Protein Backbone 1H(N)-13Calpha and 15N-13Calpha residual dipolar and J couplings: new constraints for NMR structure determination

Probing the Conformational Preference to β-Strand during Peptide Self-Assembly

Alanine-rich tetrapeptides like A₃K dominantly exist as polyproline II helices in dilute aqueous solutions. However, during self-assembly, based on the free energy calculation in implicit solvent for various peptide conformations, only the peptides in the β-strand conformation can be packed closely. This necessitates the conformational transition to the β-strand commonly observed during peptide self-assembly such as in amyloid fibril formation. In fact, the closest interpeptide distance of 4.8 Å is consistent with the interstrand distance determined from the X-ray diffraction pattern of many amyloid fibrils. The position of free energy minimum obtained from implicit solvent calculation matches exactly with the explicit solvent simulation through umbrella sampling when the peptide conformations are restrained, demonstrating the applicability of the former for rapid screening of peptide configurations favorable for self-assembly. The barrier in the free energy profile in the presence of water arises out of the entropic restriction on the interstitial water molecules while satisfying the hydrogen bonding of both the peptides by forming water mediated hydrogen bond bridge. Further, the high energy barrier observed for the β-strand suggests that peptides initially tend to self-assemble in the polyproline II structure to mitigate the desolvation energy cost; the transition to the β-strand would happen only in the later stage after crossing the barrier. The umbrella sampling simulations with peptides allowed to change conformations, relative to each other, confirm the dynamic conformational transition during the course of the self-assembly supporting the "dock and lock" mechanism suggested for amyloid fibrillar growth.

Dipole Cooperativity and Polarization Frustration Determine the Secondary Structure Distribution of Short Alanine Peptides in Water

The physical driving forces for secondary structure preferences of hydrated alanine peptide are investigated with B3LYP-D3(BJ) and the adaptive force matching (AFM) method. The AFM fit to the DFT surface, ALA2022, provides excellent agreement with the nuclear magnetic resonance scalar coupling constants from experiments. In turn, the model is used to gain insight into the physical driving forces behind secondary structure preferences of hydrated peptides. DFT calculations with and without the Conductor-like Screening Model (COSMO) show that the α helix is stabilized by solvent polarization due to dipole cooperativity. The two adjacent amide groups in β strand form a near-planar trapezoid that is not much larger than the size of water molecules. When the finite size of a water molecule is considered, the stabilization from solvent polarization for such a trapezoid is frustrated. Water molecules cannot find orientations to properly stabilize all four polar regions close to each other with such an awkward arrangement. This leads to quite substantial reduction in polarization stabilization. Although the polyproline II (PP-II) conformation is very similar to the β strand, the small twist in the backbone angles allowed much improved polarization stabilization. The improved polarization, when combined with favorable intrapeptide interactions, leads to the PP-II to be lowest in free energy. Other factors, such as the entropic TΔS and the ϕ, ψ coupling terms, are also studied but are found to play only a minor role. The insight shown in this work helps to better understand the structure of globular and intrinsic disordered proteins and facilitate future force field development.

Personal Precise Force Field for Intrinsically Disordered and Ordered Proteins Based on Deep Learning

Intrinsically disordered proteins (IDPs) are proteins without a fixed three-dimensional (3D) structure under physiological conditions and are associated with Parkinson's disease, Alzheimer's disease, cancer, cardiovascular disease, amyloidosis, diabetes, and other diseases. Experimental methods can hardly capture the ensemble of diverse conformations for IDPs. Molecular dynamics (MD) simulations can sample continuous conformations that might provide a valuable complement to experimental data. However, the accuracy of MD simulations depends on the quality of force field. In particular, the evolutionary conservation and coevolution of IDPs introduce that current force fields could not precisely reproduce the conformation of IDPs. In order to improve the performance of force field, deep learning and reweighting methods were used to automatically generate personal force field parameters for intrinsically disordered and ordered proteins. At first, the deep learning method predicted more accuracy φ/ψ dihedral of residue than the previous method. Then, reweighting optimized the personal force field parameters for each residue. Finally, typical representative systems such as IDPs, structure protein, and fast-folding protein were used to evaluate this force field. The results indicate that two personal force field parameters (named PPFF1 and PPFF1_af2) could better reproduce the experimental observables than ff03CMAP force field. In summary, this strategy will provide feasibility for the development of precise personal force fields.

