Ephemeral Protein Binding to DNA Shapes Stable Nuclear Bodies and Chromatin Domains

Polymer Physics Models Reveal Structural Folding Features of Single-Molecule Gene Chromatin Conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2 Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

Exploring protein-mediated compaction of DNA by coarse-grained simulations and unsupervised learning

Protein-DNA interactions and protein-mediated DNA compaction play key roles in a range of biological processes. The length scales typically involved in DNA bending, bridging, looping, and compaction (≥1 kbp) are challenging to address experimentally or by all-atom molecular dynamics simulations, making coarse-grained simulations a natural approach. Here, we present a simple and generic coarse-grained model for DNA-protein and protein-protein interactions and investigate the role of the latter in the protein-induced compaction of DNA. Our approach models the DNA as a discrete worm-like chain. The proteins are treated in the grand canonical ensemble, and the protein-DNA binding strength is taken from experimental measurements. Protein-DNA interactions are modeled as an isotropic binding potential with an imposed binding valency without specific assumptions about the binding geometry. To systematically and quantitatively classify DNA-protein complexes, we present an unsupervised machine learning pipeline that receives a large set of structural order parameters as input, reduces the dimensionality via principal-component analysis, and groups the results using a Gaussian mixture model. We apply our method to recent data on the compaction of viral genome-length DNA by HIV integrase and find that protein-protein interactions are critical to the formation of looped intermediate structures seen experimentally. Our methodology is broadly applicable to DNA-binding proteins and protein-induced DNA compaction and provides a systematic and semi-quantitative approach for analyzing their mesoscale complexes.

OpenNucleome for high-resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of 'fixed points' within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Polymer physics models reveal structural folding features of single-molecule gene chromatin conformations

Here, we employ polymer physics models of chromatin to investigate the 3D folding of a 2Mb wide genomic region encompassing the human LTN1 gene, a crucial DNA locus involved in key cellular functions. Through extensive Molecular Dynamics simulations, we reconstruct in-silico the ensemble of single-molecule LTN1 3D structures, which we benchmark against recent in-situ Hi-C 2.0 data. The model-derived single molecules are then used to predict structural folding features at the single-cell level, providing testable predictions for super-resolution microscopy experiments.

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 switching of segmental states can influence compaction of chromatin

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

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.

Effective model of protein-mediated interactions in chromatin

Protein-mediated interactions are ubiquitous in the cellular environment, and particularly in the nucleus, where they are responsible for the structuring of chromatin. We show through molecular-dynamics simulations of a polymer surrounded by binders that the strength of the binder-polymer interaction separates an equilibrium from a nonequilibrium regime. In the equilibrium regime, the system can be efficiently described by an effective model in which the binders are traced out. Even in this case, the polymers display features that are different from those of a standard homopolymer interacting with two-body interactions. We then extend the effective model to deal with the case where binders cannot be regarded as in equilibrium and a new phenomenology appears, including local blobs in the polymer. An effective description of this system can be useful in elucidating the fundamental mechanisms that govern chromatin structuring in particular and indirect interactions in general.

Attractive crowding effect on passive and active polymer looping kinetics

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

OpenNucleome for high resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of "fixed points" within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Polycomb repression of Hox genes involves spatial feedback but not domain compaction or phase transition

Polycomb group proteins have a critical role in silencing transcription during development. It is commonly proposed that Polycomb-dependent changes in genome folding, which compact chromatin, contribute directly to repression by blocking the binding of activating complexes. Recently, it has also been argued that liquid-liquid demixing of Polycomb proteins facilitates this compaction and repression by phase-separating target genes into a membraneless compartment. To test these models, we used Optical Reconstruction of Chromatin Architecture to trace the Hoxa gene cluster, a canonical Polycomb target, in thousands of single cells. Across multiple cell types, we find that Polycomb-bound chromatin frequently explores decompact states and partial mixing with neighboring chromatin, while remaining uniformly repressed, challenging the repression-by-compaction or phase-separation models. Using polymer simulations, we show that these observed flexible ensembles can be explained by 'spatial feedback'-transient contacts that contribute to the propagation of the epigenetic state (epigenetic memory), without inducing a globular organization.

