Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases

Miscibility and exchange chemical potential of ring polymers in symmetric ring-ring blends

Generally, differences of polymer topologies may affect polymer miscibility even with the same repeated units. In this study, the topological effect of ring polymers on miscibility was investigated by comparing symmetric ring-ring and linear-linear polymer blends. To elucidate the topological effect of ring polymers on mixing free energy, the exchange chemical potential of binary blends was numerically evaluated as a function of composition ϕ by performing semi-grand canonical Monte Carlo and molecular dynamics simulations of a bead-spring model. For ring-ring blends, an effective miscibility parameter was evaluated by comparing the exchange chemical potential with that of the Flory-Huggins model for linear-linear polymer blends. It was confirmed that in the mixed states satisfying χN > 0, ring-ring blends are more miscible and stable than the linear-linear blends with the same molecular weight. Furthermore, we investigated finite molecular weight dependence on the miscibility parameter, which reflected the statistical probability of interchain interactions in the blends. The simulation results revealed that the molecular weight dependence on the miscibility parameter was smaller in ring-ring blends. The effect of the ring polymers on miscibility was verified to be consistent with the change in the interchain radial distribution function. In ring-ring blends, it was indicated that the topology affected miscibility by reducing the effect of the direct interaction between the components of the blends.

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.

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

Keeping intracellular DNA untangled: A new role for condensin?

The DNA-passage activity of topoisomerase II accidentally produces DNA knots and interlinks within and between chromatin fibers. Fortunately, these unwanted DNA entanglements are actively removed by some mechanism. Here we present an outline on DNA knot formation and discuss recent studies that have investigated how intracellular DNA knots are removed. First, although topoisomerase II is able to minimize DNA entanglements in vitro to below equilibrium values, it is unclear whether such capacity performs equally in vivo in chromatinized DNA. Second, DNA supercoiling could bias topoisomerase II to untangle the DNA. However, experimental evidence indicates that transcriptional supercoiling of intracellular DNA boosts knot formation. Last, cohesin and condensin could tighten DNA entanglements via DNA loop extrusion (LE) and force their dissolution by topoisomerase II. Recent observations indicate that condensin activity promotes the removal of DNA knots during interphase and mitosis. This activity might facilitate the spatial organization and dynamics of chromatin.

Channels with Helical Modulation Display Stereospecific Sensitivity for Chiral Superstructures

By means of coarse-grained molecular dynamics simulations, we explore chiral sensitivity of confining spaces modelled as helical channels to chiral superstructures represented by polymer knots. The simulations show that helical channels exhibit stereosensitivity to chiral knots localized on linear chains by effect of external pulling force and also to knots embedded on circular chains. The magnitude of the stereoselective effect is stronger for torus knots, the effect is weaker in the case of twist knots, and amphichiral knots do exhibit no chiral effects. The magnitude of the effect can be tuned by the so-far investigated radius of the helix, the pitch of the helix and the strength of the pulling force. The model is aimed to simulate and address a range of practical situations that may occur in experimental settings such as designing of nanotechnological devices for the detection of topological state of molecules, preparation of new gels with tailor made stereoselective properties, or diffusion of knotted DNA in biological conditions.

Detecting Single Molecule Deoxyribonucleic Acid in a Cell Using a Three-Dimensionally Integrated Nanopore

Amplification-free genome analysis can revolutionize biology and medicine by uncovering genetic variations among individuals. Here, the authors report on a 3D-integrated nanopore for electrolysis to in situ detection of single-molecule DNA in a cell by ionic current measurements. It consists of a SiO₂ multipore sheet and a SiN_x nanopore membrane stacked vertically on a Si wafer. Single cell lysis is demonstrated by 10⁶  V m^-1 -level electrostatic field focused at the multinanopore. The intracellular molecules are then directly detected as they move through a sensing zone, wherein the authors find telegraphic current signatures reflecting folding degrees of freedom of the millimeter-long polynucleotides threaded through the SiN_x nanopore. The present device concept may enable on-chip single-molecule sequencing to multi-omics analyses at a single-cell level.

