Wilma K. Olson

3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures.

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar–phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.

Web 3DNA—a web server for the analysis, reconstruction, and visualization of three-dimensional nucleic-acid structures

The w3DNA (web 3DNA) server is a user-friendly web-based interface to the 3DNA suite of programs for the analysis, reconstruction, and visualization of three-dimensional (3D) nucleic-acid-containing structures, including their complexes with proteins and other ligands. The server allows the user to determine a wide variety of conformational parameters in a given structure—such as the identities and rigid-body parameters of interacting nucleic-acid bases and base-pair steps, the nucleotides comprising helical fragments, etc. It is also possible to build 3D models of arbitrary nucleotide sequences and helical types, customized single-stranded and double-helical structures with user-defined base-pair parameters and sequences, and models of DNA ‘decorated’ at user-defined sites with proteins and other molecules. The visualization component offers unique, publication-quality representations of nucleic-acid structures, such as ‘block’ images of bases and base pairs and stacking diagrams of interacting nucleotides. The w3DNA web server, located at http://w3dna.rutgers.edu, is free and open to all users with no login requirement.

Modeling DNA deformations.

Recent developments have been made in modeling double-helical DNA at four levels of three-dimensional structure: the all-atom level, whereby an oligonucleotide duplex is surrounded by a shroud of solvent molecules; the base-pair level, with explicit backbone atoms; the mesoscopic level, that is, a few hundred base pairs, with the local duplex conformation described by knowledge-based harmonic energy functions; and the scale of several thousand nucleotides, with the duplex described as an ideal elastic rod. Predictions of the sequence-dependent bending and twisting of the double helix, as well as solvent- and force-induced B-->A and over-stretching conformational transitions, are compared with experimental data. These subtle conformational changes are critical to the functioning of the double helix, including its packaging in the close confines of the cell, the mutual fit of DNA and protein in nucleoprotein complexes, and the effective recognition of base pairs in recombination and transcription.

Supercoiled DNA energetics and dynamics by computer simulation

A new formulation is presented for investigating supercoiled DNA configurations by deterministic techniques. Thus far, the computational difficulties involved in applying deterministic methods to supercoiled DNA studies have generally limited computer simulations to stochastic approaches. While stochastic methods, such as simulated annealing and Metropolis-Monte Carlo sampling, are successful at generating a large number of configurations and estimating thermodynamic properties of topoisomer ensembles, deterministic methods offer an accurate characterization of the minima and a systematic following of their dynamics. To make this feasible, we model circular duplex DNA compactly by a B-spline ribbon-like model in terms of a small number of control vertices. We associate an elastic deformation energy composed of bending and twisting integrals and represent intrachain contact by a 6-12 Lennard Jones potential. The latter is parameterized to yield an energy minimum at the observed DNA-helix diameter inclusive of a hydration shell. A penalty term to ensure fixed contour length is also included. First and second partial derivatives of the energy function have been derived by using various mathematical simplifications. First derivatives are essential for Newton-type minimization as well as molecular dynamics, and partial second-derivative information can significantly accelerate minimization convergence through preconditioning. Here we apply a new large-scale truncated-Newton algorithm for minimization and a Langevin/implicit-Euler scheme for molecular dynamics. Our truncated-Newton method exploits the separability of potential energy functions into terms of differing complexity. It relies on a preconditioned conjugate gradient method that is efficient for large-scale problems to solve approximately for the search direction at every step. Our dynamics algorithm is numerically stable over large time steps. It also introduces a frequency-discriminating mechanism so that vibrational modes with frequencies greater than a chosen cutoff frequency are essentially frozen by the method. With these tools, we rapidly identify corresponding circular and interwound energy minima for small DNA rings for a series of imposed linking-number differences. These structures are consistent with available electron microscopy data. The energetic exchange of stability between the circle and the figure-8, in very good agreement with analytical results, is also detailed. Molecular dynamics trajectories at 100 femtosecond time steps then reveal the rapid folding of the unstable circular state into supercoiled forms. Significant bending and twisting motions of the interwound structures are also observed. Such information may be useful for understanding transition states along the folding pathway and the role of enzymes that regulate supercoiling.(ABSTRACT TRUNCATED AT 400 WORDS)

Simulating DNA at low resolution

The past year has witnessed the development of several new mathematical approaches to analyzing the structure of double-helical DNA and to incorporating the sequence-dependent features of the chain in computer simulations of long polymers. Of special interest in this respect are the local and global structural changes induced by the binding of various proteins to DNA, ranging from subtle bending, untwisting and sliding motions at the base-pair level to the apparent organization of supercoiled structure in chains that are thousands residues long. The computational effort has also included both new ways to incorporate the polyelectrolyte character of DNA and other environmental forces in simulations of long chains and new methods to keep track of the multitude of configurations so generated. The collective advances are pointing to ways that will soon connect the sequences of base pairs in large genomes to folded three-dimensional structures based on natural bending, twisting and translational tendencies and in response to deformations produced by the binding of different proteins.

