On molecular mechanisms of nucleic acid synthesis fidelity aspects. 1. Contribution of base interactions

This paper is concerned with the molecular mechanisms of spontaneous replacements of base pairs in the processes of template synthesis of nucleic acids. The method of atom-atom potential functions was used to calculate the energies of interaction in non-complementary base pairs arranged in a common plane so that the mutual position of the glycosidic bonds does not differ appreciably from their position for Watson-Crick pairs in the DNA double helix. A number of local minima of this energy have been found, which could occur in template synthesis and result in insertion of incorrect bases into the double helix. The calculation results are indicative of formation of purine-purine pairs with one of the purine nucleotides in syn-conformation, which can be regarded as a typical pathway of transversion, and that of wobble-pairs TG and AC, which can be regarded as a typical pathway of transition. The contribution of intramolecular interactions of nucleic acids as well as interactions of polynucleotide chains with an enzyme to the fidelity of template synthesis of nucleic acids is discussed. The calculation results are compared with the experimental data on the frequency of spontaneous mutations and the frequency of errors in template synthesis of nucleic acids in vitro.     

Distances as degrees of freedom

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-1)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-1)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.     

Distances as Degrees of Freedom

Abstract

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-l)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-l)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.     

DNA bending: the prevalence of kinkiness and the virtues of normality.

DNA bending in 86 complexes with sequence-specific proteins has been examined using normal vector plots, matrices of normal vector angles between all base pairs in the helix, and one-digit roll/slide/twist tables. FREEHELIX, a new program especially designed to analyze severely bent and kinked duplexes, generates the foregoing quantities plus local roll, tilt, twist, slide, shift and rise parameters that are completely free of any assumptions about an overall helix axis. In nearly every case, bending results from positive roll at pyrimidine-purine base pair steps: C-A (= T-G), T-A, or less frequently C-G, in a direction that compresses the major groove. Normal vector plots reveal three well-defined types of bending among the 86 examples: (i) localized kinks produced by positive roll at one or two discrete base pairs steps, (ii) three-dimensional writhe resulting from positive roll at a series of adjacent base pairs steps, or (iii) continuous curvature produced by alternations of positive and negative roll every 5 bp, with side-to-side zig-zag roll at intermediate position. In no case is tilt a significant component of the bending process. In sequences with two localized kinks, such as CAP and IHF, the dihedral angle formed by the three helix segments is a linear function of the number of base pair steps between kinks: dihedral angle = 36 degrees x kink separation. Twenty-eight of the 86 examples can be described as major bends, and significant elements in the recognition of a given base sequence by protein. But even the minor bends play a role in fine-tuning protein/DNA interactions. Sequence-dependent helix deformability is an important component of protein/DNA recognition, alongside the more generally recognized patterns of hydrogen bonding. The combination of FREEHELIX, normal vector plots, full vector angle matrices, and one-digit roll/slide/twist tables affords a rapid and convenient method for assessing bending in DNA.     

MOLMOL: A program for display and analysis of macromolecular structures

MOLMOL is a molecular graphics program for display, analysis, and manipulation of three-dimensional structures of biological macromolecules, with special emphasis on nuclear magnetic resonance (NMR) solution structures of proteins and nucleic acids. MOLMOL has a graphical user interface with menus, dialog boxes, and on-line help. The display possibilities include conventional presentation, as well as novel schematic drawings, with the option of combining different presentations in one view of a molecule. Covalent molecular structures can be modified by addition or removal of individual atoms and bonds, and three-dimensional structures can be manipulated by interactive rotation about individual bonds. Special efforts were made to allow for appropriate display and analysis of the sets of typically 20–40 conformers that are conventionally used to represent the result of an NMR structure determination, using functions for superimposing sets of conformers, calculation of root mean square distance (RMSD) values, identification of hydrogen bonds, checking and displaying violations of NMR constraints, and identification and listing of short distances between pairs of hydrogen atoms.     

Measuring nanometer distances in nucleic acids using a sequence-independent nitroxide probe

This protocol describes the procedures for measuring nanometer distances in nucleic acids using a nitroxide probe that can be attached to any nucleotide within a given sequence. Two nitroxides are attached to phosphorothioates that are chemically substituted at specific sites of DNA or RNA. Inter-nitroxide distances are measured using a four-pulse double electron-electron resonance technique, and the measured distances are correlated to the parent structures using a Web-accessible computer program. Four to five days are needed for sample labeling, purification and distance measurement. The procedures described herein provide a method for probing global structures and studying conformational changes of nucleic acids and protein/nucleic acid complexes.     

