Torsional Stiffness of Extended and Plectonemic DNA

Optical Torque Calculations and Measurements for DNA Torsional Studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping, but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

SIGNIFICANCE

We developed a simulation platform based on the finite element method for force and torque calculation for particles in an angular optical trap (AOT), with considerations of tightly focused Gaussian beam, spherical aberrations, and optically anisotropic particles. Experimental measurements of focal shift ratio, force, and torque under multiple conditions were in good agreement with predictions from the simulations. We also demonstrated that intrinsic DNA torsional properties can be robustly measured under different AOT measurement conditions, strongly validating our simulations and calibrations. Our platform can facilitate trapping particle design for single-molecule assays using the AOT.

Torsion affects the calculation of DNA twisting number

The topological properties of DNA have long been a focal point in biophysics. In the 1970s, White proposed that the topology of closed DNA double helix follows White's formula: Lk=Wr+Tw. However, there has been controversy in the calculation of DNA twisting number, partly due to discrepancies in the definition of torsion in differential geometry. In this paper, we delved into a detailed study of torsion, revealing that the calculation of DNA twisting number should use the curve's geodesic torsion. Furthermore, we found that the discrepancy in DNA twisting numbers calculated using different torsion is N. This study elucidated the impact of torsion on the calculation of DNA twisting numbers, aiming to resolve controversies in the calculation of DNA topology and provided accurate computational methods and theoretical foundations for related research.

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

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

Correlating fluorescence microscopy, optical and magnetic tweezers to study single chiral biopolymers such as DNA

Biopolymer topology is critical for determining interactions inside cell environments, exemplified by DNA where its response to mechanical perturbation is as important as biochemical properties to its cellular roles. The dynamic structures of chiral biopolymers exhibit complex dependence with extension and torsion, however the physical mechanisms underpinning the emergence of structural motifs upon physiological twisting and stretching are poorly understood due to technological limitations in correlating force, torque and spatial localization information. We present COMBI-Tweez (Combined Optical and Magnetic BIomolecule TWEEZers), a transformative tool that overcomes these challenges by integrating optical trapping, time-resolved electromagnetic tweezers, and fluorescence microscopy, demonstrated on single DNA molecules, that can controllably form and visualise higher order structural motifs including plectonemes. This technology combined with cutting-edge MD simulations provides quantitative insight into complex dynamic structures relevant to DNA cellular processes and can be adapted to study a range of filamentous biopolymers.

Nucleosome Dynamics Derived at the Single-Molecule Level Bridges Its Structures and Functions

Nucleosome, the building block of chromatin, plays pivotal roles in all DNA-related processes. While cryogenic-electron microscopy (cryo-EM) has significantly advanced our understanding of nucleosome structures, the emerging field of single-molecule force spectroscopy is illuminating their dynamic properties. This technique is crucial for revealing how nucleosome behavior is influenced by chaperones, remodelers, histone variants, and post-translational modifications, particularly in their folding and unfolding mechanisms under tension. Such insights are vital for deciphering the complex interplay in nucleosome assembly and structural regulation, highlighting the nucleosome's versatility in response to DNA activities. In this Perspective, we aim to consolidate the latest advancements in nucleosome dynamics, with a special focus on the revelations brought forth by single-molecule manipulation. Our objective is to highlight the insights gained from studying nucleosome dynamics through this innovative approach, emphasizing the transformative impact of single-molecule manipulation techniques in the field of chromatin research.

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

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

Topological barrier to Cas12a activation by circular DNA nanostructures facilitates autocatalysis and transforms DNA/RNA sensing

Control of CRISPR/Cas12a trans-cleavage is crucial for biosensor development. Here, we show that small circular DNA nanostructures which partially match guide RNA sequences only minimally activate Cas12a ribonucleoproteins. However, linearizing these structures restores activation. Building on this finding, an Autocatalytic Cas12a Circular DNA Amplification Reaction (AutoCAR) system is established which allows a single nucleic acid target to activate multiple ribonucleoproteins, and greatly increases the achievable reporter cleavage rates per target. A rate-equation-based model explains the observed near-exponential rate trends. Autocatalysis is also sustained with DNA nanostructures modified with fluorophore-quencher pairs achieving 1 aM level (<1 copy/μL) DNA detection (106 times improvement), without additional amplification, within 15 min, at room temperature. The detection range is tuneable, spanning 3 to 11 orders of magnitude. We demonstrate 1 aM level detection of SNP mutations in circulating tumor DNA from blood plasma, genomic DNA (H. Pylori) and RNA (SARS-CoV-2) without reverse transcription as well as colorimetric lateral flow tests of cancer mutations with ~100 aM sensitivity.

