Chromosome positioning from activity-based segregation

Structural dynamics and optimal transport of an active polymer

We study the spontaneous configuration transitions of an active semi-flexible polymer between spiral and non-spiral states, and show that the configuration dynamics is fully described by a subcritical pitchfork bifurcation. Exploiting the fact that an active polymer barely moves in spiral states and exhibits net displacements in non-spiral states, we theoretically prove that the motion of the active polymer is consistent with a run-and-tumble-like dynamics. Moreover, we find that there exists an optimal self-propelling force that maximizes the diffusion coefficient.

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.

Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop

Several types of molecular machines move along biopolymers like chromatin. However, the details about the microscopic activity of these machines and how to distinguish their modes of action are not well understood. We propose that the activity of such machines can be classified by studying looped chromatin under shear flow. Our simulations show that a chromatin-like polymer with two types of activities-constant (type-I) or local curvature-dependent tangential forces (type-II)-exhibits very different behavior under shear flow. We show that one can distinguish both activities by measuring the nature of a globule-to-extended coil transition, tank treading, and tumbling dynamics.

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Activity-induced stiffness, entanglement network and dynamic slowdown in unentangled semidilute polymer solutions

Active polymers possess numerous unique properties that are quite different from those observed in the system of small active molecules due to the intricate interplay between their activity and topological constraints. This study focuses on the conformational changes induced by activity, impacting effective stiffness and crucially influencing entanglement and dynamics. When the two terminals of a linear chain undergo active modification through coupling to a high-temperature thermal bath, there is a substantial increase in chain size, indicating a notable enhancement in effective stiffness. Unlike in passive semiflexible chains where stiffness predominantly affects local bond angles, activity-induced stiffness manifests at the scale of tens of monomers. While activity raises the ambient temperature, it significantly decreases diffusion by over an order of magnitude. The slowdown of the dynamics observed can be attributed to increased entanglement due to chain elongation.

Active transcription and epigenetic reactions synergistically regulate meso-scale genomic organization

In interphase nuclei, chromatin forms dense domains of characteristic sizes, but the influence of transcription and histone modifications on domain size is not understood. We present a theoretical model exploring this relationship, considering chromatin-chromatin interactions, histone modifications, and chromatin extrusion. We predict that the size of heterochromatic domains is governed by a balance among the diffusive flux of methylated histones sustaining them and the acetylation reactions in the domains and the process of loop extrusion via supercoiling by RNAPII at their periphery, which contributes to size reduction. Super-resolution and nano-imaging of five distinct cell lines confirm the predictions indicating that the absence of transcription leads to larger heterochromatin domains. Furthermore, the model accurately reproduces the findings regarding how transcription-mediated supercoiling loss can mitigate the impacts of excessive cohesin loading. Our findings shed light on the role of transcription in genome organization, offering insights into chromatin dynamics and potential therapeutic targets.

The probability of chromatin to be at the nuclear lamina has no systematic effect on its transcription level in fruit flies

BACKGROUND

Multiple studies have demonstrated a negative correlation between gene expression and positioning of genes at the nuclear envelope (NE) lined by nuclear lamina, but the exact relationship remains unclear, especially in light of the highly stochastic, transient nature of the gene association with the NE.

RESULTS

In this paper, we ask whether there is a causal, systematic, genome-wide relationship between the expression levels of the groups of genes in topologically associating domains (TADs) of Drosophila nuclei and the probabilities of TADs to be found at the NE. To investigate the nature of this possible relationship, we combine a coarse-grained dynamic model of the entire Drosophila nucleus with genome-wide gene expression data; we analyze the TAD averaged transcription levels of genes against the probabilities of individual TADs to be in contact with the NE in the control and lamins-depleted nuclei. Our findings demonstrate that, within the statistical error margin, the stochastic positioning of Drosophila melanogaster TADs at the NE does not, by itself, systematically affect the mean level of gene expression in these TADs, while the expected negative correlation is confirmed. The correlation is weak and disappears completely for TADs not containing lamina-associated domains (LADs) or TADs containing LADs, considered separately. Verifiable hypotheses regarding the underlying mechanism for the presence of the correlation without causality are discussed. These include the possibility that the epigenetic marks and affinity to the NE of a TAD are determined by various non-mutually exclusive mechanisms and remain relatively stable during interphase.

