Assessing the accuracy of protein structures by quantum mechanical computations of 13C(alpha) chemical shifts

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Classification of RNA backbone conformations into rotamers using 13C' chemical shifts: exploring how far we can go

The conformational space of the ribose-phosphate backbone is very complex as it is defined in terms of six torsional angles. To help delimit the RNA backbone conformational preferences, 46 rotamers have been defined in terms of these torsional angles. In the present work, we use the ribose experimental and theoretical ¹³C′ chemical shifts data and machine learning methods to classify RNA backbone conformations into rotamers and families of rotamers. We show to what extent the experimental ¹³C′ chemical shifts can be used to identify rotamers and discuss some problem with the theoretical computations of ¹³C′ chemical shifts.

13C Chemical Shifts in Proteins: A Rich Source of Encoded Structural Information

Despite the formidable progress in Nuclear Magnetic Resonance (NMR) spectroscopy, quality assessment of NMR-derived structures remains as an important problem. Thus, validation of protein structures is essential for the spectroscopists, since it could enable them to detect structural flaws and potentially guide their efforts in further refinement. Moreover, availability of accurate and efficient validation tools would help molecular biologists and computational chemists to evaluate quality of available experimental structures and to select a protein model which is the most suitable for a given scientific problem. The ¹³C^α nuclei are ubiquitous in proteins, moreover, their shieldings are easily obtainable from NMR experiments and represent a rich source of encoded structural information that makes ¹³C^α chemical shifts an attractive candidate for use in computational methods aimed at determination and validation of protein structures. In this chapter, the basis of a novel methodology of computing, at the quantum chemical level of theory, the ¹³C^α shielding for the amino acid residues in proteins is described. We also identify and examine the main factors affecting the ¹³C^α-shielding computation. Finally, we illustrate how the information encoded in the ¹³C chemical shifts can be used for a number of applications, viz., from protein structure prediction of both α-helical and β-sheet conformations, to determination of the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH or to accurate detection of structural flaws, at a residue-level, in NMR-determined protein models.

Error assessment in molecular dynamics trajectories using computed NMR chemical shifts

Accurate chemical shifts for the atoms in molecular mechanics (MD) trajectories can be obtained from quantum mechanical (QM) calculations that depend solely on the coordinates of the atoms in the localized regions surrounding atoms of interest. If these coordinates are correct and the sample size is adequate, the ensemble average of these chemical shifts should be equal to the chemical shifts obtained from NMR spectroscopy. If this is not the case, the coordinates must be incorrect. We have utilized this fact to quantify the errors associated with the backbone atoms in MD simulations of proteins. A library of regional conformers containing 169,499 members was constructed from 6 model proteins. The chemical shifts associated with the backbone atoms in each of these conformers was obtained from QM calculations using density functional theory at the B3LYP level with a 6-311+G(2d,p) basis set. Chemical shifts were assigned to each backbone atom in each MD simulation frame using a template matching approach. The ensemble average of these chemical shifts was compared to chemical shifts from NMR spectroscopy. A large systematic error was identified that affected the ¹H atoms of the peptide bonds involved in hydrogen bonding with water molecules or peptide backbone atoms. This error was highly sensitive to changes in electrostatic parameters. Smaller errors affecting the ¹³C^a and ¹⁵N atoms were also detected. We believe these errors could be useful as metrics for comparing the force-fields and parameter sets used in MD simulation because they are directly tied to errors in atomic coordinates.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state ¹³C and ¹⁵N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Decoding the Mobility and Time Scales of Protein Loops

The flexible nature of protein loops and the time scales of their dynamics are critical for many biologically important events at the molecular level, such as protein interaction and recognition processes. In order to obtain a predictive understanding of the dynamic properties of loops, 500 ns molecular dynamics (MD) computer simulations of 38 different proteins were performed and validated using NMR chemical shifts. A total of 169 loops were analyzed and classified into three types, namely fast loops with correlation times <10 ns, slow loops with correlation times between 10 and 500 ns, and loops that are static over the course of the whole trajectory. Chemical and biophysical loop descriptors, such as amino-acid sequence, average 3D structure, charge distribution, hydrophobicity, and local contacts were used to develop and parametrize the ToeLoop algorithm for the prediction of the flexibility and motional time scale of every protein loop, which is also implemented as a public Web server (http://spin.ccic.ohio-state.edu/index.php/loop). The results demonstrate that loop dynamics with their time scales can be predicted rapidly with reasonable accuracy, which will allow the screening of average protein structures to help better understand the various roles loops can play in the context of protein-protein interactions and binding.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

