Analysis of six protein structures predicted by comparative modeling techniques

The protein structures of six comparative modeling targets were predicted in a procedure that relied on improved energy minimization, without empirical rules, to position all new atoms. The structures of human nucleoside diphosphate kinase NM23-H2, HPr from Mycoplasma capricolum, 2Fe-2S ferredoxin from Haloarcula marismortui, eosinophil-derived neurotoxin (EDN), mouse cellular retinoic acid protein I (CRABP1), and P450eryf were predicted with root mean square deviations on Cα atoms of 0.69, 0.73, 1.11, 1.48, 1.69, and 1.73 Å, respectively, compared to the target crystal structures. These differences increased as the sequence similarity between the target and parent proteins decreased from about 60 to 20% identity. More residues were predicted than form the common region shared by the two crystal structures. In most cases insertions or deletions between the target and the related protein of known structure were not correctly positioned. One two residue insertion in CRABP1 was predicted in the correct conformation, while a nine residue insertion in EDN was predicted in the correct spatial region, although not in the correct conformation. The positions of common cofactors and their binding sites were predicted correctly, even when overall sequence similarity was low. © 1995 Wiley-Liss, Inc.     

ProDCoNN: Protein design using a convolutional neural network

Designing protein sequences that fold to a given three-dimensional (3D) structure has long been a challenging problem in computational structural biology with significant theoretical and practical implications. In this study, we first formulated this problem as predicting the residue type given the 3D structural environment around the C _α atom of a residue, which is repeated for each residue of a protein. We designed a nine-layer 3D deep convolutional neural network (CNN) that takes as input a gridded box with the atomic coordinates and types around a residue. Several CNN layers were designed to capture structure information at different scales, such as bond lengths, bond angles, torsion angles, and secondary structures. Trained on a very large number of protein structures, the method, called ProDCoNN (protein design with CNN), achieved state-of-the-art performance when tested on large numbers of test proteins and benchmark datasets.     

Variability of the canonical loop conformations in serine proteinases inhibitors and other proteins

Canonical loops of protein inhibitors of serine proteinases occur in proteins having completely different folds. In this article, conformations of the loops have been analyzed for inhibitors belonging to 10 structurally different families. Using deviation in C_α-C_α distances as a criterion for loop similarity, we found that the P3-P3′ segment defines most properly the length of the loop. When conformational differences among loops of individual inhibitors were compared using root mean square deviation (rmsd) in atomic coordinates for all main chain atoms (Δr method) and rmsd operating in main chain torsion angles (Δt method), differences of up to 2.1 Å and 72.3°, respectively, were observed. Such large values indicate significant conformational differences among individual loops. Nevertheless, the overall geometry of the inhibitor-proteinase interaction is very well preserved, as judged from the similarity of C_α-C_α distances between C_α of catalytic Ser and C_α of P3-P3′ residues in various enzyme-inhibitor complexes. The mode of interaction is very well preserved both in the chymotrypsin and subtilisin families, as distances calculated for subtilisin-inhibitor complexes are almost always within the range of those for chymotrypsin-inhibitor complexes. Complex formation leads to conformational changes of up to 160° for χ₁ angle. Side chains of residue P1 and P2′ adopt in different complexes a similar orientation (χ₁ angle = −60° and −180°, respectively). To check whether the canonical conformation can be found among non–proteinase-inhibitor Brookhaven Protein Data Bank structures, two selection criteria—the allowed main chain dihedral angles and C_α-C_α distances for the P3-P3′ segment—were applied to all these structures. This procedure detected 132 unique hexapeptide segments in 121 structurally and functionally unrelated proteins. Partial preferences for certain amino acids occurring at particular positions in these hexapeptides could be noted. Further restriction of this set to hexapeptides with a highly exposed P1 residue side chain resulted in 40 segments. The possibility of complexes formation between these segments and serine proteinases was ruled out in molecular modeling due to steric clashes. Several structural features that determine the canonical conformation of the loop both in inhibitors and in other proteins can be distinguished. They include main chain hydrogen bonds both within the P3-P3′ segment and with the scaffold region, P3-P4 and P3′-P4′ hydrophobic interactions, and finally either hydrophobic or polar interactions involving the P1′ residue. Proteins 32:459–474, 1998. © 1998 Wiley-Liss, Inc.     

