Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Real-SPINE: an integrated system of neural networks for real-value prediction of protein structural properties

Proteins can move freely in three-dimensional space. As a result, their structural properties, such as solvent accessible surface area, backbone dihedral angles, and atomic distances, are continuous variables. However, these properties are often arbitrarily divided into a few classes to facilitate prediction by statistical learning techniques. In this work, we establish an integrated system of neural networks (called Real-SPINE) for real-value prediction and apply the method to predict residue-solvent accessibility and backbone psi dihedral angles of proteins based on information derived from sequences only. Real-SPINE is trained with a large data set of 2640 protein chains, sequence profiles generated from multiple sequence alignment, representative amino-acid properties, a slow learning rate, overfitting protection, and predicted secondary structures. The method optimizes more than 200,000 weights and yields a 10-fold cross-validated Pearson's correlation coefficient (PCC) of 0.74 between predicted and actual solvent accessible surface areas and 0.62 between predicted and actual psi angles. In particular, 90% of 2640 proteins have a PCC value greater than 0.6 between predicted and actual solvent-accessible surface areas. The results of Real-SPINE can be compared with the best reported correlation coefficients of 0.64-0.67 for solvent-accessible surface areas and 0.47 for psi angles. The real-SPINE server, executable programs, and datasets are freely available on http://sparks.informatics.iupui.edu.     

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.     

Local backbone structure prediction of proteins

A statistical analysis of the PDB structures has led us to define a new set of small 3D structural prototypes called Protein Blocks (PBs). This structural alphabet includes 16 PBs, each one is defined by the (phi, psi) dihedral angles of 5 consecutive residues. The amino acid distributions observed in sequence windows encompassing these PBs are used to predict by a Bayesian approach the local 3D structure of proteins from the sole knowledge of their sequences. LocPred is a software which allows the users to submit a protein sequence and performs a prediction in terms of PBs. The prediction results are given both textually and graphically.     

Efficient search on energy minima for structure prediction of nucleic acid motifs

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during conformational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Support vector machines for prediction of dihedral angle regions

MOTIVATION: Most secondary structure prediction programs target only alpha helix and beta sheet structures and summarize all other structures in the random coil pseudo class. However, such an assignment often ignores existing local ordering in so-called random coil regions. Signatures for such ordering are distinct dihedral angle pattern. For this reason, we propose as an alternative approach to predict directly dihedral regions for each residue as this leads to a higher amount of structural information. RESULTS: We propose a multi-step support vector machine (SVM) procedure, dihedral prediction (DHPRED), to predict the dihedral angle state of residues from sequence. Trained on 20,000 residues our approach leads to dihedral region predictions, that in regions without alpha helices or beta sheets is higher than those from secondary structure prediction programs. AVAILABILITY: DHPRED has been implemented as a web service, which academic researchers can access from our webpage http://www.fz-juelich.de/nic/cbb     

Efficient Search on Energy Minima for Structure Prediction of Nucleic Acid Motifs

Abstract

Structure prediction of non-canonical motifs such as mismatches, extra unmatched nucleotides or internal and hairpin loop structures in nucleic acids is of great importance for understanding the function and design of nucleic acid structures. Systematic conformational analysis of such motifs typically involves the generation of many possible combinations of backbone dihedral torsion angles for a given motif and subsequent energy minimization (EM) and evaluation. Such approach is limited due to the number of dihedral angle combinations that grows very rapidly with the size of the motif. Two conformational search approaches have been developed that allow both an effective crossing of barriers during con-formational searches and the computational demand grows much less with system size then search methods that explore all combinations of backbone dihedral torsion angles. In the first search protocol single torsion angles are flipped into favorable states using constraint EM and subsequent relaxation without constraints. The approach is repeated in an iterative manner along the backbone of the structural motif until no further energy improvement is obtained. In case of two test systems, a DNA-trinucleotide loop (sequence: GCA) and a RNA tetraloop (sequence: UUCG), the approach successfully identified low energy states close to experiment for two out of five start structures. In the second method randomly selected combinations of up to six backbone torsion angles are simultaneously flipped into preset ranges by a short constraint EM followed by unconstraint EM and acceptance according to a Metropolis acceptance criterion. This combined stochastic/EM search was even more effective than the single torsion flip approach and selected low energy states for the two test cases in between two and four cases out of five start structures.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

TANGLE: two-level support vector regression approach for protein backbone torsion angle prediction from primary sequences

