key: cord-0321948-gef9vo5c
authors: Soranno, Andrea; Incicco, J. Jeremías; De Bona, Paolo; Tomko, Eric J.; Galburt, Eric A.; Holehouse, Alex S.; Galletto, Roberto
title: Shelterin components modulate nucleic acids condensation and phase separation
date: 2021-04-30
journal: bioRxiv
DOI: 10.1101/2021.04.30.442189
sha: f7501be06dab12fe7b49dde875b7c0c5c494fd26
doc_id: 321948
cord_uid: gef9vo5c

Telomeres are nucleoprotein complexes that protect the ends of chromosomes and are essential for chromosome stability in Eukaryotes. In cells, individual telomeres form distinct globules of finite size that appear to be smaller than expected for bare DNA. Moreover, upon changes in their protein composition, telomeres can cluster to form telomere-induced-foci (TIFs) or co-localize with promyelocytic leukemia (PML) nuclear bodies. The physical basis for collapse of individual telomeres and coalescence of multiple ones remains unclear, as does the relationship between these two phenomena. By combining single-molecule measurements, optical microscopy, turbidity assays, and simulations, we show that the telomere scaffolding protein TRF2 can condense individual DNA chains and drives coalescence of multiple DNA molecules, leading to phase separation and the formation of liquid-like droplets. Addition of the TRF2 binding protein hRap1 modulates phase boundaries and tunes the specificity of solution demixing while simultaneously altering the degree of DNA compaction. Our results suggest that the condensation of single telomeres and formation of biomolecular condensates containing multiple telomeres are two different outcomes driven by the same set of molecular interactions. Moreover, binding partners, such as other telomere components, can alter those interactions to promote single-chain DNA compaction over multiple-chain phase separation.

Biomolecular condensates are non-stochiometric assemblies of biomacromolecules that underlie a variety of cellular processes including the stress response, ribosomal assembly, germ-granule formation and chromatin organization (1-8). These assemblies are commonly enriched in multivalent DNA/RNA binding proteins and nucleic acids, with multivalency being a critical feature that facilitates formation of a set of reversible intermolecular interactions (9) (10) (11) (12) (13) . As a result of this multivalency, many of the proteins that localizes in condensates have been shown to undergo phase separation in vitro and in vivo, lending support to a model in which intracellular phase separation plays a key role in cellular organization and compartmentalization (14) (15) (16) (17) .

The emergent property of biomolecular condensates parallels previously observed characteristics of ligandinduced condensation of nucleic acids, in which multivalent interactions provided by DNA/RNA binding proteins can promote either the compaction of single nucleic acid chains or condensation of multiple ones. Indeed, as proposed by Post and Zimm (18) , from a polymer physics standpoint, the condensation of a single nucleic acid chain by a ligand and the phase separation of mixtures of nucleic acids and the same ligands can be rationalized as two distinct outcomes of the same set of interactions. While the relative concentration regimes and molecular architecture of the components play key roles, the physical basis that determines whether protein-nucleic acids interactions lead to intra-molecular loops and chain compaction or to inter-chain interactions and solution demixing, remains to be fully elucidated. An important implication of this duality is that -under appropriate conditions -many proteins that can induce the condensation of single nucleic-acid chains will instead promote phase separation. Identifying how these two possible outcomes are encoded in the architecture of proteins and their interaction with specific and unspecific nucleic acids is fundamental to our understanding of how the genetic material may be organized and regulated in vivo. To address this question directly we focused on the telomeric protein TRF2 and sought to explore the symmetry between nucleic acid compaction and phase separation.

Telomeres are nucleoprotein complexes that protect the ends of linear chromosomes. Human telomeres are formed by the six shelterin subunits TRF1, TRF2, Rap1, TIN2, TPP2 and POT1 that co-assemble at the end of chromosomes (19) (Fig. 1A) , with the four-protein core complex TRF1-TIN2-TRF2-Rap1 forming the major scaffold bound to the terminal double-stranded DNA containing T 2 AG 3 repeats. Homodimers of TRF1 and TRF2 bind specifically to the telomeric repeats (20) (21) (22) , while Rap1 interacts with TRF2 with high affinity (23, 24) , and TIN2 bridges TRF1 and TRF2 (25, 26) . Furthermore, TIN2 interacts with TPP1-POT1 bound to the G-rich 3' single-stranded DNA overhang, providing a physical link with the core complex formed on the double-stranded DNA telomeric region and thus stabilizing a T-loop structure proposed to regulate telomere accessibility (27) (28) (29) .

