Dušan Račko

Harnessing the topology of ring polymers as a design motif in functional nanomaterials is becoming a promising direction in the field of soft matter. For example, the ring topology of DNA plasmids prevents the relaxation of excess twist introduced to the polymer, instead yielding helical supercoiled structures. In equilibrium semidilute solutions, tightly supercoiled rings relax faster than their torsionally relaxed counterparts, since the looser conformations of the latter allow for rings to thread through each other and entrain through entanglements. Here we use molecular simulations to explore a nonequilibrium scenario, in which a supercoiling agent, akin to gyrase enzymes, rapidly induces supercoiling in the suspensions of relaxed plasmids. The activity of the agent not only alters the conformational topology from open to branched, but also locks in threaded rings into supramolecular clusters, which relax very slowly. Ultimately, our work shows how the polymer topology under nonequilibrium conditions can be leveraged to tune dynamic behavior of macromolecular systems, suggesting a method to create a class of driven materials vitrified by activity.

Understanding of interactions between proteins and grafted hydrophilic polymer layers is crucial in the search for antifouling materials. Experimental techniques often use an external force that pushes a protein against the polymer-coated surface, which differs from the situation in living systems. The comparison of both setups using atomistic molecular dynamics simulations is provided in this work. Poly(ethylene oxide) (PEO) chains grafted onto graphene at different grafting densities interact with a fragment of C1q protein. At the lowest grafting density, contradictory outcomes are achieved, attributed to the restricted space of C1q near the grafted PEO layer. The most favorable interactions between C1q and the PEO layer are obtained for the medium grafting density. The secondary structure of C1q undergoes changes during its interactions with the PEO layer, including destabilization of β-sheets and formation of 3₁₀-helices. The orientation of C1q anchored to graphene also affects the interactions with the PEO layer.

DNA topology is essential for regulating cellular processes and maintaining genome stability, yet it is challenging to quantify due to the size and complexity of topologically constrained DNA molecules. By combining high-resolution Atomic Force Microscopy (AFM) with a new high-throughput automated pipeline, we can quantify the length, conformation, and topology of individual complex DNA molecules with sub-molecular resolution. Our pipeline uses deep-learning methods to trace the backbone of individual DNA molecules and identify crossing points, efficiently determining which segment passes over which. We use this pipeline to determine the structure of stalled replication intermediates from Xenopus egg extracts, including theta structures and late replication products, and the topology of plasmids, knots and catenanes from the E. coli Xer recombination system. We use coarse-grained simulations to quantify the effect of surface immobilisation on twist-writhe partitioning. Our pipeline opens avenues for understanding how fundamental biological processes are regulated by DNA topology.

The topology of DNA plays a crucial role in the regulation of cellular processes and genome stability. Despite its significance, DNA topology remains challenging to determine due to the length and conformational complexity of individual topologically constrained DNA molecules. We demonstrate unparalleled resolution of complex DNA topologies using Atomic Force Microscopy (AFM) in aqueous conditions. We present a new high-throughput automated pipeline to determine DNA topology from raw AFM images, using deep-learning methods to trace the backbone of individual DNA molecules and identify crossing points. Our pipeline efficiently determines which segment passes over which, including the handling of challenging crossings, where the path of each molecule may be harder to resolve. We demonstrate the wider applicability of our tracing method by determining the structure of stalled replication intermediates from Xenopus egg extracts, including theta structures and late replication products. By developing new methodologies to accurately trace the DNA path through every crossing, we determine the topology of plasmids, knots and catenanes from the E. coli Xer recombination system. In doing so we uncover a recurrent depositional effect and reveal its origins using coarse-grained simulations. Our approach is broadly applicable to a range of nucleic acid structures, including those which interact with proteins, and opens avenues for understanding fundamental biological processes which are regulated by or affect DNA topology.

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.

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.

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.

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.