Reconstruction of mechanical unfolding and refolding pathways of proteins with atomic force spectroscopy and computer simulations

Most proteins in proteomes are large, typically consist of more than one domain and are structurally complex. This often makes studying their mechanical unfolding pathways challenging. Proteins composed of tandem repeat domains are a subgroup of multi-domain proteins that, when stretched, display a saw-tooth pattern in their mechanical unfolding force extension profiles due to their repetitive structure. However, the assignment of force peaks to specific repeats undergoing mechanical unraveling is complicated because all repeats are similar and they interact with their neighbors and form a contiguous tertiary structure. Here, we describe in detail a combination of experimental and computational single-molecule force spectroscopy methods that proved useful for examining the mechanical unfolding and refolding pathways of ankyrin repeat proteins. Specifically, we explain and delineate the use of atomic force microscope-based single molecule force spectroscopy (SMFS) to record the mechanical unfolding behavior of ankyrin repeat proteins and capture their unusually strong refolding propensity that is responsible for generating impressive refolding force peaks. We also describe Coarse Grain Steered Molecular Dynamic (CG-SMD) simulations which complement the experimental observations and provide insights in understanding the unfolding and refolding of these proteins. In addition, we advocate the use of novel coiled-coils-based mechanical polypeptide probes which we developed to demonstrate the vectorial character of folding and refolding of these repeat proteins. The combination of AFM-based SMFS on native and CC-equipped proteins with CG-SMD simulations is powerful not only for ankyrin repeat polypeptides, but also for other repeat proteins and more generally to various multidomain, non-repetitive proteins with complex topologies.

Transcriptional supercoiling boosts topoisomerase II-mediated knotting of intracellular DNA

Recent studies have revealed that the DNA cross-inversion mechanism of topoisomerase II (topo II) not only removes DNA supercoils and DNA replication intertwines, but also produces small amounts of DNA knots within the clusters of nucleosomes that conform to eukaryotic chromatin. Here, we examine how transcriptional supercoiling of intracellular DNA affects the occurrence of these knots. We show that although (−) supercoiling does not change the basal DNA knotting probability, (+) supercoiling of DNA generated in front of the transcribing complexes increases DNA knot formation over 25-fold. The increase of topo II-mediated DNA knotting occurs both upon accumulation of (+) supercoiling in topoisomerase-deficient cells and during normal transcriptional supercoiling of DNA in TOP1 TOP2 cells. We also show that the high knotting probability (P^kn ≥ 0.5) of (+) supercoiled DNA reflects a 5-fold volume compaction of the nucleosomal fibers in vivo. Our findings indicate that topo II-mediated DNA knotting could be inherent to transcriptional supercoiling of DNA and other chromatin condensation processes and establish, therefore, a new crucial role of topoisomerase II in resetting the knotting–unknotting homeostasis of DNA during chromatin dynamics.

Closing the DNA replication cycle: from simple circular molecules to supercoiled and knotted DNA catenanes

Due to helical structure of DNA, massive amounts of positive supercoils are constantly introduced ahead of each replication fork. Positive supercoiling inhibits progression of replication forks but various mechanisms evolved that permit very efficient relaxation of that positive supercoiling. Some of these mechanisms lead to interesting topological situations where DNA supercoiling, catenation and knotting coexist and influence each other in DNA molecules being replicated. Here, we first review fundamental aspects of DNA supercoiling, catenation and knotting when these qualitatively different topological states do not coexist in the same circular DNA but also when they are present at the same time in replicating DNA molecules. We also review differences between eukaryotic and prokaryotic cellular strategies that permit relaxation of positive supercoiling arising ahead of the replication forks. We end our review by discussing very recent studies giving a long-sought answer to the question of how slow DNA topoisomerases capable of relaxing just a few positive supercoils per second can counteract the introduction of hundreds of positive supercoils per second ahead of advancing replication forks.

Complex DNA knots detected with a nanopore sensor

Equilibrium knots are common in biological polymers-their prevalence, size distribution, structure, and dynamics have been extensively studied, with implications to fundamental biological processes and DNA sequencing technologies. Nanopore microscopy is a high-throughput single-molecule technique capable of detecting the shape of biopolymers, including DNA knots. Here we demonstrate nanopore sensors that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding. We show the occurrence of both tight and loose knots, reconciling previous contradictory results from different experimental techniques. We evidence the occurrence of two quantitatively different modes of knot translocation through the nanopores, involving very different tension forces. With large statistics, we explore the complex knots and, for the first time, reveal the existence of rare composite knots. We use parametrized complexity, in concert with simulations, to test the theoretical assumptions of the models, further asserting the relevance of nanopores in future investigation of knots.