Regulation of chromatin architecture by transcription factor binding

Transcription factors (TF) bind to chromatin and regulate the expression of genes. The pair Myc:Max binds to E-box regulatory DNA elements throughout the genome to control the transcription of a large group of specific genes. We introduce an implicit modeling protocol for Myc:Max binding to mesoscale chromatin fibers at nucleosome resolution to determine TF effect on chromatin architecture and shed light into its mechanism of gene regulation. We first bind Myc:Max to different chromatin locations and show how it can direct fiber folding and formation of microdomains, and how this depends on the linker DNA length. Second, by simulating increasing concentrations of Myc:Max binding to fibers that differ in the DNA linker length, linker histone density, and acetylation levels, we assess the interplay between Myc:Max and other chromatin internal parameters. Third, we study the mechanism of gene silencing by Myc:Max binding to the Eed gene loci. Overall, our results show how chromatin architecture can be regulated by TF binding. The position of TF binding dictates the formation of microdomains that appear visible only at the ensemble level. At the same time, the level of linker histone and tail acetylation, or different linker DNA lengths, regulates the concentration-dependent effect of TF binding. Furthermore, we show how TF binding can repress gene expression by increasing fiber folding motifs that help compact and occlude the promoter region. Importantly, this effect can be reversed by increasing linker histone density. Overall, these results shed light on the epigenetic control of the genome dictated by TF binding.

Regulation of Chromatin Architecture by Transcription Factor Binding

Transcription factors (TF) bind to chromatin and regulate the expression of genes. The pair Myc:Max binds to E-box regulatory DNA elements throughout the genome, controlling transcription of a large group of specific genes. We introduce an implicit modeling protocol for Myc:Max binding to mesoscale chromatin fibers to determine TF effect on chromatin architecture and shed light on its mechanism of gene regulation. We first bind Myc:Max to different chromatin locations and show how it can direct fiber folding and formation of microdomains, and how this depends on the linker DNA length. Second, by simulating increasing concentrations of Myc:Max binding to fibers that differ in the DNA linker length, linker histone density, and acetylation levels, we assess the interplay between Myc:Max and other chromatin internal parameters. Third, we study the mechanism of gene silencing by Myc:Max binding to the Eed gene loci. Overall, our results show how chromatin architecture can be regulated by TF binding. The position of TF binding dictates the formation of microdomains that appear visible only at the ensemble level. On the other hand, the presence of linker histone, acetylations, or different linker DNA lengths regulates the concentration-dependent effect of TF binding. Furthermore, we show how TF binding can repress gene expression by increasing fiber folding motifs that help compact and occlude the promoter region. Importantly, this effect can be reversed by increasing linker histone density. Overall, these results shed light on the epigenetic control of the genome dictated by TF binding.

Dynamic ParB-DNA interactions initiate and maintain a partition condensate for bacterial chromosome segregation

In most bacteria, chromosome segregation is driven by the ParABS system where the CTPase protein ParB loads at the parS site to trigger the formation of a large partition complex. Here, we present in vitro studies of the partition complex for Bacillus subtilis ParB, using single-molecule fluorescence microscopy and AFM imaging to show that transient ParB-ParB bridges are essential for forming DNA condensates. Molecular Dynamics simulations confirm that condensation occurs abruptly at a critical concentration of ParB and show that multimerization is a prerequisite for forming the partition complex. Magnetic tweezer force spectroscopy on mutant ParB proteins demonstrates that CTP hydrolysis at the N-terminal domain is essential for DNA condensation. Finally, we show that transcribing RNA polymerases can steadily traverse the ParB-DNA partition complex. These findings uncover how ParB forms a stable yet dynamic partition complex for chromosome segregation that induces DNA condensation and segregation while enabling replication and transcription.

Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.

Elasticity control of entangled chromosomes: Crosstalk between condensin complexes and nucleosomes

Condensin-mediated loop extrusion is now considered as the main driving force of mitotic chromosome assembly. Recent experiments have shown, however, that a class of mutant condensin complexes deficient in loop extrusion can assemble chromosome-like structures in Xenopus egg extracts, although these structures are somewhat different from those assembled by wild-type condensin complexes. In the absence of topoisomerase II (topo II), the mutant condensin complexes produce an unusual round-shaped structure termed a bean, which consists of a DNA-dense central core surrounded by a DNA-sparse halo. The mutant condensin complexes accumulate in the core, whereas histones are more concentrated in the halo than in the core. We consider that this peculiar structure serves as a model system to study how DNA entanglements, nucleosomes, and condensin functionally crosstalk with each other. To gain insight into how the bean structure is formed, here we construct a theoretical model. Our theory predicts that the core is formed by attractive interactions between mutant condensin complexes, whereas the halo is stabilized by the energy reduction through the selective accumulation of nucleosomes. The formation of the halo increases the elastic free energy due to the DNA entanglement in the core, but the latter free energy is compensated by condensin complexes that suppress the assembly of nucleosomes.