Performance evaluation of the balanced force field ff03CMAP for intrinsically disordered and ordered proteins

Intrinsically disordered proteins (IDPs) have been found to be closely associated with various human diseases. Because IDPs have no fixed tertiary structure under physiological conditions, current experimental methods, such as X-ray spectroscopy, NMR, and CryoEM, cannot capture all the dynamic conformations. Molecular dynamics simulation is an useful tool that is widely used to study the conformer distributions of IDPs and has become an important complementary tool for experimental methods. However, the accuracy of MD simulations directly depends on utilizing a precise force field. Recently a CMAP optimized force field based on the Amber ff03 force field (termed ff03CMAP herein) was developed for a balanced sampling of IDPs and folded proteins. In order to further evaluate the performance, more types of disordered and ordered proteins were used to test the ability for conformer sampling. The results showed that simulated chemical shifts, J-coupling, and R_g distribution with the ff03CMAP force field were in better agreement with NMR measurements and were more accurate than those with the ff03 force field. The sampling conformations by ff03CMAP were more diverse than those of ff03. At the same time, ff03CMAP could stabilize the conformers of the ordered proteins. These findings indicate that ff03CMAP can be widely used to sample diverse conformers for proteins, including the intrinsically disordered regions.

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

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

Randomizing of Oligopeptide Conformations by Nearest Neighbor Interactions between Amino Acid Residues

Flory’s random coil model assumes that conformational fluctuations of amino acid residues in unfolded poly(oligo)peptides and proteins are uncorrelated (isolated pair hypothesis, IPH). This implies that conformational energies, entropies and solvation free energies are all additive. Nearly 25 years ago, analyses of coil libraries cast some doubt on this notion, in that they revealed that aromatic, but also β-branched side chains, could change the ³J(H^NH^Cα) coupling of their neighbors. Since then, multiple bioinformatical, computational and experimental studies have revealed that conformational propensities of amino acids in unfolded peptides and proteins depend on their nearest neighbors. We used recently reported and newly obtained Ramachandran plots of tetra- and pentapeptides with non-terminal homo- and heterosequences of amino acid residues to quantitatively determine nearest neighbor coupling between them with a Ising type model. Results reveal that, depending on the choice of amino acid residue pairs, nearest neighbor interactions either stabilize or destabilize pairs of polyproline II and β-strand conformations. This leads to a redistribution of population between these conformations and a reduction in conformational entropy. Interactions between residues in polyproline II and turn(helix)-forming conformations seem to be cooperative in most cases, but the respective interaction parameters are subject to large statistical errors.

Do molecular dynamics force fields accurately model Ramachandran distributions of amino acid residues in water?

Molecular dynamics (MD) is a powerful tool for studying intrinsically disordered proteins, however, its reliability depends on the accuracy of the force field. We assess Amber ff19SB, Amber ff14SB, OPLS-AA/M, and CHARMM36m with respect to their capacity to capture intrinsic conformational dynamics of 14 guest residues x (=G, A, L, V, I, F, Y, D^P, E^P, R, C, N, S, T) in GxG peptides in water. The MD-derived Ramachandran distribution of each guest residue is used to calculate 5 J-coupling constants and amide I' band profiles to facilitate a comparison to spectroscopic data through reduced χ² functions. We show that the Gaussian model, optimized to best fit the experimental data, outperforms all MD force fields by an order of magnitude. The weaknesses of the MD force fields are: (i) insufficient variability of the polyproline II (pPII) population among the guest residues; (ii) oversampling of antiparallel at the expense of transitional β-strand region; (iii) inadequate sampling of turn-forming conformations for ionizable and polar residues; and (iv) insufficient guest residue-specificity of the Ramachandran distributions. Whereas Amber ff19SB performs worse than the other three force fields with respect to χ² values, it accounts for residue-specific pPII content better than the other three force fields. Additional testing of residue-specific RSFF1 and Amber ff14SB combined with TIP4P/2005 on six guest residues x (=A, I, F, D^P, R, S) reveals that residue specificity derived from protein coil libraries or an improved water model alone do not result in significantly lower χ² values.