Protein backbone torsion angles (Phi) and (Psi) involve two rotation angles rotating around the C(α)-N bond (Phi) and the C(α)-C bond (Psi). Due to the planarity of the linked rigid peptide bonds, these two angles can essentially determine the backbone geometry of proteins. Accordingly, the accurate prediction of protein backbone torsion angle from sequence information can assist the prediction of protein structures. In this study, we develop a new approach called TANGLE (Torsion ANGLE predictor) to predict the protein backbone torsion angles from amino acid sequences. TANGLE uses a two-level support vector regression approach to perform real-value torsion angle prediction using a variety of features derived from amino acid sequences, including the evolutionary profiles in the form of position-specific scoring matrices, predicted secondary structure, solvent accessibility and natively disordered region as well as other global sequence features. When evaluated based on a large benchmark dataset of 1,526 non-homologous proteins, the mean absolute errors (MAEs) of the Phi and Psi angle prediction are 27.8° and 44.6°, respectively, which are 1% and 3% respectively lower than that using one of the state-of-the-art prediction tools ANGLOR. Moreover, the prediction of TANGLE is significantly better than a random predictor that was built on the amino acid-specific basis, with the p-value<1.46e-147 and 7.97e-150, respectively by the Wilcoxon signed rank test. As a complementary approach to the current torsion angle prediction algorithms, TANGLE should prove useful in predicting protein structural properties and assisting protein fold recognition by applying the predicted torsion angles as useful restraints. TANGLE is freely accessible at http://sunflower.kuicr.kyoto-u.ac.jp/~sjn/TANGLE/.     

Determination of dihedral Psi angles in large proteins by combining NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlation and chemical shifts

We propose a strategy based on the combination of experimental NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlated relaxation rates and chemical shift analysis for the determination of Psi torsion angles in proteins. The method allows the determination of a dihedral angle that is not easily accessible by nuclear magnetic resonance (NMR). The measurement of dihedral angle restraints can be used for structure calculation, which is known to improve the quality of NMR structures. The method is of particular interest in the case of large proteins, for which spectral assignment of the nuclear Overhauser effect spectra, and therefore straightforward structural determination, is out of reach. One advantage of the method is that it is reasonably simple to implement, and could be used in association with other methods aiming at obtaining structural information on complex systems, such as residual dipolar coupling measurements. An illustrative example is analyzed in the case of the 30-kDa protein 6-phosphogluconolactonase.     

New assessment of a structural alphabet

A statistical analysis of the Protein Databank (PDB) structures had led us to define a set of small 3D structural prototypes called Protein Blocks (PBs). This structural alphabet includes 16 PBs, each one defined by the (phi, psi) dihedral angles of 5 consecutive residues. Here, we analyze the effect of the enlargement of the PDB on the PBs' definition. The results highlight the quality of the 3D approximation ensured by the PBs. These last could be of great interest in ab initio modeling.     

Revisiting the Ramachandran plot based on statistical analysis of static and dynamic characteristics of protein structures

Ramachandran plots, which describe protein structures by plotting the dihedral angle pairs of the backbone on a two-dimensional plane, have played an important role in structural biology over the past few decades. However, despite continued discovery of new protein structures to date, the Ramachandran plot is still constructed by only a small number of data points, and further it cannot reflect the steric information of proteins. Here, we investigated the secondary structure of proteins in terms of static and dynamic characteristics. As for static feature, the Ramachandran plot was revisited for the dataset consisting of 9,148 non-redundant high-resolution protein structures released in the protein data bank until April 1, 2022. By calculating amino acid propensities, it was found that the proportion of secondary structures with respect to residue depth is directly related to their hydrophobicity. As for dynamic feature, normal mode analysis (NMA) based on an elastic network model (ENM) was carried out for the dataset using our KOSMOS web server (http://bioengineering.skku.ac.kr/kosmos/). All ENM-based NMA results were stored in the KOSMOS database, allowing researchers to use them in various ways. In this process, it was commonly found that high B-factors appeared at the edge of the alpha helix region, which was elucidated by introducing residue depth. In addition, by investigating the change in dihedral angle, it was possible to quantitatively survey the contribution of structural change of protein on the Ramachandran plot. In conclusion, our statistical analysis of protein characteristics will provide insight into a range of protein structural studies.     

Protein backbone angle prediction with machine learning approaches

MOTIVATION: Protein backbone torsion angle prediction provides useful local structural information that goes beyond conventional three-state (alpha, beta and coil) secondary structure predictions. Accurate prediction of protein backbone torsion angles will substantially improve modeling procedures for local structures of protein sequence segments, especially in modeling loop conformations that do not form regular structures as in alpha-helices or beta-strands. RESULTS: We have devised two novel automated methods in protein backbone conformational state prediction: one method is based on support vector machines (SVMs); the other method combines a standard feed-forward back-propagation artificial neural network (NN) with a local structure-based sequence profile database (LSBSP1). Extensive benchmark experiments demonstrate that both methods have improved the prediction accuracy rate over the previously published methods for conformation state prediction when using an alphabet of three or four states. AVAILABILITY: LSBSP1 and the NN algorithm have been implemented in PrISM.1, which is available from www.columbia.edu/~ay1/. SUPPLEMENTARY INFORMATION: Supplementary data for the SVM method can be downloaded from the Website www.cs.columbia.edu/compbio/backbone.     

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a–p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and β-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.