Modeling of protein loops by simulated annealing.

A method is presented to model loops of protein to be used in homology modeling of proteins. This method employs the ESAP program of Higo et al. (Higo, J., Collura, V., & Garnier, J., 1992, Biopolymers 32, 33-43) and is based on a fast Monte Carlo simulation and a simulated annealing algorithm. The method is tested on different loops or peptide segments from immunoglobulin, bovine pancreatic trypsin inhibitor, and bovine trypsin. The predicted structure is obtained from the ensemble average of the coordinates of the Monte Carlo simulation at 300 K, which exhibits the lowest internal energy. The starting conformation of the loop prior to modeling is chosen to be completely extended, and a closing harmonic potential is applied to N, CA, C, and O atoms of the terminal residues. A rigid geometry potential of Robson and Platt (1986, J. Mol. Biol. 188, 259-281) with a united atom representation is used. This we demonstrate to yield a loop structure with good hydrogen bonding and torsion angles in the allowed regions of the Ramachandran map. The average accuracy of the modeling evaluated on the eight modeled loops is 1 A root mean square deviation (rmsd) for the backbone atoms and 2.3 A rmsd for all heavy atoms.     

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.     

Euclidean sections of protein conformation space and their implications in dimensionality reduction

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality?reduction methods using the pairwise root?mean?square deviation (RMSD) as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality‐reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N‐dimensional Euclidean space R^3N. We formally define the protein conformation space as the quotient space of R^3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise RMSD is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean‐based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra‐peptide and β‐hairpin systems. Proteins 2014; 82:2585–2596. © 2014 Wiley Periodicals, Inc.     

Optimization of van der Waals energy for protein side-chain placement and design

Computational determination of optimal side-chain conformations in protein structures has been a long-standing and challenging problem. Solving this problem is important for many applications including homology modeling, protein docking, and for placing small molecule ligands on protein-binding sites. Programs available as of this writing are very fast and reasonably accurate, as measured by deviations of side-chain dihedral angles; however, often due to multiple atomic clashes, they produce structures with high positive energies. This is problematic in applications where the energy values are important, for example when placing small molecules in docking applications; the relatively small binding energy of the small molecule is drowned by the large energy due to atomic clashes that hampers finding the lowest energy state of the docked ligand. To address this we have developed an algorithm for generating a set of side-chain conformations that is dense enough that at least one of its members would have a root mean-square deviation of no more than R Å from any possible side-chain conformation of the amino acid. We call such a set a side-chain cover set of order R for the amino acid. The size of the set is constrained by the energy of the interaction of the side chain to the backbone atoms. Then, side-chain cover sets are used to optimize the conformation of the side chains given the coordinates of the backbone of a protein. The method we use is based on a variety of dead-end elimination methods and the recently discovered dynamic programming algorithm for this problem. This was implemented in a computer program called Octopus where we use side-chain cover sets with very small values for R, such as 0.1 Å, which ensures that for each amino-acid side chain the set contains a conformation with a root mean-square deviation of, at most, R from the optimal conformation. The side-chain dihedral-angle accuracy of the program is comparable to other implementations; however, it has the important advantage that the structures produced by the program have negative energies that are very close to the energies of the crystal structure for all tested proteins.     

Building native protein conformation from NMR backbone chemical shifts using Monte Carlo fragment assembly

We have been analyzing the extent to which protein secondary structure determines protein tertiary structure in simple protein folds. An earlier paper demonstrated that three-dimensional structure can be obtained successfully using only highly approximate backbone torsion angles for every residue. Here, the initial information is further diluted by introducing a realistic degree of experimental uncertainty into this process. In particular, we tackle the practical problem of determining three-dimensional structure solely from backbone chemical shifts, which can be measured directly by NMR and are known to be correlated with a protein's backbone torsion angles. Extending our previous algorithm to incorporate these experimentally determined data, clusters of structures compatible with the experimentally determined chemical shifts were generated by fragment assembly Monte Carlo. The cluster that corresponds to the native conformation was then identified based on four energy terms: steric clash, solvent-squeezing, hydrogen-bonding, and hydrophobic contact. Currently, the method has been applied successfully to five small proteins with simple topology. Although still under development, this approach offers promise for high-throughput NMR structure determination.     

