Vertebrate centromeres in mitosis are functionally bipartite structures stabilized by cohesin.

Centromeres are scaffolds for the assembly of kinetochores that ensure chromosome segregation during cell division. How vertebrate centromeres obtain a three-dimensional structure to accomplish their primary function is unclear. Using super-resolution imaging, capture-C, and polymer modeling, we show that vertebrate centromeres are partitioned by condensins into two subdomains during mitosis. The bipartite structure is found in human, mouse, and chicken cells and is therefore a fundamental feature of vertebrate centromeres. Super-resolution imaging and electron tomography reveal that bipartite centromeres assemble bipartite kinetochores, with each subdomain binding a distinct microtubule bundle. Cohesin links the centromere subdomains, limiting their separation in response to spindle forces and avoiding merotelic kinetochore-spindle attachments. Lagging chromosomes during cancer cell divisions frequently have merotelic attachments in which the centromere subdomains are separated and bioriented. Our work reveals a fundamental aspect of vertebrate centromere biology with implications for understanding the mechanisms that guarantee faithful chromosome segregation.

Ultra-long-range interactions between active regulatory elements.

Contacts between enhancers and promoters are thought to relate to their ability to activate transcription. Investigating factors that contribute to such chromatin interactions is therefore important for understanding gene regulation. Here, we have determined contact frequencies between millions of pairs of cis-regulatory elements from chromosome conformation capture data sets and analyzed a collection of hundreds of DNA-binding factors for binding at regions of enriched contacts. This analysis revealed enriched contacts at sites bound by many factors associated with active transcription. We show that active regulatory elements, independent of cohesin and polycomb, interact with each other across distances of tens of megabases in vertebrate and invertebrate genomes and that interactions correlate and change with activity. However, these ultra-long-range interactions are not dependent on RNA polymerase II transcription or individual transcription cofactors. Using simulations, we show that a model of chromatin and multivalent binding factors can give rise to long-range interactions via bridging-induced clustering. We propose that long-range interactions between cis-regulatory elements are driven by at least three distinct processes: cohesin-mediated loop extrusion, polycomb contacts, and clustering of active regions.

Polymer Simulations of Heteromorphic Chromatin Predict the 3D Folding of Complex Genomic Loci.

Chromatin folded into 3D macromolecular structures is often analyzed by chromosome conformation capture (3C) and fluorescence in situ hybridization (FISH) techniques, but these frequently provide contradictory results. Chromatin can be modeled as a simple polymer composed of a connected chain of units. By embedding data for epigenetic marks (H3K27ac), chromatin accessibility (assay for transposase-accessible chromatin using sequencing [ATAC-seq]), and structural anchors (CCCTC-binding factor [CTCF]), we developed a highly predictive heteromorphic polymer (HiP-HoP) model, where the chromatin fiber varied along its length; combined with diffusing protein bridges and loop extrusion, this model predicted the 3D organization of genomic loci at a population and single-cell level. The model was validated at several gene loci, including the complex Pax6 gene, and was able to determine locus conformations across cell types with varying levels of transcriptional activity and explain different mechanisms of enhancer use. Minimal a priori knowledge of epigenetic marks is sufficient to recapitulate complex genomic loci in 3D and enable predictions of chromatin folding paths.

HMGB2 Loss upon Senescence Entry Disrupts Genomic Organization and Induces CTCF Clustering across Cell Types.

Processes like cellular senescence are characterized by complex events giving rise to heterogeneous cell populations. However, the early molecular events driving this cascade remain elusive. We hypothesized that senescence entry is triggered by an early disruption of the cells' three-dimensional (3D) genome organization. To test this, we combined Hi-C, single-cell and population transcriptomics, imaging, and in silico modeling of three distinct cells types entering senescence. Genes involved in DNA conformation maintenance are suppressed upon senescence entry across all cell types. We show that nuclear depletion of the abundant HMGB2 protein occurs early on the path to senescence and coincides with the dramatic spatial clustering of CTCF. Knocking down HMGB2 suffices for senescence-induced CTCF clustering and for loop reshuffling, while ectopically expressing HMGB2 rescues these effects. Our data suggest that HMGB2-mediated genomic reorganization constitutes a primer for the ensuing senescent program.

