and Tyr residues [EFGYVpGKWTIK]. The significance of select diagonal interactions in the model beta-hairpin was tested by rearranging the cross-strand hydrophobic interactions to provide a folded peptide [EWFGIpGKTYWK] displaying evidence of an unusual backbone conformation at the hydrophobic cluster. This unusual conformation does not appear to be a result of the glycine residue in the beta-strand, as replacement with a serine results in a peptide [EWFSIpGKTYWK] with a similar and seemingly characteristic CD spectrum. However, an alternate arrangement of hydrophobic residues with a Trp-zip interaction in a similar position to the parent beta-hairpin [EGFWVpGKWITK] results in a folded beta-hairpin conformation. The differences between side chain packing of these peptides precludes meaningful thermodynamic analysis and illustrates the caution necessary when interpreting beta-hairpin folding thermodynamics that are driven, at least in part, by aromatic cross strand interactions.

Assessment of the role of computations in structural biology

Computations are now an integrated part of structural biology and are used in data gathering, data processing, and data storage as well as in a full spectrum of theoretical pursuits. In this review, we focus on areas of great promise and call attention to important issues of internal consistency and error analysis.

Convergence in peptide folding simulation: Multiple trajectories of a potential AIDS pharmacophore

To examine the conformational properties in aqueous solution of a 15-residue peptide that is a potential pharmacophore for AIDS vaccine development, molecular dynamics simulations were performed in water starting from structures determined experimentally in three different organic solvents. Convergence characteristics of the simulation are examined in Cartesian and conformational spaces. In addition, novel analysis tools are employed including a multidimensional scaling method to represent the distance between trajectory frames. As these methods are based on a variety of physical parameters, they provide a useful cross-check on the structural convergence. Theoretical two-dimensional (2D) 1H-NMR spectra are also generated. These are superficially quite different in appearance, demonstrating that backbone similarities difficult to identify by visual inspection of 2D NMR data can be revealed using the methods described here.

Thermotoga maritima IscU. Structural characterization and dynamics of a new class of metallochaperone

Members of the IscU family of proteins are among the most conserved of all protein groups, extending across all three kingdoms of life. IscU serves as a scaffold for the assembly of intermediate iron-sulfur cluster centers and further mediates delivery to apo protein targets. Several proteins that mediate delivery of single metal ions to apo targets (termed metallochaperones) have recently been characterized structurally. Each displays a ferredoxin-like betaalphabetabetaalphabeta motif as a structural core. Assembly and delivery of a polynuclear iron-sulfur cluster is, however, a more complex pathway and presumably would demand a distinctive protein mediator. Here, we demonstrate Thermotoga maritima IscU (Tm IscU) to display unique structural and motional characteristics that distinguish it from other members of this class of proteins. In particular, IscU adopts a mobile, physiologically relevant, molten globule-like state that is vastly different from the previously identified ferredoxin-like fold that has thus far been characterized for other metallochaperones. The secondary structural content of Tm IscU is consistent with previous circular dichroism measurements on apo and holo protein, consisting of six alpha-helices and three beta-strands, the latter forming an anti-parallel beta-sheet. Extensive dynamics studies are consistent with a protein that has reasonably well defined secondary structural elements, but with a tertiary structure that is fluxional among widely different conformational arrangements. Analogous conformational flexibility does not exist in other structurally characterized metallochaperones; however, such a dynamic molecule may account for the lack of long-range NOEs, and allow both for the flexibility that is necessary for the multiple roles of Fe-S cluster assembly, and recognition and delivery of that cluster to a target protein. Additionally, the fluxionality of IscU is unique in that the protein appears to be more compact (based on 1H/2H exchange, R1, R2, and NOE data) but yet more fluid (lack of long-range NOEs) than typical molten globule proteins.

Folding of a highly conserved diverging turn motif from the SH3 domain

Recent NMR structural characterization studies showed that a seven-residue segment (FKKGERL) from the src SH3 domain adopts the nativelike diverging type II beta-turn in aqueous solution in support of the prediction based on the I-sites library of sequence structural motifs. We study the conformational variability and folding/unfolding thermodynamics of this peptide in explicit solvent using replica-exchange molecular dynamics simulations, which greatly enhances the sampling of the conformational space. This peptide samples three main free energy basins (nativelike, intermediate, and unfolded) separated by small barriers. The nativelike basin is fractionally populated (DeltaG(300K) = 0.4 kcal/mol) with structures that satisfy a subset of the NMR-derived constraints. The intrinsic stability of the diverging turn is examined in relationship to the nature of three specific contacts: a turn-hydrogen bond, a mainchain-to-sidechain hydrogen bond, and an end-to-end hydrophobic contact. We have carried out simulations of mutants at the highly conserved GE positions in the sequence. The mutation E5D destabilizes the isolated diverging turn motif, contrary to the observation that this mutation stabilizes the fyn SH3 domain. The G4T mutation also destabilizes the isolated diverging turn; however, the extent of destabilization is smaller than that of the reverse mutation in the drk SH3.

Nascent structure in the kinase anchoring domain of microtubule-associated protein 2

Biological processes are often viewed as highly ordered interactions between well-folded protein domains. The specific interactions exhibited by certain highly abundant neuronal proteins such as microtubule-associated protein 2 (MAP2) and tau stand in stark contrast because these proteins do not show evidence of structure by standard biophysical assays, yet they do bind to specific targets. It is conceivable that there are regions of MAP2 and tau with propensity to form structural domains upon binding a target. To search for evidence of such regions, limited proteolysis experiments were carried out on MAP2c, the smallest MAP2 isoform. Increased protease resistance was observed around the binding site for the RII subunit of cAMP-dependent protein kinase. Protein constructs spanning this region were produced based on the long-lived tryptic fragments Ser44-Arg93 and Ile94-Arg182, and were probed for structure using spectroscopic methods. The results support the existence of regions of nascent structure in the N-terminal region of MAP2c, which are believed to contribute to its regulatory function.