Mechanical response of double-stranded DNA: Bend, twist, and overwind

We employed all-atom molecular dynamics simulations to explore the mechanical response of bending, twisting, and overwinding for double-stranded DNA (dsDNA). We analyzed the bending and twisting deformations, as well as their stiffnesses, using the tilt, roll, and twist modes under stretching force. Findings indicate that the roll and twist angles vary linearly with the stretching force but show opposite trends. The tilt, roll, and twist elastic moduli are considered constants, while the coupling between roll and twist modes slightly decreases under stretching force. The effect of the stretching force on the roll and twist modes, including both their deformations and elasticities, exhibits sequence-dependence, with symmetry around the base pair step. Furthermore, we examined the overwinding path and mechanism of dsDNA from the perspective of the stiffness matrix, based on the tilt, roll, and twist modes. The correlations among tilt, roll, and twist angles imply an alternative overwinding pathway via twist-roll coupling when dsDNA is stretched, wherein entropic contribution prevails.

Insights into elastic properties of coarse-grained DNA models: q-stiffness of cgDNA vs cgDNA

Coarse-grained models have emerged as valuable tools to simulate long DNA molecules while maintaining computational efficiency. These models aim at preserving interactions among coarse-grained variables in a manner that mirrors the underlying atomistic description. We explore here a method for testing coarse-grained vs all-atom models using stiffness matrices in Fourier space (q-stiffnesses), which are particularly suited to probe DNA elasticity at different length scales. We focus on a class of coarse-grained rigid base DNA models known as cgDNA and its most recent version, cgDNA+. Our analysis shows that while cgDNA+ closely follows the q-stiffnesses of the all-atom model, the original cgDNA shows some deviations for twist and bending variables, which are rather strong in the q → 0 (long length scale) limit. The consequence is that while both cgDNA and cgDNA+ give a suitable description of local elastic behavior, the former misses some effects that manifest themselves at longer length scales. In particular, cgDNA performs poorly on twist stiffness, with a value much lower than expected for long DNA molecules. Conversely, the all-atom and cgDNA+ twist are strongly length scale dependent: DNA is torsionally soft at a few base pair distances but becomes more rigid at distances of a few dozen base pairs. Our analysis shows that the bending persistence length in all-atom and cgDNA+ is somewhat overestimated.

Systematic Comparison of Atomistic Force Fields for the Mechanical Properties of Double-Stranded DNA

The response of double-stranded DNA to external mechanical stress plays a central role in its interactions with the protein machinery in the cell. Modern atomistic force fields have been shown to provide highly accurate predictions for the fine structural features of the duplex. In contrast, and despite their pivotal function, less attention has been devoted to the accuracy of the prediction of the elastic parameters. Several reports have addressed the flexibility of double-stranded DNA via all-atom molecular dynamics, yet the collected information is insufficient to have a clear understanding of the relative performance of the various force fields. In this work, we fill this gap by performing a systematic study in which several systems, characterized by different sequence contexts, are simulated with the most popular force fields within the AMBER family, bcs1 and OL15, as well as with CHARMM36. Analysis of our results, together with their comparison with previous work focused on bsc0, allows us to unveil the differences in the predicted rigidity between the newest force fields and suggests a roadmap to test their performance against experiments. In the case of the stretch modulus, we reconcile these differences, showing that a single mapping between sequence-dependent conformation and elasticity via the crookedness parameter captures simultaneously the results of all force fields, supporting the key role of crookedness in the mechanical response of double-stranded DNA.

