Base-pair Steps Research Articles

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.

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 94bp 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 36bp), 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.

The energy landscape for R-loop formation by the CRISPR-Cas Cascade complex.

Clustered regularly interspaced short palindromic repeats (CRISPR) sequences and CRISPR-associated (Cas) genes comprise CIRSPR-Cas effector complexes, which have revolutionized gene editing with their ability to target specific genomic loci using CRISPR RNA (crRNA) complementarity. Recognition of double-stranded DNA targets proceeds via DNA unwinding and base pairing between crRNA and the DNA target strand, forming an R-loop structure. Full R-loop extension is a prerequisite for subsequent DNA cleavage. However, the recognition of unintended sequences with multiple mismatches has limited therapeutic applications and is still poorly understood on a mechanistic level. Here we set up ultrafast DNA unwinding experiments on the basis of plasmonic DNA origami nanorotors to study R-loop formation by the Cascade effector complex in real time, close to base-pair resolution. We resolve a weak global downhill bias of the forming R-loop, followed by a steep uphill bias for the final base pairs. We also show that the energy landscape is modulated by base flips and mismatches. These findings suggest that Cascade-mediated R-loop formation occurs on short timescales in submillisecond single base-pair steps, but on longer timescales in six base-pair intermediate steps, in agreement with the structural periodicity of the crRNA-DNA hybrid.

Correlated motions in DNA: beyond base-pair step models of DNA flexibility.

Traditional mesoscopic models of DNA flexibility use a reductionist-local approach, which assumes that the flexibility of DNA can be expressed as local harmonic movements (at the base-pair step level) in the helical space, ignoring multimodality and correlations in DNA movements, which have in reality a large impact in modulating DNA movements. We present a new multimodal-harmonic correlated model, which takes both contributions into account, providing, with a small computational cost, results of an unprecedented local and global quality. The accuracy of this method and its computational efficiency make it an alternative to explore the dynamics of long segments of DNA, approaching the chromatin range.

A standard reference frame and geometry for nucleosomes.

The nucleosome is often described as a histone-DNA complex containing eight histones and 145-147 base pairs of DNA. The reality is more complex. Here we evaluate approximately 500 nucleosomes from the Research Collaboratory for Structural Biology with the goal of establishing a reference frame and standard geometry for describing the internal structure of mono-nucleosomes and the stacking of nucleosomes in arrays and clusters. Our reference frame places the center of mass of the nucleosome's octameric core at the origin. The positive x-axis aligns with the symmetry axis of the nucleosome and passes through the central base pair or base pair step associated with the octamer. The z-axis is defined by fitting a regular helix (constant pitch and radius) to the nucleosome. The positive direction is determined by the choice of reading strand. Two methods for defining this helix are explored. One fits a helix to the center line of the DNA, which is itself determined according to a standard reference geometry for DNA base pairs. The other fits a helix to the centers of mass obtained from the histones. The z-axes, so defined, are slightly askew. Over 100 nucleosomes are used to define a standard reference geometry for the histones and for super helices with 145, 146 and 147 base pairs. In all structures, the cumulative sum of Rise, Twist and arclength are linear functions of base pair index with R2 values in excess of 0.999. The standard geometry supports a rigorous definition of entry-exit angle and identification of structural anomalies. Select examples demonstrate how generalizations of the inter and intra base pair parameters can be utilized to analyze the internal structure of mono-nucleosomes, their stacking in arrays and clusters, and the ab initio assembly of atomic and coarse-grained structures.

Applications of machine-learned electron densities of nucleic acids.

The efficient prediction of large-scale electron densities of biological macromolecules and molecular arrays could lead to breakthroughs in quantum chemistry, structural biology, and molecular design. This work leverages a novel machine learning (ML) algorithm based on Euclidean neural networks to learn the electron densities of arbitrary sequences of DNA by performing many smaller ab initio calculations of the component base-pair steps of DNA. These electron density predictions are currently accurate to around 1% error for arbitrary sequences of DNA, and are easily size-extensible unlike traditional quantum calculations. Using this machine learning algorithm, electron density predictions of large-scale DNA structures consisting of tens-of-thousands to hundreds-of-thousands of electrons can be performed in minutes. Several applications of these large-scale machine-learned electron densities are of interest. We focus here on the accurate calculation of energies and forces from the machine-learned electron densities, allowing for dynamical propagation of the electronic system, termed ab initio molecular dynamics (AIMD). Calculation of accurate forces directly from the machine-learned electron densities is not a trivial step, as specialized basis set expansions are required to capture this information. These machine-learned electron densities would allow for AIMD simulations of systems that are much larger than can be propagated using traditional quantum calculations, leading to potential applications in biomolecular binding and structural prediction of macromolecules.

