DNA Knots Research Articles

Mesofractal Modeling of Biosystems & Organic Spintronics

Mesoscopic modeling of complex systems involves thermodynamic nonequilibrium of discrete scaling. Further from quantum correlation on a chip retrieved quantum nonlinear optics with single photons enabled by strongly interacting atoms. Accompanied by mesofractals as the development of meso & micro size fractal structures is required to mimic various biological systems for various functions. Showed through fluorapatite in gelatin‐based nanocomposite, fractal in DNA knots driven by balance of fission & fusion in mtDNA/mitochondrial DNA mechanism, for optical engines for light energy detection described the proportional integral derivative [PI(D)]‐controller set in microbial cells to HCCI/Homogeneous Charge Compression Ignition.

Diffusion of nanochannel-confined knot along a tensioned polymer* *The National Natural Science Foundation of China under Grant Nos. 11864006, 11874309, 12164007, and 12204118.

The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation. In this work, Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints. The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot. As a result, the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained. In the space without constraints or with weak constraints, the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours. On the contrary, for the knot with relatively small bending stiffness, the diffusion coefficients were monotonically reduced with increasing tension. However, in a space with strong constraints, all the curves showed one turnover behaviour regardless of the bending stiffness. The turnover behaviours divided the curves into different regimes, and the dominant diffusion mechanisms in the regimes, namely, knot-region breathing, self-reptation, and internal friction, were clearly identified. The effective friction coefficients ξ of the knots with 31, 41, 51 and 52 types as a function of the knot size N at a fixed tension were well fitted by the relation ξ ∝ N. The effective friction coefficients of the knots at relatively large tension f > 3 sharply increased with the knot complexity, which is not dependent on the spatial constraints. By contrast, the values of these coefficients at relatively small tension f ≤ 3 were remarkably dependent on the spatial constraints. Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot, but also highlights the single-molecule design for the manipulation of DNA knots in future.

Activating the abscission checkpoint: Top2α senses chromatin bridges in cytokinesis: Top2α binds to DNA knots on chromatin bridges to activate the abscission checkpoint in human cells.

How chromatin bridges are detected by the abscission checkpoint during mammalian cell division is unknown. Here, we discuss recent findings from our lab showing that the DNA topoisomerase IIα (Top2α) enzyme binds to catenated ("knotted") DNA next to the midbody and forms abortive Top2-DNA cleavage complexes (Top2ccs) on chromatin bridges. Top2ccs are then processed by the proteasome to promote localization of the DNA damage sensor protein Rad17 to Top2-generated double-strand DNA ends on DNA knots. In turn, Rad17 promotes local recruitment of the MRN protein complex and downstream ATM-Chk2-INCENP signaling to delay abscission and prevent chromatin bridge breakage in cytokinesis.

Folding and unfolding of G-rich DNA knots using single molecule FRET

Folding and unfolding of G-rich DNA knots using single molecule FRET

Catalytic Oxidation-like Nuclear Nano-fusion; Fractal Involving of Room Temperature Magnetically Induced μ-Catalyzed Fusion

The nuclear fusion reaction can be catalyzed in a suitable fusion fuel by muons (heavy electrons). “For the fractal relations, ranging from DNA knots to solar neutrino flux signals”, ever derived of scale-invariant properties distinguished between classical invariant theory & quantum invariant theory subfactors. Accompanying isomorphic & Connes FusionTensor Product retrieved to μ-catalyzed fusion where surroundings of room temperature fusion driven by the balance in mtDNA fusion & fission. On behalf of the nanometer dimension of the radius of heavy electrons & wavelength of UV-light, it assumed that muons can be produced by oxidation-like decay when UV-light impinging water.

The abscission checkpoint senses chromatin bridges through Top2α recruitment to DNA knots.

In response to chromatin bridges, the abscission checkpoint delays completion of cytokinesis to prevent chromosome breakage or tetraploidization. Here, we show that spontaneous or replication stress-induced chromatin bridges exhibit "knots" of catenated and overtwisted DNA next to the midbody. Topoisomerase IIα (Top2α) forms abortive Top2-DNA cleavage complexes (Top2ccs) on DNA knots; furthermore, impaired Top2α-DNA cleavage activity correlates with chromatin bridge breakage in cytokinesis. Proteasomal degradation of Top2ccs is required for Rad17 localization to Top2-generated double-strand DNA ends on DNA knots; in turn, Rad17 promotes local recruitment of the MRN complex and downstream ATM-Chk2-INCENP signaling to delay abscission and prevent chromatin breakage. In contrast, dicentric chromosomes that do not exhibit knotted DNA fail to activate the abscission checkpoint in human cells. These findings are the first to describe a mechanism by which the abscission checkpoint detects chromatin bridges, through generation of abortive Top2ccs on DNA knots, to preserve genome integrity.

