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The chromosome of Escherichia coli is riddled with multi-faceted complexity. The emergence of chromosome conformation capture techniques are providing newer ways to explore chromosome organization. Here we combine a beads-on-a-spring polymer-based framework with recently reported Hi–C data for E. coli chromosome, in rich growth condition, to develop a comprehensive model of its chromosome at 5 kb resolution. The investigation focuses on a range of diverse chromosome architectures of E. coli at various replication states corresponding to a collection of cells, individually present in different stages of cell cycle. The Hi–C data-integrated model captures the self-organization of E. coli chromosome into multiple macrodomains within a ring-like architecture. The model demonstrates that the position of oriC is dependent on architecture and replication state of chromosomes. The distance profiles extracted from the model reconcile fluorescence microscopy and DNA-recombination assay experiments. Investigations into writhe of the chromosome model reveal that it adopts helix-like conformation with no net chirality, earlier hypothesized in experiments. A genome-wide radius of gyration map captures multiple chromosomal interaction domains and identifies the precise locations of rrn operons in the chromosome. We show that a model devoid of Hi–C encoded information would fail to recapitulate most genomic features unique to E. coli.

The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model.

The properties of knots are exploited in a range of applications, from shoelaces to the knots used for climbing, fishing and sailing1. Although knots are found in DNA and proteins2, and form randomly in other long polymer chains3,4, methods for tying5 different sorts of knots in a synthetic nanoscale strand are lacking. Molecular knots of high symmetry have previously been synthesized by using non-covalent interactions to assemble and entangle molecular chains6-15, but in such instances the template and/or strand structure intrinsically determines topology, which means that only one type of knot is usually possible. Here we show that interspersing coordination sites for different metal ions within an artificial molecular strand enables it to be tied into multiple knots. Three topoisomers-an unknot (01) macrocycle, a trefoil (31) knot6-15, and a three-twist (52) knot-were each selectively prepared from the same molecular strand by using transition-metal and lanthanide ions to guide chain folding in a manner reminiscent of the action of protein chaperones16. We find that the metal-ion-induced folding can proceed with stereoinduction: in the case of one knot, a lanthanide(III)-coordinated crossing pattern formed only with a copper(I)-coordinated crossing of particular handedness. In an unanticipated finding, metal-ion coordination was also found to translocate an entanglement from one region of a knotted molecular structure to another, resulting in an increase in writhe (topological strain) in the new knotted conformation. The knot topology affects the chemical properties of the strand: whereas the tighter 52 knot can bind two different metal ions simultaneously, the looser 31 isomer can bind only either one copper(I) ion or one lutetium(III) ion. The ability to tie nanoscale chains into different knots offers opportunities to explore the modification of the structure and properties of synthetic oligomers, polymers and supramolecules.

Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that rotation is necessary for the accumulation of DNA writhe and for the chiral organization of the genome. We observe that although in the initial steps of the packaging reaction, the torsional strain of the genome is released by rotation of the molecule, in the later stages, it is released by the accumulation of writhe. We suggest that the molecular motor plays a key role in determining the final structure of the encapsidated genome in bacteriophages.

It's knot what you know Why is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the stability of knots and find links between topological parameters (twist charge, crossing numbers, handedness) and mechanical stability. The theory is confirmed using simulations and experiments on color-changing fibers that optically show localized stress differences in different parts of the knot as the two strands are pulled apart. The authors show why some common knots slip easily and untie, whereas others hold tight. Science , this issue p. 71

Assemblies of structural maintenance of chromosomes (SMC) proteins and kleisin subunits are essential to chromosome organization and segregation across all kingdoms of life. While structural data exist for parts of the SMC−kleisin complexes, complete structures of the entire complexes have yet to be determined, making mechanistic studies difficult. Using an integrative approach that combines crystallographic structural information about the globular subdomains, along with coevolutionary information and an energy landscape optimized force field (AWSEM), we predict atomic-scale structures for several tripartite SMC−kleisin complexes, including prokaryotic condensin, eukaryotic cohesin, and eukaryotic condensin. The molecular dynamics simulations of the SMC−kleisin protein complexes suggest that these complexes exist as a broad conformational ensemble that is made up of different topological isomers. The simulations suggest a critical role for the SMC coiled-coil regions, where the coils intertwine with various linking numbers. The twist and writhe of these braided coils are coupled with the motion of the SMC head domains, suggesting that the complexes may function as topological motors. Opening, closing, and translation along the DNA of the SMC−kleisin protein complexes would allow these motors to couple to the topology of DNA when DNA is entwined with the braided coils.