Energetics and J-coupling constants for Ala, Gly, and Val peptides demonstrated using ABEEM polarizable force field in vacuo and an aqueous solution

The development of an atom-bond electronegativity equalisation method at the σπ-level (ABEEM) polarisable force field (PFF) for peptides is presented. ABEEM PFF utilises a fluctuating charge model to explicitly describe...

Repeating Aspartic Acid Residues Prefer Turn-like Conformations in the Unfolded State: Implications for Early Protein Folding

Protein folding can be described as a motion of the polypeptide chain in a potential energy funnel, where the conformational manifold is narrowed as the chain traverses from a completely unfolded state until it reaches the folded (native) state. The initial folding stages set the tone for this process by substantially narrowing the manifold of accessible conformations. In an ideally unfolded state with no long-range stabilizing forces, local conformations (i.e., residual structures) are likely to drive the folding process. While most amino acid residues tend to predominantly adopt extended structures in unfolded proteins and peptides, aspartic acid exhibits a relatively high intrinsic preference for turn-forming conformations. Regions in an unfolded polypeptide or protein that are rich in aspartic acid residues may therefore be crucial sites for protein folding steps. By combining NMR and vibrational spectroscopies, we observed that the conformational sampling of multiple sequentially neighbored aspartic acid residues in the model peptides GDDG and GDDDG even show an on average higher propensity for turn-forming structures than the intrinsic reference system D in GDG, which suggests that nearest neighbor interactions between adjacent aspartic acid residues stabilize local turn-forming structures. In the presence of the unlike neighbor phenylalanine, nearest neighbor interactions are of a totally different nature in that it they decrease the turn-forming propensities and mutually increase the sampling of polyproline II (pPII) conformations. We hypothesize the structural role of aspartic residues in intrinsically disordered proteins in general, and particularly in small linear motifs, that are very much determined by their respective neighbors.

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

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

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

Development and Validation of a DFT-Based Force Field for a Hydrated Homoalanine Polypeptide

A new force field has been created for simulating hydrated alanine polypeptides using the adaptive force matching (AFM) method. Only density functional theory calculations using the Perdew-Burke-Ernzerhof exchange-correlation functional and the D3 dispersion correction were used to fit the force field. The new force field, AFM2020, predicts NMR scalar coupling constants for hydrated homopolymeric alanine in better agreements with experimental data than several other models including those fitted directly to such data. For Ala₇, the new force field shows about 15% helical conformations, 20% conformation in the β basin, and 65% polyproline II. The predicted helical population of short hydrated alanine is higher than previous estimates based on the same experimental data. Gas-phase simulations indicate that the force field developed by AFM solution-phase data is likely to produce a reasonable conformation distribution when hydration water is no longer present, such as the interior of a protein.

Short peptides as predictors for the structure of polyarginine sequences in disordered proteins

Intrinsically disordered proteins and intrinsically disordered regions are frequently enriched in charged amino acids. Intrinsically disordered regions are regularly involved in important biological processes in which one or more charged residues is the driving force behind a protein-biomolecule interaction. Several lines of experimental and computational evidence suggest that polypeptides and proteins that carry high net charges have a high preference for extended conformations with average end-to-end distances exceeding expectations for self-avoiding random coils. Here, we show that charged arginine residues even in short glycine-capped model peptides (GRRG and GRRRG) significantly affect the conformational propensities of each other when compared with the intrinsic propensities of a mostly unperturbed arginine in the tripeptide GRG. A conformational analysis based on experimentally determined J-coupling constants from heteronuclear NMR spectroscopy and amide I' band profiles from vibrational spectroscopy reveals that nearest-neighbor interactions stabilize extended β-strand conformations at the expense of polyproline II and turn conformations. The results from molecular dynamics simulations with a CHARMM36m force field and TIP3P water reproduce our results only to a limited extent. The use of the Ramachandran distribution of the central residue of GRRRG in a calculation of end-to-end distances of polyarginines of different length yielded the expected power law behavior. The scaling coefficient of 0.66 suggests that such peptides would be more extended than predicted by a self-avoiding random walk. Our findings thus support in principle theoretical predictions.

