Evaluation of backbone proton positions and dynamics in a small protein by liquid crystal NMR spectroscopy

Quantum Mechanical Study of Vicinal J Spin-Spin Coupling Constants for the Protein Backbone

We have performed densisty functional theory (DFT) calculations of vicinal J coupling constants involving the backbone torsional angle for the protein GB3 using our recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach (Xiao He et al. J. Phys. Chem. B 2009, 113, 10380-10388). Interestingly, the calculated values based on an NMR structure are more accurate than those based on a high-resolution X-ray strucure because the NMR structure was refined using a large number of residual dipolar couplings (RDCs) whereas the hydrogen atoms were added into the X-ray structure in idealized positions, confirming that the postioning of the hydrogen atoms relative to the backbone atoms is important to the accuracy of J coupling constant prediction. By comparing three Karplus equations, our results have demonstrated that hydrogen bonding, substituent and electrostatic effects could have significant impacts on vicinal J couplings even though they depend mostly on the intervening dihedral angles. The root-mean-square deviations (RMSDs) of the calculated (3)J(H(N),H(α)), (3)J(H(N),C(β)), (3)J(H(N),C') values based on the NMR structure are 0.52, 0.25, and 0.35 Hz, respectively, after taking the dynamic effect into consideration. The excellent accuracy demonstrates that our AF-QM/MM approach is a useful tool to study the relationship between J coupling constants and the structure and dynamics of proteins.

Transmembrane and Juxtamembrane Structure of αL Integrin in Bicelles

The accepted model for the interaction of α and β integrins in the transmembrane (TM) domain is based on the pair αIIbβ3. This involves the so-called outer and inner membrane association clasps (OMC and IMC, respectively). In the α chain, the OMC involves a GxxxG-like motif, whereas in the IMC a conserved juxtamembrane GFFKR motif experiences a backbone reversal that partially fills the void generated by TM separation towards the cytoplasmic half. However, the GFFKR motif of several α integrin cytoplasmic tails in non-bicelle environments has been shown to adopt an α-helical structure that is not membrane-embedded and which was shown to bind a variety of cytoplasmic proteins. Thus it is not known if a membrane-embedded backbone reversal is a conserved structural feature in α integrins. We have studied the system αLβ2 because of its importance in leukocytes, where integrin deactivation is particularly important. Herein we show that the backbone reversal feature is not only present in αIIb but also in αL-TM when reconstituted in bicelles. Additionally, titration with β2 TM showed eight residues clustering along one side of αL-TM, forming a plausible interacting face with β2. The latter orientation is consistent with a previously predicted reported polar interaction between αL Ser-1071 and β2 Thr-686.

Probing the effects of cysteine residues on protein adsorption onto gold nanoparticles using wild-type and mutated GB3 proteins

The role of cysteine residues in the protein binding kinetics and stability on gold nanoparticles (AuNP) was studied using AuNP localized surface plasmon resonance (LSPR) in combination with an organothiol (OT) displacement method. GB3, the third IgG-binding domain of protein G, was used to model protein-AuNP adsorption. While wild-type GB3 (GB30) contains no cysteine residues, bioengineered GB3 variants containing one (GB31) and two (GB32) cysteine residues were also tested. The cysteine content has no significant effect on GB3 binding kinetics with AuNPs, and most protein adsorption occurs within the first few seconds upon protein/AuNP mixing. However, the stability of GB3 on the AuNP surface against OT displacement depends strongly on the cysteine content and the age of the AuNP/GB3 mixture. The GB30 covered AuNPs can be completely destabilized and aggregated by OTs, regardless of the age of the GB30/AuNP mixtures. Long-time incubation of GB31 or GB32 with AuNPs can stabilize AuNPs against the OT adsorption inducted aggregation. This study indicates that multiple forces involved in the GB3/AuNP interaction, and covalent binding between cysteine and AuNP is essential for a stable protein/AuNP complex.

Protein structure validation and identification from unassigned residual dipolar coupling data using 2D-PDPA

More than 90% of protein structures submitted to the PDB each year are homologous to some previously characterized protein structure. The extensive resources that are required for structural characterization of proteins can be justified for the 10% of the novel structures, but not for the remaining 90%. This report presents the 2D-PDPA method, which utilizes unassigned residual dipolar coupling in order to address the economics of structure determination of routine proteins by reducing the data acquisition and processing time. 2D-PDPA has been demonstrated to successfully identify the correct structure of an array of proteins that range from 46 to 445 residues in size from a library of 619 decoy structures by using unassigned simulated RDC data. When using experimental data, 2D-PDPA successfully identified the correct NMR structures from the same library of decoy structures. In addition, the most homologous X-ray structure was also identified as the second best structural candidate. Finally, success of 2D-PDPA in identifying and evaluating the most appropriate structure from a set of computationally predicted structures in the case of a previously uncharacterized protein Pf2048.1 has been demonstrated. This protein exhibits less than 20% sequence identity to any protein with known structure and therefore presents a compelling and practical application of our proposed work.

The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Development of the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and side chain torsional parameters were determined by comparing to gas-phase QM (RI-TRIM MP2/CBS) conformational energies of dipeptides and to statistical distributions from the Protein Data Bank. Molecular dynamics simulations are reported for short peptides in explicit water to examine their conformational properties in solution. Overall the calculated conformational free energies and J-coupling constants are consistent with PDB statistics and experimental NMR results, respectively. In addition, the experimental crystal structures of a number of proteins are well maintained during molecular dynamics (MD) simulation. While further calculations are necessary to fully validate the force field, initial results suggest the AMOEBA polarizable multipole force field is able to describe the structure and energetics of peptides and proteins, in both gas-phase and solution environments.

Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics

The use of free-energy landscapes rationalizes a wide range of aspects of protein behavior by providing a clear illustration of the different states accessible to these molecules, as well as of their populations and pathways of interconversion. The determination of the free-energy landscapes of proteins by computational methods is, however, very challenging as it requires an extensive sampling of their conformational spaces. We describe here a technique to achieve this goal with relatively limited computational resources by incorporating nuclear magnetic resonance (NMR) chemical shifts as collective variables in metadynamics simulations. As in this approach the chemical shifts are not used as structural restraints, the resulting free-energy landscapes correspond to the force fields used in the simulations. We illustrate this approach in the case of the third Ig-binding domain of protein G from streptococcal bacteria (GB3). Our calculations reveal the existence of a folding intermediate of GB3 with nonnative structural elements. Furthermore, the availability of the free-energy landscape enables the folding mechanism of GB3 to be elucidated by analyzing the conformational ensembles corresponding to the native, intermediate, and unfolded states, as well as the transition states between them. Taken together, these results show that, by incorporating experimental data as collective variables in metadynamics simulations, it is possible to enhance the sampling efficiency by two or more orders of magnitude with respect to standard molecular dynamics simulations, and thus to estimate free-energy differences among the different states of a protein with a k(B)T accuracy by generating trajectories of just a few microseconds.

Modulating alignment of membrane proteins in liquid-crystalline and oriented gel media by changing the size and charge of phospholipid bicelles

We demonstrate that alignment of a structured peptide or small protein solubilized in mixed phospholipid:detergent micelles or bicelles, when embedded in a compressed gel or liquid crystalline medium, can be altered by either changing the phospholipid aggregate shape, charge, or both together. For the hemagglutinin fusion peptide solubilized in bicelles, we show that bicelle shape and charge do not change its helical hairpin structure but impact its alignment relative to the alignment medium, both in charged compressed acrylamide gel and in liquid crystalline d(GpG). The method can be used to generate sets of residual dipolar couplings that correspond to orthogonal alignment tensors, and holds promise for high-resolution structural refinement and dynamic mapping of membrane proteins.

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

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

Automated Fragmentation QM/MM Calculation of Amide Proton Chemical Shifts in Proteins with Explicit Solvent Model

We have performed a density functional theory (DFT) calculation of the amide proton NMR chemical shift in proteins using a recently developed automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. Systematic investigation was carried out to examine the influence of explicit solvent molecules, cooperative hydrogen bonding effects, density functionals, size of the basis sets, and the local geometry of proteins on calculated chemical shifts. Our result demonstrates that the predicted amide proton ((1)HN) NMR chemical shift in explicit solvent shows remarkable improvement over that calculated with the implicit solvation model. The cooperative hydrogen bonding effect is also shown to improve the accuracy of (1)HN chemical shifts. Furthermore, we found that the OPBE exchange-correlation functional is the best density functional for the prediction of protein (1)HN chemical shifts among a selective set of DFT methods (namely, B3LYP, B3PW91, M062X, M06L, mPW1PW91, OB98, OPBE), and the locally dense basis set of 6-311++G**/4-31G* is shown to be sufficient for (1)HN chemical shift calculation. By taking ensemble averaging into account, (1)HN chemical shifts calculated by the AF-QM/MM approach can be used to validate the performance of various force fields. Our study underscores that the electronic polarization of protein is of critical importance to stabilizing hydrogen bonding, and the AF-QM/MM method is able to describe the local chemical environment in proteins more accurately than most widely used empirical models.

Solution NMR spectroscopy for the determination of structures of membrane proteins in a lipid environment

Several recent advancements have transformed solution NMR spectroscopy into a competitive, elegant, and eminently viable technique for determining the solution structures of membrane proteins at the level of atomic resolution. Once a good level of cell-based or cell-free expression and purification of a suitably sized membrane protein has been achieved, then NMR offers a combination of several versatile strategies, for example, choice of appropriate deuterated or non-deuterated detergents, temperature, and ionic strength; isotope labelling with (2)H, (13)C, (15)N, with or without protonation of Ile (δ1), Leu, and Val methyl protons; combinatorial labelling of specific amino acids; transverse relaxation-optimized NMR spectroscopy-based, Nonuniform sampling-based, and other NMR experiments; measurement of residual dipolar couplings using stretched polyacrylamide gels or DNA nanotubes; and spin-labelling and paramagnetic relaxation enhancements. Strategic combinations of these advancements together with availability of highly sensitive cryogenically cooled probes equipped high-field NMR spectrometers (up to 1 GHz (1)H frequency) have allowed the perseverant investigator to successfully overcome several of the conventional pitfalls associated with the NMR technique and membrane proteins, viz., low sensitivity, poor sample stability, spectral crowding, and a limited number of NOEs and other constraints for structure calculations. This has resulted in an unprecedented growth in the number of successfully determined NMR structures of large and complex membrane proteins, and this technique now holds great promise for the structure determination of an ever larger body of membrane proteins.

Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles

While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large number of applications, limitations in the model with respect to the equilibrium between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non Gly, Pro) backbone CMAP potential has been refined against experimental solution NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mechanical energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mechanical energy surfaces, followed by additional empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against data not used to guide parametrization: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equilibrium folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for the modeling and simulation studies of proteins, including studies of protein folding, assembly and functionally relevant conformational changes.

