Local Helix Parameters Research Articles

Local helix parameters fitting of proteins based on dual quaternions registration method

A fitting method of calculating local helix parameters of proteins based on dual quaternions registration fitting (DQRFit) is proposed in this paper. First, the C and N atom coordinates of each residue in the protein structure data are extracted. Then the unregistered data and reference data are constructed using the sliding windows. The square sum of the distance of the data points before and after registration is regarded as an optimization goal. We calculate the optimal rotation matrix and the translation vector using the dual quaternion registration algorithm, and get the helix parameters of the secondary structure which contain the number of residues per turn( τ), helix radius( ρ)and helix pitch( p). Furthermore, we can achieve the fitting of three-helix parameters of τ, ρ, p simultaneously with the dual quaternion registration, and can adjust the sliding windows to adapt to different error levels. Compared with the traditional helix fitting method, DQRFit has some advantages such as low computational complexity, strong anti-interference, and high fitting accuracy. It is proven that the precision of proposed DQRFit for α helix detection is comparable to that of the dictionary of secondary structure of proteins (DSSP), and is better than that of other traditional methods. This is of great significance for the protein structure classification and functional prediction, drug design, protein structure visualization and other fields in the future.

Efficient characterization of protein secondary structure in terms of screw motions

A simple and efficient method is presented to describe the secondary structure of proteins in terms of orientational distances between consecutive peptide planes and local helix parameters. The method uses quaternion-based superposition fits of the protein peptide planes in conjunction with Chasles' theorem, which states that any rigid-body displacement can be described by a screw motion. The helix parameters are derived from the best superposition of consecutive peptide planes and the ;worst' fit is used to define the orientational distance. Applications are shown for standard secondary-structure motifs of peptide chains for several proteins belonging to different fold classes and for a description of structural changes in lysozyme under hydrostatic pressure. In the latter case, published reference data obtained by X-ray crystallography and by structural NMR measurements are used.

"...the tyranny of the lattice...".

A systematic comparison of crystal structures of nine different B-DNA dodecamers, in three different space groups, with and without A-tracts, shows that crystal packing or lattice forces are of secondary importance for helix axis bending, minor-groove width, and propeller twist. While other local helix parameters may be influenced or even established by crystal packing, the properties just enumerated are determined primarily by base sequence. One and the same crystal packing scheme can accommodate a bend in one of two different directions, or no bend at all. A-tract regions of B-DNA are inherently straight and unbent, with base-pair inclination no different from that of general-sequence B-DNA. Where bends are observed at junctions between G.C and A.T regions, they always involve a roll about base-pair long axes in a direction that compresses the wide major groove and, hence, are 90 degrees away from that necessary for the correctness of the junction model of A-tract bending. The G.C/A.T junction appears to be a flexible hinge, capable of adopting either a straight or a bent conformation under the local influence of weak crystal packing forces. Such forces therefore are a source of information about DNA deformability and not a curse to be deplored. But as an indication of the weakness of crystal packing forces, introduction of a single bromine atom in the major groove is sufficient to eliminate a bend, although brominated and unbrominated crystals are isomorphous.

The Crystal Structure of the Trigonal Decamer C-G-A-T-C-G- 6meA-T-C-G: a B-DNA Helix with 10·6 Base-pairs Per Turn

The β-DNA decanucleotide C-G-A-T-C-G- 6meA-T-C-G has been crystallized under the same condition used earlier for C-G-A-T-C-G-A-T-C-G, but is found to adopt a new, trigonal P3 221 packing mode instead of the expected orthorhombic P2 12 12 1 form. Unit cell dimensions a = b = 33·38 Å, c = 98·30 Å, γ = 120°, imply ten base-pairs or one complete decamer double helix per asymmetric unit. The 2282 two-sigma data to 2·0 Å refine to R = 17·2% with 45 water molecules, I·5 hexavalent hydrated magnesium complexes, and 0·5 chloride ion per asymmetric unit. Neighboring helices interlock backbone chains and major grooves, crossing at an angle of 120° in a manner that yields an excellent model for a Holiday junction. Local helix parameters differ markedly in the trigonal and orthorhombic structures, with the trigonal helix exhibiting behavior closer to that expected of B-DNA in solution. The trigonal form has an average of 10·6 base-pairs per turn, in contrast to 9·7 base-pairs per turn in the orthorhombic cell. A comparison of all known B -DNA decamer and dodecamer crystal structure analyses indicates that, the greater the cell volume per base-pair (and hence the more open the crystal structure), the closer the mean helix twist approaches an expected 10·6 base-pairs per turn.

Structure of the B-DNA decamer C-C-A-A-C-I-T-T-G-G in two different space groups: Conformational flexibility of B-DNA

For the first time, the same B-DNA oligomer has been crystallized and its structure solved in two different space groups. Crystallization of C-C-A-A-C-I-T-T-G-G with Ca2+ yields monoclinic space group C2 with a = 31.87 A, b = 25.69 A, c = 34.21 A, beta = 114.1 degrees, and five base pairs per asymmetric unit. The 5026 2 sigma data to 1.3 A refine to R = 0.152 with 72 waters, one heptavalent hydrated calcium complex, and one cacodylate ion per asymmetric unit. In contrast, crystallization with Mg2+ yields trigonal space group P3(2)21 with a = b = 33.23 A, c = 94.77 A, gamma = 120 degrees, and 10 base pairs per asymmetric unit. The 1725 2 sigma data to 2.2 A refine to R = 0.164 with 36 water molecules and one octahedral magnesium complex per asymmetric unit. The monoclinic form is virtually isostructural with previously solved monoclinic decamers, including twist angles of ca. 50 degrees at C-A and T-G steps. In contrast, the trigonal structure has quite different local helix parameters, with twist angles of ca. 36 degrees at the corresponding steps. These local parameter differences can only be attributed to crystal packing, suggesting that certain sequences of B-DNA are more flexible and influenced by their surroundings than had previously been thought. Such deformability may be important for interaction of B-DNA with control proteins, where both static structure and dynamic deformability comprise components of the recognition process. The crossing of two helices at an angle of 120 degrees in the trigonal cell is a model for an antiparallel, uncrossed Holliday junction, as has been noted earlier by Timsit and Moras [Timsit, Y., & Moras, D. (1991) J. Mol. Biol. 221, 919-940] from a rhombohedral DNA dodecamer structure analysis.

