Predicting 13Calpha chemical shifts for validation of protein structures

Simulation of oriented NMR spectra: Combining molecular dynamics and chemical shift tensor calculations

Solid state NMR is widely used to study the orientation and other structural features of proteins and peptides in lipid bilayers. Using data obtained by PISEMA (Polarization Inversion Spin Exchange at Magic Angle) experiments, periodic spectral patterns arise from well-aligned α-helical molecules. Significant problems in the interpretation of PISEMA spectra may arise for systems that do not form perfectly defined secondary structures, like α-helices, or the signal pattern is disturbed by molecular motion. Here, we present a new method that combines molecular dynamics simulation with tensorial orientational constraints (MDOC) and chemical shift tensor calculations for the simulation and interpretation of PISEMA-like spectra. The calculations include the spectra arising from non α-helical molecules and molecules with non-uniform intrinsic mobility. In a first step, dipolar or quadrupolar interaction tensors drive molecular rotations and reorientations to obtain the proper mean values as observed in corresponding NMR experiments. In a second step, the coordinate snapshots of the MDOC simulations are geometry optimized with the isotropic 15 N chemical shifts as constraints using Bond Polarization Theory (BPT) to provide reliable 15 N CS tensor data. The averaged dipolar 1 H-15 N couplings and the δzz tensor components can then be combined to simulate PISEMA patterns. We apply this method to the ß-helical peptide gramicidin A (gA) and demonstrate that this method enables the assignment of most PISEMA resonances. In addition, MDOC simulations provide local order parameters for the calculated sites. These local order parameters reveal large differences in backbone mobility between L- and D-amino acids of gA.

Assessing the One-Bond Cα-H Spin-Spin Coupling Constants in Proteins: Pros and Cons of Different Approaches

In the present work, we explore three different approaches for the computation of the one-bond spin-spin coupling constants (SSCC) 1JCαH in proteins: density functional theory (DFT) calculations, a Karplus-like equation, and Gaussian process regression. The main motivation of this work is to select the best method for fast and accurate computation of the 1JCαH SSCC, for its use in everyday applications in protein structure validation, refinement, and/or determination. Our initial results showed a poor agreement between the DFT-computed and observed 1JCαH SSCC values. Further analysis leads us to the understanding that the model chosen for the DFT computations is inappropriate and that more complex models will require a higher, if not prohibitively, computational cost. Finally, we show that the Karplus-like equation and Gaussian Process regression provide faster and more accurate results than DFT-based calculations.

Molecular Dynamics model of peptide-protein conjugation: case study of covalent complex between Sos1 peptide and N-terminal SH3 domain from Grb2

We have investigated covalent conjugation of VPPPVPPRRRX′ peptide (where X′ denotes N^ε-chloroacetyl lysine) to N-terminal SH3 domain from adapter protein Grb2. Our experimental results confirmed that the peptide first binds to the SH3 domain noncovalently before establishing a covalent linkage through reaction of X′ with the target cysteine residue C32. We have also confirmed that this reaction involves a thiolate-anion form of C32 and follows the S_N2 mechanism. For this system, we have developed a new MD-based protocol to model the formation of covalent conjugate. The simulation starts with the known coordinates of the noncovalent complex. When two reactive groups come into contact during the course of the simulation, the reaction is initiated. The reaction is modeled via gradual interpolation between the two sets of force field parameters that are representative of the noncovalent and covalent complexes. The simulation proceeds smoothly, with no appreciable perturbations to temperature, pressure or volume, and results in a high-quality MD model of the covalent complex. The validity of this model is confirmed using the experimental chemical shift data. The new MD-based approach offers a valuable tool to explore the mechanics of protein-peptide conjugation and build accurate models of covalent complexes.

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.

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.

Accurate ab initio prediction of NMR chemical shifts of nucleic acids and nucleic acids/protein complexes

NMR chemical shift predictions based on empirical methods are nowadays indispensable tools during resonance assignment and 3D structure calculation of proteins. However, owing to the very limited statistical data basis, such methods are still in their infancy in the field of nucleic acids, especially when non-canonical structures and nucleic acid complexes are considered. Here, we present an ab initio approach for predicting proton chemical shifts of arbitrary nucleic acid structures based on state-of-the-art fragment-based quantum chemical calculations. We tested our prediction method on a diverse set of nucleic acid structures including double-stranded DNA, hairpins, DNA/protein complexes and chemically-modified DNA. Overall, our quantum chemical calculations yield highly/very accurate predictions with mean absolute deviations of 0.3–0.6 ppm and correlation coefficients (r²) usually above 0.9. This will allow for identifying misassignments and validating 3D structures. Furthermore, our calculations reveal that chemical shifts of protons involved in hydrogen bonding are predicted significantly less accurately. This is in part caused by insufficient inclusion of solvation effects. However, it also points toward shortcomings of current force fields used for structure determination of nucleic acids. Our quantum chemical calculations could therefore provide input for force field optimization.

