Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type qualitatively determines their nonequilibrium behaviour. We find that activity induces opposite localisation responses in different topological families: torus knots systematically delocalise and inflate, whereas twist knots tighten and remain localised. We trace this divergent behaviour to the distinct symmetry properties of their tangent fields, which control the alignment of active forces along the chain. We show that topology also governs internal and emergent dynamics. Active torus knots behave as soft chiral self-propelled particles exhibiting persistent motion with a well-defined handedness fixed by their topological chirality. In contrast, achiral knots show no net handedness. The knot thus acts as a deformable topological quasiparticle whose morphology and propulsion are selected by topology. These results suggest potential routes toward programmable soft chiral particles with controllable morphology and emergent motility modes.

Strong evolutionary selection has maintained CpG-dense islands (CGIs) at the promoters of constitutively expressed genes throughout the vertebrate genome, suggesting an important role in regulating DNA topology. Here, using Twist-seq, a psoralen-based approach for quantitative genome-wide profiling of DNA supercoiling, we reveal distinct topological states across human gene promoters. We show that CGI promoters accumulate elevated levels of negative supercoiling relative to non-CGI promoters and define localised topological domains at highly transcribed genes. Integrating genome-wide analyses with reaction-diffusion modelling and coarse-grained molecular dynamics simulations, we find that this behaviour is encoded by the intrinsic physical properties of CGI DNA. The GC-rich sequence context promotes nucleosome depletion and focuses torsional stress onto embedded AT-rich pockets, driving localised DNA melting and plectoneme-tip bubble formation within promoter-proximal nucleosome-free regions. This provides an energetically favourable pathway for redistributing transcription-induced torsional stress through transient strand separation and writhe, consistent with increased ssDNA formation at CGI promoters observed by ssDNA-seq. We propose that CGIs function as sequence-encoded topological sinks that buffer supercoiling while maintaining a promoter architecture permissive for transcription initiation, thereby preserving promoter integrity and genome stability.

We investigate, through numerical simulations, the rheology of a dry suspension of deformable droplets under pressure-driven flow. The system exhibits two force-driven dynamical transitions. At low forcing, the suspension behaves as a yield-stress material: below a critical force, droplets remain arrested in an amorphous solid-like state. Our simulations suggest that yielding is controlled by droplet contacts and predict that the critical force strongly depends on deformability. Above yielding, the suspension does not flow steadily but rather enters an intermittent, stick-slip regime characterised by long-lived caging and non-Gaussian velocity fluctuations. This state can be interpreted as a "self-pinned” glass, in which slowly evolving droplet overlaps generate an effective rugged energy landscape that dynamically traps droplets and produces intermittent rearrangements reminiscent of near-critical dynamics in depinning models. At larger forcing, droplets deform sufficiently to continuously exchange neighbours, progressively annealing the overlap structure and driving a dynamic transition to a string-like, flowing state. Our results identify the restructuring of overlap networks as a generic mechanism which controls flow in driven suspensions of deformable particles.

Transcription is a fundamental cellular process, and the first step of gene expression. In human cells, it depends on the binding to chromatin of various proteins, including RNA polymerases and numerous transcription factors (TFs). Observations indicate that these proteins tend to form macromolecular clusters, known as transcription factories, whose morphology and composition is still debated. While some microscopy experiments have revealed the presence of specialised factories, composed of similar TFs transcribing families of related genes, sequencing experiments suggest instead that mixed clusters may be prevalent, as a panoply of different TFs binds promiscuously the same chromatin region. The mechanisms underlying the formation of specialised or mixed factories remain elusive. With the aim of finding such mechanisms, here we develop a chromatin polymer model mimicking the chromatin binding-unbinding dynamics of different types of complexes of TFs. Surprisingly, both specialised (i.e., demixed) and mixed clusters spontaneously emerge, and which of the two types forms depends mainly on cluster size. The mechanism promoting mixing is the presence of non-specific interactions between chromatin and proteins, which become increasingly important as clusters become larger. This result, that we observe both in simple polymer models and more realistic ones for human chromosomes, reconciles the apparently contrasting experimental results obtained. Additionally, we show how the introduction of different types of TFs strongly affects the emergence of transcriptional networks, providing a pathway to investigate transcriptional changes following gene editing or naturally occurring mutations.