CONCLUSIONS

At the level of TADs, the probability of chromatin being in contact with the nuclear envelope has no systematic, causal effect on the transcription level in Drosophila. The conclusion is reached by combining model-derived time-evolution of TAD locations within the nucleus with their experimental gene expression levels.

Non-equilibrium structural and dynamic behaviors of active polymers in complex and crowded environments

Active matter systems, which convert internal chemical energy or energy from the environment into directed motion, are ubiquitous in nature and exhibit a range of emerging non-equilibrium behaviors. However, most of the current works on active matter have been devoted to particles, and the study of active polymers has only recently come into the spotlight due to their prevalence within living organisms. The intricate interplay between activity and conformational degrees of freedom gives rise to novel structural and dynamical behaviors of active polymers. Research in active polymers remarkably broadens diverse concepts of polymer physics, such as molecular architecture, dynamics, scaling and so on, which is of significant importance for the development of new polymer materials with unique performance. Furthermore, active polymers are often found in strongly interacting and crowded systems and in complex environments, so that the understanding of this behavior is essential for future developments of novel polymer-based biomaterials. This review thereby focuses on the study of active polymers in complex and crowded environments, and aims to provide insights into the fundamental physics underlying the adaptive and collective behaviors far from equilibrium, as well as the open challenges that the field is currently facing.

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.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

Stability of the chiral crystal phase and breakdown of the cholesteric phase in mixtures of active-passive chiral rods

In this study, we aim to explore the effect of chirality on the phase behavior of active helical particles driven by two-temperature scalar activity. We first calculate the equation of state of soft helical particles of various intrinsic chiralities using molecular dynamics (MD) simulation. In equilibrium, the emergence of various liquid crystal (LC) phases such as nematic (N), cholesteric , smectic (Sm) and crystal (K) crucially depends on the presence of walls that induce planar alignment. Next, we introduce activity through the two-temperature model: keep increasing the temperature of half of the helical particles (labeled as 'hot' particles) while maintaining the temperature of the other half at a lower value (labeled as 'cold' particles). Starting from a homogeneous isotropic (I) phase, we find the emergence of 2-TIPS: two temperature-induced phase separations between the hot and cold particles. We also observe that the cold particles undergo an ordering transition to various LC phases even in the absence of a wall. This observation reveals that the hot-cold interface in the active system plays the role of a wall in the equilibrium system by inducing an alignment direction for the cold particles. However, in the case of a cholesteric phase, we observe that activity destabilizes the phase by inducing smectic ordering in the cold zone while an isotropic structure in the hot zone. The smectic ordering in the cold zone eventually transforms to a chiral crystal phase with high enough activity.

Locus folding mechanisms determine modes of antigen receptor gene assembly

The dynamic folding of genomes regulates numerous biological processes, including antigen receptor (AgR) gene assembly. We show that, unlike other AgR loci, homotypic chromatin interactions and bidirectional chromosome looping both contribute to structuring Tcrb for efficient long-range V(D)J recombination. Inactivation of the CTCF binding element (CBE) or promoter at the most 5'Vβ segment (Trbv1) impaired loop extrusion originating locally and extending to DβJβ CBEs at the opposite end of Tcrb. Promoter or CBE mutation nearly eliminated Trbv1 contacts and decreased RAG endonuclease-mediated Trbv1 recombination. Importantly, Trbv1 rearrangement can proceed independent of substrate orientation, ruling out scanning by DβJβ-bound RAG as the sole mechanism of Vβ recombination, distinguishing it from Igh. Our data indicate that CBE-dependent generation of loops cooperates with promoter-mediated activation of chromatin to juxtapose Vβ and DβJβ segments for recombination through diffusion-based synapsis. Thus, the mechanisms that fold a genomic region can influence molecular processes occurring in that space, which may include recombination, repair, and transcriptional programming.

