Energetically unfavorable amide conformations for N6‐acetyllysine side chains in refined protein structures

The reversible acetylation of lysine to form N6‐acetyllysine in the regulation of protein function is a hallmark of epigenetics. Acetylation of the positively charged amino group of the lysine side chain generates a neutral N‐alkylacetamide moiety that serves as a molecular “switch” for the modulation of protein function and protein–protein interactions. We now report the analysis of 381 N6‐acetyllysine side chain amide conformations as found in 79 protein crystal structures and 11 protein NMR structures deposited in the Protein Data Bank (PDB) of the Research Collaboratory for Structural Bioinformatics. We find that only 74.3% of N6‐acetyllysine residues in protein crystal structures and 46.5% in protein NMR structures contain amide groups with energetically preferred trans or generously trans conformations. Surprisingly, 17.6% of N6‐acetyllysine residues in protein crystal structures and 5.3% in protein NMR structures contain amide groups with energetically unfavorable cis or generously cis conformations. Even more surprisingly, 8.1% of N6‐acetyllysine residues in protein crystal structures and 48.2% in NMR structures contain amide groups with energetically prohibitive twisted conformations that approach the transition state structure for cis‐trans isomerization. In contrast, 109 unique N‐alkylacetamide groups contained in 84 highly accurate small molecule crystal structures retrieved from the Cambridge Structural Database exclusively adopt energetically preferred trans conformations. Therefore, we conclude that cis and twisted N6‐acetyllysine amides in protein structures deposited in the PDB are erroneously modeled due to their energetically unfavorable or prohibitive conformations. Proteins 2013; © 2012 Wiley Periodicals, Inc.     

Contact interactions method: a new algorithm for protein folding simulations.

Computer simulations of simple exact lattice models are an aid in the study of protein folding process; they have sometimes resulted in predictions experimentally proved. The contact interactions (CI) method is here proposed as a new algorithm for the conformational search in the low-energy regions of protein chains modeled as copolymers of hydrophobic and polar monomers configured as self-avoiding walks on square or cubic lattices. It may be regarded as an extension of the standard Monte Carlo method improved by the concept of cooperativity deriving from nonlocal contact interactions. A major difference with respect to other algorithms is that criteria for the acceptance of new conformations generated during the simulations are not based on the energy of the entire molecule, but cooling factors associated with each residue define regions of the model protein with higher or lower mobility. Nine sequences of length ranging from 20 to 64 residues were used on the square lattice and 15 sequences of length ranging from 46 to 136 residues were used on the cubic lattice. The CI algorithm proved very efficient both in two and three dimensions, and allowed us to localize energy minima not localized by other searching algorithms described in the literature. Use of this algorithm is not limited to the conformational search, because it allows the exploration of thermodynamic and kinetic behavior of model protein chains.     

On residues in the disallowed region of the Ramachandran map.

An analysis of the occurrence of nonglycyl residues in conformations disallowed in the Ramachandran plot is presented. Ser, Asn, Thr, and Cys have the highest propensities to exhibit such conformations, and the branched aliphatic residues the lowest. Residues cluster in five regions and there are some trends in the types of residues and their side-chain conformations (chi(1)) occupying these. Majority of the residues are found at the edge of helices and strands and in short loops, and are involved in different types of weak, stabilizing interactions. A structural motif has been identified where a residue in disallowed conformation occurs as the first residue of a short 3(10)-helix. On the basis of the types of neighboring residues, the location in the three-dimensional structure and accessibility, there are similarities with the occurrence of cis peptide bonds in protein structures.     

Beta-sheet folding of fragment (16-36) of bovine pancreatic trypsin inhibitor as predicted by Monte Carlo simulated annealing.

A tertiary structure prediction is described using Monte Carlo simulated annealing for the peptide fragment corresponding to residues 16-36 of bovine pancreatic trypsin inhibitor (BPTI). The simulation starts with randomly chosen initial conformations and is performed without imposing experimental constraints using energy functions given for generic interatomic interactions. Out of 20 simulation trials, seven conformations show a sheet-like structure--two strands connected by a turn--although this sheet-like structure is not as rigid as that observed in native BPTI. It is also shown that these conformations are mostly looped and exhibit a native-like right-handed twist. Unlike the case with the C-peptide of RNase A, no conspicuous alpha-helical structure is found in any of the final conformations obtained in the simulation. However, the lowest-energy conformation does not resemble exactly the native structure. This indicates that the rigid beta-sheet conformation of native BPTI merely corresponds to a local minimum of the energy function if the fragment with residues 16-36 is isolated from the native protein. A statistical analysis of all 20 final conformations suggests that the tendency for the peptide segments to form extended beta-strands is strong for those with residues 18-24, and moderate for those with residues 30-35. The segment of residues 25-29 does not tend to form any definite structure. In native BPTI, the former segments are involved in the beta-sheet and the latter in the turn. A folding scenario is also speculated from this analysis.     