While telomeres are usually thought of as the nucleoprotein complexes formed at the ends of individual chromosomes, they are not always observed as distinct and separate nuclear entities. Though usually restricted in their motion, telomeres can transiently cluster together (30, 31) and dysfunctional telomeres assemble into telomere dysfunction-induced foci (TIFs) (32) . Also, 10-15 % of cancer cells maintain their telomere length via Alternative Lengthening of Telomeres (ALT) (33, 34) , a telomerase-independent pathway. In these cells, multiple telomeres co-localize with a subset of promyelocytic leukemia (PML) nuclear bodies to form ALT-associated promyelocytic leukemia bodies (APBs), within which telomeres are elongated (35) (36) (37) (38) . Intriguingly, PML bodies are a type of biomolecular condensates (14, 39) , and a recent study has proposed that within APBs telomeres behave as phase separated components (40) . Whether the apparent phase-separated nature of APBs originates from an intrinsic ability of PML bodies to form biomolecular condensates or from one or more of the shelterin components to induce phase separation with telomeric DNA remains to be determined.

Of the two telomeric proteins that directly interact with DNA, TRF2 has long been implicated in DNA condensation in vitro, as monitored by gel during electrophoresis (41) or DREEM imaging (42) . The molecular nature of these TRF2-DNA condensed states remains elusive. Single-molecule experiments (43) showed that pre-formed shelterin complexes do not lead to compaction of individual DNA chains or interaction between different DNA chains, suggesting that any ability of TRF2 to collapse/condense DNA may be modulated by interaction with other shelterin components. Also, individual telomeres typically appear as distinct globules of finite size, albeit T-loops where the 3' ssDNA end is tucked into the dsDNA telomeric region can be visualized in vivo with high resolution imaging (44) . These globules seem to be more compact than expected for equivalent lengths of bare dsDNA (45, 46) , suggesting that interaction of one or more shelterin component with DNA may favor condensation of telomeres. However, studies testing the idea that decompaction of telomeres may be a means to regulate telomere accessibility in vivo reached divergent conclusions (47) (48) (49) . These observations raise key and unanswered questions -do telomeric proteins induce compaction of   telomeric DNA? -if so, what are the physical and molecular bases for regulation of telomere compaction?does phase separation play a role in establishing and regulating telomeres? To begin addressing these questions, we employed a collection of biophysical methods to directly test whether specific domains of TRF2 ( Fig. 1B) induce the compaction of individual DNA chains and to investigate if and how binding of TRF2 to DNA leads to liquid-liquid mixing of the solutions. Our results reveal a direct and quantitative symmetry between singlechain compaction and multi-chain condensation (i.e., phase separation). This symmetry is mirrored in perturbations that influence phase separation (such as salt concentration, binding of hRap1 to TRF2) and impact single-chain compaction in an equivalent manner. Taken together, our results support the notion that these emergent phenomena can be interpreted as two distinct outcomes controlled by the same set of intra-and intermolecular interactions as well as by co-solutes.

We first sought to establish if TRF2 can drive single-chain DNA compaction and, if so, to determine its molecular origins. TRF2 has a modular architecture with an N-terminal basic disordered region, a central TRFH homo-dimerization domain, a disordered linker, and a C-terminal DNA-binding domain (DBD) that specifically recognizes T 2 AG 3 telomeric repeats (Fig. 1A) . When purified homo-dimeric TRF2 ( Fig. S2A -C) is combined with telomeric repeat DNA, electrophoretic mobility into the gel is impeded in a DNA-dependent manner (Fig. S2D ), as observed previously (41) , consistent with protein-mediated DNA condensation or aggregation. To directly test whether TRF2 compacts individual DNA chains, we employed two different single-molecule approaches.

First, we used two independently steerable optical traps and a laminar flow chamber to trap a single DNA molecule in a dumb-bell configuration between two polystyrene beads ( Fig. 2A , and top panel in 2B). By turning off the downstream trap relative to the flow and modulating flow velocity, we exerted a constant drag force on the free bead (i.e., the bead on the right in Fig. 2B ) and measured how DNA extension varied in the presence and absence of TRF2. In buffer alone, the DNA extension responds reversibly to changes in flow velocity (i.e., force, Fig. 2C , black trace). Upon movement of the DNA into a channel containing TRF2, a dramatic reduction in DNA extension when the force was lowered by a reduction in flow velocity. This DNA compaction was rapid and complete, as the free bead was eventually brought all the way into the active trap, thus ending the experiment ( Fig. 2B and 2C) . As expected for a protein-dependent phenomenon, the rate of DNA compaction increases with increasing TRF2 concentration (Fig. 2C) .

