Measuring condensate formation and dissolution in cells reveals that the processes can generate as much force as a molecular motor and provides insight into the material properties of the nucleoplasm.
Biomolecular condensates are membraneless assemblies that form within living cells through liquid-liquid phase separation and related phase transitions. 1,2 These include P granules, 3 T cell receptor clusters, 4 stress granules, 5 the pyrenoid, 6 and nucleoli, 7 many of which physically interact with other cellular structures. Within the nucleus, chromatin-associated condensates are involved in nuclear functions, including chromatin remodeling, 8 transcriptional activation, 9,10 or repression 11 of specific euchromatic sequences, and formation and silencing of heterochromatin domains. [12][13][14] Aberrant spatiotemporal regulation of chromatin-interacting condensates is associated with diseased states. 8,15,16 Decades of work in soft (non-living) matter show how the processes of nucleation, growth, and coarsening can be impacted by structured environments. 17,18 Studies suggest a role for related effects in living cells, including the interactions between condensates and viscoelastic environments including the cytoskeleton, 19,20 chromatin, 21 and the nuclear F-actin network of Xenopus laevis oocytes. 22 In the nucleus, condensates form in mechanically softer regions, 23 and chromatin organization impacts condensate coarsening dynamics. 24,25 Thus, the material state of the cell, particularly the nuclear interior, impacts the formation, positioning, and organization of condensates.
While the material state of chromatin influences functions including replication, transcription, and protection from DNA damage, 26 there is no consensus model describing this material state. Several studies suggest that chromatin behaves as a solid on the mesoscale, 27,28 while others have suggested a liquid-like state. 29,30 Existing intranuclear reorganization techniques have informed functional outcomes of nuclear (re)positioning and alteration of pairwise genomic contacts, [31][32][33][34][35][36] but there are extremely few techniques for direct force-response measurements utilizing local force application on singular chromatin loci. 30 In considering possible methods of generating and harnessing forces within living cells, it is noteworthy that interfacial (surface) tension between immiscible phases can give rise to capillary forces. 7,23,[37][38][39] These mechanical forces arise from energetically unfavorable non-spherical condensates, which can decrease free energy by rounding up into a sphere to minimize interfacial area. Recent studies have shown that model condensate systems exhibit interfacial forces that drive intracellular restructuring. 19,20,40,41 Therefore, condensates could function in a manner analogous to molecular motors, 37 applying picoNewton (pN)-level forces to intracellular objects; instead of utilizing ATP hydrolysis, forces would result from free energy stored in interfaces. By exploiting such condensate-driven interfacial interactions in the nucleus, it could be possible to probe local chromatin material properties and uncover principles of genome organization and function. However, there are currently no techniques for measuring and controlling interfacial forces in living cells.
Here, we introduce ViscoElastic Chromatin Tethering and ORganization (VECTOR), a system that creates interfacial interactions between an inducible synthetic condensate and target chromatin loci to apply a pulling force on the attached loci during condensate dissolution, resulting in their repositioning. Locus repositioning is rapid ($2 min), specific, and precise over micron distances. We combine analytical simulations to understand the work done through interfacial interactions and quantitatively estimate differential viscoelasticity across chromatin regions. Additionally, we demonstrate the versatility of the VECTOR platform through automation for high-throughput locus repositioning, force generation through a variety of synthetic condensate identities, dCas9-based programmable repositioning of both telomeric and non-telomeric sequences, as well as strategies for condensate-interface mediated repositioning of nuclear bodies. Together, these studies build a more complete understanding of internal mechanical properties and processes in the nucleus and provide a powerful toolkit for the study of cellular organization and function.
To engineer condensate capillarity, we leveraged our earlier work demonstrating light-dependent condensate induction in the nucleus. 23,40,42 We induced condensates in cultured human osteosarcoma U2OS cells with the two-component Corelet system, 42 composed of an iLID-GFP-Ferritin 24-mer ''core'' and an SspB-tagged phase separation-prone intrinsically disordered region (IDR). Upon 488 nm light exposure, improved lightinduced dimer (iLID) and SspB interact, decorating each core with up to 24 sticky IDRs and triggering intracellular phase separation. By fusing the same IDR (e.g., FUS N ) to a tethering protein that binds a particular chromatin locus, in this case, the TRF1 protein that binds to repetitive telomeric TTAGGG sequences, 43 we promoted interactions between the ''condensate module'' (constructs that create the condensate) and the ''adhesion module'' (constructs that create interaction between the condensate and chromatin locus) (Figures 1A and 1B).
By directing blue light to a small region within the nucleus (1.2 mm diameter circle), we can readily nucleate condensates at tagged loci. With sustained light activation, condensates tethered to two nearby chromatin loci grow and coalesce into one, remaining associated with the target loci. Upon deactivation, the condensate shrinks, leading to a pulling force that repositions the loci (Figure 1A). In this example cell, we performed two simultaneous repositionings (Figures 1B and S1A; Video S1). With this localized light activation protocol, we achieved loci-spanning condensates with diameters up to 3 mm, enabling successful repositioning of telomeres across multiple microns of nuclear space. However, the probability of condensate merging reduces significantly if loci are separated by more than 2 mm (Figure 1C), a limitation set by achievable size of the loci-spanning condensate, which could be tuned through construct expression levels.
Tracking telomere position during the light activation/deactivation sequence reveals their capillary-force-dependent movement. We observe a jump together when the two loci-associated condensates merge (0.72 mm/min), then the loci follow the receding condensate surface as it shrinks (1.18 mm/min). Directed locus repositioning occurs over 1-2 min as the synthetic condensate dissolves, and the loci maintain their new positions for minutes after the condensate is dissipated, indicating successful long-term repositioning (Figure 1D). Notably, these micron-scale, rapid, and directed movements are achieved without use of ATP-driven motors-the most commonly described source of intracellular force generation. Instead, the forces underlying movement of these genomic loci are generated through capillary forces 37 at the interface between the condensate and chromatin locus. The scale of the capillary force is set by the relevant interfacial tension(s), which represents an energetic cost per unit area, with forces generated from surface area minimization. 37 Measurements to date on simplified in vitro systems, 7,44,45 and in some cellular contexts, 7,25 suggest condensate interfacial tensions in the range of 10 À7 -10 À3 N/m. 44 The data shown above rely on cell-specific, user-defined regions of light activation/deactivation, an approach limited in throughput capacity. To increase throughput while maintaining specificity and precision, we tested a series of automated protocols that incorporate real-time feedback into regions of interest (ROI) generation for light patterning (see STAR Methods; Figures S1B-S1E). Global activation creates temporally controllable but small condensates that fail to merge (Figure S1B, ''global'' map of possible outcomes shown in Figure S1F). A thinner activation region induces larger condensates, and sliding this activation box promotes condensate fusion, but this approach is slow (t > 60 min per frame) due to the numerous sequential activation/deactivation cycles required (Figure S1B, ''sliding box''). A square lattice pattern of punctate activation regions creates condensates that occasionally merge but are not all associated with target loci (Figure S1B ''array'').