Nonequilibrium design strategies for functional colloidal assemblies

We use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

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.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.

Phase transitions in heterochromatin organization

Heterochromatin formation has been proposed to involve phase transitions on the level of the three-dimensional folding of heterochromatin regions and the liquid-liquid demixing of heterochromatin proteins. Here, I outline the hallmarks of such transitions and the current challenges to detect them in living cells. I further discuss the abundance and properties of prominent heterochromatin proteins and relate them to their potential role in driving phase transitions. Recent data from mouse fibroblasts indicate that pericentric heterochromatin is organized via a reordering transition on the level of heterochromatin regions that does not necessarily involve liquid-liquid demixing of heterochromatin proteins. Evaluating key hallmarks of the different candidate phase transition mechanisms across cell types and species will be needed to complete the current picture.

Compartmentalization with nuclear landmarks yields random, yet precise, genome organization

The 3D organization of eukaryotic genomes plays an important role in genome function. While significant progress has been made in deciphering the folding mechanisms of individual chromosomes, the principles of the dynamic large-scale spatial arrangement of all chromosomes inside the nucleus are poorly understood. We use polymer simulations to model the diploid human genome compartmentalization relative to nuclear bodies such as nuclear lamina, nucleoli, and speckles. We show that a self-organization process based on a cophase separation between chromosomes and nuclear bodies can capture various features of genome organization, including the formation of chromosome territories, phase separation of A/B compartments, and the liquid property of nuclear bodies. The simulated 3D structures quantitatively reproduce both sequencing-based genomic mapping and imaging assays that probe chromatin interaction with nuclear bodies. Importantly, our model captures the heterogeneous distribution of chromosome positioning across cells while simultaneously producing well-defined distances between active chromatin and nuclear speckles. Such heterogeneity and preciseness of genome organization can coexist due to the nonspecificity of phase separation and the slow chromosome dynamics. Together, our work reveals that the cophase separation provides a robust mechanism for us to produce functionally important 3D contacts without requiring thermodynamic equilibration that can be difficult to achieve.

Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling

Understanding the mechanisms underlying the complex 3D architecture of mammalian genomes poses, at a more fundamental level, the problem of how two or multiple genomic sites can establish physical contacts in the nucleus of the cells. Beyond stochastic and fleeting encounters related to the polymeric nature of chromatin, experiments have revealed specific, privileged patterns of interactions that suggest the existence of basic organizing principles of folding. In this review, we focus on two major and recently proposed physical processes of chromatin organization: loop-extrusion and polymer phase-separation, both supported by increasing experimental evidence. We discuss their implementation into polymer physics models, which we test against available single-cell super-resolution imaging data, showing that both mechanisms can cooperate to shape chromatin structure at the single-molecule level. Next, by exploiting the comprehension of the underlying molecular mechanisms, we illustrate how such polymer models can be used as powerful tools to make predictions in silico that can complement experiments in understanding genome folding. To this aim, we focus on recent key applications, such as the prediction of chromatin structure rearrangements upon disease-associated mutations and the identification of the putative chromatin organizing factors that orchestrate the specificity of DNA regulatory contacts genome-wide.

Multivalent binding proteins can drive collapse and reswelling of chromatin in confinement

Collapsed conformations of chromatin have been long suspected of being mediated by interactions with multivalent binding proteins, which can bring together distant sections of the chromatin fiber. In this study, we use Langevin dynamics simulation of a coarse grained chromatin polymer to show that the role of binding proteins can be more nuanced than previously suspected. In particular, for chromatin polymer in confinement, entropic forces can drive reswelling of collapsed chromatin with increasing binder concentrations, and this reswelling transition happens at physiologically relevant binder concentrations. Both the extent of collapse, and also of reswelling depends on the strength of confinement. We also study the kinetics of collapse and reswelling and show that both processes occur in similar timescales. We characterise this reswelling of chromatin in biologically relevant regimes and discuss the non-trivial role of multivalent binding proteins in mediating the spatial organisation of the genome.