A database of 32 DNA triplets to study triple helices by molecular mechanics and dynamics

We present here a database of 32 deoxyribonucleotide triplets, that can be used as building blocks of triple helix forming deoxyribonucleotides on a computer. This database is made of all the pairing schemes of the triplets ATT, GCC⁺, ATA and GCG where the third base forms two hydrogen bonds with the purine of the first two Watson-Crick strands. The essential features of the known triple helices were preserved in the resulting structures. A triple helix can be easily built from any combination of these basic triplets. Four homogeneous and alternate triple helices thus obtained were studied by molecular mechanics and dynamics in vacuo. The results are in agreement with known experimental observations for ATT and suggest a possible structure for the GCG triple helix. In order to characterize the geometry of the structures obtained, the definitions of nucleic acid structure parameters (R.E. Dickerson et al., EMBO J. 8 (1989) 1–4) have been extended to triple helical polynucleotides.     

Theory of the influence of oligonucleotide chain conformation on double helix stability

We consider theoretical aspects of reactions that form base pairs in a double helix. The equilibrium constant for such reactions depends on the probability of finding the two bases in the correct orientation for pairing. This probability can be expressed in terms of the spatial and angular distribution of one micleotide around the other. In this paper we use Monte-Carlo techniques to calculate the distribution of distances between chosen phosphates in nonhclical oligonucleotide backbones, using crystallographic data for bond lengths and angles, and a screened Coulomb potential for phosphate–phosphate interactions. The model chosen is one that predicts correctly the observed dimensions of an unperturbed polynucleotide chain. Knowledge of distance distribution functions permits calculation of the dependence on loop size of the probability of closing a single backbone strand into a hairpin helix. Our results agree roughly, although not exactly, with the semiempirical ring-weighting functions determined by Schefller. Elson, and Baldwin. Further results are a comparison of intramolecular and bimolecular helix nucleation equilibrium constants and a calculation of the stacking free energy in a double helix.     

Location of cyanine-3 on double-stranded DNA: importance for fluorescence resonance energy transfer studies

Fluorescence resonance energy transfer provides valuable long-range distance information about macromolecules in solution. Fluorescein and Cy3 are an important donor-acceptor pair of fluorophores; the characteristic F?rster length for this pair on DNA is 56 A, so the pair can be used to study relatively long distances. Measurement of FRET efficiency for a series of DNA duplexes terminally labeled with fluorescein and Cy3 suggests that the Cy3 is close to the helical axis of the DNA. An NMR analysis of a self-complementary DNA duplex 5'-labeled with Cy3 shows that the fluorophore is stacked onto the end of the helix, in a manner similar to that of an additional base pair. This provides a known point from which distances calculated from FRET measurements are measured. Using the FRET efficiencies for the series of DNA duplexes as restraints, we have determined an effective position for the fluorescein, which is maximally extended laterally from the helix. The knowledge of the fluorophore positions can now be used for more precise interpretation of FRET data from nucleic acids.     

Crystal structure of the B-DNA hexamer d(CTCGAG): model for an A-to-B transition.

The crystal structure of the B-DNA hexamer d(CTCGAG) has been solved at 1.9 A resolution by iterative single isomorphous replacement, using the brominated derivative d(CG5BrCGAG), and refined to an R-factor of 18.6% for 120 nonhydrogen nucleic acid atoms and 32 water molecules. Although the central four base pairs form a typical B-form helix, several parameters suggest a transition to an A-like conformation at the termini. Based on this observation, a B-to-A transition was modeled, maintaining efficient base stacking across the junction. The wide minor groove (approximately 6.9 A) is reminiscent of that in the side-by-side double drug-DNA complexes and hosts a double spine of hydration. The global helix axes of the pseudo-continuous helices are at an acute angle of 60 degrees. The pseudocontinuous stacking is reinforced by the minor groove water structure extending between the two duplexes. The crossover point of two pairs of stacked duplexes is at the stacking junction, unlike that observed in the B-DNA decamers and dodecamers. This arrangement may have implications for the structure of a four-way DNA junction. The duplexes are arranged around a large (approximately 20 A diameter) channel centered on a 6(2) screw axis.     

High-resolution solution structure of the double Cys2His2 zinc finger from the human enhancer binding protein MBP-1.