Considering these limitations, we designed an approach that uses real-time image analysis feedback to identify nearby telomere pairs, then creates activation regions connecting them (Figure S1C). Bright spot detection followed by activation between nearby pairs is consistent and efficient, resulting in at least one pair of loci associated with the same condensate in 46% of cells (81 out of 176 nuclei attempted) and leading to scalability and successful repositioning in 64% of those nuclei (52 out of 81 potential locus pairs) in less than 5 min per field of view (Figure S1D; example kymographs in Figure S1E; map of potential outcomes in Figure S1F). These data exemplify how condensates can be harnessed to rearrange intracellular objects without the use of ATP-driven motors.
We hypothesized that capillary forces are transmitted to the target chromatin locus by adhesion between the shrinking FUS N condensate and the FUS N -coated telomere surface. We performed the same light activation/deactivation protocol in cells expressing a chromatin-bound fluorescent protein that has no interaction with the condensate (miRFP670-TRF1) (Figures 2A and 2B), and no sustained force was exerted on the loci, as expected (Figure 2C; Video S2).
The small expansion and contraction of the distance between chromatin loci (Figure 2C) may be due to the condensate itself displacing the chromatin network between the loci. Marking all DNA with a silicon rhodamine (SiR)-DNA dye shows that bulk chromatin is excluded from the condensate (Figure S2A), consistent with previous studies. 23,24 The distance between two nuclear locations (yellow arrows, Figure S2A) over time increases slightly during activation and recovers to the original distance during condensate dissolution (Figure S2B). These data suggest that the movement of chromatin loci not adhered to the conden-sate is due to bulk material displacement, and precise repositioning of loci depends on interfacial interaction with the condensate.
The amino acids that contribute to self-interaction underlying phase separation of FUS N have been extensively studied, 46,47 revealing that the 27 tyrosines of FUS N WT act as ''sticker residues'' separated by ''spacer residues'' (Figure 2D). To examine the role of tyrosines in facilitating chromatin-condensate adhesion, we created FUS N -miRFP670-TRF1 constructs with 3, 5, 9, 15, or 27 tyrosine-to-serine mutations (Y-to-S, Figures 2D-2F) and asked whether these mutations altered adhesion to the wild-type (WT) condensate by measuring the detachment probability. Single locus-condensate interactions were determined to be adhered or detached based on whether the telomere and condensate maintained contact or not during condensate dissolution (Figure 2E).
Detachment of FUS N WT -tagged telomeres from FUS N WT condensates is extremely rare, with 0 out of 33 loci detached (0% detachment rate, Figure 2F). Detachment becomes more likely with increasing number of Y-to-S mutations, resulting in 88% detachment rate for the FUS N
-miRFP670-TRF1 construct (Figure 2F the number of tyrosines is deterministic of the adhesion strength for a distinct pair of sequences, HNRNPA1 C , an orthogonal IDR that contains 8 tyrosines and has been reported to interact weakly with FUS N , 43,48 should have a detachment rate of about 80%. However, we find only 13 out of 23 (56%) detach, suggesting that spacing of tyrosines, neighboring amino acid context, and other sequence features contribute to intermolecular interaction strength, consistent with previous reports. 49 Until this point, we have utilized a specific IDR, FUS N , to mediate interfacial force generation. Capillary forces are a general feature of condensates, so we next sought to create a condensate module with adaptable sequence identity. We replaced FUS N in the condensate module (FUS N IDR -mCh-SspB) with phase-separation-prone IDRs from DDX4 or BRD4 [X IDR ]-mCh-SspB and replaced the chromatin-tethered FUS N IDR in the adhesion module (FUS N IDR -miRFP670-TRF1) with iLID (iLID-miRFP670-TRF1), 40 which recruits [X IDR ]-mCh-SspB upon light activation (Figures S2C and S2D). Similar to the FUS N system, during light activation, chromatin loci remain adhered to the [X IDR ] condensate surface, and upon light deactivation, loci are repositioned (Figure S2D), confirming that non-FUS N condensates can also apply force to adhered loci.
In addition to chromatin loci, other structures, including nuclear bodies, should be amenable to repositioning with VECTOR. We attempted to reposition Cajal bodies, native nuclear condensates associated with various aspects of RNA metabolism, using Coilin to generate the adhesion module FUS N -miRFP670-Coilin (Figures S2E-S2G). Interestingly, when a FUS N condensate forms at a Cajal body, FUS N -miRFP670-Coilin distributes to cover the entire surface of the FUS N condensate (Figures S2F and S2G). Nevertheless, from two original Cajal bodies, only one remains after deactivation, indicating successful repositioning (Figure S2F; Video S3). These data demonstrate that capillary forces are generated by IDR-IDR interactions and can reposition native nuclear condensates in addition to chromatin loci.
A dCas9-based approach to generate force on nontelomeric genomic elements Next, we sought to extend our intranuclear force generation approach to non-telomeric chromosomal loci using a dCas9based adhesion module (Figure 3A). 23 We targeted PPP1R2, a repetitive locus of $500 copies on Chr3q29, which enables binding of many dCas9 molecules using a single guide RNA (sgRNA). In this dCas9-based system, the condensate module is the same light-inducible FUS N Corelet as described above. The adhesion module is made of four components that target the repetitive locus: (1) a small guide RNA complementary to the target locus, and (2) dCas9 covalently linked to a SunTag, which has 24 copies of a binding site for viral protein ScFv. We covalently link (3) ScFv to HaloTag (for visualization) and iLID such that when blue light is activated, (4) FUS N -mCh-SspB binds ScFv-HaloTag-iLID, creating a dCas9-targeted telomeric locus decorated with FUS N . Precise stoichiometry between the four adhesion module components was essential for locus-specific labeling in this dCas9-based VECTOR implementation (see STAR Methods). sgRNA targeting of PPP1R2 results in three puncta in pseudotriploid U2OS cells during G1 (Figure 3B) and up to six puncta in G2 after DNA replication. As with telomeres, PPP1R2 loci within 2 mm of each other are most likely to achieve productive bivalent condensate attachment (Figure 3C), and condensate dissolution applies force to move PPP1R2 loci toward each other (Figure 3D). While the dCas9-based adhesion module is overall more detachment-prone than the FUS N -TRF1-based adhesion module, the lower number of repeats bound by sgPPP1R2 ($500 copies per locus) only slightly increases the detachment probability compared with a dCas9 adhesion module that uses a telomeric TTAGGG n -targeting sgRNA (sgTelo, >1,000 copies per locus). The sgTelo module exhibits 15/57 or 27% detachment, while the sgPPP1R2 module exhibits 24/75 or 32% detachment (Figures S3A-S3C), suggesting that 500 binding sites are sufficient for force generation at the PPP1R2 locus.
Interestingly, PPP1R2 loci repositioned using the dCas9 adhesion module recoil toward their original positions after condensate dissolution (Figures 3B and 3D; Video S4), unlike telomere loci repositioned using the TRF1 adhesion module (Figures 1, S2C, and S2D; Video S1). These disparate recoil behaviors may be due to (1) differences in the force application systems, (2) end vs. internal chromosomal location, or (3) other physical characteristics disparate between these loci. We measured recoil probability with the dCas9-based adhesion module targeting telomeres, expecting that if chromosomal positioning or other physical characteristics control recoil behavior, telomeres will remain in their repositioned locations, while if differences in the adhesion modules control recoil behavior, telomeres will recoil similar to the PPP1R2 loci.