To quantitate the force-dependence of TRF2-dependent DNA compaction, we then turned to a magnetic tweezers assay which offered the benefits of higher throughput and the ability to perform experiments at low constant force (i.e., 0.5 -5 pN). In these experiments, dsDNA molecules of ~2 kbp effective length were attached at one end to a glass coverslip and at the other to a paramagnetic bead (Fig. 2D ). DNA tethers were initially held at > 5 pN of force, the force was ramped down to < 0.5 pN, and then back to high force, with ramping at a rate of ~ 0.6 pN / min (Fig. S1 ). The force dependence of the end-to-end distance of bare DNA behaves as expected (50, 51) (Fig. 2E in red) . However, consistent with the optical tweezer experiments, the addition of TRF2 leads to DNA compaction ( Fig. 2E in blue), even at salt concentrations typically considered to be in the physiological range (Fig. 2F) . Furthermore, the presence of TRF2 leads to a significant hysteresis between relaxation (i.e., lowering the force) and pulling (i.e., increasing the force) (Fig. 2F) , suggesting a large degree of cooperativity in the compacted state. Importantly, TRF2-dependent DNA compaction and hysteresis was also observed with DNA tethers containing 0.8 kbp of human telomeric repeats ((T 2 AG 3 ) 135 ) and their decompaction is associated with substantial hysteresis as well (Fig. 2G ). In fact, on the telomeric template, many DNA tethers remained irreversibly compacted even at the highest forces applied in this assay (~ 5 pN) (Fig. S2) .

Even though the biological function of TRF2 lies in its ability to specifically interact with telomeric DNA, our results clearly revealed that DNA compaction can occur independently of telomeric repeats. Thus, we next Taken together, both experimental and computational data strongly suggest that while the DBD of TRF2 contributes to an increase of interaction strength due to the specific binding to the T 2 AG 3 repeats, weaker protein-DNA interactions in the context of the multivalent nature of TRF2 are sufficient to drive condensation of single DNA chains and required for ensuring highly cooperative compaction.

Polymer theory predicts that the same molecular interactions that lead to collapse of a single DNA chain can also lead to condensation when multiple chains are present in solution at high enough concentration (18) . Indeed, TRF2 forms complexes with DNA that during electrophoresis barely migrate into the gel (Fig. S1D ) (41) , consistent with formation of either large supramolecular assemblies, amorphous aggregates or, possibly, phase separation. With these possibilities in mind, we found that while TRF2 is a well-behaved dimer in solution ( Fig.   S1 ), at a sufficiently high concentration mixing of TRF2 with non-specific dsDNA (supercoiled or linear fragments) results in an opalescent solution that contains micron-sized droplets, as revealed by Differential Interference Contrast (DIC) microscopy ( Fig. 3A and S3A ). In addition, these droplets fuse over time (Fig. S3C ), consistent with a liquid-like character of a phase-separated state. The formation of scattering objects (i.e., droplets) was further assessed by absorbance scattering at 340 nm, where neither protein nor nucleic acid absorb. The solution absorbance displayed classical re-entrant behavior as a function of DNA concentration (Fig. 3B ). Absorbance initially increases, reflecting the formation of droplets; however, as the DNA concentration is increased further, absorbance then decreases, in line with the 're-entrance' into the one-phase regime. This re-entrant behavior is expected for a two-component system governed by a closed-loop phase-diagram (52) . Phase separation occurs over the same concentration regime with either supercoiled DNA or its linear fragments, and at a physiological range of salt concentrations (Fig. 3B) . Importantly, the salt concentrations over which phase separation is observed mirror those under which TRF2-dependent DNA compaction occurs. Taken together, our results demonstrate that the same molecule (TRF2) can induce both DNA compaction and phase separation.

Having established that TRF2 can drive phase separation with DNA, we designed a series of TRF2 constructs to assess the contribution of specific protein regions/domains to phase separation ( Fig. 1B and S1A-C). Neither deletion of the basic domain ( 86 TRF2) nor removal of the DBD and the unstructured linker (TRF2 C ) suppressed DNA-dependent phase separation (Fig. 3C ). These observations indicate that TRF2-dependent phase separation is neither dictated by the presence of the disordered N-terminal basic region nor by the DNA binding of the DBD. Moreover, neither the TRFH domain nor the N-terminal region alone promote phase separation at the same protein concentrations as observed for full length protein (Fig 3C) but can be driven to phase separate with DNA at higher concentrations (Fig. S3D) . These data strongly suggest that multivalent interactions with the nucleic acids are required for phase separation and that multi-valency is realized via both unstructured and structured domains of TRF2 that act in a synergistic fashion.

Given the specificity and high affinity with which the DBD of TRF2 binds telomeric repeat sequences (53), we would anticipate that at cellular concentrations, telomeric repeat DNA will be preferentially bound by TRF2.

