Mesoscale liquid model of chromatin recapitulates large-scale organization of eukaryotic cell nuclei

The nuclear envelope segregates the genome of eukaryota from the cytoplasm. Within nucleus chromatin is further compartmentalized into architectures that change throughout lifetime of the cell. Epigenetic patterns along the chromatin polymer strongly correlate with chromatin compartmentalization and, accordingly, also change during cell life cycle and at differentiation. Recently, it has been suggested that sub-nuclear chromatin compartmentalization might result from a process of liquidliquid phase separation orchestrated by the epigenetic marking and operated by proteins that bind to chromatin. Here, we translate these observations into a diffuse interface model of chromatin, which we named Mesoscale Liquid mOdel of Nucleus (MELON). Using this streamlined continuum model of the genome, we study the large-scale rearrangements of chromatin that happen at different stages of the growth and senescence of the cell, and during nuclear inversion events. Particularly, we investigate the role of droplet diffusion, fluctuations, and heterochromatin-lamina interactions during nuclear remodeling. Our results indicate that the physical process of liquidliquid phase separation, together with surface effects is sufficient to recapitulate much of the large-scale morphology and dynamics of chromatin along the life cycle of cells. Chromatin| Eukaryotic Nucleus | Meso-scale modeling | phase separation | Correspondence: potoyan@iastate.edu Introduction Functional compartmentalization is a ubiquitous hallmark of life; by segregating bio-molecules and their interactions cells achieve specialization and improved efficiency of many of their functions (1, 2). In eukaryotic cells, the genetic material is separated from the cytoplasm by the nuclear membrane within the few cubic micrometers of nuclear space. Within the nuclear boundary, we find further compartmentalization which, however, exists in the absence of membranes (3). The structural organization of chromosomes changes with the cell type and phase of life, chromosomal loci have been observed to move across genomic compartments during cell differentiation. As a consequence, chromatin compartmentalization is believed to play a role in gene regulation and in the definition of cellular phenotypes (4, 5). The first evidence of chromatin sub-nuclear organization in interphase was the discovery of the nucleolus in the early nineteenth century, followed by the discovery of regions in the nucleus with distinct optical properties, which were named heterochromatin and euchromatin (6). Heterochromatin appears dense and slow diffusing, containing regions of chromosomes corresponding to mostly silenced genes. Euchromatin, on the other hand, appear less dense and more mobile, composed of mostly active genes (7, 8). The latest electron microscopy tomography experiments have confirmed the DNA density variations between heterochromatic and euchromatic regions without, however, finding any structural difference between the two types of chromatin (9). Clear evidence of hierarchical compartmentalization in chromatin at multiple scales have emerged through studies employing DNA-DNA proximity ligation assays. First, two genomic compartments were observed (3), named A and B which were then refined through higher resolution experiments to reveal the existence of even smaller subcompartments (5). The A and B compartments appear to be enriched in epigenetic markings correlating with transcriptional activation and silencing respectively. Several studies have suggested that chromatin compartmentalization might results from a process of liquid-liquid phase separation orchestrated by the epigenetic marking and operated by proteins that bind along the DNA polymer (10–15). Chromatin compartmentalization is also consistent with recent experiments that have revealed the remarkable ability of intrinsically disordered proteins to phase separate and form liquid-like protein-rich droplets (16–19). Akin to oil droplets in a well shaken bottle of vinaigrette the protein rich droplets can appear and disappear according to external triggers, can divide and undergo fusion forming larger droplets (20–22). Most importantly, in the latest series of experiments, members of the family of HP1 proteins (Heterochromatin protein 1) known for regulation of heterochromatin content in the nucleus have been shown to undergo liquid-liquid phase separation both in vivo and in vitro under variety of conditions (23, 24). Consequently, protein-induced phase separation of chromosomal domains might constitute a direct physical mechanism for regulating genetic processes in space and time in the nucleus (16, 25). Henriques et al. | bioRχiv | May 10, 2019 | 1–8 DR AF T The global architecture of chromosomes appears indeed to be determined by the interplay between chromatin phase separation and motor activity (10–12, 26, 27). Besides chromatin compartmentalization, the other prominent feature of genome three-dimensional architecture, the topologically associated domains (TADs), also appear to arise through either or both the processes of phase separation and DNA extrusion (28). Theoretical models based on polymer dynamics have been successfully used to connect one-dimesional epigenetic information to the three-dimensional architecture of the genome. Indeed, it is possible to predict the structural ensembles of human chromosomes with high accuracy based exclusively on information extracted from chromatin immuno-precipitation sequencing (ChIP-seq) (11). The same theoretical framework, composed exclusively of polymer connectivity, motor activity and micro-phase separation was shown to successfully explains a wide range of experimental observations about the dynamics of chromosomal loci (12). The subdiffusive behavior of chromatin together with the heterogeneity of the individual diffusing trajectories (29), the viscoelasticity of the nuclear environment (30) , and the coherent motion of DNA observed by correlation spectroscopy (31) were all naturally predicted through theoretical and computational modelling. Here we set out to investigate the specific contribution of liquid-liquid phase separation to genome architecture and separate its effects from those of polymer connectivity and motor activity. To gain insights into the roles of phase separation and surface effects in chromatin compartmentalization, we introduce the MEsoscale Liquid mOdel of Nucleus (MELON), a physical model of nuclear organization which is rooted in the theory of complex fluids. We use diffuse interface finite element simulations to model the evolution of nuclear chromatin compartments under various developmental processes including growth and inversion/senescence. Our approach draws inspiration and integrates elements of several mesoscopic cellular models such as the two-fluid hydrodynamic model of chromatin (32), the multi-cellular growth model (33, 34), the polymer models with epigenetic coloring already mentioned and active cellular mechanics (35–37). We apply MELON framework for modeling liquid-liquid phase separation driven reorganization of chromatin compartments in Drosophila melanogaster nucleus under wide variety of conditions including both equilibrium and nonequilibrium nuclear remodeling. The generic nature of the MELON model and the minimal assumptions that we have built into it, however, allow us to draw conclusion on the physical nature of chromatin reorganization which should be generally applicable for wide variety of eukaryotic nuclei beyond the specific case of Drosophila. The meso-scale liquid model of the nucleus (MELON) In this section, we present the basic physics and motivating biology behind the MEsoscale Liquid mOdel of Nucleus (MELON). More details about the mathematical formulation and computational implementation of MELON can be found in the Supporting Information. The MELON is set up to model the micron scale liquid dynamics and epigenetically orchestrated liquid-liquid phase separation of chromatin compartments in the nucleus. To this end, we construct the global free energy functional based on essential physical features: phase separation, surface tension, volume constraints and specific interaction of chromatin types. The nuclear chromatin morphology is defined through fluctuating order parameters which resolve (i) Nuclear membrane φ0(r, t) (ii) Global i = 1, . ,N chromosome territories φi(r, t) and (iii) Epigenetic states of chromatin ψ(r, t) which smoothly varies from 0 to 1 corresponding to A and B chromatin types respectively (Fig 1). The time evolution of all the order parameters is governed by a global free energy functional. The specific forms of the free energy functional terms are motivated either by basic experimental facts about the chromosomal organization (existence of territories and types) or polymeric physics of chromosomes (excluded volume, de-mixing of types). The mesoscale resolution of chromatin naturally addresses the questions of epigenetically driven liquid-liquid phase separation, surface effects of chromatin compartment formation as well as diffusion and fluctuations of chromocenters and liquid chromatin droplets within the nucleus.