Spontaneous sharp bending of double-stranded DNA

Reversible strain-promoted DNA polymerization

Molecular strain can be introduced to influence the outcome of chemical reactions. Once a thermodynamic product is formed, however, reversing the course of a strain-promoted reaction is challenging. Here, a reversible, strain-promoted polymerization in cyclic DNA is reported. The use of nonhybridizing, single-stranded spacers as short as a single nucleotide in length can promote DNA cyclization. Molecular strain is generated by duplexing the spacers, leading to ring opening and subsequent polymerization. Then, removal of the strain-generating duplexers triggers depolymerization and cyclic dimer recovery via enthalpy-driven cyclization and entropy-mediated ring contraction. This reversibility is retained even when a protein is conjugated to the DNA strands, and the architecture of the protein assemblies can be modulated between bivalent and polyvalent states. This work underscores the utility of using DNA not only as a programmable ligand for assembly but also as a route to access restorable bonds, thus providing a molecular basis for DNA-based materials with shape-memory, self-healing, and stimuli-responsive properties.

Bending Unwinds DNA

In biology, DNA is often tightly bent to small radii. Solely based on the groove asymmetry, a 30-year-old theoretical paper predicted that such bending should unwind DNA, but this effect has not been directly experimentally quantified so far. We developed a ligation-based assay with nicked DNA circles of variable length, thereby decoupling the twist-dependent ligation efficiency from the large bending strain which dominates conventional circularization assays. We demonstrate that tightly bent DNA indeed unwinds to over 11 base pairs/turn, exactly as predicted. Our discovery requires reassessing the molecular mechanisms and energetics of all processes where DNA is tightly bent or relaxed again, including DNA packaging, gene regulation and expression.

Predictions of DNA mechanical properties at a genomic scale reveal potentially new functional roles of DNA flexibility

Mechanical properties of DNA have been implied to influence many of its biological functions. Recently, a new high-throughput method, called loop-seq, which allows measuring the intrinsic bendability of DNA fragments, has been developed. Using loop-seq data, we created a deep learning model to explore the biological significance of local DNA flexibility in a range of different species from different kingdoms. Consistently, we observed a characteristic and largely dinucleotide-composition-driven change of local flexibility near transcription start sites. In the presence of a TATA-box, a pronounced peak of high flexibility can be observed. Furthermore, depending on the transcription factor investigated, flanking-sequence-dependent DNA flexibility was identified as a potential factor influencing DNA binding. Compared to randomized genomic sequences, depending on species and taxa, actual genomic sequences were observed both with increased and lowered flexibility. Furthermore, in Arabidopsis thaliana, mutation rates, both de novo and fixed, were found to be associated with relatively rigid sequence regions. Our study presents a range of significant correlations between characteristic DNA mechanical properties and genomic features, the significance of which with regard to detailed molecular relevance awaits further theoretical and experimental exploration.

Temperature-induced DNA density transition in phage λ capsid revealed with contrast-matching SANS

Structural details of a genome packaged in a viral capsid are essential for understanding how the structural arrangement of a viral genome in a capsid controls its release dynamics during infection, which critically affects viral replication. We previously found a temperature-induced, solid-like to fluid-like mechanical transition of packaged λ-genome that leads to rapid DNA ejection. However, an understanding of the structural origin of this transition was lacking. Here, we use small-angle neutron scattering (SANS) to reveal the scattering form factor of dsDNA packaged in phage λ capsid by contrast matching the scattering signal from the viral capsid with deuterated buffer. We used small-angle X-ray scattering and cryoelectron microscopy reconstructions to determine the initial structural input parameters for intracapsid DNA, which allows accurate modeling of our SANS data. As result, we show a temperature-dependent density transition of intracapsid DNA occurring between two coexisting phases-a hexagonally ordered high-density DNA phase in the capsid periphery and a low-density, less-ordered DNA phase in the core. As the temperature is increased from 20 °C to 40 °C, we found that the core-DNA phase undergoes a density and volume transition close to the physiological temperature of infection (~37 °C). The transition yields a lower energy state of DNA in the capsid core due to lower density and reduced packing defects. This increases DNA mobility, which is required to initiate rapid genome ejection from the virus capsid into a host cell, causing infection. These data reconcile our earlier findings of mechanical DNA transition in phage.

Twist-stretch relations in nucleic acids

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

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.

