Static and Dynamic Effects on Vicinal Scalar J Couplings in Proteins and Peptides: A MD/DFT Analysis

Revealing elusive conformations of sucrose from hydrogen bond J-coupling in H2O: A combined NMR and quantum mechanics study

Hydrogen bonding is a crucial feature of biomolecules, but its characterization in glycans dissolved in aqueous solutions is challenging due to rapid hydrogen exchange between hydroxyl groups and H2O. In principle, the scalar (J) coupling constant can reveal the relative orientation of the atoms in the molecule. In contrast to J-coupling through H-bonds reported in proteins and nucleic acids, research on J-coupling through H-bonds in glycans dissolved in water is lacking. Here, we use sucrose as a model system for H-bonding studies; its structure, which consists of glucose (Glc) and fructose (Frc), is well-studied, and it is readily available. We apply the in-phase, antiphase-HSQC-TOCSY and quantify previously unreported through H-bond J-values for Frc-OH1-Glc-OH2 in H2O. While earlier reports of Brown and Levy indicate this H-bond as having only a single direction, our reported findings indicate the potential presence of two involving these same atoms, namely, G2OH ➔ F1O and F1OH ➔ G2O (where F and G stand for Frc and Glc, respectively). The calculated density functional theory J-values for the G2OH ➔ F1O agree with the experimental values. Additionally, we detected four other possible H-bonds in sucrose, which require different phi, psi (ϕ, ψ) torsion angles. The ϕ, ψ values are consistent with previous predictions of du Penhoat et al. and Venable et al. Our results will provide new insights into the molecular structure of sucrose and its interactions with proteins.

Encoding prior knowledge in ensemble refinement

The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we propose how to set the exchange rate a priori to properly balance this trade-off. We focus on gentle ensemble refinement, where the difference between the potential energy surfaces of the reference and refined models is small on a thermal scale. By relating the variance of this energy difference to the Kullback-Leibler divergence between the respective Boltzmann distributions, one can encode prior knowledge about energy uncertainties, i.e., force-field errors, in the exchange rate. The energy uncertainty is defined in the space of observables and depends on their type and number and on the thermodynamic state. We highlight the relation of gentle refinement to free energy perturbation theory. A balanced encoding of prior knowledge increases the quality and transparency of ensemble refinement. Our findings extend to non-Boltzmann distributions, where the uncertainty in energy becomes an uncertainty in information.

The relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

The impact of conformational sampling on first-principles calculations of vicinal COCH J-couplings in carbohydrates

Dihedral angles in organic molecules and biomolecules are vital structural parameters that can be indirectly probed by nuclear magnetic resonance (NMR) measurements of vicinal J-couplings. The empirical relations that map the measured couplings to dihedral angles are typically determined by fitting using static structural models, but this neglects the effects of thermal fluctuations at the finite temperature conditions under which NMR measurements are often taken. In this study, we calculate ensemble-averaged J-couplings for several structurally rigid carbohydrate derivatives using first-principles molecular dynamics simulations to sample the thermally accessible conformations around the minimum energy structure. Our results show that including thermal fluctuation effects significantly shifts the predicted couplings relative to single-point calculations at the energy minima, leading to improved agreement with experiments. This provides evidence that accounting for conformational sampling in first-principles calculations can improve the accuracy of NMR-based structure determination for structurally complex carbohydrates.

High-resolution NMR spectroscopy for measuring complex samples based on chemical-shift-difference selection

NMR spectroscopy serves as an immensely powerful tool for component assignments and molecular structure elucidations. However, proton NMR spectra are generally trapped with spectral congestion caused by limited frequency differences and complex multiplets. 2D NMR can effectively relieve spectral congestion, but its resolution and acquisition efficiency are restricted by the broad spectral bandwidth. Herein, we introduce an NMR method based on chemical-shift-difference selection by chirp excitation to record high-resolution 2D NMR spectra for extracting coupling correlation networks and multiplet structures, suitable for measurements on complex samples. The performance of the proposed method is illustrated in determining diastereotopic methylene protons, small frequency-difference coupled proton pairs of furanose, pyranose and benzene rings. This study is expected to benefit molecular structure elucidation and composition analysis of complex samples in chemistry, biochemistry and metabonomics.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

Exploring Nearest Neighbor Interactions and Their Influence on the Gibbs Energy Landscape of Unfolded Proteins and Peptides

