Probing the elasticity of DNA on short length scales by modeling supercoiling under tension

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Dynamic interplay between target search and recognition for a Type I CRISPR-Cas system

CRISPR-Cas effector complexes enable the defense against foreign nucleic acids and have recently been exploited as molecular tools for precise genome editing at a target locus. To bind and cleave their target, the CRISPR-Cas effectors have to interrogate the entire genome for the presence of a matching sequence. Here we dissect the target search and recognition process of the Type I CRISPR-Cas complex Cascade by simultaneously monitoring DNA binding and R-loop formation by the complex. We directly quantify the effect of DNA supercoiling on the target recognition probability and demonstrate that Cascade uses facilitated diffusion for its target search. We show that target search and target recognition are tightly linked and that DNA supercoiling and limited 1D diffusion need to be considered when understanding target recognition and target search by CRISPR-Cas enzymes and engineering more efficient and precise variants.

A quantitative model for the dynamics of target recognition and off-target rejection by the CRISPR-Cas Cascade complex

CRISPR-Cas effector complexes recognise nucleic acid targets by base pairing with their crRNA which enables easy re-programming of the target specificity in rapidly emerging genome engineering applications. However, undesired recognition of off-targets, that are only partially complementary to the crRNA, occurs frequently and represents a severe limitation of the technique. Off-targeting lacks comprehensive quantitative understanding and prediction. Here, we present a detailed analysis of the target recognition dynamics by the Cascade surveillance complex on a set of mismatched DNA targets using single-molecule supercoiling experiments. We demonstrate that the observed dynamics can be quantitatively modelled as a random walk over the length of the crRNA-DNA hybrid using a minimal set of parameters. The model accurately describes the recognition of targets with single and double mutations providing an important basis for quantitative off-target predictions. Importantly the model intrinsically accounts for observed bias regarding the position and the proximity between mutations and reveals that the seed length for the initiation of target recognition is controlled by DNA supercoiling rather than the Cascade structure.

Probing the stability of the SpCas9-DNA complex after cleavage

CRISPR-Cas9 is a ribonucleoprotein complex that sequence-specifically binds and cleaves double-stranded DNA. Wildtype Cas9 and its nickase and cleavage-incompetent mutants have been used in various biological techniques due to their versatility and programmable specificity. Cas9 has been shown to bind very stably to DNA even after cleavage of the individual DNA strands, inhibiting further turnovers and considerably slowing down in-vivo repair processes. This poses an obstacle in genome editing applications. Here, we employed single-molecule magnetic tweezers to investigate the binding stability of different Streptococcus pyogenes Cas9 variants after cleavage by challenging them with supercoiling. We find that different release mechanisms occur depending on which DNA strand is cleaved. After initial target strand cleavage, supercoils are only removed after the collapse of the R-loop. We identified several states with different stabilities of the R-loop. Most importantly, we find that the post-cleavage state of Cas9 exhibits a higher stability than the pre-cleavage state. After non-target strand cleavage, supercoils are immediately but slowly released by swiveling of the non-target strand around Cas9 bound to the target strand. Consequently, Cas9 and its non-target strand nicking mutant stay stably bound to the DNA for many hours even at elevated torsional stress.

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.

DNA Mechanics and Topology

We review the current understanding of the mechanics of DNA and DNA-protein complexes, from scales of base pairs up to whole chromosomes. Mechanics of the double helix as revealed by single-molecule experiments will be described, with an emphasis on the role of polymer statistical mechanics. We will then discuss how topological constraints- entanglement and supercoiling-impact physical and mechanical responses. Models for protein-DNA interactions, including effects on polymer properties of DNA of DNA-bending proteins will be described, relevant to behavior of protein-DNA complexes in vivo. We also discuss control of DNA entanglement topology by DNA-lengthwise-compaction machinery acting in concert with topoisomerases. Finally, the chapter will conclude with a discussion of relevance of several aspects of physical properties of DNA and chromatin to oncology.