The high-resolution three-dimensional structure of a synthetic 57-residue peptide comprising the double zinc finger of the human enhancer binding protein MBP-1 has been determined in solution by nuclear magnetic resonance spectroscopy on the basis of 1280 experimental restraints. A total of 30 simulated annealing structures were calculated. The backbone atomic root-mean-square distributions about the mean coordinate positions are 0.32 and 0.33 A for the N- and C-terminal fingers, respectively, and the corresponding values for all atoms, excluding disordered surface side chains, are 0.36 and 0.40 A. Each finger comprises an irregular antiparallel sheet and a helix, with the zinc tetrahedrally coordinated to two cysteines and two histidines. The overall structure is nonglobular in nature, and the angle between the long axes of the helices is 47 +/- 5 degrees. The long axis of the antiparallel sheet in the N-terminal finger is approximately parallel to that of the helix in the C-terminal finger. Comparison of this structure with the X-ray structure of the Zif-268 triple finger complexed with DNA indicates that the relative orientation of the individual zinc fingers is clearly distinct in the two cases. This difference can be attributed to the presence of a long Lys side chain in the C-terminal finger of MBP-1 at position 40, instead of a short Ala or Ser side chain at the equivalent position in Zif-268. This finding suggests that different contacts may be involved in the binding of the zinc fingers of MBP-1 and Zif-268 to DNA, consistent with the findings from methylation interference experiments that the two fingers of MBP-1 contact 10 base pairs, while the three fingers of Zif-268 contact only 9 base pairs.     

The influence of complementary base pair interactions on secondary structure formation and conformational transitions in polynucleotides]

The calculations have been carried out of interaction energy between complementary base pairs of nucleic acids in the function of conformational parametres of double helix (Arnott's parameters) by the method of atom-atom potential functions. Interaction energy as a function of conformational parametres is valley-like and varies little along the bottom of the valley. The regions of interaction energy minima are compared with experimentally determined conformational parametres of nucleic acid double helices. On the basis of calculation results the pathways of conformational transitions between different forms of double-helical polynucleotides are discussed.     

Simulation of interactions between nucleic acid bases by refined atom-atom potential functions

Energy of interaction between nitrogen bases of nucleic acid has been calculated as a function of parameters determining the mutual position of two bases. Refined atom-atom potential functions are suggested. These functions contain terms proportional to the first (electrostatics), sixth (or tenth for the atoms forming a hydrogen bond) and twelfth (repulsion of all atoms) powers of interatomic distance. Calculations have shown that there are two groups of minima of the base interaction energy. The minima of the first group correspond to coplanar arrangement of the base pairs and hydrogen bond formation. The minima of the second group correspond to the position of bases one above the other in almost parallel planes. There are 28 energy minima corresponding to the formation of coplanar pairs with two (three for the G:C pair) almost linear N-H . . . O and (or) N-H . . . N hydrogen bonds. The position of nitrogen bases paired by two such H-bonds in any crystal of nucleic acid component in polynucleotide complexes and in tRNA is close to the position in one of these minima. Besides, for each pair there are energy minima corresponding to the formation of a single N-H . . . O or N-H . . . N and one C-H . . . O or C-H . . . N hydrogen bond. The form of potential surface in the vicinity of minima has been characterized. The results of calculations agree with the experimental data and with more rigorous calculations based on quantum-mechanical approach.     

HELANAL: a program to characterize helix geometry in proteins

A detailed analysis of structural and position dependent characteristic features of helices will give a better understanding of the secondary structure formation in globular proteins. Here we describe an algorithm that quantifies the geometry of helices in proteins on the basis of their C alpha atoms alone. The Fortran program HELANAL can extract the helices from the PDB files and then characterises the overall geometry of each helix as being linear, curved or kinked, in terms of its local structural features, viz. local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. Even helices with large radius of curvature are unambiguously identified as being linear or curved. The program can also be used to differentiate a kinked helix and other motifs, such as helix-loop-helix or a helix-turn-helix (with a single residue linker) with the help of local bending angles. In addition to these, the program can also be used to characterise the helix start and end as well as other types of secondary structures.     

New insights into structure-function relationships in nitrogenase: A 1.6 A resolution X-ray crystallographic study of Klebsiella pneumoniae MoFe-protein.

The X-ray crystal structure of Klebsiella pneumoniae nitrogenase component 1 (Kp1) has been determined and refined to a resolution of 1.6 A, the highest resolution reported for any nitrogenase structure. Models derived from three 1.6 A resolution X-ray data sets are described; two represent distinct oxidation states, whilst the third appears to be a mixture of both oxidized and reduced states (or perhaps an intermediate state). The structures of the protein and the iron-molybdenum cofactor (FeMoco) appear to be largely unaffected by the redox status, although the movement of Ser beta90 and a surface helix in the beta subunit may be of functional significance. By contrast, the 8Fe-7S P-cluster undergoes discrete conformational changes involving the movement of two iron atoms. Comparisons with known component 1 structures reveal subtle differences in the FeMoco environment, which could account for the lower midpoint potential of this cluster in Kp1. Furthermore, a non-proline- cis peptide bond has been identified in the alpha subunit that may have a functional role. It is within 10 A of the FeMoco and may have been overlooked in other component 1 models. Finally, metal-metal and metal-sulphur distances within the metal clusters agree well with values derived from EXAFS studies, although they are generally longer than the values reported for the closely related protein from Azotobacter vinelandii. A number of bonds between the clusters and their ligands are distinctly longer than the EXAFS values, in particular, those involving the molybdenum atom of the FeMoco.     