The Flory isolated pair hypothesis (IPH) is one of the corner stones of the random coil model, which is generally invoked to describe the conformational dynamics of unfolded and intrinsically disordered proteins (IDPs). It stipulates, that individual residues sample the entire sterically allowed space of the Ramachandran plot without exhibiting any correlations with the conformational dynamics of its neighbors. However, multiple lines of computational, bioinformatic and experimental evidence suggest that nearest neighbors have a significant influence on the conformational sampling of amino acid residues. This implies that the conformational entropy of unfolded polypeptides and proteins is much less than one would expect based on the Ramachandran plots of individual residues. A further implication is that the Gibbs energies of residues in unfolded proteins or polypeptides are not additive. This review provides an overview of what is currently known and what has yet to be explored regarding nearest neighbor interactions in unfolded proteins.

Measuring the 3J HNHa coupling by a simple 2D-intra-HNCA IP/AP-E.COSY with simultaneous encoding of 15N chemical shift and 1J HaCa evolution

The ³J coupling values are commonly used in biomolecular NMR to extract structural information. Here we present a novel intra HNCA IP/AP E.COSY pulse sequence that allows to measure ³J H^NH^a coupling constants by a simple and rapid two-dimensional ¹H-¹⁵N correlation experiment where the ¹⁵N frequency is encoded at the same time as the ¹J H^aC^a coupling evolution. The advantage with respect to the conventional 3D HNCA E.COSY pulse sequence is the dimensionality reduction to a simple 2D experiment, which decreases acquisition time and facilitates data analysis. The performance of this new experiment is demonstrated with an ubiquitin sample at 500 MHz.

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.

Assessment of Force Field Accuracy Using Cryogenic Electron Microscopy Data of Hyper-thermostable Glutamate Dehydrogenase

Molecular dynamics (MD) simulations in biophysically relevant time scales of microseconds is a powerful tool for studying biomolecular processes, but results often display force field dependency. Therefore, assessment of force field accuracy using experimental data of biomolecules in solution is essential for simulation studies. Here, we propose the use of structural models obtained via cryo-electron microscopy (cryoEM), which provides biomolecular structures in vitreous ice mimicking the environment in solution. The accuracy of the AMBER (ff99SB-ILDN-NMR, ff14SB, ff15ipq, and ff15FB) and CHARMM (CHARMM22 and CHARMM36m) force fields was assessed by comparing their MD trajectories with the cryoEM data of thermostable hexameric glutamate dehydrogenase (GDH), which included a cryoEM map at a resolution of approximately 3 Å and structure models of subunits reflecting metastable conformations in domain motion occurring in GDH. In the assessment, we validated the force fields with respect to the reproducibility and stability of secondary structures and intersubunit interactions in the cryoEM data. Furthermore, we evaluated the force fields regarding the reproducibility of the energy landscape in the domain motion expected from the cryoEM data. As a result, among the six force fields, ff15FB and ff99SB-ILDN-NMR displayed good agreement with the experiment. The present study demonstrated the advantages of the high-resolution cryoEM map and suggested the optimal force field to reproduce experimentally observed protein structures.

A twist in the road less traveled: The AMBER ff15ipq-m force field for protein mimetics

We present a new force field, AMBER ff15ipq-m, for simulations of protein mimetics in applications from therapeutics to biomaterials. This force field is an expansion of the AMBER ff15ipq force field that was developed for canonical proteins and enables the modeling of four classes of artificial backbone units that are commonly used alongside natural α residues in blended or "heterogeneous" backbones: chirality-reversed D-α-residues, the Cα-methylated α-residue Aib, homologated β-residues (β3) bearing proteinogenic side chains, and two cyclic β residues (βcyc; APC and ACPC). The ff15ipq-m force field includes 472 unique atomic charges and 148 unique torsion terms. Consistent with the AMBER IPolQ lineage of force fields, the charges were derived using the Implicitly Polarized Charge (IPolQ) scheme in the presence of explicit solvent. To our knowledge, no general force field reported to date models the combination of artificial building blocks examined here. In addition, we have derived Karplus coefficients for the calculation of backbone amide J-coupling constants for β3Ala and ACPC β residues. The AMBER ff15ipq-m force field reproduces experimentally observed J-coupling constants in simple tetrapeptides and maintains the expected conformational propensities in reported structures of proteins/peptides containing the artificial building blocks of interest-all on the μs timescale. These encouraging results demonstrate the power and robustness of the IPolQ lineage of force fields in modeling the structure and dynamics of natural proteins as well as mimetics with protein-inspired artificial backbones in atomic detail.