The temperature dependence of the helical twist of DNA

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. Quantitative understanding and optimization of its functions requires precise experimental characterization and accurate modeling of DNA properties. A defining feature of DNA is its helicity. DNA unwinds with increasing temperature, even for temperatures well below the melting temperature. However, accurate quantitation of DNA unwinding under external forces and a microscopic understanding of the corresponding structural changes are currently lacking. Here we combine single-molecule magnetic tweezers measurements with atomistic molecular dynamics and coarse-grained simulations to obtain a comprehensive view of the temperature dependence of DNA twist. Experimentally, we find that DNA twist changes by ΔTw(T) = (-11.0 ± 1.2)°/(°C·kbp), independent of applied force, in the range of forces where torque-induced melting is negligible. Our atomistic simulations predict ΔTw(T) = (-11.1 ± 0.3)°/(°C·kbp), in quantitative agreement with experiments, and suggest that the untwisting of DNA with temperature is predominantly due to changes in DNA structure for defined backbone substates, while the effects of changes in substate populations are minor. Coarse-grained simulations using the oxDNA framework yield a value of ΔTw(T) = (-6.4 ± 0.2)°/(°C·kbp) in semi-quantitative agreement with experiments.

Probing the salt dependence of the torsional stiffness of DNA by multiplexed magnetic torque tweezers

The mechanical properties of DNA fundamentally constrain and enable the storage and transmission of genetic information and its use in DNA nanotechnology. Many properties of DNA depend on the ionic environment due to its highly charged backbone. In particular, both theoretical analyses and direct single-molecule experiments have shown its bending stiffness to depend on salt concentration. In contrast, the salt-dependence of the twist stiffness of DNA is much less explored. Here, we employ optimized multiplexed magnetic torque tweezers to study the torsional stiffness of DNA under varying salt conditions as a function of stretching force. At low forces (<3 pN), the effective torsional stiffness is ∼10% smaller for high salt conditions (500 mM NaCl or 10 mM MgCl₂) compared to lower salt concentrations (20 mM NaCl and 100 mM NaCl). These differences, however, can be accounted for by taking into account the known salt dependence of the bending stiffness. In addition, the measured high-force (6.5 pN) torsional stiffness values of C = 103 ± 4 nm are identical, within experimental errors, for all tested salt concentration, suggesting that the intrinsic torsional stiffness of DNA does not depend on salt.

Simulation of DNA Supercoil Relaxation

Several recent single-molecule experiments observe the response of supercoiled DNA to nicking endonucleases and topoisomerases. Typically in these experiments, indirect measurements of supercoil relaxation are obtained by observing the motion of a large micron-sized bead. The bead, which also serves to manipulate DNA, experiences significant drag and thereby obscures supercoil dynamics. Here we employ our discrete wormlike chain model to bypass experimental limitations and simulate the dynamic response of supercoiled DNA to a single strand nick. From our simulations, we make three major observations. First, extension is a poor dynamic measure of supercoil relaxation; in fact, the linking number relaxes so fast that it cannot have much impact on extension. Second, the rate of linking number relaxation depends upon its initial partitioning into twist and writhe as determined by tension. Third, the extensional response strongly depends upon the initial position of plectonemes.

Twist-Bend Coupling and the Torsional Response of Double-Stranded DNA

Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable wormlike chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40±10  nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago [J. Marko and E. Siggia, Macromolecules 27, 981 (1994)MAMOBX0024-929710.1021/ma00082a015], its effects on the mechanical properties of DNA have been so far largely unexplored. We expect that this coupling plays an important role in several aspects of DNA statics and dynamics.