Structure of myohemerythrin in the azidomet state at 1.7/1.3 A resolution

The molecular model of myohemerythrin, an oxygen-carrying protein from sipunculan worms, has been refined by stereochemically restrained least-squares minimization at 1.7/1.3 A resolution to a conventional R-value of 0.158. The estimated positional standard deviation is better than 0.15 A for most of the 979 protein atoms. The average isotropic displacement parameter, B, for the protein atoms is 23.1 A2. This high average B parameter appears to be due to the overall motion of the molecule, which correlates with the observed anisotropic diffraction. The side-chains of seven residues were modeled in two conformations, i.e. the side-chains were discretely disordered, and B parameters for several lysine and glutamate side-chains indicate that they are poorly localized. Of the residues in myohemerythrin, 66% are helical, with 62% occurring in four long alpha-helices with mean values for the backbone torsion angles of phi = -65 degrees, psi = -42 degrees, and for the hydrogen bonds distances of N ... O, 3.0 A and H ... O, 2.1 A, and angles of N ... O = C, 153 degrees, N-H ... O, 157 degrees, and H ... O = C, 147 degrees. For two-thirds of the alpha-helical residues, the torsional rotation of the C alpha-C beta bond, chi 1, is approximately -60 degrees, and for one-third chi 1 is approximately 180 degrees. Although most turns in myohemerythrin are well-categorized by previous classification, two do not fit in established patterns. Also included in the refined model are three sulfate ions, all partially occupied, and 157 water molecules, 40% of which are modeled fully occupied. Only one water molecule is internal to the protein, the remainder occur on the surface and are observed principally between symmetry-related molecules contributing, along with van der Waals' contacts, most of the interactions between molecules. There are eight intermolecular protein-protein hydrogen bonds, of which only four are between well-located atoms.     

A generic program for multistate protein design

Some protein design tasks cannot be modeled by the traditional single state design strategy of finding a sequence that is optimal for a single fixed backbone. Such cases require multistate design, where a single sequence is threaded onto multiple backbones (states) and evaluated for its strengths and weaknesses on each backbone. For example, to design a protein that can switch between two specific conformations, it is necessary to to find a sequence that is compatible with both backbone conformations. We present in this paper a generic implementation of multistate design that is suited for a wide range of protein design tasks and demonstrate in silico its capabilities at two design tasks: one of redesigning an obligate homodimer into an obligate heterodimer such that the new monomers would not homodimerize, and one of redesigning a promiscuous interface to bind to only a single partner and to no longer bind the rest of its partners. Both tasks contained negative design in that multistate design was asked to find sequences that would produce high energies for several of the states being modeled. Success at negative design was assessed by computationally redocking the undesired protein-pair interactions; we found that multistate design's accuracy improved as the diversity of conformations for the undesired protein-pair interactions increased. The paper concludes with a discussion of the pitfalls of negative design, which has proven considerably more challenging than positive design.     

Rebuilding flavodoxin from C alpha coordinates: a test study

The tertiary structure of flavodoxin has been model built from only the X-ray crystallographic alpha-carbon coordinates. Main-chain atoms were generated from a dictionary of backbone structures. Side-chain conformations were initially set according to observed statistical distributions, clashes were resolved with reference to other knowledge-based parameters, and finally, energy minimization was applied. The RMSD of the model was 1.7 A across all atoms to the native structure. Regular secondary structural elements were modeled more accurately than other regions. About 40% of the chi 1 torsional angles were modeled correctly. Packing of side chains in the core was energetically stable but diverged significantly from the native structure in some regions. The modeling of protein structures is increasing in popularity but relatively few checks have been applied to determine the accuracy of the approach. In this work a variety of parameters have been examined. It was found that close contacts, and hydrogen-bonding patterns could identify poorly packed residues. These tests, however, did not indicate which residues had a conformation different from the native structure or how to move such residues to bring them into agreement. To assist in the modeling of interacting side chains a database of known interactions has been prepared.     