Telomeres repositioned via the dCas9 adhesion module recoil after force application, similar to PPP1R2 loci (Figures 3E and 3F). We examined whether overexpression of TRF1 in combination with the dCas9 sgTelo adhesion module would prevent recoil (Figures 3G and 3H). Indeed, while PPP1R2 loci and telomeres repositioned with the dCas9 adhesion module recoil after force application in more than 90% of cases (16 out of 17 locus pairs recoil in sgPPP1R2; 17 out of 18 locus pairs recoil in sgTelo), sgTelo-labeled telomeres only recoil in 50% of cases when TRF1 was also overexpressed (8 out of 16 locus pairs recoil). This suggests that the apparent liquid-like coalescence of telomeres 40 is impacted by stoichiometry of shelterin complex components and is consistent with previous reports that non-stoichiometric expression of TRF1 can lead to aberrant telomere clustering and telomeric DNA fusions. 40,50,51 Notably, during light activation, dCas9-labeled PPP1R2 loci extend to coat the surface of the condensate, while FUS N -miRFP670-TRF1-labeled loci remain punctate (Figure S3D). This observation may reflect differences in the internal cohesion, mechanical properties, or condensate wetting behavior of these structures (see schematic Figure S3E). Overall, these findings suggest that chromatin-bound IDR-containing proteins mediate stable contacts between distal chromosomal loci, consistent with 3D genome mapping results implicating IDRs in long-range interactions. 52 Chromatin is a viscoelastic liquid with mesoscale heterogeneity The material state of the nuclear interior is technically difficult to probe, and previous measurement methods include confounding contributions from the nuclear lamina and envelope, as with micropipette manipulation of whole nuclei, 53 or atomic force microscopy (AFM) compression. 54 We sought to perform direct active rheological measurements from within the nucleus with VECTOR, then observe detachment rates and post-detachment locus recoil trajectories, which yield insight into relaxation behaviors of mechanically stressed chromatin (Figure 4A).
If chromatin behaves as a purely elastic material, we expect locus-condensate detachment most often when the locus is moved far from its initial position, when the strain is highest. We measured the probability of locus detachment as a function of strain, where d 0 is the initial distance between two loci, and d d is the distance between loci under force, so dimensionless strain is defined by fractional deformation (d 0 À d d )/d 0 but did not observe a strain-dependent trend (Figure S4A). This suggests that chromatin is not a purely elastic material but rather exhibits fluid-like dissipation. Materials with partially liquid-like behavior are characterized by stresses that depend not only on the magnitude of deformation but also on the rate of change of deformation (e.g., velocity or strain rate). With VECTOR, the moving locus follows the receding condensate surface during light deactivation; therefore, velocity is dependent on the rate of condensate diameter shrinking, which we observed to range between 0.1 and 1.2 mm/min. Chromatin loci attached to condensates with full adhesion strength (FUS N WT -miRFP670-TRF1) did not detach from the shrinking condensate at any tested velocity, while loci attached by the very-weak-adhesion construct FUS N 15YS -miRFP670-TRF1 showed a higher probability of detachment at a broad range of tested velocities, though this did not trend with velocity (Figure S4B). Loci attached with the moderately mutated construct FUS N 5YS -miRFP670-TRF1 exhibited a velocity-dependent detachment, with detachments more frequent at lower velocities (Figure S4B; < 0.5 mm/min, chi-squared test trend ****p = 0.0004), a behavior not expected for purely elastic materials. We note that interpretation of velocity dependence is confounded by the fact that the pulling velocity is coupled to the size-dependent condensate dissolution rate. Nonetheless, these data point to chromatin exhibiting significant liquid-like properties rather than being a purely elastic material. We next built an analytical simulation to examine the expected relative influence of elastic-and liquid-like chromatin properties on locus recoil behaviors. The simulation mimics dissolutiondependent repositioning by light-inducible condensates (green) wetting a second phase (magenta, representing the chromatin locus) (Figure 4B). The condensate forms upon light-induced association of the core and IDR, with the free energy of mixing defined by the Flory-Huggins theory. 55 As we observed experimentally, these simulations show that both condensate coalescence and dissolution lead to the associated loci moving toward each other (Figure S4C), with adhesion required for repositioning (Figure S4D). Additional characterization and parameters of these simulations are described in the method details (Figures S4E-S4M; Video S5).
The addition of linear viscoelasticity to this simulation imparts resistance to locus movement (Figures 4B and 4C). Starting with a system of two loci attached to a single condensate, we simulated the chromatin locus movement during the force of repositioning and considered the chromatin material to be either (1) a viscoelastic solid following the Kelvin-Voigt model, which (B) Simulating locus detachment from a shrinking condensate and subsequent recoil with a viscoelastic solid (Kelvin-Voigt) model predicts that, during recoil, the chromatin loci always return to their original positions, as the energy of the elastic spring must be dissipated. (C-E) (C) Simulating locus detachment and recoil in a viscoelastic liquid (Jeffreys or Rouse polymer) model predicts that the chromatin loci will not return all the way to their original positions, as some of the energy is dissipated through the viscous dashpot. Graphs of locus distance and estimated force over time from experiments in live cells show that some detachments result in elastic-like recoil (D), while others result in viscous-like recoil (E). anchors the locus at its original position by a spring and dashpot in parallel (Figure 4B, graph inset), or (2) a viscoelastic liquid following the Jeffreys model, 56 which adds a dashpot in series with the spring (Figure 4C, left graph inset), or the Rouse polymer model, based on polymer relaxation-controlled viscoelasticity [57][58][59][60] (Figure 4C, right graph inset and S4K-S4M). While these are not the only possible models of viscoelastic solids and liquids, we chose them as our initial models because they are the simplest and most well-known models that make qualitatively different predictions.
In the viscoelastic solid Kelvin-Voigt model, the single spring spanning the unit dictates that the loci will always return to their original positions (Figure 4B). By contrast, in the viscoelastic liquid Jeffreys or Rouse polymer models, a detached locus would not necessarily return all the way back to its original position (Figure 4C), since some of the energy is dissipated by viscous relaxation. This relaxation is governed by the dashpot in the Jeffreys model, where a short spring relaxation time compared with repositioning time implies less recoil, while within the molecular picture of the Rouse polymer model, it is governed by polymer relaxation timescales. We observed locus detachments with the FUS N 5YS -and FUS N 15YS -miRFP670-TRF1 weak-adhesion mutants (Figure 4A) and tracked post-detachment recoil behaviors. Interestingly, we observed both elasticlike recoil, with detached loci returning entirely to their original positions (Figure 4D), as well as viscous-like recoil, with detached loci returning only partially to their original positions (Fig- ure 4E). Over 15 detachment and recoil events using the FUS N 15YS -miRFP670-TRF1 mutant, we observed a wide spread of recoil recovery, with some loci presenting viscous-like recoveries (green, Figure 4G, bottom) and others presenting elasticlike recoveries (magenta, Figure 4G, top). Utilizing the dCas9based adhesion module, we also observe a spread of recovery behaviors of PPP1R2 and telomeres (Figure 4H), consistent with the recoil dynamics reflecting intrinsic chromatin viscoelasticity.
