# Phase transitions in heterochromatin organization

Fabian Erdel

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Fabian Erdel. Phase transitions in heterochromatin organization. Current Opinion in Structural Biology, 2023, 80, pp.102597. 10.1016/j.sbi.2023.102597. hal-04298201

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# Phase transitions in heterochromatin organization

Fabian Erdel

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## Abstract

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.

## Addresses

MCD, Center for Integrative Biology (CBI), CNRS, UPS, Toulouse, France

Corresponding author: Erdel, Fabian (fabian.erdel@cnrs.fr)

**Current Opinion in Structural Biology** 2023, 80:102597

This review comes from a themed issue on **3D Genome Chromatin Organization and Regulation (2023)**

Edited by Genevieve Almouzni and Juanma Vaquerizas

For complete overview of the section, please refer the article collection - 3D Genome Chromatin Organization and Regulation (2023)

Available online 21 April 2023

https://doi.org/10.1016/j.sbi.2023.102597

0959-440X/© 2023 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

## What is a phase transition?

The concept of phase transitions has been used over decades to describe various phenomena across the natural and life sciences [1,2]. It has more recently been adopted to describe the behavior of chromatin and the nuclear proteins that interact with it. In general terms, a phase transition is characterized by an abrupt change in at least one large-scale physical property of a system, called ‘order parameter’, as a function of a small change of another property, called ‘control parameter’ (Figure 1). The values of the order parameter before and after the transition define the individual phases of the system. A classic example of a

phase transition is boiling water, which evaporates and thereby abruptly changes its density as the temperature is gradually increased beyond the boiling point. The two respective phases, liquid and vapor, are characterized by their distinct densities. Phase transitions in thermodynamic systems can be put into two categories, first-order and higher-order (continuous) transitions, depending on which parameters or, more precisely, which derivatives of the free energy, change abruptly. For a more extensive review about the theory of phase transitions see for example [2]. Phase separation processes can be understood as phase transitions as they involve an abrupt change of local concentrations in the different phases [3,4]. As discussed in the sections below, potential order parameters in the context of heterochromatin could be the compaction and number of heterochromatin clusters, as well as the local concentration and mobility of heterochromatin proteins. The motivation to assess if these features can serve as order parameters in the context of phase transitions is that analogies to other systems undergoing phase transitions can be drawn. This can aid for example in the generation of hypotheses about the global behavior of heterochromatin, e.g. its response to drugs and other perturbations. Moreover, predictions about the physicochemical properties of heterochromatin can be made, which are expected to differ from those of the surrounding chromatin if liquid-liquid demixing is involved.

## Which types of phase transitions might occur in the context of heterochromatin?

Considering phase transitions that may occur in the context of chromatin, it is instructive to distinguish between transitions occurring on the level of chromosomal regions and those occurring on the level of the much smaller nuclear proteins and RNAs that transiently bind to them. Although both chromosomes, nuclear proteins and RNAs, fall in the category of biopolymers, they behave very differently in many respects (Box 1). One consequence is that the minimum binding valency required to drive demixing of chromosomal regions is lower than the valency required to drive liquid-liquid demixing of nuclear proteins and RNAs (Box 1). The distinction between both types of phase transitions does not imply that both processes have to be uncoupled. It rather reflects the fact that both processes differ from each other and that they involve distinct constraints for the molecules that can trigger them,
<figure><img src="image_3.png" /><figcaption>Figure 1</figcaption></figure>

Phase transitions

Phase transitions involve an abrupt change in at least one large-scale
physical property of a system, the so-called ‘order parameter’, as a
function of a small change of another property, the so-called ‘control
parameter’. First-order transitions show a discontinuity of the order
parameter (a), while higher-order (continuous) transitions show a kink in
the order parameter (b).

which is for example relevant for the identification of
candidate driver proteins (see below).

