Analyzing DNA curvature and its impact on the ionic environment: application to molecular dynamics simulations of minicircles

Structure and dynamics of double-stranded DNA rotaxanes

A DNA rotaxane, with its unique mechanically interlocked architecture consisting of a circular DNA molecule threaded onto a linear DNA axle, holds promise as a fundamental component for nanoscale functional devices. Nevertheless, its structural and dynamic behaviors, essential for advancing molecular machinery, remain largely unexplored. Using extensive all-atom molecular dynamics simulations, we investigated the behaviors of double-stranded DNA (dsDNA) rotaxanes, concentrating on the effects of shape distortion induced by torsional stress in small circular dsDNA containing 70-90 base pairs. We analyzed structural characteristics, including shape, intermolecular distances, and tilt angles, while also exploring dynamic properties such as translational diffusion and toroidal rotation. Our results indicate that shape distortion brings the circular and linear dsDNA components into closer proximity and causes a slight increase in translational diffusion yet a minor decrease in toroidal rotation. Nevertheless, there is no apparent evidence of coupling between translation and rotation. Overall, the insights from this study indicate that such shape distortion does not significantly alter their structure and dynamics. This finding provides flexibility for the design of DNA rotaxanes in nanoscale applications.

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.

Sequence-dependent twist-bend coupling in DNA minicircles

Looping of double-stranded DNA molecules with 100-200 base pairs into minicircles, catenanes, and rotaxanes has been suggested as a potential tool for DNA nanotechnologies. However, sharp DNA bending into a minicircle with a diameter of several to ten nanometers occurs with alterations in the DNA helical structure and may lead to defective kink formation that hampers the use of DNA minicircles, catenanes, and rotaxanes in nanoscale DNA applications. Here, we investigated local variations of a helical twist in sharply bent DNA using microsecond-long all-atom molecular dynamics simulations of six different DNA minicircles, focusing on the sequence dependence of the coupling between DNA bending and its helical twist. Twist angles between consecutive base pairs were analyzed at different locations relative to the direction of DNA bending and, among 10 unique dinucleotide steps, we identified four dinucleotide steps with strong twist-bend coupling, the pyrimidine-purine dinucleotide steps of TA/TA, CG/CG, and CA/TG and the purine-purine dinucleotide step of GA/TC. This work suggests the sequence-dependent structural responses of DNA to strong mechanical deformation, providing new molecular-level insights into the structure and stability of sharply bent DNA minicircles for nanoscale applications.

Length-scale-dependent elasticity in DNA from coarse-grained and all-atom models

We investigate the influence of nonlocal couplings on the torsional and bending elasticities of DNA. Such couplings have been observed in the past by several simulation studies. Here, we use a description of DNA conformations based on the variables tilt, roll, and twist. Our analysis of both coarse-grained (oxDNA) and all-atom models indicates that these share strikingly similar features: there are strong off-site couplings for tilt-tilt and twist-twist, while they are much weaker in the roll-roll case. By developing an analytical framework to estimate bending and torsional persistence lengths in nonlocal DNA models, we show how off-site interactions generate a length-scale-dependent elasticity. Based on the simulation-generated elasticity data, the theory predicts a significant length-scale-dependent effect on torsional fluctuations but only a modest effect on bending fluctuations. These results are in agreement with experiments probing DNA mechanics from single base pair to kilobase pair scales.

A perspective on the molecular simulation of DNA from structural and functional aspects

As genetic material, DNA not only carries genetic information by sequence, but also affects biological functions ranging from base modification to replication, transcription and gene regulation through its structural and dynamic properties and variations. The motion and structural properties of DNA involved in related biological processes are also multi-scale, ranging from single base flipping to local DNA deformation, TF binding, G-quadruplex and i-motif formation, TAD establishment, compartmentalization and even chromosome territory formation, just to name a few. The sequence-dependent physical properties of DNA play vital role in all these events, and thus it is interesting to examine how simple sequence information affects DNA and the formation of the chromatin structure in these different hierarchical orders. Accordingly, molecular simulations can provide atomistic details of interactions and conformational dynamics involved in different biological processes of DNA, including those inaccessible by current experimental methods. In this perspective, which is mainly based on our recent studies, we provide a brief overview of the atomistic simulations on how the hierarchical structure and dynamics of DNA can be influenced by its sequences, base modifications, environmental factors and protein binding in the context of the protein-DNA interactions, gene regulation and structural organization of chromatin. We try to connect the DNA sequence, the hierarchical structures of DNA and gene regulation.