Cross-platform comparisons for targeted bisulfite sequencing of MGISEQ-2000 and NovaSeq6000

BACKGROUND

An accurate and reproducible next-generation sequencing platform is essential to identify malignancy-related abnormal DNA methylation changes and translate them into clinical applications including cancer detection, prognosis, and surveillance. However, high-quality DNA methylation sequencing has been challenging because poor sequence diversity of the bisulfite-converted libraries severely impairs sequencing quality and yield. In this study, we tested MGISEQ-2000 Sequencer's capability of DNA methylation sequencing with a published non-invasive pancreatic cancer detection assay, using NovaSeq6000 as the benchmark.

RESULTS

We sequenced a series of synthetic cell-free DNA (cfDNA) samples with different tumor fractions and found MGISEQ-2000 yielded data with similar quality as NovaSeq6000. The methylation levels measured by MGISEQ-2000 demonstrated high consistency with NovaSeq6000. Moreover, MGISEQ-2000 showed a comparable analytic sensitivity with NovaSeq6000, suggesting its potential for clinical detection. As to evaluate the clinical performance of MGISEQ-2000, we sequenced 24 clinical samples and predicted the pathology of the samples with a clinical diagnosis model, PDACatch classifier. The clinical model performance of MGISEQ-2000's data was highly consistent with that of NovaSeq6000's data, with the area under the curve of 1. We also tested the model's robustness with MGISEQ-2000's data when reducing the sequencing depth. The results showed that MGISEQ-2000's data showed matching robustness of the PDACatch classifier with NovaSeq6000's data.

CONCLUSIONS

Taken together, MGISEQ-2000 demonstrated similar data quality, consistency of the methylation levels, comparable analytic sensitivity, and matching clinical performance, supporting its application in future non-invasive early cancer detection investigations by detecting distinct methylation patterns of cfDNAs.

Deciphering the mechanical code of the genome and epigenome

Diverse DNA-deforming processes are impacted by the local mechanical and structural properties of DNA, which in turn depend on local sequence and epigenetic modifications. Deciphering this mechanical code (that is, this dependence) has been challenging due to the lack of high-throughput experimental methods. Here we present a comprehensive characterization of the mechanical code. Utilizing high-throughput measurements of DNA bendability via loop-seq, we quantitatively established how the occurrence and spatial distribution of dinucleotides, tetranucleotides and methylated CpG impact DNA bendability. We used our measurements to develop a physical model for the sequence and methylation dependence of DNA bendability. We validated the model by performing loop-seq on mouse genomic sequences around transcription start sites and CTCF-binding sites. We applied our model to test the predictions of all-atom molecular dynamics simulations and to demonstrate that sequence and epigenetic modifications can mechanically encode regulatory information in diverse contexts.

Phase transition of DNA knotting in spherical space

Knots have been discovered in various biological systems, such as DNA. The knotting probability of DNA in free space depends non-monotonically on its bending rigidity and has a prominent peak. The current work aims to understand the underlying mechanism of the non-monotonic dependence of DNA knotting probability on bending rigidity. Monte Carlo simulations are performed on a closed DNA molecule confined in spherical space described by a worm-like chain model and a flexible kink model, respectively. The closed DNA's contour length and the spherical space radius both increase knotting probability, but also alter the unimodal dependence of knotting probability on bending rigidity. This is generalized using universal phase diagrams based on the two models. Under the flexible kink model, the total knotting probability of closed DNA is obviously increased at a relatively high excited energy. This supports the expectation that the entropy effect of knot size favours knot formation at a relatively low bending rigidity. In a given spherical space, the increasing contour length of closed DNA described by the worm-like chain model results in a visible shift in the knotting probability distribution. At the same time, the gyration radius of non-trivial closed DNA becomes comparable to that of trivial closed DNA, so that their ratio is not anti-correlated with average knot length. For closed DNA of various contour lengths, the relationship between average knot length and bending rigidity has a universal behaviour: the average knot length decreases to a local minimum at a bending rigidity of ∼5 and then gradually increases to a constant value. The existence of the local minimum is determined by the cut-off distance in repulsive Lennard-Jones potential. The bending rigidity corresponding to the beginning of the constant average knot length is consistent with that at the peak in the knotting distribution. At this point, the knot-size effect balances with the fragment free-energy effect and, at an even greater bending rigidity, knot length breathes around the average knot length value.

