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.     

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.     

New stochastic strategy to analyze helix folding

We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good alpha-helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the Phi x Psi backbone angles to the allowed regions in the Ramachandran map. For polyalanines we obtained stable alpha-helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size. These conformations were generated by performing 2880 stochastic molecular optimizations with a continuum medium approach. When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.     

How different are structurally flexible and rigid binding sites? Sequence and structural features discriminating proteins that do and do not undergo conformational change upon ligand binding

Proteins are dynamic molecules and often undergo conformational change upon ligand binding. It is widely accepted that flexible loop regions have a critical functional role in enzymes. Lack of consideration of binding site flexibility has led to failures in predicting protein functions and in successfully docking ligands with protein receptors. Here we address the question: which sequence and structural features distinguish the structurally flexible and rigid binding sites? We analyze high-resolution crystal structures of ligand bound (holo) and free (apo) forms of 41 proteins where no conformational change takes place upon ligand binding, 35 examples with moderate conformational change, and 22 cases where a large conformational change has been observed. We find that the number of residue-residue contacts observed per-residue (contact density) does not distinguish flexible and rigid binding sites, suggesting a role for specific interactions and amino acids in modulating the conformational changes. Examination of hydrogen bonding and hydrophobic interactions reveals that cases that do not undergo conformational change have high polar interactions constituting the binding pockets. Intriguingly, the large, aromatic amino acid tryptophan has a high propensity to occur at the binding sites of examples where a large conformational change has been noted. Further, in large conformational change examples, hydrophobic-hydrophobic, aromatic-aromatic, and hydrophobic-polar residue pair interactions are dominant. Further analysis of the Ramachandran dihedral angles (phi, psi) reveals that the residues adopting disallowed conformations are found in both rigid and flexible cases. More importantly, the binding site residues adopting disallowed conformations clustered narrowly into two specific regions of the L-Ala Ramachandran map. Examination of the dihedral angles changes upon ligand binding shows that the magnitude of phi, psi changes are in general minimal, although some large changes particularly between right-handed alpha-helical and extended conformations are seen. Our work further provides an account of conformational changes in the dihedral angles space. The findings reported here are expected to assist in providing a framework for predicting protein-ligand complexes and for template-based prediction of protein function.     

Conformational analysis of short polar side-chain amino-acids through umbrella sampling and DFT calculations

Molecular and quantum mechanics calculations were carried out in a series of tripeptides (GXG, where X?=?D, N and C) as models of the unfolded states of proteins. The selected central amino acids, especially aspartic acid (D) and asparagine (N) are known to present significant average conformations in partially allowed areas of the Ramachandran plot, which have been suggested to be important in unfolded protein regions. In this report, we present the calculation of the propensity values through an umbrella sampling procedure in combination with the calculation of the NMR J-coupling constants obtained by a DFT model. The experimental NMR observations can be reasonably explained in terms of a conformational distribution where PP_II and β basins sum up propensities above 0.9. The conformational analysis of the side chain dihedral angle (χ₁), along with the computation of ³J(H^αH^β), revealed a preference for the g _? and g ₊ rotamers. These may be connected with the presence of intermolecular H-bonding and carbonyl–carbonyl interactions sampled in the PP_II and β basins. Taking into account all those results, it can be established that these residues show a similar behavior to other amino acids in short peptides regarding backbone φ,ψ dihedral angle distribution, in agreement with some experimental analysis of capped dipeptides.     

Straight-chain non-polar amino acids are good helix-formers in water

For comparison with earlier data on naturally occurring non-polar amino acids (Ala, Leu, Phe, Val, Ile), the comparative helix-forming tendencies have been measured for non-polar amino acid residues that have unbranched side-chains, with an ethyl, propyl or butyl group, and also for methionine. The substitutions are made in a 17-residue alanine-based peptide. The results show that straight-chain non-polar amino acids have high helix-forming tendencies compared to beta-branched non-polar amino acids. Restriction of side-chain conformations in the helix, with a corresponding reduction in conformational entropy, is the likely explanation. There is a small increase in helix-forming tendency as the side-chain increases in length from ethyl to butyl, which suggests that a helix-stabilizing hydrophobic interaction is being detected.     

Assessing side-chain perturbations of the protein backbone: a knowledge-based classification of residue Ramachandran space