Very large residual dipolar couplings from deuterated ubiquitin

Main-chain (1)H(N)-(15)N residual dipolar couplings (RDCs) ranging from approximately -200 to 200 Hz have been measured for ubiquitin under strong alignment conditions in Pf1 phage. This represents a ten-fold increase in the degree of alignment over the typical weakly aligned samples. The measurements are made possible by extensive proton-dilution of the sample, achieved by deuteration of the protein with partial back-substitution of labile protons from 25 % H(2)O / 75 % D(2)O buffer. The spectral quality is further improved by application of deuterium decoupling. Since standard experiments using fixed-delay INEPT elements cannot accommodate a broad range of couplings, the measurements were conducted using J-resolved and J-modulated versions of the HSQC and TROSY sequences. Due to unusually large variations in dipolar couplings, the trosy (sharp) and anti-trosy (broad) signals are often found to be interchanged in the TROSY spectra. To distinguish between the two, we have relied on their respective (15)N linewidths. This strategy ultimately allowed us to determine the signs of RDCs. The fitting of the measured RDC values to the crystallographic coordinates of ubiquitin yields the quality factor Q = 0.16, which confirms the perturbation-free character of the Pf1 alignment. Our results demonstrate that RDC data can be successfully acquired not only in dilute liquid crystals, but also in more concentrated ones. As a general rule, the increase in liquid crystal concentration improves the stability of alignment media and makes them more tolerant to variations in sample conditions. The technical ability to measure RDCs under moderately strong alignment conditions may open the door for development of alternative alignment media, including new types of media that mimic biologically relevant systems.

Construction of covalent membrane protein complexes and high-throughput selection of membrane mimics

The association of transmembrane (TM) helices underlies membrane protein structure and folding. Structural studies of TM complexes are limited by complex stability and the often time-consuming selection of suitable membrane mimics. Here, methodology for the efficient, preparative scale construction of covalent TM complexes and the concomitant high-throughput selection of membrane mimics is introduced. For the employed integrin αIIbβ3 model system, the methodology identified phospholipid bicelles, including their specific composition, as the best membrane mimic. The method facilitates structure determination by NMR spectroscopy as exemplified by the measurement of previously inaccessible residual dipolar couplings and (15)N relaxation parameters.

Imino hydrogen positions in nucleic acids from density functional theory validated by NMR residual dipolar couplings

Hydrogen atom positions of nucleotide bases in RNA structures solved by X-ray crystallography are commonly derived from heavy-atom coordinates by assuming idealized geometries. In particular, N1-H1 vectors in G and N3-H3 vectors in U are commonly positioned to coincide with the bisectors of their respective heavy-atom angles. We demonstrate that quantum-mechanical optimization of the hydrogen positions relative to their heavy-atom frames considerably improves the fit of experimental residual dipolar couplings to structural coordinates. The calculations indicate that deviations of the imino N-H vectors in RNA U and G bases result from H-bonding within the base pair and are dominated by the attractive interaction between the H atom and the electron density surrounding the H-bond-acceptor atom. DFT optimization of H atom positions is impractical in structural biology studies. We therefore have developed an empirical relation that predicts imino N-H vector orientations from the heavy-atom coordinates of the base pair. This relation agrees very closely with the DFT results, permitting its routine application in structural studies.

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.

Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson-Boltzmann) model. Our calculated chemical shifts of (1)H and (13)C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of (15)N, the results do not agree with experimental values as well as (1)H and (13)C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for (13)C(α) atoms in proteins, and using the (1)H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.

Protein loop closure using orientational restraints from NMR data

Protein loops often play important roles in biological functions. Modeling loops accurately is crucial to determining the functional specificity of a protein. Despite the recent progress in loop prediction approaches, which led to a number of algorithms over the past decade, few rigorous algorithmic approaches exist to model protein loops using global orientational restraints, such as those obtained from residual dipolar coupling (RDC) data in solution nuclear magnetic resonance (NMR) spectroscopy. In this article, we present a novel, sparse data, RDC-based algorithm, which exploits the mathematical interplay between RDC-derived sphero-conics and protein kinematics, and formulates the loop structure determination problem as a system of low-degree polynomial equations that can be solved exactly, in closed-form. The polynomial roots, which encode the candidate conformations, are searched systematically, using provable pruning strategies that triage the vast majority of conformations, to enumerate or prune all possible loop conformations consistent with the data; therefore, completeness is ensured. Results on experimental RDC datasets for four proteins, including human ubiquitin, FF2, DinI, and GB3, demonstrate that our algorithm can compute loops with higher accuracy, a three- to six-fold improvement in backbone RMSD, versus those obtained by traditional structure determination protocols on the same data. Excellent results were also obtained on synthetic RDC datasets for protein loops of length 4, 8, and 12 used in previous studies. These results suggest that our algorithm can be successfully applied to determine protein loop conformations, and hence, will be useful in high-resolution protein backbone structure determination, including loops, from sparse NMR data. Proteins 2012. © 2011 Wiley Periodicals, Inc.

