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 ϕ and ψ (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 ϕ and ψ angles, equals ±13°. 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. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Protein backbone angle restraints from searching a database for chemical shift and sequence homology

Chemical shifts of backbone atoms in proteins are exquisitely sensitive to local conformation, and homologous proteins show quite similar patterns of secondary chemical shifts. The inverse of this relation is used to search a database for triplets of adjacent residues with secondary chemical shifts and sequence similarity which provide the best match to the query triplet of interest. The database contains 13C, 13C, 13C, 1H and 15N chemical shifts for 20 proteins for which a high resolution X-ray structure is available. The computer program TALOS was developed to search this database for strings of residues with chemical shift and residue type homology. The relative importance of the weighting factors attached to the secondary chemical shifts of the five types of resonances relative to that of sequence similarity was optimized empirically. TALOS yields the 10 triplets which have the closest similarity in secondary chemical shift and amino acid sequence to those of the query sequence. If the central residues in these 10 triplets exhibit similar and backbone angles, their averages can reliably be used as angular restraints for the protein whose structure is being studied. Tests carried out for proteins of known structure indicate that the root-mean-square difference (rmsd) between the output of TALOS and the X-ray derived backbone angles is about 15°. Approximately 3% of the predictions made by TALOS are found to be in error.     

Fast Assignment of <Superscript>15</Superscript>N-HSQC Peaks using High-Resolution 3D HNcocaNH Experiments with Non-Uniform Sampling

We describe an efficient NMR triple resonance approach for fast assignment of backbone amide resonance peaks in the ¹⁵N-HSQC spectrum. The exceptionally high resolutions achieved in the 3D HncocaNH and hNcocaNH experiments together with non-uniform sampling facilitate error-free sequential connection of backbone amides. Data required for the complete backbone amide assignment of the 56-residue protein GB1 domain were obtained in 14 h. Data analysis was vastly streamlined using a ‘backbone NH walk’ method to determine sequential connectivities without the need for ¹³C chemical shifts comparison. Amino acid residues in the sequentially connected NH chains are classified into two groups by a simple variation of the NMR pulse sequence, and the resulting ‘ZeBra’ stripe patterns are useful for mapping these chains to the protein sequence. In addition to resolving ambiguous assignments derived from conventional backbone experiments, this approach can be employed to rapidly assign small proteins or flexible regions in larger proteins, and to transfer assignments to mutant proteins or proteins in different ligand-binding states.     

Accurate geometries for “Mountain pass” regions of the Ramachandran plot using quantum chemical calculations

Unusual local arrangements of protein in Ramachandran space are not well represented by standard geometry tools used in either protein structure refinement using simple harmonic geometry restraints or in protein simulations using molecular mechanics force fields. In contrast, quantum chemical computations using small poly‐peptide molecular models can predict accurate geometries for any well‐defined backbone Ramachandran orientation. For conformations along transition regions—ϕ from −60 to 60°—a very good agreement with representative high‐resolution experimental X‐ray (≤1.5 Å) protein structures is obtained for both backbone C⁻¹‐N‐C_α angle and the nonbonded O⁻¹…C distance, while “standard geometry” leads to the “clashing” of O…C atoms and Amber FF99SB predicts distances too large by about 0.15 Å. These results confirm that quantum chemistry computations add valuable support for detailed analysis of local structural arrangements in proteins, providing improved or missing data for less understood high‐energy or unusual regions.     

Crystal structure of a tripeptide containing aminocyclododecane carboxylic acid: a supramolecular twisted parallel β‐sheet in crystals

The crystal structure of a tripeptide Boc‐Leu‐Val‐Ac₁₂c‐OMe ( 1 ) is determined, which incorporates a bulky 1‐aminocyclododecane‐1‐carboxylic acid (Ac₁₂c) side chain. The peptide adopts a semi‐extended backbone conformation for Leu and Val residues, while the backbone torsion angles of the C^α,α‐dialkylated residue Ac₁₂c are in the helical region of the Ramachandran map. The molecular packing of 1 revealed a unique supramolecular twisted parallel β‐sheet coiling into a helical architecture in crystals, with the bulky hydrophobic Ac₁₂c side chains projecting outward the helical column. This arrangement resembles the packing of peptide helices in crystal structures. Although short oligopeptides often assemble as parallel or anti‐parallel β‐sheet in crystals, twisted or helical β‐sheet formation has been observed in a few examples of dipeptide crystal structures. Peptide 1 presents the first example of a tripeptide showing twisted β‐sheet assembly in crystals. Copyright © 2016 European Peptide Society and John Wiley & Sons, Ltd.     