Magnetic tweezers principles and promises

Magnetic tweezers have become popular with the outbreak of single molecule micromanipulation: catching a single molecule of DNA, RNA or a single protein and applying mechanical constrains using micron-size magnetic beads and magnets turn out to be easy. Various factors have made this possible: the fact that manufacturers have been preparing these beads to catch various biological entities-the ease of use provided by magnets which apply a force or a torque at a distance thus inside a flow cell-some chance: since the forces so generated are in the right range to stretch a single molecule. This is a little less true for torque. Finally, one feature which also appears very important is the simplicity of their calibration using Brownian motion. Here we start by describing magnetic tweezers used routinely in our laboratory where we have tried to develop a device as simple as possible so that the experimentalist can really focus on the biological aspect of the biomolecules that he/she is interested in. We discuss the implications of the various components and their important features. Next, we summarize what is easy to achieve and what is less easy. Then we refer to contributions by other groups who have brought valuable insights to improve magnetic tweezers.

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.

Energetics of twisted elastic filament pairs

We investigate the elastic energy stored in a filament pair as a function of applied twist by measuring torque under prescribed end-to-end separation conditions. We show that the torque increases rapidly to a peak with applied twist when the filaments are initially separate, then decreases to a minimum as the filaments cross and come into contact. The torque then increases again while the filaments form a double helix with increasing twist. A nonlinear elasto-geometric model that combines the effect of geometrical nonlinearities with large stretching and self-twist is shown to capture the evolution of the helical geometry, torque profile, and stored energy with twist. We find that a large fraction of the total energy is stored in stretching the filaments, which increases with separation distance and applied tension. We find that only a small fraction of energy is stored in the form of bending energy, and that the contribution due to contact energy is negligible. Further, we provide analytical formulas for the torque observed as a function of the applied twist and the inverse relation of the observed angle for a given applied torque in the Hookean limit. Our study highlights the consequences of stretchablility on filament twisting, which is a fundamental topological transformation relevant to making ropes, tying shoelaces, actuating robots, and the physical properties of entangled polymers.

Supercoiling-dependent DNA binding: quantitative modeling and applications to bulk and single-molecule experiments

DNA stores our genetic information and is ubiquitous in applications, where it interacts with binding partners ranging from small molecules to large macromolecular complexes. Binding is modulated by mechanical strains in the molecule and can change local DNA structure. Frequently, DNA occurs in closed topological forms where topology and supercoiling add a global constraint to the interplay of binding-induced deformations and strain-modulated binding. Here, we present a quantitative model with a straight-forward numerical implementation of how the global constraints introduced by DNA topology modulate binding. We focus on fluorescent intercalators, which unwind DNA and enable direct quantification via fluorescence detection. Our model correctly describes bulk experiments using plasmids with different starting topologies, different intercalators, and over a broad range of intercalator and DNA concentrations. We demonstrate and quantitatively model supercoiling-dependent binding in a single-molecule assay, where we directly observe the different intercalator densities going from supercoiled to nicked DNA. The single-molecule assay provides direct access to binding kinetics and DNA supercoil dynamics. Our model has broad implications for the detection and quantification of DNA, including the use of psoralen for UV-induced DNA crosslinking to quantify torsional tension in vivo, and for the modulation of DNA binding in cellular contexts.

Chromatinization modulates topoisomerase II processivity

Type IIA topoisomerases are essential DNA processing enzymes that must robustly and reliably relax DNA torsional stress. While cellular processes constantly create varying torsional stress, how this variation impacts type IIA topoisomerase function remains obscure. Using multiple single-molecule approaches, we examined the torsional dependence of eukaryotic topoisomerase II (topo II) activity on naked DNA and chromatin. We observed that topo II is ~50-fold more processive on buckled DNA than previously estimated. We further discovered that topo II relaxes supercoiled DNA prior to plectoneme formation, but with processivity reduced by ~100-fold. This relaxation decreases with diminishing torsion, consistent with topo II capturing transient DNA loops. Topo II retains high processivity on buckled chromatin (~10,000 turns) and becomes highly processive even on chromatin under low torsional stress (~1000 turns), consistent with chromatin's predisposition to readily form DNA crossings. This work establishes that chromatin is a major stimulant of topo II function.

Chromatinization Modulates Topoisomerase II Processivity

Type IIA topoisomerases are essential DNA processing enzymes that must robustly and reliably relax DNA torsional stress in vivo. While cellular processes constantly create different degrees of torsional stress, how this stress feeds back to control type IIA topoisomerase function remains obscure. Using a suite of single-molecule approaches, we examined the torsional impact on supercoiling relaxation of both naked DNA and chromatin by eukaryotic topoisomerase II (topo II). We observed that topo II was at least ~ 50-fold more processive on plectonemic DNA than previously estimated, capable of relaxing > 6000 turns. We further discovered that topo II could relax supercoiled DNA prior to plectoneme formation, but with a ~100-fold reduction in processivity; strikingly, the relaxation rate in this regime decreased with diminishing torsion in a manner consistent with the capture of transient DNA loops by topo II. Chromatinization preserved the high processivity of the enzyme under high torsional stress. Interestingly, topo II was still highly processive (~ 1000 turns) even under low torsional stress, consistent with the predisposition of chromatin to readily form DNA crossings. This work establishes that chromatin is a major stimulant of topo II function, capable of enhancing function even under low torsional stress.