Temperature-dependent elasticity of DNA, RNA, and hybrid double helices

Nucleic acid double helices in their DNA, RNA, and DNA-RNA hybrid form play a fundamental role in biology and are main building blocks of artificial nanostructures, but how their properties depend on temperature remains poorly understood. Here, we report thermal dependence of dynamic bending persistence length, twist rigidity, stretch modulus, and twist-stretch coupling for DNA, RNA, and hybrid duplexes between 7°C and 47°C. The results are based on all-atom molecular dynamics simulations using different force field parameterizations. We first demonstrate that unrestrained molecular dynamics can reproduce experimentally known mechanical properties of the duplexes at room temperature. Beyond experimentally known features, we also infer the twist rigidity and twist-stretch coupling of the hybrid duplex. As for the temperature dependence, we found that increasing temperature softens all the duplexes with respect to bending, twisting, and stretching. The relative decrease of the stretch moduli is 0.003-0.004/°C, similar for all the duplex variants despite their very different stretching stiffness, whereas RNA twist stiffness decreases by 0.003/°C, and smaller values are found for the other elastic moduli. The twist-stretch couplings are nearly unaffected by temperature. The stretching, bending, and twisting stiffness all include an important entropic component. Relation of our results to the two-state model of DNA flexibility is discussed. Our work provides temperature-dependent elasticity of nucleic acid duplexes at the microsecond scale relevant for initial stages of protein binding.

Temperature-Dependent Twist of Double-Stranded RNA Probed by Magnetic Tweezer Experiments and Molecular Dynamics Simulations

RNA plays critical roles in the transmission and regulation of genetic information and is increasingly used in biomedical and biotechnological applications. Functional RNAs contain extended double-stranded regions, and the structure of double-stranded RNA (dsRNA) has been revealed at high resolution. However, the dependence of the properties of the RNA double helix on environmental effects, notably temperature, is still poorly understood. Here, we use single-molecule magnetic tweezer measurements to determine the dependence of the dsRNA twist on temperature. We find that dsRNA unwinds with increasing temperature, even more than DNA, with ΔTwRNA = -14.4 ± 0.7°/(°C·kbp), compared to ΔTwDNA = -11.0 ± 1.2°/(°C·kbp). All-atom molecular dynamics (MD) simulations using a range of nucleic acid force fields, ion parameters, and water models correctly predict that dsRNA unwinds with rising temperature but significantly underestimate the magnitude of the effect. These MD data, together with additional MD simulations involving DNA and DNA-RNA hybrid duplexes, reveal a linear correlation between the twist temperature decrease and the helical rise, in line with DNA but at variance with RNA experimental data. We speculate that this discrepancy might be caused by some unknown bias in the RNA force fields tested or by as yet undiscovered transient alternative structures in the RNA duplex. Our results provide a baseline to model more complex RNA assemblies and to test and develop new parametrizations for RNA simulations. They may also inspire physical models of the temperature-dependent dsRNA structure.

Sequence-Dependent Properties of the RNA Duplex

Sequence-dependent properties of the DNA duplex have been accurately described using extensive molecular dynamics simulations. The RNA duplex meanwhile─which is typically represented as a sequence-averaged rigid rod─does not benefit from having equivalent molecular dynamics simulations. In this paper, we present a massive simulation effort using a set of ABC-optimized duplexes from which we derived tetramer-resolution properties of the RNA duplex and a simple mesoscopic model that can represent elastic properties of long RNA duplexes. Despite the extreme chemical similarity between DNA and RNA, the local and global elastic properties of the duplexes are very different. DNA duplexes show a complex and nonelastic pattern of flexibility, for instance, while RNA duplexes behave as an elastic system whose deformations can be represented by simple harmonic potentials. In RNA duplexes (RNA2), not only are intra- and interbase pair parameters (equilibrium and mechanical) different from those in the equivalent DNA duplex sequences (DNA2) but the correlations between movements also differ. Simple statements on the relative flexibility or stability of both polymers are meaningless and should be substituted by a more detailed description depending on the sequence and the type of deformation considered.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

Rigid Base Biasing in Molecular Dynamics Enables Enhanced Sampling of DNA Conformations