Single-Molecule Insight Into Target Recognition by CRISPR-Cas Complexes

Ribonucleoprotein (RNP) complexes from CRISPR-Cas systems have attracted enormous interest since they can be easily and flexibly reprogrammed to target any desired locus for genome engineering and gene regulation applications. Basis for the programmability is a short RNA (crRNA) inside these complexes that recognizes the target nucleic acid by base pairing. For CRISPR-Cas systems that target double-stranded DNA this results in local DNA unwinding and formation of a so-called R-loop structure. Here we provide an overview how this target recognition mechanism can be dissected in great detail at the level of a single molecule. Specifically, we demonstrate how magnetic tweezers are applied to measure the local DNA unwinding at the target in real time. To this end we introduce the technique and the measurement principle. By studying modifications of the consensus target sequence, we show how different sequence elements contribute to the target recognition mechanism. From these data, a unified target recognition mechanism can be concluded for the RNPs Cascade and Cas9 from types I and II CRISPR-Cas systems. R-loop formation is hereby initiated on the target at an upstream element, called protospacer adjacent motif (PAM), from which the R-loop structure zips directionally toward the PAM-distal end of the target. At mismatch positions, the R-loop propagation stalls and further propagation competes with collapse of the structure. Upon full R-loop zipping conformational changes within the RNPs trigger degradation of the DNA target. This represents a shared labor mechanism in which zipping between nucleic acid strands is the actual target recognition mechanism while sensing of the R-loop arrival at the PAM-distal end just verifies the success of the full zipping.

Probing the mechanical properties, conformational changes, and interactions of nucleic acids with magnetic tweezers

Nucleic acids are central to the storage and transmission of genetic information. Mechanical properties, along with their sequence, both enable and fundamentally constrain the biological functions of DNA and RNA. For small deformations from the equilibrium conformations, nucleic acids are well described by an isotropic elastic rod model. However, external forces and torsional strains can induce conformational changes, giving rise to a complex force-torque phase diagram. This review focuses on magnetic tweezers as a powerful tool to precisely determine both the elastic parameters and conformational transitions of nucleic acids under external forces and torques at the single-molecule level. We review several variations of magnetic tweezers, in particular conventional magnetic tweezers, freely orbiting magnetic tweezers and magnetic torque tweezers, and discuss their characteristic capabilities. We then describe the elastic rod model for DNA and RNA and discuss conformational changes induced by mechanical stress. The focus lies on the responses to torque and twist, which are crucial in the mechanics and interactions of nucleic acids and can directly be measured using magnetic tweezers. We conclude by highlighting several recent studies of nucleic acid-protein and nucleic acid-small-molecule interactions as further applications of magnetic tweezers and give an outlook of some exciting developments to come.

TrmBL2 from Pyrococcus furiosus Interacts Both with Double-Stranded and Single-Stranded DNA

In many hyperthermophilic archaea the DNA binding protein TrmBL2 or one of its homologues is abundantly expressed. TrmBL2 is thought to play a significant role in modulating the chromatin architecture in combination with the archaeal histone proteins and Alba. However, its precise physiological role is poorly understood. It has been previously shown that upon binding TrmBL2 covers double-stranded DNA, which leads to the formation of a thick and fibrous filament. Here we investigated the filament formation process as well as the stabilization of DNA by TrmBL2 from Pyroccocus furiosus in detail. We used magnetic tweezers that allow to monitor changes of the DNA mechanical properties upon TrmBL2 binding on the single-molecule level. Extended filaments formed in a cooperative manner and were considerably stiffer than bare double-stranded DNA. Unlike Alba, TrmBL2 did not form DNA cross-bridges. The protein was found to bind double- and single-stranded DNA with similar affinities. In mechanical disruption experiments of DNA hairpins this led to stabilization of both, the double- (before disruption) and the single-stranded (after disruption) DNA forms. Combined, these findings suggest that the biological function of TrmBL2 is not limited to modulating genome architecture and acting as a global repressor but that the protein acts additionally as a stabilizer of DNA secondary structure.