DNA supercoiling, where the DNA strand forms a writhe to relieve torsional stress, plays a vital role in packaging the genetic material in cells. Experiment, simulation, and theory have all demonstrated how supercoiling emerges due to the over- or underwinding of the DNA strand. Nucleoid-associated proteins (NAPs) help structure DNA in prokaryotes, yet the role that they play in the supercoiling process has not been as thoroughly investigated. We develop a coarse-grained simulation to model DNA supercoiling in the presence of proteins, providing a rigorous physical understanding of how NAPs affect supercoiling behavior. Specifically, we demonstrate how the force and torque necessary to form supercoils are affected by the presence of NAPs. NAPs that bend DNA stabilize the supercoil, thus shifting the transition between extended and supercoiled DNAs. We develop a theory to explain how NAP binding affects DNA supercoiling. This provides insight into how NAPs modulate DNA compaction via a combination of supercoiling and local protein-dependent deformations.

For a real algebraic link in $${{\mathbb {RP}}}^3$$, we prove that its encomplexed writhe (an invariant introduced by Viro) is maximal for a given degree and genus if and only if its self-linking number with respect to the framing by the osculating planes is maximal for a given degree.

We have investigated the structure of the most compact 30-nm chromatin fibres by modelling those with 2-start or 1-start crossed-linker organisations. Using an iterative procedure we obtained possible structural solutions for fibres of the highest possible compaction permitted by physical constraints, including the helical repeat of linker DNA. We find that this procedure predicts a quantized nucleosome repeat length (NRL) and that only fibres with longer NRLs (≥197 bp) can more likely adopt the 1-start organisation. The transition from 2-start to 1-start fibres is consistent with reported differing binding modes of the linker histone. We also calculate that in 1-start fibres the DNA constrains more torsion (as writhe) than 2-start fibres with the same NRL and that the maximum constraint obtained is in accord with previous experimental results. We posit that the coiling of the fibre is driven by overtwisting of linker DNA which, in the most compact forms - for example, in echinoderm sperm and avian erythrocytes - could adopt a helical repeat of ∼10 bp/turn. We argue that in vivo the total twist of linker DNA could be modulated by interaction with other abundant chromatin-associated proteins and by epigenetic modifications of the C-terminal tail of linker histones.

We employ reconnection-capable, vortex filament methods and finite-volume, Navier–Stokes flow solvers to investigate the topological and helicity dynamics of vortex links for medium and high Reynolds numbers. Our vortex-dynamical model is based on discretization of vortex tubes into bundles of numerical analogues of vortex lines. Due to their nearly singular nature, the numerical vortex lines have topological writhe but not twist. By means of our reconnecting vortex tube model, it is shown that the helicity of a vortex link is conserved during the unknotting process. The dynamics of linking and writhe topological measures indicate that most of the initial linking becomes writhe during the post-reconnection evolution. The helicity spectra of the vortex link present alternating-sign helicity fluctuations at all (potential flow) scales up to the vortex core. At pre-reconnection times, these fluctuations are damped by Biot–Savart vortex stretching and helicity becomes single signed. The post-reconnection spectra indicate an inverse helicity cascade corresponding to the creation of a homogenized vortex blob, a process reminiscent of coherent structure formation in turbulence. An accompanying Navier–Stokes calculation of vortex link dynamics at Reynolds numbers Re=1500 confirms the post-reconnection transformation of linking into different topological measures, the pre-reconnection damping of helicity spectra fluctuations and the spectral shift to low wavenumbers at post-reconnection times. Due to viscous dissipation action, however, this shift is accompanied by progressive reduction of helicity peak values.

The common sense regarding twisting or untwisting a ribbon is that it requires the application of an external rotation to happen. However, at nanoscale, the application of precise amounts of rotation on a nanoribbon is not a trivial task. Here, the concept of an alternative method to add twist to or remove twist from a twisted graphene nanoribbon (TGNR) without rotation is presented. The method consists of suspending a TGNR on two separate substrates and by changing only their distance, the total amount of twist of the TGNR is shown to change. The possibility to fine-tuning the amount of twist of a TGNR is also shown. The concept is demonstrated through fully atomistic molecular dynamics simulations and numerical calculations of the topological parameters twist and writhe of a TGNR. It is shown that the above process satisfies the so-called linking number theorem of space curves. Besides being experimentally feasible, this concept reveals a new kind of twist to writhe transition phenomenon that is tension-free and does not require controlling neither the nanoribbon end-to-end distance nor its critical twist density., This is the submitted version of the paper, that was published in PRB