Sequence-Dependent Kink Formation in Short DNA Loops: Theory and Molecular Dynamics Simulations

Kink formation is essential in highly bent DNA complexed with gene regulatory proteins such as histones to release the bending stress stored within the DNA duplex. Local opening of the double-stranded DNA creates a sharp turn along the specific sequence, which leads to the global bending of the DNA strand. Despite the critical role of kink formation, it is still challenging to predict the position of kink formation for a given DNA sequence. In this study, we propose a theoretical model and perform molecular dynamics simulations to quantify the sequence-dependent kink probability of a strongly bent DNA. By incorporating the elastic bending energy and the sequence-specific thermodynamic parameters, we investigate the importance of the DNA sequence on kink formation. We find that the sequence with TA dinucleotide repeats flanked by GC steps increases the kink propensity by more than an order of magnitude under the same bending stress. The number of base pairs involved in the local opening is found to be coupled with the sequence-specific bubble formation free energy. Our study elucidates the molecular origin of the sequence heterogeneity on kink formation, which is fundamental to understanding protein-DNA recognition.

Elasticity of connected semiflexible quadrilaterals

Using the positional-orientational propagator of a semiflexible filament in the weakly bending regime, we analytically calculate the probability densities associated with the fluctuating tip and the corners of a grafted system of connected quadrilaterals. We calculate closed analytic expressions for the probability densities within the framework of the worm-like chain model, which are valid in the weakly bending regime. The probability densities give the physical quantities related to the elasticity of the system such as the force-extension relation in the fixed extension ensemble, the Poisson's ratio and the average of the force exerted to a confining stiff planar wall by the fluctuating tip of the system. Our analysis reveals that the force-extension relations depend on the contour length of the system (material content), the bending stiffness (chemical nature), the geometrical angle and the number of the quadrilaterals, while the Poisson's ratio depends only on the geometrical angle and the number of the quadrilaterals, and is thus a purely geometric property of the system.

Chromatin Compaction Multiscale Modeling: A Complex Synergy Between Theory, Simulation, and Experiment

Understanding the mechanisms that trigger chromatin compaction, its patterns, and the factors they depend on, is a fundamental and still open question in Biology. Chromatin compacts and reinforces DNA and is a stable but dynamic structure, to make DNA accessible to proteins. In recent years, computational advances have provided larger amounts of data and have made large-scale simulations more viable. Experimental techniques for the extraction and reconstitution of chromatin fibers have improved, reinvigorating theoretical and experimental interest in the topic and stimulating debate on points previously considered as certainties regarding chromatin. A great assortment of approaches has emerged, from all-atom single-nucleosome or oligonucleosome simulations to various degrees of coarse graining, to polymer models, to fractal-like structures and purely topological models. Different fiber-start patterns have been studied in theory and experiment, as well as different linker DNA lengths. DNA is a highly charged macromolecule, making ionic and electrostatic interactions extremely important for chromatin topology and dynamics. Indeed, the repercussions of varying ionic concentration have been extensively examined at the computational level, using all-atom, coarse-grained, and continuum techniques. The presence of high-curvature AT-rich segments in DNA can cause conformational variations, attesting to the fact that the role of DNA is both structural and electrostatic. There have been some tentative attempts to describe the force fields governing chromatin conformational changes and the energy landscapes of these transitions, but the intricacy of the system has hampered reaching a consensus. The study of chromatin conformations is an intrinsically multiscale topic, influenced by a wide range of biological and physical interactions, spanning from the atomic to the chromosome level. Therefore, powerful modeling techniques and carefully planned experiments are required for an overview of the most relevant phenomena and interactions. The topic provides fertile ground for interdisciplinary studies featuring a synergy between theoretical and experimental scientists from different fields and the cross-validation of respective results, with a multi-scale perspective. Here, we summarize some of the most representative approaches, and focus on the importance of electrostatics and solvation, often overlooked aspects of chromatin modeling.