Supercoiling in a Protein Increases its Stability

The supercoiling motif is the most complex type of nontrivial topology found in proteins with at least one disulfide bond and, to the best of our knowledge, it has not been studied before. We show that a protein from extremophilic species with such a motif can fold; however, the supercoiling changes a smooth landscape observed in reduced conditions into a two-state folding process in the oxidative conditions, with a deep intermediate state. The protein takes advantage of the hairpinlike motif to overcome the topological barrier and thus to supercoil. We find that the depth of the supercoiling motif, i.e., the length of the threaded terminus, has a crucial impact on the folding rates of the studied protein. We show that fluctuations of the minimal surface area can be used to measure local stability, and we find that supercoiling introduces stability into the protein. We suggest that the supercoiling motif enables the studied protein to live in physically extreme conditions, which are detrimental to most life on Earth.

Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA

The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.

DNA knots occur in intracellular chromatin

In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.

TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami

Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.

Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Topological entanglement of interlocked knotted-unknotted polymer rings

Topological entanglements in biopolymers could drive them to certain internal statics and dynamics with important implications for biological functions. In this study, by means of molecular dynamics simulations, we demonstrate that the minimal crossing pattern of a braid plays a major role in its structural and dynamical properties; the braid consists of a knotted ring and an interlocked entwined unknotted polymer ring. In particular, we show that depending on the bending rigidity of the chains, the conformational energy of the braid can be either lower or higher than the unlocked polymer rings. Additionally, we find that a non-identical crossing pattern in the braid could distinctly enforce concerted internal conformational fluctuations between the interlocked rings.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

A ring-polymer model shows how macromolecular crowding controls chromosome-arm organization in Escherichia coli

Macromolecular crowding influences various cellular processes such as macromolecular association and transcription, and is a key determinant of chromosome organization in bacteria. The entropy of crowders favors compaction of long chain molecules such as chromosomes. To what extent is the circular bacterial chromosome, often viewed as consisting of “two arms”, organized entropically by crowding? Using computer simulations, we examine how a ring polymer is organized in a crowded and cylindrically-confined space, as a coarse-grained bacterial chromosome. Our results suggest that in a wide parameter range of biological relevance crowding is essential for separating the two arms in the way observed with Escherichia coli chromosomes at fast-growth rates, in addition to maintaining the chromosome in an organized collapsed state. Under different conditions, however, the ring polymer is centrally condensed or adsorbed onto the cylindrical wall with the two arms laterally collapsed onto each other. We discuss the relevance of our results to chromosome-membrane interactions.

Topological transformations in proteins: effects of heating and proximity of an interface

Using a structure-based coarse-grained model of proteins, we study the mechanism of unfolding of knotted proteins through heating. We find that the dominant mechanisms of unfolding depend on the temperature applied and are generally distinct from those identified for folding at its optimal temperature. In particular, for shallowly knotted proteins, folding usually involves formation of two loops whereas unfolding through high-temperature heating is dominated by untying of single loops. Untying the knots is found to generally precede unfolding unless the protein is deeply knotted and the heating temperature exceeds a threshold value. We then use a phenomenological model of the air-water interface to show that such an interface can untie shallow knots, but it can also make knots in proteins that are natively unknotted.

A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains

We determine knotting probabilities and typical sizes of knots in double-stranded DNA for chains of up to half a million base pairs with computer simulations of a coarse-grained bead-stick model: Single trefoil knots and composite knots which include at least one trefoil as a prime factor are shown to be common in DNA chains exceeding 250,000 base pairs, assuming physiologically relevant salt conditions. The analysis is motivated by the emergence of DNA nanopore sequencing technology, as knots are a potential cause of erroneous nucleotide reads in nanopore sequencing devices and may severely limit read lengths in the foreseeable future. Even though our coarse-grained model is only based on experimental knotting probabilities of short DNA strands, it reproduces the correct persistence length of DNA. This indicates that knots are not only a fine gauge for structural properties, but a promising tool for the design of polymer models.