Predicting accurate ab initio DNA electron densities with equivariant neural networks

One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean neural network framework to obtain accurate ab initio electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA basepair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes reasonably to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. The model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is essentially linear. We also show that this machine learning electron density model can be used to calculate accurate electrostatic potentials for DNA. These electrostatic potentials produce more accurate results compared with classical force fields and do not show the usual deficiencies at short range.

Revisiting DNA Sequence-Dependent Deformability in High-Resolution Structures: Effects of Flanking Base Pairs on Dinucleotide Morphology and Global Chain Configuration.

DNA carries more than the list of biochemical ingredients that drive the basic functions of living systems. The sequence of base pairs includes a multitude of structural and energetic signals, which determine the degree to which the long, threadlike molecule moves and how it responds to proteins and other molecules that control its processing and govern its packaging. The chemical composition of base pairs directs the spatial disposition and fluctuations of successive residues. The observed arrangements of these moieties in high-resolution protein–DNA crystal structures provide one of the best available estimates of the natural, sequence-dependent structure and deformability of the double-helical molecule. Here, we update the set of knowledge-based elastic potentials designed to describe the observed equilibrium structures and configurational fluctuations of the ten unique base-pair steps. The large number of currently available structures makes it possible to characterize the configurational preferences of the DNA base-pair steps within the context of their immediate neighbors, i.e., tetrameric context. Use of these knowledge-based potentials shows promise in accounting for known effects of sequence in long chain molecules, e.g., the degree of curvature reported in classic gel mobility studies and the recently reported sequence-dependent responses of supercoiled minicircles to nuclease cleavage.

Computational Investigation of Bending Properties of RNA AUUCU, CCUG, CAG, and CUG Repeat Expansions Associated With Neuromuscular Disorders.

Expansions of RNA AUUCU, CCUG, CAG, and CUG repeats cause spinocerebellar ataxia type 10, myotonic dystrophy type 2, Huntington’s disease, and myotonic dystrophy type 1, respectively. By performing extensive molecular dynamic simulations, we investigated the bending propensities and conformational landscapes adopted by 3×3, 2×2, and 1×1 internal loops observed in RNA AUUCU, CCUG, CAG, and CUG repeat expansions using model systems having biologically relevant repeat sizes. We show that the conformational variability experienced by these loops is more complex than previous reports where a variety of unconventional hydrogen bonds are formed. At the global scale, strong bending propensity was observed in r(AUUCU)10, r(CCUG)15, r(CAG)20, and r(CUG)20, and, to a lesser extent, in r(AUUCU)4, r(CCUG)10, r(CAG)10, and r(CUG)10. Furthermore, RNA CAG repeats exhibit a tendency toward bent states with more than 50% of observed conformations having bending angles greater than 50°, while RNA CUG repeats display relatively linear-like conformations with extremely bent conformations accounting for less than 25% of the observed structures. Conformations experienced by RNA AUUCU repeats are a combination of strongly bent and kinked structures. The bent states in RNA CCUG repeats mostly fall into the moderately bent category with a marginal ensemble experiencing extreme bending. The general pattern observed in all the bent structures indicates the collapse of the major groove width as the mechanical trigger for bending, which is caused by alteration of base pair step parameters at multiple locations along the RNA due to local distortions at the loop sites. Overextension is also observed in all the RNA repeats that is attributed to widening of the major groove width as well as undertwisting phenomenon. This information and the rich structural repository could be applied for structure based small molecule design targeting disease-causing RNAs. The bending propensities of these constructs, at the global level, could also have implications on how expanded RNA repeats interact with proteins.