Do Molecular Dynamics Force Fields Capture Conformational Dynamics of Alanine in Water?

We examine the ability of six molecular dynamics (MD) force fields (Amber ff14SB, Amber ff99SBnmr1, Amber ff03ws, OPLS-AA/L, OPLS-AA/M, and CHARMM36) to reproduce conformational ensembles of the central alanine in GAG and AAA in a way that is consistent with five (GAG) or six (AAA) J coupling constants and amide I' profiles. MD-derived Ramachandran plots for all six force fields under study differ from those obtained by the Gaussian fit to experimental data in three major ways: (i) the polyproline II (pPII) basin in the Ramachandran plot is too concentrated, (ii) the antiparallel β (aβ) basin is overpopulated, and (iii) the transitional β (βt) basin is underpopulated. Amber ff14SB outperforms the other five MD force fields and yields the highest pPII populations of the central alanine residue in GAG (55%) and AAA (63%), in good agreement with the predictions of the Gaussian model (59 and 76%). The analysis of the hydration layer around the central alanine residue reveals considerable reorientation of water molecules and reduction in both the average number of water molecules and the average number of water-water hydrogen bonds when glycines (in GAG) are replaced by alanines (in AAA), elucidating water-mediated nearest neighbor effects on alanine's conformational dynamics.

Efficient Ensemble Refinement by Reweighting

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

Distance-independent Cross-correlated Relaxation and Isotropic Chemical Shift Modulation in Protein Dynamics Studies

Cross-correlated relaxation (CCR) in multiple-quantum coherences differs from other relaxation phenomena in its theoretical ability to be mediated across an infinite distance. The two interfering relaxation mechanisms may be dipolar interactions, chemical shift anisotropies, chemical shift modulations or quadrupolar interactions. These properties make multiple-quantum CCR an attractive probe for structure and dynamics of biomacromolecules not accessible from other measurements. Here, we review the use of multiple-quantum CCR measurements in dynamics studies of proteins. We compile a list of all experiments proposed for CCR rate measurements, provide an overview of the theory with a focus on protein dynamics, and present applications to various protein systems.

Analysis of NMR Spin-Relaxation Data Using an Inverse Gaussian Distribution Function

Spin relaxation in solution-state NMR spectroscopy is a powerful approach to explore the conformational dynamics of biological macromolecules. Probability distribution functions for overall or internal correlation times have been used previously to model spectral density functions central to spin-relaxation theory. Applications to biological macromolecules rely on transverse relaxation rate constants, and when studying nanosecond timescale motions, sampling at ultralow frequencies is often necessary. Consequently, appropriate distribution functions necessitate spectral density functions that are accurate and convergent as frequencies approach zero. In this work, the inverse Gaussian probability distribution function is derived from general properties of spectral density functions at low and high frequencies for macromolecules in solution, using the principle of maximal entropy. This normalized distribution function is first used to calculate the correlation function, followed by the spectral density function. The resulting model-free spectral density functions are finite at a frequency of zero and can be used to describe distributions of either overall or internal correlation times using the model-free ansatz. To validate the approach, ¹⁵N spin-relaxation data for the bZip transcription factor domain of the Saccharomyces cerevisiae protein GCN4, in the absence of cognate DNA, were analyzed using the inverse Gaussian probability distribution for intramolecular correlation times. The results extend previous models for the conformational dynamics of the intrinsically disordered, DNA-binding region of the bZip transcription factor domain.

Significantly different contact patterns between Aβ40 and Aβ42 monomers involving the N-terminal region

Aβ42 peptide, with two additional residues at C-terminus, aggregates much faster than Aβ40. We performed equilibrium replica-exchange molecular dynamics simulations of their monomers using our residue-specific force field. Simulated ³ J_{HNH α} -coupling constants agree excellently with experimental data. Aβ40 and Aβ42 have very similar local conformational features, with considerable β-strand structures in the segments: A2-H6 (A), L17-A21 (B), A30-V36 (C) of both peptides and V39-I41 (D) of Aβ42. Both peptides have abundant A-B and B-C contacts, but Aβ40 has much more contacts between A and C than Aβ42, which may retard its aggregation. Only Aβ42 has considerable A-B-C-D topology. Decreased probability of A-C contact in Aβ42 relates to the competition from C-D contact. Increased A-C contact probability may also explain the slower aggregation of A2T and A2V mutants of Aβ42.