Kineto-Mechanistic Investigation of Effect of Macromolecular Crowding on the Breathing of DNA Bubble

Macromolecular crowding along with hydrogen bonding or stacking interactions and hydration reportedly has enormous repercussions on elementary biochemical processes, such as the folding of proteins or nucleic acids involving the stability of DNA base pairing. By using the mismatch-induced DNA bubble as a mesoscopic model, the complex interplay of macromolecular crowding on the dynamical fluctuations at the bubble region within the thermodynamic limit has been monitored using single-molecule fluorescence resonance energy transfer (sm-FRET). These single-molecule experimental results have been further corroborated using physical models such as "scaled particle theory" (SPT) and "Gaussian cloud model" (GCM), to predict the biological activity of DNA. The two-state fluctuation of the DNA bubble has been visualized as a function of the nature, size, and concentration of the crowder. The influence of crowders on the DNA conformation has been investigated with the help of the m-factor, the eccentricity, and the kinetic and thermodynamic parameters without any prior assumption. The clear effect of crowding on the dynamics of such a simple biomolecular system emphasizes the power of single-molecule methods and the dependency of the radius of gyration of the co-solute as well as the preferential interaction with the crowder on the distinct conformational states adopted by the bubble. This study provides an idea and hypothesizes the preferential propensity of the DNA bubble to adopt a conformation with the single-stranded domains being far apart, independent of the crowder size, that may be beneficial for efficient recognition by proteins for an uninterrupted procession of the biological process of the central dogma.

Single-Molecule Methods for Investigating the Double-Stranded DNA Bendability

The various DNA-protein interactions associated with the expression of genetic information involve double-stranded DNA (dsDNA) bending. Due to the importance of the formation of the dsDNA bending structure, dsDNA bending properties have long been investigated in the biophysics field. Conventionally, DNA bendability is characterized by innate averaging data from bulk experiments. The advent of single-molecule methods, such as atomic force microscopy, optical and magnetic tweezers, tethered particle motion, and single-molecule fluorescence resonance energy transfer measurement, has provided valuable tools to investigate not only the static structures but also the dynamic properties of bent dsDNA. Here, we reviewed the single-molecule methods that have been used for investigating dsDNA bendability and new findings related to dsDNA bending. Single-molecule approaches are promising tools for revealing the unknown properties of dsDNA related to its bending, particularly in cells.

OUP accepted manuscript

DNA mechanical properties play a critical role in every aspect of DNA-dependent biological processes. Recently a high throughput assay named loop-seq has been developed to quantify the intrinsic bendability of a massive number of DNA fragments simultaneously. Using the loop-seq data, we develop a software tool, DNAcycP, based on a deep-learning approach for intrinsic DNA cyclizability prediction. We demonstrate DNAcycP predicts intrinsic DNA cyclizability with high fidelity compared to the experimental data. Using an independent dataset from in vitro selection for enrichment of loopable sequences, we further verified the predicted cyclizability score, termed C-score, can well distinguish DNA fragments with different loopability. We applied DNAcycP to multiple species and compared the C-scores with available high-resolution chemical nucleosome maps. Our analyses showed that both yeast and mouse genomes share a conserved feature of high DNA bendability spanning nucleosome dyads. Additionally, we extended our analysis to transcription factor binding sites and surprisingly found that the cyclizability is substantially elevated at CTCF binding sites in the mouse genome. We further demonstrate this distinct mechanical property is conserved across mammalian species and is inherent to CTCF binding DNA motif.

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.

DNA sequence and methylation prescribe the inside-out conformational dynamics and bending energetics of DNA minicircles

Eukaryotic genome and methylome encode DNA fragments' propensity to form nucleosome particles. Although the mechanical properties of DNA possibly orchestrate such encoding, the definite link between 'omics' and DNA energetics has remained elusive. Here, we bridge the divide by examining the sequence-dependent energetics of highly bent DNA. Molecular dynamics simulations of 42 intact DNA minicircles reveal that each DNA minicircle undergoes inside-out conformational transitions with the most likely configuration uniquely prescribed by the nucleotide sequence and methylation of DNA. The minicircles' local geometry consists of straight segments connected by sharp bends compressing the DNA's inward-facing major groove. Such an uneven distribution of the bending stress favors minimum free energy configurations that avoid stiff base pair sequences at inward-facing major grooves. Analysis of the minicircles' inside-out free energy landscapes yields a discrete worm-like chain model of bent DNA energetics that accurately account for its nucleotide sequence and methylation. Experimentally measuring the dependence of the DNA looping time on the DNA sequence validates the model. When applied to a nucleosome-like DNA configuration, the model quantitatively reproduces yeast and human genomes' nucleosome occupancy. Further analyses of the genome-wide chromatin structure data suggest that DNA bending energetics is a fundamental determinant of genome architecture.