EmDNA – A Tool for Modeling Protein-decorated DNA Loops and Minicircles at the Base-pair Step Level

Computational modeling of nucleic acids plays an important role in molecular biology, enhancing our general understanding of the relationship between structure and function. Biophysical studies have provided a wealth of information on how double-helical DNA responds to proteins and other molecules in its local environment but far less understanding of the larger scale structural responses found in protein-decorated loops and minicircles. Current computational models of DNA range from detailed all-atom molecular dynamics studies, which produce rich time and spatially dependent depictions of small DNA fragments, to coarse-grained simulations, which sacrifice detailed physical and chemical information to treat larger-scale systems. The treatment of DNA used here, at the base-pair step level with rigid-body parameters, allows one to develop models hundreds of base pairs long from local, sequence-specific features found from experiment. The emDNA software takes advantage of this framework, producing optimized structures of DNA at thermal equilibrium with built-in or user-generated elastic models. The program, in combination with the case studies included in this article, allows users of any skill level to develop and investigate mesoscale models of their own design. The functionality of emDNA includes a tool to incorporate experiment-specific configurations, e.g., protein-bound and/or melted DNA from known high-resolution structures, within higher-order 3D models by fixing the orientation and position of user-specified base pairs. The software provides a new avenue into multiscale genetic modeling, giving a wide range of users a deeper understanding of DNA mesoscale organization and the opportunity to pose new questions in genetic research. The publicly available emDNA software, including build instructions and usage information, is available on GitHub (https://nicocvn.github.io/emDNA/).

Modelling DNA-strand displacement reactions from single base-pair steps to reaction networks

DNA strand displacement reactions are the most abundantly used method to achieve dynamic switching in DNA-based nanotechnology. A single-stranded ‘invader' strand binds to the ‘toehold' overhang of a target strand and replaces a target-bound 'incumbent' strand. Hereby, complementarity of the invader to the single-stranded toehold provides the energetic bias of the reaction. Precise knowledge and easy tunability of the kinetics of the strand displacement process is highly important when establishing dynamic devices and complex chemical reaction networks.

A framework for mutational signature analysis based on DNA shape parameters.

The mutation risk of a DNA locus depends on its oligonucleotide context. In turn, mutability of oligonucleotides varies across individuals, due to exposure to mutagenic agents or due to variable efficiency and/or accuracy of DNA repair. Such variability is captured by mutational signatures, a mathematical construct obtained by a deconvolution of mutation frequency spectra across individuals. There is a need to enhance methods for inferring mutational signatures to make better use of sparse mutation data (e.g., resulting from exome sequencing of cancers), to facilitate insight into underlying biological mechanisms, and to provide more accurate mutation rate baselines for inferring positive and negative selection. We propose a conceptualization of mutational signatures that represents oligonucleotides via descriptors of DNA conformation: base pair, base pair step, and minor groove width parameters. We demonstrate how such DNA structural parameters can accurately predict mutation occurrence due to DNA repair failures or due to exposure to diverse mutagens such as radiation, chemical exposure, and the APOBEC cytosine deaminase enzymes. Furthermore, the mutation frequency of DNA oligomers classed by structural features can accurately capture systematic variability in mutagenesis of >1,000 tumors originating from diverse human tissues. A nonnegative matrix factorization was applied to mutation spectra stratified by DNA structural features, thereby extracting novel mutational signatures. Moreover, many of the known trinucleotide signatures were associated with an additional spectrum in the DNA structural descriptor space, which may aid interpretation and provide mechanistic insight. Overall, we suggest that the power of DNA sequence motif-based mutational signature analysis can be enhanced by drawing on DNA shape features.

Ethidium bromide interactions with DNA: an exploration of a classic DNA-ligand complex with unbiased molecular dynamics simulations.

Visualization of double stranded DNA in gels with the binding of the fluorescent dye ethidium bromide has been a basic experimental technique in any molecular biology laboratory for >40 years. The interaction between ethidium and double stranded DNA has been observed to be an intercalation between base pairs with strong experimental evidence. This presents a unique opportunity for computational chemistry and biomolecular simulation techniques to benchmark and assess their models in order to see if the theory can reproduce experiments and ultimately provide new insights. We present molecular dynamics simulations of the interaction of ethidium with two different double stranded DNA models. The first model system is the classic sequence d(CGCGAATTCGCG)2 also known as the Drew–Dickerson dodecamer. We found that the ethidium ligand binds mainly stacked on, or intercalated between, the terminal base pairs of the DNA with little to no interaction with the inner base pairs. As the intercalation at the terminal CpG steps is relatively rapid, the resultant DNA unwinding, rigidification, and increased stability of the internal base pair steps inhibits further intercalation. In order to reduce these interactions and to provide a larger groove space, a second 18-mer DNA duplex system with the sequence d(GCATGAACGAACGAACGC) was tested. We computed molecular dynamics simulations for 20 independent replicas with this sequence, each with ∼27 μs of sampling time. Results show several spontaneous intercalation and base-pair eversion events that are consistent with experimental observations. The present work suggests that extended MD simulations with modern DNA force fields and optimized simulation codes are allowing the ability to reproduce unbiased intercalation events that we were not able to previously reach due to limits in computing power and the lack of extensively tested force fields and analysis tools.

