Application of a genetic algorithm in the conformational analysis of methylene-acetal-linked thymine dimers in DNA: Comparison with distance geometry calculations

The three-dimensional spatial structure of a methylene-acetal-linked thymine dimer presentin a 10 base-pair (bp) sense–antisense DNA duplex was studied with a geneticalgorithm designed to interpret NOE distance restraints. Trial solutions were represented bytorsion angles. This means that bond angles for the dimer trial structures are kept fixed duringthe genetic algorithm optimization. Bond angle values were extracted from a 10 bpsense–antisense duplex model that was subjected to energy minimization by means ofa modified AMBER force field. A set of 63 proton–proton distance restraints definingthe methylene-acetal-linked thymine dimer was available. The genetic algorithm minimizesthe difference between distances in the trial structures and distance restraints. A largeconformational search space could be covered in the genetic algorithm optimization byallowing a wide range of torsion angles. The genetic algorithm optimization in all cases ledto one family of structures. This family of the methylene-acetal-linked thymine dimer in theduplex differs from the family that was suggested from distance geometry calculations. It isdemonstrated that the bond angle geometry around the methylene-acetal linkage plays animportant role in the optimization.     

Packing analysis of carbohydrates and polysaccharides. IV. A new method for detailed crystal structure refinement of polysaccharides and its application to V-amylose

A method is described for predicting and solving crystal structures of linear homopolysaccharides. The method is based on the refinement of the structure with respect to either stereochemical constraints or x-ray diffraction intensities. In the refinement process, all conformational and packing features of the molecule, such as bond lengths, bond angles, conformational angles, nonbonded contacts, hydrogen bonds, etc., can be allowed to vary until the structure reaches both a conformation and crystalline packing that are in minimum disagreement with the stereochemical restraints and the diffraction data. In this fashion, both packing and conformational features of the structure can be simultaneously refined, and not separately as has been the custom in the past. The refinement procedure is based on a method of constrained optimization which possesses improved characteristics of reaching a solution and avoiding false minima, in comparison with least squares methods. The procedure is, in addition, capable of easily finding molecules of solvent of crystallization. The method was applied to further refining the previously solved crystal structure of V-amylose. The results indicated that contrary to the previously found six-fold molecular symmetry in the P2₁2₁2₁ space group, the V-amylose molecule exhibits only two-fold symmetry with the asymmetric unit consisting of three glucose residues in one-half turn of the helix. The three residues are nonequivalent principally due to unequal rotational positions of the hydroxymethyl groups. The crystal structure of V-amylose predicted from stereochemical refinement was identical in all details with that obtained from refining against X-ray data. The excellent agreement with the diffraction data was indicated by the crystallographic disagreement index R = 0.25.     

Geometry of the five-membered ring mathematical demonstration of the pseudorotation formulae

The geometrical relations between the 15 typical parameters (bond lengths and angles, torsion angles) of a five-membered ring are derived for any ring then for a regular one. It is demonstrated that for the case of the 20 symmetrical C ₂ and C _sconformations, only geometrical considerations are needed to obtain the pseudorotation formulae for the torsion angles. However, the puckering intensity as well as the bond angle values cannot be expressed from geometrical constraints alone but would require energetical considerations.     

Geno3D: automatic comparative molecular modelling of protein

Geno3D (http://geno3d-pbil.ibcp.fr) is an automatic web server for protein molecular modelling. Starting with a query protein sequence, the server performs the homology modelling in six successive steps: (i) identify homologous proteins with known 3D structures by using PSI-BLAST; (ii) provide the user all potential templates through a very convenient user interface for target selection; (iii) perform the alignment of both query and subject sequences; (iv) extract geometrical restraints (dihedral angles and distances) for corresponding atoms between the query and the template; (v) perform the 3D construction of the protein by using a distance geometry approach and (vi) finally send the results by e-mail to the user.     