Thermodynamics of long supercoiled molecules: insights from highly efficient Monte Carlo simulations

Supercoiled DNA polymer models for which the torsional energy depends on the total twist of molecules (Tw) are a priori well suited for thermodynamic analysis of long molecules. So far, nevertheless, the exact determination of Tw in these models has been based on a computation of the writhe of the molecules (Wr) by exploiting the conservation of the linking number, Lk=Tw+Wr, which reflects topological constraints coming from the helical nature of DNA. Because Wr is equal to the number of times the main axis of a DNA molecule winds around itself, current Monte Carlo algorithms have a quadratic time complexity, O(L(2)), with respect to the contour length (L) of the molecules. Here, we present an efficient method to compute Tw exactly, leading in principle to algorithms with a linear complexity, which in practice is O(L(1.2)). Specifically, we use a discrete wormlike chain that includes the explicit double-helix structure of DNA and where the linking number is conserved by continuously preventing the generation of twist between any two consecutive cylinders of the discretized chain. As an application, we show that long (up to 21 kbp) linear molecules stretched by mechanical forces akin to magnetic tweezers contain, in the buckling regime, multiple and branched plectonemes that often coexist with curls and helices, and whose length and number are in good agreement with experiments. By attaching the ends of the molecules to a reservoir of twists with which these can exchange helix turns, we also show how to compute the torques in these models. As an example, we report values that are in good agreement with experiments and that concern the longest molecules that have been studied so far (16 kbp).

Sequence Affects the Cyclization of DNA Minicircles

Understanding how the sequence of a DNA molecule affects its dynamic properties is a central problem affecting biochemistry and biotechnology. The process of cyclizing short DNA, as a critical step in molecular cloning, lacks a comprehensive picture of the kinetic process containing sequence information. We have elucidated this process by using coarse-grained simulations, enhanced sampling methods, and recent theoretical advances. We are able to identify the types and positions of structural defects during the looping process at a base-pair level. Correlations along a DNA molecule dictate critical sequence positions that can affect the looping rate. Structural defects change the bending elasticity of the DNA molecule from a harmonic to subharmonic potential with respect to bending angles. We explore the subelastic chain as a possible model in loop formation kinetics. A sequence-dependent model is developed to qualitatively predict the relative loop formation time as a function of DNA sequence.

DNA, flexibly flexible

Investigators have constructed dsDNA molecules with several different base modifications and have characterized their bending and twisting flexibilities using atomic force microscopy, DNA ring closure, and single-molecule force spectroscopy with optical tweezers. The three methods provide persistence length measurements that agree semiquantitatively, and they show that the persistence length is surprisingly similar for all of the modified DNAs. The circular dichroism spectra of modified DNAs differ substantially. Simple explanations based on base stacking strength, polymer charge, or groove occupancy by functional groups cannot explain the results, which will guide further high-resolution theory and experiments.

Collapse and coexistence for a molecular braid with an attractive interaction component subject to mechanical forces

Dual mechanical braiding experiments provide a useful tool with which to investigate the nature of interactions between rod-like molecules, for instance actin and DNA. In conditions close to molecular condensation, one would expect an appearance of a local minimum in the interaction potential between the two molecules. We investigate this situation, introducing an attractive component into the interaction potential, using a model developed for describing such experiments. We consider both attractive interactions that do not depend on molecular structure and those which depend on a DNA-like helix structure. In braiding experiments, an attractive term may lead to certain effects. A local minimum may cause molecules to collapse from a loosely braided configuration into a tight one, occurring at a critical value of the moment applied about the axis of the braid. For a fixed number of braid pitches, this may lead to coexistence between the two braiding states, tight and loose. Coexistence implies certain proportions of the braid are in each state, their relative size depending on the number of braid pitches. This manifests itself as a linear dependence in numerically calculated quantities as functions of the number of braid pitches. Also, in the collapsed state, the braid radius stays roughly constant. Furthermore, if the attractive interaction is helix dependent, the left-right handed braid symmetry is broken. For a DNA like charge distribution, using the Kornyshev-Leikin interaction model, our results suggest that significant braid collapse and coexistence only occurs for left handed braids. Regardless of the interaction model, the study highlights the possible qualitative physics of braid collapse and coexistence; and the role helix specific forces might play, if important. The model could be used to connect other microscopic theories of interaction with braiding experiments.