We sought to estimate the magnitude of forces generated with VECTOR, building from a framework recently deployed to analyze intracellular force generation by magnetic tweezers. 30 In particular, we estimated forces during the light activation/deactivation sequence by calibrating a Rouse polymer model using telomere mean squared displacement (MSD) data, then calculating the fluctuating forces required to move loci on observed trajectories. 30 Here, the Rouse polymer model is used to represent force being applied at a point source along the chromatin polymer, which allows the system to be calibrated by passive microrheological approaches (see STAR Methods). This force estimation approach yields results on the order of $0.36 pN during condensate dissolution (Figures 4D-4F, bottom), which is comparable to individual molecular motor forces (e.g., kinesin). 61 Note that force estimation is calculated based on the relative distance between two loci, with positive force indicating loci moving toward each other and negative force moving them apart. The force hovers around zero before condensate growth and during late activation when the condensate is not changing size (À0.02, À0.01 pN, respectively, Figure 4I ''preactivation,'' ''activation''), then spikes during condensate coalescence (0.15 pN, Figure 4I ''merge'') and exhibits sustained force during locus repositioning due to condensate dissolution (0.36 pN, Figure 4I ''pull force,'' see STAR Methods). In examples where loci recoil after collision, the force drops to near-zero after detachment (À0.02 pN, Figure 4I ''recoil''), while in examples where loci remain attached (Figure 4H), forces slowly decrease through viscous dissipation; this sets the scale of the minimum sustained adhesion required between chromatin-bound IDRs to counteract the restoring force of the viscoelastic medium (0.18 pN, Figure 4I ''restoring'').
Taken together, our data are most consistent with a viscoelastic liquid model of chromatin material state at the mesoscale that arises from Rouse polymer-like movement of the chromatin. However, the broad spread of recoil behaviors indicates significant heterogeneity in the viscoelastic response of the chromatin network.
We next sought to examine the origins of heterogeneity in chromatin viscoelasticity that may arise from differential organization states of heterochromatic and euchromatic regions of the nucleus. Tracking diffusion of telomere loci in U2OS cells every 3 s for 30 min and plotting their pairwise MSD trajectories reveals that telomeres exhibit sub-diffusive motion with an average exponent of a z 0.46 (Figure S5A). This is close to a Rouse polymer model prediction of exponent a = 0.5 and consistent with previous studies. 24,40,62 The nuclear periphery of most human cell types is enriched in heterochromatin, 63 the epigenetically methylated, densely compacted, and transcriptionally silenced regions of chromatin. 63 Since heterochromatin is more densely compacted and thus presumably stiffer than nuclear interiorlocalized euchromatin, we plotted these pairwise MSDs binned into two categories by their nuclear location (Figure S5A); pairs where both loci were located within 0.55 mm of the nuclear periphery were considered peripheral (blue), or pairs where both loci were located greater than 0.55 mm from any periphery were considered internal (mauve). Peripheral pairs exhibit slightly lower diffusion coefficient than internal pairs (peripheral D = 0.001168 mm 2 /s a , internal D = 0.001316 mm 2 /s a ), consistent with previous reports 64 indicating higher viscoelastic resistance near the nuclear periphery, potentially due to heterochromatic state (Figure S5B).
Given these indications of heterochromatin-associated mechanical heterogeneity, we reasoned that we may be able to use VECTOR to quantify chromatin's mechanical heterogeneity across mesoscale (1-2 mm) nuclear regions. To examine this, we use simulations to predict the movement of chromatin loci across either mechanically homogeneous or heterogeneous systems (Figure 5A). We define a dimensionless parameter, r, which represents the mechanical resistance of the spring-anddashpot viscoelastic system, with r 1 and r 2 indicating resistance of the two respective loci attached to a singular condensate. In the homogeneous case r 2 = r 1 = 1, the viscoelastic parameters between the two loci are equal, which result in symmetric locus movement, each traversing 50% of the distance between them. By contrast, when the movement of loci is simulated in an heterogeneous system with unequal resistance (r 2 = r 1 = 5), we find asymmetric movement (77%, 22%; Figures 5A, bottom, and 5B). Simulations where r 2 = r 1 = 2; 4; 6; 8; 10 reveal the linear relationship between differential viscoelastic properties and the ratio of distance traveled by each locus (d 2 /d 1 ) (Figures 5C and S5C-S5K).
Consistent with local heterogeneity in mechanical response manifesting in unequal loci displacement, in experiments we frequently observe both symmetric (Figure 5D, top) and asymmetric (Figure 5D, bottom) movement of loci pairs using the FUS N -TRF1 adhesion module (Video S6). Moreover, we find that when both loci are nuclear ''internal'' ( > 0.5 mm from a nuclear or nucleolar periphery) or ''peripheral'' ( < 0.5 mm from a nuclear or nuclear periphery), movement is relatively symmetric, while ''mixed'' pairs (one peripheral locus and one internal locus) are asymmetric (Figure 5E). Given the linear relationship between differential viscoelastic properties and the ratio of distance traveled by each locus established in simulations (Figure 5C), these data imply that mixed pairs connect loci from environments with greater heterogeneity (r 2 = r 1 s1; Figure 5E). Together, these results support a model of a viscoelastic liquid nuclear interior with an average of 3.1-fold increased resistance within 0.5 mm of nuclear and nucleolar peripheries.
Both DNA density and epigenetic state are thought to contribute to total nuclear mechanics 53,65 and could determine local mechanical heterogeneity of chromatin. However, until now, we have lacked the tools to investigate the relationship between local and global material properties with sufficient resolution. In order to understand the mechanistic basis of local chromatin material state, we sought to determine whether local compaction state is correlated with asymmetric movement. We measured the local chromatin density at telomeres by quantifying B C D E F G H Figure 6. DNA density and epigenetic inhibitors control local chromatin viscoelasticity (A) Example images and quantification pipeline of Hoechst intensities at target loci in U2OS cells. Ratio of DNA density (H 2 /H 1 ) of the Hoechst channel fluorescent intensities measured within a 0.33 mm radius (2 pixels) of the loci. Asymmetric travel (d 1 /d 2 ) is the ratio of the distance traveled by the first telomere over the distance traveled by the second telomeres. (B) Graph of Asymmetric travel (d 1 /d 2 , left axis) or viscoelastic ratio (r 2 = r 1 , right axis) vs. ratio of DNA density (H 2 /H 1 ) for telomeres measured with FUS N -TRF1adhesion module in n = 14 loci pairs from U2OS nuclei. (C) Example images and Hoechst quantification for NIH3T3 cells. Arrows: interior chromocenters. (D) Graph of asymmetric travel (d 1 /d 2 , left axis) or viscoelastic ratio (r 2 = r 1 , right axis) vs. Hoechst difference for telomeres in n = 7 loci pairs from NIH3T3 nuclei. (E) Example images demonstrating DNA density by Hoechst intensity in untreated (left), TSA-treated (center), and methylstat-treated (right) U2OS cell nuclei.
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Hoechst-labeled intensity in a 0.33 mm radius around each telomere locus labeled with FUS N -miRFP670-TRF1 (Figure 6A). We find that the ratio of chromatin density in telomeric pairs is correlated with their asymmetric movement and therefore differential viscoelasticity (Figure 6B, R 2 = 0.403, *p = 0.019). This intensity correlation holds true in mouse fibroblast NIH3T3 cells, whose DNA-dense heterochromatic domains, or chromocenters, are found internally as well as peripherally (Figures 6C and 6D), suggesting that DNA density is correlated with local viscoelasticity, independent of nuclear position.