SRLS analysis of 15N spin relaxation from E. coli ribonuclease HI: the tensorial perspective

15N–H relaxation parameters from ribonuclease HI (RNase H), acquired in previous work at magnetic fields of 14.1 and 18.8 T, and at 300 K, are analyzed with the mode-coupling slowly relaxing local structure (SRLS) approach. In accordance with standard theoretical treatments of restricted motions, SRLS approaches N-H bond dynamics from a tensorial perspective. As shown previously, a physically adequate description of this phenomenon has to account for the asymmetry of the local spatial restrictions. So far, we used rhombic local ordering tensors; this is straightforward but computationally demanding. Here, we propose substantiating the asymmetry of the local spatial restrictions in terms of tilted axial local ordering (S) and local diffusion (D2) tensors. Although less straightforward, this description provides physically sound structural and dynamic information and is efficient computationally. We find that the local order parameter, S(0)2, is on average 0.89 (0.84, and may be as small as 0.6) for the secondary structure elements (loops). The main local ordering axis deviates from the C(i-1)α-C(i)α axis by less than 6°. At 300 K, D(2,perpendicular) is virtually the same as the global diffusion rate, D1 = 1.8 × 10(7) s(-1). The correlation time 1/6D(2,parallel) ranges from 3-125 (208-344) ps for the secondary structure elements (loops) and is on average 125 ps for the C-terminal segment. The main local diffusion axis deviates from the N-H bond by less than 2° (10°) for the secondary structure elements (loops). An effective data-fitting protocol, which leads in most cases to unambiguous results with limited uncertainty, has been devised. A physically sound and computationally effective methodology for analyzing 15N relaxation in proteins, that provides a new picture of N–H bond structural dynamics in proteins, has been set forth.

An environment-dependent structural switch underlies the regulation of carnitine palmitoyltransferase 1A

The enzyme carnitine palmitoyltransferase 1 (CPT1), which is anchored in the outer mitochondrial membrane (OMM), controls the rate-limiting step in fatty acid β-oxidation in mammalian tissues. It is inhibited by malonyl-CoA, the first intermediate of fatty acid synthesis, and it responds to OMM curvature and lipid characteristics, which reflect long term nutrient/hormone availability. Here, we show that the N-terminal regulatory domain (N) of CPT1A can adopt two complex amphiphilic structural states, termed Nα and Nβ, that interchange in a switch-like manner in response to offered binding surface curvature. Structure-based site-directed mutageneses of native CPT1A suggest Nα to be inhibitory and Nβ to be noninhibitory, with the relative Nα/Nβ ratio setting the prevalent malonyl-CoA sensitivity of the enzyme. Based on the amphiphilic nature of N and molecular modeling, we propose malonyl-CoA sensitivity to be coupled to the properties of the OMM by Nα-OMM associations that alter the Nα/Nβ ratio. For enzymes residing at the membrane-water interface, this constitutes an integrative regulatory mechanism of exceptional sophistication.

Peptide bond distortions from planarity: new insights from quantum mechanical calculations and peptide/protein crystal structures

By combining quantum-mechanical analysis and statistical survey of peptide/protein structure databases we here report a thorough investigation of the conformational dependence of the geometry of peptide bond, the basic element of protein structures. Different peptide model systems have been studied by an integrated quantum mechanical approach, employing DFT, MP2 and CCSD(T) calculations, both in aqueous solution and in the gas phase. Also in absence of inter-residue interactions, small distortions from the planarity are more a rule than an exception, and they are mainly determined by the backbone ψ dihedral angle. These indications are fully corroborated by a statistical survey of accurate protein/peptide structures. Orbital analysis shows that orbital interactions between the σ system of C(α) substituents and the π system of the amide bond are crucial for the modulation of peptide bond distortions. Our study thus indicates that, although long-range inter-molecular interactions can obviously affect the peptide planarity, their influence is statistically averaged. Therefore, the variability of peptide bond geometry in proteins is remarkably reproduced by extremely simplified systems since local factors are the main driving force of these observed trends. The implications of the present findings for protein structure determination, validation and prediction are also discussed.

Domain cooperativity in multidomain proteins: what can we learn from molecular alignment in anisotropic media?

Many proteins have modular design with multiple globular domains connected via flexible linkers. As a simple model of such system, we study a tandem construct consisting of two identical SH3 domains and a variable-length Gly/Ser linker. When the linker is short, this construct represents a dumbbell-shaped molecule with limited amount of domain-domain mobility. Due to its elongated shape, this molecule efficiently aligns in steric alignment media. As the length of the linker increases, the two domains become effectively uncoupled and begin to behave as independent entities. Consequently, their degree of alignment drops, approaching that found in the (near-spherical) isolated SH3 domains. To model the dependence of alignment parameters on the length of the interdomain linker, we have generated in silico a series of conformational ensembles representing SH3 tandems with different linker length. These ensembles were subsequently used as input for alignment prediction software PALES. The predicted alignment tensors were compared with the results of experimental measurements using a series of tandem-SH3 samples in PEG/hexanol alignment media. This comparison broadly confirmed the expected trends. At the same time, it has been found that the isolated SH3 domain aligns much stronger than expected. This finding can be attributed to complex morphology of the PEG/hexanol media and/or to weak site-specific interactions between the protein and the media. In the latter case, there are strong indications that electrostatic interactions may play a role. The fact that PEG/hexanol does not behave as a simple steric media should serve as a caution for studies that use PALES as a quantitative prediction tool (especially for disordered proteins). Further progress in this area depends on our ability to accurately model the anisotropic media and its site-specific interactions with protein molecules. Once this ability is improved, it should be possible to use the alignment parameters as a measure of domain-domain cooperativity, thus identifying the situations where two domains transiently interact with each other or become coupled through a partially structured linker.