acACS: improving the prediction accuracy of protein subcellular locations and protein classification by incorporating the average chemical shifts composition

The chemical shift is sensitive to changes in the local environments and can report the structural changes. The structure information of a protein can be represented by the average chemical shifts (ACS) composition, which has been broadly applied for enhancing the prediction accuracy in protein subcellular locations and protein classification. However, different kinds of ACS composition can solve different problems. We established an online web server named acACS, which can convert secondary structure into average chemical shift and then compose the vector for representing a protein by using the algorithm of auto covariance. Our solution is easy to use and can meet the needs of users.

A geometrical parametrization of C1'-C5' RNA ribose chemical shifts calculated by density functional theory

It has been recently shown that NMR chemical shifts can be used to determine the structures of proteins. In order to begin to extend this type of approach to nucleic acids, we present an equation that relates the structural parameters and the (13)C chemical shifts of the ribose group. The parameters in the equation were determined by maximizing the agreement between the DFT-derived chemical shifts and those predicted through the equation for a database of ribose structures. Our results indicate that this type of approach represents a promising way of establishing quantitative and computationally efficient analytical relationships between chemical shifts and structural parameters in nucleic acids.

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.

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.

Improved chemical shift prediction by Rosetta conformational sampling

Chemical shift frequencies represent a time-average of all the conformational states populated by a protein. Thus, chemical shift prediction programs based on sequence and database analysis yield higher accuracy for rigid rather than flexible protein segments. Here we show that the prediction accuracy can be significantly improved by averaging over an ensemble of structures, predicted solely from amino acid sequence with the Rosetta program. This approach to chemical shift and structure prediction has the potential to be useful for guiding resonance assignments, especially in solid-state NMR structural studies of membrane proteins in proteoliposomes.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 2. Level of Theory, Basis Set, and Solvents Model Dependence

It has been demonstrated that the fragmentation scheme of our adjustable density matrix assembler (ADMA) approach for the quantum chemical calculations of very large systems is well-suited to calculate NMR chemical shifts of proteins [ Frank et al. Proteins2011, 79, 2189-2202 ]. The systematic investigation performed here on the influences of the level of theory, basis set size, inclusion or exclusion of an implicit solvent model, and the use of partial charges to describe additional parts of the macromolecule on the accuracy of NMR chemical shifts demonstrates that using a valence triple-ζ basis set leads to large improvement compared to the results given in the previous publication. Additionally, moving from the B3LYP to the mPW1PW91 density functional and including partial charges and implicit solvents gave the best results with mean absolute errors of 0.44 ppm for hydrogen atoms excluding H(N) atoms and between 1.53 and 3.44 ppm for carbon atoms depending on the size and also on the accuracy of the protein structure. Polar hydrogen and nitrogen atoms are more difficult to predict. For the first, explicit hydrogen bonds to the solvents need to be included and, for the latter, going beyond DFT to post-Hartree-Fock methods like MP2 is probably required. Even if empirical methods like SHIFTX+ show similar performance, our calculations give for the first time very reliable chemical shifts that can also be used for complexes of proteins with small-molecule ligands or DNA/RNA. Therefore, taking advantage of its ab initio nature, our approach opens new fields of application that would otherwise be largely inaccessible due to insufficient availability of data for empirical parametrization.

Identification of helix capping and b-turn motifs from NMR chemical shifts

We present an empirical method for identification of distinct structural motifs in proteins on the basis of experimentally determined backbone and (13)C(β) chemical shifts. Elements identified include the N-terminal and C-terminal helix capping motifs and five types of β-turns: I, II, I', II' and VIII. Using a database of proteins of known structure, the NMR chemical shifts, together with the PDB-extracted amino acid preference of the helix capping and β-turn motifs are used as input data for training an artificial neural network algorithm, which outputs the statistical probability of finding each motif at any given position in the protein. The trained neural networks, contained in the MICS (motif identification from chemical shifts) program, also provide a confidence level for each of their predictions, and values ranging from ca 0.7-0.9 for the Matthews correlation coefficient of its predictions far exceed those attainable by sequence analysis. MICS is anticipated to be useful both in the conventional NMR structure determination process and for enhancing on-going efforts to determine protein structures solely on the basis of chemical shift information, where it can aid in identifying protein database fragments suitable for use in building such structures.