Global nuclear mechanics can be altered with small molecule drugs that affect epigenetic modifying enzymes, including trichostatin A (TSA), a histone deacetylase inhibitor that increases acetylation and reduces variation in chromatin density across the nucleus, 53 and methylstat, a histone demethylase inhibitor that increases methylation and increases variation in chromatin density. 53 These treatments lead to the expected DNA distributions in U2OS cells (Figures 6E and 6F), and telomeres are found throughout these differentially compacted regions (Figures S6A-S6C). MSD of tracked telomeres in TSA-treated U2OS cells shows that they diffuse with a higher exponent (a = 0.6678) than untreated cells (a = 0.6227), while telomeres in methylstattreated cells exhibit a lower diffusive exponent (a = 0.4685) (Figures S6D-S6F), consistent with previous reports. 53,65 After calibrating the Rouse polymer-based force estimation model on these MSD data, we confirm that FUS N condensates apply the same 0.2-1 pN range of force in each condition (Figure S6G). We find that these epigenetic inhibitors decouple movement asymmetry and viscoelasticity from local DNA density in TSAand methylstat-treated cells (Figures 6G and 6H), suggesting that DNA density is not the only determinant of local viscoelastic state and that averaged measurements like MSD miss important local variations in mechanics.
Taken together, though the number of loci measured under these perturbations is not extensive, the data point to a mechanism in which local mechanical heterogeneity of chromatin arises from a combination of compaction state and epigenetic modifications. The lack of direct correlation between local and global mechanical states is an engaging concept that will undoubtedly be the subject of future studies.
In this work, we developed VECTOR, a technique that deploys synthetic light-controlled condensates to impart force on specific chromatin loci in living cells and consequently reposition them. Using VECTOR, we showed how biomolecular condensates generate pN-level forces and harnessed these forces to characterize material responses across nuclear positions. Our findings on (1) lack of significant correlation between degree of displacement (strain) and detachment probability, (2) velocity rate-dependence of detachment probability, and (3) high fre-quency of incomplete locus recoil suggest that the material state of chromatin at the mesoscale is consistent with a viscoelastic fluid. Together with locus MSD data, these findings are generally consistent with predictions of a Rouse polymer. However, chromatin exhibits heterogeneity in viscoelastic resistance, coupled to nuclear position. Our findings demonstrate the utility of condensate capillarity in applying precise forces onto subcellular targets and underscore the complexity and heterogeneity of the viscoelastic chromatin material state within the nucleus (Figure 7).
VECTOR demonstrates that condensates can generate appreciable interfacial forces up to the pN-level, a magnitude comparable to ATP-fueled molecular motors, though in this case the energy is stored in condensate interfaces. Light deactivation shrinks the loci-spanning condensate, dictating the rate of loci movement, which we find to be between 0.75 and 1.25 mm/min. This speed is comparable to whole-chromosome movement in mitosis but not as rapid as individual molecular motors such as kinesin, which walk along microtubules (MTs) at 2-3 mm/s. 66 Work is generated by dissolving condensates, reminiscent of force generation through disassembling MTs. 67 Sustained attachment to the object against which force is applied is key (e.g., Dam1 in the case of MTs, 67 IDR-mediated adhesion in VECTOR).
VECTOR harnesses and directs these interfacial forces via IDR-mediated adhesion between the condensate and targeted telomeric or non-telomeric repetitive loci, which are efficient nucleation seeds for synthetic condensates. 23,43 Regulated assembly and disassembly of endogenous chromatin-interacting condensates like transcription factor hubs, 68,69 which form and dissolve on the order of minutes, may represent an additional layer of spatiotemporal regulation of pairwise locus interactions related to mammalian gene expression. Long-lived nuclear bodies like nuclear speckles, histone locus bodies, and Cajal bodies may also shape the 3D genomic landscape and transcriptional activity, serving as anchor points for adhesion of linearly distant loci and explaining long-range and inter-chromosomal interactions observed using chromatin conformation capture techniques. 33,70,71 We showed that VECTOR can also reposition non-chromatin nuclear bodies, namely Cajal bodies (Figures S2E-S2G), suggesting that a variety of cellular structures may be targeted by condensate-generated forces. Further adaptations of VECTOR could enable examination of the nature of pairwise locus interactions, locus positioning relative to nuclear bodies/compartments, 34,72 and kinetics of associated functional outcomes.
Adhesion between chromatin-bound, self-interacting proteins like TRF1 can counteract a locus' tendency to recoil upon repositioning, suggesting that chromatin-bound IDRs mediate stable long-distance or interchromosomal genomic interactions as observed with telomere clustering, heterochromatic domain coalescence, and even certain enhancer-promoter contacts. 52 (F) Frequency distribution of normalized DNA density in a 0. Endogenous levels of shelterin proteins (including TRF1) poorly mediate this long-term self-interaction between repositioned telomeres, while non-stoichiometric overexpression of TRF1 does, suggesting that while miscibility of telomeric DNA regions 40 is sufficient for fusion of proximal telomeres, it is not sufficient to counteract the restoring force of the chromatin network. Potentially, imbalanced stoichiometry due to TRF1 overexpression results in increased strength of telomere associations that prevent recoil in our synthetic clustering system and lead to aberrant telomere clustering and formation of dicentric chromosome bridges in previous studies. 50,51 Future studies will unravel differences between cases where long-distance locus associations are functional, 73,74 as with enhancer-promoter interactions, and dysfunctional as with telomere bridges.
Chromatin loci experiencing forces via VECTOR show forceresponse and recoil behavior consistent with a viscoelastic liquid. Previously, the discrepancy between lack of intermixing of chromatin with itself (e.g., labeled histones or replicationlabeled DNA) and rapid fluorescence recovery after photobleaching (FRAP) recovery of chromatin-binding proteins (e.g., heterochromatic factors) have been interpreted as a solid-like chromatin scaffold surrounded by a nucleoplasmic liquid. 27,28 However, here we have directly measured chromatin mechanics with VECTOR as an active rheology tool, illustrating that at the mesoscale ($1 mm), chromatin has both viscous and elastic components. We find that loci recoil incompletely, indicating a partially dissipative viscoelastic liquid rather than a purely elastic solid model of chromatin. Our active rheological measurements can be explained equally well by a phenomenological springdashpot Jeffreys viscoelastic liquid model or Rouse polymer model, but the Rouse model is more consistent with all data, including the observed slope of a $ 0.5 in MSD. A viscoelastic liquid model arising from Rouse-like chromatin polymer movement is consistent with previous work, including constrained and coordinated diffusion of chromatin 75,76 and scale-dependent protein mobility within the chromatin environment. 77,78 Importantly, we measured mechanical heterogeneity within the nucleus up to 3-fold higher near nuclear and nucleolar pe-ripheries than in the interior, which is consistent with known subnuclear localization of heterochromatin. 79 Increased chromatin compaction of heterochromatic sequences 80 correlate with asymmetric locus repositioning in both U2OS and NIH3T3 cell types, and increased rigidity at the nuclear periphery would explain observations of high mechanical stiffness of the whole nucleus, 53,81 even while interior genomic elements exhibit more fluid-like viscoelastic response. Interestingly, recoil behaviors of a chromosomal-internal locus (PPP1R2) do not differ from those of end loci (telomeres), suggesting that linear chromosomal positioning is not a strong predictor of viscoelasticity. Our results highlight the complex relationship between local and global mechanics within the nucleus and underscore contributions of nuclear positioning, chromatin compaction, and epigenetic alterations to nuclear organization and function.