Backbone resonance assignment and order tensor estimation using residual dipolar couplings

An NMR investigation of proteins with known X-ray structures is of interest in a number of endeavors. Performing these studies through nuclear magnetic resonance (NMR) requires the costly step of resonance assignment. The prevalent assignment strategy does not make use of existing structural information and requires uniform isotope labeling. Here we present a rapid and cost-effective method of assigning NMR data to an existing structure-either an X-ray or computationally modeled structure. The presented method, Exhaustively Permuted Assignment of RDCs (EPAR), utilizes unassigned residual dipolar coupling (RDC) data that can easily be obtained by NMR spectroscopy. The algorithm uses only the backbone N-H RDCs from multiple alignment media along with the amino acid type of the RDCs. It is inspired by previous work from Zweckstetter and provides several extensions. We present results on 13 synthetic and experimental datasets from 8 different structures, including two homodimers. Using just two alignment media, EPAR achieves an average assignment accuracy greater than 80%. With three media, the average accuracy is higher than 94%. The algorithm also outputs a prediction of the assignment accuracy, which has a correlation of 0.77 to the true accuracy. This prediction score can be used to establish the needed confidence in assignment accuracy.

How uniform is the peptide plane geometry? A high-accuracy NMR study of dipolar Cα-C'/H N-N cross-correlated relaxation

Highly precise and accurate measurements of very small NMR cross-correlated relaxation rates, namely those between protein H (i) (N) -N(i) and C (i-1) (α) -C(i-1)' dipoles, are demonstrated with an error of 0.03 s(-1) for GB3. Because the projection angles between the two dipole vectors are very close to the magic angle the rates range only from -0.2 to +0.2 s(-1). Small changes of the average vector orientations have a dramatic impact on the relative values. The rates suggest deviation from idealized peptide plane geometry caused by twists around the C'-N bonds and/or pyramidalization of the nitrogen atoms. A clear alternating pattern along the sequence is observed in β strands 1, 3 and 4 of GB3, where the side chains of almost all residues with large positive rates are solvent exposed. In the α helix all rates are relatively large and positive. Some of the currently most accurate structures of GB3 determined by both high resolution X-ray crystallography and NMR are in satisfactory agreement with the experimental rates in the helix and β strand 3, but not in the loops and the two central strands of the sheet for which no alternating pattern is predicted.

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

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

Density functional calculations of backbone 15N shielding tensors in beta-sheet and turn residues of protein G

We performed density functional calculations of backbone (15)N shielding tensors in the regions of beta-sheet and turns of protein G. The calculations were carried out for all twenty-four beta-sheet residues and eight beta-turn residues in the protein GB3 and the results were compared with the available experimental data from solid-state and solution NMR measurements. Together with the alpha-helix data, our calculations cover 39 out of the 55 residues (or 71%) in GB3. The applicability of several computational models developed previously (Cai et al. in J Biomol NMR 45:245-253, 2009) to compute (15)N shielding tensors of alpha-helical residues is assessed. We show that the proposed quantum chemical computational model is capable of predicting isotropic (15)N chemical shifts for an entire protein that are in good correlation with experimental data. However, the individual components of the predicted (15)N shielding tensor agree with experiment less well: the computed values show much larger spread than the experimental data, and there is a profound difference in the behavior of the tensor components for alpha-helix/turns and beta-sheet residues. We discuss possible reasons for this.

Dioxygen transmembrane distributions and partitioning thermodynamics in lipid bilayers and micelles

Cellular respiration, mediated by the passive diffusion of oxygen across lipid membranes, is key to many basic cellular processes. In this work, we report the detailed distribution of oxygen across lipid bilayers and examine the thermodynamics of oxygen partitioning via NMR studies of lipids in a small unilamellar vesicle (SUV) morphology. Dissolved oxygen gives rise to paramagnetic chemical shift perturbations and relaxation rate enhancements, both of which report on local oxygen concentration. From SUVs containing the phospholipid sn-2-perdeuterio-1-myristelaidoyl, 2-myristoyl-sn-glycero-3-phosphocholine (MLMPC), an analogue of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), we deduced the complete trans-bilayer oxygen distribution by measuring (13)C paramagnetic chemical shifts perturbations for 18 different sites on MLMPC arising from oxygen at a partial pressure of 30 bar. The overall oxygen solubility at 45 °C spans a factor of 7 between the bulk water (23.7 mM) and the bilayer center (170 mM) and is lowest in the vicinity of the phosphocholine headgroup, suggesting that oxygen diffusion across the glycerol backbone should be the rate-limiting step in diffusion-mediated passive transport of oxygen across the lipid bilayer. Lowering of the temperature from 45 to 25 °C gave rise to a slight decrease of the oxygen solubility within the hydrocarbon interior of the membrane. An analysis of the temperature dependence of the oxygen solubility profile, as measured by (1)H paramagnetic relaxation rate enhancements, reveals that oxygen partitioning into the bilayer is entropically favored (ΔS° = 54 ± 3 J K(-1) mol(-1)) and must overcome an enthalpic barrier (ΔH° = 12.0 ± 0.9 kJ mol(-1)).