Furthermore, recent simulations of condensation showed that high-affinity interactions disfavor phase separation (54) . Therefore, we asked whether the presence of telomeric repeat sequences would impair the phaseseparation propensity of TRF2 and DNA. However, in contrast to expectation, solution demixing was still observed in the presence of telomeric repeat-containing DNA and TRF2 (Fig. 3D) , suggesting that these specific interactions do not suppress phase separation. We then tested whether other regions of the protein may be compensating via non-specific interactions. Paralleling its ability to collapse individual DNA chains, we found that the TRF2 ΔC construct, which lacks the DBD, is still able to drive DNA-dependent phase separation with dsDNA that contains multiple telomeric repeats (Fig. 3D ). Taken at face value, these data could be interpreted to suggest that DNA-dependent phase separation is driven by non-specific interactions of TRF2 with DNA, with the specific recognition of telomeric repeats by the DBD playing a limited role in the process. Alternatively, the multivalent interactions mediated by different TRF2 domains and the DNA may mask the impact of DNA specificity encoded by the DBD in the context of telomeric repeat sequences.

To delineate between these two interpretations, we sought to test for the presence of DNA-specific interactions with shorter DNA repeat sequences. For this, we turned to a short dsDNA fragment of 24 bps that contains a single (T 2 AG 3 ) 2 repeat in its center and a length-matched control that lacks the (T 2 AG 3 ) 2 repeat (random dsDNA). Strikingly, at the protein concentration used in the assay, phase separation occurs only in the presence of telomeric repeats (Fig. 3E) . Furthermore, independent of the presence of repeats, no phase separation was observed with the TRF2 ΔC construct that lacks the DBD (Fig. 3E) , in stark contrast to what was observed with longer DNA substrates. Thus, once the valency of the nucleic acid is reduced by decreasing its length, the importance of DBD-encoded specificity for telomeric repeats is clearly unmasked.

The importance of DBD-mediated specific interaction is further supported by fluorescence confocal imaging experiments. Droplets of TRF2 and a fluorescein-labeled 24 bp dsDNA containing the (T 2 AG 3 ) 2 repeat, formed in the presence of different concentrations of unlabeled DNA (Fig. 3F) , recapitulate the absorbance scattering experiments. As the concentration of DNA increases larger and more numerous droplets form, followed by their disappearance at high DNA concentration as expected for a re-entrant phase. Similar results are obtained when Alexa-488 labeled TRF2 is used in place of labeled DNA (Fig. 3G ). In addition, Fluorescence Recovery After Photobleaching (FRAP) of the fluorescent droplets indicates that a large fraction of the DNA within the droplet remains mobile (Fig. 2H) , consistent with a liquid-like character of the dense phase. Furthermore, TRF2 inside the droplets is mobile as well, albeit to a lesser extent than DNA. Droplet liquidity is maintained for at least 24 hours (Fig. S4A) , suggesting that if further molecular re-arrangements lead to solidification (e.g., fibril formation), this occurs at significantly longer timescales (55, 56) . In stark contrast, TRF2 does not form significant droplets with the random 24 bp dsDNA (Fig. S5B ) and TRF2 ΔC does not form droplets independent of the presence of the telomeric repeat ( Fig. S4C and S4D) , consistent with the results of the turbidity experiments.

Our data are consistent with a model in which the multivalency of both the protein and the DNA dictate the phase separation propensity of the system. Once the valence of the DNA is reduced by shortening its length, non-specific TRF2-DNA interactions are no longer sufficient to drive phase separation and the specific recognition of a telomeric repeat by the DBD becomes essential. On the other hand, this model also predicts that as the valence of the DNA increases TRF2 should phase separate in a seemingly non-specific manner even in the absence of its DBD. Indeed, consistent with the absorbance scattering and DIC experiments in Figure 3D , droplets are also observed with a dsDNA that contains 19 T 2 AG 3 repeats (Fig. 3I) , independent of the presence of the DNA binding domain (Fig. S4E) . Interestingly, the droplets formed by TRF2 and the (T 2 AG 3 ) 19 telomeric substrate do not recover after photo-bleaching, independent of whether the DNA or TRF2 are being monitored (Fig. 2I) . This behavior is different to that observed from the 24 bp dsDNA and two T 2 AG 3 repeats and it suggests that the increase in valence with multiple telomeric repeats leads to a dramatic change in the physical properties of the phase separated state. While these droplets show slow internal dynamics, they are still able to fuse over long timescales (Fig. S5 ).

Phase separation with single-stranded nucleic acids.

Transcription of telomeric repeats leads to telomeric repeat-containing RNA (TERRA), a long non-coding RNA proposed to play a role in telomeric protection (57, 58) . The interaction between TERRA and TRF2 has been proposed to facilitate heterochromatin formation, while TERRA depletion leads to an increase in TIFs (59) .