A critical assessment of force field accuracy against NMR data for cyclic peptides containing β-amino acids

Hybrid cyclic α/β-peptides, in which one or more β-amino acids are incorporated into the backbone, are gaining increasing interest as potential therapeutics, thanks to their ability to achieve enhanced binding affinities for a biological target through pre-organization in solution. The in silico prediction of their three dimensional structure through strategies such as MD simulations would substantially advance the rational design process. However, whether the molecular mechanics force fields are accurate in sampling highly constrained cyclopeptides containing β-amino acids remains to be verified. Here, we present a systematic assessment of the ability of 8 widely used force fields to reproduce 79 NMR observables (including chemical shifts and 3J scalar couplings) on five cyclic α/β-peptides that contain the integrin recognition motif isoDGR. Most of the investigated force fields, which include force fields from AMBER, OPLS, CHARMM and GROMOS families, display very good agreement with experimental 3J(HN,Hα), suggesting that MD simulations could be an appropriate tool in the rational design of therapeutic cyclic α-peptides. However, for NMR observables directly related to β-amino acids, we observed a poor agreement with experiments and a remarkable dependence of our evaluation on the choice of Karplus parameters. The force field weaknesses herein unveiled might constitute a source of inspiration for further force field optimization.

Links between the charge model and bonded parameter force constants in biomolecular force fields

The ff15ipq protein force field is a fixed charge model built by automated tools based on the two charge sets of the implicitly polarized charge method: one set (appropriate for vacuum) for deriving bonded parameters and the other (appropriate for aqueous solution) for running simulations. The duality is intended to treat water-induced electronic polarization with an understanding that fitting data for bonded parameters will come from quantum mechanical calculations in the gas phase. In this study, we compare ff15ipq to two alternatives produced with the same fitting software and a further expanded data set but following more conventional methods for tailoring bonded parameters (harmonic angle terms and torsion potentials) to the charge model. First, ff15ipq-Qsolv derives bonded parameters in the context of the ff15ipq solution phase charge set. Second, ff15ipq-Vac takes ff15ipq's bonded parameters and runs simulations with the vacuum phase charge set used to derive those parameters. The IPolQ charge model and associated protocol for deriving bonded parameters are shown to be an incremental improvement over protocols that do not account for the material phases of each source of their fitting data. Both force fields incorporating the polarized charge set depict stable globular proteins and have varying degrees of success modeling the metastability of short (5-19 residues) peptides. In this particular case, ff15ipq-Qsolv increases stability in a number of α-helices, correctly obtaining 70% helical character in the K19 system at 275 K and showing appropriately diminishing content up to 325 K, but overestimating the helical fraction of AAQAA₃ by 50% or more, forming long-lived α-helices in simulations of a β-hairpin, and increasing the likelihood that the disordered p53 N-terminal peptide will also form a helix. This may indicate a systematic bias imparted by the ff15ipq-Qsolv parameter development strategy, which has the hallmarks of strategies used to develop other popular force fields, and may explain some of the need for manual corrections in this force fields' evolution. In contrast, ff15ipq-Vac incorrectly depicts globular protein unfolding in numerous systems tested, including Trp cage, villin, lysozyme, and GB3, and does not perform any better than ff15ipq or ff15ipq-Qsolv in tests on short peptides. We analyze the free energy surfaces of individual amino acid dipeptides and the electrostatic potential energy surfaces of each charge model to explain the differences.

Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15

The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.

Evaluation of the Coupled Two-Dimensional Main Chain Torsional Potential in Modeling Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) carry out crucial biological functions in essential biological processes of life. Because of the highly dynamic and conformationally heterogeneous nature of the disordered states of IDPs, molecular dynamics simulations are becoming an indispensable tool for the investigation of the conformational ensembles and dynamic properties of IDPs. Nevertheless, there is still no consensus on the most reliable force field in molecular dynamics simulations for IDPs hitherto. In this work, the recently proposed AMBER99SB^2D force field is evaluated in modeling some disordered polypeptides and proteins by checking its ability to reproduce experimental NMR data. The results highlight that when the ildn side-chain corrections are included, AMBER99SB^2D-ildn exhibits reliable results that agree with experiments compared with its predecessors, the AMBER14SB, AMBER99SB, AMBER99SB-ildn, and AMBER99SB^2D force fields, and that decreasing the overall magnitude of protein-protein interactions in favor of protein-water interactions is a key ingredient behind the improvement.