We study the effect of transcription on the kinetics of DNA supercoiling in three dimensions by means of Brownian dynamics simulations of a single-nucleotide–resolution coarse-grained model for double-stranded DNA. By explicitly accounting for the action of a transcribing RNA polymerase (RNAP), we characterize the geometry and nonequilibrium dynamics of the ensuing twin supercoiling domains. Contrary to the typical textbook picture, we find that the generation of twist by RNAP results in the formation of plectonemes (writhed DNA) some distance away. We further demonstrate that this translates into an “action at a distance” on DNA-binding proteins; for instance, positive supercoils downstream of an elongating RNAP destabilize nucleosomes long before the transcriptional machinery reaches the histone octamer. We also analyze the relaxation dynamics of supercoiled double-stranded DNA, and characterize the widely different timescales of twist diffusion, which is a simple and fast process, and writhe relaxation, which is much slower and entails multiple steps.

DNA topoisomerase VI (topo VI) is a type IIB DNA topoisomerase found predominantly in archaea and some bacteria, but also in plants and algae. Since its discovery, topo VI has been proposed to be a DNA decatenase, however robust evidence and a mechanism for its preferential decatenation activity was lacking. Using single-molecule magnetic tweezers measurements and supporting ensemble biochemistry, we demonstrate that Methanosarcina mazei topo VI preferentially unlinks, or decatenates, DNA crossings, in comparison to relaxing supercoils, through a preference for certain DNA crossing geometries. In addition, topo VI demonstrates a dramatic increase in ATPase activity, DNA binding and rate of strand passage, with increasing DNA writhe, providing further evidence that topo VI is a DNA crossing sensor. Our study strongly suggests that topo VI has evolved an intrinsic preference for the unknotting and decatenation of interlinked chromosomes by sensing and preferentially unlinking DNA crossings with geometries close to 90°.

Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive amino acids along the protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in Plaxco et al. (2000).

This paper proposes to enrich robot motion data with trajectory curvature information. To do so, we use an approximate implementation of a topological feature named writhe, which measures the curling of a closed curve around itself, and its analog feature for two closed curves, namely the linking number. Despite these features have been established for closed curves, their definition allows for a discrete calculation that is well-defined for non-closed curves and can thus provide information about how much a robot trajectory is curling around a line in space. Such lines can be predefined by a user, observed by vision or, in our case, inferred as virtual lines in space around which the robot motion is curling. We use these topological features to augment the data of a trajectory encapsulated as a Movement Primitive (MP). We propose a method to determine how many virtual segments best characterize a trajectory and then find such segments. This results in a generative model that permits modulating curvature to generate new samples, while still staying within the dataset distribution and being able to adapt to contextual variables., Thiswork has been carried out within the projectCLOTHILDE (“CLOTH manIpulation Learning from DEmonstrations”) funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Advanced Grant agreementNo 741930).Research at IRI is also supported by the Spanish State Research Agency through theMaría de Maeztu Seal of Excellence to IRI MDM-2016-0656.

Several classification systems of the spinal curves in adolescent idiopathic scoliosis (AIS) have been developed to guide surgical decision-making. The current classification systems are based on the spinal deformity patterns or deformity magnitudes in one or two anatomical planes. Considering the 3D nature of the spinal deformity in AIS, these classifications fail to capture the spine's curve in its entirety. We proposed a classification based on the axial plane and showed that mathematical analysis of the 3D spinal curve, using differential geometry, supports the differences between the subtypes in this classification system. We calculated the writhe and twist of the entire spinal centerline, elements of the Calugareanu-White-Fuller theorem, in a cohort of 30 right thoracic AIS patients. We also classified this cohort manually based on the vertebral level at which the direction of vertebral rotation caudal to the thoracic curve changes: Lumbar in Group I (V-shaped axial projection) or thoracolumbar in Group II (S-shaped axial projection). The writhe and twist of the spinal curve were significantly different between these manual classification subgroups. Our manual classification distinguished the axial subgroups of right thoracic AIS supported by mathematical specifications of the entire curve in three dimensions. Graphical abstract.

It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due to the fact that reduced alternating link diagrams of the same link are obtainable from each other via flypes and flypes do not change writhe. In this paper, we introduce several quantities that are derived from Seifert graphs of reduced alternating link diagrams. We prove that they are "writhe-like" invariants in the sense that they are also link invariants among reduced alternating link diagrams. The determination of these invariants are elementary and non-recursive so they are easy to calculate. We demonstrate that many different alternating links can be easily distinguished by these new invariants, even for large, complicated knots for which other invariants such as the Jones polynomial are hard to compute. As an application, we also derive an if and only if condition for a strongly invertible rational link., 16 pages, 18 figures

We introduce the Writhe Application Software Package (WASP) which can be used to characterisze the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterization is achieved by the general twist–writhe decomposition of both open and closed ribbons, in particular through a quantity termed the polar writhe. We demonstrate how this decomposition is far more natural and straightforward than artificial closure methods commonly utilized in DNA modelling. In particular, we demonstrate how the decomposition of the polar writhe into local and non-local components distinctly characterizes the local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As example applications, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations, and it is shown that the decomponsition into local and non-local components is particularly important for the detection of plectonemes. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.

