We present the results of microsecond molecular dynamics simulations carried out by the ABC group of laboratories on a set of B-DNA oligomers containing the 136 distinct tetranucleotide base sequences. We demonstrate that the resulting trajectories have extensively sampled the conformational space accessible to B-DNA at room temperature. We confirm that base sequence effects depend strongly not only on the specific base pair step, but also on the specific base pairs that flank each step. Beyond sequence effects on average helical parameters and conformational fluctuations, we also identify tetranucleotide sequences that oscillate between several distinct conformational substates. By analyzing the conformation of the phosphodiester backbones, it is possible to understand for which sequences these substates will arise, and what impact they will have on specific helical parameters.

Helices are among the simplest shapes that are observed in the filamentary and molecular structures of nature. The local mechanical properties of such structures are often modeled by a uniform elastic potential energy dependent on bending and twist, which is what we term a rod model. Our first result is to complete the semi-inverse classification, initiated by Kirchhoff, of all infinite, helical equilibria of inextensible, unshearable uniform rods with elastic energies that are a general quadratic function of the flexures and twist. Specifically, we demonstrate that all uniform helical equilibria can be found by means of an explicit planar construction in terms of the intersections of certain circles and hyperbolas. Second, we demonstrate that the same helical centerlines persist as equilibria in the presence of realistic distributed forces modeling nonlocal interactions as those that arise, for example, for charged linear molecules and for filaments of finite thickness exhibiting self-contact. Third, in the absence of any external loading, we demonstrate how to construct explicitly two helical equilibria, precisely one of each handedness, that are the only local energy minimizers subject to a nonconvex constraint of self-avoidance.

A Monte Carlo code applied to the cgDNA coarse-grain rigid-base model of B-form double-stranded DNA is used to predict a sequence-averaged persistence length of l_F = 53.5 nm in the sense of Flory, and of l_p = 160 bp or 53.5 nm in the sense of apparent tangent–tangent correlation decay. These estimates are slightly higher than the consensus experimental values of 150 bp or 50 nm, but we believe the agreement to be good given that the cgDNA model is itself parametrized from molecular dynamics simulations of short fragments of length 10–20 bp, with no explicit fit to persistence length. Our Monte Carlo simulations further predict that there can be substantial dependence of persistence lengths on the specific sequence of a fragment. We propose, and confirm the numerical accuracy of, a simple factorization that separates the part of the apparent tangent–tangent correlation decay attributable to intrinsic shape, from a part attributable purely to stiffness, i.e., a sequence-dependent version of what has been called sequence-averaged dynamic persistence length l̅_d (=58.8 nm within the cgDNA model). For ensembles of both random and λ-phage fragments, the apparent persistence length has a standard deviation of 4 nm over sequence, whereas our dynamic persistence length has a standard deviation of only 1 nm. However, there are notable dynamic persistence length outliers, including poly(A) (exceptionally straight and stiff), poly(TA) (tightly coiled and exceptionally soft), and phased A-tract sequence motifs (exceptionally bent and stiff). The results of our numerical simulations agree reasonably well with both molecular dynamics simulation and diverse experimental data including minicircle cyclization rates and stereo cryo-electron microscopy images.

cgDNA is a package for the prediction of sequence-dependent configuration-space free energies for B-form DNA at the coarse-grain level of rigid bases. For a fragment of any given length and sequence, cgDNA calculates the configuration of the associated free energy minimizer, i.e. the relative positions and orientations of each base, along with a stiffness matrix, which together govern differences in free energies. The model predicts non-local (i.e. beyond base-pair step) sequence dependence of the free energy minimizer. Configurations can be input or output in either the Curves+ definition of the usual helical DNA structural variables, or as a PDB file of coordinates of base atoms. We illustrate the cgDNA package by comparing predictions of free energy minimizers from (a) the cgDNA model, (b) time-averaged atomistic molecular dynamics (or MD) simulations, and (c) NMR or X-ray experimental observation, for (i) the Dickerson–Drew dodecamer and (ii) three oligomers containing A-tracts. The cgDNA predictions are rather close to those of the MD simulations, but many orders of magnitude faster to compute. Both the cgDNA and MD predictions are in reasonable agreement with the available experimental data. Our conclusion is that cgDNA can serve as a highly efficient tool for studying structural variations in B-form DNA over a wide range of sequences.

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that correlates the reconstructed shapes and groups them into distinct categories. We conclude that the presence of the TATA box sequence, which is believed to be easily bent, does not significantly affect the observed shapes.