Different types of phase transitions that may occur in the context of heterochromatin are shown in Figure 2. On the one hand, heterochromatin proteins and/or RNAs establishing multivalent interactions with one another may demix and form condensates at heterochromatin regions (Figure 2, top), either by undergoing a prewetting transition to form surface condensates that coat the nucleosome chain or by further undergoing liquid-liquid phase separation (LLPS) [4,5]. On the other hand, bridging interactions between heterochromatic chromosomal regions may drive a reordering transition that brings these regions into spatial proximity to each other (Figure 2, bottom), or a further collapse transition that additionally

increases their compaction [6–9]. The latter transitions
can be considered as different variants of
polymer–polymer phase separation (PPPS) [10], as they
describe changes of the chromosomal polymer confor-
mation that go along with changes in the local concen-
tration of heterochromatin regions. By default, both
LLPS- and PPPS-type transitions can be expected to
resemble first-order phase transitions [3–5,9,11],
although higher-order (continuous) transitions can be
observed in special cases, e.g. when active processes such
as the deposition of histone marks that modulate nucle-
osomal interactions are considered [12]. PPPS-type
transitions have more relaxed constraints on the valency
of the underlying interactions than LLPS-type transi-
tions (Box 1). In particular, PPPS can be driven by pro-
teins (or protein complexes) with only two binding sites
for chromatin, while LLPS requires higher binding
valencies [13–17]. As many heterochromatin proteins
contain (at least) one reader domain for chromatin and
can form homo- and hetero-dimers [18], all these pro-
teins are candidates for driving PPPS. However, only
heterochromatin proteins that form multivalent in-
teractions with one another and/or with other proteins
and RNAs are candidates for driving LLPS. As pointed
out above, PPPS-type transitions and LLPS-type transi-
tions can conceptually be coupled, i.e. if heterochromatin
proteins undergo liquid–liquid demixing and if the
resulting condensates mediate bridging interactions be-
tween heterochromatic chromosomal regions. In the
following, I will discuss the current evidence for or against
the occurrence of the different types of phase transitions
in heterochromatin, along with the potential molecu-
lar drivers.

Phase transitions linked to liquid demixing of
heterochromatin proteins

Heterochromatin proteins might in principle be able to
undergo prewetting transitions or LLPS, similarly to
most other cellular proteins [19–21]. Prominent can-
didates are shown in Figure 3a, along with their disorder
score [19] and their relative abundance in selected
species [22], which are two informative parameters in
the context of phase transitions. The list is not meant to
be exhaustive, and more candidates can be considered,
e.g. [23]. The challenge in deciding if a given protein
actually undergoes an LLPS-type transition within
heterochromatin is to experimentally detect the
respective condensates in living cells. This has proven to
be notoriously difficult, as proteins that merely bind to
heterochromatin regions via low-valency interactions
that do not drive LLPS-type transitions behave very
similarly in most assays [24,25]. In particular, they can
show similar recovery kinetics in classic fluorescence
recovery after photobleaching (FRAP) experiments, and
their localization can be sensitive or not to the exposure
to 1,6-hexanediol, an aliphatic alcohol that has often
been used to probe the stability of cellular substructures
[25]. Furthermore, chromatin regions merely decorated
Box 1. Phase transitions on the level of proteins and chromosomes.

Although chromosomes, nuclear proteins and RNA molecules are bio-
polymers that follow the same physical laws, chromosomes are distinct
with respect to their large size and low copy number in the cell. While
most proteins and RNA molecules can move through the nucleus in a
few seconds or minutes, chromosomes as well as their megabase-sized
pericentric heterochromatin regions move much more slowly and mostly
stay in their 'territories' over hours [53]. The spatial separation of chro-
mosomes into these 'territories' is likely linked to their low mobility [71].
There are also fundamental differences when comparing individual nu-
cleosomes on the chromosome to similar-sized protein or RNA mole-
cules. For example, nucleosomes always reside in close spatial
proximity to the neighboring nucleosomes on the same chromosome,
which sets a lower limit for the local nucleosome concentration around
each nucleosome, independently of the chromosomal conformation and
the inter-nucleosomal interaction strength. Proteins or RNAs that asso-
ciate only transiently with chromosomes do not experience such topo-
logical constraints, so that they can form dilute phases with arbitrarily low
concentrations. Another consequence of this topological constraint is
that the energetic cost for spatially rearranging nucleosomes residing on