Supercoiling and looping promote DNA base accessibility and coordination among distant sites

DNA in cells is supercoiled and constrained into loops and this supercoiling and looping influence every aspect of DNA activity. We show here that negative supercoiling transmits mechanical stress along the DNA backbone to disrupt base pairing at specific distant sites. Cooperativity among distant sites localizes certain sequences to superhelical apices. Base pair disruption allows sharp bending at superhelical apices, which facilitates DNA writhing to relieve torsional strain. The coupling of these processes may help prevent extensive denaturation associated with genomic instability. Our results provide a model for how DNA can form short loops, which are required for many essential processes, and how cells may use DNA loops to position nicks to facilitate repair. Furthermore, our results reveal a complex interplay between site-specific disruptions to base pairing and the 3-D conformation of DNA, which influences how genomes are stored, replicated, transcribed, repaired, and many other aspects of DNA activity.

Base pair fluctuations in helical models for nucleic acids

A statistical method is developed to estimate the maximum amplitude of the base pair fluctuations in a three dimensional mesoscopic model for nucleic acids. The base pair thermal vibrations around the helix diameter are viewed as a Brownian motion for a particle embedded in a stable helical structure. The probability to return to the initial position is computed, as a function of time, by integrating over the particle paths consistent with the physical properties of the model potential. The zero time condition for the first-passage probability defines the constraint to select the integral cutoff for various macroscopic helical conformations, obtained by tuning the twist, bending, and slide motion between adjacent base pairs along the molecule stack. Applying the method to a short homogeneous chain at room temperature, we obtain meaningful estimates for the maximum fluctuations in the twist conformation with ∼10.5 base pairs per helix turn, typical of double stranded DNA helices. Untwisting the double helix, the base pair fluctuations broaden and the integral cutoff increases. The cutoff is found to increase also in the presence of a sliding motion, which shortens the helix contour length, a situation peculiar of dsRNA molecules.

DNA mechanics and its biological impact

Almost all nucleoprotein interactions and DNA manipulation events involve mechanical deformations of DNA. Extraordinary progresses in single-molecule, structural, and computational methods have characterized the average mechanical properties of DNA, such as bendability and torsional rigidity, in high resolution. Further, the advent of sequencing technology has permitted measuring, in high-throughput, how such mechanical properties vary with sequence and epigenetic modifications along genomes. We review these recent technological advancements, and discuss how they have contributed to the emerging idea that variations in the mechanical properties of DNA play a fundamental role in regulating, genome-wide, diverse processes involved in chromatin organization.

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.

Measuring DNA mechanics on the genome scale

Mechanical deformations of DNA such as bending are ubiquitous and implicated in diverse cellular functions¹. However, the lack of high-throughput tools to directly measure the mechanical properties of DNA limits our understanding of whether and how DNA sequences modulate DNA mechanics and associated chromatin transactions genome-wide. We developed an assay called loop-seq to measure the intrinsic cyclizability of DNA – a proxy for DNA bendability – in high throughput. We measured the intrinsic cyclizabilities of 270,806 50 bp DNA fragments that span the entire length of S. cerevisiae chromosome V and other genomic regions, and also include random sequences. We discovered sequence-encoded regions of unusually low bendability upstream of Transcription Start Sites (TSSs). These regions disfavor the sharp DNA bending required for nucleosome formation and are co-centric with known Nucleosome Depleted Regions (NDRs). We show biochemically that low bendability of linker DNA located about 40 bp away from a nucleosome edge inhibits nucleosome sliding into the linker by the chromatin remodeler INO80. The observation explains how INO80 can create promoter-proximal nucleosomal arrays in the absence of any other factors² by reading the DNA mechanical landscape. We show that chromosome wide, nucleosomes are characterized by high DNA bendability near dyads and low bendability near the linkers. This contrast increases for nucleosomes deeper into gene bodies, suggesting that DNA mechanics plays a previously unappreciated role in organizing nucleosomes far from the TSS, where nucleosome remodelers predominate. Importantly, random substitution of synonymous codons does not preserve this contrast, suggesting that the evolution of codon choice has been impacted by selective pressure to preserve sequence-encoded mechanical modulations along genes. We also provide evidence that transcription through the TSS-proximal nucleosomes is impacted by local DNA mechanics. Overall, this first genome-scale map of DNA mechanics hints at a ‘mechanical code’ with broad functional implications.