Impact of 15N R2/R1 relaxation restraints on molecular size, shape, and bond vector orientation for NMR protein structure determination with sparse distance restraints

(15)N R(2)/R(1) relaxation data contain information on molecular shape and size as well as on bond vector orientations relative to the diffusion tensor. Since the diffusion tensor can be directly calculated from the molecular coordinates, direct inclusion of (15)N R(2)/R(1) restraints in NMR structure calculations without any a priori assumptions is possible. Here we show that (15)N R(2)/R(1) restraints are particularly valuable when only sparse distance restraints are available. Using three examples of proteins of varying size, namely, GB3 (56 residues), ubiquitin (76 residues), and the N-terminal domain of enzyme I (EIN, 249 residues), we show that incorporation of (15)N R(2)/R(1) restraints results in large and significant increases in coordinate accuracy that can make the difference between being able or unable to determine an approximate global fold. For GB3 and ubiquitin, good coordinate accuracy was obtained using only backbone hydrogen-bond restraints supplemented by (15)N R(2)/R(1) relaxation restraints. For EIN, the global fold could be determined using sparse nuclear Overhauser enhancement (NOE) distance restraints involving only NH and methyl groups in conjunction with (15)N R(2)/R(1) restraints. These results are of practical significance in the study of larger and more complex systems, where the increasing spectral complexity and number of chemical shift degeneracies reduce the number of unambiguous NOE assignments that can be readily obtained, resulting in progressively reduced NOE coverage as the size of the protein increases.

Nuclear magnetic resonance provides a quantitative description of protein conformational flexibility on physiologically important time scales

A complete description of biomolecular activity requires an understanding of the nature and the role of protein conformational dynamics. In recent years, novel nuclear magnetic resonance-based techniques that provide hitherto inaccessible detail concerning biomolecular motions occurring on physiologically important time scales have emerged. Residual dipolar couplings (RDCs) provide precise information about time- and ensemble-averaged structural and dynamic processes with correlation times up to the millisecond and thereby encode key information for understanding biological activity. In this review, we present the application of two very different approaches to the quantitative description of protein motion using RDCs. The first is purely analytical, describing backbone dynamics in terms of diffusive motions of each peptide plane, using extensive statistical analysis to validate the proposed dynamic modes. The second is based on restraint-free accelerated molecular dynamics simulation, providing statistically sampled free energy-weighted ensembles that describe conformational fluctuations occurring on time scales from pico- to milliseconds, at atomic resolution. Remarkably, the results from these two approaches converge closely in terms of distribution and absolute amplitude of motions, suggesting that this kind of combination of analytical and numerical models is now capable of providing a unified description of protein conformational dynamics in solution.

Three-dimensional structure of the weakly associated protein homodimer SeR13 using RDCs and paramagnetic surface mapping

The traditional NMR-based method for determining oligomeric protein structure usually involves distinguishing and assigning intra- and intersubunit NOEs. This task becomes challenging when determining symmetric homo-dimer structures because NOE cross-peaks from a given pair of protons occur at the same position whether intra- or intersubunit in origin. While there are isotope-filtering strategies for distinguishing intra from intermolecular NOE interactions in these cases, they are laborious and often prove ineffectual in cases of weak dimers, where observation of intermolecular NOEs is rare. Here, we present an efficient procedure for weak dimer structure determination based on residual dipolar couplings (RDCs), chemical shift changes upon dilution, and paramagnetic surface perturbations. This procedure is applied to the Northeast Structural Genomics Consortium protein target, SeR13, a negatively charged Staphylococcus epidermidis dimeric protein (K(d) 3.4 ± 1.4 mM) composed of 86 amino acids. A structure determination for the monomeric form using traditional NMR methods is presented, followed by a dimer structure determination using docking under orientation constraints from RDCs data, and scoring under residue pair potentials and shape-based predictions of RDCs. Validation using paramagnetic surface perturbation and chemical shift perturbation data acquired on sample dilution is also presented. The general utility of the dimer structure determination procedure and the possible relevance of SeR13 dimer formation are discussed.

Improved fitting of solution X-ray scattering data to macromolecular structures and structural ensembles by explicit water modeling

A new procedure, AXES, is introduced for fitting small-angle X-ray scattering (SAXS) data to macromolecular structures and ensembles of structures. By using explicit water models to account for the effect of solvent, and by restricting the adjustable fitting parameters to those that dominate experimental uncertainties, including sample/buffer rescaling, detector dark current, and, within a narrow range, hydration layer density, superior fits between experimental high resolution structures and SAXS data are obtained. AXES results are found to be more discriminating than standard Crysol fitting of SAXS data when evaluating poorly or incorrectly modeled protein structures. AXES results for ensembles of structures previously generated for ubiquitin show improved fits over fitting of the individual members of these ensembles, indicating these ensembles capture the dynamic behavior of proteins in solution.

NMR studies on domain diffusion and alignment in modular GB1 repeats

Modular proteins contain individual domains that are often connected by flexible, unstructured linkers. Using a model system based on the GB1 domain, we constructed tandem repeat proteins and investigated the rotational diffusion and long-range angular ordering behavior of individual domains by measuring NMR relaxation parameters and residual dipolar couplings. Although they display almost identical protein-solvent interfaces, each domain exhibits distinct rotational diffusion and alignment properties. The diffusion tensor anisotropy of the N-terminal domain (NTD) is D(‖)/D(⊥) = 1.5-1.6, similar to that of single-GB1 domains (D(‖)/D(⊥) = 1.6-1.7), whereas the value for the C-terminal domain (CTD) is D(‖)/D(⊥) = 2.0-2.2. In addition, the two domains have different rotational correlation times. These effects are observed for linkers of three to 24 residues, irrespective of linker length. The NTD and CTD also differ in their degree of magnetic alignment, even with a flexible linker of 18 residues, exhibiting D(a) values of 7.7 Hz and 9.7 Hz, respectively. Our results suggest that diffusion differences and long-range influences may persist in modular protein systems, even for systems that have highly flexible linkers and exhibit no domain-domain or domain-linker interactions.

