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

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.

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

Simple Summary

Chromatin dynamics and chromatin structure are a two-way relationship governed by polymer physics and active biological processes. Thanks to the research in the field of computational biology and modeling, computer simulations became indispensable in studying these complex relationships. It is now generally accepted that looped structures occurring in the intermediate range of ordering of chromatin are formed by a loop extrusion mechanism involving specialized proteins (structural maintenance complexes or SMCs). Although the motor activity of SMCs has been speculated for a long time, the motor activity of cohesin was discovered only recently (Davidson 2019). While evidence of the cohesin’s motor activity is missing, other mechanisms that could efficiently drive the loop extrusion without motor activity of SMCs have been discovered by computer simulations. These mechanisms account for transcriptionally driven loop extrusion or entropically driven loop extrusion by osmotic pressure. In our previous model, we have shown that the cohesin in handcuffed conformation can be pushed mechanically by emerging plectoneme formed during transcription, exerting pressure on the joint section of handcuffs. In the current work, we use coarse-grained molecular simulation to further explore the extrusion driven by supercoiling while employing much lower levels of supercoiling. Moreover, recent works favor non-topological binding of cohesin on fibers, which would solve a range of topological problems while bypassing other molecular machinery sitting on DNA. We show by means of computer simulations that supercoiling can drive loop extrusion without taking advantage of mechanic push on the joint section of cohesin handcuffs. As such, the work addresses current problems in molecular biology and employs advanced methods and original solutions in the study.

Abstract

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.

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.

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.