The interrelationships of side-chain and main-chain conformations in proteins

The accurate determination of a large number of protein structures by X-ray crystallography makes it possible to conduct a reliable statistical analysis of the distribution of the main-chain and side-chain conformational angles, how these are dependent on residue type, adjacent residue in the sequence, secondary structure, residue-residue interactions and location at the polypeptide chain termini. The interrelationship between the main-chain (phi, psi) and side-chain (chi 1) torsion angles leads to a classification of amino acid residues that simplify the folding alphabet considerably and can be a guide to the design of new proteins or mutational studies. Analyses of residues occurring with disallowed main-chain conformation or with multiple conformations shed some light on why some residues are less favoured in thermophiles.     

Structural determinants of the conformations of medium-sized loops in proteins

Loops are integral components of protein structures, providing links between elements of secondary structure, and in many cases contributing to catalytic and binding sites. The conformations of short loops are now understood to depend primarily on their amino acid sequences. In contrast, the structural determinants of longer loops involve hydrogen-bonding and packing interactions within the loop and with other parts of the protein. By searching solved protein structures for regions similar in main chain conformation to the antigen-binding loops in immunoglobulins, we identified medium-sized loops of similar structure in unrelated proteins, and compared the determinants of their conformations. For loops that form compact substructures the major determinant of the conformation is the formation of hydrogen bonds to inward-pointing main chain atoms. For loops that have more extended conformations, the major determinant of their structure is the packing of a particular residue or residues against the rest of the protein. The following picture emerges: Medium-sized loops of similar conformation are stabilized by similar interactions. The groups that interact with the loop have very similar spatial dispositions with respect to the loop. However, the residues that provide these interactions may arise from dissimilar parts of the protein: The conformation of the loop requires certain interactions that the protein may provide in a variety of ways.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.     

A minimal physically realistic protein-like lattice model: designing an energy landscape that ensures all-or-none folding to a unique native state

A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended beta-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key beta-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.     

Propensities,probabilities, and the Boltzmann hypothesis

The relative strengths of interactions involving polypeptide chains can be estimated with reasonable accuracy with statistical potentials, free-energy functions derived from the frequency of occurrence of structural arrangements of residues or atoms in collections of protein structures. Recent published work has shown that the energetics of side-chain/backbone interactions can be modeled by the phi/psi propensities of the 20 amino acids. In this report, the more commonly used phi/psi probabilities are demonstrated to fail in evaluating the free energies of protein conformations because of an overriding preference for all helical structures. Comparison of the hypothetical reactions implied by these two different statistics-propensities versus probabilities-leads to the conclusion that the Boltzmann hypothesis may only be applicable for the calculation of statistical potentials after the starting conformation has been specified. This conclusion supports a simple conjecture: The surprising success of the Boltzmann hypothesis in explaining the energetics of protein structures is a direct consequence of a real equilibrium, one extending over evolutionary time that has maintained the stability of each protein within a narrow range of values.     

Simultaneous modeling of multiple loops in proteins.

The most reliable methods for predicting protein structure are by way of homologous extension, using structural information from a closely related protein, or by "threading" through a set of predefined protein folds ("inverse folding"). Both sets of methods provide a model for the core of the protein--the structurally conserved secondary structures. Due to the large variability both in sequence and size of the loops that connect these secondary structures, they generally cannot be modeled using these techniques. Loop-closure algorithms are aimed at predicting loop structures, given their end-to-end distance. Various such algorithms have been described, and all have been tested by predicting the structure of a single loop in a known protein. In this paper we propose a method, which is based on the bond-scaling-relaxation loop-closure algorithm, for simultaneously predicting the structures of multiple loops, and demonstrate that, for two spatially close loops, simultaneous closure invariably leads to more accurate predictions than sequential closure. The accuracy of the predictions obtained for pairs of loops in the size range of 5-7 residues each is comparable to that obtained by other methods, when predicting the structures of single loops: the RMS deviations from the native conformations of various test cases modeled are approximately 0.6-1.7 A for backbone atoms and 1.1-3.3 A for all-atoms.     