How topoisomerase IV can efficiently unknot and decatenate negatively supercoiled DNA molecules without causing their torsional relaxation

Freshly replicated DNA molecules initially form multiply interlinked right-handed catenanes. In bacteria, these catenated molecules become supercoiled by DNA gyrase before they undergo a complete decatenation by topoisomerase IV (Topo IV). Topo IV is also involved in the unknotting of supercoiled DNA molecules. Using Metropolis Monte Carlo simulations, we investigate the shapes of supercoiled DNA molecules that are either knotted or catenated. We are especially interested in understanding how Topo IV can unknot right-handed knots and decatenate right-handed catenanes without acting on right-handed plectonemes in negatively supercoiled DNA molecules. To this end, we investigate how the topological consequences of intersegmental passages depend on the geometry of the DNA-DNA juxtapositions at which these passages occur. We observe that there are interesting differences between the geometries of DNA-DNA juxtapositions in the interwound portions and in the knotted or catenated portions of the studied molecules. In particular, in negatively supercoiled, multiply interlinked, right-handed catenanes, we detect specific regions where DNA segments belonging to two freshly replicated sister DNA molecules form left-handed crossings. We propose that, due to its geometrical preference to act on left-handed crossings, Topo IV can specifically unknot supercoiled DNA, as well as decatenate postreplicative catenanes, without causing their torsional relaxation.

Consistent rationalization of type-2 topoisomerases' unknotting, decatenating, supercoil-relaxing actions and their scaling relation

How type-2 topoisomerases discern global topology from local properties of DNA is not known precisely but the hypothesis that the enzymes selectively pass double-helix strands at hook-like juxtapositions is promising. Building upon an investigation of unknotting and decatenating using an improved wormlike DNA model, here we focus primarily on the enzymes' action in narrowing the distribution of linking number (Lk) in supercoiled DNA. Consistent with experiments, with selective passage at a hooked juxtaposition, the simulated narrowing factor RLk diminishes with decreasing DNA circle size but approaches an asymptotic RLk ≈ 1.7-1.8 for circle size ≳3.5 kb. For the larger DNA circles, we found that (RLk - 1) ≈ 0.42log10RK ≈ 0.68log10RL and thus RK ≈ (RL)(1.6) holds for the computed RLk and knot and catenane reduction factors RK and RL attained by selective passage at different juxtaposition geometries. Remarkably, this general scaling relation is essentially identical to that observed experimentally for several type-2 topoisomerases from a variety of organisms, indicating that the different disentangling powers of the topoisomerases likely arise from variations in the hooked geometries they select. Taken together, our results suggest strongly that type-2 topoisomerases recognize not only the curvature of the G-segment but also that of the T-segment.

Adenylylation of Gyrase and Topo IV by FicT Toxins Disrupts Bacterial DNA Topology

Toxin-antitoxin (TA) modules are ubiquitous molecular switches controlling bacterial growth via the release of toxins that inhibit cell proliferation. Most of these toxins interfere with protein translation, but a growing variety of other mechanisms hints at a diversity that is not yet fully appreciated. Here, we characterize a group of FIC domain proteins as toxins of the conserved and abundant FicTA family of TA modules, and we reveal that they act by suspending control of cellular DNA topology. We show that FicTs are enzymes that adenylylate DNA gyrase and topoisomerase IV, the essential bacterial type IIA topoisomerases, at their ATP-binding site. This modification inactivates both targets by blocking their ATPase activity, and, consequently, causes reversible growth arrest due to the knotting, catenation, and relaxation of cellular DNA. Our results give insight into the regulation of DNA topology and highlight the remarkable plasticity of FIC domain proteins.

Generation of supercoils in nicked and gapped DNA drives DNA unknotting and postreplicative decatenation

Due to the helical structure of DNA the process of DNA replication is topologically complex. Freshly replicated DNA molecules are catenated with each other and are frequently knotted. For proper functioning of DNA it is necessary to remove all of these entanglements. This is done by DNA topoisomerases that pass DNA segments through each other. However, it has been a riddle how DNA topoisomerases select the sites of their action. In highly crowded DNA in living cells random passages between contacting segments would only increase the extent of entanglement. Using molecular dynamics simulations we observed that in actively supercoiled DNA molecules the entanglements resulting from DNA knotting or catenation spontaneously approach sites of nicks and gaps in the DNA. Type I topoisomerases, that preferentially act at sites of nick and gaps, are thus naturally provided with DNA–DNA juxtapositions where a passage results in an error-free DNA unknotting or DNA decatenation.