An associative memory Hamiltonian model for DNA and nucleosomes

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), reproduces the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similar to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM is designed to emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, is ready to be scaled up to molecular systems large enough to investigate the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use.

DNA fluctuations reveal the size and dynamics of topological domains

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here, we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real time and at the single-molecule level. Our approach is based on quantifying the extension fluctuations-in addition to the mean extension-of supercoiled DNA in magnetic tweezers (MT). Using a combination of high-speed MT experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime, the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how the transient (partial) dissociation of DNA-bridging proteins results in the dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our results to further the understanding and optimization of magnetic tweezer measurements and to enable quantification of the dynamics and reaction pathways of DNA processing enzymes in the context of physiologically relevant forces and supercoiling densities.

Equilibrium fluctuations of DNA plectonemes

Plectonemes are intertwined helically looped domains which form when a DNA molecule is supercoiled, i.e., over- or underwound. They are ubiquitous in cellular DNA, and their physical properties have attracted significant interest both from the experimental side and from the modeling side. In this paper, we investigate fluctuations of the end-point distance z of supercoiled linear DNA molecules subject to external stretching forces. Our analysis is based on a two-phase model, which describes the supercoiled DNA as composed of a stretched phase and a plectonemic phase. A variety of mechanisms are found to contribute to extension fluctuations, characterized by the variance 〈Δz^{2}〉. We find the dominant contribution to 〈Δz^{2}〉 to originate from phase-exchange fluctuations, the transient shrinking and expansion of plectonemes, which is accompanied by an exchange of molecular length between the two phases. We perform Monte Carlo simulations of the twistable wormlike chain and analyze the fluctuation of various quantities, the results of which are found to agree with the two-phase model predictions. Furthermore, we show that the extension and its variance at high forces are very well captured by the two-phase model, provided that one goes beyond quadratic approximations.

Accurate Sequence-Dependent Coarse-Grained Model for Conformational and Elastic Properties of Double-Stranded DNA

We introduce MADna, a sequence-dependent coarse-grained model of double-stranded DNA (dsDNA), where each nucleotide is described by three beads localized at the sugar, at the base moiety, and at the phosphate group, respectively. The sequence dependence is included by considering a step-dependent parametrization of the bonded interactions, which are tuned in order to reproduce the values of key observables obtained from exhaustive atomistic simulations from the literature. The predictions of the model are benchmarked against an independent set of all-atom simulations, showing that it captures with high fidelity the sequence dependence of conformational and elastic features beyond the single step considered in its formulation. A remarkably good agreement with experiments is found for both sequence-averaged and sequence-dependent conformational and elastic features, including the stretching and torsion moduli, the twist–stretch and twist–bend couplings, the persistence length, and the helical pitch. Overall, for the inspected quantities, the model has a precision comparable to atomistic simulations, hence providing a reliable coarse-grained description for the rationalization of single-molecule experiments and the study of cellular processes involving dsDNA. Owing to the simplicity of its formulation, MADna can be straightforwardly included in common simulation engines. Particularly, an implementation of the model in LAMMPS is made available on an online repository to ease its usage within the DNA research community.

Resonator nanophotonic standing-wave array trap for single-molecule manipulation and measurement

Nanophotonic tweezers represent emerging platforms with significant potential for parallel manipulation and measurements of single biological molecules on-chip. However, trapping force generation represents a substantial obstacle for their broader utility. Here, we present a resonator nanophotonic standing-wave array trap (resonator-nSWAT) that demonstrates significant force enhancement. This platform integrates a critically-coupled resonator design to the nSWAT and incorporates a novel trap reset scheme. The nSWAT can now perform standard single-molecule experiments, including stretching DNA molecules to measure their force-extension relations, unzipping DNA molecules, and disrupting and mapping protein-DNA interactions. These experiments have realized trapping forces on the order of 20 pN while demonstrating base-pair resolution with measurements performed on multiple molecules in parallel. Thus, the resonator-nSWAT platform now meets the benchmarks of a table-top precision optical trapping instrument in terms of force generation and resolution. This represents the first demonstration of a nanophotonic platform for such single-molecule experiments.

Applications of nanophotonic tweezers have been limited by the low trapping force. Here, the authors present enhanced force generation in a nanophotonic standing-wave array trap by integrating a critically-coupled resonator design and demonstrate common single-molecule experiments.

Angular Optical Trapping to Directly Measure DNA Torsional Mechanics

Angular optical trapping (AOT) is a powerful technique that permits direct angular manipulation of a trapped particle with simultaneous measurement of torque and rotation, while also retaining the capabilities of position and force detection. This technique provides unique approaches to investigate the torsional properties of nucleic acids and DNA-protein complexes, as well as impacts of torsional stress on fundamental biological processes, such as transcription and replication. Here we describe the principle, construction, and calibration of the AOT in detail and provide a guide to the performance of single-molecule torque measurements on DNA molecules. We include the constant-force method and, notably, a new constant-extension method that enables measurement of the twist persistence length of both extended DNA, under an extremely low force, and plectonemic DNA. This chapter can assist in the implementation and application of this technique for general researchers in the single-molecule field.