Grouping the 20 residues is a classic strategy to discover ordered patterns and insights about the fundamental nature of proteins, their structure, and how they fold. Usually, this categorization is based on the biophysical and/or structural properties of a residue's side-chain group. We extend this approach to understand the effects of side chains on backbone conformation and to perform a knowledge-based classification of amino acids by comparing their backbone phi, psi distributions in different types of secondary structure. At this finer, more specific resolution, torsion angle data are often sparse and discontinuous (especially for nonhelical classes) even though a comprehensive set of protein structures is used. To ensure the precision of Ramachandran plot comparisons, we applied a rigorous Bayesian density estimation method that produces continuous estimates of the backbone phi, psi distributions. Based on this statistical modeling, a robust hierarchical clustering was performed using a divergence score to measure the similarity between plots. There were seven general groups based on the clusters from the complete Ramachandran data: nonpolar/beta-branched (Ile and Val), AsX (Asn and Asp), long (Met, Gln, Arg, Glu, Lys, and Leu), aromatic (Phe, Tyr, His, and Cys), small (Ala and Ser), bulky (Thr and Trp), and, lastly, the singletons of Gly and Pro. At the level of secondary structure (helix, sheet, turn, and coil), these groups remain somewhat consistent, although there are a few significant variations. Besides the expected uniqueness of the Gly and Pro distributions, the nonpolar/beta-branched and AsX clusters were very consistent across all types of secondary structure. Effectively, this consistency across the secondary structure classes implies that side-chain steric effects strongly influence a residue's backbone torsion angle conformation. These results help to explain the plasticity of amino acid substitutions on protein structure and should help in protein design and structure evaluation.     

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.     

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.     

Conformational similarity indices between different residues in proteins and alpha-helix propensities

Various amino acid similarity matrices have been derived using data on physicochemical properties and molecular evolution. Conformational similarity indices, CS(XX'), between different residues are computed here using the distribution of the main-chain and side-chain torsion angles and the values have been used to cluster amino acids in proteins. A subset of these parameters, CS(AX') indicates the extent of similarity in the main-chain and side-chain conformations (phi,psi and chi1) of different residues (X) with Ala (A) and is found to have strong correlation with alpha-helix propensities. However, no subset of CS(XX') provides any linear relationship with beta-sheet propensities, suggesting that the conformational feature favouring the location of a residue in an alpha-helix is different from the one favouring the beta-sheet. Conformationally similar residues (close CS(AX) values) have similar steric framework of the side-chain (linear/branched, aliphatic/aromatic), irrespective of the polarity or hydrophobicity. Cooperative nucleation of helix may be facile for a contiguous stretch of residues with high overall CS(AX) values.     

The Ramachandran plots of glycine and pre-proline

Background  

The Ramachandran plot is a fundamental tool in the analysis of protein structures. Of the 4 basic types of Ramachandran plots, the interactions that determine the generic and proline Ramachandran plots are well understood. The interactions of the glycine and pre-proline Ramachandran plots are not.     

Identification of a key structural element for protein folding within beta-hairpin turns

Specific residues in a polypeptide may be key contributors to the stability and foldability of the unique native structure. Identification and prediction of such residues is, therefore, an important area of investigation in solving the protein folding problem. Atypical main-chain conformations can help identify strains within a folded protein, and by inference, positions where unique amino acids may have a naturally high frequency of occurrence due to favorable contributions to stability and folding. Non-Gly residues located near the left-handed alpha-helical region (L-alpha) of the Ramachandran plot are a potential indicator of structural strain. Although many investigators have studied mutations at such positions, no consistent energetic or kinetic contributions to stability or folding have been elucidated. Here we report a study of the effects of Gly, Ala and Asn substitutions found within the L-alpha region at a characteristic position in defined beta-hairpin turns within human acidic fibroblast growth factor, and demonstrate consistent effects upon stability and folding kinetics. The thermodynamic and kinetic data are compared to available data for similar mutations in other proteins, with excellent agreement. The results have identified that Gly at the i+3 position within a subset of beta-hairpin turns is a key contributor towards increasing the rate of folding to the native state of the polypeptide while leaving the rate of unfolding largely unchanged.     

Molecular mechanics evaluation of the proposed mechanisms for the degradation of urea by urease

A thorough conformational search of all the conformations available to oxygen-bound urea within wild-type urease was carried out. Identical low energy urea conformations were obtained by a Ramachandran type plot for the NHis272-Ni1-O-Curea, and Ni1-O-Curea-Nurea dihedral angles. Ramachandran plots, with active sites and protonation states modified to model the different urease mechanisms, were used to evaluate the different mechanisms. Based upon the low energy conformations available to urea in the active site of wild-type urease one can conclude that the traditional "His320 acts as a base" mechanism is unlikely. while the N,O urea bridged and the reverse protonation mechanisms cannot be ruled out. A consensus hydrogen-bonding network that does not favor any of the mechanisms has been reconfirmed by the extensive conformational search.     

The conformations of polypeptide chains where the main-chain parts of successive residues are enantiomeric. Their occurrence in cation and anion-binding regions of proteins.

We have investigated the shapes of polypeptides where successive residues have main-chain phi,psi conformations of opposite hand. A graph not unlike a Ramachandran plot is presented illustrating the various possible conformations. All are ring-shaped or extended. Some of these conformations occur in native proteins, the commonest approximating to a feature we propose calling a nest, described in the accompanying paper, where the main-chain NH groups point inwards relative to the ring and give rise to an anion-binding site. Another conformation is related but more extended and is found uniquely in the four stretches of polypeptide that line the tetrameric K(+) channel; their CO groups bind the K ions in the channel. In a different ring-shaped conformation that we propose calling a catgrip, the main-chain CO groups point into the ring; this is employed for specific Ca ion binding in the annexin, phospholipase A2 and subtilisin loops, and the regularly arranged beta-roll loops of the serralysin protease family.     

