Computer simulation of DNA supercoiling

Topology, Geometry, and Mechanics of Strongly Stretched and Twisted Filaments: Solenoids, Plectonemes, and Artificial Muscle Fibers

Soft elastic filaments that can be stretched, bent, and twisted exhibit a range of topologically and geometrically complex morphologies. Recently, a number of experiments have shown how to use these building blocks to create filament-based artificial muscles that use the conversion of writhe to extension or contraction, exposing the connection between topology, geometry, and mechanics. Here, we combine numerical simulations of soft elastic filaments that account for geometric nonlinearities and self-contact to map out the basic structures underlying artificial muscle fibers in a phase diagram that is a function of the extension and twist density. We then use ideas from computational topology to track the interconversion of link, twist, and writhe in these geometrically complex physical structures to explain the physical principles underlying artificial muscle fibers and provide guidelines for their design.

Ring and zipper formation is the key to understanding the structural variety in all-beta proteins

A novel structural classification of beta proteins is presented from the viewpoint of the ring-shaped structure and the zipper-like contact pattern, based on the fact that 92% and 60% of beta proteins have the ring topology and the zippered contact pattern, respectively. We discuss the implication of the unexpectedly high preference for the ring and zippered structures in connection with the folding process of beta proteins.

Electrostatic-undulatory theory of plectonemically supercoiled DNA

We present an analytical calculation of the electrostatic interaction in a plectonemic supercoil within the Poisson-Boltzmann approximation. Undulations of the supercoil strands arising from thermal motion couple nonlinearly with the electrostatic interaction, giving rise to a strong enhancement of the bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution containing the bending and torsional energies and an electrostatic-undulatory free energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the usual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monovalent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In particular, we confirm the experimental observation that the writhe is a virtually constant fraction of the excess linking number over a wide range of superhelical densities. Another important prediction is the ionic strength dependence of the plectonemic parameters, which is in reasonable agreement with the results from computer simulations.

Modeling chain folding in protein-constrained circular DNA

An efficient method for sampling equilibrium configurations of DNA chains binding one or more DNA-bending proteins is presented. The technique is applied to obtain the tertiary structures of minimal bending energy for a selection of dinucleosomal minichromosomes that differ in degree of protein-DNA interaction, protein spacing along the DNA chain contour, and ring size. The protein-bound portions of the DNA chains are represented by tight, left-handed supercoils of fixed geometry. The protein-free regions are modeled individually as elastic rods. For each random spatial arrangement of the two nucleosomes assumed during a stochastic search for the global minimum, the paths of the flexible connecting DNA segments are determined through a numerical solution of the equations of equilibrium for torsionally relaxed elastic rods. The minimal energy forms reveal how protein binding and spacing and plasmid size differentially affect folding and offer new insights into experimental minichromosome systems.

Configurational transitions in Fourier series-represented DNA supercoils

A new Fourier series representation of supercoiled DNA is employed in Langevin dynamics simulations to study large-scale configurational motions of intermediate-length chains. The polymer is modeled as an ideal elastic rod subject to long-range van der Waals' interactions. The van der Waals' term prevents the self-contact of distant chain segments and also mimics attractive forces thought to stabilize the association of closely spaced charged rods. The finite Fourier series-derived polymer formulation is an alternative to the piecewise B-spline curves used in past work to describe the motion of smoothly deformed supercoiled DNA in terms of a limited number of independent variables. This study focuses on two large-scale configurational events: the interconversion between circular and figure-8 forms at a relatively low level of supercoiling, and the transformation between branched and interwound structures at a higher superhelical density.

Modeling protein-induced configurational changes in DNA minicircles

A method is offered for obtaining minimum energy configurations of DNA minicircles constrained by one or more DNA-binding proteins. The minicircles are modeled as elastic rods, while the presence of bound protein is implied by rigidly fixing portions of these chains. The configurations of the geometrically constrained circular rods are sampled stochastically and optimized according to a simple elastic energy model of nicked DNA. The shapes of the minimum energy structures identified after a simulated annealing process are analyzed in terms of relative protein orientation and writhing number. The procedure is applied to minicircles 500 base pairs in length, bound to two evenly spaced DNA-wrapping proteins. The presence of histone octamers is suggested by rigidly fixing the two protein-bound portions of each minicircle as small superhelices similar in dimension to nucleosomal DNA. The folded minimum energy forms of sample chains with different degrees of protein wrapping are noteworthy in themselves in that they offer a new resolution to the well-known minichromosome linking number paradox and point to future minicircle simulations of possible import.

Flexing and folding double helical DNA

DNA base sequence, once thought to be interesting only as a carrier of the genetic blueprint, is now recognized as playing a structural role in modulating the biological activity of genes. Primary sequences of nucleic acid bases describe real three-dimensional structures with properties reflecting those structures. Moreover, the structures are base sequence dependent with individual residues adopting characteristic spatial forms. As a consequence, the double helix can fold into tertiary arrangements, although the deformation is much more gradual and spread over a larger molecular scale than in proteins. As part of an effort to understand how local structural irregularities are translated at the macromolecular level in DNA and recognized by proteins, a series of calculations probing the structure and properties of the double helix have been performed. By combining several computational techniques, complementary information as well as a series of built-in checks and balances for assessing the significance of the findings are obtained. The known sequence dependent bending, twisting, and translation of simple dimeric fragments have been incorporated into computer models of long open DNAs of varying length and chemical composition as well as in closed double helical circles and loops. The extent to which the double helix can be forced to bend and twist is monitored with newly parameterized base sequence dependent elastic energy potentials based on the observed configurations of adjacent base pairs in the B-DNA crystallographic literature.

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.