Reconstruction of protein conformations from estimated positions of the C alpha coordinates.

Protein C alpha coordinates are used to accurately reconstruct complete protein backbones and side-chain directions. This work employs potentials of mean force to align semirigid peptide groups around the axes that connect successive C alpha atoms. The algorithm works well for all residue types and secondary structure classes and is stable for imprecise C alpha coordinates. Tests on known protein structures show that root mean square errors in predicted main-chain and C beta coordinates are usually less than 0.3 A. These results are significantly more accurate than can be obtained from competing approaches, such as modeling of backbone conformations from structurally homologous fragments.     

Smooth statistical torsion angle potential derived from a large conformational database via adaptive kernel density estimation improves the quality of NMR protein structures

Statistical potentials that embody torsion angle probability densities in databases of high‐quality X‐ray protein structures supplement the incomplete structural information of experimental nuclear magnetic resonance (NMR) datasets. By biasing the conformational search during the course of structure calculation toward highly populated regions in the database, the resulting protein structures display better validation criteria and accuracy. Here, a new statistical torsion angle potential is developed using adaptive kernel density estimation to extract probability densities from a large database of more than 10⁶ quality‐filtered amino acid residues. Incorporated into the Xplor‐NIH software package, the new implementation clearly outperforms an older potential, widely used in NMR structure elucidation, in that it exhibits simultaneously smoother and sharper energy surfaces, and results in protein structures with improved conformation, nonbonded atomic interactions, and accuracy.     

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, ≥90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed (?, ψ) torsion angles of ca 12º. TALOS-N also reports sidechain χ¹ rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.     

Surface‐based protein binding pocket similarity

Protein similarity comparisons may be made on a local or global basis and may consider sequence information or differing levels of structural information. We present a local three‐dimensional method that compares protein binding site surfaces in full atomic detail. The approach is based on the morphological similarity method which has been widely applied for global comparison of small molecules. We apply the method to all‐by‐all comparisons two sets of human protein kinases, a very diverse set of ATP‐bound proteins from multiple species, and three heterogeneous benchmark protein binding site data sets. Cases of disagreement between sequence‐based similarity and binding site similarity yield informative examples. Where sequence similarity is very low, high pocket similarity can reliably identify important binding motifs. Where sequence similarity is very high, significant differences in pocket similarity are related to ligand binding specificity and similarity. Local protein binding pocket similarity provides qualitatively complementary information to other approaches, and it can yield quantitative information in support of functional annotation. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

Expression of rat intestinal fatty acid binding protein in E. coli and its subsequent structural analysis: a model system for studying the molecular details of fatty acid-protein interaction