Intriguingly, a splice-variant of TRF2 lacking the linker and DBD (similar to TRF2 C ) co-localizes with neuronal granules, ribonuclear biomolecular condensates that facilitate the transport of mRNAs in axons (60, 61) . Based on our work here, one interpretation of this observation is that while the shorter TRF2 splice variant loses its ability to interact with telomeres it retains non-specific binding affinity for RNA, possibly via interactions within its basic N-terminus domain. With this in mind, we wondered if the DNA-dependent phase separation of TRF2 was truly actually dependent on dsDNA, or if phase separation could also be driven and modulated by other types of single-stranded nucleic acids (ssNAs).

To our surprise, absorbance scattering experiments and DIC imaging indicate that TRF2 phase separation occurs with both ssDNA (Fig. 4A ) and ssRNA (Fig. 4C ) over a similar range of salt concentrations as it did with dsDNA. As with dsDNA, this phase separation requires only the N-terminal basic domain or the DBD (Fig. 4B and 4D). However, in contrast to the lack of phase separation observed with the short 24 bp DNA of random composition, at the same protein concentration non-specific interaction of TRF2 with an oligo-dT ssDNA as short as 20 nt is sufficient to induce phase separation (Fig. S6A) .

We have described the high propensity of TRF2-dependent DNA condensation and phase separation.

However, given that TRF2 is only one component of the shelterin complex, we next asked how these processes might be modulated by the presence of a binding partner. More specifically, within the core-complex (TRF2-hRap1-Tin2-TRF1), hRap1 is unique in that it interacts directly and exclusively with TRF2 (19, 23, 24), making hRap1 a clear partner to test. In vitro, TRF2 and hRap1 form a tight complex (23) and, at the protein concentrations used in our experiments (> 300 nM), the TRF2-hRap1 complex can be considered as a single component. Binding of hRap1 to TRF2 lowers the DNA binding affinity of TRF2 (23); moreover, the TRF2 interacting domain of hRap1 (RCT in Fig. 1D ) is preceded by a highly acidic region that may interfere with the function of the basic domain of TRF2. Thus, it is reasonable to postulate that interaction of hRap1 with TRF2 may modulate both the TRF2-dependent compaction of a single DNA chain and the DNA-dependent phaseseparation propensity of TRF2. Indeed, magnetic tweezers experiments indicate that, compared to TRF2, the TRF2-hRap1 complex induces a smaller extent of compaction of DNA tethers containing the telomeric repeats and a lower degree of hysteresis (Fig. 5A) . These observations are consistent with hRap1 reducing the affinity of TRF2 for DNA (23) , effectively altering the valence of TRF2, and modulating the properties of the collapsed state.

Although TRF2-hRap1 interaction with non-specific DNA still leads to formation of large micron-size droplets ( Fig. 5B and S3A) , the change in absorbance scattering in the presence of hRap1 suggest that the phase boundaries have shifted. Importantly, binding of hRap1 to TRF2 does not suppress phase separation with dsDNA that contains telomeric repeats (Fig. 5C, 5D, and S3B) . Interestingly, the presence of hRap1 leads to an increase in the recovery after photobleaching of the labeled DNA in the droplets (Fig. 5E) , consistent with its ability to reduce the strength of TRF2-DNA binding.

Finally, under the concentration regimes explored in our experiments, interaction of hRap1 with TRF2 abolishes (or shifts at significantly higher concentrations) phase separation with either ssDNA or ssRNA (Fig.   5F ), suggesting a breaking of symmetry from the behavior of the system in the presence of dsDNA. It is important to note that the effect of hRap1 is mediated by its direct interaction with TRF2, as hRap1 has no effect on the phase separation of the truncated variant TRF2 ΔC that lacks the interaction region with hRap1 (Fig. 5G ).

