Spectral analysis of DNA superhelical dynamics from molecular minicircle simulations.

Torsional and bending deformations of DNA molecules often occur in vivo and are important for biological functions. DNA "under stress" is a conformational state, which is by far the most frequent state during DNA-protein and gene regulation. In DNA minicircles of length <100 base pairs (bp), the combined effect of torsional and bending stresses can cause local unusual conformations, with certain base pair steps often absorbing most of the stress, leaving other steps close to their relaxed conformation. To better understand the superhelical dynamics of DNA under stress, molecular simulations of 94 bp minicircles with different torsional linking numbers were interpreted using Fourier analyses and principal component analyses. Sharp localized bends of nearly 90° in the helical axis were observed, which in turn decreased fluctuations of the rotational register and helped redistribute the torsional stress into writhe, i.e., superhelical turn up to 360°. In these kinked minicircles, only two-thirds of the DNA molecule bends and writhes and the remaining segment stays close to straight and preserves a conformational flexibility typical of canonical B-DNA (bending of 39° ± 17° distributed parsimoniously across 36 bp), which was confirmed and visualized by principal component analysis. These results confirm that stressed DNA molecules are highly heterogeneous along their sequence, with segments designed to locally store and release stress so that nearby segments can stay relaxed.

Graph-based sampling for approximating global helical topologies of RNA.

A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.

Adaptive conformational sampling based on replicas.

Computer simulations of biomolecules such as molecular dynamics simulations are limited by the time scale of conformational rearrangements. Several sampling techniques are available to search the multi-minima free energy landscape but most efficient, time-dependent methods do generally not produce a canonical ensemble. A sampling algorithm based on a self-regulating ladder of searching copies in the dihedral subspace is developped in this paper. The learning process using short- and long-term memory functions allows an efficient search in phase space while combining a deterministic dynamics and stochastic swaps with the searching copies conserves a canonical limit. The sampling efficiency and accuracy are indicated by comparing the ansatz with conventional molecular dynamics and replica exchange simulations.

Elbow flexibility of the kt38 RNA kink-turn motif investigated by free-energy molecular dynamics simulations.

Kink-turns (K-turns) are common structural motifs that can introduce sharp kinks into double-stranded RNA, and have been proposed to mediate large-scale motions in the ribosome. K-turns consist of a bulge loop region flanked by trans sugar-Hoogsteen G:A pairs, and the sharp kink conformation is stabilized by A-minor interactions (adenine contacting a G:C basepair in the minor groove). Umbrella-sampling molecular dynamics simulations were used to disrupt an A-minor interaction in the ribosomal kt38 turn and to calculate the associated free-energy change. Coupling of umbrella sampling with replica exchanges between neighboring umbrella-sampling intervals could further improve the convergence of the free-energy calculations. The simulations revealed a coupled A-minor disruption and global opening of the K-turn motif, and allowed us to characterize several intermediate A-minor conformations. The calculated free-energy profile indicated a meta-stable, semi-open structure of slightly higher free energy ( approximately 1 kcal mol(-1)), separated by a small free-energy barrier ( approximately 1.5 kcal mol(-1)) from the closed (highly kinked) form. Both K-turn states are stabilized by distinct variants of the A-minor interaction. Further opening of the K-turn structure required significantly larger free-energy changes. The semi-open form had a reduced kink angle compatible with experimental data on K-turn solution structures, and opening was coupled to a continuous global unwinding of the K-turn motif. The range of free-energy changes associated with kt38 opening and unwinding are compatible with the idea that K-turns may facilitate biologically relevant motions during large-scale ribosome dynamics.

Local and global effects of strong DNA bending induced during molecular dynamics simulations.

DNA bending plays an important role in many biological processes, but its molecular and energetic details as a function of base sequence remain to be fully understood. Using a recently developed restraint, we have studied the controlled bending of four different B-DNA oligomers using molecular dynamics simulations. Umbrella sampling with the AMBER program and the recent parmbsc0 force field yield free energy curves for bending. Bending 15-base pair oligomers by 90 degrees requires roughly 5 kcal mol(-1), while reaching 150 degrees requires of the order of 12 kcal mol(-1). Moderate bending occurs mainly through coupled base pair step rolls. Strong bending generally leads to local kinks. The kinks we observe all involve two consecutive base pair steps, with disruption of the central base pair (termed Type II kinks in earlier work). A detailed analysis of each oligomer shows that the free energy of bending only varies quadratically with the bending angle for moderate bending. Beyond this point, in agreement with recent experiments, the variation becomes linear. An harmonic analysis of each base step yields force constants that not only vary with sequence, but also with the degree of bending. Both these observations suggest that DNA is mechanically more complex than simple elastic rod models would imply.

Enhanced conformational sampling of nucleic acids by a new Hamiltonian replica exchange molecular dynamics approach.

Although molecular dynamics (MD) simulations have been applied frequently to study flexible molecules, the sampling of conformational states separated by barriers is limited due to currently possible simulation time scales. Replica-exchange (Rex)MD simulations that allow for exchanges between simulations performed at different temperatures (T-RexMD) can achieve improved conformational sampling. However, in the case of T-RexMD the computational demand grows rapidly with system size. A Hamiltonian RexMD method that specifically enhances coupled dihedral angle transitions has been developed. The method employs added biasing potentials as replica parameters that destabilize available dihedral substates and was applied to study coupled dihedral transitions in nucleic acid molecules. The biasing potentials can be either fixed at the beginning of the simulation or optimized during an equilibration phase. The method was extensively tested and compared to conventional MD simulations and T-RexMD simulations on an adenine dinucleotide system and on a DNA abasic site. The biasing potential RexMD method showed improved sampling of conformational substates compared to conventional MD simulations similar to T-RexMD simulations but at a fraction of the computational demand. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions including explicit solvent and ions and can be easily extended to other types of molecules.

Magnitude and direction of DNA bending induced by screw-axis orientation: influence of sequence, mismatches and abasic sites.

DNA-bending flexibility is central for its many biological functions. A new bending restraining method for use in molecular mechanics calculations and molecular dynamics simulations was developed. It is based on an average screw rotation axis definition for DNA segments and allows inducing continuous and smooth bending deformations of a DNA oligonucleotide. In addition to controlling the magnitude of induced bending it is also possible to control the bending direction so that the calculation of a complete (2-dimensional) directional DNA-bending map is now possible. The method was applied to several DNA oligonucleotides including A(adenine)-tract containing sequences known to form stable bent structures and to DNA containing mismatches or an abasic site. In case of G:A and C:C mismatches a greater variety of conformations bent in various directions compared to regular B-DNA was found. For comparison, a molecular dynamics implementation of the approach was also applied to calculate the free energy change associated with bending of A-tract containing DNA, including deformations significantly beyond the optimal curvature. Good agreement with available experimental data was obtained offering an atomic level explanation for stable bending of A-tract containing DNA molecules. The DNA-bending persistence length estimated from the explicit solvent simulations is also in good agreement with experiment whereas the adiabatic mapping calculations with a GB solvent model predict a bending rigidity roughly two times larger.