Energy spectrum of the ideal DNA knot on a torus.

In this study, we consider DNA as a torus knot that is formed by an elastic string. In order to determine what kinds of knot could be formed, we present its energy spectrum by combining Euler rotation, DNA's mechanical properties, and the modified Faddeev-Skyrme model. Our results theoretically demonstrated that the flexural rigidity of DNA plays an important role. If it is smaller than a critical value, DNA is likely to form a coiled structure. Conversely, above the critical value, DNA forms a twisting structure. The energy spectrum provides a way to identify the types of knots that are most likely to be created by DNA, according to the principle of energy minimisation, and with implications for its functional and packaging states in the cell nucleus.

Influence of ionic conditions on knotting in a coarse-grained model for DNA.

We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and can be used for guiding future experiments on DNA knots.

Biomolecular Topology: Modelling and Analysis.

With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases. The high dimensionality, structural complexity, the nonlinearity, and entanglements of biomolecular data, ranging from DNA knots, RNA secondary structures, protein folding configurations, chromosomes, DNA origami, molecular assembly, to others at the macromolecular level, pose a severe challenge in their analysis and characterization. In the past few decades, mathematical concepts, models, algorithms, and tools from algebraic topology, combinatorial topology, computational topology, and topological data analysis, have demonstrated great power and begun to play an essential role in tackling the biomolecular data challenge. In this work, we introduce biomolecular topology, which concerns the topological problems and models originated from the biomolecular systems. More specifically, the biomolecular topology encompasses topological structures, properties and relations that are emerged from biomolecular structures, dynamics, interactions, and functions. We discuss the various types of biomolecular topology from structures (of proteins, DNAs, and RNAs), protein folding, and protein assembly. A brief discussion of databanks (and databases), theoretical models, and computational algorithms, is presented. Further, we systematically review related topological models, including graphs, simplicial complexes, persistent homology, persistent Laplacians, de Rham-Hodge theory, Yau-Hausdorff distance, and the topology-based machine learning models.

Knot formation of dsDNA pushed inside a nanochannel

Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.

Quantifying the effects of slit confinement on polymer knots using the tube model.

Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.

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.

Influences of flexible defect on the interplay of supercoiling and knotting of circular DNA* *The National Natural Science Foundation of China under Grant Nos. 11464004, 11864006 and 11564015, Guizhou Scientific and Technological Program (20185781 and 20185781-15), the Foundation of Key Laboratory of Animal Genetics, Breeding and Reproduction in The Plateau Mountainous Region, Ministry of Education (Guizhou University), KY2020243.

Knots are discovered in biophysical systems, such as DNA and proteins. Knotted portions in knotted DNA are significantly bent and their corresponding bending angles are comparable with or larger than the sharp bending angle resulting in flexible defects. The role of flexible defects in the interplay of supercoiling and knotting of circular DNA were predicted by a Monte Carlo simulation. In knotted DNA with a particular knot type, a flexible defect noticeably enhances the supercoiling of the knotted DNA and the decreasing excitation energy makes the knotted portion more compact. A reduction in twist rigidity and unwinding of flexible defects are incorporated into the numerical simulations, so that interplay of supercoiling and knotting of circular DNA is studied under torsional conditions. Increasing unwinding not only results in a wider linking number distribution, but also leads to a drift of the distribution to lower values. A flexible defect has obvious effects on knotting probability. The summation of equilibrium distribution probability for nontrivial knotted DNA with different contour length does not change with excitation energy monotonically and has a maximum at an intermediate value of excitation energy around 5k B T. In the phase space of knot length and gyration radius of knotted DNA, knot length does not anticorrelate with its gyration radius, which is attributed to the flexible defect in the knotted portion, which leads to the release of bending energy and inhibited the competition between entropy and bending energy.

AN OVERVIEW ON MECHANISM OF GENE EXPRESSION REGULATION

Transcription factors, enhancers, promoters, and translation of genetic code is still in a wide argument of different views in many living organisms for their poorly characterized at the molecular level. It was shown that the coexistence of high mono – methylation levels of lysine 4 of histone H3 is considered a signature of enhancers. Gene expression could be altered by epigenetic and some biotic and abiotic stresses. Some sugars, hormones or amino acids could also alter gene expression. However, some investigators have shown that increased methylation at promoters was associated with down – regulated protein – coding gene expression . In genomic DNA methylation levels, it was found 24 nt small RNAs only were correlated with methylation. Other investigators have set framework for modelling gene regulation, three dimensions were set to draw the graph framework; DNA microstates (vertices), the transitions between microstates, (edges) and the transition rates (edge labels). They believed that their graph will provide a broader foundation for understanding how genes regulate their expressions. More recently, a team of Australian investigators in Medical Res. have shown a new i-motifs; a four–stranded DNA knot in living human cells. These i- motifs were believed to be responsible in helping genes to switch on or off. Future investigations in gene expression will probably be shown in different models than we have learned.