ModLoop: automated modeling of loops in protein structures

SUMMARY: ModLoop is a web server for automated modeling of loops in protein structures. The input is the atomic coordinates of the protein structure in the Protein Data Bank format, and the specification of the starting and ending residues of one or more segments to be modeled, containing no more than 20 residues in total. The output is the coordinates of the non-hydrogen atoms in the modeled segments. A user provides the input to the server via a simple web interface, and receives the output by e-mail. The server relies on the loop modeling routine in MODELLER that predicts the loop conformations by satisfaction of spatial restraints, without relying on a database of known protein structures. For a rapid response, ModLoop runs on a cluster of Linux PC computers. AVAILABILITY: The server is freely accessible to academic users at http://salilab.org/modloop     

Crystal structure of thioredoxin from Escherichia coli at 1.68 A resolution

The crystal structure of thioredoxin from Escherichia coli has been refined by the stereochemically restrained least-squares procedure to a crystallographic R-factor of 0.165 at 1.68 A resolution. In the final model, the root-mean-square deviation from ideality for bond distances is 0.015 A and for angle distances 0.035 A. The structure contains 1644 protein atoms from two independent molecules, two Cu2+, 140 water molecules and seven methylpentanediol molecules. Ten residues have been modeled in two alternative conformations. E. coli thioredoxin is a compact molecule with 90% of its residues in helices, beta-strands or reverse turns. The molecule consists of two conformational domains, beta alpha beta alpha beta and beta beta alpha, connected by a single-turn alpha-helix and a 3(10) helix. The beta-sheet forms the core of the molecule packed on either side by clusters of hydrophobic residues. Helices form the external surface. The active site disulfide bridge between Cys32 and Cys35 is located at the amino terminus of the second alpha-helix. The positive electrostatic field due to the helical dipole is probably important for stabilizing the anionic intermediate during the disulfide reductase function of the protein. The more reactive cysteine, Cys32, has its sulfur atom exposed to solvent and also involved in a hydrogen bond with a backbone amide group. Residues 29 to 37, which include the active site cysteine residues, form a protrusion on the surface of the protein and make relatively fewer interactions with the rest of the structure. The disulfide bridge exhibits a right-handed conformation with a torsion angle of 81 degrees and 72 degrees about the S-S bond in the two molecules. Twenty-five pairs of water molecules obey the noncrystallographic symmetry. Most of them are involved in establishing intramolecular hydrogen-bonding interactions between protein atoms and thus serve as integral parts of the folded protein structure. Methylpentanediol molecules often pack against the loops and stabilize their structure. Cu2+ used for crystallization exhibit a distorted octahedral square bipyramid co-ordination and provide essential packing interactions in the crystal. The two independent protein molecules are very similar in conformation but distinctly different in atomic detail (root-mean-square = 0.94 A). The differences, which may be related to the crystal contacts, are localized mostly to regions far from the active site.     

Tryptophan rich peptides: influence of indole rings on backbone conformation

Synthetic peptides with defined secondary structure scaffolds, namely hairpins and helices, containing tryptophan residues, have been investigated in this study to probe the influence of a large number of aromatic amino acids on backbone conformations. Solution NMR investigations of Boc-W-L-W-(D)P-G-W-L-W-OMe (peptide 1), designed to form a well-folded hairpin, clearly indicates the influence of flanking aromatic residues at the (D)Pro-Gly region on both turn nucleation and strand propagation. Indole-pyrrolidine interactions in this peptide lead to the formation of the less-frequent type I' turn at the (D)Pro-Gly segment and frayed strand regions, with the strand residues adopting local helical conformations. An analog of peptide 1 with an Aib-Gly turn-nucleated hairpin (Boc-W-L-W-U-G-W-L-W-OMe (peptide 2)) shows a preference for helical structures in solution, in both chloroform and methanol. Peptides with either one (Boc-W-L-W-U-W-L-W-OMe (peptide 3)) or two (Boc-U-W-L-W-U-W-L-W-OMe (peptide 4)) helix-nucleating Aib residues give rise to the well-folded helical conformations in the chloroform solution. The results are indicative of a preference for helical folding in peptides containing a large number of Trp residues. Investigation of a tetrapeptide analog of peptide 2, Boc-W-U-G-W-OMe (peptide 5), in solution and in the crystal state (by X-ray diffraction), also indicates a preference for a helical fold. Additionally, peptide 5 is stabilized in crystals by both aromatic interactions and an array of weak interactions. Examination of Trp-rich sequences in protein structures, however, reveals no secondary structure preference, suggesting that other stabilizing interactions in a well-folded protein may offset the influence of indole rings on backbone conformations.     