A prokaryotic expression vector containing the rec A promoter and a translational enhancer element from the gene 10 leader of bacteriophage T7 was used to direct efficient synthesis of rat intestinal fatty acid binding protein (I-FABP) in E. coli. Expression of I-FABP in E. coli has no apparent, deleterious effects on the organism. High levels of expression of I-FABP mRNA in supE⁺ strains of E. coli, such as JM101, is associated with suppression of termination at its UGA stop codon. This can be eliminated by using a sup-Estrain as MG1655 and by site-directed mutagenesis of the cDNA to create an in frame UAA stop codon. E. coli-derived rat I-FABP lacks its initiator Met residues. It has been crystallized with and without bound palmitate. High resolution x-ray crystallographic studies of the 131 residue apo- and holo-proteins have revealed the following. I-FABP contains 10 anti-parallel -strands organized into two orthogonally situated -sheets. The overall conformation of the protein resembles that of a clam — hence the term -clam. The bound ligand is located in the interior of the protein. Its carboxylate group forms part of a unique five member hydrogen bonding network consisting of two ordered solvent molecules as well as the side chains of Arg¹⁰⁶ and Gln¹¹⁵. The hydrocarbon chain of the bound C16:0 fatty acid has a distinctive bent conformation with a slight left-handed helical twist. This conformation is maintained by interactions with the side chains of a number of hydrophobic and aromatic amino acids. Apo-I-FABP has a similar overall conformation to holo-I-FABP indicating that the -clam structure is stable even without bound ligand. The space occupied by bound ligand in the core of the holo-protein is occupied by additional ordered solvent molecules in the apo-protein. Differences in the side chain orientations pf several residues located over a potential opening to the cores of the apo- and holo-proteins suggest that solvent may play an important role in the binding mechanism. Comparison of the C coordinates of apo- and holo-I-FABP with those of other proteins indicates it is a member of a superfamily that currently includes (i) 10 mammalian intracellular lipid binding proteins, (ii) the photoactive yellow protein from the purple photoautotrophic bacterium Ectothiorhodospira halophila and (iii) a group of extracellular lipid binding proteins from a diverse number of phyla that have a common barrel consisting of 8 anti-parallel -strands stacked in two nearly orthogonal sheets. In summary, E. coli-derived I-FABP not only represents a useful model for assessing the atomic details of fatty acid-protein interactions and the mechanisms which regulate acquisition and release of this type of ligand, but also structure/function relationships in other superfamily members.Abbreviations I-FABP Intestinal Fatty Acid Binding Protein - r.m.s root mean square     

Solution structures of polcalcin Phl p 7 in three ligation states: Apo‐, hemi‐Mg2+‐bound,and fully Ca2+‐bound

Polcalcins are small EF‐hand proteins believed to assist in regulating pollen‐tube growth. Phl p 7, from timothy grass (Phleum pratense), crystallizes as a domain‐swapped dimer at low pH. This study describes the solution structures of the recombinant protein in buffered saline at pH 6.0, containing either 5.0 mM EDTA, 5.0 mM Mg²⁺, or 100 μM Ca²⁺. Phl p 7 is monomeric in all three ligation states. In the apo‐form, both EF‐hand motifs reside in the closed conformation, with roughly antiparallel N‐ and C‐terminal helical segments. In 5.0 mM Mg²⁺, the divalent ion is bound by EF‐hand 2, perturbing interhelical angles and imposing more regular helical structure. The structure of Ca²⁺‐bound Phl p 7 resembles that previously reported for Bet v 4—likewise exposing apolar surface to the solvent. Occluded in the apo‐ and Mg²⁺‐bound forms, this surface presumably provides the docking site for Phl p 7 targets. Unlike Bet v 4, EF‐hand 2 in Phl p 7 includes five potential anionic ligands, due to replacement of the consensus serine residue at –x (residue 55 in Phl p 7) with aspartate. In the Phl p 7 crystal structure, D55 functions as a helix cap for helix D. In solution, however, D55 apparently serves as a ligand to the bound Ca²⁺. When Mg²⁺ resides in site 2, the D55 carboxylate withdraws to a distance consistent with a role as an outer‐sphere ligand. ¹⁵N relaxation data, collected at 600 MHz, indicate that backbone mobility is limited in all three ligation states. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

GSAFold: a new application of GSA to protein structure prediction

The folding process defines three‐dimensional protein structures from their amino acid chains. A protein's structure determines its activity and properties; thus knowing such conformation on an atomic level is essential for both basic and applied studies of protein function and dynamics. However, the acquisition of such structures by experimental methods is slow and expensive, and current computational methods mostly depend on previously known structures to determine new ones. Here we present a new software called GSAFold that applies the generalized simulated annealing (GSA) algorithm on ab initio protein structure prediction. The GSA is a stochastic search algorithm employed in energy minimization and used in global optimization problems, especially those that depend on long‐range interactions, such as gravity models and conformation optimization of small molecules. This new implementation applies, for the first time in ab initio protein structure prediction, an analytical inverse for the Visitation function of GSA. It also employs the broadly used NAMD Molecular Dynamics package to carry out energy calculations, allowing the user to select different force fields and parameterizations. Moreover, the software also allows the execution of several simulations simultaneously. Applications that depend on protein structures include rational drug design and structure‐based protein function prediction. Applying GSAFold in a test peptide, it was possible to predict the structure of mastoparan‐X to a root mean square deviation of 3.00 Å. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Conformational analysis of protein and nucleic acid fragments with the new grid search algorithm FOUND