Rotation Tracking Using DNA Origami Rotors Reveals Single Base Pair Steps During Transcription by RNA Polymerase

Protein-DNA reactions such as transcription, editing and repair consist of a series of mechanical movements, yet the vast majority of these minute movements have remained challenging or impossible to measure. We have developed a method to track DNA rotation, origami-rotor-based imaging and tracking (ORBIT), that uses fluorescently labeled nano-rotors to amplify and track the movements of single DNA molecules. We used ORBIT to study transcription and discovered that RNA polymerase (RNAP) rotates DNA in single base pair steps during transcription elongation, revealing a close coupling between the enzyme and the helical structure of the DNA template. Intriguingly, these single base pair rotational steps did not appear identical in magnitude. Rather, they ranged from 25° to 40°, suggesting a heterogeneity of movement that we speculate is caused by the sequence-dependent local geometry of DNA. Consistent with this interpretation, twist angles between subsequent base pairs in B-DNA have been reported to range from 27° to 40° in a sequence-dependent manner. Due to its simplicity and generalizability, we anticipate that ORBIT will have broad applications in illuminating the rotational movements of a wide variety of protein-DNA reactions.

Base-Pairing and Base-Stacking Contributions to Double-Stranded DNA Formation.

Double-stranded (ds)DNA formation and dissociation are of fundamental biological importance. The negative DNA charge influences the dsDNA stability. However, the base pairing and the stacking between neighboring bases are responsible for the sequence-dependent stability of dsDNA. The stability of a dsDNA molecule can be estimated from empirical nearest-neighbor models based on contributions assigned to base-pair steps along the DNA and additional parameters because of DNA termini. In efforts to separate contributions, it has been concluded that base stacking dominates dsDNA stability, whereas base pairing contributes negligibly. Using a different model for dsDNA formation, we reanalyze dsDNA stability contributions and conclude that base stacking contributes already at the level of separate ssDNAs but that pairing contributions drive the dsDNA formation. The theoretical model also predicts that stability contributions of base-pair steps that contain only guanine/cytosine, mixed steps, and steps with only adenine/thymine follow the order 6:5:4, respectively, as expected based on the formed hydrogen bonds. The model is fully consistent with the available stacking data and the nearest-neighbor dsDNA parameters. It allows assigning a narrowly distributed value for the effective free energy contribution per formed hydrogen bond during dsDNA formation of -0.72 kcal·mol-1 based entirely on the experimental data.

Duplex formation in a G-quadruplex bulge.

Beyond the consensus definition of G-quadruplex-forming motifs with tracts of continuous guanines, G-quadruplexes harboring bulges in the G-tetrad core are prevalent in the human genome. Here, we study the incorporation of a duplex hairpin within a bulge of a G-quadruplex. The NMR solution structure of a G-quadruplex containing a duplex bulge was resolved, revealing the structural details of the junction between the duplex bulge and the G-quadruplex. Unexpectedly, instead of an orthogonal connection the duplex stem was observed to stack below the G-quadruplex forming a unique quadruplex–duplex junction. Breaking up of the immediate base pair step at the junction, coupled with a narrowing of the duplex groove within the context of the bulge, led to a progressive transition between the quadruplex and duplex segments. This study revealed that a duplex bulge can be formed at various positions of a G-quadruplex scaffold. In contrast to a non-structured bulge, the stability of a G-quadruplex slightly increases with an increase in the duplex bulge size. A G-quadruplex structure containing a duplex bulge of up to 33 nt in size was shown to form, which was much larger than the previously reported 7-nt bulge. With G-quadruplexes containing duplex bulges representing new structural motifs with potential biological significance, our findings would broaden the definition of potential G-quadruplex-forming sequences.

Microscopic insight to specificity of metal ion cofactor in DNA cleavage by restriction endonuclease EcoRV.