Spatially coherent diffusion of human RNA Pol II depends on transcriptional state rather than chromatin motion

Gene transcription by RNA polymerase II (RNAPol II) is a tightly regulated process in the genomic, temporal, and spatial context. Recently, we have shown that chromatin exhibits spatially coherently moving regions over the entire nucleus, which is enhanced by transcription. Yet, it remains unclear how the mobility of RNA Pol II molecules is affected by transcription regulation and whether this response depends on the coordinated chromatin movement. We applied our Dense Flow reConstruction and Correlation method to analyze nucleus-wide coherent movements of RNA Pol II in living human cancer cells. We observe a spatially coherent movement of RNA Pol II molecules over ≈ 1 μm, which depends on transcriptional activity. Inducing transcription in quiescent cells decreased the coherent motion of RNA Pol II. We then quantify the spatial correlation length of RNA Pol II in the context of DNA motion. RNA Pol II and chromatin spatially coherent motions respond oppositely to transcriptional activities. Our study holds the potential of studying the chromatin environment in different nuclear processes.

Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates

Phase separation is as familiar as watching vinegar separating from oil in vinaigrette. The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicates that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviors, which in turn may have biological significance. The aim of this Perspective is to review the state-of-the-art of this quickly emerging field focusing on the material and rheological properties of protein condensates. Finally, we discuss the different techniques that can be employed to quantify the viscoelasticity of condensates and highlight potential future directions and opportunities for interdisciplinary cross-talk between chemists, physicists, and biologists.

Phase Separation-Mediated Chromatin Organization and Dynamics: From Imaging-Based Quantitative Characterizations to Functional Implications

As an effective and versatile strategy to compartmentalize cellular components without the need for lipid membranes, phase separation has been found to underpin a wide range of intranuclear processes, particularly those involving chromatin. Many of the unique physico-chemical properties of chromatin-based phase condensates are harnessed by the cell to accomplish complex regulatory functions in a spatially and temporally controlled manner. Here, we survey key recent findings on the mechanistic roles of phase separation in regulating the organization and dynamics of chromatin-based molecular processes across length scales, packing states and intranuclear functions, with a particular emphasis on quantitative characterizations of these condensates enabled by advanced imaging-based approaches. By illuminating the complex interplay between chromatin and various chromatin-interacting molecular species mediated by phase separation, this review sheds light on an emerging multi-scale, multi-modal and multi-faceted landscape that hierarchically regulates the genome within the highly crowded and dynamic nuclear space. Moreover, deficiencies in existing studies also highlight the need for mechanism-specific criteria and multi-parametric approaches for the characterization of chromatin-based phase separation using complementary techniques and call for greater efforts to correlate the quantitative features of these condensates with their functional consequences in close-to-native cellular contexts.

On the stability and layered organization of protein-DNA condensates

Multi-component phase separation is emerging as a key mechanism for the formation of biological condensates that play essential roles in signal sensing and transcriptional regulation. The molecular factors that dictate these condensates' stability and spatial organization are not fully understood, and it remains challenging to predict their microstructures. Using a near-atomistic, chemically accurate force field, we studied the phase behavior of chromatin regulators that are crucial for heterochromatin organization and their interactions with DNA. Our computed phase diagrams recapitulated previous experimental findings on different proteins. They revealed a strong dependence of condensate stability on the protein-DNA mixing ratio as a result of balancing protein-protein interactions and charge neutralization. Notably, a layered organization was observed in condensates formed by mixing HP1, histone H1, and DNA. This layered organization may be of biological relevance, as it enables cooperative DNA packaging between the two chromatin regulators: histone H1 softens the DNA to facilitate the compaction induced by HP1 droplets. Our study supports near-atomistic models as a valuable tool for characterizing the structure and stability of biological condensates.

Capturing a Crucial ‘Disorder-to-Order Transition’ at the Heart of the Coronavirus Molecular Pathology—Triggered by Highly Persistent, Interchangeable Salt-Bridges

