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.     

Structural compromise of disallowed conformations in peptide and protein structures

Using a data set of 454 crystal structures of peptides and 80 crystal structures of non-homologous proteins solved at ultra high resolution of 1.2 A or better we have analyzed the occurrence of disallowed Ramachandran (phi, psi) angles. Out of 1492 and 13508 non-glycyl residues in peptides and proteins respectively 12 and 76 residues in the two datasets adopt clearly disallowed combinations of Ramachandran angles. These examples include a number of conformational points which are far away from any of the allowed regions in the Ramachandran map. According to the Ramachandran map a given (phi, psi) combination is considered disallowed when two non-bonded atoms in a system of two-linked peptide units with ideal geometry are prohibitively proximal in space. However, analysis of the disallowed conformations in peptide and protein structures reveals that none of the observations of disallowed conformations in the crystal structures correspond to a short contact between non-bonded atoms. A further analysis of deviations of bond lengths and angles, from the ideal peptide geometry, at the residue positions of disallowed conformations in the crystal structures suggest that individual bond lengths and angles are all within acceptable limits. Thus, it appears that the rare tolerance of disallowed conformations is possible by gentle and acceptable deviations in a number of bond lengths and angles, from ideal geometry, over a series of bonds resulting in a net gross effect of acceptable non-bonded inter-atomic distances.     

Lysozyme folded in silico according to the limited conformational sub-space

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Structural requirements for thymosin beta4 in its contact with actin. An NMR-analysis of thymosin beta4 mutants in solution and correlation with their biological activity.

We examined the conformational preferences of mutants of thymosin beta4, an actin monomer sequestering protein by NMR spectroscopy in 60% (v/v) trifluoroethanol. Under these conditions, the wild-type thymosin beta4 conformation consists of an alpha-helix (helix I) extending from residues 5-16 with a more stable fragment from lysine 11 to lysine 16 and a second alpha-helix (helix II) encompassing residues 31-39. The point mutations studied here are located in helix I or in the LKKTET segment (residues 17-22) that form the two main entities of interaction with the actin molecule. The alpha-1H conformational shifts allow us to investigate the helicity of the polypeptides at the residue level and to correlate these structures with their biological activity. We determine that an extension of helix I at its C-terminal end over the LKK-segment results in loss of activity. The correct termination of this helix is connected to a specific orientation of the polypeptide essential for a cooperative action of the thymosin beta4 binding entities required for full activity.     

Standard conformations of a polypeptide chain in irregular protein regions

A detailed stereochemical analysis of known protein structures has been made which shows that: (1) irregular regions of proteins consist of a limited number of standard structures formed by three, four of more residues; (2) an amino acid residue of a protein can adopt one of the six sterically allowed conformations designated here as alpha, alpha L, beta, gamma, delta, and epsilon. It is shown that there are two allowed conformations of a polypeptide chain at the N-end of an alpha-helix, beta alpha n- and beta gamma alpha n-conformations, where n is a number of residues in the alpha-helix. At the C-end of the alpha-helix there are two conformations as well, alpha n gamma beta- and alpha n gamma alpha L beta-ones. Two beta-strands in a beta-hairpin can be joined, for example, by standard structures with beta beta alpha L beta-, beta alpha gamma alpha L beta-, beta alpha alpha gamma alpha L beta-conformations which are referred to as turns. In the regions where a polypeptide chain passes from one layer to another there are standard structures with beta gamma beta-, beta alpha beta beta-, beta alpha gamma beta-conformations etc., referred to as cross-overs. A structure of any protein irregular region can be represented as a combination of these and other standard turns and cross-overs considered in the paper. The major part of the turns and cross-overs has residues in alpha L- or epsilon-conformations which must be glycine or other residues with small or flexible side chains. Massive hydrophobic residues must not occupy the first beta-positions of the most standard structures. The results obtained can be successfully applied for prediction of the location of the turns and cross-overs in proteins from their amino acid sequences and for interpretation of electron density maps.     