In this work, we have deployed synthetic biomolecular condensates for systematic and programmable generation of intracellular forces and used these forces to interrogate mechanical properties of the genome. We have described the utility of capillary forces and interfacial adhesion between condensates and cellular objects to do organizational work within living cells and suggest that endogenous condensates may utilize their interfacial interactions for similar purposes. Our results underscore the ubiquitous nature of such intracellular interfacial forces and their potential importance in regulating physical changes of the 3D genome and other structures. 37 The interplay between forces generated by condensates and the mechanical resistance of cellular structures provides an exciting perspective on the rich regulatory landscape underlying chromatin compartmentalization, nuclear organization, and their consequences for cellular physiology and disease.
Limitations of the study VECTOR is limited by several aspects of the light-induced condensates for force application: the total distance a locus can be moved is set by the achievable diameter of the condensate, and the velocity at which it moves is set by the condensate's dissolution rate. Using the dCas9-based adhesion module of
Target locus Target locus VECTOR system expressed Nuclear interior Chromatin viscoelasticity Nuclear periphery Engineered 'sticky' target loci Light Activation Chromatin-tethered condensate formation F F Low Viscoelastic Resistance High Viscoelastic Resistance Light De-activation Force applied to target loci
Chromatin locus repositioning Asymmetric locus movement
Target chromatin loci are bound by VECTOR system proteins, creating seeding sites for light-inducible condensates to grow and fuse during a few minutes of localized blue light activation. Upon light deactivation, target loci remain attached to the shrinking condensate due to interfacial interactions, leading to equal forces applied on the attached loci. Uneven viscoelastic resistance of the attached loci leads to asymmetric repositioning events, revealing increased local chromatin viscoelasticity near the nuclear periphery.
VECTOR, we can reposition repetitive PPP1R2 and telomeres, though this large number of bound proteins could alter the endogenous material state of the locus, and repositioning of non-repetitive loci will require further methodological development. For future applications of the dCas9 adhesion module to unique loci, a tiled array of 30-100 guides may still efficiently label loci, 82 though the lower limit of number of chromatin-binding sites required to transmit force to the chromatin is currently unknown. Our simulations accurately predict the relative mechanical stiffness difference between two loci, but the reported force values are estimates. With VECTOR, we can compare mechanical measurements of chromatin loci across nuclear positions with high spatial resolution; however, future studies are needed to determine whether rapid movement of a locus is sufficient to induce changes in gene expression and nuclear function.
Detailed methods are provided in the online version of this paper and include the following:
TABLE d RESOURCE AVAILABILITY B Lead contact B Materials availability B Data and code availability d EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS B Cell culture B Construct design and cloning B Lentivirus production and lentiviral transduction B Cell culture small molecule inhibitor treatment B Optimization for dCas9-based adhesion module d METHOD DETAILS B Microscopy B Optogenetic stimulation B Automated imaging protocol B Limitations of preceding automated activation protocols B Physical model d QUANTIFICATION AND STATISTICAL ANALYSIS B Kymograph production B Loci tracking during repositioning B Detachment probability B Estimating number of IDR-IDR interactions at the chromatincondensate interface B Detachment probability as a function of strain and velocity B Symmetric/asymmetric locus movement characterization B Heterogeneity in chromatin viscoelasticity B Hoechst intensity analysis B Mean squared displacement analyses B Passive microrheology to determine viscoelastic moduli B Initial order of magnitude force estimation from telomere trajectories B Generating pull-force estimation plots B Statistical analysis METHOD DETAILS Microscopy Cells for all live cell imaging experiments were plated on 96-well glass-bottom plates and incubated at 37 C and 5% CO 2 by an Okolab microscope stage incubator with a 96-well insert. Images were taken on a spinning disk (Yokogawa CSU-X1) confocal microscope with an Andor DU-897 EMCCD camera on a Nikon Eclipse Ti body and a 100x oil immersion Apo TIRF objective (NA 1.49 MRD01991), and a Nikon LU-NV laser launch. A second spinning disk confocal microscope with a Nikon Plan Apo VC 100x 1.4 oil immersion objective, Nikon LU-N4 laser launch, and Oko Labs Bold Line Cage Incubator with a 96-well plate insert with 0.1% accuracy CO 2 control at 37 C was used to take optogenetic stimulation images and the automated imaging experiments. 488 nm, 561 nm, and 640 nm lasers were used to image mGFP, mCherry, and miRFP670 constructs, respectively, on both microscopes.
Specific regions in the nuclei of cells were locally activated by using a Mightex Polygon digital micromirror device (DMD) to pattern blue light (488 nm) activation from a Lumencor SpectraX light engine. U2OS cells expressing FUS N -miRFP670-TRF1, NLS-GFP-iLID-Fe and FUS N -mCherry-SspB were imaged using a specific local activation protocol: 1) Pre-activation, imaging the mCherry (541 nm) and miRFP670 (640 nm) channels every 5 s for 10 s; 2) Activation, using a circular region of interest (ROI) (with diameter of 1.2 mm) to locally activate two genomic loci/nuclear bodies to seed, grow, and fuse FUS N Corelet condensates using the 485 nm DMD every 5 s for 2-10 min; 3) De-activation, back to only imaging the 561 and 640 nm channels every 5 s to allow the FUS N Corelet condensates to dissolve and pull together attached loci/structures.
All automated imaging protocols were created by using the JOBS module of the Nikon NIS-Elements software. All protocols included this workflow: 1) Define well selection, 2) Set up the autofocus, 3) Designate the 541 nm and 640 nm lasers as the 'Capture Definition,' and 3) Pre-define points with cells expressing all relevant constructs listed above in the optogenetic stimulation section. Each of the following automated imaging protocols used the DMD to stimulate at pre-defined ROIs at 395 nm wavelength at 30% intensity unless noted otherwise:
In order to mimic a slow scan across a cell from left to right, we defined a rectangular box (1.2 mm wide, 64 mm tall boxes) as the ROI and stimulated two of these boxes at a time with one box remaining from the previous activation sequence to maintain condensates formed from the previous sequence and the second box to form new condensates in the current loop). For each predefined point, the JOBS protocol took a Z-stack before and after the optogenetic activation/de-activation segment. After the first Z-stack, cells were imaged with two ROI boxes for 2-5 min (5 sec/frame) using the Capture Definition ND Stimulation with Sequential Stimulation feature every second. The ND Acquisition sequence was then used to image cells for the de-activation segment (5 sec/frame) for 5 minutes.
The array patterning protocol used the following parameters on the Polygon pad: 0.405 mm diameter of the stimulation ROI with each ROI 2.835 mm apart from its closest neighboring ROI with the array pattern covering an area of 56.7 mm by 56.7 mm of the field of view. The protocol stimulated the ROIs using the 395 nm wavelength at 100% intensity. Cells were imaged for 10 minutes (5 sec/frame).
All telomeres were detected using the 'Bright spot detection' with the NIS-Elements General Analysis 3 program. All bright spots were then converted into ROIs and the same workflow laid out in the 'sliding box' section was applied.