a chromosome is different from that for rearranging molecules that
associate only transiently with chromosomes: On the one hand, bringing
patches of already connected nucleosomes together is entropically
easier than bringing individual nucleosome-sized proteins or RNAs
together out of a homogenous solution [15]. On the other hand, rear-
ranging nucleosomes might involve an additional energetic cost if tethers
between the chromosome and the nuclear lamina or other nuclear
subcompartments have to be broken. Due to these differences, it seems
useful to separately consider LLPS-type demixing transitions on the level
of nuclear proteins/RNAs andPPPS-type refolding transitions on the
level of chromosomal segments [10]. As shown in the adjacent scheme,
there are different constraints for proteins that drive these transitions:
LLPS-type transitions require multivalent self-interactions (valency ≥3),
whilePPPS-type transitions can also be driven by proteins that bind to
chromatin and only dimerize (valency ≥1) [13–17]. Here, interaction
surfaces are colored in black, and “self-interactions” refer to interactions
among all molecules that drive the respective transition, i.e., they include
interactions among different molecular species if multicomponent con-
densates are considered.

<figure><img src="image_4.png" /></figure>

with bound proteins and chromatin regions associated
with protein condensates can be expected to coalesce
with each other upon contact [10,26,27]. Although the
coalescence kinetics might in principle be used to
distinguish the two cases, this approach might be
fraught with difficulties in living cells where these ki-
netics are modulated by the local chromatin properties
[28], which are spatially heterogeneous and not readily
experimentally accessible. Similar limitations apply to
the interpretation of the spatial variation of diffusion
coefficients, which can be modulated not only by the
presence of a condensate of interest but also by the
presence of other obstacles [29] and ‘immobile’ binding
sites on chromosomes [30,31], whose spatial distribu-
tions and biochemical properties are usually unknown.

We have recently developed a half-FRAP assay to
distinguish proteins undergoing liquid–liquid demixing
from proteins merely undergoing low-valency in-
teractions with spatially clustered binding sites (ICBS)
on chromosomes [25,32]. This assay resolves the barrier
at the interface of a condensate, which arises from the
multivalent interactions that drive liquid–liquid demix-
ing. The higher this barrier is, the more likely will mol-
ecules move within the condensate instead of moving
across the interface into the surrounding dilute phase. We
have used the method to study several proteins in mouse
fibroblasts [25,32], including HP1α and MECP2 that
have been suggested to undergo LLPS [33–35]. Unlike
for proteins in stress granules, germ granules, and
nucleoli, we did not find any interfacial barrier for HP1α
<figure><img src="image_5.png" /><figcaption>Figure 2</figcaption></figure>

Candidate phase transition mechanisms in heterochromatin.

Two different types of phase transitions that might conceptually take place in the context of heterochromatin are shown: LLPS-type transitions, involving liquid demixing of heterochromatin proteins via multivalent interactions (top), and PPPS-type transitions, involving the spatial reorganization of heterochromatin regions via bridging interactions (bottom). Both types of transitions come in two flavors, depending on the strength and frequency of interactions: For weak and scarce multivalent interactions, molecules can undergo a prewetting transition to form a surface condensate that coats the nucleosome chain (top, center). For stronger and more frequent interactions, molecules can undergo LLPS (top, right). For weak and scarce bridging interactions, molecules can drive a reordering transition of the chromosome (bottom, center), for stronger and more frequent bridging interactions, they can drive a collapse transition (bottom, right). Both types of transitions have different constraints for the binding valency of the respective interactions (see also Box 1). For valencies that are sufficient to drive LLPS-type transitions, both LLPS- and PPPS-type transitions may occur simultaneously, depending on the ability of surface condensates or droplets of heterochromatin proteins to bridge heterochromatic chromosomal regions. Both LLPS- and PPPS-type transitions might go along with changes in the material properties of the respective domains, which will not be discussed here. LLPS, liquid-liquid phase separation; PPPS, polymer-polymer phase separation.