Predicting genome organisation and function with mechanistic modelling.

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future.

Topological gelation of reconnecting polymers.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids-e.g., DNA-based complex fluids or living polymer networks-with desired topologies.

Topological Spectra and Entropy of Chromatin Loop Networks.

The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fiber is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to the natural emergence of clusters of proteins and binding sites, accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. Here, we combine numerics and analytics to first classify these networks and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and this leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favor rosettelike structures with a local cloud of loops with respect to more complicated nonlocal topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, which can be robustly characterized by the framework we propose here.

Nonequilibrium dynamics and action at a distance in transcriptionally driven DNA supercoiling.

We study the effect of transcription on the kinetics of DNA supercoiling in three dimensions by means of Brownian dynamics simulations of a single-nucleotide-resolution coarse-grained model for double-stranded DNA. By explicitly accounting for the action of a transcribing RNA polymerase (RNAP), we characterize the geometry and nonequilibrium dynamics of the ensuing twin supercoiling domains. Contrary to the typical textbook picture, we find that the generation of twist by RNAP results in the formation of plectonemes (writhed DNA) some distance away. We further demonstrate that this translates into an "action at a distance" on DNA-binding proteins; for instance, positive supercoils downstream of an elongating RNAP destabilize nucleosomes long before the transcriptional machinery reaches the histone octamer. We also analyze the relaxation dynamics of supercoiled double-stranded DNA, and characterize the widely different timescales of twist diffusion, which is a simple and fast process, and writhe relaxation, which is much slower and entails multiple steps.

Mechanistic modeling of chromatin folding to understand function.

Experimental approaches have been applied to address questions in understanding three-dimensional chromatin organization and function. As datasets increase in size and complexity, it becomes a challenge to reach a mechanistic interpretation of experimental results. Polymer simulations and mechanistic modeling have been applied to explain experimental observations and their links to different aspects of genome function. Here we provide a guide for biologists, explaining different simulation approaches and the contexts in which they have been used.

Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels.

We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one. We show that composition inhomogeneities are important in the latter phase, where we find three types of possible dynamical regimes. First, we observe regular patterns with defects and vortices: these exist close to the passive-active transition. Second, for larger activity, or deeper in the nematic phase, we find active turbulence, as in active gels of uniform composition, but with exceedingly large composition variation. In the third regime, which is uniquely associated with inhomogeneity and occurs for large nematic tendency and low activity, we observe spontaneous microphase separation into active and passive domains. The microphase separated regime is notable in view of the absence of an explicit demixing term in the underlying free energy which we use, and we provide a theoretical analysis based on the common tangent construction which explains its existence. We hope this regime can be probed experimentally in the future.

Motility induced phase separation of deformable cells.

Using a multi-phase field model, we examine how particle deformability, which is a proxy for cell stiffness, affects motility induced phase separation (MIPS). We show that purely repulsive deformable, i.e., squishy, cells phase separate more effectively than their rigid counterparts. This can be understood as due to the fact that deformability increases the effective duration of collisions. In addition, the dense regions become increasingly disordered as deformability increases. Our results contextualize the applicability of MIPS to biological systems and have implications for how cells in biological systems may self-organize.

Local Yield and Compliance in Active Cell Monolayers.

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Nucleosome positions alone can be used to predict domains in yeast chromosomes.

We use molecular dynamics simulations based on publicly available micrococcal nuclease sequencing data for nucleosome positions to predict the 3D structure of chromatin in the yeast genome. Our main aim is to shed light on the mechanism underlying the formation of chromosomal interaction domains, chromosome regions of around 0.5 to 10 kbp which show enriched self-interactions, which were experimentally observed in recent MicroC experiments (importantly these are at a different length scale from the 100- to 1,000-kbp-sized domains observed in higher eukaryotes). We show that the sole input of nucleosome positioning data is already sufficient to determine the patterns of chromatin interactions and domain boundaries seen experimentally to a high degree of accuracy. Since the nucleosome spacing so strongly affects the larger-scale domain structure, we next examine the genome-wide linker-length distribution in more detail, finding that it is highly irregular and varies in different genomic regions such as gene bodies, promoters, and active and inactive genes. Finally we use our simple simulation model to characterize in more detail how irregular nucleosome spacing may affect local chromatin structure.

Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology.

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Rotation and propulsion in 3D active chiral droplets.

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, actomyosin filaments, and microtubule bundles are active systems that are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, many features of intrinsically chiral systems still need to be explored and explained. To address this gap in knowledge, here we study the effects of internal active forces and torques on a 3-dimensional (3D) droplet of cholesteric liquid crystal (CLC) embedded in an isotropic liquid. We consider tangential anchoring of the liquid crystal director at the droplet surface. Contrary to what happens in nematics, where moderate extensile activity leads to droplet rotation, cholesteric active droplets exhibit more complex and variegated behaviors. We find that extensile force dipole activity stabilizes complex defect configurations, in which orbiting dynamics couples to thermodynamic chirality to propel screw-like droplet motion. Instead, dipolar torque activity may either tighten or unwind the cholesteric helix and if tuned, can power rotations with an oscillatory angular velocity of 0 mean.

Actomyosin Contraction Induces In-Bulk Motility of Cells and Droplets.

Cell crawling on two-dimensional surfaces is a relatively well-understood phenomenon that is based on actin polymerization at a cell's front edge and anchoring on a substrate, allowing the cell to pull itself forward. However, some cells, such as cancer cells invading a three-dimensional matrigel, can also swim in the bulk, where surface adhesion is impossible. Although there is strong evidence that the self-organized engine that drives cells forward in the bulk involves myosin, the specific propulsion mechanism remains largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and locally enhanced flow. The symmetry of such flow is then spontaneously broken through actomyosin-membrane interactions, leading to self-organized droplet motility relative to the underlying solvent. Depending on the balance between contraction, diffusion, detachment rate of myosin, and effective surface tension, this motion can be either straight or circular. Our simulations and analytical results shed new light on in-bulk myosin-driven cell motility in living cells and provide a framework to design a novel type of synthetic active matter droplet potentially resembling the motility mechanism of biological cells.

capC-MAP: software for analysis of Capture-C data.

SUMMARY: Capture-C is a member of the chromosome-conformation-capture family of experimental methods which probes the 3D organization of chromosomes within the cell nucleus. It provides high-resolution information on the genome-wide chromatin interactions from a set of 'target' genomic locations, and is growing in popularity as a tool for improving our understanding of cis-regulation and gene function. Yet, analysis of the data is complicated, and to date there has been no dedicated or easy-to-use software to automate the process. We present capC-MAP, a software package for the analysis of Capture-C data. AVAILABILITY AND IMPLEMENTATION: Implemented with both ease of use and flexibility in mind, capC-MAP is a suit of programs written in C++ and Python, where each program can be run separately, or an entire analysis can be performed with a single command line. It is available under an open-source licence at https://github.com/cbrackley/capC-MAP, as well as via the conda package manager, and should run on any standard Unix-style system. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Solid-Liquid Transition of Deformable and Overlapping Active Particles.

Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.

Darcy's Law without Friction in Active Nematic Rheology.

We study the dynamics of a contractile active nematic fluid subjected to a Poiseuille flow. In a quasi-1D geometry, we find that the linear rheology of this material is reminiscent of Darcy's law in complex fluids, with a pluglike flow decaying to zero over a well-defined "permeation" length. As a result, the viscosity increases with size, but never diverges, thereby evading the yield stress predicted by previous theories. We find strong shear thinning controlled by an active Ericksen number quantifying the ratio between external pressure difference and internal active stresses. In 2D, the increase of linear regime viscosity with size only persists up to a critical length beyond which we observe active turbulent patterns, with very low apparent viscosity. The ratio between the critical and permeation length determining the stability of the Darcy regime can be made indefinitely large by varying the flow aligning parameter or magnitude of nematic order.

Pattern formation in active model C with anchoring: bands, aster networks, and foams.

We study the dynamics of pattern formation in a minimal model for active mixtures made of microtubules and molecular motors. We monitor the evolution of the (conserved) microtubule density and of the (non-conserved) nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred microtubule direction and their density gradient. The key control parameter is the ratio between activity and elasticity. When elasticity dominates, the interplay between activity and anchoring leads to formation of banded structures that can undergo additional bending, rotational or splaying instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, disordered foams and spindle-like patterns. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analogue of the microtubule cytoskeleton.