Molecular thermodynamic model to predict the alpha-helical secondary structure of polypeptide chains in solution.

The native state of a protein molecule in aqueous solutions represents one of the lowest states of Gibbs energy [Anfinsen, C.B. (1973) Science 181, 223-230]. Much progress has been made about the rules of protein folding [King, J. (1989) Chem. Eng. News 67, 32-54] and the dominant forces in protein folding [Dill, K.A. (1990) Biochemistry 29, 7133-7155]. However, the quantitative contributions of different Gibbs energy terms to protein stability remains a controversial issue [Moult, J., & Unger, R. (1991) Biochemistry 30, 3816-3824]. A molecular thermodynamic model has been proposed for the Gibbs energy of folding a residue in aqueous homopolypeptides from a random-coiled state to either the alpha-helix state or the beta-sheet state [Chen, C.-C., Zhu, Y., King, J.A., & Evans, L.B. (1992) Biopolymers 32, 1375-1392]. In this work, we present a generalization of the molecular thermodynamic model for the Gibbs energy of folding natural and synthetic heteropolypeptides from random-coiled conformations into alpha-helical conformations. The generalized model incorporates the intrinsic folding potential due to residue-solvent interactions, the cooperative folding effect due to residue-residue interactions, and the location and length of alpha-helices. The utility of the model was demonstrated by examining the stability of alpha-helical conformations of a number of natural polypeptides including C-peptide (residues 1-13) and S-peptide (residues 1-20) of RNase A (bovine pancreatic ribonuclease A), the P alpha fragment in BPTI (bovine pancreatic trypsin inhibitor), and synthetic polypeptides (the copolymers of different amino acid residues) including alanine-based peptides (16 or 17 residues long) in water. The computed Gibbs energies correspond well with the experimental data on helicity. The results also accounted for the effects of amino acid substitution and temperature on the stability of alpha-helical conformations of the test polypeptides.     

Myoglobin cavities provide interior ligand pathway

The myoglobin protein binds oxygen and catalyzes NO oxidation. As a key model protein, its dynamics have been well studied by spectroscopy and by crystallography as well as by simulation. Nonetheless, visualization of the mechanism of movement of ligands within myoglobin has been difficult. Coordinates of the A1 and A3 taxonomic spectral states of myoglobin from the 1 A crystal structure (1a6g) are generated as consistent sets of correlated clusters of residues with A or B crystal alternates. Analysis of cavities in these A1 and A3 conformations clarifies the pathway of ligand motion from distal entry through interior movement to the proximal side of the heme. Cavities opened up by buried alternate conformations link the distal to the proximal side of the heme. Structural conservation highlights the relevance of this pathway to human neuroglobin. Cavity migration via myoglobin crystal alternates provides a specific link of protein structure to protein dynamics and protein function and demonstrates the relevance of substates (discrete disorder) to function for all proteins.     

Ricin A-chain structural determinant for binding substrate analogues: A molecular dynamics simulation analysis

Ricin A-chain is a cytotoxic protein that attacks ribosomes by hydrolyzing a specific adenine base from a highly conserved, single-stranded rRNA hairpin containing the tetraloop sequence GAGA. Molecular-dynamics simulation methods are used to analyze the structural determinant for three substrate analogues bound to the ricin A-chain molecule. Simulations were applied to the binding of the dinucleotide adenyl-3′,5′-guanosine employing the x-ray crystal structure of the ricin complex and a modeled CGAGAG hexanucleotide loop taken from the NMR solution structure of a 29-mer oligonucleotide hairpin. A third simulation model is also presented describing a conformational search of the docked 29-mer structure by using a simulated-annealing method. Analysis of the structural interaction energies for each model shows the overall binding dominated by nonspecific interactions, which are mediated by specific arginine contacts from the highly basic region on the protein surface. The tetraloop conformation of the 29-mer was found to make specific interactions with conserved protein residues, in a manner that favored the GAGA sequence. A comparison of the two docked loop conformations with the NMR structure revealed significant positional deviations, suggesting that ricin may use an induced fit mechanism to recognize and bind the rRNA substrate. The conserved Tyr-80 may play an important confirmational entropic role in the binding and release of the target adenine in the active site. Proteins 27:80–95 © 1997 Wiley-Liss, Inc.