Effect of confinement and topology: 2-TIPS vs. MIPS

2-TIPS (two temperature induced phase separation) refers to the phase separation phenomenon observed in mixtures of active and passive particles which are modelled using scalar activity. The active particles are connected to a thermostat at high temperature while the passive particles are connected to the thermostat at low temperature and the relative temperature difference between "hot" and "cold" particles is taken as the measure of the activity χ of the non-equilibrium system. The study of such binary mixtures of hot and cold particles under various kinds of confinement is an important problem in many physical and biological processes. The nature and extent of phase separation are heavily influenced by the geometry of confinement, activity, and density of the non-equilibrium binary mixture. Investigating such 3D binary mixtures confined by parallel walls, we observe that the active and passive particles phase separate, but the extent of phase separation is reduced compared to bulk phase separation at high densities and enhanced at low densities. However, when the binary mixture of active and passive particles is confined inside a spherical cavity, the phase separation is radial for small radii of the confining sphere and the extent of phase separation is higher compared to their bulk counterparts. Confinement leads to interesting properties in the passive (cold) region like enhanced layering and high compression in the direction parallel to the confining wall. In 2D, both the bulk and confined systems of the binary mixture show a significant decrement in the extent of phase separation at higher densities. This observation is attributed to the trapping of active particles inside the passive cluster, which increases with density. Thus the 2D systems show structures more akin to dense-dilute phase co-existence, which is observed in motility induced phase separation in 2D active systems. The binary mixture constrained on the spherical surface also shows similar phase co-existence. Our analyses reveal that the coexistent densities observed in 2-TIPS on the spherical surface agree with the findings of previous studies on MIPS in active systems on a sphere.

Enhanced diffusion of tracer particles in nonreciprocal mixtures

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.

Fundamental insights into the correlation between chromosome configuration and transcription

Eukaryotic chromosomes exhibit a hierarchical organization that spans a spectrum of length scales, ranging from sub-regions known as loops, which typically comprise hundreds of base pairs, to much larger chromosome territories that can encompass a few mega base pairs. Chromosome conformation capture experiments that involve high-throughput sequencing methods combined with microscopy techniques have enabled a new understanding of inter- and intra-chromosomal interactions with unprecedented details. This information also provides mechanistic insights on the relationship between genome architecture and gene expression. In this article, we review the recent findings on three-dimensional interactions among chromosomes at the compartment, topologically associating domain, and loop levels and the impact of these interactions on the transcription process. We also discuss current understanding of various biophysical processes involved in multi-layer structural organization of chromosomes. Then, we discuss the relationships between gene expression and genome structure from perturbative genome-wide association studies. Furthermore, for a better understanding of how chromosome architecture and function are linked, we emphasize the role of epigenetic modifications in the regulation of gene expression. Such an understanding of the relationship between genome architecture and gene expression can provide a new perspective on the range of potential future discoveries and therapeutic research.

Polymeric nature of tandemly repeated genes enhances assembly of constitutive heterochromatin in fission yeast

Motivated by our recent experiments that demonstrate that the tandemly repeated genes become heterochromatin, here we show a theory of heterochromatin assembly by taking into account the connectivity of these genes along the chromatin in the kinetic equations of small RNA production and histone methylation, which are the key biochemical reactions involved in the heterochromatin assembly. Our theory predicts that the polymeric nature of the tandemly repeated genes ensures the steady production of small RNAs because of the stable binding of nascent RNAs produced from the genes to RDRC/Dicers at the surface of nuclear membrane. This theory also predicts that the compaction of the tandemly repeated genes suppresses the production of small RNAs, consistent with our recent experiments. This theory can be extended to the small RNA-dependent gene silencing in higher organisms.

Predicting scale-dependent chromatin polymer properties from systematic coarse-graining

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations.

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.

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.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium

In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.

Consistencies and contradictions in different polymer models of chromatin architecture

Genetic information is stored in very long DNA molecules, which are folded to form chromatin, a similarly long polymer fibre that is ultimately organised into chromosomes. The organisation of chromatin is fundamental to many cellular functions, from the expression of the genetic information to cell division. As a long polymer, chromatin is very flexible and may adopt a myriad of shapes. Globally, the polymer physics governing chromatin dynamics is very well understood. But chromatin is not uniform and regions of it, with chemical modifications and bound effectors, form domains and compartments through mechanisms not yet clear. Polymer models have been successfully used to investigate these mechanisms to explain cytological observations and build hypothesis for experimental validation. Many different approaches to conceptualise chromatin in polymer models can be envisioned and each reflects different aspects. Here, we compare recent approaches that aim at reproducing prominent features of interphase chromatin organisation: the compartmentalisation into eu- and heterochromatin compartments, the formation of a nucleolus, chromatin loops and the rosette and Rabl conformations of interphase chromosomes. We highlight commonalities and contradictions that point to a modulation of the mechanisms involved to fine degree. Consolidating models will require the inclusion of yet hidden or neglected parameters.

