Determination method of the balance of the secondary-structure-forming tendencies of force fields

We propose a new method of optimisation of backbone torsion-energy parameters in the force field for molecular simulations of protein systems. This method is based on the idea of balancing the secondary-structure-forming tendencies, namely, those of α-helix and β-sheet structures. We perform a minimisation of the backbone dihedral angle-based root-mean-square deviation of the helix and β structure regions in many protein structures. As an example, we optimised the backbone torsion-energy parameters of AMBER parm96 force field using 100 protein molecules from the Protein Data Bank. We then performed folding simulations of α-helical and β-hairpin peptides, using the optimised force field. The results imply that the new force-field parameters give structures more consistent with the experimental implications than the original AMBER parm96 force field.     

Real-value prediction of backbone torsion angles

The backbone structure of a protein is largely determined by the phi and psi torsion angles. Thus, knowing these angles, even if approximately, will be very useful for protein-structure prediction. However, in a previous work, a sequence-based, real-value prediction of psi angle could only achieve a mean absolute error of 54 degrees (83 degrees, 35 degrees, 33 degrees for coil, strand, and helix residues, respectively) between predicted and actual angles. Moreover, a real-value prediction of phi angle is not yet available. This article employs a neural-network based approach to improve psi prediction by taking advantage of angle periodicity and apply the new method to the prediction to phi angles. The 10-fold-cross-validated mean absolute error for the new method is 38 degrees (58 degrees, 33 degrees, 22 degrees for coil, strand, and helix, respectively) for psi and 25 degrees (35 degrees, 22 degrees, 16 degrees for coil, strand, and helix, respectively) for phi. The accuracy of real-value prediction is comparable to or more accurate than the predictions based on multistate classification of the phi-psi map. More accurate prediction of real-value angles will likely be useful for improving the accuracy of fold recognition and ab initio protein-structure prediction. The Real-SPINE 2.0 server is available on the website http://sparks.informatics.iupui.edu.     

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.     

Folding simulations of three proteins having all α-helix,all β-strand and α/β-structures

We performed folding simulations of three proteins using four force fields, AMBER parm96, AMBER parm99, CHARMM 27 and OPLS-AA/L, in order to examine the features of these force fields. We studied three proteins, protein A (all α-helix), cold-shock protein (all β-strand) and protein G (α/β-structures), for the folding simulations. For the simulation, we used the simulated annealing molecular dynamics method, which was performed 50 times for each protein using the four force fields. The results showed that the secondary-structure-forming tendencies are largely different among the four force fields. AMBER parm96 favours β-bridge structures and extended β-strand structures, and AMBER parm99 favours α-helix structures and 3₁₀-helix structures. CHARMM 27 slightly favours α-helix structures, and there are also π-helix and β-bridge structures. OPLS-AA/L favours α-helix structures and 3₁₀-helix structures.     

Optimisation of OPLS–UA force-field parameters for protein systems using protein data bank

We have previously proposed a method for refining force-field parameters of protein systems, which consists of minimising the summation of the square of the force acting on each atom in the proteins with the structures from the protein data bank (PDB). The results showed that the modified force-field parameters for all-atom model gave structures more consistent with the experimental implications than the original force fields. In this work, we applied this method and a new method to the OPLS–UA force field. In the new method, we perform a minimisation of the average of the root-mean-square deviation of various protein structures from the native structure. We selected some torsion-energy parameters for this optimisation, and 100 molecules from the PDB were used. The results imply that the new force-field parameters gave structures of two peptides more consistent with the experimental implications for the secondary structure-forming tendencies than the original OPLS–UA force field.     

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

CSSI-PRO: a method for secondary structure type editing,assignment and estimation in proteins using linear combination of backbone chemical shifts

Estimation of secondary structure in polypeptides is important for studying their structure, folding and dynamics. In NMR spectroscopy, such information is generally obtained after sequence specific resonance assignments are completed. We present here a new methodology for assignment of secondary structure type to spin systems in proteins directly from NMR spectra, without prior knowledge of resonance assignments. The methodology, named Combination of Shifts for Secondary Structure Identification in Proteins (CSSI-PRO), involves detection of specific linear combination of backbone ¹H^α and ¹³C′ chemical shifts in a two-dimensional (2D) NMR experiment based on G-matrix Fourier transform (GFT) NMR spectroscopy. Such linear combinations of shifts facilitate editing of residues belonging to α-helical/β-strand regions into distinct spectral regions nearly independent of the amino acid type, thereby allowing the estimation of overall secondary structure content of the protein. Comparison of the predicted secondary structure content with those estimated based on their respective 3D structures and/or the method of Chemical Shift Index for 237 proteins gives a correlation of more than 90% and an overall rmsd of 7.0%, which is comparable to other biophysical techniques used for structural characterization of proteins. Taken together, this methodology has a wide range of applications in NMR spectroscopy such as rapid protein structure determination, monitoring conformational changes in protein-folding/ligand-binding studies and automated resonance assignment. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Comparing short protein substructures by a method based on backbone torsion angles