Direct Evidence for the Formation of Precatenanes during DNA Replication

The dynamics of DNA topology during replication are still poorly understood. Bacterial plasmids are negatively supercoiled. This underwinding facilitates strand separation of the DNA duplex during replication. Leading the replisome, a DNA helicase separates the parental strands that are to be used as templates. This strand separation causes overwinding of the duplex ahead. If this overwinding persists, it would eventually impede fork progression. In bacteria, DNA gyrase and topoisomerase IV act ahead of the fork to keep DNA underwound. However, the processivity of the DNA helicase might overcome DNA gyrase and topoisomerase IV. It was proposed that the overwinding that builds up ahead of the fork could force it to swivel and diffuse this positive supercoiling behind the fork where topoisomerase IV would also act to maintain replicating the DNA underwound. Putative intertwining of sister duplexes in the replicated region are called precatenanes. Fork swiveling and the formation of precatenanes, however, are still questioned. Here, we used classical genetics and high resolution two-dimensional agarose gel electrophoresis to examine the torsional tension of replication intermediates of three bacterial plasmids with the fork stalled at different sites before termination. The results obtained indicated that precatenanes do form as replication progresses before termination.

Extracting physics of life at the molecular level: A review of single-molecule data analyses

Studying individual biomolecules at the single-molecule level has proved very insightful recently. Single-molecule experiments allow us to probe both the equilibrium and nonequilibrium properties as well as make quantitative connections with ensemble experiments and equilibrium thermodynamics. However, it is important to be careful about the analysis of single-molecule data because of the noise present and the lack of theoretical framework for processes far away from equilibrium. Biomolecular motion, whether it is free in solution, on a substrate, or under force, involves thermal fluctuations in varying degrees, which makes the motion noisy. In addition, the noise from the experimental setup makes it even more complex. The details of biologically relevant interactions, conformational dynamics, and activities are hidden in the noisy single-molecule data. As such, extracting biological insights from noisy data is still an active area of research. In this review, we will focus on analyzing both fluorescence-based and force-based single-molecule experiments and gaining biological insights at the single-molecule level. Inherently nonequilibrium nature of biological processes will be highlighted. Simulated trajectories of biomolecular diffusion will be used to compare and validate various analysis techniques.

Topological constraints strongly affect chromatin reconstitution in silico

The fundamental building block of chromatin, and of chromosomes, is the nucleosome, a composite material made up from DNA wrapped around a histone octamer. In this study we provide the first computer simulations of chromatin self-assembly, starting from DNA and histone proteins, and use these to understand the constraints which are imposed by the topology of DNA molecules on the creation of a polynucleosome chain. We take inspiration from the in vitro chromatin reconstitution protocols which are used in many experimental studies. Our simulations indicate that during self-assembly, nucleosomes can fall into a number of topological traps (or local folding defects), and this may eventually lead to the formation of disordered structures, characterised by nucleosome clustering. Remarkably though, by introducing the action of topological enzymes such as type I and II topoisomerase, most of these defects can be avoided and the result is an ordered 10-nm chromatin fibre. These findings provide new insight into the biophysics of chromatin formation, both in the context of reconstitution in vitro and in terms of the topological constraints which must be overcome during de novo nucleosome formation in vivo, e.g. following DNA replication or repair.

Topological friction strongly affects viral DNA ejection

Bacteriophages initiate infection by releasing their double-stranded DNA into the cytosol of their bacterial host. However, what controls and sets the timescales of DNA ejection? Here we provide evidence from stochastic simulations which shows that the topology and organization of DNA packed inside the capsid plays a key role in determining these properties. Even with similar osmotic pressure pushing out the DNA, we find that spatially ordered DNA spools have a much lower effective friction than disordered entangled states. Such spools are only found when the tendency of nearby DNA strands to align locally is accounted for. This topological or conformational friction also depends on DNA knot type in the packing geometry and slows down or arrests the ejection of twist knots and very complex knots. We also find that the family of (2, 2k+1) torus knots unravel gradually by simplifying their topology in a stepwise fashion. Finally, an analysis of DNA trajectories inside the capsid shows that the knots formed throughout the ejection process mirror those found in gel electrophoresis experiments for viral DNA molecules extracted from the capsids.