CURVATURE: software for the analysis of curved DNA.

Software is presented to plot the sequence-dependent spatial trajectory of the DNA double helix and/or distribution of curvature along the DNA molecule. The nearest-neighbor wedge model is implemented to calculate overall DNA path using local helix parameters: helix twist angle, wedge (deflection) angle and direction (of deflection) angle. The procedures described proved to be very convenient as tools for investigation of a relationship between overall DNA curvature and its gel electrophoretic mobility. All parameters of the model had been estimated from experimental data. Using these wedge parameters the program takes, as input, any DNA sequence and calculates the likely degree of curvature at each point along the molecule. This information is displayed both graphically and in the form of simplified representations of curved double helices. The Software, CURVATURE, can thus be used to investigate possible roles of curvature in modulation of gene expression and for location of curved portions of DNA, which may play an important role in sequence-specific protein--DNA interactions.

Structure of a B-DNA decamer with a central T-A step: C-G-A-T-T-A-A-T-C-G

The X-ray crystal structure analysis of the decamer C-G-A-T-T-A-A-T-C-G has been carried out to a resolution of 1.5 Å. The crystals are space group P2 12 12 1, cell dimensions a = 38.60 A ̊ , b = 39.10 A ̊ , c = 33.07 A ̊ . The structure was solved by molecular replacement and refined with X-PLOR and NUCLSQ. The final R factor for a model with 404 DNA atoms, 108 water molecules and one magnesium hexahydrate cation is 15.7%. The double helix is essentially isostructural with C-G-A-T-C-G-A-T-C-G, with closely similar local helix parameters. The structure of the T-T-A-A center differs from that found in C-G-C-G-T-T-A-A-C-G-C-G in that the minor groove in our decamer is wide at the central T-A step rather than narrow, and the twist angle of the T-A step is small (31.1 °) rather than large. Whereas the tetrad model provides a convenient framework for discussing local DNA helix structure, it cannot be the entire story. The articulated helix model of DNA structure proposes that certain sequence regions of DNA show preferential twisting or bending properties, whereas other regions are less capable of deformation, in a manner that may be useful in sequence recognition by drugs and protein. Further crystal structure analyses should help to delineate the precise nature of sequence-dependent articulation in the DNA double helix.

Computer graphics program to reveal the dependence of the gross three-dimensional structure of the B-DNA double helix on primary structure.

Programs are presented to plot the gross three-dimensional structure of the DNA double helix with the base sequence as input information. The rules that determine the overall structure of the double helix are those that predict the dependence of local helix parameters (specifically, helix twist angle and relative basepair roll angle) on sequence. For this purpose, the user can select either the Calladine-Dickerson parameters or the Tung-Harvey parameters. These programs can be used as tools to investigate the variation of DNA tertiary structure with sequence, which may play an important role in the sequence-specific recognition of DNA by proteins.

Structure of a B-DNA dodecamer : II. Influence of base sequence on helix structure

Detailed examination of the structure of the B-DNA dodecamer C-G-C-G-A-A-T-T-C-G-C-G, obtained by single-crystal X-ray analysis (Drew et al., 1981), reveals that the local helix parameters, twist, tilt and roll, are much more strongly influenced by base sequence than by crystal packing or any other external forces. The central EcoRI restriction endonuclease recognition site, G-A-A-T-T-C, is a B helix with an average of 9.8 base-pairs per turn. It is flanked on either side by single-base-pair steps having aspects of an A-like helix character. The dodecamer structure suggests several general principles, whose validity must be tested by other B-DNA analyses. (1) When an external bending moment is applied to a B-DNA double helix, it bends smoothly, without kinks or breaks, and with relatively little effect on local helix parameters. (2) Purine-3′,5′-pyrimidine steps open their base planes towards the major groove, pyrimidine-purine steps open toward the minor groove, and homopolymer (Pur-Pur, Pyr-Pyr) steps resist rolling in either direction. This behavior is related to the preference of pyrimidines for more negative glycosyl torsion angles. (3) CpG steps have smaller helical twist angles than do GpC, as though in compensation for their smaller intrinsic base overlap. Data on A-T steps are insufficient for generalization. (4) G.C base-pairs have smaller propellor twist than A · T, and this arises mainly from interstrand base overlap rather than the presence of the third hydrogen bond. (5) DNAase I cuts preferentially at positions of high helical twist, perhaps because of increased exposure of the backbone to attack. The correlation of the digestion patterns in solution and helical twist in the crystal argues for the essential identity of the helix structure in the two environments. (6) In the two places where the sequence TpCpG occurs, the C slips from under T in order to stack more efficiently over G. At the paired bases of this CpG step, the G and C are tilted so the angle between base planes is splayed out to the outside of the helix. This TpC is the most favored cutting site for DNAase I by a factor of 4.5 (Lomonossoff et al., 1981). (7) The EcoRI restriction endonuclease and methylase both appear to prefer a cutting site of the type purine-purine-A-T-T-pyrimidine, involving two adjacent homopolymer triplets, and this may be a consequence of the relative stiffness of homopolymer base-stacking observed in the dodecamer.