DNA Knot Malleability in Single-Digit Nanopores

Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.

Translocation of DNA through Ultrathin Nanoslits.

2D nanoslit devices, where two crystals with atomically flat surfaces are separated by only a few nanometers, have attracted considerable attention because their tunable control over the confinement allows for the discovery of unusual transport behavior of gas, water, and ions. Here, the passage of double-stranded DNA molecules is studied through nanoslits fabricated from exfoliated 2D materials, such as graphene or hexagonal boron nitride, and the DNA polymer behavior is examined in this tight confinement. Two types of events are observed in the ionic current: long current blockades that signal DNA translocation and short spikes where DNA enters the slits but withdraws. DNA translocation events exhibit three distinct phases in their current-blockade traces-loading, translation, and exit. Coarse-grained molecular dynamics simulation allows the different polymer configurations of these phases to be identified. DNA molecules, including folds and knots in their polymer structure, are observed to slide through the slits with near-uniform velocity without noticeable frictional interactions of DNA with the confining graphene surfaces. It is anticipated that this new class of 2D-nanoslit devices will provide unique ways to study polymer physics and enable lab-on-a-chip biotechnology.

Condensin minimizes topoisomerase II‐mediated entanglements of DNA in vivo

The juxtaposition of intracellular DNA segments, together with the DNA‐passage activity of topoisomerase II, leads to the formation of DNA knots and interlinks, which jeopardize chromatin structure and gene expression. Recent studies in budding yeast have shown that some mechanism minimizes the knotting probability of intracellular DNA. Here, we tested whether this is achieved via the intrinsic capacity of topoisomerase II for simplifying the equilibrium topology of DNA; or whether it is mediated by SMC (structural maintenance of chromosomes) protein complexes like condensin or cohesin, whose capacity to extrude DNA loops could enforce dissolution of DNA knots by topoisomerase II. We show that the low knotting probability of DNA does not depend on the simplification capacity of topoisomerase II nor on the activities of cohesin or Smc5/6 complexes. However, inactivation of condensin increases the occurrence of DNA knots throughout the cell cycle. These results suggest an in vivo role for the DNA loop extrusion activity of condensin and may explain why condensin disruption produces a variety of alterations in interphase chromatin, in addition to persistent sister chromatid interlinks in mitotic chromatin.

An experimental investigation of attraction between knots in a stretched DNA molecule

It has been predicted through simulations that two knots in a stretched polymer will feel an attraction towards one another and will tend to be found in close proximity. Here, we examine data from experiments in which we stretched knotted DNA molecules and investigate a subset which contained two or more knots. In contrast to the expected behavior of an isolated knot in an elongational field, we observe that pairs of knots move towards each other from distant sections of the molecule. After meeting, pairs of knots fluctuate in and out of visual contact, and can remain in proximity for minutes at a time. Our experimental results suggest that knots on an extended polymer experience an attractive interaction.

Compression and Stretching of Single DNA Molecules under Channel Confinement.

We study the compression and extension response of single dsDNA (double-stranded DNA) molecules confined in cylindrical channels by means of Monte Carlo simulations. The elastic response of micrometer-sized DNA to the external force acting through the chain ends or through the piston is markedly affected by the size of the channel. The interpretation of the force (f)-displacement (R) functions under quasi-one-dimensional confinement is facilitated by resolving the overall change of displacement ΔR into the confinement contribution ΔRD and the force contribution ΔRf. The external stretching of confined DNA results in a characteristic pattern of f-R functions involving their shift to the larger extensions due to the channel-induced pre-stretching ΔRD. A smooth end-chain compression into loop-like conformations observed in moderately confined DNA can be accounted for by the relationship valid for a Gaussian chain in bulk. In narrow channels, the considerably pre-stretched DNA molecules abruptly buckle on compression by the backfolding into hairpins. On the contrary, the piston compression of DNA is characterized by a gradual reduction of the chain span S and by smooth f-S functions in the whole spatial range from the 3d near to 1d limits. The observed discrepancy between the shape of the f-R and f-S functions from two compression methods can be important for designing nanopiston experiments of compaction and knotting of single DNA in nanochannels.