Improvement of hydrogen bond geometry in protein NMR structures by residual dipolar couplings – an assessment of the interrelation of NMR restraints

We have examined how the hydrogen bond geometry in three different proteins is affected when structural restraints based on measurements of residual dipolar couplings are included in the structure calculations. The study shows, that including restraints based solely on (1)H(N)-(15)N residual dipolar couplings has pronounced impact on the backbone rmsd and Ramachandran plot but does not improve the hydrogen bond geometry. In the case of chymotrypsin inhibitor 2 the addition of (13)CO-(13)C(alpha) and (15)N-(13)CO one bond dipolar couplings as restraints in the structure calculations improved the hydrogen bond geometry to a quality comparable to that obtained in the 1.8 A resolution X-ray structure of this protein. A systematic restraint study was performed, in which four types of restraints, residual dipolar couplings, hydrogen bonds, TALOS angles and NOEs, were allowed in two states. This study revealed the importance of using several types of residual dipolar couplings to get good hydrogen bond geometry. The study also showed that using a small set of NOEs derived only from the amide protons, together with a full set of residual dipolar couplings resulted in structures of very high quality. When reducing the NOE set, it is mainly the side-chain to side-chain NOEs that are removed. Despite of this the effect on the side-chain packing is very small when a reduced NOE set is used, which implies that the over all fold of a protein structure is mainly determined by correct folding of the backbone.     

The solution structure of a B-DNA undecamer comprising a portion of the specific target site for the cAMP receptor protein in the gal operon. Refinement on the basis of interproton distance data.

A restrained least squares refinement of the solution structure of the double-stranded DNA undecamer 5'd(AAGTGT-GACAT).5'd(ATGTCACACTT) comprising a portion of the specific target site of the cAMP receptor protein in the gal operon is presented. The structure is refined on the basis of both distance and planarity restraints, 2331 in all. The distance restraints comprise 150 interproton distances determined from pre-steady state nuclear Overhauser enhancement measurements and 2159 other interatomic distances derived from idealized geometry (i.e., distances between covalently bonded atoms, between atoms defining fixed bond angles, and between atoms defining hydrogen bonding in AT and GC base pairs). Two refinements were carried out and in both cases the final RMS difference between the experimental and calculated interproton distances was 0.2 A. The difference between the two refined structures is small (overall RMS difference of 0.23 A) and represents the error in the refined coordinates. Although the refined structures have an overall B-type conformation there are large variations in many of the local conformational parameters including backbone and glycosidic bond torsion angles, helical twist and propellor twist, base roll and base tilt angles.     

Conformational transitions and geometry differences between low-energy conformers of N-acetyl-N′-methyl alanineamide: An ab initio study at the 4-21G level with gradient relaxed geometries

Energy pathways between the α_R, β′, C, and β-regions of the conformational energy surface of N-acetyl-N′-methylalanyl amide were obtained by SCF ab initio calculations on the 4-21G level, with gradient geometry optimization at each point. The calculations indicate that no barrier exists at this computational level between α_R and β′. The variation of geometry (bond distances and bond angles) with conformation is analyzed in detail, and the most important geometrical parameters that should be treated as variables in both empirical energy calculations and in the fitting of polypeptide chains in proteins by x-ray methods are identified. In addition to the ?,ψ correlation discussed previously for the helical state, a correlation of these dihedral angles in the β-region is described.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ? and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Geometry of guanidinium groups in arginines

The restraints in common usage today have been obtained based on small molecule X‐ray crystal structures available 25 years ago and recent reports have shown that the values of bond lengths and valence angles can be, in fact, significantly different from those stored in libraries, for example for the peptide bond or the histidine ring geometry. We showed that almost 50% of outliers found in protein validation reports released in the Protein Data Bank on 23 March 2016 come from geometry of guanidine groups in arginines. Therefore, structures of small molecules and atomic resolution protein crystal structures have been used to derive new target values for the geometry of this group. The most significant difference was found for NE‐CZ‐NH1 and NE‐CZ‐NH2 angles, showing that the guanidinium group is not symmetric. The NE‐CZ‐NH1 angle is larger, 121.5(10)?, than NE‐CZ‐NH2, 119.2(10)?, due to the repulsive interaction between NH1 and CD1 atom.     

