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We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatcially deform and inflate under shear [Liebetreu et al., Commun. Mater. 1, 4 (2020)], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number., Comment: 19 pages, 12 figures; accepted for publication in Nanoscale

Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single ring level, other works show pairs of rings also thread each other - a feature overlooked in the tree theories. Here we reconcile this dichotomy using Monte-Carlo simulations of the ring melts with different bending rigidity. We find that rings are double-folded (more strongly for stiffer rings) on and above the entanglement length scale, while the threadings are localized on smaller scales. The different theories disagree on the details of the tree structure, i.e the fractal dimension of the backbone of the tree. In the stiffer melts we find an indication of a self-avoiding scaling of the backbone, while more flexible chains do not exhibit such a regime. Moreover, the theories commonly neglect threadings, and assign different importance to the impact of the progressive constraint release (tube dilation) on single ring relaxation due to the motion of other rings. Despite each threading creates only a small opening in the double-folded structure, the threading loops can be numerous and their length can exceed substantially the entanglement scale. We link the threading constraints to the divergence of the relaxation time of a ring, if the tube dilation is hindered by pinning a fraction of other rings in space. Current theories do not predict such divergence and predict faster than measured diffusion of rings, pointing at the relevance of the threading constraints in unpinned systems as well. Revision of the theories with explicit threading constraints might elucidate the validity of the conjectured existence of topological glass., Comment: 42 pages, 12 figures in the main text, 6 supplementary figures. Submitted for publication

Motivated by chromosomes enclosed in nucleus and the recently discovered active topological glass, we study a spherically confined melt of long nonconcatenated active polymer rings. Without activity, the rings exhibit the same average large-scale conformational properties as chromatin fiber. Upon activating consecutive monomer segments on the rings, the system arrives at a glassy steady state due to activity-enhanced topological constraints. The latter generate coherent motions of the system, however the resulting large-scale structures are inconsistent with the fractal globule model. We observe microphase separation between active and passive segments without systematic trends in the positioning of active domains within the confining sphere. We find that tank-treading of active segments along the ring contour enhances active-passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Finally, although the present model of partly-active rings is not compatible with the large-scale chromatin organization, our results suggest that the activity-enhanced entanglements that result in facilitated intra- and inter-chromosomal contacts might be relevant for chromatin structure at smaller scales., Comment: 11 pages, 6 figures, 3 tables, supporting information

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes {\it decelerate} with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett. 116, 058301 (2016)] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells., Comment: 18 pages (including main text + supplemental material), 4 main figures + 8 suppl. figures. Submitted for publication

DNA is increasingly employed for bio and nanotechnology thanks to its exquisite versatility and designability. Most of its use is limited to linearised and torsionally relaxed DNA but non-trivial architectures and torsionally constrained -- or supercoiled -- DNA plasmids are largely neglected; this is partly due to the limited understanding of how supercoiling affects the rheology of entangled DNA. To address this open question we perform large scale Molecular Dynamics (MD) simulations of entangled solutions of DNA plasmids modelled as twistable chains. We discover that, contrarily to what generally assumed in the literature, larger supercoiling increases the average size of plasmids in the entangled regime. At the same time, we discover that this is accompanied by an unexpected increase of diffusivity. We explain our findings as due to a decrease in inter-plasmids threadings and entanglement

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer - a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically-tunable bulk rheological properties., Comment: Accepted in ACS Macroletters

Recent theoretical studies found that mixtures of active and passive colloidal particles phase separate but only at very high activity ratio. The high value poses serious obstacles for experimental exploration of this phenomenon. Here we show using simulations that when the active and passive particles are polymers, the critical activity ratio decreases with the polymer length. This not only facilitates the experiments but also has implications on the DNA organization in living cell nuclei. Entropy production can be used as an accurate indicator of this non-equilibrium phase transition.

Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the recently developed Flory theory of unentangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of ring relaxation time and diffusion coefficient with ring length, as well as time dependence of stress relaxation modulus, zero shear viscosity and mean square averaged displacements of both individual monomers and ring's mass center. Our results agree within error bars with all available experimental and simulations data of the ring melt, although the quality of the data so far is insufficient to make a definitive judgment for or against the annealed tree theory. In the end we review briefly the relation between our findings and experimental data on chromatin dynamics., Comment: 12 pages, 8 figures

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically-simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both., Comment: 26 pages, 5 figures Added and updated references, corrected typos. Figures 2 and 4 improved, content remained unchanged. Figure 5 edited to contain only human cell data. Figure captions improved to reflect the changes. Some paragraphs in sections IV B 2, IV B 3, IV D, VI F 2, VII are edited or added for clarity and to be up to date. All results are unchanged

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the basic model is sharply peaked around its mean value. Since the model was originally developed to mimic the social network of acquaintances, to broaden the degree distribution we propose its generalization. We show that when heterogeneity is introduced to the model, it is possible to obtain fat tails of the degree distribution. Meanwhile, the small-world phenomenon present in the basic model is not affected. To support our claims, both analytical and numerical results are obtained., Comment: 6 pages, 4 figures, minor clarifications and references added