and MECP2 in heterochromatin foci [25,32], indicating that in mouse fibroblasts, both proteins bind to heterochromatin without undergoing liquid-liquid demixing. In principle, it is possible that heterochromatin foci exhibit an interfacial barrier that is even shallower than the already quite shallow barriers of the above-mentioned cellular condensates we used for comparison, and potentially too shallow to detect in our half-FRAP assay. However, it is unclear which functional relevance such a shallow barrier would have, and which experimentally accessible features an LLPS-type model would predict more accurately than an alternative PPPS-type model without liquid-liquid demixing. In fact, the local viscosity [25,32] and solvent polarity [36] of heterochromatin foci in mouse fibroblasts were found to be similar to those in the surrounding chromatin regions (and different from HP1α condensates *in vitro*), which is in line with the prediction from ICBS/PPPS that both types of chromatin are percolated by the same nucleoplasmic fluid. Furthermore, the local HP1 concentration in heterochromatin foci did not abruptly decrease when global

HP1 levels were gradually reduced by transfection of small interfering RNAs (Figure 3b), arguing against demixing of the HP1 pool via an abrupt LLPS-type first-order transition. The difference to the published *in vitro* work might be that both HP1α and MECP2 are not very abundant in mouse fibroblasts (Figure 3a) and that the environment in the nucleus differs from that in the test tube. Interestingly, HP1α levels are similar in mice and humans while HP1α in fruit flies seems to be much more abundant [18,22,37], suggesting species-specific differences in heterochromatin regulation.

Surface condensates have recently been described for transcription factors on nucleosome-free DNA *in vitro* [11,38]. The prewetting transition that leads to their formation can occur at much lower protein concentrations than LLPS. While a single surface condensate that is held together by multivalent interactions should show an interfacial barrier, which is at odds with our half-FRAP experiments of HP1α and MECP2 in mouse fibroblasts [25,32], the presence of several small surface
<figure><img src="image_6.png" /><figcaption>Figure 3</figcaption></figure>

Candidate driver proteins and order parameters of phase transitions in heterochromatin.

(a) Candidate proteins that might drive heterochromatin phase transitions are shown together with their disorder score [19] and their average abundance in the respective organism [22]. Histone methyltransferases are colored in blue, readers of DNA/histone marks are colored in orange. Note that the abundance of some proteins varies strongly across cell types, e.g. the abundance of MECP2 in mouse neurons is much higher than the average value shown here [72]. The disorder score is most relevant for LLPS-type transitions, which require high binding valencies (Box 1) that are typically found for disordered proteins. Interactions with high valencies might also promote PPPS-type transitions, although interactions with lower valencies, e.g., dimerization, can be more relevant if they are stronger. (b) Local HP1 levels in heterochromatin foci of mouse fiboblasts change gradually with the total cellular HP1 level when the latter is reduced by siRNA transfection, pointing to the absence of a first-order LLPS-type demixing transition of the HP1 pool. Gray points reflect HP1 levels measured by immunostaining of cells transfected with different amounts of siRNA against HP1 [18]. (c) The compaction of heterochromatin regions changes abruptly upon recruitment of dCas9-VPR, which presumably reduces bridging interactions among heterochromatin regions. This is in line with a first-order PPPS-type transition. Gray points are taken from [32]. (d) The number of heterochromatin clusters varies considerably between mouse cells of the same and of different types (see points and their error bars), without showing an abrupt change between any two sets of cell types. Accordingly, the genome can adopt different three-dimensional arrangements with gradually varying degrees of spatial heterochromatin clustering. Considering our incomplete knowledge about the molecular mechanisms that regulate heterochromatin clustering in the respective cells, i.e. the control parameter, this is both consistent with the absence of a phase transition and with the presence of an arrested PPPS-type transition, e.g. [54]. Blue points correspond to developing rod photoreceptors analyzed at the indicated postnatal day [45], black points correspond to the cell types analyzed in [43]: lymph, lymphocytes; macro, macrophages; ES, embryonic stem cells; fib, fibroblasts; LLPS, liquid-liquid phase separation; PPPS, polymer-polymer phase separation.