Hypothesis-driven probabilistic modelling enables a principled perspective of genomic compartments

The Hi-C method has revolutionized the study of genome organization, yet interpretation of Hi-C interaction frequency maps remains a major challenge. Genomic compartments are a checkered Hi-C interaction pattern suggested to represent the partitioning of the genome into two self-interacting states associated with active and inactive chromatin. Based on a few elementary mechanistic assumptions, we derive a generative probabilistic model of genomic compartments, called deGeco. Testing our model, we find it can explain observed Hi-C interaction maps in a highly robust manner, allowing accurate inference of interaction probability maps from extremely sparse data without any training of parameters. Taking advantage of the interpretability of the model parameters, we then test hypotheses regarding the nature of genomic compartments. We find clear evidence of multiple states, and that these states self-interact with different affinities. We also find that the interaction rules of chromatin states differ considerably within and between chromosomes. Inspecting the molecular underpinnings of a four-state model, we show that a simple classifier can use histone marks to predict the underlying states with 87% accuracy. Finally, we observe instances of mixed-state loci and analyze these loci in single-cell Hi-C maps, finding that mixing of states occurs mainly at the cell level.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.

Phase Separation and Correlated Motions in Motorized Genome

The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation-dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.

Epigenetic-structural changes in X chromosomes promote Xic pairing during early differentiation of mouse embryonic stem cells

X chromosome inactivation center (Xic) pairing occurs during the differentiation of embryonic stem (ES) cells from female mouse embryos, and is related to X chromosome inactivation, the circadian clock, intra-nucleus architecture, and metabolism. However, the mechanisms underlying the identification and approach of X chromosome pairs in the crowded nucleus are unclear. To elucidate the driving force of Xic pairing, we developed a coarse-grained molecular dynamics model of intranuclear chromosomes in ES cells and in cells 2 days after the onset of differentiation (2-day cells) by considering intrachromosomal epigenetic-structural feature-dependent mechanics. The analysis of the experimental data showed that X-chromosomes exhibit the rearrangement of their distributions of open/closed chromatin regions on their surfaces during cell differentiation. By simulating models where the excluded volume effects of closed chromatin regions are stronger than those of open chromatin regions, such rearrangement of open/closed chromatin regions on X-chromosome surfaces promoted the mutual approach of the Xic pair. These findings suggested that local intrachromosomal epigenetic features may contribute to the regulation of cell species-dependent differences in intranuclear architecture.

Active Topological Glass Confined within a Spherical Cavity

We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved "tank-treading" dynamic mode of active segments along the ring contour. This mode can enhance active-passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell.

How enzymatic activity is involved in chromatin organization

Spatial organization of chromatin plays a critical role in genome regulation. Previously, various types of affinity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways and perturb the chromatin. Here, we construct a polymer physics model following the mechanistic scheme of Topoisomerase-II, an enzyme resolving topological constraints of chromatin, and investigate how it affects interphase chromatin organization. Our computer simulations demonstrate Topoisomerase-II's ability to phase separate chromatin into eu- and heterochromatic regions with a characteristic wall-like organization of the euchromatic regions. We realized that the ability of the euchromatic regions to cross each other due to enzymatic activity of Topoisomerase-II induces this phase separation. This realization is based on the physical fact that partial absence of self-avoiding interaction can induce phase separation of a system into its self-avoiding and non-self-avoiding parts, which we reveal using a mean-field argument. Furthermore, motivated from recent experimental observations, we extend our model to a bidisperse setting and show that the characteristic features of the enzymatic activity-driven phase separation survive there. The existence of these robust characteristic features, even under the non-localized action of the enzyme, highlights the critical role of enzymatic activity in chromatin organization.

Heating leads to liquid-crystal and crystalline order in a two-temperature active fluid of rods

We report phase separation and liquid-crystal ordering induced by scalar activity in a system of soft repulsive spherocylinders (SRSs) of shape anisotropy L/D=5 using molecular dynamics (MD) simulations. Activity is introduced by increasing the temperature of half of the SRSs (labeled hot) while maintaining the temperature of the other half constant at a lower value (labeled cold). The difference between the two temperatures scaled by the lower temperature provides a measure of the activity. Starting from different equilibrium initial phases, we find that activity leads to segregation of the hot and cold particles. Activity also drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. The cold components of a homogeneous isotropic structure acquire nematic and, at higher activity, crystalline order. Similarly, the cold zone of a nematic initial state undergoes smectic and crystal ordering above a critical value of activity while the hot component turns isotropic. We find that the hot particles occupy a larger volume and exert an extra kinetic pressure, confining, compressing, and provoking an ordering transition of the cold-particle domains.

