Are TADs supercoiled?

Topologically associating domains (TADs) are megabase-sized building blocks of interphase chromosomes in higher eukaryotes. TADs are chromosomal regions with increased frequency of internal interactions. On average a pair of loci separated by a given genomic distance contact each other 2-3 times more frequently when they are in the same TAD as compared to a pair of loci located in two neighbouring TADs. TADs are also functional blocks of chromosomes as enhancers and their cognate promoters are normally located in the same TAD, even if their genomic distance from each other can be as large as a megabase. The internal structure of TADs, causing their increased frequency of internal interactions, is not established yet. We survey here experimental studies investigating presence of supercoiling in interphase chromosomes. We also review numerical simulation studies testing whether transcription-induced supercoiling of chromatin fibres can explain how TADs are formed and how they can assure very efficient interactions between enhancers and their cognate promoters located in the same TAD.

Transcription-induced supercoiling as the driving force of chromatin loop extrusion during formation of TADs in interphase chromosomes.

Using molecular dynamics simulations, we show here that growing plectonemes resulting from transcription-induced supercoiling have the ability to actively push cohesin rings along chromatin fibres. The pushing direction is such that within each topologically associating domain (TAD) cohesin rings forming handcuffs move from the source of supercoiling, constituted by RNA polymerase with associated DNA topoisomerase TOP1, towards borders of TADs, where supercoiling is released by topoisomerase TOPIIB. Cohesin handcuffs are pushed by continuous flux of supercoiling that is generated by transcription and is then progressively released by action of TOPIIB located at TADs borders. Our model explains what can be the driving force of chromatin loop extrusion and how it can be ensured that loops grow quickly and in a good direction. In addition, the supercoiling-driven loop extrusion mechanism is consistent with earlier explanations proposing why TADs flanked by convergent CTCF binding sites form more stable chromatin loops than TADs flanked by divergent CTCF binding sites. We discuss the role of supercoiling in stimulating enhancer promoter contacts and propose that transcription of eRNA sends the first wave of supercoiling that can activate mRNA transcription in a given TAD.

Transcription-induced supercoiling explains formation of self-interacting chromatin domains in S. pombe.

The question of how self-interacting chromatin domains in interphase chromosomes are structured and generated dominates current discussions on eukaryotic chromosomes. Numerical simulations using standard polymer models have been helpful in testing the validity of various models of chromosome organization. Experimental contact maps can be compared with simulated contact maps and thus verify how good is the model. With increasing resolution of experimental contact maps, it became apparent though that active processes need to be introduced into models to recapitulate the experimental data. Since transcribing RNA polymerases are very strong molecular motors that induce axial rotation of transcribed DNA, we present here models that include such rotational motors. We also include into our models swivels and sites for intersegmental passages that account for action of DNA topoisomerases releasing torsional stress. Using these elements in our models, we show that transcription-induced supercoiling generated in the regions with divergent-transcription and supercoiling relaxation occurring between these regions are sufficient to explain formation of self-interacting chromatin domains in chromosomes of fission yeast (S. pombe).

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.

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.

Effects of physiological self-crowding of DNA on shape and biological properties of DNA molecules with various levels of supercoiling.

DNA in bacterial chromosomes and bacterial plasmids is supercoiled. DNA supercoiling is essential for DNA replication and gene regulation. However, the density of supercoiling in vivo is circa twice smaller than in deproteinized DNA molecules isolated from bacteria. What are then the specific advantages of reduced supercoiling density that is maintained in vivo? Using Brownian dynamics simulations and atomic force microscopy we show here that thanks to physiological DNA-DNA crowding DNA molecules with reduced supercoiling density are still sufficiently supercoiled to stimulate interaction between cis-regulatory elements. On the other hand, weak supercoiling permits DNA molecules to modulate their overall shape in response to physiological changes in DNA crowding. This plasticity of DNA shapes may have regulatory role and be important for the postreplicative spontaneous segregation of bacterial chromosomes.

Spectral characteristics of carbonyl substituted 2,2'-bithiophenes in polymer matrices and low polar solvents.

The spectral characteristics of monosubstituted derivatives of 2,2'-bithiophene (1-BT) with simple carbonyl substituents, including -COCF3 (trifluoroacetyl, 2-BTCF), -COCH2CN (oxopropanenitrile, 3-BTCN) and -COCH3 (acetyl, 4-BTCE), and the more complex 5'-((9H-fluoren-9-ylidene)methyl)-3-methyl, 5-methyl carboxylate (5-BTFL) were investigated. Absorption and fluorescence spectra and fluorescence lifetimes were measured in solvents with various polarities and compared with those in polymer matrices (polystyrene, PS; polymethyl methacrylate, PMMA; and polyvinyl chloride, PVC). Although the parent, 1-BT, absorbed near 300 nm and exhibited no or weak fluorescence, the substitution of 1-BTwith simple substituents at position 5 resulted in a bathochromic shift of approximately 50 nm or more in absorption and distinct fluorescence above 400 nm. The largest shift in absorption and fluorescence was observed for the complex 5-BTFL with fluorene as a substituent for 1-BT. The most intense fluorescence was observed for the derivative 2-BTCF with trifluoroacetyl as a substituent in the polar PVC matrix. The lifetimes of fluorescence of all substituted 2,2'-bithiophenes were in the range from 0.3 to 3 ns. The polymer matrices increased the intensity of fluorescence to some extent and prolonged the lifetime of the 2,2'-bithiophene derivatives. The reasons for the variation in the fluorescence intensity resulting from the substitution of the parent dimer are discussed.