A systematic study on RNA NMR chemical shift calculation based on the automated fragmentation QM/MM approach

¹H, ¹³C and ¹⁵N NMR chemical shift calculations on RNAs were performed using the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach.

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.

Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods

We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

My 65 years in protein chemistry

This is a tour of a physical chemist through 65 years of protein chemistry from the time when emphasis was placed on the determination of the size and shape of the protein molecule as a colloidal particle, with an early breakthrough by James Sumner, followed by Linus Pauling and Fred Sanger, that a protein was a real molecule, albeit a macromolecule. It deals with the recognition of the nature and importance of hydrogen bonds and hydrophobic interactions in determining the structure, properties, and biological function of proteins until the present acquisition of an understanding of the structure, thermodynamics, and folding pathways from a linear array of amino acids to a biological entity. Along the way, with a combination of experiment and theoretical interpretation, a mechanism was elucidated for the thrombin-induced conversion of fibrinogen to a fibrin blood clot and for the oxidative-folding pathways of ribonuclease A. Before the atomic structure of a protein molecule was determined by x-ray diffraction or nuclear magnetic resonance spectroscopy, experimental studies of the fundamental interactions underlying protein structure led to several distance constraints which motivated the theoretical approach to determine protein structure, and culminated in the Empirical Conformational Energy Program for Peptides (ECEPP), an all-atom force field, with which the structures of fibrous collagen-like proteins and the 46-residue globular staphylococcal protein A were determined. To undertake the study of larger globular proteins, a physics-based coarse-grained UNited-RESidue (UNRES) force field was developed, and applied to the protein-folding problem in terms of structure, thermodynamics, dynamics, and folding pathways. Initially, single-chain and, ultimately, multiple-chain proteins were examined, and the methodology was extended to protein-protein interactions and to nucleic acids and to protein-nucleic acid interactions. The ultimate results led to an understanding of a variety of biological processes underlying natural and disease phenomena.

NMR structure validation in relation to dynamics and structure determination

NMR spectroscopy is a key technique for understanding the behaviour of proteins, especially highly dynamic proteins that adopt multiple conformations in solution. Overall, protein structures determined from NMR spectroscopy data constitute just over 10% of the Protein Data Bank archive. This review covers the validation of these NMR protein structures, but rather than describing currently available methodology, it focuses on concepts that are important for understanding where and how validation is most relevant. First, the inherent characteristics of the protein under study have an influence on quality and quantity of the distinct types of data that can be acquired from NMR experiments. Second, these NMR data are necessarily transformed into a model for use in a structure calculation protocol, and the protein structures that result from this reflect the types of NMR data used as well as the protein characteristics. The validation of NMR protein structures should therefore take account, wherever possible, of the inherent behavioural characteristics of the protein, the types of available NMR data, and the calculation protocol. These concepts are discussed in the context of 'knowledge based' and 'model versus data' validation, with suggestions for questions to ask and different validation categories to consider. The principal aim of this review is to stimulate discussion and to help the reader understand the relationships between the above elements in order to make informed decisions on which validation approaches are the most relevant in particular cases.