Theory of sequence-dependent DNA elasticity

The elastic properties of a molecule of duplex DNA are strongly dependent on nucleotide sequence. In the theory developed here the contribution ψn of the nth base-pair step to the elastic energy is assumed to be given by a function ψn of six kinematical variables, called tilt, roll, twist, shift, slide, and rise, that describe the relative orientation and displacement of the nth and (n+1)th base pairs. The sequence dependence of elastic properties is determined when one specifies the way ψn depends on the nucleotides of the two base pairs of the nth step. Among the items discussed are the symmetry relations imposed on ψn by the complementarity of bases, i.e., of A to T and C to G, the antiparallel nature of the DNA sugar–phosphate chains, and the requirement that ψn be independent of the choice of the direction of increasing n. Variational equations of mechanical equilibrium are here derived without special assumptions about the form of the functions ψn, and numerical solutions of those equations are...

Trefoil Knotting Revealed by Molecular Dynamics Simulations of Supercoiled DNA

Computer simulations of the supercoiling of DNA, largely limited to stochastic search techniques, can offer important information to complement analytical models and experimental data. Through association of an energy function, minimum-energy supercoiled conformations,fluctuations about these states, and interconversions among forms may be sought. In theory, the observation of such large-scale conformational changes is possible, but modeling and numerical considerations limit the picture obtained in practice. A new computational approach is reported that combines an idealized elastic energy model, a compact B-spline representation of circular duplex DNA, and deterministic minimization and molecular dynamics algorithms. A trefoil knotting result, made possible by a large time-step dynamics scheme, is described. The simulated strand passage supports and details a supercoiled-directed knotting mechanism. This process may be associated with collective bending and twisting motions involved in supercoiling propagation and interwound branching. The results also demonstrate the potential effectiveness of the Langevin/ implicit-Euler dynamics scheme for studying biomolecular folding and reactions over biologically interesting time scales.

Finite element analysis of DNA supercoiling

A DNA polymer with hundreds or thousands of base pairs is modeled as a thin elastic rod. To find the equilibrium configurations and associated elastic energies as a function of linking number difference (ΔLk), a finite element scheme based on Kirchhoff’s rod theory is newly formulated so as to be able to treat self‐contact. The numerical results obtained here agree well with those already published, both analytical and numerical, but a much more detailed picture emerges of the several equilibrium states which can exist for a given ΔLk. Of particular interest is the discovery of interwound states having odd integral values of the writhing number and very small twist energy. The existence of a noncircular cross section, inhomogeneous elastic constants, intrinsic curvature, and sequence‐dependent bending and twisting can all be readily incorporated into the new formalism.

Base sequence effects in double helical DNA. I. Potential energy estimates of local base morphology.

A series of potential energy calculations have been carried out to estimate base sequence dependent structural differences in B-DNA. Attention has been focused on the simplest dimeric fragments that can be used to build long chains, computing the energy as a function of the orientation and displacement of the 16 possible base pair combinations within the double helix. Calculations have been performed, for simplicity, on free base pairs rather than complete nucleotide units. Conformational preferences and relative flexibilities are reported for various combinations of the roll, tilt, twist, lateral displacement, and propeller twist of individual residues. The predictions are compared with relevant experimental measures of conformation and flexibility, where available. The energy surfaces are found to fit into two distinct categories, some dimer duplexes preferring to bend in a symmetric fashion and others in a skewed manner. The effects of common chemical substitutions (uracil for thymine, 5-methyl cytosine for cytosine, and hypoxanthine for guanine) on the preferred arrangements of neighboring residues are also examined, and the interactions of the sugar-phosphate backbone are included in selected cases. As a first approximation, long range interactions between more distant neighbors, which may affect the local chain configuration, are ignored. A rotational isomeric state scheme is developed to describe the average configurations of individual dimers and is used to develop a static picture of overall double helical structure. The ability of the energetic scheme to account for documented examples of intrinsic B-DNA curvature is presented, and some new predictions of sequence directed chain bending are offered.

The dependence of DNA tertiary structure on end conditions: Theory and implications for topological transitions

Explicit expressions are derived for the equilibrium configurations of long segments of a DNA double helix subject to boundary conditions of the type imposed by DNA‐bending proteins at the ends of otherwise free segments. The expressions, which are exact within the framework of Kirchhoff’s theory of elastic rods, show that, in appropriate ranges of parameters, small changes in end conditions can result in large changes in tertiary structure. A discussion is given of the implications of this observation for understanding the action of bending proteins and of proteins that induce topological transitions that change the linking number of closed loops of DNA.