Glycine in Water Favors the Polyproline II State

Conformational preferences of amino acid residues in water are determined by the backbone and side-chain properties. Alanine is known for its high polyproline II (pPII) propensity. The question of relative contributions of the backbone and side chain to the conformational preferences of alanine and other amino acid residues in water is not fully resolved. Because glycine lacks a heavy-atom side chain, glycine-based peptides can be used to examine to which extent the backbone properties affect the conformational space. Here, we use published spectroscopic data for the central glycine residue of cationic triglycine in water to demonstrate that its conformational space is dominated by the pPII state. We assess three commonly used molecular dynamics (MD) force fields with respect to their ability to capture the conformational preferences of the central glycine residue in triglycine. We show that pPII is the mesostate that enables the functional backbone groups of the central residue to form the most hydrogen bonds with water. Our results indicate that the pPII propensity of the central glycine in GGG is comparable to that of alanine in GAG, implying that the water-backbone hydrogen bonding is responsible for the high pPII content of these residues.

Well-Balanced Force Field ff03CMAP for Folded and Disordered Proteins

Molecular dynamics simulation as an important complement of experiment is widely used to study protein structures and functions. However, previous studies indicate that the current force fields cannot, simultaneously, provide accurate descriptions of folded proteins and intrinsically disordered proteins (IDPs). Therefore, a correction maps (CMAP)-optimized force field based on the Amber ff03 force field (termed ff03CMAP herein) was developed for a balanced sampling of folded proteins and IDPs. Extensive validations of short peptides, folded proteins, disordered proteins, and fast-folding proteins show that simulated chemical shifts, J-coupling constants, order parameters, and residual dipolar couplings (RDCs) with the ff03CMAP force field are in very good agreement with nuclear magnetic resonance measurements and are more accurate than other ff03-series force fields. The influence of solvent models was also investigated. It was found that the combination of ff03CMAP/TIP4P-Ew is suitable for folded proteins, and that of ff03CMAP/TIP4PD is better for disordered proteins. These findings confirm that the newly developed force field ff03CMAP can improve the balance of conformer sampling between folded proteins and IDPs.

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

A J-modulated protonless NMR experiment characterizes the conformational ensemble of the intrinsically disordered protein WIP

Intrinsically disordered proteins (IDPs) are multi-conformational polypeptides that lack a single stable three-dimensional structure. It has become increasingly clear that the versatile IDPs play key roles in a multitude of biological processes, and, given their flexible nature, NMR is a leading method to investigate IDP behavior on the molecular level. Here we present an IDP-tailored J-modulated experiment designed to monitor changes in the conformational ensemble characteristic of IDPs by accurately measuring backbone one- and two-bond J(¹⁵N,¹³Cα) couplings. This concept was realized using a unidirectional (H)NCO ¹³C-detected experiment suitable for poor spectral dispersion and optimized for maximum coverage of amino acid types. To demonstrate the utility of this approach we applied it to the disordered actin-binding N-terminal domain of WASp interacting protein (WIP), a ubiquitous key modulator of cytoskeletal changes in a range of biological systems. One- and two-bond J(¹⁵N,¹³Cα) couplings were acquired for WIP residues 2-65 at various temperatures, and in denaturing and crowding environments. Under native conditions fitted J-couplings identified in the WIP conformational ensemble a propensity for extended conformation at residues 16-23 and 45-60, and a helical tendency at residues 28-42. These findings are consistent with a previous study of the based upon chemical shift and RDC data and confirm that the WIP^2-65 conformational ensemble is biased towards the structure assumed by this fragment in its actin-bound form. The effects of environmental changes upon this ensemble were readily apparent in the J-coupling data, which reflected a significant decrease in structural propensity at higher temperatures, in the presence of 8 M urea, and under the influence of a bacterial cell lysate. The latter suggests that crowding can cause protein unfolding through protein-protein interactions that stabilize the unfolded state. We conclude that J-couplings are a useful measureable in characterizing structural ensembles in IDPs, and that the proposed experiment provides a practical method for accurately performing such measurements, once again emphasizing the power of NMR in studying IDP behavior.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