13C Chemical Shifts in Proteins: A Rich Source of Encoded Structural Information

Despite the formidable progress in Nuclear Magnetic Resonance (NMR) spectroscopy, quality assessment of NMR-derived structures remains as an important problem. Thus, validation of protein structures is essential for the spectroscopists, since it could enable them to detect structural flaws and potentially guide their efforts in further refinement. Moreover, availability of accurate and efficient validation tools would help molecular biologists and computational chemists to evaluate quality of available experimental structures and to select a protein model which is the most suitable for a given scientific problem. The ¹³C^α nuclei are ubiquitous in proteins, moreover, their shieldings are easily obtainable from NMR experiments and represent a rich source of encoded structural information that makes ¹³C^α chemical shifts an attractive candidate for use in computational methods aimed at determination and validation of protein structures. In this chapter, the basis of a novel methodology of computing, at the quantum chemical level of theory, the ¹³C^α shielding for the amino acid residues in proteins is described. We also identify and examine the main factors affecting the ¹³C^α-shielding computation. Finally, we illustrate how the information encoded in the ¹³C chemical shifts can be used for a number of applications, viz., from protein structure prediction of both α-helical and β-sheet conformations, to determination of the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH or to accurate detection of structural flaws, at a residue-level, in NMR-determined protein models.

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts--sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond ((h3)J(NC')) spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.

Physics-based method to validate and repair flaws in protein structures

A method that makes use of information provided by the combination of (13)C(α) and (13)C(β) chemical shifts, computed at the density functional level of theory, enables one to (i) validate, at the residue level, conformations of proteins and detect backbone or side-chain flaws by taking into account an ensemble average of chemical shifts over all of the conformations used to represent a protein, with a sensitivity of ∼90%; and (ii) provide a set of (χ1/χ2) torsional angles that leads to optimal agreement between the observed and computed (13)C(α) and (13)C(β) chemical shifts. The method has been incorporated into the CheShift-2 protein validation Web server. To test the reliability of the provided set of (χ1/χ2) torsional angles, the side chains of all reported conformations of five NMR-determined protein models were refined by a simple routine, without using NOE-based distance restraints. The refinement of each of these five proteins leads to optimal agreement between the observed and computed (13)C(α) and (13)C(β) chemical shifts for ∼94% of the flaws, on average, without introducing a significantly large number of violations of the NOE-based distance restraints for a distance range ≤ 0.5 , in which the largest number of distance violations occurs. The results of this work suggest that use of the provided set of (χ1/χ2) torsional angles together with other observables, such as NOEs, should lead to a fast and accurate refinement of the side-chain conformations of protein models.

Solid-state NMR in macromolecular systems: insights on how molecular entities move

The function of synthetic and natural macromolecularsystems critically depends on the packing and dynamics of the individual components of a given system. Not only can solid-state NMR provide structural information with atomic resolution, but it can also provide a way to characterize the amplitude and time scales of motions over broad ranges of length and time. These movements include molecular dynamics, rotational and translational motions of the building blocks, and also the motion of the functional species themselves, such as protons or ions. This Account examines solid-state NMR methods for correlating dynamics and function in a variety of chemical systems. In the early days, scientists thought that the rotationalmotions reflected the geometry of the moving entities. They described these phenomena as jumps about well-defined axes, such as phenyl flips, even in amorphous polymers. Later, they realized that conformational transitions in macromolecules happen in a much more complex way. Because the individual entities do not rotate around well-defined axes, they require much less space. Only recently researchers have appreciated the relative importance of large angle fluctuations of polymers over rotational jumps. Researchers have long considered that cooperative motions might be at work, yet only recently they have clearly detected these motions by NMR in macromolecular and supramolecular systems. In correlations of dynamics and function, local motions do not always provide the mechanism of long-range transport. This idea holds true in ion conduction but also applies to chain transport in polymer melts and semicrystalline polymers. Similar chain motions and ion transport likewise occur in functional biopolymers, systems where solid-state NMR studies are also performed. In polymer science, researchers have appreciated the unique information on molecular dynamics available from advanced solid-state NMR at times, where their colleagues in the biomacromolecular sciences have emphasized structure. By contrast, following X-ray crystallographers, researchers studying proteins using solution NMR introduced the combination of NMR with computer simulation before that became common practice in solid-state NMR. Today's simulation methods can handle partially ordered or even disordered systems common in synthetic polymers. Thus, the multitechnique approaches employed in NMR of synthetic and biological macromolecules have converged. Therefore, this Account will be relevant to both researchers studying synthetic macromolecular and supramolecular systems and those studying biological complexes.