condensates that are not connected to each other might be consistent with the currently available data. HP1α has been shown to be able to co-condense with nucleosome-free DNA *in vitro* [39], although the respective condensates have been described to be positionally stable, in contrast to the surface condensates formed by transcription factors whose positions fluctuated along the DNA [38]. The effects of HP1α condensates that coat the chromatin fiber have also been considered in recent simulations that were inspired by mammalian heterochromatin [40]. It remains to be seen if such condensates will be experimentally identified in living cells and if they play a role in organizing heterochromatin.

## Phase transitions linked to demixing of heterochromatic chromosomal regions

Heterochromatic chromosomal regions tend to spatially cluster in multiple species and cell types [41,42]. In most cases, pericentric heterochromatin regions form multiple clusters [41,43], with the exception of rod photoreceptors found in nocturnal mammals [44,45], where all pericentric heterochromatin regions come together in a single cluster. The number of heterochromatin clusters is thought to be regulated by the balance between heterochromatin self-interactions and heterochromatin–lamina interactions [9,44]. On the molecular level, these self-interactions might arise both from interactions between nucleosomes and from interactions between
heterochromatin proteins that are bound to them. The heterochromatin proteins involved can, in principle, act as isolated monomers/multimers that bridge different heterochromatin loci or as surface condensates or droplets that mediate bridging. Clustered heterochromatin regions also show an increased compaction degree, i.e. a higher local chromatin concentration, which varies across cell types and species [18,46–49]. Conceptually, spatial clustering and increased compaction are not necessarily coupled, which is also supported by recent work integrating Hi-C, microscopy, and simulations [7,9,44]. As discussed above, both processes can be considered as phase transitions if they involve an abrupt change of an order parameter. Indeed, recent simulation work has suggested that heterochromatin clustering resembles a first-order phase transition [9], with an abrupt change in the localization of the respective chromosomal regions. The simulated system also showed hysteresis, a feature often associated with phase transitions: Heterochromatin regions tended to retain their current spatial arrangement when lamina-heterochromatin interactions were altered to trigger a change in nuclear organization [9]. Similarly, simulations describing heterochromatin clustering in rod photoreceptors of nocturnal mammals found that the transition is irreversible, i.e. that clustered heterochromatin regions in a cell without lamina-heterochromatin interactions stay together even when interactions with the lamina are reintroduced [44].

For increasing self-interactions, heterochromatin is expected to undergo an abrupt collapse transition to adopt a compact folding state [6, 40, 50, 51]. In an attempt to experimentally characterize this transition (in the reverse direction), we recently recruited the strong viral transcriptional activator VPR (VP64-p65-Rta) to heterochromatin regions in mouse fibroblasts [32]. Judged from the dose-response curve we obtained in these experiments, the transition might indeed resemble an abrupt first-order transition (Figure 3c), with chromatin adopting one of two well-defined folding/compaction states. Notably, the difference between the compaction levels in both states is much smaller than the concentration difference observed in experiments with short nucleosomes arrays undergoing LLPS [26], likely reflecting the impact of the topological constraints encountered by nucleosomes on long chromosomes as discussed in Box 1 and in our recent work [10, 52, 53]. Interestingly, the number of heterochromatin clusters varies considerably across different mouse cell types [43], indicating that heterochromatin as a whole can adopt more than two well-defined spatial arrangements (Figure 3d). This behavior can be compatible with an arrested phase separation scenario [54], but more work is required to identify the molecular determinants of heterochromatin clustering, i.e. the appropriate control parameter, across cell types.

