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.

Bridging condensins mediate compaction of mitotic chromosomes.

Eukaryotic chromosomes compact during mitosis into elongated cylinders-and not the spherical globules expected of self-attracting long flexible polymers. This process is mainly driven by condensin-like proteins. Here, we present Brownian-dynamic simulations involving two types of such proteins with different activities. One, which we refer to as looping condensins, anchors long-lived chromatin loops to create bottlebrush structures. The second, referred to as bridging condensins, forms multivalent bridges between distant parts of these loops. We show that binding of bridging condensins leads to the formation of shorter and stiffer mitotic-like cylinders without requiring any additional energy input. These cylinders have several features matching experimental observations. For instance, the axial condensin backbone breaks up into clusters as found by microscopy, and cylinder elasticity qualitatively matches that seen in chromosome pulling experiments. Additionally, simulating global condensin depletion or local faulty condensin loading gives phenotypes seen experimentally and points to a mechanistic basis for the structure of common fragile sites in mitotic chromosomes.

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.

Transcription modulates chromatin dynamics and locus configuration sampling.

In living cells, the 3D structure of gene loci is dynamic, but this is not revealed by 3C and FISH experiments in fixed samples, leaving a notable gap in our understanding. To overcome these limitations, we applied the highly predictive heteromorphic polymer (HiP-HoP) model to determine chromatin fiber mobility at the Pax6 locus in three mouse cell lines with different transcription states. While transcriptional activity minimally affects movement of 40-kbp regions, we observed that motion of smaller 1-kbp regions depends strongly on local disruption to chromatin fiber structure marked by H3K27 acetylation. This also substantially influenced locus configuration dynamics by modulating protein-mediated promoter-enhancer loops. Importantly, these simulations indicate that chromatin dynamics are sufficiently fast to sample all possible locus conformations within minutes, generating wide dynamic variability within single cells. This combination of simulation and experimental validation provides insight into how transcriptional activity influences chromatin structure and gene dynamics.

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.

Yield-stress transition in suspensions of deformable droplets.

Yield-stress materials, which require a sufficiently large forcing to flow, are currently ill-understood theoretically. To gain insight into their yielding transition, we study numerically the rheology of a suspension of deformable droplets in 2D. We show that the suspension displays yield-stress behavior, with droplets remaining motionless below a critical body-force. In this phase, droplets jam to form an amorphous structure, whereas they order in the flowing phase. Yielding is linked to a percolation transition in the contacts of droplet-droplet overlaps and requires strict conservation of the droplet area to exist. Close to the transition, we find strong oscillations in the droplet motion that resemble those found experimentally in confined colloidal glasses. We show that even when droplets are static, the underlying solvent moves by permeation so that the viscosity of the composite system is never truly infinite, and its value ceases to be a bulk material property of the system.

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.

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.

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.

Universal properties of active membranes.

We put forward a general field theory for nearly flat fluid membranes with embedded activators and analyze their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z=1 and 2, respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, leads to an early-time behavior, which is representative of the spatiotemporal patterns observed at the leading edge of motile cells, such as oscillations superposed on the growth of the membrane width. In the case of mean-field diffusive scaling, one-loop corrections to the mean-field exponents reveal universal behavior distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behavior.

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws.

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

Predictive Polymer Models for 3D Chromosome Organization.

Polymer simulations and predictive mechanistic modelling are increasingly used in conjunction with experiments to study the organization of eukaryotic chromosomes. Here we review some of the most prevalent models for mechanisms which drive different aspects of chromosome organization, as well as a recent simulation scheme which combines several of these mechanisms into a single predictive model. We give some practical details of the modelling approach, as well as review some of the key results obtained by these and similar models in the last few years.

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.

RNA polymerase II is required for spatial chromatin reorganization following exit from mitosis.

Mammalian chromosomes are three-dimensional entities shaped by converging and opposing forces. Mitotic cell division induces marked chromosome condensation, but following reentry into the G1 phase of the cell cycle, chromosomes reestablish their interphase organization. Here, we tested the role of RNA polymerase II (RNAPII) in this transition using a cell line that allows its auxin-mediated degradation. In situ Hi-C showed that RNAPII is required for both compartment and loop establishment following mitosis. RNAPs often counteract loop extrusion, and in their absence, longer and more prominent loops arose. Evidence from chromatin binding, super-resolution imaging, and in silico modeling allude to these effects being a result of RNAPII-mediated cohesin loading upon G1 reentry. Our findings reconcile the role of RNAPII in gene expression with that in chromatin architecture.

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.

Bridging-induced phase separation induced by cohesin SMC protein complexes.

Structural maintenance of chromosome (SMC) protein complexes are able to extrude DNA loops. While loop extrusion constitutes a fundamental building block of chromosomes, other factors may be equally important. Here, we show that yeast cohesin exhibits pronounced clustering on DNA, with all the hallmarks of biomolecular condensation. DNA-cohesin clusters exhibit liquid-like behavior, showing fusion of clusters, rapid fluorescence recovery after photobleaching and exchange of cohesin with the environment. Strikingly, the in vitro clustering is DNA length dependent, as cohesin forms clusters only on DNA exceeding 3 kilo-base pairs. We discuss how bridging-induced phase separation, a previously unobserved type of biological condensation, can explain the DNA-cohesin clustering through DNA-cohesin-DNA bridges. We confirm that, in yeast cells in vivo, a fraction of cohesin associates with chromatin in a manner consistent with bridging-induced phase separation. Biomolecular condensation by SMC proteins constitutes a new basic principle by which SMC complexes direct genome organization.

Soft matter science and the COVID-19 pandemic.

Much of the science underpinning the global response to the COVID-19 pandemic lies in the soft matter domain. Coronaviruses are composite particles with a core of nucleic acids complexed to proteins surrounded by a protein-studded lipid bilayer shell. A dominant route for transmission is via air-borne aerosols and droplets. Viral interaction with polymeric body fluids, particularly mucus, and cell membranes controls their infectivity, while their interaction with skin and artificial surfaces underpins cleaning and disinfection and the efficacy of masks and other personal protective equipment. The global response to COVID-19 has highlighted gaps in the soft matter knowledge base. We survey these gaps, especially as pertaining to the transmission of the disease, and suggest questions that can (and need to) be tackled, both in response to COVID-19 and to better prepare for future viral pandemics.

Electrostatic potential between charged particles at an oil-water interface.

Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble their bulk counterparts. For instance, the electrostatic potential of a point charge at an air-water interface falls off as r^{-3}, where r is the distance from the charge, exhibiting a dipolar behavior. This behavior is often assumed to be generic, and is widely referred to when interpreting experimental results. Here we explicitly calculate the in-plane potential of a point charge at an interface between two electrolyte solutions with different, finite dielectric permittivities and Debye screening lengths, such as oil and water. We show that the asymptotic behavior of this potential is neither a dipole, which characterizes the potential at air-water interfaces, nor a screened monopole, which describes the bulk behavior in a single electrolyte solution. By considering the same problem in arbitrary dimensions, we find that the physics behind this difference can be traced to the asymmetric propagation of the interaction in the two media. Our results should be relevant to understand the effective potential acting between interfacial proteins in biofilms, and the self-assembly of charged colloids at droplet surfaces in oil-water emulsions.

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.

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.