Backbone dynamics of deoxy and carbonmonoxy hemoglobin by NMR/SRLS

The slowly relaxing local structure (SRLS) approach, developed for NMR spin relaxation analysis in proteins, is applied herein to amide ¹⁵N relaxation in deoxy and carbonmonoxy hemoglobin. Experimental data including ¹⁵N T₁, T₂ and ¹⁵N-{¹H} NOE, acquired at 11.7 and 14.1 T, and 29 and 34 °C, are analyzed. The restricted local motion of the N-H bond is described in terms of the principal value (S(0)(2)) and orientation (β(D)) of an axial local ordering tensor, S, and the principal values (R(||)(L) and R(⊥)(L)) and orientation (β(O)) of an axial local diffusion tensor, R(L). The parameters c₀² (the potential coefficient in terms of which S(0)(2) is defined), R(||)(L), β(D), and β(O) are determined by data fitting; R(⊥)(L) is set equal to the global motional rate, R(C), found previously to be (5.2-5.8) × 10⁶ 1/s in the temperature range investigated. The principal axis of S is (nearly) parallel to the C(i-1)(α)-C(i)(α) axis; when the two axes are parallel, β(D) = -101.3° (in the frame used). The principal axis of R(L) is (nearly) parallel to the N-H bond; when the two axes are parallel, β(O) = -101.3°. For "rigid" N-H bonds located in secondary structure elements the best-fit parameters are S(0)(2) = 0.88-0.95 (corresponding to local potentials of 8.6-19.9 k(B)T), R(||)(L) = 10⁹-10¹⁰ 1/s, β(D) = -101.3° ± 2.0°, and β(O) = -101.3° ± 4°. For flexible N-H bonds located in loops the best-fit values are S(0)(2) = 0.75-0.80 (corresponding to local potentials of 4.5-5.5 k(B)T), R(||)(L) = (1.0-6.3) × 10⁸ 1/s, β(D) = -101.3° ± 4.0°, and β(O) = -101.3° ± 10°. These results are important in view of their physical clarity, inherent potential for further interpretation, consistency, and new qualitative insights provided (vide infra).

Residual dipolar couplings: are multiple independent alignments always possible?

RDCs for the 14 kDa protein hen egg-white lysozyme (HEWL) have been measured in eight different alignment media. The elongated shape and strongly positively charged surface of HEWL appear to limit the protein to four main alignment orientations. Furthermore, low levels of alignment and the protein's interaction with some alignment media increases the experimental error. Together with heterogeneity across the alignment media arising from constraints on temperature, pH and ionic strength for some alignment media, these data are suitable for structure refinement, but not the extraction of dynamic parameters. For an analysis of protein dynamics the data must be obtained with very low errors in at least three or five independent alignment media (depending on the method used) and so far, such data have only been reported for three small 6-8 kDa proteins with identical folds: ubiquitin, GB1 and GB3. Our results suggest that HEWL is likely to be representative of many other medium to large sized proteins commonly studied by solution NMR. Comparisons with over 60 high-resolution crystal structures of HEWL reveal that the highest resolution structures are not necessarily always the best models for the protein structure in solution.

The impact of hydrogen bonding on amide 1H chemical shift anisotropy studied by cross-correlated relaxation and liquid crystal NMR spectroscopy

Site-specific ¹H chemical shift anisotropy (CSA) tensors have been derived for the well-ordered backbone amide moieties in the B3 domain of protein G (GB3). Experimental input data include residual chemical shift anisotropy (RCSA), measured in six mutants that align differently relative to the static magnetic field when dissolved in a liquid crystalline Pf1 suspension, and cross-correlated relaxation rates between the ¹H^N CSA tensor and either the ¹H−¹⁵N, the ¹H−¹³C′, or the ¹H−¹³C^α dipolar interactions. Analyses with the assumption that the ¹H^N CSA tensor is symmetric with respect to the peptide plane (three-parameter fit) or without this premise (five-parameter fit) yield very similar results, confirming the robustness of the experimental input data, and that, to a good approximation, one of the principal components orients orthogonal to the peptide plane. ¹H^N CSA tensors are found to deviate strongly from axial symmetry, with the most shielded tensor component roughly parallel to the N−H vector, and the least shielded component orthogonal to the peptide plane. DFT calculations on pairs of N-methyl acetamide and acetamide in H-bonded geometries taken from the GB3 X-ray structure correlate with experimental data and indicate that H-bonding effects dominate variations in the ¹H^N CSA. Using experimentally derived ¹H^N CSA tensors, the optimal relaxation interference effect needed for narrowest ¹H^N TROSY line widths is found at ∼1200 MHz.

A combinatorial NMR and EPR approach for evaluating the structural ensemble of partially folded proteins

Partially folded proteins, characterized as exhibiting secondary structure elements with loose or absent tertiary contacts, represent important intermediates in both physiological protein folding and pathological protein misfolding. To aid in the characterization of the structural state(s) of such proteins, a novel structure calculation scheme is presented that combines structural restraints derived from pulsed EPR and NMR spectroscopy. The methodology is established for the protein alpha-synuclein (alphaS), which exhibits characteristics of a partially folded protein when bound to a micelle of the detergent sodium lauroyl sarcosinate (SLAS). By combining 18 EPR-derived interelectron spin label distance distributions with NMR-based secondary structure definitions and bond vector restraints, interelectron distances were correlated and a set of theoretical ensemble basis populations was calculated. A minimal set of basis structures, representing the partially folded state of SLAS-bound alphaS, was subsequently derived by back-calculating correlated distance distributions. A surprising variety of well-defined protein-micelle interactions was thus revealed in which the micelle is engulfed by two differently arranged antiparallel alphaS helices. The methodology further provided the population ratios between dominant ensemble structural states, whereas limitation in obtainable structural resolution arose from spin label flexibility and residual uncertainties in secondary structure definitions. To advance the understanding of protein-micelle interactions, the present study concludes by showing that, in marked contrast to secondary structure stability, helix dynamics of SLAS-bound alphaS correlate with the degree of protein-induced departures from free micelle dimensions.