Mechanical Flexibility of DNA: A Quintessential Tool for DNA Nanotechnology

The mechanical properties of DNA have enabled it to be a structural and sensory element in many nanotechnology applications. While specific base-pairing interactions and secondary structure formation have been the most widely utilized mechanism in designing DNA nanodevices and biosensors, the intrinsic mechanical rigidity and flexibility are often overlooked. In this article, we will discuss the biochemical and biophysical origin of double-stranded DNA rigidity and how environmental and intrinsic factors such as salt, temperature, sequence, and small molecules influence it. We will then take a critical look at three areas of applications of DNA bending rigidity. First, we will discuss how DNA's bending rigidity has been utilized to create molecular springs that regulate the activities of biomolecules and cellular processes. Second, we will discuss how the nanomechanical response induced by DNA rigidity has been used to create conformational changes as sensors for molecular force, pH, metal ions, small molecules, and protein interactions. Lastly, we will discuss how DNA's rigidity enabled its application in creating DNA-based nanostructures from DNA origami to nanomachines.

Improving therapeutic potential of non-viral minimized DNA vectors

The tragic deaths of three patients in a recent AAV-based X-linked myotubular myopathy clinical trial highlight once again the pressing need for safe and reliable gene delivery vectors. Non-viral minimized DNA vectors offer one possible way to meet this need. Recent pre-clinical results with minimized DNA vectors have yielded promising outcomes in cancer therapy, stem cell therapy, stem cell reprograming, and other uses. Broad clinical use of these vectors, however, remains to be realized. Further advances in vector design and production are ongoing. An intriguing and promising potential development results from manipulation of the specific shape of non-viral minimized DNA vectors. By improving cellular uptake and biodistribution specificity, this approach could impact gene therapy, DNA nanotechnology, and personalized medicine.

Determinants of cyclization-decyclization kinetics of short DNA with sticky ends

Cyclization of DNA with sticky ends is commonly used to measure DNA bendability as a function of length and sequence, but how its kinetics depend on the rotational positioning of the sticky ends around the helical axis is less clear. Here, we measured cyclization (looping) and decyclization (unlooping) rates (k_loop and k_unloop) of DNA with sticky ends over three helical periods (100-130 bp) using single-molecule fluorescence resonance energy transfer (FRET). k_loop showed a nontrivial undulation as a function of DNA length whereas k_unloop showed a clear oscillation with a period close to the helical turn of DNA (∼10.5 bp). The oscillation of k_unloop was almost completely suppressed in the presence of gaps around the sticky ends. We explain these findings by modeling double-helical DNA as a twisted wormlike chain with a finite width, intrinsic curvature, and stacking interaction between the end base pairs. We also discuss technical issues for converting the FRET-based cyclization/decyclization rates to an equilibrium quantity known as the J factor that is widely used to characterize DNA bending mechanics.

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.

DNA Nunchucks: Nanoinstrumentation for Single-Molecule Measurement of Stiffness and Bending

Bending of double-stranded DNA (dsDNA) has important applications in biology and engineering, but measurement of DNA bend angles is notoriously difficult and rarely dynamic. Here we introduce a nanoscale instrument that makes dynamic measurement of the bend in short dsDNAs easy enough to be routine. The instrument works by embedding the ends of a dsDNA in stiff, fluorescently labeled DNA nanotubes, thereby mechanically magnifying their orientations. The DNA nanotubes are readily confined to a plane and imaged while freely diffusing. Single-molecule bend angles are rapidly and reliably extracted from the images by a neural network. We find that angular variance across a population increases with dsDNA length, as predicted by the worm-like chain model, although individual distributions can differ significantly from one another. For dsDNAs with phased A₆-tracts, we measure an intrinsic bend of 17 ± 1° per A₆-tract, consistent with other methods, and a length-dependent angular variance that indicates A₆-tracts are (80 ± 30)% stiffer than generic dsDNA.

Dynamical control of denaturation bubble nucleation in supercoiled DNA minicircles

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending- or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

Strongly Bent Double-Stranded DNA: Reconciling Theory and Experiment

The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hull of the deformation energy function. For double-stranded DNA, the effective bending deformation energy becomes non-convex for bends greater than ~ 2° per base-pair, equivalent to the curvature of a closed circular loop of ~ 160 base pairs. A simple equation is derived for the polymer loop energy that covers both the weak and strong bending regimes. The theory shows quantitative agreement with recent DNA cyclization experiments on short DNA fragments, while maintaining the expected agreement with experiment in the weak bending regime. Counter-intuitively, cyclization probability (j-factor) of very short DNA loops is predicted to increase with decreasing loop length; the j-factor reaches its minimum for loops of ≃ 45 base pairs. Atomistic simulations reveal that the attractive component of the short-range Lennard-Jones interaction between the backbone atoms can explain the underlying non-convexity of the DNA effective bending energy, leading to the linear bending regime. Applicability of the theory to protein-DNA complexes, including the nucleosome, is discussed.