The COVID-19 origin debate has greatly been influenced by genome comparison studies of late, revealing the emergence of the Furin-like cleavage site at the S1/S2 junction of the SARS-CoV-2 Spike (FLCSSpike) containing its 681PRRAR685 motif, absent in other related respiratory viruses. Being the rate-limiting (i.e., the slowest) step, the host Furin cleavage is instrumental in the abrupt increase in transmissibility in COVID-19, compared to earlier onsets of respiratory viral diseases. In such a context, the current paper entraps a ‘disorder-to-order transition’ of the FLCSSpike (concomitant to an entropy arrest) upon binding to Furin. The interaction clearly seems to be optimized for a more efficient proteolytic cleavage in SARS-CoV-2. The study further shows the formation of dynamically interchangeable and persistent networks of salt-bridges at the Spike–Furin interface in SARS-CoV-2 involving the three arginines (R682, R683, R685) of the FLCSSpike with several anionic residues (E230, E236, D259, D264, D306) coming from Furin, strategically distributed around its catalytic triad. Multiplicity and structural degeneracy of plausible salt-bridge network archetypes seem to be the other key characteristic features of the Spike–Furin binding in SARS-CoV-2, allowing the system to breathe—a trademark of protein disorder transitions. Interestingly, with respect to the homologous interaction in SARS-CoV (2002/2003) taken as a baseline, the Spike–Furin binding events, generally, in the coronavirus lineage, seems to have preference for ionic bond formation, even with a lesser number of cationic residues at their potentially polybasic FLCSSpike patches. The interaction energies are suggestive of characteristic metastabilities attributed to Spike–Furin interactions, generally to the coronavirus lineage, which appears to be favorable for proteolytic cleavages targeted at flexible protein loops. The current findings not only offer novel mechanistic insights into the coronavirus molecular pathology and evolution, but also add substantially to the existing theories of proteolytic cleavages.

Three-dimensional loop extrusion

Loop extrusion convincingly describes how certain structural maintenance of chromosome (SMC) proteins mediate the formation of large DNA loops. Yet most of the existing computational models cannot reconcile recent in vitro observations showing that condensins can traverse each other, bypass large roadblocks, and perform steps longer than their own size. To fill this gap, we propose a three-dimensional (3D) "trans-grabbing" model for loop extrusion, which not only reproduces the experimental features of loop extrusion by one SMC complex but also predicts the formation of so-called Z-loops via the interaction of two or more SMCs extruding along the same DNA substrate. By performing molecular dynamics simulations of this model, we discover that the experimentally observed asymmetry in the different types of Z-loops is a natural consequence of the DNA tethering in vitro. Intriguingly, our model predicts this bias to disappear in the absence of tethering and a third type of Z-loop, which has not yet been identified in experiments, to appear. Our model naturally explains roadblock bypassing and the appearance of steps larger than the SMC size as a consequence of non-contiguous DNA grabbing. Finally, this study is the first, to our knowledge, to address how Z-loops and bypassing might occur in a way that is broadly consistent with existing cis-only 1D loop extrusion models.

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.

Current Understanding of Molecular Phase Separation in Chromosomes

Biomolecular phase separation denotes the demixing of a specific set of intracellular components without membrane encapsulation. Recent studies have found that biomolecular phase separation is involved in a wide range of cellular processes. In particular, phase separation is involved in the formation and regulation of chromosome structures at various levels. Here, we review the current understanding of biomolecular phase separation related to chromosomes. First, we discuss the fundamental principles of phase separation and introduce several examples of nuclear/chromosomal biomolecular assemblies formed by phase separation. We also briefly explain the experimental and computational methods used to study phase separation in chromosomes. Finally, we discuss a recent phase separation model, termed bridging-induced phase separation (BIPS), which can explain the formation of local chromosome structures.

Complex small-world regulatory networks emerge from the 3D organisation of the human genome

The discovery that overexpressing one or a few critical transcription factors can switch cell state suggests that gene regulatory networks are relatively simple. In contrast, genome-wide association studies (GWAS) point to complex phenotypes being determined by hundreds of loci that rarely encode transcription factors and which individually have small effects. Here, we use computer simulations and a simple fitting-free polymer model of chromosomes to show that spatial correlations arising from 3D genome organisation naturally lead to stochastic and bursty transcription as well as complex small-world regulatory networks (where the transcriptional activity of each genomic region subtly affects almost all others). These effects require factors to be present at sub-saturating levels; increasing levels dramatically simplifies networks as more transcription units are pressed into use. Consequently, results from GWAS can be reconciled with those involving overexpression. We apply this pan-genomic model to predict patterns of transcriptional activity in whole human chromosomes, and, as an example, the effects of the deletion causing the diGeorge syndrome.