Probing slowly exchanging protein systems via ¹³Cα-CEST: monitoring folding of the Im7 protein

A¹³C(α) chemical exchange saturation transfer based experiment is presented for the study of protein systems undergoing slow interconversion between an 'observable' ground state and one or more 'invisible' excited states. Here a labeling strategy whereby [2-(13)C]-glucose is the sole carbon source is exploited, producing proteins with ¹³C at the C(α) position, while the majority of residues remain unlabeled at CO or C(β). The new experiment is demonstrated with an application to the folding reaction of the Im7 protein that involves an on-pathway excited state. The obtained excited state (13)C(α) chemical shifts are cross validated by comparison to values extracted from analysis of CPMG relaxation dispersion profiles, establishing the utility of the methodology.

Chemical shifts in biomolecules

NMR chemical shifts are sensitive probes of structure and dynamics in proteins. Empirical models, based on a large database of measured shifts, take an input structure and provide increasingly accurate estimates of the corresponding shifts. Quantum chemical calculations can provide the same information, with greater generality but (currently) with less accuracy. These methods are now providing new ways to approach NMR structure determination, and new insights into the conformational dynamics of proteins.

CheShift-2 resolves a local inconsistency between two X-ray crystal structures

Since chemical shifts provide important and relatively accessible information about protein structure in solution, a Web server, CheShift-2, was developed for structure interrogation, based on a quantum mechanics database of (13)C( α ) chemical shifts. We report the application of CheShift-2 to a local inconsistency between two X-ray crystal structures (PDB IDs 1IKN and 1NFI) of the complex between the p65/p50 heterodimer of NFκB and its inhibitor IκBα. The availability of NMR resonance assignments that included the region of the inconsistency provided an opportunity for independent validation of the CheShift-2 server. Application of the server showed that the (13)C( α ) chemical shifts measured for the Gly270-Pro281 sequence close to the C-terminus of IκBα were unequivocally consistent with the backbone structure modeled in the 1IKN structure, and were inconsistent with the 1NFI structure. Previous NOE measurements had demonstrated that the position of a tryptophan ring in the region immediately N-terminal in this region was not consistent with either structure. Subsequent recalculation of the local structure in this region, based on the electron density of the deposited structure factors for 1IKN, confirmed that the local backbone structure was best modeled by 1IKN, but that the rotamer of Trp258 is consistent with the 1NFI structure, including the presence of a hydrogen bond between the ring NεH of Trp258 and the backbone carbonyl group of Gln278. The consensus between all of these measures suggests that the CheShift-2 server operates well under circumstances in which backbone chemical shifts are available but where local plasticity may render X-ray structural data ambiguous.

CheShift-2: graphic validation of protein structures

Summary: The differences between observed and predicted ¹³C^α chemical shifts can be used as a sensitive probe with which to detect possible local flaws in protein structures. For this reason, we previously introduced CheShift, a Web server for protein structure validation. Now, we present CheShift-2 in which a graphical user interface is implemented to render such local flaws easily visible. A series of applications to 15 ensembles of conformations illustrate the ability of CheShift-2 to locate the main structural flaws rapidly and accurately on a per-residue basis. Since accuracy plays a central role in CheShift predictions, the treatment of histidine (His) is investigated here by exploring which form of His should be used in CheShift-2.

Availability:CheShift-2 is free of charge for academic use and can be accessed from www.cheshift.com

Contact:has5@cornell.edu; jv84@cornell.edu

Supplementary information:Supplementary data are available at the Bioinformatics online.

Limiting values of the 15N chemical shift of the imidazole ring of histidine at high pH