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

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

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.

Applications of high dimensionality experiments to biomolecular NMR

High dimensionality NMR experiments facilitate resonance assignment and precise determination of spectral parameters such as coupling constants. Sparse non-uniform sampling enables acquisition of experiments of high dimensionality with high resolution in acceptable time. In this review we present and compare some significant applications of NMR experiments of dimensionality higher than three in the field of biomolecular studies in solution.

MERA: a webserver for evaluating backbone torsion angle distributions in dynamic and disordered proteins from NMR data

MERA (Maximum Entropy Ramachandran map Analysis from NMR data) is a new webserver that generates residue-by-residue Ramachandran map distributions for disordered proteins or disordered regions in proteins on the basis of experimental NMR parameters. As input data, the program currently utilizes up to 12 different parameters. These include three different types of short-range NOEs, three types of backbone chemical shifts ((15)N, (13)C(α), and (13)C'), six types of J couplings ((3)JHNHα, (3)JC'C', (3)JC'Hα, (1)JHαCα, (2)JCαN and (1)JCαN), as well as the (15)N-relaxation derived J(0) spectral density. The Ramachandran map distributions are reported in terms of populations of their 15° × 15° voxels, and an adjustable maximum entropy weight factor is available to ensure that the obtained distributions will not deviate more from a newly derived coil library distribution than required to account for the experimental data. MERA output includes the agreement between each input parameter and its distribution-derived value. As an application, we demonstrate performance of the program for several residues in the intrinsically disordered protein α-synuclein, as well as for several static and dynamic residues in the folded protein GB3.

ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB

Molecular mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Average errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a physically motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reproduction of NMR χ1 scalar coupling measurements for proteins in solution. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.

Peptide Conformation Analysis Using an Integrated Bayesian Approach

Unlike native proteins that are amenable to structural analysis at atomic resolution, unfolded proteins occupy a manifold of dynamically interconverting structures. Defining the conformations of unfolded proteins is of significant interest and importance, for folding studies and for understanding the properties of intrinsically disordered proteins. Short chain protein fragments, i.e., oligopeptides, provide an excellent test-bed in efforts to define the conformational ensemble of unfolded chains. Oligomers of alanine in particular have been extensively studied as minimalist models of the intrinsic conformational preferences of the peptide backbone. Even short alanine peptides occupy an ensemble of substates that are distinguished by small free energy differences, so that the problem of quantifying the conformational preferences of the backbone remains a fundamental challenge in protein biophysics. Here, we demonstrate an integrated computational-experimental-Bayesian approach to quantify the conformational ensembles of the model trialanine peptide in water. In this approach, peptide conformational substates are first determined objectively by clustering molecular dynamics snapshots based on both structural and dynamic information. Next, a set of spectroscopic data for each conformational substate is computed. Finally, a Bayesian statistical analysis of both experimentally measured spectroscopic data and computational results is carried out to provide a current best estimate of the substate population ensemble together with corresponding confidence intervals. This distribution of substates can be further systematically refined with additional high-quality experimental data and more accurate computational modeling. Using an experimental data set of NMR coupling constants, we have also applied this approach to characterize the conformation ensemble of trivaline in water.