Protein sequence randomness and sequence/structure correlations.

We investigated protein sequence/structure correlation by constructing a space of protein sequences, based on methods developed previously for constructing a space of protein structures. The space is constructed by using a representation of the amino acids as vectors of 10 property factors that encode almost all of their physical properties. Each sequence is represented by a distribution of overlapping sequence fragments. A distance between any two sequences can be calculated. By attaching a weight to each factor, intersequence distances can be varied. We optimize the correlation between corresponding distances in the sequence and structure spaces. The optimal correlation between the sequence and structure spaces is significantly better than that which results from correlating randomly generated sequences, having the overall composition of the data base, with the structure space. However, sets of randomly generated sequences, each of which approximates the composition of the real sequence it replaces, produce correlations with the structure space that are as good as that observed for the actual protein sequences. A connection is proposed with previous studies of the protein folding code. It is shown that the most important property factors for the correlation of the sequence and structure spaces are related to helix/bend preference, side chain bulk, and beta-structure preference.     

Structural details of ribonuclease H from Escherichia coli as refined to an atomic resolution.

The crystal structure of RNase H from Escherichia coli has been determined by the multiple isomorphous replacement method, and refined by the stereochemically restrained least-squares procedure to a crystallographic R-factor of 0.196 at 1.48 A resolution. In the final structure, the root-mean-square (r.m.s.) deviation for bond lengths is 0.017 A, and for angle distances 0.036 A. The structure is composed of a five-stranded beta-sheet and five alpha-helices, and reveals the details of hydrogen bonding, electrostatic and hydrophobic interactions between intra- and intermolecular residues. The refined structure allows an explanation of the particular interactions between the basic protrusion, consisting of helix alpha III and the following loop, and the remaining major domain. The beta-sheet, alpha II, alpha III and alpha IV form a central hydrophobic cleft that contains all six tryptophan residues, and presumably serves to fix the orientation of the basic protrusion. Two parallel adjacent helices, alpha I and alpha IV, are associated with a few triads of hydrophobic interactions, including many leucine residues, that are similar to the repeated leucine motif. The well-defined electron density map allows detailed discussion of amino acid residues likely to be involved in binding a DNA/RNA hybrid, and construction of a putative model of the enzyme complexed with a DNA/RNA hybrid oligomer. In this model, a protein region, from the Mg(2+)-binding site to the basic protrusion, covers roughly two turns of a DNA/RNA hybrid double helix. A segment (11-23) containing six glycine residues forms a long loop between the beta A and beta B strands. This loop, which protrudes into the solvent region, lies on the interface between the enzyme and a DNA/RNA hybrid in the model of the complex. The mean temperature factors of main-chain atoms show remarkably high values in helix alpha III that constitutes the basic protrusion, suggesting some correlation between its flexibility and the nucleic acid binding function. The Mg(2+)-binding site, surrounded by four invariant acidic residues, can now be described more precisely in conjunction with the catalytic activity. The arrangement of molecules within the crystal appears to be dominated by the cancelling out of a remarkably biased charge distribution on the molecular surface, which is derived in particular from the separation between the acidic Mg(2+)-binding site and the basic protrusion.     

Excluded volume approximation to protein-solvent interaction. The solvent contact model.

Important properties of globular proteins, such as the stability of its folded state, depend sensitively on interactions with solvent molecules. Existing methods for estimating these interactions, such as the geometrical surface model, are either physically misleading or too time consuming to be applied routinely in energy calculations. As an alternative, we derive here a simple model for the interactions between protein atoms and solvent atoms in the first hydration layer, the solvent contact model, based on the conservation of the total number of atomic contacts, a consequence of the excluded-volume effect. The model has the conceptual advantage that protein-protein contacts and protein-solvent contacts are treated in the same language and the technical advantage that the solvent term becomes a particularly simple function of interatomic distances. The model allows rapid calculation of any physical property that depends only on the number and type of protein-solvent nearest-neighbor contacts. We propose use of the method in the calculation of protein solvation energies, conformational energy calculations, and molecular dynamics simulations.