Tautomeric identification by direct observation of (15)N chemical shifts of the imidazole ring of histidine (His) has become a common practice in NMR spectroscopy. However, such applications require knowledge of the "canonical" limiting values of the (15)N chemical shift of the imidazole ring of His in which each form of His, namely, the protonated (H(+)) and the tautomeric N(ε2)-H and N(δ1)-H forms, respectively, is present to the extent of 100%. So far, the adopted canonical limiting values of the (15)N chemical shift have been those available from model compounds. Whether these canonical values reflect those of the individual pure forms of His is investigated here by carrying out an analysis of the second-order shielding differences, ΔΔ = |Δ(ε) - Δ(δ) |, with Δ(ξ) (ξ = ε or δ) being the density functional theory (DFT)-computed average shielding differences between the two nitrogens of the imidazole ring of His in each pure tautomeric form. In the high-pH limit, the results indicate that (i) the ΔΔ values from the DFT-computed shielding, but not from the commonly used canonical limiting values, are in closer agreement with those obtained with experimental chemical shift data from model compounds in solution and solid-state NMR; and (ii) the commonly used canonical limiting values of the (15)N chemical shifts lead to an average tautomeric equilibrium constant that differs by a factor of ∼2.6 from the one computed by using DFT-based (15)N limiting values, raising concern about the practice of using canonical limiting (15)N values. This can be avoided by reporting tautomeric equilibrium constants computed by using only limiting (15)N values for the N(ε2)-H tautomer.

Respice, adspice, and prospice

The title, "Look to the past, Look to the present, and Look to the future," the motto of City College of New York, expresses how my family life and education led me to an academic career in physical chemistry and ultimately to a study of proteins. The economic depression of the 1930s left a lasting impression on my outlook and career aspirations. With fortunate experiences at several stages in my life, I was able to participate in the great adventure of the last half of the twentieth century: the revolution in biology that advanced the field of protein chemistry to so great an extent. The future is bright and limitless, with greater understanding of biology yet to come.

Structure-based prediction of methyl chemical shifts in proteins

Protein methyl groups have recently been the subject of much attention in NMR spectroscopy because of the opportunities that they provide to obtain information about the structure and dynamics of proteins and protein complexes. With the advent of selective labeling schemes, methyl groups are particularly interesting in the context of chemical shift based protein structure determination, an approach that to date has exploited primarily the mapping between protein structures and backbone chemical shifts. In order to extend the scope of chemical shifts for structure determination, we present here the CH3Shift method of performing structure-based predictions of methyl chemical shifts. The terms considered in the predictions take account of ring current, magnetic anisotropy, electric field, rotameric type, and dihedral angle effects, which are considered in conjunction with polynomial functions of interatomic distances. We show that the CH3Shift method achieves an accuracy in the predictions that ranges from 0.133 to 0.198 ppm for (1)H chemical shifts for Ala, Thr, Val, Leu and Ile methyl groups. We illustrate the use of the method by assessing the accuracy of side-chain structures in structural ensembles representing the dynamics of proteins.

Assessing the fractions of tautomeric forms of the imidazole ring of histidine in proteins as a function of pH

A method is proposed to determine the fraction of the tautomeric forms of the imidazole ring of histidine in proteins as a function of pH, provided that the observed and chemical shifts and the protein structure, or the fraction of H(+) form, are known. This method is based on the use of quantum chemical methods to compute the (13)C NMR shieldings of all the imidazole ring carbons ((13)C(γ), , and ) for each of the two tautomers, N(δ1)-H and N(ε2)-H, and the protonated form, H(+), of histidine. This methodology enabled us (i) to determine the fraction of all the tautomeric forms of histidine for eight proteins for which the and chemical shifts had been determined in solution in the pH range of 3.2 to 7.5 and (ii) to estimate the fraction of tautomeric forms of eight histidine-containing dipeptide crystals for which the chemical shifts had been determined by solid-state (13)C NMR. Our results for proteins indicate that the protonated form is the most populated one, whereas the distribution of the tautomeric forms for the imidazole ring varies significantly among different histidines in the same protein, reflecting the importance of the environment of the histidines in determining the tautomeric forms. In addition, for ∼70% of the neutral histidine-containing dipeptides, the method leads to fairly good agreement between the calculated and the experimental tautomeric form. Coexistence of different tautomeric forms in the same crystal structure may explain the remaining 30% of disagreement.