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.

Toward the quantum chemical calculation of nuclear magnetic resonance chemical shifts of proteins

Despite the many protein structures solved successfully by nuclear magnetic resonance (NMR) spectroscopy, quality control of NMR structures is still by far not as well established and standardized as in crystallography. Therefore, there is still the need for new, independent, and unbiased evaluation tools to identify problematic parts and in the best case also to give guidelines that how to fix them. We present here, quantum chemical calculations of NMR chemical shifts for many proteins based on our fragment-based quantum chemical method: the adjustable density matrix assembler (ADMA). These results show that (13)C chemical shifts of reasonable accuracy can be obtained that can already provide a powerful measure for the structure validation. (1)H and even more (15)N chemical shifts deviate more strongly from experiment due to the insufficient treatment of solvent effects and conformational averaging.

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.

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

Two major techniques have been used to determine the three-dimensional structures of proteins: X-ray diffraction and NMR spectroscopy. In particular, the validation of NMR-derived protein structures is one of the most challenging problems in NMR spectroscopy. Therefore, researchers have proposed a plethora of methods to determine the accuracy and reliability of protein structures. Despite these proposals, there is a growing need for more sophisticated, physics-based structure validation methods. This approach will enable us to (a) characterize the "quality" of the NMR-derived ensemble as a whole by a single parameter, (b) unambiguously identify flaws in the sequence at a residue level, and (c) provide precise information, such as sets of backbone and side-chain torsional angles, that we can use to detect local flaws. Rather than reviewing all of the existing validation methods, this Account describes the contributions of our research group toward a solution of the long-standing problem of both global and local structure validation of NMR-derived protein structures. We emphasize a recently introduced physics-based methodology that makes use of observed and computed (13)C(alpha) chemical shifts (at the density functional theory (DFT) level of theory) for an accurate validation of protein structures in solution and in crystals. By assessing the ability of computed (13)C(alpha) chemical shifts to reproduce observed (13)C(alpha) chemical shifts of a single structure or ensemble of structures in solution and in crystals, we accomplish a global validation by using the conformationally averaged root-mean-square deviation, ca-rmsd, as a scoring function. In addition, the method enables us to provide local validation by identifying a set of individual amino acid conformations for which the computed and observed (13)C(alpha) chemical shifts do not agree within a certain error range and may represent a nonreliable fold of the protein model. Although it is computationally intensive, our validation method has several advantages, which we illustrate through a series of applications. This method makes use of the (13)C(alpha) chemical shifts, not shielding, that are ubiquitous to proteins and can be computed precisely from the phi, psi, and chi torsional angles. There is no need for a priori knowledge of the oligomeric state of the protein, and no knowledge-based information or additional NMR data are required. The primary limitation at this point is the computational cost of such calculations. However, we anticipate that enhancements in the speed of calculating these chemical shifts coupled with the ever-increasing computational power should soon make this a standard method accessible to the general NMR community.

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.

TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts

NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between 13C, 15N and 1H chemical shifts and backbone torsion angles phi and psi (Cornilescu et al. J Biomol NMR 13 289-302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted phi and psi angles, equals +/-13 degrees . Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy.

What can we learn by computing 13Calpha chemical shifts for X-ray protein models?

The room-temperature X-ray structures of ubiquitin (PDB code 1ubq) and of the RNA-binding domain of nonstructural protein 1 of influenza A virus (PDB code 1ail) solved at 1.8 and 1.9 A resolution, respectively, were used to investigate whether a set of conformations rather than a single X-ray structure provides better agreement with both the X-ray data and the observed 13Calpha chemical shifts in solution. For this purpose, a set of new conformations for each of these proteins was generated by fitting them to the experimental X-ray data deposited in the PDB. For each of the generated structures, which show R and Rfree factors similar to those of the deposited X-ray structure, the 13Calpha chemical shifts of all residues in the sequence were computed at the DFT level of theory. The sets of conformations were then evaluated by their ability to reproduce the observed 13Calpha chemical shifts by using the conformational average root-mean-square-deviation (ca-r.m.s.d.). For ubiquitin, the computed set of conformations is a better representation of the observed 13Calpha chemical shifts in terms of the ca-r.m.s.d. than a single X-ray-derived structure. However, for the RNA-binding domain of nonstructural protein 1 of influenza A virus, consideration of an ensemble of conformations does not improve the agreement with the observed 13Calpha chemical shifts. Whether an ensemble of conformations rather than any single structure is a more accurate representation of a protein structure in the crystal as well as of the observed 13Calpha chemical shifts is determined by the dispersion of coordinates, in terms of the all-atom r.m.s.d. among the generated models; these generated models satisfy the experimental X-ray data with accuracy as good as the PDB structure. Therefore, generation of an ensemble is a necessary step to determine whether or not a single structure is sufficient for an accurate representation of both experimental X-ray data and observed 13Calpha chemical shifts in solution.