Tethered tracer in a mixture of hot and cold Brownian particles: can activity pacify fluctuations?

We study how an interacting mixture of components with differing levels of activity can affect the fluctuations of an embedded object such as a tracer. In particular, we consider a simple model of a tracer that is harmonically bound within a mixture of hot and cold Brownian particles, which, like a mixture of active and passive particles, can phase separate. By measuring the fluctuations of the tracer, we find that this collective behavior gives rise to an effective temperature for the tracer. Additionally, we find that there is an increased tendency for cold particles to accumulate on the surface of the tracer due to the hot particles, potentially dampening its fluctuations and decreasing its effective temperature. These results suggest that the phase separation of a mixture of hot/cold or active/passive particles may have strong effects on the fluctuations of an embedded object. We discuss potential implications of these results for experiments on fluctuations of nuclear envelope affected by the activity in the chromatin.

The Stochastic Genome and Its Role in Gene Expression

Mammalian genomes have distinct levels of spatial organization and structure that have been hypothesized to play important roles in transcription regulation. Although much has been learned about these architectural features with ensemble techniques, single-cell studies are showing a new universal trend: Genomes are stochastic and dynamic at every level of organization. Stochastic gene expression, on the other hand, has been studied for years. In this review, we probe whether there is a causative link between the two phenomena. We specifically discuss the functionality of chromatin state, topologically associating domains (TADs), and enhancer biology in light of their stochastic nature and their specific roles in stochastic gene expression. We highlight persistent fundamental questions in this area of research.

Topological Constraints with Optimal Length Promote the Formation of Chromosomal Territories at Weakened Degree of Phase Separation

It is generally agreed that the nuclei of eukaryotic cells at interphase are partitioned into disjointed territories, with distinct regions occupied by certain chromosomes. However, the underlying mechanism for such territorialization is still under debate. Here we model chromosomes as coarse-grained block copolymers and to investigate the effect of loop domains (LDs) on the formation of compartments and territories based on dissipative particle dynamics. A critical length of LDs, which depends sensitively on the length of polymeric blocks, is obtained to minimize the degree of phase separation. This also applies to the two-polymer system: The critical length not only maximizes the degree of territorialization but also minimizes the degree of phase separation. Interestingly, by comparing with experimental data, we find the critical length for LDs and the corresponding length of blocks to be respectively very close to the mean length of topologically associating domains (TADs) and chromosomal segments with different densities of CpG islands for human chromosomes. The results indicate that topological constraints with optimal length can contribute to the formation of territories by weakening the degree of phase separation, which likely promotes the chromosomal flexibility in response to genetic regulations.

Nanorheology of active-passive polymer mixtures differentiates between linear and ring polymer topology

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes decelerate with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett., 2016, 116, 058301] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.

Active bath-induced localization and collapse of passive semiflexible polymers

The conformational and dynamical properties of a passive polymer embedded in a bath of active Brownian particles (ABPs) are studied by Langevin dynamics simulations. Various activities and ABP concentrations below and above the critical values for motility-induced phase separation (MIPS) are considered. In a homogeneous ABP fluid, the embedded polymer swells with increasing bath activity, with stronger swelling for larger densities. The polymer dynamics is enhanced, with the diffusion coefficient increasing by a power-law with increasing activity, where the exponent depends on the ABP concentration. For ABP concentrations in the MIPS regime, we observe a localization of the polymer in the low-density ABP phase associated with polymer collapse for moderate activities and a reswelling for high activities accompanied by a preferred localization in the high-density ABP phase. Localization and reswelling are independent of the polymer stiffness, with stiff polymers behaving similarly to flexible polymers. The polymer collapse is associated with a slowdown of its dynamics and a significantly smaller center-of-mass diffusion coefficient. In general, the polymer dynamics can only partially be described by an effective (bath) temperature. Moreover, the properties of a polymer embedded in a homogeneous active bath deviate quantitatively from those of a polymer composed of active monomers, i.e., linear chains of ABPs; however, such a polymer exhibits qualitatively similar activity-dependent features.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Orc4 spatiotemporally stabilizes centromeric chromatin