Selected candidates that might drive a demixing transition of heterochromatic chromosomal regions are

listed in Figure 3a. In general terms, the probability of a protein to trigger a PPPS-type transition scales with its binding strength, valency, and abundance in the cell. According to these criteria, linker histone H1 is the top candidate in mammalian cells, as it is on average more abundant than the other candidates considered here combined. H1 is known to induce chromatin compaction *in vitro* and in living cells [55], and it has also been implicated in phase transition processes [26,52,56]. Due to the presence of multiple H1 genes and the fact that depletion of too many of them causes embryonic lethality [57], the availability of knockout models to assess heterochromatin compaction phenotypes in the absence of H1 is unfortunately limited. This is different for most other candidates in Figure 3a whose depletion causes milder phenotypes. In particular, mouse cells lacking HP1α/β/γ, SUV39H1/H2 or MECP2, which have recently been suggested to drive heterochromatin phase transitions [33–35,58], are available. These knockout cells contain distinct heterochromatin clusters that are readily visible in microscopy images where their DNA/chromatin has been stained with the DAPI (4',6-diamidino-2-phenylindole) dye [59–62]. The respective clusters resemble more closely wildtype heterochromatin than dCas9-VPR-decorated heterochromatin, which is not discernible in DAPI stains [32]. Similarly, depletion of HMGA1 by siRNA impairs heterochromatin clustering, although distinct heterochromatin regions are still visible in DAPI stains [63]. Depletion of cohesin, which might be able to drive chromatin phase transitions independently from loop extrusion [17], also seemed to have only mild effects on the morphologies of heterochromatin clusters [64,65]. These observations suggest that none of the respective proteins on its own is essential for the organization of heterochromatin into distinct clusters on the mesoscale that can be assessed in the respective microscopy experiments, although at least some of these proteins are able to exert this activity when overexpressed or artificially tethered to chromatin [66,67]. It is therefore conceivable that multiple proteins act redundantly with each other to organize heterochromatin clustering, so that cells can compensate the loss of one of them. In fruit flies, the top candidate is HP1a, which seems to be much more abundant than mammalian HP1α/β (Figure 3a). HP1a has been shown to drive heterochromatin clustering in fly embryos [68], and HP1a depletion causes embryonic lethality [69], which is a notable difference compared to HP1α depletion in mice [70]. Accordingly, HP1a in fruit flies might play a more prominent role in driving a heterochromatin phase transition than HP1α in mammals.

## Conclusion

It is currently not fully understood how cells package heterochromatin into compact subcompartments, how this process is regulated across different cell types and
species, and how accurately it follows the predictions from the theory of phase transitions. The currently available data point to a model in which heterochromatin proteins bind to pericentric regions and establish bridging interactions among them to induce their spatial clustering. Depending on the species, this transition can either resemble a reordering transition resulting in heterochromatin clusters that are not very compact on the mesoscale, or a collapse transition resulting in more compact clusters. The critical bridging interactions might be established by several different proteins that act redundantly to each other, with linker histone H1 potentially playing a prominent role in mammals due to its high abundance. With the emergence of the different models for heterochromatin organization described above, which involve either simple low-valency binding, surface condensation or LLPS of the proteins that bridge heterochromatin regions, it will be helpful to compare experimental results to the predictions from all these models side-by-side to systematically identify the most suitable one(s). More broadly, the development of inducible and reversible systems to trigger the assembly and disassembly of heterochromatin clusters in living cells could be beneficial to investigate dose-response relationships and other key hallmarks of phase transitions like bistability and hysteresis, thereby shedding more light on the inherent nature of the euchromatin/heterochromatin transition.

**Conflict of interest statement**

Nothing declared.

**Data availability**

No data was used for the research described in the article.

**Acknowledgments**

The author thanks Wolfgang Fischle, Olivier Cuvier, and the members of his group for feedback and discussions. The author apologizes to all colleagues whose work could not be cited due to space constraints. Research in his lab is funded by a grant from the European Research Council under the European Union Horizon 2020 Research and Innovation Program (grant agreement 804023 to F.E.).

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