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.

Finding Our Way in the Dark Proteome

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

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.

Direct Investigation of Slow Correlated Dynamics in Proteins via Dipolar Interactions

The synchronization of native state motions as they transition between microstates influences catalysis kinetics, mediates allosteric interactions, and reduces the conformational entropy of proteins. However, it has proven difficult to describe native microstates because they are usually minimally frustrated and may interconvert on the micro- to millisecond time scale. Direct observation of concerted equilibrium fluctuations would therefore be an important tool for describing protein native states. Here we propose a strategy that relates NMR cross-correlated relaxation (CCR) rates between dipolar interactions to residual dipolar couplings (RDCs) of individual consecutive H(N)-N and H(α)-C(α) bonds, which act as a proxy for the peptide planes and the side chains, respectively. Using Xplor-NIH ensemble structure calculations restrained with the RDC and CCR data, we observe collective motions on time scales slower than nanoseconds in the backbone for GB3. To directly access the correlations from CCR, we develop a structure-free data analysis. The resulting dynamic correlation map is consistent with the ensemble-restrained simulations and reveals a complex network. In general, we find that the bond motions are on average slightly correlated and that the local environment dominates many observations. Despite this, some patterns are typical over entire secondary structure elements. In the β-sheet, nearly all bonds are weakly correlated, and there is an approximately binary alternation in correlation intensity corresponding to the solvent exposure/shielding alternation of the side chains. For α-helices, there is also a weak correlation in the H(N)-N bonds. The degree of correlation involving H(α)-C(α) bonds is directly affected by side-chain fluctuations, whereas loops show complex and nonuniform behavior.

Molecular Dynamics Simulations of 441 Two-Residue Peptides in Aqueous Solution: Conformational Preferences and Neighboring Residue Effects with the Amber ff99SB-ildn-NMR Force Field

Understanding the intrinsic conformational preferences of amino acids and the extent to which they are modulated by neighboring residues is a key issue for developing predictive models of protein folding and stability. Here we present the results of 441 independent explicit-solvent MD simulations of all possible two-residue peptides that contain the 20 standard amino acids with histidine modeled in both its neutral and protonated states. (3)J(HNHα) coupling constants and δ(Hα) chemical shifts calculated from the MD simulations correlate quite well with recently published experimental measurements for a corresponding set of two-residue peptides. Neighboring residue effects (NREs) on the average (3)J(HNHα) and δ(Hα) values of adjacent residues are also reasonably well reproduced, with the large NREs exerted experimentally by aromatic residues, in particular, being accurately captured. NREs on the secondary structure preferences of adjacent amino acids have been computed and compared with corresponding effects observed in a coil library and the average β-turn preferences of all amino acid types have been determined. Finally, the intrinsic conformational preferences of histidine, and its NREs on the conformational preferences of adjacent residues, are both shown to be strongly affected by the protonation state of the imidazole ring.

Physicochemical Properties of Ion Pairs of Biological Macromolecules

Ion pairs (also known as salt bridges) of electrostatically interacting cationic and anionic moieties are important for proteins and nucleic acids to perform their function. Although numerous three-dimensional structures show ion pairs at functionally important sites of biological macromolecules and their complexes, the physicochemical properties of the ion pairs are not well understood. Crystal structures typically show a single state for each ion pair. However, recent studies have revealed the dynamic nature of the ion pairs of the biological macromolecules. Biomolecular ion pairs undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. This dynamic behavior is reasonable in light of the fundamental concepts that were established for small ions over the last century. In this review, we introduce the physicochemical concepts relevant to the ion pairs and provide an overview of the recent advancement in biophysical research on the ion pairs of biological macromolecules.

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.

High accuracy of Karplus equations for relating three-bond J couplings to protein backbone torsion angles

(3) JC'C' and (3) JHNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$, including H-bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small. The solution NMR structure of protein GB3, newly refined by using extensive sets of residual dipolar couplings, yields 50-60 % better Karplus equation agreement between ${\varphi }$ angles and experimental (3) JC'C' and (3) JHNHα values than does the high-resolution X-ray structure. In intrinsically disordered proteins, (3) JC'C' and (3) JHNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on (3) J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ${\varphi }$ angles sampled by each residue.

ff14ipq: A Self-Consistent Force Field for Condensed-Phase Simulations of Proteins

