Biology and Physics of Heterochromatin-Like Domains/Complexes

The hallmarks of constitutive heterochromatin, HP1 and H3K9me2/3, assemble heterochromatin-like domains/complexes outside canonical constitutively heterochromatic territories where they regulate chromatin template-dependent processes. Domains are more than 100 kb in size; complexes less than 100 kb. They are present in the genomes of organisms ranging from fission yeast to human, with an expansion in size and number in mammals. Some of the likely functions of domains/complexes include silencing of the donor mating type region in fission yeast, preservation of DNA methylation at imprinted germline differentially methylated regions (gDMRs) and regulation of the phylotypic progression during vertebrate development. Far cis- and trans-contacts between micro-phase separated domains/complexes in mammalian nuclei contribute to the emergence of epigenetic compartmental domains (ECDs) detected in Hi-C maps. A thermodynamic description of micro-phase separation of heterochromatin-like domains/complexes may require a gestalt shift away from the monomer as the “unit of incompatibility” that determines the sign and magnitude of the Flory–Huggins parameter, χ. Instead, a more dynamic structure, the oligo-nucleosomal “clutch”, consisting of between 2 and 10 nucleosomes is both the long sought-after secondary structure of chromatin and its unit of incompatibility. Based on this assumption we present a simple theoretical framework that enables an estimation of χ for domains/complexes flanked by euchromatin and thereby an indication of their tendency to phase separate. The degree of phase separation is specified by χN, where N is the number of “clutches” in a domain/complex. Our approach could provide an additional tool for understanding the biophysics of the 3D genome.


Diagram B: Micro-phase separation and segregation of heterochromatin-like domain/complexes.
Bridging of H3K9me3-marked nucleosomes by HP1 results in micro-phase separation of heterochromatin-like domains/complexes (middle loop). Bridging results in stabilisation of zig-zag geometry of H3K9me3-marked nucleosomes in heterochromatin-like "clutches" (middle box at top of figure; modified from [1]). This contrasts with euchromatic "clutches" (box on left) where the nucleosomes are disorganised with only partial zig-zag geometry. Like-with-like attraction (binding potential), due to an entropic effect (see text for details), results in cis-(shown in Diagram B) and trans-(not shown) interactions between domain/complexes. Interactions are stabilised by bridging of H3K9me3-marked nucleosome fibers by HP1 (box on right) and stabilises segregation of domains/complexes. Contacts resulting from segregation are detected as contact enrichments that contribute to ECDs in Hi-C experiments. Segregation of micro-phase separated domains/complexes is unlikely to be static (as drawn). Micro-phase separated domains/complexes within segregated assemblies will be subject to constant disassociation and association Cis-and trans-contacts that result from segregation of heterochromatin-like and Pc-G domains/complexes emerge as ECDs in Hi-C maps (Diagram C). Notably, screens for genes that are necessary to safeguard cellular identity identified genes that encode CAF-1, the SUMO-conjugating enzyme UBE2i, SUMO2, SETDB1, ATRX and DAXX proteins [11,12]. All are involved in either nucleation or replication of heterochromatin-like domains/complexes thus providing a link between safeguarding cellular identity and ECDs [1].
Diagram C: Cis-and trans-contacts involving micro-phase separated heterochromatin-like or Pc-G domains/complexes generate ECDs. Heterochromatin-like or Pc-G domains/complexes (red lines) segregate through like-with-like cis-(red double-headed arrows) and trans-(red arrows) interactions. These interactions generate contact enrichments that emerge as epigenetic compartmental domains (red EDCs in the cartoon Hi-C map). For euchromatin, cis-(blue double-headed arrows) and trans-(blue arrows) contacts generate the A-type compartmental domains (blue contact enrichments in cartoon Hi-C map). The cartoon Hi-C map was taken and modified from [4]. B-type compartmental domains are unlikely to be precisely equivalent to ECDs, i.e., it is unlikely that B-type compartments are generated solely by contact enrichments that are a consequence of segregation of micro-phase separated heterochromatin-like and Pc-G domains/complexes. For example, it is known that B3 sub-compartment includes contact enrichments that result from interactions between lamin-associated loci [13]. HP1 proteins are also known to associate with the nuclear lamina [14] but the degree to which heterochromatin-like domains/complexes are involved in interactions between lamin-associated loci that generate the contact enrichments is not known. Functional experiments will be needed to define the precise extent to which ECDs overlap with B-type heterochromatic compartmental domains.
Box S2. The Flory-Huggins parameter () and the monomer as the "unit of incompatibility".
. Polymers are very long molecules formed from small repeating units called monomers. Polymers come in many varieties but the standard types are formed from small hydrophobic hydrocarbon monomers (~100Da) that have low ionisation and polarization potential.