The new computer algorithm FOUND, which is implemented as an integrated module of the DYANA structure calculation program, is capable of performing systematic local conformation analyses by exhaustive grid searches for arbitrary contiguous fragments of proteins and nucleic acids. It uses torsion angles as the only degrees of freedom to identify all conformations that fulfill the steric and NMR-derived conformational restraints within a contiguous molecular fragment, as defined either by limits on the maximal restraint violations or by the fragment-based DYANA target function value. Sets of mutually dependent torsion angles, for example in ribose rings, are treated as a single degree of freedom. The results of the local conformation analysis include allowed torsion angle ranges and stereospecific assignments for diastereotopic substituents, which are then included in the input of a subsequent structure calculation. FOUND can be used for grid searches comprising up to 13 torsion angles, such as the backbone of a complete -helical turn or dinucleotide fragments in nucleic acids, and yields a significantly higher number of stereospecific assignments than the precursor grid search algorithm HABAS.     

Design of Peptides Using α,β-Dehydro-residues: Synthesis,Crystal Structure and Molecular Conformation of N-Boc-L-Val-ΔPhe–ΔPhe-L-Ala-OCH3

To obtain general rules of peptide design using α,β-dehydro-residues, a sequence with two consecutive ΔPhe-residues, Boc-L -Val-ΔPhe–ΔPhe- L -Ala-OCH₃, was synthesized by azlactone method in solution phase. The peptide was crystallized from its solution in an acetone/water mixture (70:30) in space group P6₁ with a=b=14.912(3) Å, c= 25.548(5) Å, V=4912.0(6) ų. The structure was determined by direct methods and refined by a full matrix least-squares procedure to an R value of 0.079 for 2891 observed [I?3σ(I)] reflections. The backbone torsion angles ?₁=?54(1)°, ψ₁= 129(1)°, ω₁=?177(1)°, ?₂ =57(1)°, ψ₂=15(1)°, ω₂ =?170(1)°, ?₃=80(1)°, ψ₃ =7(2)°, ω₃=?177(1)°, ?₄ =?108(1)° and ψ^T₄=?34 (1)° suggest that the peptide adopts a folded conformation with two overlapping β-turns of types II and III′. These turns are stabilized by two intramolecular hydrogen bonds between the CO of the Boc group and the NH of ΔPhe³ and the CO of Val¹ and the NH of Ala⁴. The torsion angles of ΔPhe² and ΔPhe³ side chains are similar and indicate that the two ΔPhe residues are essentially planar. The folded molecules form head-to- tail intermolecular hydrogen bonds giving rise to continuous helical columns which run parallel to the c-axis. This structure established the formation of two β-turns of types II and III′ respectively for sequences containing two consecutive ΔPhe residues at (i+2) and (i+3) positions with a branched β-carbon residue at one end of the tetrapeptide.     

Tanford-Kirkwood theory for concentric dielectric continua: application to dimethylphosphate

The Tanford–Kirkwood theory for evaluating the electrostatic free energy of a discrete charge distribution in the presence of ion atmosphere is extended to concentric dielectric continua. The theory is applied to study the conformational preferences with respect to phosphodiester torsion angles in the dimethylphosphate anion (DMP^?) and the sodium dimethylphosphate ion pair (Na⁺DMP^?), in the absence and presence of ion atmosphere and at varying local dielectric constants. Results indicate that phosphodiester torsion angles in DMP^? prefer the gauche-gauche conformation in aqueous solutions.