A maximum entropy approach to the study of residue-specific backbone angle distributions in α-synuclein, an intrinsically disordered protein

α-Synuclein is an intrinsically disordered protein of 140 residues that switches to an α-helical conformation upon binding phospholipid membranes. We characterize its residue-specific backbone structure in free solution with a novel maximum entropy procedure that integrates an extensive set of NMR data. These data include intraresidue and sequential H(N) − H(α) and H(N) − H(N) NOEs, values for (3) JHNHα, (1) JHαCα, (2) JCαN, and (1) JCαN, as well as chemical shifts of (15)N, (13)C(α), and (13)C' nuclei, which are sensitive to backbone torsion angles. Distributions of these torsion angles were identified that yield best agreement to the experimental data, while using an entropy term to minimize the deviation from statistical distributions seen in a large protein coil library. Results indicate that although at the individual residue level considerable deviations from the coil library distribution are seen, on average the fitted distributions agree fairly well with this library, yielding a moderate population (20-30%) of the PPII region and a somewhat higher population of the potentially aggregation-prone β region (20-40%) than seen in the database. A generally lower population of the αR region (10-20%) is found. Analysis of (1)H − (1)H NOE data required consideration of the considerable backbone diffusion anisotropy of a disordered protein.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

Using J-coupling constants for force field validation: application to hepta-alanine

A computational solution to the protein folding problem is the holy grail of biomolecular simulation and of the corresponding force fields. The complexity of the systems used for folding simulations precludes a direct feedback between the simulations and the force fields, thus necessitating the study of simpler systems with sufficient experimental data to allow force field optimization and validation. Recent studies on short polyalanine peptides of increasing length (up to penta-alanine) indicated the presence of a systematic deviation between the experimental (NMR-derived) J-couplings and the great majority of biomolecular force fields, with the χ(2) values for even the best-performing force fields being in the 1.4-1.8 range. Here we show that by increasing the number of residues to seven and by achieving convergence through an increase of the simulation time to 2 μs, we can identify one force field (the AMBER99SB force field, out of the three force fields studied) which when compared with the experimental J-coupling data (and for a specific set of Karplus equation parameters and estimated J-coupling errors previously used in the literature) gave a value of χ(2) = 0.99, indicating that full statistical consistency between experiment and simulation is feasible. However, and as a detailed analysis of the effects of estimated errors shows, the χ(2) values may be unsuitable as indicators of the goodness of fit of the various biomolecular force fields.

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.

Optimizing Protein-Solvent Force Fields to Reproduce Intrinsic Conformational Preferences of Model Peptides

While most force field efforts in biomolecular simulation have focused on the parametrization of the protein, relatively little attention has been paid to the quality of the accompanying solvent model. These considerations are especially relevant for simulations of intrinsically disordered peptides and proteins, for which energy differences between conformations are small and interactions with water are enhanced. In this work, we investigate the accuracy of the AMBER ff99SB force field when combined with the standard TIP3P model or the more recent TIP4P-Ew water model, to generate conformational ensembles for disordered trialanine (Ala3), triglycine (Gly3), and trivaline (Val3) peptides. We find that the TIP4P-Ew water model yields significantly better agreement with experimentally measured scalar couplings-and therefore more accurate conformational ensembles-for both Ala3 and Gly3. For Val3, however, we find that the TIP3P and TIP4P-Ew ensembles are equivalent in their performance. To further improve the protein-water force field combination and obtain more accurate intrinsic conformational preferences, we derive a straightforward perturbation to the ϕ' backbone dihedral potential that shifts the β-PPII equilibrium. We find that the revised ϕ' backbone dihedral potential yields improved conformational ensembles for a variety of small peptides and maintains the stability of the globular ubiquitin protein in TIP4P-Ew water.

