Melts of nonconcatenated rings in spherical confinement

Topology-mediated organization of Escherichia coli chromosome in fast-growth conditions

The mechanism underlying the spatiotemporal chromosome organization in Escherichia coli cells remains an open question, though experiments have been able to visually see the evolving chromosome organization in fast- and slow-growing cells. We had proposed [D. Mitra et al., Soft Matter 18, 5615 (2022)1744-683X10.1039/D2SM00734G] that the DNA ring polymer adopts a specific polymer topology as it goes through its cell cycle, which in turn self-organizes the chromosome by entropic forces during slow growth. The fast-growing E. coli cells have four (or more) copies of the replicating DNA, with overlapping rounds of replication going on simultaneously. This makes the spatial segregation and the subsequent organization of the multiple generations of DNA a complex task. Here, we establish that the same simple principles of entropic repulsion between polymer segments which provided an understanding of self-organization of DNA in slow-growth conditions also explains the organization of chromosomes in the much more complex scenario of fast-growth conditions. Repulsion between DNA-polymer segments through entropic mechanisms is harnessed by modifying polymer topology. The ring-polymer topology is modified by introducing crosslinks (emulating the effects of linker proteins) between specific segments. Our simulation reproduces the emergent evolution of the organization of chromosomes as seen in vivo in fluorescent in situ hybridization experiments. Furthermore, we reconcile the mechanism of longitudinal organization of the chromosomes arms in fast-growth conditions by a suitable adaptation of the model. Thus, polymer physics principles, previously used to understand chromosome organization in slow-growing E. coli cells also resolve DNA organization in more complex scenarios with multiple rounds of replication occurring in parallel.

Transient crosslinking controls the condensate formation pathway within chromatin networks

The network structure of densely packed chromatin within the nucleus of eukaryotic cells acts in concert with nonequilibrium processes. Using statistical physics simulations, we explore the control provided by transient crosslinking of the chromatin network by structural-maintenance-of-chromosome (SMC) proteins over (i) the physical properties of the chromatin network and (ii) condensate formation of embedded molecular species. We find that the density and lifetime of transient SMC crosslinks regulate structural relaxation modes and tune the sol-vs-gel state of the chromatin network, which imparts control over the kinetic pathway to condensate formation. Specifically, lower density, shorter-lived crosslinks induce sollike networks and a droplet-fusion pathway, whereas higher density, longer-lived crosslinks induce gellike networks and an Ostwald-ripening pathway.

Active Topological Glass Confined within a Spherical Cavity

We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved "tank-treading" dynamic mode of active segments along the ring contour. This mode can enhance active-passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell.

Intrinsic structure and dynamics of monolayer ring polymer melts

We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.

Multiscale Approaches for Confined Ring Polymer Solutions

We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.