Directional R-Loop Formation by the CRISPR-Cas Surveillance Complex Cascade Provides Efficient Off-Target Site Rejection

CRISPR-Cas systems provide bacteria and archaea with adaptive immunity against foreign nucleic acids. In type I CRISPR-Cas systems, invading DNA is detected by a large ribonucleoprotein surveillance complex called Cascade. The crRNA component of Cascade is used to recognize target sites in foreign DNA (protospacers) by formation of an R-loop driven by base-pairing complementarity. Using single-molecule supercoiling experiments with near base-pair resolution, we probe here the mechanism of R-loop formation and detect short-lived R-loop intermediates on off-target sites bearing single mismatches. We show that R-loops propagate directionally starting from the protospacer-adjacent motif (PAM). Upon reaching a mismatch, R-loop propagation stalls and collapses in a length-dependent manner. This unambiguously demonstrates that directional zipping of the R-loop accomplishes efficient target recognition by rapidly rejecting binding to off-target sites with PAM-proximal mutations. R-loops that reach the protospacer end become locked to license DNA degradation by the auxiliary Cas3 nuclease/helicase without further target verification.

Plectoneme tip bubbles: coupled denaturation and writhing in supercoiled DNA

We predict a novel conformational regime for DNA, where denaturation bubbles form at the tips of plectonemes, and study its properties using coarse-grained simulations. For negative supercoiling, this regime lies between bubble-dominated and plectoneme-dominated phases, and explains the broad transition between the two observed in experiment. Tip bubbles cause localisation of plectonemes within thermodynamically weaker AT-rich sequences, and can greatly suppress plectoneme diffusion by a pinning mechanism. They occur for supercoiling densities and forces that are typically encountered for DNA in vivo, and may be exploited for biological control of genomic processes.

Atomic force microscopy study of DNA flexibility on short length scales: smooth bending versus kinking

The apparently anomalous flexibility of DNA on short length scales has attracted a lot of attention in recent years. We use atomic force microscopy (AFM) in solution to directly study the DNA bending statistics for small lengths down to one helical turn. The accuracy of experimental estimates could be improved due to a large data volume and a refined algorithm for image processing and measuring bend angles. It is found that, at length scales beyond two helical turns (7 nm), DNA is well described by the harmonic worm-like chain (WLC) model with the bending persistence length of 56 nm. Below this threshold, the AFM data are also described by the WLC model assuming that the accuracy of measured bend angles is limited by the physical width of the double helix. We conclude that the double helical DNA behaves as a uniform elastic rod even at very short length scales. Strong bends due to kinks, melting bubbles and other deviations from the WLC model are statistically negligible.

Double-stranded RNA under force and torque: similarities to and striking differences from double-stranded DNA

RNA plays myriad roles in the transmission and regulation of genetic information that are fundamentally constrained by its mechanical properties, including the elasticity and conformational transitions of the double-stranded (dsRNA) form. Although double-stranded DNA (dsDNA) mechanics have been dissected with exquisite precision, much less is known about dsRNA. Here we present a comprehensive characterization of dsRNA under external forces and torques using magnetic tweezers. We find that dsRNA has a force-torque phase diagram similar to that of dsDNA, including plectoneme formation, melting of the double helix induced by torque, a highly overwound state termed "P-RNA," and a highly underwound, left-handed state denoted "L-RNA." Beyond these similarities, our experiments reveal two unexpected behaviors of dsRNA: Unlike dsDNA, dsRNA shortens upon overwinding, and its characteristic transition rate at the plectonemic buckling transition is two orders of magnitude slower than for dsDNA. Our results challenge current models of nucleic acid mechanics, provide a baseline for modeling RNAs in biological contexts, and pave the way for new classes of magnetic tweezers experiments to dissect the role of twist and torque for RNA-protein interactions at the single-molecule level.

Probing the elastic limit of DNA bending

Sharp bending of double-stranded DNA (dsDNA) plays an essential role in genome structure and function. However, the elastic limit of dsDNA bending remains controversial. Here, we measured the opening rates of small dsDNA loops with contour lengths ranging between 40 and 200 bp using single-molecule Fluorescence Resonance Energy Transfer. The relationship of loop lifetime to loop size revealed a critical transition in bending stress. Above the critical loop size, the loop lifetime changed with loop size in a manner consistent with elastic bending stress, but below it, became less sensitive to loop size, indicative of softened dsDNA. The critical loop size increased from ∼60 bp to ∼100 bp with the addition of 5 mM magnesium. We show that our result is in quantitative agreement with the kinkable worm-like chain model, and furthermore, can reproduce previously reported looping probabilities of dsDNA over the range between 50 and 200 bp. Our findings shed new light on the energetics of sharply bent dsDNA.