Lysozyme Folded In Silico According to the Limited Conformational Sub-space

Abstract

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Automatic definition of recurrent local structure motifs in proteins

An automatic procedure for defining recurrent folding motifs in proteins of known structure is described. These motifs are formed by short polypeptide fragments of equal size containing between four and seven residues. The method applies a classical clustering algorithm that operates on distances between selected backbone atoms. In one application, we use it to cluster all protein fragments into only four structural classes. This classification is rough considering the observed diversity of local structures, but comparable in homogeneity to the four classes of secondary structure (alpha-helix, beta-strand, turn and coil). Yet, it discriminates between extended and curved coil and distinguishes beta-bulges from beta-strands. In a second application, the clustering procedure is combined with assignment of backbone dihedral angles to allowed regions in the Ramachandran map. This produces an exhaustive repertoire of highly homogeneous families of structural motifs that contains all the beta-hairpins, beta alpha- and alpha beta-loops previously defined by manual procedures, and new structural families of which two examples, a beta alpha-loop and an alpha-helix beginning, are analyzed in detail. The described automatic procedures should be useful in categorizing structure information in proteins, thereby increasing our ability to analyze relations between structure and sequence.     

Conformational properties of a peptide model for unfolded alpha-helices

Models of protein folding often hypothesize that the first step is local secondary structure formation. The assumption is that unfolded polypeptide chains possess an intrinsic propensity to form these local secondary structures. On the basis of this idea, it is tempting to model the local conformational properties of unfolded proteins using well-established residue secondary structure propensities, in particular, alpha-helix forming propensities. We have used spectroscopic methods to investigate the conformational behavior of a host-guest series of peptides designed to model unfolded alpha-helices. A suitable peptide model for unfolded alpha-helices was determined from studies of the length dependence of the conformational properties of alanine-based peptides. The chosen host peptide possessed a small, detectable, alpha-helix content. Substituting various representative guest residues into the central position of the host peptide at times changed the conformational behavior dramatically, and often in ways that could not be predicted from known alpha-helix forming propensities. The data presented can be used to rationalize some of these propensities. However, it is clear that secondary structure propensities cannot be used to predict the local conformational properties of unfolded proteins.     

The conformational free-energy map for solvated neocarrabiose

A Ramachandran map of the conformational potential of mean force (pmf) for neocarrabiose in water was obtained using molecular dynamics (MD) simulations with umbrella sampling. The potential energy map calculated in a previous study for this molecule in vacuum exhibited a global minimum located at (phi = 81 degrees, psi = -141 degrees). However, the global minimum on the new pmf map in aqueous solution is located in an area centered around (phi = 175 degrees, psi = 180 degrees), indicating a considerable solvent shift. This new global minimum-energy solution conformation was found to correspond to the experimental value obtained from NMR-NOE measurements, and is also consistent with the experimental crystal structure for neocarrabiose and the fiber diffraction conformation for iota-carrageenan. The global minimum of the solution pmf and its local topology were found to be approximately reproduced by quick vacuum conformational energy mapping using several approximations that mimic solvation effects by de-emphasizing intramolecular hydrogen bonding.     

Approaching a complete classification of protein secondary structure

A complete classification of types of the protein secondary structure is developed on the basis of computer analysis of the crystallographic structural data deposited in the protein Data Bank. The majority of amino acid residues fall into five conformation types. A conclusion is drawn that the number of sequence variants of torsion angles phi, psi in globular proteins is limited and is essentially less than the number of possible amino acid sequences for this chain length. Along with alpha-helix and beta-structure, the distribution analysis assigning every maximum of distribution of amino acid conformations on Ramachandran map to a certain type of the secondary structure exposed a third type of the secondary structure that was previously neglected. This type of the structure is extended left-handed helical conformation, designated as mobile (M-) conformation. A full set of M-conformation fragments that seems to play a major role in protein globule dynamics has been obtained, a small radius of correlation for the polypeptide chain in M-conformation is demonstrated. It explains a prevalence of short segments of mobile conformation revealed in globular proteins. For secondary structure types, the frequency of occurrence of amino acid residues has been computed.     