All-atom simulations have become increasingly popular to study conformational and dynamical properties of nucleic acids as they are accurate and provide high spatial and time resolutions. This high resolution, however, comes at a heavy computational cost, and, within the time scales of simulations, nucleic acids weakly fluctuate around their ideal structure exploring a limited set of conformations. We introduce the RBB-NA algorithm (available as a package in the Open Source Library PLUMED), which is capable of controlling rigid base parameters in all-atom simulations of nucleic acids. With suitable biasing potentials, this algorithm can "force" a DNA or RNA molecule to assume specific values of the six rotational (tilt, roll, twist, buckle, propeller, opening) and/or the six translational parameters (shift, slide, rise, shear, stretch, stagger). The algorithm enables the use of advanced sampling techniques to probe the structure and dynamics of locally strongly deformed nucleic acids. We illustrate its performance showing some examples in which DNA is strongly twisted, bent, or locally buckled. In these examples, RBB-NA reproduces well the unconstrained simulations data and other known features of DNA mechanics, but it also allows one to explore the anharmonic behavior characterizing the mechanics of nucleic acids in the high deformation regime.

Mechanical properties of nucleic acids and the non-local twistable wormlike chain model

Mechanical properties of nucleic acids play an important role in many biological processes that often involve physical deformations of these molecules. At sufficiently long length scales (say, above ∼20-30 base pairs), the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales, this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites get coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model that clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables that describe the twist and bending of the molecule. Different from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior that matches experimental data.

Nearest-Neighbor dsDNA Stability Analysis Using Alchemical Free-Energy Simulations

The thermodynamic stability of double-stranded (ds)DNA depends on its sequence. It is influenced by the base pairing and stacking with neighboring bases along DNA molecules. Semiempirical schemes are available that allow us to predict the thermodynamic stability of DNA sequences based on empirically derived nearest-neighbor contributions of base pairs formed in the context of all possible nearest-neighbor base pairs. Current molecular dynamics (MD) simulations allow one to simulate the dynamics of DNA molecules in good agreement with experimentally obtained structures and available data on conformational flexibility. However, the suitability of current force field methods to reproduce dsDNA stability and its sequence dependence has been much less well tested. We have employed alchemical free-energy simulations of whole base pair transversions in dsDNA and in unbound single-stranded partner molecules. Such transversions change the sequence context but not the nucleotide content or base pairing in dsDNA and allow a direct comparison with the empirical nearest-neighbor dsDNA stability model. For the alchemical free-energy changes in the unbound single-stranded (ss)DNA partner molecules, we tested different setups assuming either complete unstacking or unrestrained simulations with partial stacking in the unbound ssDNA. The free-energy simulations predicted nearest-neighbor effects of similar magnitude, as observed experimentally but showed overall limited correlation with experimental data. An inaccurate description of stacking interactions and other possible reasons such as the neglect of electronic polarization effects are discussed. The results indicate the need to improve the realistic description of stacking interactions in current molecular mechanic force fields.

Homologous basic helix–loop–helix transcription factors induce distinct deformations of torsionally-stressed DNA: a potential transcription regulation mechanism

Changing torsional restraints on DNA is essential for the regulation of transcription. Torsional stress, introduced by RNA polymerase, can propagate along chromatin facilitating topological transitions and modulating the specific binding of transcription factors (TFs) to DNA. Despite the importance, the mechanistic details on how torsional stress impacts the TFs-DNA complexation remain scarce. Herein, we address the impact of torsional stress on DNA complexation with homologous human basic helix–loop–helix (BHLH) hetero- and homodimers: MycMax, MadMax and MaxMax. The three TF dimers exhibit specificity towards the same DNA consensus sequence, the E-box response element, while regulating different transcriptional pathways. Using microseconds-long atomistic molecular dynamics simulations together with the torsional restraint that controls DNA total helical twist, we gradually over- and underwind naked and complexed DNA to a maximum of ± 5°/bp step. We observe that the binding of the BHLH dimers results in a similar increase in DNA torsional rigidity. However, under torsional stress the BHLH dimers induce distinct DNA deformations, characterised by changes in DNA grooves geometry and a significant asymmetric DNA bending. Supported by bioinformatics analyses, our data suggest that torsional stress may contribute to the execution of differential transcriptional programs of the homologous TFs by modulating their collaborative interactions.