The establishment of centromeric chromatin and its propagation by the centromere-specific histone CENPA is mediated by epigenetic mechanisms in most eukaryotes. DNA replication origins, origin binding proteins, and replication timing of centromere DNA are important determinants of centromere function. The epigenetically regulated regional centromeres in the budding yeast Candida albicans have unique DNA sequences that replicate earliest in every chromosome and are clustered throughout the cell cycle. In this study, the genome-wide occupancy of the replication initiation protein Orc4 reveals its abundance at all centromeres in C. albicans Orc4 is associated with four different DNA sequence motifs, one of which coincides with tRNA genes (tDNA) that replicate early and cluster together in space. Hi-C combined with genome-wide replication timing analyses identify that early replicating Orc4-bound regions interact with themselves stronger than with late replicating Orc4-bound regions. We simulate a polymer model of chromosomes of C. albicans and propose that the early replicating and highly enriched Orc4-bound sites preferentially localize around the clustered kinetochores. We also observe that Orc4 is constitutively localized to centromeres, and both Orc4 and the helicase Mcm2 are essential for cell viability and CENPA stability in C. albicans Finally, we show that new molecules of CENPA are recruited to centromeres during late anaphase/telophase, which coincides with the stage at which the CENPA-specific chaperone Scm3 localizes to the kinetochore. We propose that the spatiotemporal localization of Orc4 within the nucleus, in collaboration with Mcm2 and Scm3, maintains centromeric chromatin stability and CENPA recruitment in C. albicans.

Inferring chromosome radial organization from Hi-C data

BACKGROUND

The nonrandom radial organization of eukaryotic chromosome territories (CTs) inside the nucleus plays an important role in nuclear functional compartmentalization. Increasingly, chromosome conformation capture (Hi-C) based approaches are being used to characterize the genome structure of many cell types and conditions. Computational methods to extract 3D arrangements of CTs from this type of pairwise contact data will thus increase our ability to analyze CT organization in a wider variety of biological situations.

RESULTS

A number of full-scale polymer models have successfully reconstructed the 3D structure of chromosome territories from Hi-C. To supplement such methods, we explore alternative, direct, and less computationally intensive approaches to capture radial CT organization from Hi-C data. We show that we can infer relative chromosome ordering using PCA on a thresholded inter-chromosomal contact matrix. We simulate an ensemble of possible CT arrangements using a force-directed network layout algorithm and propose an approach to integrate additional chromosome properties into our predictions. Our CT radial organization predictions have a high correlation with microscopy imaging data for various cell nucleus geometries (lymphoblastoid, skin fibroblast, and breast epithelial cells), and we can capture previously documented changes in senescent and progeria cells.

CONCLUSIONS

Our analysis approaches provide rapid and modular approaches to screen for alterations in CT organization across widely available Hi-C data. We demonstrate which stages of the approach can extract meaningful information, and also describe limitations of pairwise contacts alone to predict absolute 3D positions.

Chromatin as an active polymeric material

The patterns of the large-scale spatial organization of chromatin in interphase human somatic cells are not random. Such patterns include the radial separation of euchromatin and heterochromatin, the territorial organization of individual chromosomes, the non-random locations of chromosome territories and the differential positioning of the two X chromosomes in female cells. These features of large-scale nuclear architecture follow naturally from the hypothesis that ATP-consuming non-equilibrium processes associated with highly transcribed regions of chromosomes are a source of 'active' forces. These forces are in excess of those that arise from Brownian motion. Simulations of model chromosomes that incorporate such activity recapitulate these features. In addition, they reproduce many other aspects of the spatial organization of chromatin at large scales that are known from experiments. Our results, reviewed here, suggest that the distribution of transcriptional activity across chromosomes underlies many aspects of large-scale nuclear architecture that were hitherto believed to be unrelated.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

The rich inner life of the cell nucleus: dynamic organization, active flows, and emergent rheology

The cell nucleus stores the genetic material essential for life, and provides the environment for transcription, maintenance, and replication of the genome. Moreover, the nucleoplasm is filled with subnuclear bodies such as nucleoli that are responsible for other vital functions. Overall, the nucleus presents a highly heterogeneous and dynamic environment with diverse functionality. Here, we propose that its biophysical complexity can be organized around three inter-related and interactive facets: heterogeneity, activity, and rheology. Most nuclear constituents are sites of active, ATP-dependent processes and are thus inherently dynamic: The genome undergoes constant rearrangement, the nuclear envelope flickers and fluctuates, nucleoli migrate and coalesce, and many of these events are mediated by nucleoplasmic flows and interactions. And yet there is spatiotemporal organization in terms of hierarchical structure of the genome, its coherently moving regions and membrane-less compartmentalization via phase-separated nucleoplasmic constituents. Moreover, the non-equilibrium or activity-driven nature of the nucleus gives rise to emergent rheology and material properties that impact all cellular processes via the central dogma of molecular biology. New biophysical insights into the cell nucleus can come from appreciating this rich inner life.