We present the ff14ipq force field, implementing the previously published IPolQ charge set for simulations of complete proteins. Minor modifications to the charge derivation scheme and van der Waals interactions between polar atoms are introduced. Torsion parameters are developed through a generational learning approach, based on gas-phase MP2/cc-pVTZ single-point energies computed of structures optimized by the force field itself rather than the quantum benchmark. In this manner, we sacrifice information about the true quantum minima in order to ensure that the force field maintains optimal agreement with the MP2/cc-pVTZ benchmark for the ensembles it will actually produce in simulations. A means of making the gas-phase torsion parameters compatible with solution-phase IPolQ charges is presented. The ff14ipq model is an alternative to ff99SB and other Amber force fields for protein simulations in programs that accommodate pair-specific Lennard-Jones combining rules. The force field gives strong performance on α-helical and β-sheet oligopeptides as well as globular proteins over microsecond time scale simulations, although it has not yet been tested in conjunction with lipid and nucleic acid models. We show how our choices in parameter development influence the resulting force field and how other choices that may have appeared reasonable would actually have led to poorer results. The tools we developed may also aid in the development of future fixed-charge and even polarizable biomolecular force fields.

FragBuilder: an efficient Python library to setup quantum chemistry calculations on peptides models

We present a powerful Python library to quickly and efficiently generate realistic peptide model structures. The library makes it possible to quickly set up quantum mechanical calculations on model peptide structures. It is possible to manually specify a specific conformation of the peptide. Additionally the library also offers sampling of backbone conformations and side chain rotamer conformations from continuous distributions. The generated peptides can then be geometry optimized by the MMFF94 molecular mechanics force field via convenient functions inside the library. Finally, it is possible to output the resulting structures directly to files in a variety of useful formats, such as XYZ or PDB formats, or directly as input files for a quantum chemistry program. FragBuilder is freely available at https://github.com/jensengroup/fragbuilder/ under the terms of the BSD open source license.

Side chain conformational averaging in human dihydrofolate reductase

The three-dimensional structures of the dihydrofolate reductase enzymes from Escherichia coli (ecDHFR or ecE) and Homo sapiens (hDHFR or hE) are very similar, despite a rather low level of sequence identity. Whereas the active site loops of ecDHFR undergo major conformational rearrangements during progression through the reaction cycle, hDHFR remains fixed in a closed loop conformation in all of its catalytic intermediates. To elucidate the structural and dynamic differences between the human and E. coli enzymes, we conducted a comprehensive analysis of side chain flexibility and dynamics in complexes of hDHFR that represent intermediates in the major catalytic cycle. Nuclear magnetic resonance relaxation dispersion experiments show that, in marked contrast to the functionally important motions that feature prominently in the catalytic intermediates of ecDHFR, millisecond time scale fluctuations cannot be detected for hDHFR side chains. Ligand flux in hDHFR is thought to be mediated by conformational changes between a hinge-open state when the substrate/product-binding pocket is vacant and a hinge-closed state when this pocket is occupied. Comparison of X-ray structures of hinge-open and hinge-closed states shows that helix αF changes position by sliding between the two states. Analysis of χ₁ rotamer populations derived from measurements of ³J_CγCO and ³J_CγN couplings indicates that many of the side chains that contact helix αF exhibit rotamer averaging that may facilitate the conformational change. The χ₁ rotamer adopted by the Phe31 side chain depends upon whether the active site contains the substrate or product. In the holoenzyme (the binary complex of hDHFR with reduced nicotinamide adenine dinucleotide phosphate), a combination of hinge opening and a change in the Phe31 χ₁ rotamer opens the active site to facilitate entry of the substrate. Overall, the data suggest that, unlike ecDHFR, hDHFR requires minimal backbone conformational rearrangement as it proceeds through its enzymatic cycle, but that ligand flux is brokered by more subtle conformational changes that depend on the side chain motions of critical residues.