Proteins can diffuse micrometers in seconds, yet bacterial cells are able to maintain stable protein gradients. The best studied bacterial protein gradient is the Min system of Escherichia coli . In rod-shaped bacteria the MinCD proteins prevent formation of minicells by inhibiting FtsZ polymerization close to the cell poles. In E. coli these proteins oscillate between cell poles within a minute, resulting in an increased MinCD concentration at the poles. This oscillation is caused by the interaction between MinD and the protein MinE, which form an ATP-driven reaction-diffusion system, whereby the ATPase MinD cycles between a monomeric cytosolic and a dimeric membrane attached states. Bacillus subtilis also has MinCD, but lacks MinE. In this case MinCD form a static gradient that requires the transmembrane protein MinJ, located at cell poles and cell division sites. A recent reaction-diffusion model was successful in recreating the MinD gradient in B. subtilis , assuming that MinD cycles between cytosol and membrane, like in E. coli . Here we show that the monomeric and dimeric states of B. subtilis MinD have comparable membrane affinities, that MinD interacts with MinJ as a dimer, and that MinJ is not required for membrane localization of MinD. Based on these new findings we tested different models, using kinetic Monte Carlo simulations, and found that a difference in diffusion rate between the monomer and dimer, rather than a difference in membrane affinity, is important for B. subtilis MinCD gradient formation.

In this study, we combine coarse-grained Brownian dynamics simulations and mean-field theory to study supercoiling dynamics, as well as the steady-state profiles of twist and writhe, in an open DNA polymer where one of the free ends is subjected to a constant torque. Even though the other end is free, and hence can spin and release torsional stress, we observe that the entire chain transitions between a swollen and a plectonemic phase as the torque increases beyond a critical threshold. In the plectonemic phase, we observe a non-linear twist profile in the steady state, resulting from the mutual interconversion between the injected twist and geometrical writhe, which distributes inhomogeneously along the chain. We also show that the non-equilibrium dynamics of twist accumulation is diffusive, and that writhe diffusion is negligible in this geometry, as plectonemes remain localised near the end that is being rotated. We discuss the feasibility of testing our results with single-molecule experiments.

Many RNA molecules function within confined environments, but the effect of confinement on RNA folding remains poorly understood. Proximity ligation experiments reveal altered long-range contacts in confined versus unconfined states, yet they do not explain how spatial constraints give rise to these differences. Here, we develop a physical modeling approach that incorporates proximity ligation data into coarse-grained molecular dynamics simulations to reconstruct RNA 3D structures under confinement. We test our model on the ~11 kb genome of the Zika virus, comparing the folding in virions (confined) and in cells (unconfined). We observe that the probability of contact between two regions of the genome vs. linear distance follows different scaling laws in the confined and unconfined cases, in agreement with proximity ligation experiments. We find that genome circularization -- an interaction that regulates replication in Zika -- occurs more frequently under confinement in both experiments and simulations. Our model reveals that the formation of long double-stranded stems through stacking confers local nematic liquid crystalline order to the RNA, and predicts pseudoknot topologies consistent with those seen in crystallographic structures of shorter RNAs. These results provide insight into the mechanism through which confinement alters the ensemble of 3D structures accessible to a long RNA molecule. ### Competing Interest Statement The authors have declared no competing interest. Medical Research Council, https://ror.org/03x94j517, Grant MC\_FE\_00035

Understanding how the topology of network forming materials influences their physical properties remains a longstanding challenge. Here, we investigate the topology of experimentally compatible atomistic models of amorphous silica together with the crystalline polymorphs cristobalite and quartz. By comparing multiple atomistic models of amorphous silica that equally reproduce neutron-scattering data, we show that different microscopic descriptions can imply different topological interpretations of glass stability. To characterize the network beyond conventional geometric descriptors, we introduce the linking valence, which quantifies the average number of topological links per network loop. This topological descriptor separates silica into two distinct classes: the mechanically harder quartz exhibit values more than an order of magnitude larger than those of amorphous silica and cristobalite, despite their common tetrahedral building blocks. Spectral analysis of the loop-linking networks provides a complementary distinction, separating amorphous from crystalline phases and revealing differences in the long-range organization of topological constraints. These results establish topological linking as a new framework for connecting the structure and physical properties of network-forming materials.

Abstract Cell-to-cell transcriptional heterogeneity, or noise, is an intrinsic property of the transcriptome with implications for development, disease progression, and aging. Bulk RNA-seq masks this variability by averaging gene expression across cells, whereas single-cell RNA sequencing (scRNA-seq) resolves it. Nevertheless, separating biological noise from technical variance remains challenging, particularly across platforms with different chemistries. We benchmarked two widely adopted technologies, Evercode WT (SPLiT-seq, Parse Biosciences) and Chromium (10x Genomics), on human lymphoblastoid nuclei. Evercode WT achieved targeted sequencing depth and nuclei number far more reliably, and its random-hexamer priming yielded more intronic reads and non-coding RNA genes; Chromium recovered more cells and detected polyadenylated transcripts and cell-line markers more sensitively. Despite these opposing biases, the platforms showed comparable gene detection and strongly correlated expression profiles. Using datasets from both platforms, we defined a noise metric detrended from mean expression and showed that per-gene estimates were reproducible across chemistries. Noise was lower in G2M than in G1 and was most strongly associated with gene length rather than exonic length. Expression of genes with CpG-island promoters was less variable than that of those without. This study establishes a platform-independent basis for quantifying transcriptional noise and a framework for selecting an appropriate scRNA-seq platform. Highlights Parse Evercode WT demonstrates superior predictability in targeted cell recovery and sequencing depth estimations compared to 10x Chromium. Distinct biases: Parse captures intronic sequences; 10x targets polyadenylated mRNA. Detrended transcriptional noise is reproducible across both barcoding chemistries. Noise scales with gene length, not exonic length, and is lower at CGI promoters.