Each telomere was detected similarly as the 'All telomere stimulation' protocol. Using General Analysis 3, each bright spot's centroid x, y positions were measured and two bright spots whose centroids were 10 pixels (1.35 mm) or less apart were connected with a thin line. These measurements made and overlaid a binary image of these connecting lines on the telomere channel that were then converted into ROIs for stimulation.
First, we attempted a global activation pattern across the entire nucleus, which results in Corelet condensates nucleating at each telomere, but infrequent condensate coalescence events due to small overall condensate size (Figure S1B, Global). The smaller an area of the nucleus that is activated, the larger each condensate grows; in our next attempt we activated a smaller rectangular region, then shifted the activation region of interest (ROI) across the nucleus over time to activate the nuclear area sequentially (Figure S1B, Sliding box). This sliding box pattern resulted in larger condensates that do fuse, but is prohibitively time-consuming at 60 minutes per nucleus. Next, we tested an array pattern of activation sites, reasoning that some of the array positions will nucleate between closely positioned telomeres and lead to coalescence events (Figure S1B, Array); while this pattern does sporadically create condensates at productive locations, most are not aligned with telomere loci positions, and thus its efficiency in merging multiple condensates associated with telomeres is low. The best approach for successful repositioning was to identify close telomere pairs at most 1.4 microns apart using a feedback protocol and to only activate those identified pairs, forming condensates at those positions (Figure S1B, Activate each locus).
We perform simulations of pulling and merging condensates with the Corelet system via capillary forces, using a phase field model coupled with linear viscoelastic models. The Corelet construct consists of a 'core' (A) with 24 binding sites that can bind to the IDR component (B) when light-activated due to iLID-SspB association. 42 The other component of interest is the telomere and the telomere binding protein (FUS N -TRF1), which we treat as a single species that forms a phase that is distinct from the Corelet condensate, and which we intend to move via capillary forces due to its interaction with the condensate. All other species are considered as the buffer (S). We model the mixture using the Flory-Huggins free energy of mixing Dg. 55,87 When there is no light activation, A and B do not associate, and thus do not undergo phase separation. When light-activated, A and B bind (A + B / AB), and the majority exists in the associated form AB which forms the Corelet droplet. Hence for simplicity, we set the interaction parameter between A, B, and other species to zero and only consider the interaction parameter between AB, C, and S,
where Dg is the free energy of mixing per lattice site based on the Flory-Huggins lattice theory, k B is the Boltzmann constant, T is the temperature, f i is the volume fraction of component i, where i ∈ {A, B, AB, C, S}, v i is the number of lattice sites occupied by species i, and c i,j is the Flory interaction parameter between component i and j. The volume fractions satisfy the constraint that P i fi = 1. For a phase-separating system, in addition to the bulk Dg, the total free energy of mixing also includes the contribution from the concentration gradient, which we assume to have the same coefficient l 2
where c 0 is the number density of lattice sites, and Dg = Dg=k B T is the non-dimensionalized bulk free energy. This free energy is used by Cahn and Hilliard for non-uniform systems and in Cahn-Hilliard equation, 88 which is conventionally used to model phase separation. Due to the energy associated with the concentration gradient, the diffuse interface between phases is on the order of l.
We define the chemical potential to be the variational derivative
Notice that the variational derivative is taken while satisfying the P i f i = 1 constraint, in other words, the buffer is treated as a reference component whose volume fraction is a function of those of other components f S = 1 À P iss f i . We define the activity a i by
The equilibrium condition for the association reaction A + B / AB is a A a B = K d a AB , where K d is the dissociation constant that changes with the light intensity. The kinetics of association can be described by a rate that follows detailed balance R = k(a A a B À K d a AB ). 89 Both the kinetic prefactor k and the dissociation constant K d depend on the light intensity, which we denote with subscripts ''on'' and ''off'' to refer to when the light is on (R = k on (a A a B À K d,on a AB )) and off (R = k off (a A a B À K d,off a AB )). Suppose the association is a volume-conserving reaction, that is,
As modeled previously for light-activated droplet systems, 89 the gradient in the chemical potential causes a diffusive flux and we assume a constant mobility M i for species i. In summary, the governing equations for all the species are 5) 6) 7)
The model above considers C to be a freely moving fluidic species. However, we are also interested in the case where C interacts with certain regions of the chromatin, such as telomeric chromatin. Because TRF1 binds to telomeric DNA, which may experience viscoelastic forces, we model the interaction between C and the telomere using an isotropic interaction kernel K(|r À r i |), which acts as a potential well around the telomere that TRF1 binds to, where r is any point in space as defined above, and r i is the center of the telomere locus i. In other words, extending Equation 2, the total free energy is now
where the summation over i refers to all the telomere loci of interest. Here, we use a Gaussian interaction kernel Kðjr À r i jÞ = U 0 exp À ðjr À r i j 2 =l 2 Þ, which has the same length scale as the diffuse interface. Note that U 0 is dimensionless. Due to the interaction between the telomere and the droplets, the droplets also exert a force F i on the telomere: 10)
The equation of motion of the center of the telomere locus can be described using various viscoelastic models which we study later: 11) 12) 13) 14)
where the dot refers to the time derivative, E i is the stiffness constant of the spring element, h i is the friction coefficient (inverse mobility) of the dashpot, h i 0 is the friction coefficient of the additional dashpot in series with dashpot in the Maxwell and Jeffreys models. The time scales of these models are important to consider and have significant impact on the dynamics. Therefore, we define them here. Because we are interested in the dissolution and coalescence time of the Corelet condensate, we define time scales based on R 0 , defined to be half the distance between the two telomere loci which are located on opposite sides of and in contact with the synthetic condensate, or approximately the radius of it.
The diffusion-limited dissolution/growth time scale of the condensate can be derived based on the Cahn-Hilliard equation (eliminating the reaction term in Equations 5, 6, and 7) to be $
MABg , 90 where g is the interfacial tension between the condensate and the buffer phase. In the Cahn-Hilliard formulation, the interfacial tension is defined by the excess free energy per unit area between two phases at equilibrium that form a flat interface. By integrating in the normal direction of the interface from one phase to another, 15)
where m j0 is the chemical potential of component j, f j0 is the volume fraction of component j in either phase far away from the interface. It can be shown that g $ lc 0 k B T. 88,91 Therefore, we define a characteristic diffusion time scale t d hR 3 0 =ðM AB l). Similarly, the reaction-limited dissolution/growth time scale of the condensate can be derived based on the Allen-Cahn equation (eliminating the diffusion term in Equations 5, 6, and 7) t r hR 2 0 =ðk off l 2 ). 90 Based on the diffusion and reaction time, we define Damko ¨hler number Da h t d / t r = k off R 0 l / M AB .
The equation of motion of the center of the telomere locus using the Newtonian model motivates us to define another viscously dominated coalescence time t v,i . Because the length scale of the interaction kernel is l, depending on the dimensionality n, the force
We may define a dimensionless stiffness constant based on the ratio of the elastic force $ R 0 E i and capillary force (|F i | above), Ẽ i h R 0 E i /(c 0 k B Tl nÀ1 ). Similarly, for the Kelvin-Voigt and Maxwell models, we define the retardation time t i = h i /E i , and the Maxwell relaxation time t Mi = h i 0 /E i . We nondimensionalize these time scales by t d . We visualize the simulation in images and movies where the red (R), green (G), and blue (B) values are R = B = f C , G = f A + f B + f AB , in other words, magenta is used to denote component C, and green is used to denote the Corelet concentration. The kymographs show the simulation results at the symmetry line connecting the two telomere loci over time.