Sequential nearest-neighbor effects on computed 13Calpha chemical shifts

To evaluate sequential nearest-neighbor effects on quantum-chemical calculations of (13)C(alpha) chemical shifts, we selected the structure of the nucleic acid binding (NAB) protein from the SARS coronavirus determined by NMR in solution (PDB id 2K87). NAB is a 116-residue alpha/beta protein, which contains 9 prolines and has 50% of its residues located in loops and turns. Overall, the results presented here show that sizeable nearest-neighbor effects are seen only for residues preceding proline, where Pro introduces an overestimation, on average, of 1.73 ppm in the computed (13)C(alpha) chemical shifts. A new ensemble of 20 conformers representing the NMR structure of the NAB, which was calculated with an input containing backbone torsion angle constraints derived from the theoretical (13)C(alpha) chemical shifts as supplementary data to the NOE distance constraints, exhibits very similar topology and comparable agreement with the NOE constraints as the published NMR structure. However, the two structures differ in the patterns of differences between observed and computed (13)C(alpha) chemical shifts, Delta(ca,i), for the individual residues along the sequence. This indicates that the Delta(ca,i)-values for the NAB protein are primarily a consequence of the limited sampling by the bundles of 20 conformers used, as in common practice, to represent the two NMR structures, rather than of local flaws in the structures.

Analysis of 13Calpha and 13Cbeta chemical shifts of cysteine and cystine residues in proteins: a quantum chemical approach

Cysteines possess a unique property among the 20 naturally occurring amino acids: it can be present in proteins in either the reduced or oxidized form, and can regulate the activity of some proteins. Consequently, to augment our previous treatment of the other types of residues, the 13Calpha and 13Cbeta chemical shifts of 837 cysteines in disulfide-bonded cystine from a set of seven non-redundant proteins, determined by X-ray crystallography and NMR spectroscopy, were computed at the DFT level of theory. Our results indicate that the errors between observed and computed 13Calpha chemical shifts of such oxidized cysteines can be attributed to several effects such as: (a) the quality of the NMR-determined models, as evaluated by the conformational-average (ca) rmsd value; (b) the existence of high B-factor or crystal-packing effects for the X-ray-determined structures; (c) the dynamics of the disulfide bonds in solution; and (d) the differences in the experimental conditions under which the observed 13Calpha chemical shifts and the protein models were determined by either X-ray crystallography or NMR-spectroscopy. These quantum-chemical-based calculations indicate the existence of two, almost non-overlapped, basins for the oxidized and reduced -SH 13Cbeta, but not for the 13Calpha, chemical shifts, in good agreement with the observation of 375 13Calpha and 337 13Cbeta resonances from 132 proteins by Sharma and Rajarathnam (2000). Overall, our results indicate that explicit consideration of the disulfide bonds is a necessary condition for an accurate prediction of 13Calpha and 13Cbeta chemical shifts of cysteines in cystines.

Quantum-mechanics-derived 13Calpha chemical shift server (CheShift) for protein structure validation

A server (CheShift) has been developed to predict (13)C(alpha) chemical shifts of protein structures. It is based on the generation of 696,916 conformations as a function of the phi, psi, omega, chi1 and chi2 torsional angles for all 20 naturally occurring amino acids. Their (13)C(alpha) chemical shifts were computed at the DFT level of theory with a small basis set and extrapolated, with an empirically-determined linear regression formula, to reproduce the values obtained with a larger basis set. Analysis of the accuracy and sensitivity of the CheShift predictions, in terms of both the correlation coefficient R and the conformational-averaged rmsd between the observed and predicted (13)C(alpha) chemical shifts, was carried out for 3 sets of conformations: (i) 36 x-ray-derived protein structures solved at 2.3 A or better resolution, for which sets of (13)C(alpha) chemical shifts were available; (ii) 15 pairs of x-ray and NMR-derived sets of protein conformations; and (iii) a set of decoys for 3 proteins showing an rmsd with respect to the x-ray structure from which they were derived of up to 3 A. Comparative analysis carried out with 4 popular servers, namely SHIFTS, SHIFTX, SPARTA, and PROSHIFT, for these 3 sets of conformations demonstrated that CheShift is the most sensitive server with which to detect subtle differences between protein models and, hence, to validate protein structures determined by either x-ray or NMR methods, if the observed (13)C(alpha) chemical shifts are available. CheShift is available as a web server.