The benefit of DNA supercoiling during replication

DNA topology changes dynamically during DNA replication. Supercoiling, precatenation, catenation and knotting interplay throughout the process that is finely regulated by DNA topoisomerases. In the present article, we provide an overview of theoretical and experimental approaches to understand the interplay between various manifestations of topological constraints acting on replicating DNA molecules. Data discussed reveal that DNA entanglements (supercoils and catenanes) play an active role in preventing the formation of deleterious knots.

Network Theory Tools for RNA Modeling

An introduction into the usage of graph or network theory tools for the study of RNA molecules is presented. By using vertices and edges to define RNA secondary structures as tree and dual graphs, we can enumerate, predict, and design RNA topologies. Graph connectivity and associated Laplacian eigenvalues relate to biological properties of RNA and help understand RNA motifs as well as build, by computational design, various RNA target structures. Importantly, graph theoretical representations of RNAs reduce drastically the conformational space size and therefore simplify modeling and prediction tasks. Ongoing challenges remain regarding general RNA design, representation of RNA pseudoknots, and tertiary structure prediction. Thus, developments in network theory may help advance RNA biology.

Crossing-sign discrimination and knot-reduction for a lattice model of strand passage

By performing strand-passages on DNA, type II topoisomerases are known to resolve topological constraints that impede normal cellular functions. The full details of this enzyme–DNA interaction mechanism are, however, not completely understood. To better understand this mechanism, researchers have proposed and studied a variety of random polygon models of enzyme-induced strand-passage. In the present article, we review results from one such model having the feature that it is amenable to combinatorial and asymptotic analysis (as polygon length goes to infinity). The polygons studied, called Θ-SAPs, are on the simple-cubic lattice and contain a specific strand-passage structure, called Θ, at a fixed site. Another feature of this model is the availability of Monte Carlo methods that facilitate the estimation of crossing-sign-dependent knot-transition probabilities. From such estimates, it has been possible to investigate how knot-reduction depends on the crossing-sign and the local juxtaposition geometry at the strand-passage site. A strong relationship between knot-reduction and a crossing-sign-dependent crossing-angle has been observed for this model. In the present article, we review these results and present heuristic geometrical arguments to explain this crossing-sign and angle-dependence. Finally, we discuss potential implications for other models of type II topoisomerase action on DNA.

Topo IV is the topoisomerase that knots and unknots sister duplexes during DNA replication

DNA topology plays a crucial role in all living cells. In prokaryotes, negative supercoiling is required to initiate replication and either negative or positive supercoiling assists decatenation. The role of DNA knots, however, remains a mystery. Knots are very harmful for cells if not removed efficiently, but DNA molecules become knotted in vivo. If knots are deleterious, why then does DNA become knotted? Here, we used classical genetics, high-resolution 2D agarose gel electrophoresis and atomic force microscopy to show that topoisomerase IV (Topo IV), one of the two type-II DNA topoisomerases in bacteria, is responsible for the knotting and unknotting of sister duplexes during DNA replication. We propose that when progression of the replication forks is impaired, sister duplexes become loosely intertwined. Under these conditions, Topo IV inadvertently makes the strand passages that lead to the formation of knots and removes them later on to allow their correct segregation.

Human topoisomerase II-DNA interaction study by using atomic force microscopy

Type II topoisomerases (Topo II) are unique enzymes that change the DNA topology by catalyzing the passage of two double-strands across each other by using the energy from ATP hydrolysis. In vitro, human Topo II relaxes positive supercoiled DNA around 10-fold faster than negative supercoiled DNA. By using atomic force microscopy (AFM) we found that human Topo II binds preferentially to DNA cross-overs. Around 50% of the DNA crossings, where Topo II was bound to, presented an angle in the range of 80-90°, suggesting a favored binding geometry in the chiral discrimination by Topo II. Our studies with AFM also helped us visualize the dynamics of the unknotting action of Topo II in knotted molecules.