If TRF2 undergoes bona fide phase separation with dsDNA, then it should be possible to construct a complete two-dimensional phase diagrams with a closed-loop binodal, as predicted by analytical theories of polymer mixtures (62) (63) (64) (65) . Moreover, if hRap1 weakens DNA compaction and phase separation by modulating protein-DNA interaction then that phase diagram should be systematically tuned by the presence of hRap1, shifting towards higher saturation concentrations (66) . At the same time, binding of hRap1 to TRF2 will introduce further excluded volume in the dense phase and therefore cause a shift toward lower concentrations of TRF2 in the dense phase. In support of this hypothesis, we were able to infer the close-loop nature of the two-dimensional phase diagram for TRF2 with dsDNA by measuring the concentrations of TRF2 and nucleic acids in the light and dense phase (Fig. 6A) . Variation of the length of the DNA segment systematically alters the phase boundaries as predicted by theory and in strong agreement with a three-component (solvent, DNA, protein) phase diagram (Fig. 6B) . Also, upon addition of hRap1, the phase boundary relative to the saturation concentrations recesses toward higher values, reporting on a systematic diminution in protein-DNA interaction driven by hRap1, as anticipated based on the force experiments (Fig. 5B) . This behavior is recapitulated in simple coarse-grained simulations. Longer DNA molecules lead to an increased propensity to undergo phase separation as reported on by the reduction in saturation concentration (Fig 6C) . Moreover, when we weakened intermolecular interactions in the same manner as in Fig. 2H and S7 (which lead to a decrease in compaction) we systematically shift the saturation concentration to higher values (Fig. 6C) , analogous to the change observed upon addition of hRap1 (Fig. 6B) . Finally, the concentration of TRF2 in the dense phase is also affected by binding of hRap1, in agreement with our excluded volume argument (Fig. 6B) . It is interesting to note that across the phase-diagram, addition of hRap1 alters the FRAP (which is consistent with a weakening of interactions between TRF2 and nucleic acids), but hRap1 does not significantly affect the diffusion time of either DNA or TRF2 in the dense phase (Fig. S8) . This observation can be interpreted as due to an increase in the fraction of the mobile species, where these are not largely dissimilar from the ones observed in absence of hRap1. Overall, these observations support a general mechanism whereby the interaction of specific ligands (such as hRap1) can control both phase separation (phase boundaries, selectivity for specific nucleic acids, transport properties) and chain compaction through the same physical mechanism.

Here we showed that two of the shelterin components, TRF2 and hRap1, modulate both protein-protein and protein-DNA interactions and lead to either compaction of individual DNA chains or phase separation of proteins and DNA at higher DNA concentrations. Similar results can be recapitulated using coarse-grained simulations that captures the overall trends of DNA compaction and phase separation propensity in presence of a ligand.

Taken all together, our observations support the original interpretation proposed by Post and Zimm (18) and are consistent with the idea that protein-dependent collapse of a single nucleic acid chain and the phase separation of mixtures of protein and nucleic acids are two distinct outcomes of the same set of molecular interactions (54, 67, 68) .

The multi-valence encoded in both proteins and nucleic acids is clearly key for creating the network of molecular interactions that can engage both intra-molecularly (single-chain condensation) and inter-molecularly (phase separation). In particular, our experiments reveal that the modular architecture of TRF2 encodes for a certain redundancy, such that phase separation with nucleic acids is robust even in absence of either the Nterminal basic domain or the DBD itself. Droplets also form when DNA is assembled in poly-nucleosomes (Fig.   S6B ), suggesting that TRF2-dependent phase separation may occur with more complex protein-DNA assembly that are formed in cells. Furthermore, despite of the presence of a domain with high specificity, TRF2 is generally promiscuous in its interaction with nucleic acids, including specific and non-specific dsDNA as well as ssDNA and ssRNA, raising a question about how these types of interactions are being regulated in cells. We find that TRF2's propensity to condense and phase-separate nucleic acids is modulated by binding partners, with binding of hRap1 significantly altering both the single DNA chain collapse by TRF2 and its phase separation propensity.

Furthermore, binding of hRap1 to TRF2 selectively abolishes phase separation with ssNAs, thereby imparting a dsDNA substrate specificity for the full-length protein. Deletion of the TRF2 region where hRap1 binds, which mimics the natural splicing form interacting with RNA, restores phase separation with single-stranded nucleic acids and suppresses specificity for dsDNA. In other words, the tight binding of hRap1 acts as a switch control that alters the balance between promiscuous and specific interactions of TRF2 with nucleic acids. We propose that this mechanism may be important in the cell to discriminate TRF2 functions at telomeres versus the functions of its spliced variant in RNA transport in neurons.

These observations suggest the possibility that, as for the case of TRF2 and hRap1, different shelterin components may play a role in dictating the degree of collapse of single telomeres and favoring or disfavoring the phase separation with multiple nucleic acids. It is important to stress that though TRF2 undergoes phase separation with both non-specific and specific dsDNA, the specificity of telomeric DNA sequences and the number of specific telomeric sites have an impact on the transport properties of the phase-separated state, as monitored by FRAP. Specific sequences may have different mobility and miscibility, de facto contributing to separate different nucleic acids components.

To avoid ambiguity, we would like to clarify that our results do not imply that individual telomeres are a bona fide phase-separated state. Rather, we propose that the mode of interaction between shelterin components and telomeric DNA determines whether single telomeres remain distinct entities or merge in larger bodies. This does not exclude the possibility that specific local regions of nucleic acid may favor a local partitioning of proteins, analogous to the pre-wetting demixing that occurs near to surfaces (69) and as recently shown for the interaction of FUS in proximity of stretched DNA (70) . Furthermore, coalescence and assembly of the multiple telomeres or fragment of telomeres may explain the recent observation and proposal that telomeres in APBs have properties consistent with being a phase-separated state (40) .