Atomic Resolution Structure of a Protein Prepared by Non-Enzymatic His-Tag Removal. Crystallographic and NMR Study of GmSPI-2 Inhibitor

Purification of suitable quantity of homogenous protein is very often the bottleneck in protein structural studies. Overexpression of a desired gene and attachment of enzymatically cleavable affinity tags to the protein of interest made a breakthrough in this field. Here we describe the structure of Galleria mellonella silk proteinase inhibitor 2 (GmSPI-2) determined both by X-ray diffraction and NMR spectroscopy methods. GmSPI-2 was purified using a new method consisting in non-enzymatic His-tag removal based on a highly specific peptide bond cleavage reaction assisted by Ni(II) ions. The X-ray crystal structure of GmSPI-2 was refined against diffraction data extending to 0.98 Å resolution measured at 100 K using synchrotron radiation. Anisotropic refinement with the removal of stereochemical restraints for the well-ordered parts of the structure converged with R factor of 10.57% and R _free of 12.91%. The 3D structure of GmSPI-2 protein in solution was solved on the basis of 503 distance constraints, 10 hydrogen bonds and 26 torsion angle restraints. It exhibits good geometry and side-chain packing parameters. The models of the protein structure obtained by X-ray diffraction and NMR spectroscopy are very similar to each other and reveal the same β₂αβ fold characteristic for Kazal-family serine proteinase inhibitors.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Benchmarking of copper(II) LFMM parameters for studying amyloid-β peptides

Ligand field molecular mechanics (LFMM) parameters have been benchmarked for copper (II) bound to the amyloid-β_1–16 peptide fragment. Several density functional theory (DFT) optimised small test models, representative of different possible copper coordination modes, have been used to test the accuracy of the LFMM copper bond lengths and angles, resulting in errors typically less than 0.1 Å and 5°. Ligand field molecular dynamics (LFMD) simulations have been carried out on the copper bound amyloid-β_1–16 peptide and snapshots extracted from the subsequent trajectory. Snapshots have been optimised using DFT and the semi-empirical PM7 method resulting in good agreement against the LFMM calculated geometry. Analysis of substructures within snapshots shows that the larger contribution of geometrical difference, as measured by RMSD, lies within the peptide backbone, arising from differences in DFT and AMBER, and the copper coordination sphere is reproduced well by LFMM. PM7 performs excellently against LFMM with an average RMSD of 0.2 Å over 21 tested snapshots. Further analysis of the LFMD trajectory shows that copper bond lengths and angles have only small deviations from average values, with the exception of a carbonyl moiety from the N-terminus, which can act as a weakly bound fifth ligand.     

The unusual conformation of cross-strand disulfide bonds is critical to the stability of β-hairpin peptides

The cross-strand disulfides (CSDs) found in β-hairpin antimicrobial peptides (β-AMPs) show a unique disulfide geometry that is characterized by unusual torsion angles and a short Cα-Cα distance. While the sequence and disulfide bond connectivity of disulfide-rich peptides is well studied, much less is known about the disulfide geometry found in CSDs and their role in the stability of β-AMPs. To address this, we solved the nuclear magnetic resonance (NMR) structure of the β-AMP gomesin (Gm) at 278, 298, and 310 K, examined the disulfide bond geometry of over 800 disulfide-rich peptides, and carried out extensive molecular dynamics (MD) simulation of the peptides Gm and protegrin. The NMR data suggests Cα-Cα distances characteristic for CSDs are independent of temperature. Analysis of disulfide-rich peptides from the Protein Data Bank revealed that right-handed and left-handed rotamers are equally likely in CSDs. The previously reported preference for right-handed rotamers was likely biased by restricting the analysis to peptides and proteins solved using X-ray crystallography. Furthermore, data from MD simulations showed that the short Cα-Cα distance is critical for the stability of these peptides. The unique disulfide geometry of CSDs poses a challenge to biomolecular force fields and to retain the stability of β-hairpin fold over long simulation times, restraints on the torsion angles might be required.     

Stereochemical quality of protein structure coordinates.

Methods have been developed to assess the stereochemical quality of any protein structure both globally and locally using various criteria. Several parameters can be derived from the coordinates of a given structure. Global parameters include the distribution of phi, psi and chi 1 torsion angles, and hydrogen bond energies. There are clear correlations between these parameters and resolution; as the resolution improves, the distribution of the parameters becomes more clustered. These features show a broad distribution about ideal values derived from high-resolution structures. Some structures have tightly clustered distributions even at relatively low resolutions, while others show abnormal scatter though the data go to high resolution. Additional indicators of local irregularity include proline phi angles, peptide bond planarities, disulfide bond lengths, and their chi 3 torsion angles. These stereochemical parameters have been used to generate measures of stereochemical quality which provide a simple guide as to the reliability of a structure, in addition to the most important measures, resolution and R-factor. The parameters used in this evaluation are not novel, and are easily calculated from structure coordinates. A program suite is currently being developed which will quickly check a given structure, highlighting unusual stereochemistry and possible errors.     