The structural code of cyanobacterial genomes

A periodic bias in nucleotide frequency with a period of about 11 bp is characteristic for bacterial genomes. This signal is commonly interpreted to relate to the helical pitch of negatively supercoiled DNA. Functions in supercoiling-dependent RNA transcription or as a 'structural code' for DNA packaging have been suggested. Cyanobacterial genomes showed especially strong periodic signals and, on the other hand, DNA supercoiling and supercoiling-dependent transcription are highly dynamic and underlie circadian rhythms of these phototrophic bacteria. Focusing on this phylum and dinucleotides, we find that a minimal motif of AT-tracts (AT2) yields the strongest signal. Strong genome-wide periodicity is ancestral to a clade of unicellular and polyploid species but lost upon morphological transitions into two baeocyte-forming and a symbiotic species. The signal is intermediate in heterocystous species and weak in monoploid picocyanobacteria. A pronounced 'structural code' may support efficient nucleoid condensation and segregation in polyploid cells. The major source of the AT2 signal are protein-coding regions, where it is encoded preferentially in the first and third codon positions. The signal shows only few relations to supercoiling-dependent and diurnal RNA transcription in Synechocystis sp. PCC 6803. Strong and specific signals in two distinct transposons suggest roles in transposase transcription and transpososome formation.

Direct observation of R-loop formation by single RNA-guided Cas9 and Cascade effector complexes

Clustered, regularly interspaced, short palindromic repeats (CRISPR)/CRISPR-associated (Cas) systems protect bacteria and archaea from infection by viruses and plasmids. Central to this defense is a ribonucleoprotein complex that produces RNA-guided cleavage of foreign nucleic acids. In DNA-targeting CRISPR-Cas systems, the RNA component of the complex encodes target recognition by forming a site-specific hybrid (R-loop) with its complement (protospacer) on an invading DNA while displacing the noncomplementary strand. Subsequently, the R-loop structure triggers DNA degradation. Although these reactions have been reconstituted, the exact mechanism of R-loop formation has not been fully resolved. Here, we use single-molecule DNA supercoiling to directly observe and quantify the dynamics of torque-dependent R-loop formation and dissociation for both Cascade- and Cas9-based CRISPR-Cas systems. We find that the protospacer adjacent motif (PAM) affects primarily the R-loop association rates, whereas protospacer elements distal to the PAM affect primarily R-loop stability. Furthermore, Cascade has higher torque stability than Cas9 by using a conformational locking step. Our data provide direct evidence for directional R-loop formation, starting from PAM recognition and expanding toward the distal protospacer end. Moreover, we introduce DNA supercoiling as a quantitative tool to explore the sequence requirements and promiscuities of orthogonal CRISPR-Cas systems in rapidly emerging gene-targeting applications.

Undulations in a weakly interacting mechanically generated molecular braid under tension

We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid, steric interactions between the molecules, and external mechanical forces. In this model, both sets of ends, of the two molecules, are considered to be separated by a fixed distance much larger than the radius of the braid. One set of ends is rotated to generate a braid of a certain number of pitches (or turns), while the other set remains fixed. This model may describe the situation in which the ends of each molecule are attached to a substrate and a magnetic bead; to the latter a pulling force and rotational torque can be applied. We discuss various aspects of our model. Most importantly, an expression for the free energy is given, from which equations, determining the various geometric parameters of the braid, can be obtained. By numerically solving these equations, we give predictions from the model for the external torque needed to produce a braid with a certain number of turns per bending persistence length, as well as the end to end extension of the two molecules for a given pulling force. Other geometric parameters, as well as the lateral force required to keep the ends of the two molecules apart, are also calculated.