Active processes in living systems generate nonequilibrium forces that deform embedded passive macromolecules. To understand how such dynamics influence polymer conformation, we study a flexible passive chain in an active nematic fluid. Using hybrid simulations, we uncover a length-dependent transition in polymer behavior: long chains align with and stretch along defect-driven flows, while short chains bend and collapse due to localized stresses. These responses are controlled by a competition between the polymer size and the emergent length scale of the active turbulence. Our results reveal a defect-mediated mechanism for conformational control and point toward general physical principles for designing responsive soft materials that couple passive structure to active dynamics.

Defect lines in 3D active nematic systems are intriguing topological singularities whose out-of-equilibrium dynamics remain elusive in confined settings. Here, we numerically study 3D active nematics confined within closed cylinders to elucidate the roles of geometry and activity. We reveal a competition between passive elasticity, which causes localisation of defects near edges, and activity, which endows defects with motility and gives rise to disorderly, delocalised dynamics. Varying boundary curvature, activity strength, and cylinder radius reveals a state space of static and dynamic localisation states, including handle-like configurations and chaotic motion bounded within the cylinder endcap. As activity is tuned to induce delocalisation, we identify phase transition signatures, including pronounced fluctuations and an emergent power law scaling of defect number and average defect length. We find that these scaling properties are strongly altered by confinement: unlike in bulk systems where activity governs length distributions, confinement tunes an activity-independent characteristic length, with an exponent reminiscent of self-avoiding confined polymers. These results establish confinement of inhomogeneous curvature as a versatile mechanism for controlling active topological dynamics.

Lyotropic liquid crystals can display rich phase behavior and self-organization, yet the physical principles underlying their self-assembly into large scale patterns remains understudied. Here, we combine theory, simulations, and experiments on Sunset Yellow-water chromonic mixtures to show that such materials spontaneously phase separate, even without assuming any underlying microscopic attraction between the molecular species. In our minimal model, demixing depends solely on the Onsager-like coupling between local nematogen density and orientational order. If such a coupling is sufficiently strong, nematic defects trigger the nucleation of isotropic droplets, which then coalesce due to elastic or interfacial tensions. We further show that strong anchoring of the director field at the interface arrests this coarsening process, resulting in a stable microphase-separated lamellar pattern. This self-assembled lamellar phase has striking and unusual features, including spontaneous undulations, heterogeneous layer spacing, long-lived glassy defect patterns and lamellar onions. Our results identify orientational-density coupling and elastocapillarity as fundamental mechanisms to guide self-assembly in lyotropic and chromonic liquid crystals.

Abstract Chromatin must fold tightly enough to protect the genome while being sufficiently accessible for DNA dependent processes such as transcription. The physical rules that balance these competing roles remain unclear, as DNA sequence encodes both biochemical information such as transcription factor binding sites, and biophysical cues that shape chromatin structure. Here, using synthetic chromatin fibres assembled from physiologically relevant DNA sequences, we show that nucleosome positioning dictates the material state of chromatin. Heterochromatin-like sequences produce compact fibres stabilised by nucleosome stacking, whereas euchromatin-like sequences generate irregular nucleosome positioning that yields disrupted, heterogeneous, and mechanically deformable fibres. Quantitative polymer modelling reveals that these irregular arrays are highly dynamic, continually sampling a broad ensemble of conformations as nucleosome stacking breaks down. We identify two previously unrecognised thresholds encoded by nucleosome positioning: minimal positional irregularity (2–3 bp) triggers a transition from an ordered paracrystalline state to a liquid-like phase, whereas an order of magnitude greater irregularity (∼18 bp) is required to generate accessibility and mechanical fragility permissive for transcription factor binding. Euchromatin-like arrays reside at this accessibility threshold. These findings indicate that nucleosome positioning tunes chromatin toward or away from critical structural states that couple genome protection, chromatin dynamics, and transcriptional potential—providing a physical mechanism that helps connect DNA sequence to gene expression.