A novel approach to segregate and identify functional loop regions in protein structures using their Ramachandran maps

The loops which connect or flank helices/sheets in protein structures are known to be functionally important. However, ironically they also belong to the part of protein whose structure is least accurately predicted. Here, a new method to isolate and analyze loop regions in protein structure is proposed using the spatial coordinates of the solved three‐dimensional structure. The extent of dispersion among points of successive amino acid residues in the Ramachandran map of protein region is utilized to calculate the Mean Separation between these points in the Ramachandran Plot (MSRP). Based on analysis of 2935 protein secondary structure regions obtained using DSSP software, spanning a range from 2 to 64 residues, taken from a set of 170 proteins, it is shown that helices (MSRP < 17) and strands (MSRP < 64) stand effectively demarcated from the loop regions (MSRP > 130). Analysis of 43 DNA binding and 98 ligand binding proteins revealed several loop regions with clear change in MSRP subsequent to binding. The population of such loops correlated with the magnitude of backbone displacement in the protein subsequent to binding. Can changes in MSRP quantify the temporal oscillations in dihedral angles among structured/unstructured regions in proteins? Molecular dynamics simulations (10 ns) revealed that deviations in MSRP among different snapshots in the trajectory were at least twofold higher for unstructured proteins in comparison with ordered proteins. The above results validate the use of MSRP parameter as a tool to identify and investigate functionally active loops and unstructured regions in protein structures. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Automated prediction of 15N, 13Cα, 13Cβ and 13C′ chemical shifts in proteins using a density functional database

A database of peptide chemical shifts, computed at the density functional level, has been used to develop an algorithm for prediction of ¹⁵N and ¹³C shifts in proteins from their structure; the method is incorporated into a program called SHIFTS (version 4.0). The database was built from the calculated chemical shift patterns of 1335 peptides whose backbone torsion angles are limited to areas of the Ramachandran map around helical and sheet configurations. For each tripeptide in these regions of regular secondary structure (which constitute about 40% of residues in globular proteins) SHIFTS also consults the database for information about sidechain torsion angle effects for the residue of interest and for the preceding residue, and estimates hydrogen bonding effects through an empirical formula that is also based on density functional calculations on peptides. The program optionally searches for alternate side-chain torsion angles that could significantly improve agreement between calculated and observed shifts. The application of the program on 20 proteins shows good consistency with experimental data, with correlation coefficients of 0.92, 0.98, 0.99 and 0.90 and r.m.s. deviations of 1.94, 0.97, 1.05, and 1.08 ppm for ¹⁵N, ¹³C, ¹³C and ¹³C, respectively. Reference shifts fit to protein data are in good agreement with `random-coil' values derived from experimental measurements on peptides. This prediction algorithm should be helpful in NMR assignment, crystal and solution structure comparison, and structure refinement.     

Carbonyl-carbonyl interactions stabilize the partially allowed Ramachandran conformations of asparagine and aspartic acid

Asparagine and aspartate are known to adopt conformations in the left-handed alpha-helical region and other partially allowed regions of the Ramachandran plot more readily than any other non-glycyl amino acids. The reason for this preference has not been established. An examination of the local environments of asparagine and aspartic acid in protein structures with a resolution better than 1.5 A revealed that their side-chain carbonyls are frequently within 4 A of their own backbone carbonyl or the backbone carbonyl of the previous residue. Calculations using protein structures with a resolution better than 1.8 A reveal that this close contact occurs in more than 80% of cases. This carbonyl-carbonyl interaction offers an energetic sabilization for the partially allowed conformations of asparagine and aspartic acid with respect to all other non-glycyl amino acids. The non-covalent attractive interactions between the dipoles of two carbonyls has recently been calculated to have an energy comparable to that of a hydrogen bond. The preponderance of asparagine in the left-handed alpha-helical region, and in general of aspartic acid and asparagine in the partially allowed regions of the Ramachandran plot, may be a consequence of this carbonyl-carbonyl stacking interaction.     

Spectral fitting for signal assignment and structural analysis of uniformly <Superscript>13</Superscript>C-labeled solid proteins by simulated annealing based on chemical shifts and spin dynamics

We describe an approach for the signal assignment and structural analysis with a suite of two-dimensional (13)C-(13)C magic-angle-spinning solid-state NMR spectra of uniformly (13)C-labeled peptides and proteins. We directly fit the calculated spectra to experimental ones by simulated annealing in restrained molecular dynamics program CNS as a function of atomic coordinates. The spectra are calculated from the conformation dependent chemical shift obtained with SHIFTX and the cross-peak intensities computed for recoupled dipolar interactions. This method was applied to a membrane-bound 14-residue peptide, mastoparan-X. The obtained C', C(alpha) and C(beta) chemical shifts agreed with those reported previously at the precisions of 0.2, 0.7 and 0.4 ppm, respectively. This spectral fitting program also provides backbone dihedral angles with a precision of about 50 degrees from the spectra even with resonance overlaps. The restraints on the angles were improved by applying protein database program TALOS to the obtained chemical shifts. The peptide structure provided by these restraints was consistent with the reported structure at the backbone RMSD of about 1 A.     