Main-chain conformational tendencies of amino acids

A Ramachandran plot is a visual representation of the main-chain conformational tendencies of an amino acid. Despite forty years of research, the shape of Ramachandran plots is still a matter of debate. The issue in making a Ramachandran plot based on experimental data is deciding whether sparse data represent genuine conformations. We present here a simple solution to settle the ambiguities of the sparse data, and explain how we verified the accuracies of our plots using an independent dataset. To obtain our results, we then measured the pair-wise distances of main-chain conformational tendencies among amino acids, and showed that the conformational relationships of amino acids are well preserved in a two-dimensional map, leading to the conclusion that the conformational diversity space of amino acids is largely two dimensional. We further noticed that amino acids in early and late evolutionary stages are located in different zones in the two-dimensional map. In addition to these conclusions, we here present an amino acid substitution table derived from experimental data.     

Can conformational change be described by only a few normal modes?

We suggest a simple method to assess how many normal modes are needed to map a conformational change. By projecting the conformational change onto a subspace of the normal-mode vectors and using root mean square deviation as a test of accuracy, we find that the first 20 modes only contribute 50% or less of the total conformational change in four test cases (myosin, calmodulin, NtrC, and hemoglobin). In some allosteric systems, like the molecular switch NtrC, the conformational change is localized to a limited number of residues. We find that many more modes are necessary to accurately map this collective displacement. In addition, the normal-mode "spectra" can provide useful information about the details of the conformational change, especially when comparing structures with different bound ligands, in this case, calmodulin. Indeed, this approach presents normal-mode analysis as a useful basis in which to capture the mechanism of conformational change, and shows that the number of normal modes needed to capture the essential collective motions of atoms should be chosen according to the required accuracy.     

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.     

Structure of papain refined at 1.65 A resolution

Papain is a sulfhydryl protease from the latex of the papaya fruit. Its molecules consist of one polypeptide chain with 212 amino acid residues. The chain is folded into two domains with the active site in a groove between the domains. We have refined the crystal structure of papain, in which the sulfhydryl group was oxidized, by a restrained least-squares procedure at 1.65 A to an R-factor of 16.1%. The estimated accuracy in the atomic co-ordinates is 0.1 A, except for disordered atoms. All phi/psi angles for non-glycine residues are found within the outer limit boundary of a Ramachandran plot and this provides another check on the quality of the model. In the alpha-helical parts of the structure, the C = O bonds are directed more away from the helix axis than in a classical alpha-helix, leading to somewhat longer hydrogen bonds, 2.98 A, compared to 2.89 A. The hydrogen-bonding parameters and conformational angles in the anti-parallel beta-sheet structure show a large diversity. Hydrogen bonds in the core of the sheet are generally shorter than those at the more twisted ends. The average value is 2.91 A. The hydrogen bond distance Ni+3-Oi in turns is relatively long and the geometry is far from linear. Hydrogen bond formation, therefore, is perhaps not an essential prerequisite for turn formation. Although the crystallization medium is 62% (w/w) methanol in water, only 29 out of 224 solvent molecules can be regarded with any certainty as methanol molecules. The water molecules play an important role in maintaining structural stability. This is specially true for internal water. Twenty-one water molecules are located in contact areas between adjacent papain molecules. It seems as if the enzyme is trapped in a grid of water molecules with only a limited number of direct interactions between the protein molecules. The residues in the active site cleft belong to the most static parts of the structure. In general, disorder in atomic positions increases when going from the interior of the protein molecule to its surface. This behavior was quantified and it was found that the point of minimum disorder is near the molecular centroid.     

Recognition of alpha-helix transmembrane domains with an amphipathy scale generated by molecular dynamics using only the primary sequence of proteins

We recently developed an amphipathy scale, elaborated from molecular dynamics data that can be used for the identification of hydrophobic or hydrophilic regions in proteins. This amphipathy scale reflects side chain/water molecule interaction energies. We have now used this amphipathy scale to find candidates for transmembrane segments, by examining a large sample of membrane proteins with alpha-helix segments. The candidates were selected based on an amphipathy coefficient value range and the minimum number of residues in a segment. We compared our results with the transmembrane segments previously identified in the PDB_TM database by the TMDET algorithm. We expected that the hydrophobic segments would be identified using only the primary structures of the proteins and the amphipathy scale. However, some of these hydrophobic segments may pertain to hydrophobic pockets not included in transmembrane regions. We found that our amphipathy scale could identify alpha-helix transmembrane regions with a probability of success of 76% when all segments were included and 90% when all membrane proteins were included.     