Spinal deformities in adolescent idiopathic scoliosis (AIS) are measured on 2D radiographs. Due to the 3D nature of the curve in AIS, such 2D measurements fail to differentiate between the true curve patterns, which in turn may adversly impact the clinical care and surgical planning. The use of 3D models of the spinal radiographs largely remains limited to the 3D measurements of the 2D parameters. The use of the true 3D variables of the spinal curves in describing the differences between the AIS patients is not fully explored. A cohort of 141 Lenke 1 AIS with two-view spinal stereoradiographs and 3D models of the spines were included. The 3D model of the spine was used to determine the spinal centerlines. The writhe and torsion of the 3D centerlines, which, respectively, quantify the coiling and twist of the curve, were calculated using differential geometry. Patients were clustered based on the writhe and torsion values to determine the patient groups with significantly different 3D curve characteristics. The relationship between the writhe and torsion was statistically determined. The distribution of the writhe and torsion groups between the lumbar modifier types was determined. Two writhe and two torsion clusters were determined. Lumbar orientation of plane of maximum curvature (PMC) was significantly different between the torsion clusters and thoracic and lumbar PMC and thoracic Cobb angles were significantly different between the writhe groups, p

Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we consider a duality between lattice fermions and bosons in (2+1) spacetime dimensions, relating free massive Dirac fermions to Abelian Chern-Simons Higgs (ACSH) bosons. To establish the duality we represent the exact partition function of the lattice fermions in terms of the writhe of fermionic worldlines. On the bosonic side the partition function is expressed in the writhe of the vortex loops of the particle-vortex dual of the ACSH Lagrangian. In the continuum and scaling limit we show these to be identical. This result can be understood from the closed fermionic worldlines being direct mappings of the ACSH vortex loops, with the writhe keeping track of particle statistics., Comment: 13 pages, 4 figures; v2 matches published version

We develop a general method for constructing knotted flux tubes with finite thickness, arbitrary shape and tunable twist. The central axis of the knotted tube is specified by a smooth and non-degenerate parametric equation. The helicity of the corresponding solenoidal knotted field can be explicitly decomposed into writhe, normalized total torsion and intrinsic twist. We construct several knotted magnetic flux tubes with various twisting degrees, and investigate the effect of twist on their evolution in resistive magnetohydrodynamic flows using direct numerical simulation. For large twist, the magnetic knot gradually shrinks to a tight stable state, similar to the relaxation process in ideal magnetohydrodynamic flows. For small twist, the knotted flux tube splits at early times, accompanied by a rising magnetic dissipation rate. We elucidate the mechanism of the tube splitting using the phase portrait of the Lorentz force projected onto divergence-free space. For finite twist, the Hopf bifurcation from an unstable spiral point to a limit cycle occurs on the phase plane. In the evolution, field lines inside the limit cycle form invariant tori, whereas they become chaotic outside the limit cycle.

A fundamental process in a plasma is the magnetic reconnection of one pair of flux tubes (such as solar coronal loops) to produce a new pair. During this process magnetic helicity is conserved, but mutual helicity can be transformed to self-helicity, so that the new tubes acquire twist. However, until recently, when Wright (Astrophys. J.878, 102, 2019) supplied a solution, the partition of self-helicity between the two tubes was an outstanding puzzle. Here we examine Wright’s result in detail and apply it to a variety of cases. The simplest case, which Wright himself used to illustrate the result, is that of thin ribbons or flux sheets. We first explicitly apply his method to the usually expected standard case (when the tubes approach one another without twisting before reconnection) and confirm his result is valid for flux sheaths and tubes as well as sheets.For the reconnection of sheets, it is shown that the orientation of the sheets needs to be chosen carefully. For flux sheaths and tubes, Wright’s results are demonstrated to hold for the standard case. There is both a local and a global aspect to the effect of reconnection. The local effect of reconnection is to produce an equipartition of the added self-helicity (and therefore of twist), but the extra global effect of the location and orientation of the feet of the sheet, shell or tube in general adds different amounts of magnetic helicity to the two structures.It is important, as Wright realized, to account for any twist or writhe already existing in the fluxes prior to reconnection. Here we show explicitly that, if a section of a flux sheet is twisted by a multiple of $\pi $π with its ends held fixed and is then reconnected with another sheet, then the effect of the reconnection is to add that multiple of $\pi $π to one sheet and subtract it from the other, while conserving the total helicity. If, on the other hand, the central part of a flux sheath is twisted before reconnection by any angle, then the effect of reconnection is to add that amount of twist to one sheath and subtract it from the other, while conserving the total helicity. Thus, for the local part of the process in both sheets and sheaths, there is no longer helicity equipartition.Finally, we apply Wright’s results explicitly to flux tubes, and in particular to determine the twist that is acquired by an erupting flux rope due to reconnection during an eruptive solar flare or coronal mass ejection.