Self-consistent treatment of electrostatics in molecular DNA braiding through external forces

In this paper we consider a physical system in which two DNA molecules braid about each other. The distance between the two molecular ends, on either side of the braid, is held at a distance much larger than supercoiling radius of the braid. The system is subjected to an external pulling force, and a moment that induces the braiding. In a model, developed for understanding such a system, we assume that each molecule can be divided into a braided and unbraided section. We also suppose that the DNA is nicked so that there is no constraint of the individual linking numbers of the molecules. Included in the model are steric and electrostatic interactions, thermal fluctuations of the braided and unbraided sections of the molecule, as well as the constraint on the braid linking (catenation) number. We compare two approximations used in estimating the free energy of the braided section. One is where the amplitude of undulations of one molecule with respect to the other is determined only by steric interactions. The other is a self-consistent determination of the mean-squared amplitude of these undulations. In this second approximation electrostatics should play an important role in determining this quantity, as suggested by physical arguments. We see that if the electrostatic interaction is sufficiently large there are indeed notable differences between the two approximations. We go on to test the self-consistent approximation-included in the full model-against experimental data for such a system, and we find good agreement. However, there seems to be a slight left-right-handed braid asymmetry in some of the experimental results. We discuss what might be the origin of this small asymmetry.

DNA flexibility on short length scales probed by atomic force microscopy

Unusually high bending flexibility has been recently reported for DNA on short length scales. We use atomic force microscopy (AFM) in solution to obtain a direct estimate of DNA bending statistics for scales down to one helical turn. It appears that DNA behaves as a Gaussian chain and is well described by the wormlike chain model at length scales beyond 3 helical turns (10.5 nm). Below this threshold, the AFM data exhibit growing noise because of experimental limitations. This noise may hide small deviations from the Gaussian behavior, but they can hardly be significant.

Rationally designed coiled-coil DNA looping peptides control DNA topology

Artificial DNA looping peptides were engineered to study the roles of protein and DNA flexibility in controlling the geometry and stability of protein-mediated DNA loops. These LZD (leucine zipper dual-binding) peptides were derived by fusing a second, C-terminal, DNA-binding region onto the GCN4 bZip peptide. Two variants with different coiled-coil lengths were designed to control the relative orientations of DNA bound at each end. Electrophoretic mobility shift assays verified formation of a sandwich complex containing two DNAs and one peptide. Ring closure experiments demonstrated that looping requires a DNA-binding site separation of 310 bp, much longer than the length needed for natural loops. Systematic variation of binding site separation over a series of 10 constructs that cyclize to form 862-bp minicircles yielded positive and negative topoisomers because of two possible writhed geometries. Periodic variation in topoisomer abundance could be modeled using canonical DNA persistence length and torsional modulus values. The results confirm that the LZD peptides are stiffer than natural DNA looping proteins, and they suggest that formation of short DNA loops requires protein flexibility, not unusual DNA bendability. Small, stable, tunable looping peptides may be useful as synthetic transcriptional regulators or components of protein–DNA nanostructures.

Strong bending of the DNA double helix

During the past decade, the issue of strong bending of the double helix has attracted a lot of attention. Here, we overview the major experimental and theoretical developments in the field sorting out reliably established facts from speculations and unsubstantiated claims. Theoretical analysis shows that sharp bends or kinks have to facilitate strong bending of the double helix. It remains to be determined what is the critical curvature of DNA that prompts the appearance of the kinks. Different experimental and computational approaches to the problem are analyzed. We conclude that there is no reliable evidence that any anomalous behavior of the double helix happens when DNA fragments in the range of 100 bp are circularized without torsional stress. The anomaly starts at the fragment length of about 70 bp when sharp bends or kinks emerge in essentially every molecule. Experimental data and theoretical analysis suggest that kinks may represent openings of isolated base pairs, which had been experimentally detected in linear DNA molecules. The calculation suggests that although the probability of these openings in unstressed DNA is close to 10⁻⁵, it increases sharply in small DNA circles reaching 1 open bp per circle of 70 bp.