Motional timescale predictions by molecular dynamics simulations: case study using proline and hydroxyproline sidechain dynamics

We propose a new approach for force field optimizations which aims at reproducing dynamics characteristics using biomolecular MD simulations, in addition to improved prediction of motionally averaged structural properties available from experiment. As the source of experimental data for dynamics fittings, we use ¹³C NMR spin-lattice relaxation times T₁ of backbone and sidechain carbons, which allow to determine correlation times of both overall molecular and intramolecular motions. For structural fittings, we use motionally averaged experimental values of NMR J couplings. The proline residue and its derivative 4-hydroxyproline with relatively simple cyclic structure and sidechain dynamics were chosen for the assessment of the new approach in this work. Initially, grid search and simplexed MD simulations identified large number of parameter sets which fit equally well experimental J couplings. Using the Arrhenius-type relationship between the force constant and the correlation time, the available MD data for a series of parameter sets were analyzed to predict the value of the force constant that best reproduces experimental timescale of the sidechain dynamics. Verification of the new force-field (termed as AMBER99SB-ILDNP) against NMR J couplings and correlation times showed consistent and significant improvements compared to the original force field in reproducing both structural and dynamics properties. The results suggest that matching experimental timescales of motions together with motionally averaged characteristics is the valid approach for force field parameter optimization. Such a comprehensive approach is not restricted to cyclic residues and can be extended to other amino acid residues, as well as to the backbone. Proteins 2014; 82:195–215. © 2013 Wiley Periodicals, Inc.

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.

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Side-chain conformational heterogeneity of intermediates in the Escherichia coli dihydrofolate reductase catalytic cycle

Escherichia coli dihydrofolate reductase (DHFR) provides a paradigm for the integrated study of the role of protein dynamics in enzyme function. Previous studies of backbone and side chain dynamics have yielded unprecedented insights into the mechanism by which DHFR progresses through the structural changes that occur during its catalytic cycle. Here we report a comprehensive study of the χ1 rotamer populations of the aromatic and γ-methyl containing residues for complexes of the catalytic cycle, based on NMR measurement of (3)JCγCO and (3)JCγN coupling constants. We report conformational and dynamic information for eight distinct complexes, where transitions between rotamer wells may occur on a broad picosecond to millisecond time scale. This large volume of (3)J data has allowed us to fit new Karplus parameterizations for aromatic side chains and to select the best available of previously determined parameters for Ile, Thr, and Val. The (3)JCγCO and (3)JCγN coupling constants are found to be extremely sensitive measures of side chain χ1 rotamers and to give important insights into the extent of conformational averaging. For a subset of residues in DHFR, the extent of rotamer averaging is invariant to the nature of the bound ligand, while for other residues the rotamer averaging differs in one or more complexes of the enzymatic cycle. These variable-averaging residues are generally located near the active site, but the phenomenon extends into the adenosine binding domain. For several residues, the rotamer populations in different DHFR complexes appear to depend on whether the complex is in the closed or occluded state, and some residues are exquisitely sensitive to small changes in the nature of the bound ligand.

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.

Are Protein Force Fields Getting Better? A Systematic Benchmark on 524 Diverse NMR Measurements

Recent hardware and software advances have enabled simulation studies of protein systems on biophysically-relevant timescales, often revealing the need for improved force fields. Although early force field development was limited by the lack of direct comparisons between simulation and experiment, recent work from several labs has demonstrated direct calculation of NMR observables from protein simulations. Here we quantitatively evaluate recent molecular dynamics force fields against a suite of 524 chemical shift and J coupling ((3)JH(N)H(α), (3)JH(N)C(β), (3)JH(α)C', (3)JH(N)C', and (3)JH(α)N) measurements on dipeptides, tripeptides, tetra-alanine, and ubiquitin. Of the force fields examined (ff96, ff99, ff03, ff03*, ff03w, ff99sb*, ff99sb-ildn, ff99sb-ildn-phi, ff99sb-ildn-nmr, CHARMM27, OPLS-AA), two force fields (ff99sb-ildn-phi, ff99sb-ildn-nmr) combining recent side chain and backbone torsion modifications achieve high accuracy in our benchmark. For the two optimal force fields, the calculation error is comparable to the uncertainty in the experimental comparison. This observation suggests that extracting additional force field improvements from NMR data may require increased accuracy in J coupling and chemical shift prediction. To further investigate the limitations of current force fields, we also consider conformational populations of dipeptides, which were recently estimated using vibrational spectroscopy.

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.