Comparative study of SP[6-11] and its analogs using simulated annealing

In this study we compared the steric structures of the bioactive part of substance P (SP[6-11]) and its analogs (NY3460 and pHOPA-SP5). The molecular dynamics-simulated annealing method was used to explore the conformational space, and the structural differences and similarities of these molecules were identified. For the three peptides, the conformational distributions were represented in Ramachandran density plots. The occurring secondary structural elements of the investigated molecules were identified, namely alpha-Helix, type III beta-Turn, gamma-Turn, and inverse gamma-Turn. For SP[6-11] and its two analogs, different intramolecular interactions (H-bonds between the main-chain atoms, aromatic-aromatic interactions, and amino-aromatic interactions) that can stabilize the various conformations of the three peptides were investigated. Detailed examination of these intramolecular interactions revealed that H-bonds between the main-chain atoms are relevant in the determination and stabilization of the conformer structures of the peptides, while the aromatic-aromatic interactions do not play an important stabilizing role. Furthermore, in the conformers of NY3460 and pHOPA-SP5, different types of amino-aromatic interactions were identified that contribute to the formation of the various structures of these peptides. For all three molecules, the orientations of the side chains were investigated and the rotamer populations were determined.     

Conformational Similarity Indices Between Different Residues in Proteins and α-Helix Propensities

Abstract

Various amino acid similarity matrices have been derived using data on physicochemical properties and molecular evolution. Conformational similarity indices, CS_XX′, between different residues are computed here using the distribution of the main-chain and side-chain torsion angles and the values have been used to cluster amino acids in proteins. A subset of these parameters, CS_AX′ indicates the extent of similarity in the main-chain and side-chain conformations (φ ψ and χ₁) of different residues (X) with Ala (A) and is found to have strong correlation with α-helix propensities. However, no subset of CS_XX′ provides any linear relationship with β-sheet propensities, suggesting that the conformational feature favouring the location of a residue in an a-helix is different from the one favouring the β-sheet. Conformationally similar residues (close CS_AX values) have similar steric framework of the side-chain (linear/branched, aliphatic/aromatic), irrespective of the polarity or hydrophobicity. Cooperative nucleation of helix may be facile for a contiguous stretch of residues with high overall CS_AX values.     

Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure

Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.     

Revisiting the Ramachandran plot: hard-sphere repulsion, electrostatics, and H-bonding in the alpha-helix

What determines the shape of the allowed regions in the Ramachandran plot? Although Ramachandran explained these regions in terms of 1–4 hard‐sphere repulsions, there are discrepancies with the data where, in particular, the α_R, α_L, and β‐strand regions are diagonal. The α_R‐region also varies along the α‐helix where it is constrained at the center and the amino terminus but diffuse at the carboxyl terminus. By analyzing a high‐resolution database of protein structures, we find that certain 1–4 hard‐sphere repulsions in the standard steric map of Ramachandran do not affect the statistical distributions. By ignoring these steric clashes (N···H_i+1 and O_i?1···C), we identify a revised set of steric clashes (C^β···O, O_i?1···N_i+1, C^β···N_i+1, O_i?1···C^β, and O_i?1···O) that produce a better match with the data. We also find that the strictly forbidden region in the Ramachandran plot is excluded by multiple steric clashes, whereas the outlier region is excluded by only one significant steric clash. However, steric clashes alone do not account for the diagonal regions. Using electrostatics to analyze the conformational dependence of specific interatomic interactions, we find that the diagonal shape of the α_R and α_L‐regions also depends on the optimization of the N···H_i+1 and O_i?1···C interactions, and the diagonal β‐strand region is due to the alignment of the CO and NH dipoles. Finally, we reproduce the variation of the Ramachandran plot along the α‐helix in a simple model that uses only H‐bonding constraints. This allows us to rationalize the difference between the amino terminus and the carboxyl terminus of the α‐helix in terms of backbone entropy.     

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.     

Molecular Mechanics Evaluation of the Proposed Mechanisms for the Degradation of Urea by Urease

Abstract

A thorough conformational search of all the conformations available to oxygen-bound urea within wild-type urease was carried out. Identical low energy urea conformations were obtained by a Ramachandran type plot for the N_His272-Ni1-O-C_urea and Ni1-O-Curea-N_urea dihedral angles. Ramachandran plots, with active sites and protonation states modified to model the different urease mechanisms, were used to evaluate the different mechanisms. Based upon the low energy conformations available to urea in the active site of wild-type urease one can conclude that the traditional “His320 acts as a base” mechanism is unlikely, while the N,O urea bridged and the reverse protonation mechanisms cannot be ruled out. A consensus hydrogen-bonding network that does not favor any of the mechanisms has been reconfirmed by the extensive conformational search.