Active Topological Glass Confined within a Spherical Cavity

Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization

Given the wide range of length scales, the analysis of polymer systems often requires coarse-graining, for which various levels of description may be possible depending on the phenomenon under consideration. Here, we provide a super-coarse grained description, where polymers are represented as a succession of mesosopic soft beads which are allowed to overlap with others. We then investigate the phase separation behaviors in a mixture of such homopolymers based on mean-field theory, and discuss universal aspects of the miscibility phase diagram in comparison with the numerical simulation. We also discuss an extension of our analysis to mixtures involving random copolymers, which might be interesting in the context of chromatin organization in a cell nucleus.

Modeling properties of chromosome territories using polymer filaments in diverse confinement geometries

Interphase chromosomes reside within distinct nuclear regions known as chromosome territories (CTs). Recent observations from Hi-C analyses, a method mapping chromosomal interactions, have revealed varied decay in contact probabilities among different chromosomes. Our study explores the relationship between this contact decay and the particular shapes of the chromosome territories they occupy. For this, we employed molecular dynamics (MD) simulations to examine how confined polymers, resembling chromosomes, behave within different confinement geometries similar to chromosome territory boundaries. Our simulations unveil so far unreported relationships between contact probabilities and end-to-end distances varying based on different confinement geometries. These findings highlight the crucial impact of chromosome territories on shaping the larger-scale properties of 3D genome organization. They emphasize the intrinsic connection between the shapes of these territories and the contact behaviors exhibited by chromosomes. Understanding these correlations is key to accurately interpret Hi-C and microscopy data, and offers vital insights into the foundational principles governing genomic organization.

Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement

In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.

Topology-Based Detection and Tracking of Deadlocks Reveal Aging of Active Ring Melts

Connecting the viscoelastic behavior of stressed ring melts to the various forms of entanglement that can emerge in such systems is still an open challenge. Here, we consider active ring melts, where stress is generated internally, and introduce a topology-based method to detect and track consequential forms of ring entanglements, namely, deadlocks. We demonstrate that, as stress accumulates, more and more rings are co-opted in a growing web of deadlocks that entrap many other rings by threading, bringing the system to a standstill. The method ought to help the study of topological aging in more general polymer contexts.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

Migration of active rings in porous media

Inspired by how the shape deformations in active organisms help them to migrate through disordered porous environments, we simulate active ring polymers in two-dimensional random porous media. Flexible and inextensible active ring polymers navigate smoothly through the disordered media. In contrast, semiflexible rings undergo transient trapping inside the pore space; the degree of trapping is inversely correlated with the increase in activity. We discover that flexible rings swell while inextensible and semiflexible rings monotonically shrink upon increasing the activity. Together, our findings identify the optimal migration of active ring polymers through porous media.

Hi-C embedded polymer model of Escherichia coli reveals the origin of heterogeneous subdiffusion in chromosomal loci

Underneath its apparently simple architecture, the circular chromosome of Escherichia coli is known for displaying complex dynamics in its cytoplasm, with past investigations hinting at inherently diverse mobilities of chromosomal loci across the genome. To decipher its origin, we simulate the dynamics of genome-wide spectrum of E. coli chromosomal loci, via integrating its experimentally derived Hi-C interaction matrix within a polymer-based model. Our analysis demonstrates that, while the dynamics of the chromosome is subdiffusive in a viscoelastic media, the diffusion constants are strongly dependent of chromosomal loci coordinates and diffusive exponents (α) are widely heterogenous with α ≈ 0.36-0.60. The loci-dependent heterogeneous dynamics and mean first-passage times of interloci encounter were found to be modulated via genetically distant interloci communications and is robust even in the presence of active, ATP-dependent noises. Control investigations reveal that the absence of Hi-C-derived interactions in the model would have abolished the traits of heterogeneous loci diffusion, underscoring the key role of loci-specific genetically distant interaction in modulating the underlying heterogeneity of the loci diffusion.