Data-Driven Polymer Model for Mechanistic Exploration of Diploid Genome Organization

Chromosomes are positioned nonrandomly inside the nucleus to coordinate with their transcriptional activity. The molecular mechanisms that dictate the global genome organization and the nuclear localization of individual chromosomes are not fully understood. We introduce a polymer model to study the organization of the diploid human genome. It is data-driven because all parameters can be derived from Hi-C data; it is also a mechanistic model because the energy function is explicitly written out based on a few biologically motivated hypotheses. These two features distinguish the model from existing approaches and make it useful both for reconstructing genome structures and for exploring the principles of genome organization. We carried out extensive validations to show that simulated genome structures reproduce a wide variety of experimental measurements, including chromosome radial positions and spatial distances between homologous pairs. Detailed mechanistic investigations support the importance of both specific interchromosomal interactions and centromere clustering for chromosome positioning. We anticipate the polymer model, when combined with Hi-C experiments, to be a powerful tool for investigating large-scale rearrangements in genome structure upon cell differentiation and tumor progression.

The self-stirred genome: large-scale chromatin dynamics, its biophysical origins and implications

The organization and dynamics of human genome govern all cellular processes - directly impacting the central dogma of biology - yet are poorly understood, especially at large length scales. Chromatin, the functional form of DNA in cells, undergoes frequent local remodeling and rearrangements to accommodate processes such as transcription, replication and DNA repair. How these local activities contribute to nucleus-wide coherent chromatin motion, where micron-scale regions of chromatin move together over several seconds, remains unclear. Activity of nuclear enzymes was found to drive the coherent chromatin dynamics, however, its biological nature and physical mechanism remain to be revealed. The coherent dynamics leads to a perpetual stirring of the genome, leading to collective gene dynamics over microns and seconds, thus likely contributing to local and global gene-expression patterns. Hence, a possible biological role of chromatin coherence may involve gene regulation.

GPSeq reveals the radial organization of chromatin in the cell nucleus

With the exception of lamina-associated domains, the radial organization of chromatin in mammalian cells remains largely unexplored. Here, we describe genomic loci positioning by sequencing (GPSeq), a genome-wide method for inferring distances to the nuclear lamina all along the nuclear radius. GPSeq relies on gradual restriction digestion of chromatin from the nuclear lamina towards the nucleus center, followed by sequencing of the generated cut sites. Using GPSeq, we mapped the radial organization of the human genome at 100 kb resolution, which revealed radial patterns of genomic and epigenomic features, gene expression, as well as A/B subcompartments. By combining radial information with chromosome contact frequencies measured by Hi-C, we substantially improved the accuracy of whole-genome structure modeling. Finally, we charted the radial topography of DNA double-strand breaks, germline variants and cancer mutations, and found that they have distinctive radial arrangements in A/B subcompartments. We conclude that GPSeq can reveal fundamental aspects of genome architecture.

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.

A Lamin-Associated Chromatin Model for Chromosome Organization

We propose a simple model for chromatin organization based on the interaction of the chromatin fibers with lamin proteins along the nuclear membrane. Lamin proteins are known to be a major factor that influences chromatin organization and hence gene expression in the cells. We provide a quantitative understanding of lamin-associated chromatin organization in a crowded macromolecular environment by systematically varying the heteropolymer segment distribution and the strength of the lamin-chromatin attractive interaction. Our minimal polymer model reproduces the formation of lamin-associated-domains and provides an in silico tool for quantifying domain length distributions for different distributions of heteropolymer segments. We show that a Gaussian distribution of heteropolymer segments, coupled with strong lamin-chromatin interactions, can qualitatively reproduce observed length distributions of lamin-associated-domains. Further, lamin-mediated interaction can enhance the formation of chromosome territories as well as the organization of chromatin into tightly packed heterochromatin and the loosely packed gene-rich euchromatin regions.