Performance of density functional models to reproduce observed (13)C(alpha) chemical shifts of proteins in solution

The purpose of this work is to test several density functional models (namely, OPBE, O3LYP, OPW91, BPW91, OB98, BPBE, B971, OLYP, PBE1PBE, and B3LYP) to determine their accuracy and speed for computing (13)C(alpha) chemical shifts in proteins. The test is applied to 10 NMR-derived conformations of the 76-residue alpha/beta protein ubiquitin (protein data bank id 1D3Z). With each functional, the (13)C(alpha) shielding was computed for 760 amino acid residues by using a combination of approaches that includes, but is not limited to, treating each amino acid X in the sequence as a terminally blocked tripeptide with the sequence Ac-GXG-NMe in the conformation of the regularized experimental protein structure. As computation of the (13)C(alpha) chemical shifts, not their shielding, is the main goal of this work, a computation of the (13)C(alpha) shielding of the reference, namely, tetramethylsilane, is investigated here and an effective and a computed tetramethylsilane shielding value for each of the functionals is provided. Despite observed small differences among all functionals tested, the results indicate that four of them, namely, OPBE, OPW91, OB98, and OLYP, provide the most accurate functionals with which to reproduce observed (13)C(alpha) chemical shifts of proteins in solution, and are among the faster ones. This study also provides evidence for the applicability of these functionals to proteins of any size or class, and for the validation of our previous results and conclusions, obtained from calculations with the slower B3LYP functional.

Quantum chemical 13C(alpha) chemical shift calculations for protein NMR structure determination, refinement, and validation

A recently determined set of 20 NMR-derived conformations of a 48-residue all-alpha-helical protein, (PDB ID code 2JVD), is validated here by comparing the observed (13)C(alpha) chemical shifts with those computed at the density functional level of theory. In addition, a recently introduced physics-based method, aimed at determining protein structures by using NOE-derived distance constraints together with observed and computed (13)C(alpha) chemical shifts, was applied to determine a new set of 10 conformations, (Set-bt), as a blind test for the same protein. A cross-validation of these two sets of conformations in terms of the agreement between computed and observed (13)C(alpha) chemical shifts, several stereochemical quality factors, and some NMR quality assessment scores reveals the good quality of both sets of structures. We also carried out an analysis of the agreement between the observed and computed (13)C(alpha) chemical shifts for a slightly longer construct of the protein solved by x-ray crystallography at 2.0-A resolution (PDB ID code 3BHP) with an identical amino acid residue sequence to the 2JVD structure for the first 46 residues. Our results reveal that both of the NMR-derived sets, namely 2JVD and Set-bt, are somewhat better representations of the observed (13)C(alpha) chemical shifts in solution than the 3BHP crystal structure. In addition, the (13)C(alpha)-based validation analysis appears to be more sensitive to subtle structural differences across the three sets of structures than any other NMR quality-assessment scores used here, and, although it is computationally intensive, this analysis has potential value as a standard procedure to determine, refine, and validate protein structures.

Factors affecting the use of 13C(alpha) chemical shifts to determine, refine, and validate protein structures