Revisiting the Ramachandran plot from a new angle

The pioneering work of Ramachandran and colleagues emphasized the dominance of steric constraints in specifying the structure of polypeptides. The ubiquitous Ramachandran plot of backbone dihedral angles (φ and ψ) defined the allowed regions of conformational space. These predictions were subsequently confirmed in proteins of known structure. Ramachandran and colleagues also investigated the influence of the backbone angle τ on the distribution of allowed φ/ψ combinations. The “bridge region” (φ ≤ 0° and −20° ≤ ψ ≤ 40°) was predicted to be particularly sensitive to the value of τ. Here we present an analysis of the distribution of φ/ψ angles in 850 non-homologous proteins whose structures are known to a resolution of 1.7 Å or less and sidechain B-factor less than 30 Ų. We show that the distribution of φ/ψ angles for all 87,000 residues in these proteins shows the same dependence on τ as predicted by Ramachandran and colleagues. Our results are important because they make clear that steric constraints alone are sufficient to explain the backbone dihedral angle distributions observed in proteins. Contrary to recent suggestions, no additional energetic contributions, such as hydrogen bonding, need be invoked.     

Improvement of hydrogen bond geometry in protein NMR structures by residual dipolar couplings – an assessment of the interrelation of NMR restraints

We have examined how the hydrogen bond geometry in three different proteins is affected when structural restraints based on measurements of residual dipolar couplings are included in the structure calculations. The study shows, that including restraints based solely on (1)H(N)-(15)N residual dipolar couplings has pronounced impact on the backbone rmsd and Ramachandran plot but does not improve the hydrogen bond geometry. In the case of chymotrypsin inhibitor 2 the addition of (13)CO-(13)C(alpha) and (15)N-(13)CO one bond dipolar couplings as restraints in the structure calculations improved the hydrogen bond geometry to a quality comparable to that obtained in the 1.8 A resolution X-ray structure of this protein. A systematic restraint study was performed, in which four types of restraints, residual dipolar couplings, hydrogen bonds, TALOS angles and NOEs, were allowed in two states. This study revealed the importance of using several types of residual dipolar couplings to get good hydrogen bond geometry. The study also showed that using a small set of NOEs derived only from the amide protons, together with a full set of residual dipolar couplings resulted in structures of very high quality. When reducing the NOE set, it is mainly the side-chain to side-chain NOEs that are removed. Despite of this the effect on the side-chain packing is very small when a reduced NOE set is used, which implies that the over all fold of a protein structure is mainly determined by correct folding of the backbone.     

Refined structures of mouse P‐glycoprotein

The recently determined C. elegans P‐glycoprotein (Pgp) structure revealed significant deviations compared to the original mouse Pgp structure, which suggested possible misinterpretations in the latter model. To address this concern, we generated an experimental electron density map from single‐wavelength anomalous dispersion phasing of an original mouse Pgp dataset to 3.8 Å resolution. The map exhibited significantly more detail compared to the original MAD map and revealed several regions of the structure that required de novo model building. The improved drug‐free structure was refined to 3.8 Å resolution with a 9.4 and 8.1% decrease in R_work and R_free, respectively, (R_work = 21.2%, R_free = 26.6%) and a significant improvement in protein geometry. The improved mouse Pgp model contains ～95% of residues in the favorable Ramachandran region compared to only 57% for the original model. The registry of six transmembrane helices was corrected, revealing amino acid residues involved in drug binding that were previously unrecognized. Registry shifts (rotations and translations) for three transmembrane (TM)4 and TM5 and the addition of three N‐terminal residues were necessary, and were validated with new mercury labeling and anomalous Fourier density. The corrected position of TM4, which forms the frame of a portal for drug entry, had backbone atoms shifted >6 Å from their original positions. The drug translocation pathway of mouse Pgp is 96% identical to human Pgp and is enriched in aromatic residues that likely play a collective role in allowing a high degree of polyspecific substrate recognition.     