Integration host factor bends and bridges DNA in a multiplicity of binding modes with varying specificity

Nucleoid-associated proteins (NAPs) are crucial in organizing prokaryotic DNA and regulating genes. Vital to these activities are complex nucleoprotein structures, however, how these form remains unclear. Integration host factor (IHF) is an Escherichia coli NAP that creates very sharp bends in DNA at sequences relevant to several functions including transcription and recombination, and is also responsible for general DNA compaction when bound non-specifically. We show that IHF–DNA structural multimodality is more elaborate than previously thought, and provide insights into how this drives mechanical switching towards strongly bent DNA. Using single-molecule atomic force microscopy and atomic molecular dynamics simulations we find three binding modes in roughly equal proportions: ‘associated’ (73° of DNA bend), ‘half-wrapped’ (107°) and ‘fully-wrapped’ (147°), only the latter occurring with sequence specificity. We show IHF bridges two DNA double helices through non-specific recognition that gives IHF a stoichiometry greater than one and enables DNA mesh assembly. We observe that IHF-DNA structural multiplicity is driven through non-specific electrostatic interactions that we anticipate to be a general NAP feature for physical organization of chromosomes.

Transcription organizes euchromatin via microphase separation

In eukaryotes, DNA is packed inside the cell nucleus in the form of chromatin, which consists of DNA, proteins such as histones, and RNA. Euchromatin, which is permissive for transcription, is spatially organized into transcriptionally inactive domains interspersed with pockets of transcriptional activity. While transcription and RNA have been implicated in euchromatin organization, it remains unclear how their interplay forms and maintains transcription pockets. Here we combine theory and experiment to analyze the dynamics of euchromatin organization as pluripotent zebrafish cells exit mitosis and begin transcription. We show that accumulation of RNA induces formation of transcription pockets which displace transcriptionally inactive chromatin. We propose that the accumulating RNA recruits RNA-binding proteins that together tend to separate from transcriptionally inactive euchromatin. Full phase separation is prevented because RNA remains tethered to transcribed euchromatin through RNA polymerases. Instead, smaller scale microphases emerge that do not grow further and form the typical pattern of euchromatin organization.

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.

A DNA Sequence Based Polymer Model for Chromatin Folding

The recent development of sequencing technology and imaging methods has provided an unprecedented understanding of the inter-phase chromatin folding in mammalian nuclei. It was found that chromatin folds into topological-associated domains (TADs) of hundreds of kilo base pairs (kbps), and is further divided into spatially segregated compartments (A and B). The compartment B tends to be located near to the periphery or the nuclear center and interacts with other domains of compartments B, while compartment A tends to be located between compartment B and interacts inside the domains. These spatial domains are found to highly correlate with the mosaic CpG island (CGI) density. High CGI density corresponds to compartments A and small TADs, and vice versa. The variation of contact probability as a function of sequential distance roughly follows a power-law decay. Different chromosomes tend to segregate to occupy different chromosome territories. A model that can integrate these properties at multiple length scales and match many aspects is highly desired. Here, we report a DNA-sequence based coarse-grained block copolymer model that considers different interactions between blocks of different CGI density, interactions of TAD formation, as well as interactions between chromatin and the nuclear envelope. This model captures the various single-chromosome properties and partially reproduces the formation of chromosome territories.

Predicting Genome Architecture: Challenges and Solutions

Genome architecture plays a pivotal role in gene regulation. The use of high-throughput methods for chromatin profiling and 3-D interaction mapping provide rich experimental data sets describing genome organization and dynamics. These data challenge development of new models and algorithms connecting genome architecture with epigenetic marks. In this review, we describe how chromatin architecture could be reconstructed from epigenetic data using biophysical or statistical approaches. We discuss the applicability and limitations of these methods for understanding the mechanisms of chromatin organization. We also highlight the emergence of new predictive approaches for scoring effects of structural variations in human cells.

Computational methods for the prediction of chromatin interaction and organization using sequence and epigenomic profiles

The exploration of three-dimensional chromatin interaction and organization provides insight into mechanisms underlying gene regulation, cell differentiation and disease development. Advances in chromosome conformation capture technologies, such as high-throughput chromosome conformation capture (Hi-C) and chromatin interaction analysis by paired-end tag (ChIA-PET), have enabled the exploration of chromatin interaction and organization. However, high-resolution Hi-C and ChIA-PET data are only available for a limited number of cell lines, and their acquisition is costly, time consuming, laborious and affected by theoretical limitations. Increasing evidence shows that DNA sequence and epigenomic features are informative predictors of regulatory interaction and chromatin architecture. Based on these features, numerous computational methods have been developed for the prediction of chromatin interaction and organization, whereas they are not extensively applied in biomedical study. A systematical study to summarize and evaluate such methods is still needed to facilitate their application. Here, we summarize 48 computational methods for the prediction of chromatin interaction and organization using sequence and epigenomic profiles, categorize them and compare their performance. Besides, we provide a comprehensive guideline for the selection of suitable methods to predict chromatin interaction and organization based on available data and biological question of interest.