The Contribution of Backbone Electrostatic Repulsion to DNA Mechanical Properties is Length-Scale-Dependent

The mechanics of DNA bending is crucially related to many vital biological processes. Recent experiments reported anomalous flexibility for DNA on short length scales, calling into doubt the validity of the harmonic worm-like chain (WLC) model in this region. In the present work, we systematically probed the bending dynamics of DNA at different length scales. In contrast to the remarkable deviation from the WLC description for DNA duplexes of less than three helical turns, our atomistic studies indicate that the neutral "null isomer" behaves in accord with the ideal elastic WLC and exhibits a uniform decay for the directional correlation of local bending. The backbone neutralization weakens the anisotropy in the effective bending preference and the helical periodicity of bend correlation that have previously been observed for normal DNA. The contribution of electrostatic repulsion to stretching cooperativity and the mechanical properties of DNA strands is length-scale-dependent: the phosphate neutralization increases the stiffness of DNA below two helical turns, but it is decreased for longer strands. We find that DNA rigidity is largely determined by base pair stacking, with electrostatic interactions contributing only around 10% of the total persistence length.

Orientationally ordered states of a wormlike chain in spherical confinement

One of the basic characteristics of a linear dsDNA molecule is its persistence length, typically of order 50 nm. The DNA chain inflicts a large energy penalty if it is bent sharply at that length scale. Viruses of bacteria, known as bacteriophages, typically have a dimension of a few tens of nanometers. Yet, it is known that a bacteriophage actively packages viral DNA inside the capsid and ejects it afterwards. Here, adopting a commonly used polymer model known as the wormlike chain, we answer an idealized question: Placing a linear DNA molecule inside a spherical cavity, what ordered states can we derive from known tools in statistical physics? Solving the model in a rigorous field-theory framework, we report a universal phase diagram for four orientationally ordered and disordered states, in terms of two relevant physical parameters.

Identifying Physical Causes of Apparent Enhanced Cyclization of Short DNA Molecules with a Coarse-Grained Model

DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart—with the deviation larger for shorter molecules—because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.

Rolling circle amplification shows a sinusoidal template length-dependent amplification bias

Biophysical properties of DNA such as its longitudinal and torsional persistence length govern many processes and phenomena in biology, DNA nanotechnology and biotechnology. It has, for example, long been known that the circularization efficiency of short DNA fragments shows a periodic pattern where fragments with integer helical turns circularize much more efficiently than those with odd helical half turns due to stronger stacking of duplex ends. Small DNA circles can serve as templates for rolling circle amplification (RCA), which is a common and extremely robust amplification mechanism for nucleic acids. We discovered a strong template length-dependent amplification efficiency bias of RCA with the same periodicity as B-DNA. However, stacking cannot explain the mechanism behind this bias as the presence of the polymerase in the bifurcation fork inhibits base stacking of ends. Instead, coarse-grained molecular dynamics simulations imply that different amplification efficiencies come from a varying fraying probability of the last two downstream base pairs. We conclude that an increased strain-promoted fraying probability can increase the polymerization rate compared to a relaxed template.

Submicrometer elasticity of double-stranded DNA revealed by precision force-extension measurements with magnetic tweezers

Submicrometer elasticity of double-stranded DNA (dsDNA) governs nanoscale bending of DNA segments and their interactions with proteins. Single-molecule force spectroscopy, including magnetic tweezers (MTs), is an important tool for studying DNA mechanics. However, its application to short DNAs under 1 μm is limited. We developed an MT-based method for precise force-extension measurements in the 100-nm regime that enables in situ correction of the error in DNA extension measurement, and normalizes the force variability across beads by exploiting DNA hairpins. The method reduces the lower limit of tractable dsDNA length down to 198 base pairs (bp) (67 nm), an order-of-magnitude improvement compared to conventional tweezing experiments. Applying this method and the finite worm-like chain model we observed an essentially constant persistence length across the chain lengths studied (198 bp to 10 kbp), which steeply depended on GC content and methylation. This finding suggests a potential sequence-dependent mechanism for short-DNA elasticity.