In this paper we give two new criteria of detecting the checkerboard colorability of virtual links by using odd writhe and arrow polynomial of virtual links, respectively. By applying new criteria, we prove that 6 virtual knots are not checkerboard colorable, leaving only one virtual knot whose checkerboard colorability is unknown among all virtual knots up to four classical crossings., 16 pages, 17 figures

A new concept for tensile artificial muscles is introduced in which the torsional actuation of a twisted polymer fibre drives a twist to writhe conversion in a serially attached elastomeric fibre. Thermally induced torsional rotation of the twisted fibre caused formation of coils in the elastomeric fibre which resulted in overall muscle length contraction. Theoretical predictions of the muscle strain were developed by means of a modified single-helix theory. Experimental tests were conducted to measure the isotonic contraction strains for elastomeric fibres of different diameters and lengths. A good agreement between the measured and calculated results was found. Practical applicability of this muscle is evaluated by using different mechanical loading conditions. Actuation contraction strains as high as 10% were observed with excellent reversibility. Unlike original coiled fibre tensile actuators, these twist-coil artificial muscles did not require any pre-conditioning cycles. (C) 2018 Elsevier B.V. All rights reserved.

In the 1980’s, knotting in DNA became a fundamental research dimension in the study of the mechanisms by which enzymes act on it. Later, the first compelling identification of knotting in proteins, in 2000, launched the study of knotting in protein structures, and linear macromolecules more generally, following on theoretical efforts of the 1960’s. The linking occurring in structures such as DNA, with the articulation of the relationship between linking, twisting, and writhe, and, more directly, linking in Olympic gels has been of interest to geometers, molecular biologists, and polymer physicists since the 1960’s. More recently, a new mathematical analysis of both global and local facets of knotting and linking is providing promising discoveries. Following a discussion of the topological structures of knotting and linking, we will consider some of their applications, and close with a consideration of new questions that suggest attractive directions for future research.

Supercoiling can alter the form and base pairing of the double helix and directly impact protein binding. More indirectly, changes in protein binding and the stress of supercoiling also influence the thermodynamic stability of regulatory, protein-mediated loops and shift the equilibria of fundamental DNA/chromatin transactions. For example, supercoiling affects the hierarchical organization and function of chromatin in topologically associating domains (TADs) in both eukaryotes and bacteria. On the other hand, a protein-mediated loop in DNA can constrain supercoiling within a plectonemic structure. To characterize the extent of constrained supercoiling, 400 bp, lac repressor-secured loops were formed in extensively over- or under-wound DNA under gentle tension in a magnetic tweezer. The protein-mediated loops constrained variable amounts of supercoiling that often exceeded the maximum writhe expected for a 400 bp plectoneme. Loops with such high levels of supercoiling appear to be entangled with flanking domains. Thus, loop-mediating proteins operating on supercoiled substrates can establish topological domains that may coordinate gene regulation and other DNA transactions across spans in the genome that are larger than the separation between the binding sites.

In this work, we report results from the study of a filament/prominence eruption on 2014 May 4. This eruption belongs to the class of rarely reported causally linked eruptions of two coupled flux tubes (FTs) of a quiet region filament. We made a comparative analysis based on multiwave observations from Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations Observatory (STEREO) A and B combining the high temporal and spatial data taken from three different viewpoints. The main results of the study are as follows: (1) The source of the eruptive prominence consists of two coupled FTs located near the eastern limb: top-located one (FT1) and bottom-located one (FT2). (2) FT1 and FT2 had the same helicity, i.e. left-handed twist and writhe. Their untwisting motion during eruption suggests that kink instability seems to act. (3) The kinematic evolution of the FT1 suggests a slow successful eruption that was associated with a slow CME. (4) The FT2 exhibited failed kinked eruption with a non-radial propagation followed by its reformation. This eruption was accompanied of apparent mass draining in the legs, flare-ribbons and post-flare EUV arcade.