Pressure-dependent <Superscript>13</Superscript>C chemical shifts in proteins: origins and applications

Pressure-dependent ¹³C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH₃, CH₂ and CH carbon shifts change on average by +0.23, −0.09 and −0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the γ-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual ¹³Cα shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas ¹³Cβ shifts retain significant dependence on local compression, making them less useful as structural restraints.     

Atomic resolution structures of oxidized [4Fe-4S] ferredoxin from Bacillus thermoproteolyticus in two crystal forms: systematic distortion of [4Fe-4S] cluster in the protein

Diffraction data of two crystal forms (forms I and II) of [4Fe-4S] ferredoxin from Bacillus thermoproteolyticus have been collected to 0.92 A and 1.00 A resolutions, respectively, at 100 K using synchrotron radiation. Anisotropic temperature factors were introduced for all non-hydrogen atoms in the refinement with SHELX-97, in which stereochemical restraints were applied to the protein chain but not to the [4Fe-4S] cluster. The final crystallographic R-factors are 9.8 % for 7.0-0.92 A resolution data of the form I and 11.2 % for the 13.3-1.0 A resolution data of the form II. Many hydrogen atoms as well as multiple conformations for several side-chains have been identified. The present refinement has revised the conformations of several peptide bonds and side-chains assigned previously at 2.3 A resolution; the largest correction was that the main-chain of Pro1 and the side-chain of Lys2 were changed by rotating the C(alpha)-C bond of Lys2. Although the overall structures in the two crystal forms are very similar, conformational differences are observed in the two residues at the middle (Glu29 and Asp30) and the C-terminal residues, which have large temperature factors. The [4Fe-4S] cluster is a distorted cube with non-planar rhombic faces. Slight but significant compression of the four Fe-S bonds along one direction is observed in both crystal forms, and results in the D(2d) symmetry of the cluster. The compressed direction of the cluster relative to the protein is conserved in the two crystal forms and consistent with that in one of the clusters in Clostridium acidurici ferredoxin.     

Ferredoxin Competes with Bacterial Frataxin in Binding to the Desulfurase IscS

The bacterial iron-sulfur cluster (isc) operon is an essential machine that is highly conserved from bacteria to primates and responsible for iron-sulfur cluster biogenesis. Among its components are the genes for the desulfurase IscS that provides sulfur for cluster formation, and a specialized ferredoxin (Fdx) whose role is still unknown. Preliminary evidence suggests that IscS and Fdx interact but nothing is known about the binding site and the role of the interaction. Here, we have characterized the interaction using a combination of biophysical tools and mutagenesis. By modeling the Fdx·IscS complex based on experimental restraints we show that Fdx competes for the binding site of CyaY, the bacterial ortholog of frataxin and sits in a cavity close to the enzyme active site. By in vivo mutagenesis in bacteria we prove the importance of the surface of interaction for cluster formation. Our data provide the first structural insights into the role of Fdx in cluster assembly.     

Small-angle X-ray scattering constraints and local geometry like secondary structures can construct a coarse-grained protein model at amino acid residue resolution

We have developed a new methodology that determines protein structures using small-angle X-ray scattering (SAXS) data. The current bottlenecks in determining the protein structures require a new strategy using the simple design of an experiment, and SAXS is suitable for this purpose in spite of its low information content. First we demonstrated that SAXS constraints work additively to NMR-derived information in calculating structures. Next, structure calculations for nine proteins taking different folds were performed using the SAXS constraints combined with the NMR-derived distance restraints for local geometry such as secondary structures or those for tertiary structure. The results show that the SAXS constraints complemented the tertiary-structural information for all the proteins, and that accuracy of the structures thus obtained with SAXS constraints and local geometrical restraints ranged from 1.85 to 4.33 Å. Based on these results, we were able to construct a coarse-grained protein model at amino acid residue resolution.