Programming Protein Polymerization with DNA

A strategy that utilizes DNA for controlling the association pathway of proteins is described. This strategy uses sequence-specific DNA interactions to program energy barriers for polymerization, allowing for either step-growth or chain-growth pathways to be accessed. Two sets of mutant green fluorescent protein (mGFP)-DNA monomers with single DNA modifications have been synthesized and characterized. Depending on the deliberately controlled sequence and conformation of the appended DNA, these monomers can be polymerized through either a step-growth or chain-growth pathway. Cryo-electron microscopy with Volta phase plate technology enables the visualization of the distribution of the oligomer and polymer products, and even the small mGFP-DNA monomers. Whereas cyclic and linear polymer distributions were observed for the step-growth DNA design, in the case of the chain-growth system linear chains exclusively were observed, and a dependence of the chain length on the concentration of the initiator strand was noted. Importantly, the chain-growth system possesses a living character whereby chains can be extended with the addition of fresh monomer. This work represents an important and early example of mechanistic control over protein assembly, thereby establishing a robust methodology for synthesizing oligomeric and polymeric protein-based materials with exceptional control over architecture.

Strong deformations of DNA: Effect on the persistence length

Extreme deformations of the DNA double helix attracted a lot of attention during the past decades. Particularly, the determination of the persistence length of DNA with extreme local disruptions, or kinks, has become a crucial problem in the studies of many important biological processes. In this paper we review an approach to calculate the persistence length of the double helix by taking into account the formation of kinks of arbitrary configuration. The reviewed approach improves the Kratky-Porod model to determine the type and nature of kinks that occur in the double helix, by measuring a reduction of the persistence length of the kinkable DNA.

Ionic liquids make DNA rigid

Persistence length of double-stranded DNA (dsDNA) is known to decrease with an increase in ionic concentration of the solution. In contrast to this, here we show that the persistence length of dsDNA increases dramatically as a function of ionic liquid (IL) concentration. Using all atom explicit solvent molecular dynamics simulations and theoretical models, we present, for the first time, a systematic study to determine the mechanical properties of dsDNA in various hydrated ILs at different concentrations. We find that dsDNA in 50 wt % ILs have lower persistence length and stretch modulus in comparison to 80 wt % ILs. We further observe that both the persistence length and stretch modulus of dsDNA increase as we increase the concentration of ILs. The present trend of the stretch modulus and persistence length of dsDNA with IL concentration supports the predictions of the macroscopic elastic theory, in contrast to the behavior exhibited by dsDNA in monovalent salt. Our study further suggests the preferable ILs that can be used for maintaining DNA stability during long-term storage.

Form factor for distorted semi-flexible polymer chains

The statistical presence of kinks which form defects in semi-flexible polymer chains leads to a polydispersity in the effective persistence length. The form factor of a distorted semi-flexible polymer results as an average over this persistence polydispersity. It turns out that the scattering behavior of an ensemble of distorted semi-flexible polymer chains is quite well approximated by a form factor of an undistorted chain with a R_g-equivalent persistence length. An apparent length polydispersity is observed for short distorted chains. The R_g-equivalent persistence length is significantly smaller than the innate persistence length multiplied by the fraction of regular monomers. The results are compared to related work on DNA from the literature.

Tensile elasticity of semiflexible polymers with hinge defects

It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a prestressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible segments connected by a hinge. As such, they may also be relevant to cytoskeletal filaments (F-actin, microtubules), where one may treat the cross-link connecting two filaments as a hinge defect.

Evaluating the role of coherent delocalized phonon-like modes in DNA cyclization

The innate flexibility of a DNA sequence is quantified by the Jacobson-Stockmayer's J-factor, which measures the propensity for DNA loop formation. Recent studies of ultra-short DNA sequences revealed a discrepancy of up to six orders of magnitude between experimentally measured and theoretically predicted J-factors. These large differences suggest that, in addition to the elastic moduli of the double helix, other factors contribute to loop formation. Here, we develop a new theoretical model that explores how coherent delocalized phonon-like modes in DNA provide single-stranded "flexible hinges" to assist in loop formation. We combine the Czapla-Swigon-Olson structural model of DNA with our extended Peyrard-Bishop-Dauxois model and, without changing any of the parameters of the two models, apply this new computational framework to 86 experimentally characterized DNA sequences. Our results demonstrate that the new computational framework can predict J-factors within an order of magnitude of experimental measurements for most ultra-short DNA sequences, while continuing to accurately describe the J-factors of longer sequences. Further, we demonstrate that our computational framework can be used to describe the cyclization of DNA sequences that contain a base pair mismatch. Overall, our results support the conclusion that coherent delocalized phonon-like modes play an important role in DNA cyclization.