Segregation of semiflexible macromolecules in nanochannel.

Investigation of segregation of polymer coils in open channel was extended relative to previous studies from flexible chains to semiflexible chains. Our results are based on simulation of confinement free energy of a chain in channel and on direct simulation of coil segregation process. For confinement free energy, we confirm the predicted opposite trend with increasing chain stiffness for the weak and for strong confinement regimes. Results of two different approaches are consistent, in agreement with theoretical analysis and indicate a stronger segregation tendency of flexible chains in channel relative to semiflexible chains both in its extent and dynamics.

Knot Formation on DNA Pushed Inside Chiral Nanochannels.

We performed coarse-grained molecular dynamics simulations of DNA polymers pushed inside infinite open chiral and achiral channels. We investigated the behavior of the polymer metrics in terms of span, monomer distributions and changes of topological state of the polymer in the channels. We also compared the regime of pushing a polymer inside the infinite channel to the case of polymer compression in finite channels of knot factories investigated in earlier works. We observed that the compression in the open channels affects the polymer metrics to different extents in chiral and achiral channels. We also observed that the chiral channels give rise to the formation of equichiral knots with the same handedness as the handedness of the chiral channels.

Knot Factories with Helical Geometry Enhance Knotting and Induce Handedness to Knots.

We performed molecular dynamics simulations of DNA polymer chains confined in helical nano-channels under compression in order to explore the potential of knot-factories with helical geometry to produce knots with a preferred handedness. In our simulations, we explore mutual effect of the confinement strength and compressive forces in a range covering weak, intermediate and strong confinement together with weak and strong compressive forces. The results find that while the common metrics of polymer chain in cylindrical and helical channels are very similar, the DNA in helical channels exhibits greatly different topology in terms of chain knottedness, writhe and handedness of knots. The results show that knots with a preferred chirality in terms of average writhe can be produced by using channels with a chosen handedness.

The free volume of poly(vinyl methylether) as computed in a wide temperature range and at length scales up to the nanoregion.

In the present work, we focus on the free volume evaluations from different points of view, including the aspect of probe sizes, temperature, and cavity threshold. The free volume structure is analyzed on structures of poly(vinyl methylether) prepared by fully atomistic molecular dynamics. At first, the temperature behavior of an overall free volume and a free volume separated into individual cavities is shown. The origin of large free volume cavities is explained. A complex view on the cavity number is provided, while a complicated behavior previously observed is now explained. The number of large cavities remained almost constant with the temperature. Oppositely, the number of small cavities related to the atomic packing changes with temperature in a distinct way for glassy and supercooled regions. The cavity number maxima determine a percolation threshold according to percolation theory. The change in polymer properties with temperature can be related to a percolation of the free volume according to the free volume theory, when proper probe radii ∼0.8 Å are used for its observation. A construction of probabilistic distribution of free volume sizes is suggested. The free volume distributions reported here are bimodal. The bimodal character is explained by two different packings--atomic and segmental--forming a prepeak and a main peak on the distribution. Further attention is dedicated to comparisons of the computed free volume sizes and the ortho-positronium (o-Ps) lifetimes. The prepeak of the free volume distribution is probably unseen by o-Ps because of a cavity threshold limit. The effect of the shape factor on the computed o-Ps lifetimes is tested. The quasicavities obtained by redistributing the free volume maintain the ratio of the main dimensions with temperature. Finally, novel data on the cavity environment are provided, while it is suggested how these can be useful with the recent developments in the positron annihilation methods. The coordination number of large cavities with the polymer segments is around 1, as predicted in the free volume theory. Similarly to the percolation and the cavity number, the coordination number exhibits a change when explored by a suitable probe radius ∼0.8 Å. The insightful visualizations showed properties of interest investigated within the actual work.

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.

Entropic Competition between Supercoiled and Torsionally Relaxed Chromatin Fibers Drives Loop Extrusion through Pseudo-Topologically Bound Cohesin.