Redrawn from [15] Homo-polymers formed from such monomers were the concern of Flory [16] and Huggins [17] when they set out to describe the thermodynamics of polymer mixing in simple solvents and, more importantly, the conditions under which they de-mix i.e., phase separate into polymer-rich and solvent-rich phases. For such homo-polymers the tendency to phase separate is described by the Flory-Huggins parameter  (Equation (S1) below), which quantifies the balance between the three types of interaction that take place when homo-polymers are added to a solvent, namely polymer-solvent, polymer-polymer and solvent-solvent interactions.
(S1) These interactions can be modelled using mean-field lattice theory where polymer and solvent molecules arrange themselves randomly within in an infinite lattice structure of co-ordination number z (see below for two-dimensional lattice where z = 8), each occupying one lattice position. The lattice is set at the volume occupied by one monomer segment of the polymer; it is assumed that the lattice is incompressible so the volume of the solvent is equivalent to that of one monomer unit: Taken and modified from [18] Whether the polymer phase separates or not depends on the mean field energies per lattice site, i.e., the energetic cost (in terms of thermal energy kBT) of having pairs of polymer-solvent monomer units (ps), pairs of polymer units (pp) and pairs of solvent units (ss) next to each other in the lattice. In the case of highly unfavourable interactions, where there is an energetic cost for having the polymer monomer site adjacent to the solvent site, monomers will prefer to be near each other (like-with-like) and phase separation is likely to occur (poor solvent; >0). Above a particular value, crit, the critical value of the Flory-Huggins parameter where the energy of interaction overcomes the entropy of mixing, the polymer will collapse and phase separation is observed (see [18] for a more detailed discussion of the Flory-Huggins free energy of mixing equation). < 0 in the case of highly favourable interactions between monomer and solvent, where monomers will avoid being near each other whereupon the polymer chain swells (good solvent). Thus  is a measure of the degree of incompatibility of the polymer with the solvent and, as defined in Equation (S1), is inversely proportional to temperature. The sign of  (+ve or -ve) is dependent upon the choice of monomer repeating unit; the "unit of incompatibility" for the Flory-Huggins approach to the miscibility of polymers is the monomer. Box S3. The segregation product N and order-disorder (ODT) transition of BCPs.
. The degree of micro-phase separation of bulk (undiluted) di-block copolymers (di-BCPs), where the A and B blocks are incompatible, is determined by the segregation product, N, where N is the number of repeat units (monomers) that make up the polymer chain. Self-consistent field theory predicts that micro-phase separation takes place when N≈10.5 [19], which has been confirmed experimentally [15]. When the di-BCP is symmetrical (volume fraction f = 0.5) and N>10.5 phase separation takes on the character of lamellae. The reason for this is that the covalent linkages stop the A and B blocks from macro-phase separating: the thermodynamic forces driving separation are counterbalanced by entropic forces from the covalent linkage. The resulting chain elasticity keeps the dissimilar A and B portions of the di-BCP apart. As a consequence, symmetric di-BCPs adopt extended configurations seen as lamellae that are in length scales similar to the molecular dimensions of the di-BCPs themselves (0.05-0.1m).
Taken from [20] When N<<10 for symmetric di-BCPs entropic factors dominate and they possess a homogeneous composition profile when plotting composition, A, versus the ensemble average of the bond vectors <r>. When  or N are increased so that N ≈10 there are local fluctuations in composition owing to small variations in system entropy (~N -1 ) or energy (~) and this results in disordered states (N ≤10). As N is increased further there is an order-disorder transition (ODT; NODT) where the disordered microstructure is replaced by a periodic lamellae mesophase (N ≥10) albeit weak A-B interactions still occur and, as consequence, the interfaces are weak and "wavy" (see A vs r⊥ for N ≥10).
Taken from [20] At the limit when N>>10 energetic factors prevail and a strongly segregated lamellae pattern is observed where interfaces become narrow and micro-domains are composed of pure A or B and the ensemble bond vectors, r, are essentially perpendicular to the periodic mesophase. The evolution of the structures as the product N increases shows that phase separation close to the ODT (N≥10) gives rise to interfaces that are weak, wavy, almost liquid-like, while much greater than the ODT (N>>10) interfaces are narrow and sharp. The relationship between N, NODT and degree of phase separation defined analytically with BCPs may provide insight into the character (degree) of the phase separation observed with heterochromatin-like domain/complexes compared to that seen with Pc-G domain/complexes. An important caveat is the domains/complexes are unlikely to behave like simple flexible chains governed by Gaussian statistics as assumed for bulk BCPs [15,19]. Because of this, heterochromatin-like and Pc-G domains/complexes in the interphase nucleus will have their own values for order-disorder transition, NODT_HC and NODT_PC respectively.