An efficient algorithm was characterized that determines the similarity in main chain conformation between short protein substructures. The algorithm computes Δt, the root mean square difference in ? and ψ torsion angles over a small number of amino acids (typically 3–5). Using this algorithm, large number of protein substrates comparisons were feasible. The parameter Δt was sensitive to variations in local protein conformation, and it correlates with Δr, the root mean square deviation in atomic coordinates. Values for Δt were obtained that define similarity thresholds, which determine whether two substructure are considered structurally similar. To set a lower bound on the similarity threshold, we estimated the component of Δt due to measurement noise fromcomparisons of independently refined coordinates of the same protein. A sample distribution of Δt from nonhomologous protein comparisons identified an upper bound on the similarity threshold, one that refrains from incorporating large numbers of nonmatching comparisons large numbers of nonmatching comparisons. Unlike methods based on Cα atoms alone, Δt was sensitive to rotations in the peptide plane, shown to occur in several proteins. Comparisons of homologus proteins by Δt showed that the active site torsion angles are highly conserved. The Δt method was applied to the α-chain of human hemoglobin, where it readily demonstrated the local differences in the structures of different ligation states.     

Improving the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins by guided-learning through a two-layer neural network

This article attempts to increase the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins through improved learning. Most methods developed for improving the backpropagation algorithm of artificial neural networks are limited to small neural networks. Here, we introduce a guided-learning method suitable for networks of any size. The method employs a part of the weights for guiding and the other part for training and optimization. We demonstrate this technique by predicting residue solvent accessibility and real-value backbone torsion angles of proteins. In this application, the guiding factor is designed to satisfy the intuitive condition that for most residues, the contribution of a residue to the structural properties of another residue is smaller for greater separation in the protein-sequence distance between the two residues. We show that the guided-learning method makes a 2-4% reduction in 10-fold cross-validated mean absolute errors (MAE) for predicting residue solvent accessibility and backbone torsion angles, regardless of the size of database, the number of hidden layers and the size of input windows. This together with introduction of two-layer neural network with a bipolar activation function leads to a new method that has a MAE of 0.11 for residue solvent accessibility, 36 degrees for psi, and 22 degrees for phi. The method is available as a Real-SPINE 3.0 server in http://sparks.informatics.iupui.edu.     

Nearest-neighbor effects on backbone alpha and beta carbon chemical shifts in proteins

We present a method for analyzing the chemical shift database to yield information on nearest-neighbor effects on carbon-13 chemical shift values for alpha and beta carbons of amino acids in proteins. For each amino acid sequence XYZ, we define two correction factors, Delta(XY) s and Delta(YZ) s , representing the effects on (delta13 Calpha-delta13 Cbeta) for residue Y from the preceding residue (X) and the following residue (Z), where X, Y, and Z represent one of the 20 naturally occurring amino acids, Delta designates the change in value or the correction factor (in ppm), and s is an index standing for one of three "pseudo secondary structure states" derived from chemical shift dispersions, which we show represent residues in primarily alpha-helix, beta-strand, and non-alphabeta(coil). The correction factors were obtained from maximum likelihood fitting of (delta13 Calpha-delta13 Cbeta) values from the chemical shifts of 651 proteins to a mixture of three Gaussians. These correction factors were derived strictly from the analysis of assigned chemical shifts, without regard to the three-dimensional structures of these proteins. The corrections factors were found to differ according to the secondary structural environment of the central residue (deduced from the chemical shift distribution) as well as by different identities of the nearest neighboring residues in the sequence. The areas subsumed by the sequence-dependent chemical shift distributions report on the relative energies of the sequences in different pseudo secondary structural environments, and the positions of the peaks indicate the chemical shifts of lowest energy conformations. As such, these results have potential applications to the determination of dihedral angle restraints from chemical shifts for structure determination and to more accurate predictions of chemical shifts in proteins of known structure. From a database of chemical shifts associated well-defined three-dimensional structures, comparisons were made between DSSP designations derived from three-dimensional structure and pseudo secondary structure designations derived from nearest-neighbor corrected chemical shift analysis. The high level of agreement between the two approaches to classifying secondary structure provides a measure of confidence in this chemical shift-based approach to the analysis of protein structure.     