We propose a model for cohesin-mediated loop extrusion, where the loop extrusion is driven entropically by the energy difference between supercoiled and torsionally relaxed chromatin fibers. Different levels of negative supercoiling are controlled by varying imposed friction between the cohesin ring and the chromatin fiber. The speed of generation of negative supercoiling by RNA polymerase associated with TOP1 is kept constant and corresponds to 10 rotations per second. The model was tested by coarse-grained molecular simulations for a wide range of frictions between 2 to 200 folds of that of generic fiber and the surrounding medium. The higher friction allowed for the accumulation of higher levels of supercoiling, while the resulting extrusion rate also increased. The obtained extrusion rates for the given range of investigated frictions were between 1 and 10 kbps, but also a saturation of the rate at high frictions was observed. The calculated contact maps indicate a qualitative improvement obtained at lower levels of supercoiling. The fits of mathematical equations qualitatively reproduce the loop sizes and levels of supercoiling obtained from simulations and support the proposed mechanism of entropically driven extrusion. The cohesin ring is bound on the fibers pseudo-topologically, and the model suggests that the topological binding is not necessary.

The free-volume structure of a polymer melt, poly(vinyl methylether) from molecular dynamics simulations and cavity analysis.

In this work we analyze and compare the free volume of a polymer system poly(vinyl methylether) (PVME) at 300 K obtained by the two direct but different approaches: Positron annihilation lifetime spectroscopy (PALS) and computer simulations. The free volume is calculated from the simulated cells of PVME by means of numerical methods based on grid scanning and probing the structure with a probe of a given radius R(P). The free-volume structure was found to be percolated for small probes at R(P)=0.53 A. As the probe radius increases, the cavity structure breaks into isolated cavities, reaching a maximum of the cavity number at R(P)=0.78 A. We further develop methods for a geometrical analysis of the free-volume cavities by considering their shape. The geometrical computations show that the cavities have elongated shape with side-to-length ratio corresponding to approximately 1:0.55 and with an average length of 6 A. Based on the overlap between the computed cavities and simplified geometrical representations, the best match of the cavity shape is obtained for the approximation to the ellipsoidal shape (overlap on 84.4%). A match with other examined shapes follows the sequence: ellipsoid>cylinder>bar>sphere>cube. Finally, the computed geometrical parameters are used as input parameters into the quantum-mechanical models for the orthopositronium (o-Ps) lifetime in various free-volume hole geometries. Comparison with the experimental data gives support for two ideas about the existence of an o-Ps particle in the polymeric matrix: (i) the positronium cannot localize in a portion of very small cavities; (ii) and in the case of the percolated cavities, several o-Ps particles occupy some subcavities in the same cavity. Additionally, radial distribution functions of the free volume indicate the existence of two kinds of free volume, a structured one, corresponding to interstitial spaces along the polymer chain, and the so-called "bulk free volume," distributed randomly in the structure. PALS measurements seem to be mainly related with this bulk free volume. The cavities represented by the idealized geometries are visualized in three-dimensional space providing a unique representation on the free-volume structures.

Chromatin Loop Extrusion and Chromatin Unknotting.

It has been a puzzle how decondensed interphase chromosomes remain essentially unknotted. The natural expectation is that in the presence of type II DNA topoisomerases that permit passages of double-stranded DNA regions through each other, all chromosomes should reach the state of topological equilibrium. The topological equilibrium in highly crowded interphase chromosomes forming chromosome territories would result in formation of highly knotted chromatin fibres. However, Chromosome Conformation Capture (3C) methods revealed that the decay of contact probabilities with the genomic distance in interphase chromosomes is practically the same as in the crumpled globule state that is formed when long polymers condense without formation of any knots. To remove knots from highly crowded chromatin, one would need an active process that should not only provide the energy to move the system from the state of topological equilibrium but also guide topoisomerase-mediated passages in such a way that knots would be efficiently unknotted instead of making the knots even more complex. We perform coarse-grained molecular dynamics simulations of the process of chromatin loop extrusion involving knotted and catenated chromatin fibres to check whether chromatin loop extrusion may be involved in active unknotting of chromatin fibres. Our simulations show that the process of chromatin loop extrusion is ideally suited to actively unknot, decatenate and demix chromatin fibres in interphase chromosomes.

Molecular Dynamics Simulation of Supercoiled, Knotted, and Catenated DNA Molecules, Including Modeling of Action of DNA Gyrase.

A detailed protocol of molecular dynamics simulations of supercoiled DNA molecules that can be in addition knotted or catenated is described. We also describe how to model ongoing action of DNA gyrase that introduces negative supercoing into DNA molecules. The protocols provide detailed instructions about model parameters, equations of used potentials, simulation, and visualization. Implementation of the model into a frequently used molecular dynamics simulation environment, ESPResSo, is shown step by step.

Arm retraction and escape transition in semi-flexible star polymer under cylindrical confinement.

We studied the structure and dynamics of star-shaped polymers by means of coarse-grained molecular dynamics simulations and analysis of structural transitions of semi-flexible macromolecules confined in nano-channels. The conformation of star arms in narrow channels is given by the channel width, arm flexibility and number of arms aligned together in the given region along the channel. We focused on the conformation transition, where all arms are initially stretched in one direction of the narrow channel and were interested in the process of how individual arms escape into a free volume region of channel. We found that the escape transition does not proceed from arm ends but progresses by extension of a loop starting from the branch point; the arms escape in individual steps and the extension of arms depends on how many arms align in parallel in the channel.