Finally, the phase-separation propensity of TRF2 and its modulation by interaction with hRap1 may be part of a more general mechanism for the regulation of nucleic acids in cells. Indeed, recent experimental evidence indicates that HP1a, a major component of heterochromatin, can also form liquid droplets and such phenomenon is proposed to be the basis of heterochromatin organization (7, 8, 71) . One interpretation of these results reflects a model in which HP1a drives heterochromatin territories through bona fide liquid-liquid phase separation (7, 8, 71) . Another is that the intrinsically multivalent nature HP1a and many other DNA binding proteins (such as TRF2) drives DNA compaction through distributed multivalent interactions which will inevitably also drive phase separation with sufficiently short nucleic acid molecules in vitro (54, 67, 72) . Altering the degree of DNA compaction by modulating the same interactions that would also drive phase separation could allow for the rheostatic control of access to genomic loci. These interactions may be modulated through subtle changes in the complement of available binding partners (e.g., with hRap1, as we show here), but also by chemical modifications to proteins or nucleic acids (e.g., histone acetylation or DNA methylation). Similarly, superenhancers have been proposed to assemble through phase separation of transcription factors at specific locations in the genome (73) (74) (75) (76) . Another example is the recent finding that the nucleocapsid protein of the SARS-CoV-2, which plays a role in the viral RNA condensation and packaging, can also undergo phase separation and localize in biomolecular condensates within the cell (77) (78) (79) . This observation has led to a proposed model in which viral genome compaction is driven by the same interactions that can also form biomolecular condensates (54) . In this respect, the finding that telomeric components can lead to solution demixing supports the idea that the underlying physics of phase separation may be a general mechanism through which the access and state of genetic material is controlled. Furthermore, our results highlight how phase behavior can be modulated by specific protein-ligand interactions, stressing the importance of investigating thcontribution of linkage effects to phase separation (66) . Indeed, our results suggest that at telomeres specific interactions within the shelterin complex may be a means to regulate and suppress the phase-separation propensity of single components, such as TRF2. Finally, the overall picture emerging from the parallelism between single chain condensation and multiple chain phase separation, as originally proposed by Post and Zimm (18) (see SI Appendix and Fig. S9 for additional discussion on this aspect), suggests that phase separation can be used as a readout for the condensation of single chains and, as such, can be used as a convenient macroscopic tool to investigate and test therapeutics (80, 81) .

A detailed description of the experimental and computational methods and approaches used in this work is provided in Supplementary Information.

All the data have been included in the figures or provided in the SI Appendix.

A.S.H. is a scientific consultant with Dewpoint Therapeutics. The DNA end-to-end distance was constrained via a harmonic potential with a variable force constant, mimicking force experiments. When only protein-DNA interactions were included, we observed a continuous increase in chain dimensions as a function of force constant, both under weak (blue) and strong (red) protein-DNA interactions (top). When protein-protein interactions were also included (at a strength of ½ protein-DNA interactions) we observe apparent two-state behavior, whereby the DNA is either compact or expanded, as characterized by the sharp transition as a function of force and the co-existing populations giving rise to a bimodal distribution. I. The continuous transitions in DNA dimensions observed in the absence of protein-DNA interactions is clearly shown when individual simulation trajectories. J. By contrast, the two-state behavior is similarly revealed by examining individual trajectories in the presence of protein-protein interaction, whereby for a single simulation with a for a single simulation, the system oscillates between compact and expanded, analogues to an infinitely cooperative transition upon sitting at a phase boundary. 

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Liquid phase condensation in cell physiology and disease

Theory of DNA condensation: collapse versus aggregation

Human telomeres contain two distinct Myb-related, TRF1 and TRF2

TRF1 binds a bipartite telomeric site with extreme spatial flexibility

Telomeric localization of TRF2, a novel human telobox protein

Human Rap1 modulates TRF2 attraction to telomeric DNA

Identification of human Rap1: implications for telomere evolution

TIN2 mediates functions of TRF2 at human telomeres

TIN2 binds TRF1 and TRF2 simultaneously and stabilizes the TRF2 complex on telomeres

TRF2-tethered TIN2 can mediate telomere protection by TPP1/POT1

Structural and functional analyses of the mammalian TIN2-TPP1-TRF2 telomeric complex

Telomere protection by TPP1/POT1 requires tethering to TIN2

Visualizing telomere dynamics in living mammalian cells using PNA probes

Telomere associations in interphase nuclei: possible role in maintenance of interphase chromosome topology

DNA damage foci at dysfunctional telomeres

Alternative lengthening of telomeres: models, mechanisms and implications

Alternative lengthening of telomeres in mammalian cells

PML body meets telomere: the beginning of an ALTernate ending

Probing PML body function in ALT cells reveals spatiotemporal requirements for telomere recombination