Polymer Modeling Predicts Chromosome Reorganization in Senescence

Lamina-associated domains (LADs) cover a large part of the human genome and are thought to play a major role in shaping the nuclear architectural landscape. Here, we perform polymer simulations, microscopy, and mass spectrometry to dissect the roles played by heterochromatin- and lamina-mediated interactions in nuclear organization. Our model explains the conventional organization of heterochromatin and euchromatin in growing cells and the pathological organization found in oncogene-induced senescence and progeria. We show that the experimentally observed changes in the locality of contacts in senescent and progeroid cells can be explained as arising due to phase transitions in the system. Within our simulations, LADs are highly stochastic, as in experiments. Our model suggests that, once established, the senescent phenotype should be metastable even if lamina-mediated interactions were reinstated. Overall, our simulations uncover a generic physical mechanism that can regulate heterochromatin segregation and LAD formation in a wide range of mammalian nuclei.

Archaeal Chromatin Proteins Cren7 and Sul7d Compact DNA by Bending and Bridging

Archaeal chromatin proteins Cren7 and Sul7d from Sulfolobus are DNA benders. To better understand their architectural roles in chromosomal DNA organization, we analyzed DNA compaction by Cren7 and Sis7d, a Sul7d family member, from Sulfolobus islandicus at the single-molecule (SM) level by total single-molecule internal reflection fluorescence microscopy (SM-TIRFM) and atomic force microscopy (AFM). We show that both Cren7 and Sis7d were able to compact singly tethered λ DNA into a highly condensed structure in a three-step process and that Cren7 was over an order of magnitude more efficient than Sis7d in DNA compaction. The two proteins were similar in DNA bending kinetics but different in DNA condensation patterns. At saturating concentrations, Sis7d formed randomly distributed clusters whereas Cren7 generated a single and highly condensed core on plasmid DNA. This observation is consistent with the greater ability of Cren7 than of Sis7d to bridge DNA. Our results offer significant insights into the mechanism and kinetics of chromosomal DNA organization in Crenarchaea.IMPORTANCE A long-standing question is how chromosomal DNA is packaged in Crenarchaeota, a major group of archaea, which synthesize large amounts of unique small DNA-binding proteins but in general contain no archaeal histones. In the present work, we tested our hypothesis that the two well-studied crenarchaeal chromatin proteins Cren7 and Sul7d compact DNA by both DNA bending and bridging. We show that the two proteins are capable of compacting DNA, albeit with different efficiencies and in different manners, at the single molecule level. We demonstrate for the first time that the two proteins, which have long been regarded as DNA binders and benders, are able to mediate DNA bridging, and this previously unknown property of the proteins allows DNA to be packaged into highly condensed structures. Therefore, our results provide significant insights into the mechanism and kinetics of chromosomal DNA organization in Crenarchaeota.

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.

Phase separation driven by production of architectural RNA transcripts

We here use an extension of the Flory-Huggins theory to predict that phase separation is driven by the production of architectural RNA (arcRNA) at a DNA locus with a constant rate. The arcRNA molecules diffuse in the nucleoplasm and show attractive interactions via proteins that are bound to the arcRNA. Our theory predicts that when the Flory interaction parameter is larger than the value at the critical point, the volume fraction of arcRNA jumps between the two values corresponding to the volume fraction of the two coexisting phases at equilibrium at a distance from the DNA locus due to the local equilibrium condition. The distance defines the radius of the condensate that is assembled by the phase separation. When the interaction parameter is large, the volume of the condensates is proportional to the production rate of arcRNA and inversely proportional to the degradation rate of arcRNA. These results imply that most arcRNA molecules are degraded before they diffuse out from the condensates due to the strong segregation of arcRNA.

Nonequilibrium Strategy for Fast Target Search on the Genome

Vital biological processes such as genome repair require fast and efficient binding of selected proteins to specific target sites on DNA. Here we propose an active target search mechanism based on "chromophoresis," the dynamics of DNA-binding proteins up or down gradients in the density of epigenetic marks, or colors (biochemical tags on the genome). We focus on a set of proteins that deposit marks from which they are repelled-a case which is only encountered away from thermodynamic equilibrium. For suitable ranges of kinetic parameter values, chromophoretic proteins can perform undirectional motion and are optimally redistributed along the genome. Importantly, they can also locally unravel a region of the genome which is collapsed due to self-interactions and "dive" deep into its core, for a striking enhancement of the efficiency of target search on such an inaccessible substrate. We discuss the potential relevance of chromophoresis for DNA repair.