Abstract Existing databases of interphase chromosome conformations typically store three-dimensional coordinates of genomic segments. However, since interphase chromatin is highly dynamic, such databases are dominated by transient configurations and unstructured regions, whose positions vary continuously between cells and over time, unlike folded proteins such as globin, which adopt similar structures in every cell. These drawbacks motivated the inception of a database based on ‘strion’ (a portmanteau of a string capturing str ucture and funct ion ). A strion concisely describes the structure and activity of all transcription units in one cell, by retaining only functionally relevant positional information. Sets of strions describing structures in different cells sampled at different times are compiled into a ‘super-strion’. Then, 46 super-strions summarise the range of structure and activity of a human cell type, including information on all transcription units, how often each co-fires and co-clusters with others in transcription factories/hubs, enhancer interactomes and small-world expression networks. Graphical abstract

The cell nucleus is a dynamic environment where ATP-driven processes - like transcription, replication, and epigenetic modifications - continually drive the genome far from thermodynamic equilibrium. Recent interdisciplinary efforts combining cell biology and physics have introduced coarse-grained polymer models that reveal how these active processes shape chromosome organization in space and time. We review how these models have shed light on selected key features of nuclear function: the maintenance of epigenetic memory, the coupling between transcriptional activity and chromatin motion, and the emergence of replication factories. These approaches provide mechanistic insight and predictive power that are beyond experiments alone. We conclude by outlining future directions toward viewing the genome as an active polymer maintained far from equilibrium.

Bacterial chromosome replication occurs in the absence of a canonical spindle apparatus; yet it reliably produces organised and segregated genomes. While both passive and active mechanisms have been investigated, DNA replication itself is a non-equilibrium process that continuously generates new genetic material and reorganizes the nucleoid. Here, we investigate how replication-driven dynamics, combined with nucleoid-associated protein (NAP) interactions, shape spatiotemporal chromosome organisation using a three-dimensional polymer model that explicitly simulates DNA synthesis. We show that NAP-mediated interactions induce dynamic clustering of DNA, generating density fluctuations in the nucleoid. When coupled to replication, these clusters undergo cycles of stress buildup and release that produce stepwise expansion dynamics consistent with experimental observations. Chromosome segregation occurs naturally in this regime, but only within a finite range of interaction strengths: weak interactions fail to structure the nucleoid, whereas strong interactions hinder replication progression. Within this optimal balance, replication also promotes the spontaneous formation of replication factories. Our results demonstrate that bacterial chromosome organisation can be understood as a non-equilibrium system in which the interplay between replication forces and protein-mediated interactions generates nucleoid mechanics, dynamics, and segregation.

We study the equilibrium properties of a model of magnetic diblock copolymer where each monomer is decorated with an Ising-like spin. Spins interact ferromagnetically within each block and antiferromagnetically across blocks, generating frustration between magnetic ordering and spatial organization. By employing a mean-field approach and Monte Carlo simulations for self-avoiding walks on the cubic lattice, we investigate the system's response to an external magnetic field. We discover a rich phase diagram that includes: a swollen phase with both filaments magnetically disordered and spatially extended; a mixed compact phase characterized by a single globule in which the two filaments are strongly intertwined; a segregated compact phase composed of two globular, magnetically ordered, and spatially separated blocks. Furthermore, if the magnitude of the intra-block ferromagnetic interaction differs between the two blocks, we observe a hybrid segregated ("tadpole") phase where one extended block coexists with a collapsed one. Mean-field predictions of the location of the phase boundaries are in quantitative agreement with Monte Carlo results. These findings provide a minimal statistical-mechanical framework for field-controlled self-assembly of tunable patterns by magnetically heterogeneous polymers, which may also serve as a simple platform for future investigations of the coupling between internal epigenetic-like states and chromatin folding.

Current biophysical models for transcriptionally active chromatin view this as a polymer with sticky sites, mimicking transcription units such as promoters and enhancers which interact via the binding of multivalent complexes of chromatin-binding proteins. It has been demonstrated that this model spontaneously leads to microphase separation, resulting in the formation of a network of loops with transcription units serving as anchors. Here, we demonstrate how to compute the topological weights of loop networks with an arbitrary 1D pattern of transcription units along the fibre (or `polydisperse' loop networks), finding an analogy with networks of electric resistors in parallel or in series. We also show how the BEST (de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte) theorem in combinatorics can be used to find the combinatorial multiplicity of any class of loop networks. Our results can be used to compute the structural diversity, or Shannon entropy, of loop networks: we show that this quantity depends on the 1D patterning of transcription units along the chain, possibly providing a pathway to control transcriptional noise in eukaryotic genes.