De novo assembly of a PML nuclear subcompartment occurs through multiple pathways and induces telomere elongation

Alternative Lengthening of Telomeres through Two Distinct Break-Induced Replication Pathways

Nucleoli and Promyelocytic Leukemia Protein (PML) bodies are phase separated nuclear protein quality control compartments for misfolded proteins

Nuclear body phase separation drives telomere clustering in ALT cancer cells

The N-terminal domains of TRF1 and TRF2 regulate their ability to condense telomeric DNA

Enhanced electrostatic force microscopy reveals higher-order DNA looping mediated by the telomeric protein TRF2

Telomere Recognition and Assembly Mechanism of Mammalian Shelterin

Super-resolution fluorescence imaging of telomeres reveals TRF2-dependent T-loop formation

Is DNA a Good Model Polymer?

Diffusion of isolated DNA molecules: Dependence on length and topology

Shelterin Protects Chromosome Ends by Compacting Telomeric Chromatin

The DDR at telomeres lacking intact shelterin does not require substantial chromatin decompaction

The telomeric DNA damage response occurs in the absence of chromatin decompaction

Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules

Reentrant Phase Transition Drives Dynamic Substructure Formation in Ribonucleoprotein Droplets

Characterization of the DNA binding specificity of Shelterin complexes

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

Formation and Maturation of Phase-Separated Liquid Droplets by RNA-Binding Proteins

A Liquid-to-Solid Phase Transition of the ALS Protein FUS Accelerated by Disease Mutation

The Emerging Roles of TERRA in Telomere Maintenance and Genome Stability

TERRA: telomeric repeat-containing RNA

TERRA RNA binding to TRF2 facilitates heterochromatin formation and ORC recruitment at telomeres

The long and the short of TRF2 in neurogenesis

Alternative Splicing of Neuronal Differentiation Factor TRF2 Regulated by HNRNPH1/H2

Calculation of liquid-liquid phase separation in a ternary system of a polymer in a mixture of a solvent and a nonsolvent

Segregation and Association in Mixed Polymer Solutions from Flory−Huggins Model Calculations

Thermodynamics of Polymer Compatibility in Ternary Systems

Interacting multivalent molecules: affinity and valence impact the extent and symmetry of phase separation

Ligand effects on phase separation of multivalent macromolecules

DNA length tunes the fluidity of DNA-based condensates

Sequence-dependent DNA condensation as a driving force of DNA phase separation

Surface condensation of a pioneer transcription factor on DNA

Co-condensation of proteins with single-and double-stranded DNA

HP1 proteins compact DNA into mechanically and positionally stable phase separated domains

Mouse Heterochromatin Adopts Digital Compaction States without Showing Hallmarks of HP1-Driven Liquid-Liquid Phase Separation

Transcription Factors Activate Genes through the Phase-Separation Capacity of Their Activation Domains

Organization and regulation of gene transcription

YAP/TAZ phase separation for transcription

Coactivator condensation at super-enhancers links phase separation and gene control

Genomic RNA Elements Drive Phase Separation of the SARS-CoV-2 Nucleocapsid

Nucleocapsid protein of SARS-CoV-2 phase separates into RNA-rich polymerase-containing condensates

SARS-CoV-2 nucleocapsid protein undergoes liquid-liquid phase separation into stress granules through its N-terminal intrinsically disordered region

Liquid-liquid phase transitions and amyloid aggregation in proteins related to cancer and neurodegenerative diseases

SARS CoV-2 nucleocapsid protein forms condensates with viral genomic RNA

Rap1 binding motif. The dashed lines represent unstructured linkers connecting the TRFH to the DBD

Disorder/order predictions of TRF2 (IUPred) and schematics of the TRF2 constructs studied in this work. C. Schematic of Rap1: BRCT, BRCA1 C-terminal domain

experiments of solution containing non-specific X174 RF-I in presence of truncation variants of the protein at fixed concentration of 10 M monomer. Turbidity is suppressed for the TRFH construct and strongly reduced for the N-terminal tail fragment. D. Turbidity measurements of TRF2 and TRF2  C variant reveals phase separation in presence of specific ds-DNA sequences

Under identical conditions truncation of the C-terminus (TRF2  C ) suppresses phase separation also for specific DNA

Re-entrant behavior of the phase separation with increasing concentration of specific dsDNA. H-I. FRAP of labeled TRF2 and specific DNA mixtures shows order of magnitude decrease in mobility with increasing length (from 2 to 19) of the number of specific telomeric binding sites on the dsDNA substrate

We would like to thank John Cooper for access to the microscope for DIC imaging. This work was supported by the National Institutes of Health 2R01GM098509 to R.G.; 1R01AG062837 to A.S.