Composites of local structure propensities: Evidence for local encoding of long-range structure

To estimate how extensively the ensemble of denatured-state conformations is constrained by local side-chain–backbone interactions, propensities of each of the 20 amino acids to occur in mono- and dipeptides mapped to discrete regions of the Ramachandran map are computed from proteins of known structure. In addition, propensities are computed for the trans, gauche−, and gauche+ rotamers, with or without consideration of the values of phi and psi. These propensities are used in scoring functions for fragment threading, which estimates the energetic favorability of fragments of protein sequence to adopt the native conformation as opposed to hundreds of thousands of incorrect conformations. As finer subdivisions of the Ramachandran plot, neighboring residue phi/psi angles, and rotamers are incorporated, scoring functions become better at ranking the native conformation as the most favorable. With the best composite propensity function, the native structure can be distinguished from 300,000 incorrect structures for 71% of the 2130 arbitrary protein segments of length 40, 48% of 2247 segments of length 30, and 20% of 2368 segments of length 20. A majority of fragments of length 30–40 are estimated to be folded into the native conformation a substantial fraction of the time. These data suggest that the variations observed in amino acid frequencies in different phi/psi/chi1 environments in folded proteins reflect energetically important local side-chain–backbone interactions, interactions that may severely restrict the ensemble of conformations populated in the denatured state to a relatively small subset with nativelike structure.     

Noncanonical and Strongly Disallowed Conformations of the Backbone in Polypeptide Chains of Globular Proteins

An analog of the Ramachandran map was drawn, a new representation proposed, and thorough analysis performed using modern recognition and classification methods. Very large maps with a density of more than 50 million dots were created based on the data sets derived from the latest releases of globular protein- structure data banks. A, B, B', C, and D regions that correspond to strongly disallowed conformations were defined and found to occupy 25% of the plot area. A region of noncanonical conformations was determined by subtracting strongly disallowed and permitted conformation regions from the total plot area. Arguments are provided to support the new classification of backbone conformations of the protein polypeptide chain.     

Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model

Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1) input data size and criteria for structure inclusion (resolution, R-factor, etc.); 2) filtering of suspect conformations and outliers using B-factors or other features; 3) secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included); 4) the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5) whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately) have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp.     

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.     

Classification of protein families and detection of the determinant residues with an improved self-organizing map

 Using a SOM (self-organizing map) we can classify sequences within a protein family into subgroups that generally correspond to biological subcategories. These maps tend to show sequence similarity as proximity in the map. Combining maps generated at different levels of resolution, the structure of relations in protein families can be captured that could not otherwise be represented in a single map. The underlying representation of maps enables us to retrieve characteristic sequence patterns for individual subgroups of sequences. Such patterns tend to correspond to functionally important regions. We present a modified SOM algorithm that includes a convergence test that dynamically controls the learning parameters to adapt them to the learning set instead of being fixed and externally optimized by trial and error. Given the variability of protein family size and distribution, the addition of this feature is necessary. The method is successfully tested with a number of families. The rab family of small GTPases is used to illustrate the performance of the method. Received: 25 July 1996 / Accepted in revised form: 13 February 1997     

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and ¹³C^β chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and ¹³C^β atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for δ¹⁵N, δ¹³C’, δ¹³C^α, δ¹³C^β, δ¹H^α and δ¹H^N, respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2–10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts.     

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein ¹H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6–17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for ¹Hα, ¹HN, ¹³Cα, ¹³Cβ, ¹³CO and backbone ¹⁵N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at .     

163 Enhanced sampling of peptides and proteins with a new biasing replica exchange method

Classical MD simulations (cMD) are limited by the sampling of relevant states of the peptides. Replica exchange (REMD) methods aim to search the conformational space of proteins more efficiently (reviewed in Ostermeir & Zacharias, 2013). We have developed a Hamiltonian REMD method that takes advantage of an intrinsic property of proteins, the specific Φ ? dihedral angle combinations along the polymer backbone. By employing a coupled two-dimensional biasing potential the energy barriers along the polymer backbone are reduced more effectively than by a previous approach based on a one-D biasing potential (Kannan & Zacharias, 2007). Thus, adjacent amino acids along the polymers backbone can easily switch between favourable regions in the Ramachandran plot. Additionally, energy barriers of rotameric states of amino acid side chains of proteins are also biased in the replica runs. The method improves the sampling of conformational substates of proteins at a modest number of replicas (nine replicas in the standard set-up with one replica running without biasing potential) compared to much larger numbers necessary in the case of standard temperature (T)-REMD simulations. A further improvement is achieved by a dynamical adjustment of the penalty potential levels in the replicas such that high exchange rates and improved mixing of conformations between different replicas are guaranteed. The biasing potential (BP)-REMD method turns out to be suitable to speed up both the folding of spaghetti-like test peptides and the refinement of loop decoy structures. Starting from extended structures, an α-helical oligo-alanine and β-hairpin chignolin and the Trp-cage protein fold more rapidly in near-native structures than in cMD simulations. The BP-REMD simulations not only accelerate the folding process of test proteins but also enlarge the variety of sampled configurations in conformational space. Since flexible parts of the protein can be penalized selectively, this method provides a precise tool to investigate regions of interest of the protein.