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

We propose a method for analyzing the magnitude and direction of curvature within nucleic acids, based on the curvilinear helical axis calculated by Curves+. The method is applied to analyzing curvature within minicircles constructed with varying degrees of over- or under-twisting. Using the molecular dynamics trajectories of three different minicircles, we are able to quantify how curvature varies locally both in space and in time. We also analyze how curvature influences the local environment of the minicircles, notably via increased heterogeneity in the ionic distributions surrounding the double helix. The approach we propose has been integrated into Curves+ and the utilities Canal (time trajectory analysis) and Canion (environmental analysis) and can be used to study a wide variety of static and dynamic structural data on nucleic acids.

Towards quantitative analysis of gene regulation by enhancers

Enhancers are regulatory DNA sequences that can activate transcription over large distances. Recent studies have revealed the widespread role of distant activation in eukaryotic gene regulation and in the development of various human diseases, including cancer. Here we review recent progress in the field, focusing on new experimental and computational approaches that quantify the role of chromatin structure and dynamics during enhancer-promoter interactions in vitro and in vivo.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

Binding of DNA-bending non-histone proteins destabilizes regular 30-nm chromatin structure

Why most of the in vivo experiments do not find the 30-nm chromatin fiber, well studied in vitro, is a puzzle. Two basic physical inputs that are crucial for understanding the structure of the 30-nm fiber are the stiffness of the linker DNA and the relative orientations of the DNA entering/exiting nucleosomes. Based on these inputs we simulate chromatin structure and show that the presence of non-histone proteins, which bind and locally bend linker DNA, destroys any regular higher order structures (e.g., zig-zag). Accounting for the bending geometry of proteins like nhp6 and HMG-B, our theory predicts phase-diagram for the chromatin structure as a function of DNA-bending non-histone protein density and mean linker DNA length. For a wide range of linker lengths, we show that as we vary one parameter, that is, the fraction of bent linker region due to non-histone proteins, the steady-state structure will show a transition from zig-zag to an irregular structure-a structure that is reminiscent of what is observed in experiments recently. Our theory can explain the recent in vivo observation of irregular chromatin having co-existence of finite fraction of the next-neighbor (i + 2) and neighbor (i + 1) nucleosome interactions.

Effect of sequence-dependent rigidity on plectoneme localization in dsDNA

We use Monte-Carlo simulations to study the effect of variable rigidity on plectoneme formation and localization in supercoiled double-stranded DNA. We show that the presence of soft sequences increases the number of plectoneme branches and that the edges of the branches tend to be localized at these sequences. We propose an experimental approach to test our results in vitro, and discuss the possible role played by plectoneme localization in the search process of transcription factors for their targets (promoter regions) on the bacterial genome.

Revisiting the Anomalous Bending Elasticity of Sharply Bent DNA

Several recent experiments suggest that sharply bent DNA has a surprisingly high bending flexibility, but the cause of this flexibility is poorly understood. Although excitation of flexible defects can explain these results, whether such excitation can occur with the level of DNA bending in these experiments remains unclear. Intriguingly, the DNA contained preexisting nicks in most of these experiments but whether nicks might play a role in flexibility has never been considered in the interpretation of experimental results. Here, using full-atom molecular dynamics simulations, we show that nicks promote DNA basepair disruption at the nicked sites, which drastically reduces DNA bending energy. In addition, lower temperatures suppress the nick-dependent basepair disruption. In the absence of nicks, basepair disruption can also occur but requires a higher level of DNA bending. Therefore, basepair disruption inside B-form DNA can be suppressed if the DNA contains preexisting nicks. Overall, our results suggest that the reported mechanical anomaly of sharply bent DNA is likely dependent on preexisting nicks, therefore the intrinsic mechanisms of sharply bent nick-free DNA remain an open question.

Anisotropy of B-DNA Groove Bending

DNA bending is critical for DNA packaging, recognition, and repair, and occurs toward either the major or the minor groove. The anisotropy of B-DNA groove bending was quantified for eight DNA sequences by free energy simulations employing a novel reaction coordinate. The simulations show that bending toward the major groove is preferred for non-A-tracts while the A-tract has a high tendency of bending toward the minor groove. Persistence lengths were generally larger for bending toward the minor groove, which is thought to originate from differences in groove hydration. While this difference in stiffness is one of the factors determining the overall preference of bending direction, the dominant contribution is shown to be a free energy offset between major and minor groove bending. The data suggests that, for the A-tract, this offset is largely determined by inherent structural properties, while differences in groove hydration play a large role for non-A-tracts. By quantifying the energetics of DNA groove bending and rationalizing the origins of the anisotropy, the calculations provide important new insights into a key biological process.