Facile measurement of ¹H-¹5N residual dipolar couplings in larger perdeuterated proteins

We present a simple method, ARTSY, for extracting ¹J(NH) couplings and ¹H-¹⁵N RDCs from an interleaved set of two-dimensional ¹H-¹⁵N TROSY-HSQC spectra, based on the principle of quantitative J correlation. The primary advantage of the ARTSY method over other methods is the ability to measure couplings without scaling peak positions or altering the narrow line widths characteristic of TROSY spectra. Accuracy of the method is demonstrated for the model system GB3. Application to the catalytic core domain of HIV integrase, a 36 kDa homodimer with unfavorable spectral characteristics, demonstrates its practical utility. Precision of the RDC measurement is limited by the signal-to-noise ratio, S/N, achievable in the 2D TROSY-HSQC spectrum, and is approximately given by 30/(S/N) Hz.

Structural assembly of molecular complexes based on residual dipolar couplings

We present and evaluate a rigid-body molecular docking method, called PATIDOCK, that relies solely on the three-dimensional structure of the individual components and the experimentally derived residual dipolar couplings (RDCs) for the complex. We show that, given an accurate ab initio predictor of the alignment tensor from a protein structure, it is possible to accurately assemble a protein-protein complex by utilizing the RDCs' sensitivity to molecular shape to guide the docking. The proposed docking method is robust against experimental errors in the RDCs and computationally efficient. We analyze the accuracy and efficiency of this method using experimental or synthetic RDC data for several proteins, as well as synthetic data for a large variety of protein-protein complexes. We also test our method on two protein systems for which the structure of the complex and steric-alignment data are available (Lys48-linked diubiquitin and a complex of ubiquitin and a ubiquitin-associated domain) and analyze the effect of flexible unstructured tails on the outcome of docking. The results demonstrate that it is fundamentally possible to assemble a protein-protein complex solely on the basis of experimental RDC data and the prediction of the alignment tensor from 3D structures. Thus, despite the purely angular nature of RDCs, they can be converted into intermolecular distance/translational constraints. Additionally, we show a method for combining RDCs with other experimental data, such as ambiguous constraints from interface mapping, to further improve structure characterization of protein complexes.

Comparison of fast backbone dynamics at amide nitrogen and carbonyl sites in dematin headpiece C-terminal domain and its S74E mutant

We perform a detailed comparison of fast backbone dynamics probed at amide nitrogen versus carbonyl carbon sites for dematin headpiece C-terminal domain (DHP) and its S74E mutant (DHPS74E). Carbonyl dynamics is probed via auto-correlated longitudinal rates and transverse C'/C'-C(alpha) CSA/dipolar and C'/C'-N CSA/dipolar cross-correlated rates, while (15)N data are taken from a previous study. Resulting values of effective order parameters and internal correlation times support the conclusion that C' relaxation reports on a different subset of fast motions compared to those probed at N-H bond vectors in the same peptide planes. (13)C' order parameters are on the average 0.08 lower than (15)N order parameters with the exception of the flexible loop region in DHP. The reduction of mobility in the loop region upon the S74E mutation can be seen from the (15)N order parameters but not from the (13)C order parameters. Internal correlation times at (13)C' sites are on the average an order of magnitude longer than those at (15)N sites for the well-structured C-terminal subdomains, while the more flexible N-terminal subdomains have more comparable average internal correlation times.

Quantitative determination of NOE rates in perdeuterated and protonated proteins: practical and theoretical aspects

Precision and accuracy are the limiting factors in extracting structural and dynamic information from experimental NOEs. In this study, error sources at all stages of such an analysis are identified and errors are estimated. The data set of H(N)-H(N) cross-relaxation rates obtained from triple-labeled ubiquitin presented in [B. Vögeli, T.F. Segawa, D. Leitz, A. Sobol, A. Choutko, D. Trzesniak, W. van Gunsteren, R. Riek, J. Am. Chem. Soc. 131 (47) (2009) 17215-17225] is extended to rates obtained from a double-labeled sample. Analog data sets are presented for GB3. It is shown that quantitative NOE rates can be determined with high accuracy from both triple-labeled as well as double-labeled samples. The quality of experimental cross-relaxation rates obtained from 3D HXQC-NOESY and NOESY-HXQC experiments is discussed. It is shown that NOESY-HXQC experiments provide rates of the same quality as HXQC-NOESY if both diagonal and cross peaks for a spin pair can be resolved. Expressions for cross-relaxation rates for anisotropically tumbling molecules exhibiting fast and slow motion are derived. The impact of anisotropy on the prediction of cross-relaxation rates and on the conversion of experimental rates into effective distances is discussed. For molecules with anisotropy D(II)/D( perpendicular) up to five the distance error is smaller than 2%. Finally, "averaged order parameters" are calculated for specific secondary-structural elements showing similar trends for ubiquitin and GB3.