Intrinsic secondary structure propensities of the amino acids,using statistical ϕ–ψ matrices: Comparison with experimental scales

Today there are several different experimental scales for the intrinsic α-helix as well as β-strand, propensities of the 20 amino acids obtained from the thermodynamic analysis of various model systems. These scales do not compare well with those extracted from statistical analysis of three-dimensional structure databases. Possible explanations for this could be the limited size of the databases used, the definitions of intrinsic propensities, or the theoretical approach. Here we report a statistical determination of α-helix and β-strand propensities derived from the analysis of a database of 279 three-dimensional structures. Contrary to what has been generally done, we have considered a particular residue as in α-helix or β-strand conformation by looking only at its dihedral angles (?–ψ matrices). Neither the identity nor the conformation of the surrounding residues in the amino acid sequence has been taken into consideration. Pseudoenergy empirical scales have been calculated from the statistical propensities. These scales agree very well with the experimental ones in relative and absolute terms. Moreover, its correlation with the average of the experimental scales for α-helix or β-strand is as good as the correlations of the individual experimental scales with the average. These results show that by using a large enough database and a proper definition for the secondary structure propensities, it is possible to obtain a scale as good as any of experimental origin. Interestingly the ?–ψ analysis of the Ramachandran plot suggests that the amino acids could have different β-strand propensities in different subregions of the β-strand area. © 1994 Wiley-Liss, Inc.     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

Refinement of protein structures in explicit solvent

We present a CPU efficient protocol for refinement of protein structures in a thin layer of explicit solvent and energy parameters with completely revised dihedral angle terms. Our approach is suitable for protein structures determined by theoretical (e.g., homology modeling or threading) or experimental methods (e.g., NMR). In contrast to other recently proposed refinement protocols, we put a strong emphasis on consistency with widely accepted covalent parameters and computational efficiency. We illustrate the method for NMR structure calculations of three proteins: interleukin-4, ubiquitin, and crambin. We show a comparison of their structure ensembles before and after refinement in water with and without a force field energy term for the dihedral angles; crambin was also refined in DMSO. Our results demonstrate the significant improvement of structure quality by a short refinement in a thin layer of solvent. Further, they show that a dihedral angle energy term in the force field is beneficial for structure calculation and refinement. We discuss the optimal weight for the energy constant for the backbone angle omega and include an extensive discussion of meaning and relevance of the calculated validation criteria, in particular root mean square Z scores for covalent parameters such as bond lengths.     

Description and recognition of regular and distorted secondary structures in proteins using the automated protein structure analysis method

The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in three‐dimensional space and characterizes it by curvature κ and torsion τ as a function of arc length s, was applied on 77 proteins to determine all secondary structural units via specific κ(s) and τ(s) patterns. A total of 533 α‐helices and 644 β‐strands were recognized by APSA, whereas DSSP gives 536 and 651 units, respectively. Kinks and distortions were quantified and the boundaries (entry and exit) of secondary structures were classified. Similarity between proteins can be easily quantified using APSA, as was demonstrated for the roll architecture of proteins ubiquitin and spinach ferridoxin. A twenty‐by‐twenty comparison of all α domains showed that the curvature‐torsion patterns generated by APSA provide an accurate and meaningful similarity measurement for secondary, super secondary, and tertiary protein structure. APSA is shown to accurately reflect the conformation of the backbone effectively reducing three‐dimensional structure information to two‐dimensional representations that are easy to interpret and understand. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Analysis of the steric strain in the polypeptide backbone of protein molecules.

The extent to which local strain is present in the polypeptide backbone of folded protein molecules has been examined. The occurrence of steric strain associated with nonproline cis peptide bonds and energetically unfavorable main chain dihedral angles can be identified reliably from the well ordered parts of high resolution, refined crystal structures. The analysis reveals that there are relatively few sterically strained features. Those that do occur are located overwhelmingly in regions concerned with function. We attribute this to the greater precision necessary for ligand binding and catalysis, compared with the requirements of satisfactory folding.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Generation of pseudonative protein structures for threading

The threading approach to protein structure prediction suffers from the limited number of substantially different folds available as templates. A method is presented for the generation of artificial protein structures, amenable to threading, by modification of native ones. The artificial structures so generated are compared to the native ones and it is shown that, within the accuracy of the pseudoenergy function or force field used, these two types of structures appear equally useful for threading. Since a multitude of pseudonative artificial structures can be generated per native structure, the pool of pseudonative template structures for threading can be enormously enlarged by the inclusion of the pseudonative artificial structures. Proteins 28:522–529, 1997. © 1997 Wiley-Liss, Inc.     

Correlation between sequence hydrophobicity and surface-exposure pattern of database proteins

Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tend to occur at the surface of a folded protein. By analyzing the known protein structures, we quantify the degree to which the hydrophobicity sequence of a protein correlates with its pattern of surface exposure. We have assessed the statistical significance of this correlation for several hydrophobicity scales in the literature, and find that the computed correlations are significant but far from optimal. We show that this less than optimal correlation arises primarily from the large degree of mutations that naturally occurring proteins can tolerate. Lesser effects are due in part to forces other than hydrophobicity, and we quantify this by analyzing the surface-exposure distributions of all amino acids. Lastly, we show that our database findings are consistent with those found from an off-lattice hydrophobic-polar model of protein folding.