Structure and dynamics of the first archaeal parvulin reveal a new functionally important loop in parvulin-type prolyl isomerases

Parvulins are a group of peptidyl-prolyl isomerases (PPIases) responsible for important biological processes in all kingdoms of life. The PinA protein from the psychrophilic archaeon Cenarchaeum symbiosum is a parvulin-like PPIase. Due to its striking similarity to the human parvulins Pin1 and Par14, PinA constitutes an interesting subject for structural and functional studies. Here, we present the first high resolution NMR structure of an archaeal parvulin, PinA, based on 1798 conformational restraints. Structure calculation yields an ensemble of 20 convergent low energy structures with a backbone r.m.s.d. value of 0.6 Å within the secondary structure elements. The overall fold of PinA comprises the β-α(3)-β-α-β(2) fold typical for all parvulin structures known so far, but with helix III being a short 3(10)-helix. A detailed comparison of this high resolution structure of the first archaeal PinA protein with bacterial and eukaryotic parvulin PPIase structures reveals an atypically large catalytic binding site. This feature provides an explanation for cold-adapted protein function. Moreover, the residues in and around 3(10)-helix III exhibit strong intramolecular dynamics on a microsecond to millisecond timescale and display structural heterogeneity within the NMR ensemble. A putative peptide ligand was found for PinA by phage display and was used for (1)H-(15)N-HSQC titrations. Again, the flexible region around 3(10)-helix III as well as residues of the peptide binding pocket showed the strongest chemical shift perturbations upon peptide binding. The local flexibility of this region also was modulated by ligand binding. A glycine and two positively charged residues are conserved in most parvulin proteins in this flexible loop region, which may be of general functional importance for parvulin-type PPIases.

Measurement of one and two bond N-C couplings in large proteins by TROSY-based J-modulation experiments

Residual dipolar couplings (RDCs) between NC' and NC(alpha) atoms in polypeptide backbones of proteins contain information on the orientation of bond vectors that is complementary to that contained in NH RDCs. The (1)J(NC)(alpha) and (2)J(NC)(alpha) scalar couplings between these atoms also display a Karplus relation with the backbone torsion angles and report on secondary structure. However, these N-C couplings tend to be small and they are frequently unresolvable in frequency domain spectra having the broad lines characteristic of large proteins. Here a TROSY-based J-modulated approach for the measurement of small (15)N-(13)C couplings in large proteins is described. The cross-correlation interference effects inherent in TROSY methods improve resolution and signal to noise ratios for large proteins, and the use of J-modulation to encode couplings eliminates the need to remove frequency distortions from overlapping peaks during data analysis. The utility of the method is demonstrated by measurement of (1)J(NC'), (1)J(NC)(alpha) , and (2)J(NC)(alpha) scalar couplings and (1)D(NC') and D(NC)(alpha) residual dipolar couplings for the myristoylated yeast ARF1.GTPgammas protein bound to small lipid bicelles, a system with an effective molecule weight of approximately 70kDa.

Simultaneous determination of one- and two-bond scalar and residual dipolar couplings between 13C', 13Calpha and 15N spins in proteins

Four simple and sensitive HNCO-based methods for measurement of 1J(C'Calpha), 1J(NCalpha) and 2J(NCalpha) coupling constants in protein main chains are presented. Three of these experiments enable the simultaneous measurement of 1J(C'Calpha), 1J(NCalpha) and 2J(NCalpha) couplings. Exploitation of the E.COSY principle provides excellent dispersion of cross peaks in the resulting 3D spectra. The couplings can be retrieved with good accuracy from peak-to-peak separations. Karplus parameterizations are provided for 1J(NCalpha) and 2J(NCalpha), obtained from a nearly complete set of couplings of human ubiquitin. In addition, feasibility of the proposed methodology for measuring several residual dipolar couplings (RDCs) simultaneously is assessed.

A protein backbone psi and phi angle dependence of 2J(N(i),C alpha(i-1)): the new NMR experiment and quantum chemical calculations

A new pulse sequence exploiting double- and zero-quantum evolution of two-spin 15N-13C' coherence is proposed for the accurate measurements of 2J(N(i),C alpha(i-1)) coupling constants. Application of the new experiment is presented for 13C,15N-labeled ubiquitin sample. The density functional theory calculations of 2J(N(i),C alpha(i-1)) coupling constants have been performed to study their dependence on both psi(i - 1) and phi(i - 1) angle in model peptides, and the results exhibit a good correlation with experimental data.