Restriction endonucleases protect bacterial cells against bacteriophage infection by cleaving the incoming foreign DNA into fragments. In presence of Mg2+ ions, EcoRV is able to cleave the DNA but not in presence of Ca2+ , although the protein binds to DNA in presence of both metal ions. We make an attempt to understand this difference using conformational thermodynamics. We calculate the changes in conformational free energy and entropy of conformational degrees of freedom, like DNA base pair steps and dihedral angles of protein residues in Mg2+ (A)-EcoRV-DNA complex compared to Ca2+ (S)-EcoRV-DNA complex using all-atom molecular dynamics (MD) trajectories of the complexes. We find that despite conformational stability and order in both complexes, the individual degrees of freedom behave differently in the presence of two different metal ions. The base pairs in cleavage region are highly disordered in Ca2+ (S)-EcoRV-DNA compared to Mg2+ (A)-EcoRV-DNA. One of the acidic residues ASP90, coordinating to the metal ion in the vicinity of the cleavage site, is conformationally destabilized and disordered, while basic residue LYS92 gets conformational stability and order in Ca2+ (S) bound complex than in Mg2+ (A) bound complex. The enhanced fluctuations hinder placement of the metal ion in the vicinity of the scissile phosphate of DNA. Similar loss of conformational stability and order in the cleavage region is observed by the replacement of the metal ion. Considering the placement of the metal ion near scissile phosphate as requirement for cleavage action, our results suggest that the changes in conformational stability and order of the base pair steps and the protein residues lead to cofactor sensitivity of the enzyme. Our method based on fluctuations of microscopic conformational variables can be applied to understand enzyme activities in other protein-DNA systems.

CHD4 slides nucleosomes by decoupling entry- and exit-side DNA translocation

Chromatin remodellers hydrolyse ATP to move nucleosomal DNA against histone octamers. The mechanism, however, is only partially resolved, and it is unclear if it is conserved among the four remodeller families. Here we use single-molecule assays to examine the mechanism of action of CHD4, which is part of the least well understood family. We demonstrate that the binding energy for CHD4-nucleosome complex formation—even in the absence of nucleotide—triggers significant conformational changes in DNA at the entry side, effectively priming the system for remodelling. During remodelling, flanking DNA enters the nucleosome in a continuous, gradual manner but exits in concerted 4–6 base-pair steps. This decoupling of entry- and exit-side translocation suggests that ATP-driven movement of entry-side DNA builds up strain inside the nucleosome that is subsequently released at the exit side by DNA expulsion. Based on our work and previous studies, we propose a mechanism for nucleosome sliding.

Compensatory Mechanisms in Temperature Dependence of DNA Double Helical Structure: Bending and Elongation.

Changes in the structure of double-stranded (ds) DNA with temperature affect processes in thermophilic organisms and are important for nanotechnological applications. Here we investigate temperature-dependent conformational changes of dsDNA at the scale of several helical turns and at the base pair step level, inferred from extensive all-atom molecular dynamics simulations of DNA at temperatures from 7 to 47 °C. Our results suggest that, contrary to twist, the overall bending of dsDNA without A-tracts depends only very weakly on temperature, due to the mutual compensation of directional local bends. Investigating DNA length as a function of temperature, we find that the sum of distances between base pair centers (the wire length) exhibits a large expansion coefficient of ∼2 × 10-4 °C-1, similar to values reported for thermoplastic materials. However, the wire length increase with temperature is absorbed by expanding helix radius, so the length measured along the helical axis (the spring length) seems to suggest a very small negative thermal expansion coefficient. These compensatory mechanisms contribute to thermal stability of DNA structure on the biologically relevant scale of tens of base pairs and longer.

Genome Dashboards: Framework and Examples

Genomics is a sequence-based informatics science and a three-dimensional-structure-based material science. However, in practice, most genomics researchers utilize sequence-based informatics approaches or three-dimensional-structure-based material science techniques, not both. This division is, at least in part, the result of historical developments rather than a fundamental necessity. The underlying computational tools, experimental techniques, and theoretical models were developed independently. The primary result presented here is a framework for the unification of informatics- and physics-based data associated with DNA, nucleosomes, and chromatin. The framework is based on the mathematical representation of geometrically exact rods and the generalization of DNA basepair step parameters. Data unification enables researchers to integrate computational, experimental, and theoretical approaches for the study of chromatin biology. The framework can be implemented using model-view-controller design principles, existing genome browsers, and existing molecular visualization tools. We developed a minimal, web-based genome dashboard, G-Dash-min, and applied it to two simple examples to demonstrate the usefulness of data unification and proof of concept. Genome dashboards developed using the framework and design principles presented here are extensible and customizable and are therefore more broadly applicable than the examples presented. We expect a number of purpose-specific genome dashboards to emerge as a novel means of investigating structure-function relationships for genomes that range from basepairs to entire chromosomes and for generating, validating, and testing mechanistic hypotheses.