Conformation of a peptide ligand bound to its G-protein coupled receptor

Many peptide hormones elicit a wide array of physiological effects by binding to G-protein coupled receptors. We have determined the conformation of pituitary adenylate cyclase activating polypeptide, PACAP(1--21)NH(2), bound to a PACAP-specific receptor by NMR spectroscopy. Residues 3--7 form a unique beta-coil structure that is preceded by an N-terminal extended tail. This beta-coil creates a patch of hydrophobic residues that is important for receptor binding. In contrast, the C-terminal region (residues 8--21) forms an alpha-helix, similar to that in the micelle-bound PACAP. Thus, the conformational difference between PACAP in the receptor-bound and the micelle-bound states is limited to the N-terminal seven residues. This observation is consistent with the two-step ligand transportation model in which PACAP first binds to the membrane nonspecifically and then diffuses two-dimensionally in search of its receptor; a conformational change at the N-terminal region then allows specific interactions between the ligand and the receptor.     

Fast and accurate computation of the 13C chemical shifts for an alanine-rich peptide

The purpose of this work is, first, to present a fast and accurate technique to compute Boltzmann-averaged values of the quantum-chemical 13C chemical shifts for each amino acid in oligopeptides, demonstrated here by an application to the peptide Ac-XXAAAAAAAOO-NH2 (where X denotes diaminobutyric acid, A is alanine, and O is ornithine) [XAO] and, second, to discuss the capability of the 13Calpha and 13Cbeta chemical shifts to distinguish the PP(II) conformation from the alpha-helix and statistical-coil conformations. Use is made of a combination of approaches, summarized as follows: (1) derivation of an ensemble of conformations by using a molecular mechanics technique; (2) use of a clustering procedure to form families and build a reduced set of conformations consisting of the lowest-energy conformations of each family, and (3) computation of the 13C chemical shifts for the lowest-energy conformations of each family, using a quantum-chemical approach that treats a selected residue, or group of residues, with a 6-311+G(2d,p) locally-dense basis set, while the remaining residues in the sequence are treated with a 3-21G basis set. The whole procedure is quite accurate and speeds up the computation of the Boltzmann-averaged values of the 13C-chemical shifts by several orders of magnitude. The present application sheds some light on the conformational preference for alanine and non-alanine residues to occupy the PP(II) helical region of the Ramachandran map.     

Molecular dynamics study of kaliotoxin in water

Kaliotoxin (KTX), a potassium channel blocker found in the venom of the scorpion Androctonous Mauretanicus is a 38 residue polypeptide with a well defined structure consisting of a alpha-helix and a three strand antiparallel beta-sheet interconnected by three disulfide bonds. Although the 3D structure has been determined by NMR, there is a number of features, mainly concerning the conformation and flexibility of the side chains, but also the long range order in the peptide and its fluctuations, that may have escaped the experimental study. These questions are now being addressed using molecular dynamics (MD) simulations. Accordingly, the present work reports the analysis of a 430 ps molecular dynamics trajectory of the polypeptide soaked with 4700 TIP3 water molecules inside a 56 A box. MD calculations were performed with periodic boundary conditions. Analysis of the conformational space sampled by each of the residues along the trajectory, suggests a special behavior of Pro17 and Lys19 both located on the helix. Furthermore, analysis of the relative movements of the secondary structure elements indicates that the alpha-helix and beta-sheets fluctuate in a correlated motion, preserving the tertiary structure of the polypeptide along the trajectory. Finally, analysis of the charge distribution was also examined. The direction of the dipole moment, computed from the center of masses appears to be an interesting feature of the structure probably related to the biological function of the molecule.