A measure of bending in nucleic acids structures applied to A-tract DNA.

A method is proposed to measure global bending in DNA and RNA structures. It relies on a properly defined averaging of base-fixed coordinate frames, computes mean frames of suitably chosen groups of bases and uses these mean frames to evaluate bending. The method is applied to DNA A-tracts, known to induce considerable bend to the double helix. We performed atomistic molecular dynamics simulations of sequences containing the A(4)T(4) and T(4)A(4) tracts, in a single copy and in two copies phased with the helical repeat. Various temperature and salt conditions were investigated. Our simulations indicate bending by roughly 10 degrees per A(4)T(4) tract into the minor groove, and an essentially straight structure containing T(4)A(4), in agreement with electrophoretic mobility data. In contrast, we show that the published NMR structures of analogous sequences containing A(4)T(4) and T(4)A(4) tracts are significantly bent into the minor groove for both sequences, although bending is less pronounced for the T(4)A(4) containing sequence. The bending magnitudes obtained by frame averaging are confirmed by the analysis of superhelices composed of repeated tract monomers.

Conformational analysis of nucleic acids revisited: Curves+.

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algorithmically simpler and computationally much faster than the earlier Curves approach, although it still provides both helical and backbone parameters, including a curvilinear axis and parameters relating the position of the bases to this axis. It additionally provides a full analysis of groove widths and depths. Curves+ can also be used to analyse molecular dynamics trajectories. With the help of the accompanying program Canal, it is possible to produce a variety of graphical output including parameter variations along a given structure and time series or histograms of parameter variations during dynamics.

On the parameterization of rigid base and basepair models of DNA from molecular dynamics simulations.

A method is described to extract a complete set of sequence-dependent material parameters for rigid base and basepair models of DNA in solution from atomistic molecular dynamics simulations. The method is properly consistent with equilibrium statistical mechanics, leads to effective shape, stiffness and mass parameters, and employs special procedures for treating spontaneous torsion angle flips and H-bond breaks, both of which can have a significant effect on the results. The method is accompanied by various analytical consistency checks that can be used to assess the equilibration of statistical averages, and different modeling assumptions pertaining to the rigidity of the bases and basepairs and the locality of the quadratic internal energy. The practicability of the approach is verified by estimating complete parameter sets for the 16-basepair palindromic oligomer G(TA)(7)C simulated in explicit water and counterions. Our results indicate that the method is capable of resolving sequence-dependent variations in each of the material parameters. Moreover, they show that the assumptions of rigidity and locality hold rather well for the base model, but not for the basepair model. For the latter, it is shown that the non-local nature of the internal energy can be understood in terms of a certain compatibility relation involving Schur complements.

A rigorous framework for diffusion tensor calculus.

In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data.