Atomistic insight into sequence-directed DNA bending and minicircle formation propensity in the absence and presence of phased A-tracts

Bending of double-stranded (ds) DNA plays a crucial role in many important biological processes and is relevant for nanotechnological applications. Among all the elements that have been studied in relation to dsDNA bending, A-tracts stand out as one of the most controversial. The "ApA wedge" theory was disproved when a series of linear polynucleotides containing phased 5'-A₄T₄-3' or 5'-T₄A₄-3' runs were shown to be bent or straight, respectively, and crystallographic evidence revealed that A-tracts are unbent. Furthermore, some of the smallest dsDNA minicircles described to date (~ 100 bp in size) lack A-tracts and are subjected to varying levels of torsional stress. Representative DNA sequences from this experimental background were modeled in atomic detail and their dynamic behavior was simulated over hundreds of nanoseconds using the AMBER force field ParmBSC1. Subsequent analysis of the resulting trajectories allowed us to (i) unambiguously establish the location of the bends in all cases; (ii) identify the structural elements that are directly responsible for the macroscopically detected curvature; and (iii) reveal the importance not only of coherently summing the effects of the bending elements when they are in synchrony with the natural repeat of the helix (i.e. separated by an integral number of helical turns) but also when alternated with a half-integral separation of opposite effects. We conclude that the major determinant of the macroscopically observed bending is the proper grouping and phasing of the positive roll imposed by pyrimidine-purine (YR) steps and the negative or null roll characteristic of RY steps and A-tracts, respectively. This conclusion is in very good agreement with the structural parameters experimentally derived for much smaller DNA molecules either alone or as found in DNA-protein complexes. We expect that this work will pave the way for future studies on drug-induced DNA bending, DNA shape readout by transcription factors, structure of circular extrachromosomal DNA, and custom design of curved DNA origami scaffolds.

SerraNA: a program to determine nucleic acids elasticity from simulation data

AT-rich motifs can generate extreme mechanical properties, which are critical for creating strong global bends when phased properly.

Overtwisting induces polygonal shapes in bent DNA

By combining analytical results and simulations of various coarse-grained models, we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternation of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, rather than the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants.

Modeling and Simulation of Oligonucleotide Hybrids: Outlining a Strategy

Molecular dynamics simulations with a state-of-the-art force field provide an atomistic detailed description of the structural and thermodynamic features of biomolecules. Effects of chemical modifications and of the environment such as sequence, solvent, and ionic strength can explicitly be taken into account. Molecular simulation techniques can also provide insight in change in binding affinity, in protonation (pK_a shift) and tautomeric propensity due to changes in the environment or in the molecular system. The quality and reliability of a simulation depend on the quality of the force field and on the reproducibility of the data, and validation depends on the availability of suitable experimental data. Here, we describe the workflow to investigate oligonucleotide hybrids using molecular simulation including hardware and software information.

Representation of DNA environment: Spiral staircase distribution function

In the present study, we investigated the local structure of DNA and its environment using a new visualization technique. The spiral staircase distribution function (SSDF) is determined as two-dimensional density distribution of atoms of water and ligands in local reference frames linked with each base pair of poly-DNA molecule, either GC or AT. This property of SSDF provides opportunity to study sequence-specific binding of ions, peptides, and other agents derived from a molecular dynamics computer simulation. The spatial structure of double-stranded DNA environment in water solution containing either Mg²⁺ or Na⁺ ions was investigated using of SSDF. The distributions of ions around GC and AT base pairs are shown separately. It is observed that Mg²⁺ ions interact with DNA atoms by means of the layer of water molecules and penetrate into the major groove only. Na⁺ ions have a direct contact with DNA atoms and penetrate both into the major and minor grooves of DNA. © 2018 Wiley Periodicals, Inc.

Sequence-dependent response of DNA to torsional stress: a potential biological regulation mechanism

Torsional restraints on DNA change in time and space during the life of the cell and are an integral part of processes such as gene expression, DNA repair and packaging. The mechanical behavior of DNA under torsional stress has been studied on a mesoscopic scale, but little is known concerning its response at the level of individual base pairs and the effects of base pair composition. To answer this question, we have developed a geometrical restraint that can accurately control the total twist of a DNA segment during all-atom molecular dynamics simulations. By applying this restraint to four different DNA oligomers, we are able to show that DNA responds to both under- and overtwisting in a very heterogeneous manner. Certain base pair steps, in specific sequence environments, are able to absorb most of the torsional stress, leaving other steps close to their relaxed conformation. This heterogeneity also affects the local torsional modulus of DNA. These findings suggest that modifying torsional stress on DNA could act as a modulator for protein binding via the heterogeneous changes in local DNA structure.