Signature of mobile hydrogen bonding of lysine side chains from long-range 15N-13C scalar J-couplings and computation

Amino acid side chains involved in hydrogen bonds and electrostatic interactions are crucial for protein function. However, detailed investigations of such side chains in solution are rare. Here, through the combination of long-range (15)N-(13)C scalar J-coupling measurements and an atomic-detail molecular dynamics (MD) simulation, direct insight into the structural dynamic behavior of lysine side chains in human ubiquitin has been gained. On the basis of (1)H/(13)C/(15)N heteronuclear correlation experiments selective for lysine NH(3)(+) groups, we analyzed two different types of long-range (15)N-(13)C J-coupling constants: one between intraresidue (15)Nζ and (13)Cγ nuclei ((3)J(NζCγ)) and the other between (15)Nζ and carbonyl (13)C' nuclei across a hydrogen bond ((h3)J(NζC')). The experimental (3)J(NζCγ) data confirm the highly mobile nature of the χ(4) torsion angles of lysine side chains seen in the MD simulation. The NH(3)(+) groups of Lys29 and Lys33 exhibit measurable (h3)J(NζC') couplings arising from hydrogen bonds with backbone carbonyl groups of Glu16 and Thr14, respectively. When interpreted together with the (3)J(NζCγ)-coupling constants and NMR-relaxation-derived S(2) order parameters of the NH(3)(+) groups, they strongly suggest that hydrogen bonds involving NH(3)(+) groups are of a transient and highly dynamic nature, in remarkably good agreement with the MD simulation results.

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.

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.

Free-energy landscape of the GB1 hairpin in all-atom explicit solvent simulations with different force fields: Similarities and differences

Although it is now possible to fold peptides and miniproteins in molecular dynamics simulations, it is well appreciated that force fields are not all transferable to different proteins. Here, we investigate the influence of the protein force field and the solvent model on the folding energy landscape of a prototypical two-state folder, the GB1 hairpin. We use extensive replica-exchange molecular dynamics simulations to characterize the free-energy surface as a function of temperature. Most of these force fields appear similar at a global level, giving a fraction folded at 300 K between 0.2 and 0.8 in all cases, which is a difference in stability of 2.8 kT, and are generally consistent with experimental data at this temperature. The most significant differences appear in the unfolded state, where there are different residual secondary structures which are populated, and the overall dimensions of the unfolded states, which in most of the force fields are too collapsed relative to experimental Förster Resonance Energy Transfer (FRET) data.

Experimental verification of force fields for molecular dynamics simulations using Gly-Pro-Gly-Gly

Experimental NMR verification of MD simulations using 12 different force fields (AMBER, CHARMM, GROMOS, and OPLS-AA) and 5 different water models has been undertaken to identify reliable MD protocols for structure and dynamics elucidations of small open chain peptides containing Gly and Pro. A conformationally flexible tetrapeptide Gly-Pro-Gly-Gly was selected for NMR (3)J-coupling, chemical shift, and internuclear distance measurements, followed by their calculations using 2 μs long MD simulations in water. In addition, Ramachandran population maps for Pro-2 and Gly-3 residues of GPGG obtained from MD simulations were used for detailed comparisons with similar maps from the protein data bank (PDB) for large number of Gly and Pro residues in proteins. The MD simulations revealed strong dependence of the populations and geometries of preferred backbone and side chain conformations, as well as the time scales of the peptide torsional transitions on the force field used. On the basis of the analysis of the measured and calculated data, AMBER99SB is identified as the most reliable force field for reproducing NMR measured parameters, which are dependent on the peptide backbone and the Pro side chain geometries and dynamics. Ramachandran maps showing the dependence of conformational populations as a function of backbone ϕ/ψ angles for Pro-2 and Gly-3 residues of GPGG from MD simulations using AMBER99SB, AMBER03, and CHARMM were found to resemble similar maps for Gly and Pro residues from the PDB survey. Three force fields (AMBER99, AMBER99ϕ, and AMBER94) showed the least satisfactory agreement with both the solution NMR and the PDB survey data. The poor performance of these force fields is attributed to their propensity to overstabilize helical peptide backbone conformations at the Pro-2 and Gly-3 residues. On the basis of the similarity of the MD and PDB Ramachandran plots, the following sequence of transitions is suggested for the Gly backbone conformation: α(L) ⇆ β(PR) ⇆ β(S) ⇆ β(P) ⇆ α, where backbone secondary structures α(L) and α are associated with helices and turns, β(P) and β(PR) correspond to the left- and right-handed polyproline II structures and β(S) denotes the fully stretched backbone conformation. Compared to the force field dependence, less significant, but noteworthy, variations in the populations of the peptide backbone conformations were observed. For different solvent models considered, a correlation was noted between the number of torsional transitions in GPGG and the water self-diffusion coefficient on using TIP3P, TIP4P, and TIP5P models. In addition to MD results, we also report DFT derived Karplus relationships for Gly and Pro residues using B972 and B3LYP functionals.