Interest centers here on the analysis of two different, but related, phenomena that affect side-chain conformations and consequently 13C(alpha) chemical shifts and their applications to determine, refine, and validate protein structures. The first is whether 13C(alpha) chemical shifts, computed at the DFT level of approximation with charged residues is a better approximation of observed 13C(alpha) chemical shifts than those computed with neutral residues for proteins in solution. Accurate computation of 13C(alpha) chemical shifts requires a proper representation of the charges, which might not take on integral values. For this analysis, the charges for 139 conformations of the protein ubiquitin were determined by explicit consideration of protein binding equilibria, at a given pH, that is, by exploring the 2(xi) possible ionization states of the whole molecule, with xi being the number of ionizable groups. The results of this analysis, as revealed by the shielding/deshielding of the 13C(alpha) nucleus, indicated that: (i) there is a significant difference in the computed 13C(alpha) chemical shifts, between basic and acidic groups, as a function of the degree of charge of the side chain; (ii) this difference is attributed to the distance between the ionizable groups and the 13C(alpha) nucleus, which is shorter for the acidic Asp and Glu groups as compared with that for the basic Lys and Arg groups; and (iii) the use of neutral, rather than charged, basic and acidic groups is a better approximation of the observed 13C(alpha) chemical shifts of a protein in solution. The second is how side-chain flexibility influences computed 13C(alpha) chemical shifts in an additional set of ubiquitin conformations, in which the side chains are generated from an NMR-derived structure with the backbone conformation assumed to be fixed. The 13C(alpha) chemical shift of a given amino acid residue in a protein is determined, mainly, by its own backbone and side-chain torsional angles, independent of the neighboring residues; the conformation of a given residue itself, however, depends on the environment of this residue and, hence, on the whole protein structure. As a consequence, this analysis reveals the role and impact of an accurate side-chain computation in the determination and refinement of protein conformation. The results of this analysis are: (i) a lower error between computed and observed 13C(alpha) chemical shifts (by up to 3.7 ppm), was found for approximately 68% and approximately 63% of all ionizable residues and all non-Ala/Pro/Gly residues, respectively, in the additional set of conformations, compared with results for the model from which the set was derived; and (ii) all the additional conformations exhibit a lower root-mean-square-deviation (1.97 ppm < or = rmsd < or = 2.13 ppm), between computed and observed 13C(alpha) chemical shifts, than the rmsd (2.32 ppm) computed for the starting conformation from which this additional set was derived. As a validation test, an analysis of the additional set of ubiquitin conformations, comparing computed and observed values of both 13C(alpha) chemical shifts and chi(1) torsional angles (given by the vicinal coupling constants, 3J(N-Cgamma) and 3J(C'-Cgamma), is discussed.

Use of 13C(alpha) chemical shifts for accurate determination of beta-sheet structures in solution

A physics-based method, aimed at determining protein structures by using NOE-derived distance constraints together with observed and computed 13C(alpha) chemical shifts, is applied to determine the structure of a 20-residue all-beta peptide (BS2). The approach makes use of 13C(alpha) chemical shifts, computed at the density functional level of theory, to derive backbone and side-chain torsional constraints for all of the amino acid residues, without making use of information about residue occupancy in any region of the Ramachandran map. In addition, the torsional constraints are derived dynamically--i.e., they are redefined at each step of the algorithm. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than existing NMR-derived models of the peptide, in terms of the agreement between predicted and observed 13C(beta) chemical shifts, and some stereochemical quality indicators. The accumulated evidence indicates that, for a highly flexible BS2 peptide in solution, it may not be possible to determine a single structure (or a small set of structures) that would satisfy all of the constraints exactly and simultaneously because the observed NOEs and 13C(alpha) chemical shifts correspond to a dynamic ensemble of conformations. Analysis of the structural flexibility, carried out by molecular dynamics simulations in explicit water, revealed that the whole peptide can be characterized as having liquid-like behavior, according to the Lindemann criterion. In summary, a beta-sheet structure of a highly flexible peptide in solution can be determined by a quantum-chemical-based procedure.

Use of 13Calpha chemical shifts in protein structure determination

A physics-based method aimed at determining protein structures by using NOE-derived distances together with observed and computed 13C chemical shifts is proposed. The approach makes use of 13Calpha chemical shifts, computed at the density functional level of theory, to obtain torsional constraints for all backbone and side-chain torsional angles without making a priori use of the occupancy of any region of the Ramachandran map by the amino acid residues. The torsional constraints are not fixed but are changed dynamically in each step of the procedure, following an iterative self-consistent approach intended to identify a set of conformations for which the computed 13Calpha chemical shifts match the experimental ones. A test is carried out on a 76-amino acid, all-alpha-helical protein; namely, the Bacillus subtilis acyl carrier protein. It is shown that, starting from randomly generated conformations, the final protein models are more accurate than an existing NMR-derived structure model of this protein, in terms of both the agreement between predicted and observed 13Calpha chemical shifts and some stereochemical quality indicators, and of similar accuracy as one of the protein models solved at a high level of resolution. The results provide evidence that this methodology can be used not only for structure determination but also for additional protein structure refinement of NMR-derived models deposited in the Protein Data Bank.