Polymer compaction and bridging-induced clustering of protein-inspired patchy particles

There are many proteins or protein complexes which have multiple DNA binding domains. This allows them to bind to multiple points on a DNA molecule (or chromatin fibre) at the same time. There are also many proteins which have been found to be able to compact DNAin vitro, and many others have been observed in foci or puncta when fluorescently labelled and imagedin vivo. In this work we study, using coarse-grained Langevin dynamics simulations, the compaction of polymers by simple model proteins and a phenomenon known as the 'bridging-induced attraction'. The latter is a mechanism observed in previous simulations [Brackleyet al2013Proc. Natl Acad. Sci. USA110E3605], where proteins modelled as spheres form clusters via their multivalent interactions with a polymer, even in the absence of any explicit protein-protein attractive interactions. Here we extend this concept to consider more detailed model proteins, represented as simple 'patchy particles' interacting with a semi-flexible bead-and-spring polymer. We find that both the compacting ability and the effect of the bridging-induced attraction depend on the valence of the model proteins. These effects also depend on the shape of the protein, which determines its ability to form bridges.

Bridging-induced microphase separation: photobleaching experiments, chromatin domains and the need for active reactions

We review the mechanism and consequences of the ‘bridging-induced attraction’, a generic biophysical principle that underpins some existing models for chromosome organization in 3D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains that conform well with the observation of A/B compartments in HiC experiments.

Polymer models for the mechanisms of chromatin 3D folding: review and perspective

In this perspective paper, classical physical models for mammalian interphase chromatin folding are reviewed.

Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus

Understanding the spatial organization of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical-or epigenetic-marks that are deposited along the genome are thought to play an important, yet poorly understood, role in determining genome organization and cell identity. The physical principles underlying the interplay between epigenetic dynamics and genome folding remain elusive. Here we propose and study a theory that assumes a coupling between epigenetic mark and genome densities, and which can be applied at the scale of the whole nucleus. We show that equilibrium models are not compatible with experiments and a qualitative agreement is recovered by accounting for nonequilibrium processes that can stabilize microphase separated epigenomic domains. We finally discuss the potential biophysical origin of these terms.

Magnetic polymer models for epigenetics-driven chromosome folding

Epigenetics is a driving force of important and ubiquitous phenomena in nature such as cell differentiation or even metamorphosis. Opposite to its widespread role, understanding the biophysical principles that allow epigenetics to control and rewire gene regulatory networks remains an open challenge. In this work we study the effects of epigenetic modifications on the spatial folding of chromosomes-and hence on the expression of the underlying genes-by mapping the problem to a class of models known as magnetic polymers. In this work we show that a first order phase transition underlies the simultaneous spreading of certain epigenetic marks and the conformational collapse of a chromosome. Further, we describe Brownian dynamics simulations of the model in which the topology of the polymer and thermal fluctuations are fully taken into account and that confirm our mean field predictions. Extending our models to allow for nonequilibrium terms yields new stable phases which qualitatively agrees with observations in vivo. Our results show that statistical mechanics techniques applied to models of magnetic polymers can be successfully exploited to rationalize the outcomes of experiments designed to probe the interplay between a dynamic epigenetic landscape and chromatin organization.

Dilution of contact frequency between superenhancers by loop extrusion at interfaces

The loop extrusion theory predicts that cohesin acts as a molecular motor that extrudes chromatin fibers to produce loops. Hi-C experiments have detected relatively high contact frequencies between superenhancers. These probably result from the fact that superenhancers are localized at condensates of transcriptional activators and coactivators. The contact frequency between superenhancers is enhanced by auxin treatment that removes cohesin from chromatin. Motivated by these experimental results, we here treat chromatin at the surface of a condensate as a loop extruding polymer brush. Our theory predicts that the lateral pressure generated by the brush decreases with decreasing the loading rate of cohesin. This is because loop extrusion actively transfers chain segments at the vicinity of the interface. Our theory thus predicts that the increase of contact frequency by auxin treatment results from the fact that suppressing the loop extrusion process induces the dissolution of molecular components to the nucleoplasm, decreasing the average distance between superenhancers.