Here, we provide a summary of the simulations and the corresponding dimensionless parameters.
The purpose of the first simulation is to illustrate the possibility that capillary forces can reposition attached objects. A simulation using the dashpot model reproduces the merging of two telomeres pulled by the condensate, shown in Figure S4C. Denoting the interfacial tension between the AB-rich (C-rich) phase and the buffer-rich phase by g AB,S and g C,S , and that between the AB-rich and C-rich phases by g AB,C , then bringing AB-rich and C-rich phases into contact, the affinity between the AB-rich and C-rich phases can be quantified by g AB,S +g C,S Àg AB,C . In the Cahn-Hilliard formulation, the interfacial tensions defined in Equation 15 are related to the interaction parameters c ij . 91 In Figure S4C, c AB,S = c C,S = c AB,C = 2.
Because we are interested in the capillary interaction between the condensate and the chromatin locus, we choose a set of thermodynamic parameters that can give the desired capillary adhesion between components AB and C qualitatively. The precise quantification of the saturation concentration and phase diagram 42,43 is beyond the scope of the modeling here. For the base case simulation where AB is the FUS N Corelet condensate (FUS N -mCh-SspB + iLID-GFP-Fe, in activated/interacting state), C is FUS
Suppose when under light activation the association between A and B is strong and K d = K d,on = 0, k = k on , while when not illuminated K d = K d,off = 0.2, k = k off . Based on the free energy of mixing (Equation 1) and the volume fraction, the activities of A and B are on the order of 10 À2 while that of AB is on the order of 1. In order for the initial rate of association $ k on a A a B when light is turned on and the initial rate of dissociation $ k off K d,off a AB when light is off to have the same order of magnitude, we set k on /k off = 4 3 10 3 .
We make the assumption that the diffusivity of component C is the same as that of the Corelet condensate component (AB). Based on the measurement of the diffusivities of FUS N -mCh-SspB and iLID-GFP-Fe S12 , we set M A = M B = 10M AB = 10M C . For the base case, we set the average composition to be f A +f B +f AB = 0.164, f C = 0.041, and suppose the constituents (A and B) of the condensate have the same volume fractions.
For the time scale, we set Da = t r /t d = 2000; t v1 /t d = t v2 /t d = 0.02, that is, the two telomere loci have the same inverse mobility and are set to a small value so that it does not have a significant effect. Without yet considering the viscoelastic properties, we use the Newtonian model for the base case. Here in this section, the purpose of the simulation is to illustrate the possibility that telomere droplets can be pulled to merge with capillary forces. The ratios of time scales above remain to be studied and validated in later sections given other experimental evidence.
The simulations are performed in a 2D periodic L 3 L domain to capture the dynamics qualitatively. For the base case L/l = 36. R 0 /l = 9. As an example, in Figure 4 R 0 z 0.245 mm, which corresponds to l z 27 nm. Initially, the system is fully equilibrated with the presence of two droplets that are rich in component C (which represents the FUS N -TRF1-marked telomeres that are observed in microscopy and henceforth called droplet C) and the light is off. With the imposed average composition, the radii of droplet C are 2.5l (defined by the region where f C > 0.5). Their centers are located at r 1 (t = 0) = [Àd 0 /2,0], r 2 (t = 0) = [d 0 /2,0], where d 0 /l = 26. At t = 0, a circular region {|r| % d 0 /2} is illuminated. Upon light activation, two Corelet droplets that are rich in AB nucleate in the circular region next to the telomeres. We let the system fully equilibrate until the two droplets merge and form a single condensate in between the two telomere loci. The distance between the two telomere loci becomes 2R 0 , where R 0 /l = 9, and then turn off the light and let the condensate dissolve. The equations are solved on a grid of [128,128], that is, the grid spacing is 0.3l.
In the following sections where we study the effect of certain parameters, other parameters remain unchanged unless otherwise stated.
Increasing c AB,C is expected to increase the energy of interaction between AB-rich phase and C-rich phase and hence the interfacial tension g AB,C , resulting in a decrease in the affinity between AB-rich and C-rich phases, modeling the changes in the condensate and telomere loci. We performed two pairs of control simulations where the only difference between them is the value of c AB,C . We see that when c AB,S = c C,S = c AB,C = 2, the adhesion between the telomere and Corelet droplet is strong, the telomeres stay attached to the condensate and eventually merge (Figures S4C and S4E), whereas when c AB,S = c C,S = 2, c AB,C = 3.5, the telomeres detach and do not merge (Figures S4D and S4F). In Figures S4C and S4D, additional parameters are chosen to match the observed length and time scales in Figures 1A and 2A, while as a control experiment to illustrate the effect of adhesion, Figures S4E and S4F have identical parameters except for c AB,C .
Specifically, compared to Figure S4C, in Figure S4D we increase c AB,C to 3.5 and keep all parameters identical to the 'base case simulation' section except for the sizes of droplets and the average composition to better reflect the relevant experimental length and time scales: the average compositions are f A + f B + f AB = 0.141, f C = 0.038. The distance between the two telomeres initially is d 0 /l = 27.3. The illumination region is {|r| % d 0 /2}. When the two Corelet droplets merge into a single droplet, the merged droplet radius is 6.7l. Again, t r and t d are still defined using R 0 = 9l as the characteristic length scale. For reasons we will explain in the 'single telomere interaction with condensate' section, we increase the viscous resistance of the telomere loci to t v1 /t d = t v2 /t d = 1, and increase the Damko ¨hler number to Da = t r /t d = 10 4 in order to slow down droplet dissolution because, at this level of viscous resistance, it becomes easier for the telomere to detach even for the base Flory interaction parameter of c AB,C = 2.
To illustrate the effect of c AB,C , we perform a controlled pair of simulations where the only difference is c AB,C shown in Figures S4E and S4F. The average compositions are identical and set to f A + f B + f AB = 0.167, f C = 0.038, and the initial distance to d 0 /l = 26.7. The illumination region is {|r| % d 0 /2}. In Figures S5H-S5K, we repeat the analysis above using the Jeffreys model. Again, we assume that all dashpot and spring elements have proportionately higher values near the nuclear periphery, that is, r 2 =r 1 hE 2 =E 1 = h 2 h 1 = h ; 2 =h ; 1 . In other words, both telomeres have the same retardation time and Maxwell relaxation time. We set t 1 /t d = t 2 /t d = 2 and t M,1 /t d = t M,2 /t d = 2. Again, we find that Equation 16 is a good approximation for the ratio of displacement and the fitted value of R is 0.042 and 0.041 in Figures S5I and S5K, respectively.
The consistency in the fitted R indicates that Equation 16provides a useful estimate of the asymmetry. More importantly, Equation 16provides an upper bound to the ratio of the displacement equation 17)
In other words, given the ratio of displacement observed in experiments, Equation 17 provides a lower bound for the ratio of local resistance.
In this section, we consider another model for describing the viscoelasticity of the genomic locus-the Rouse model, which describes the motion of an ideal polymer chain without hydrodynamic interactions. The equation that governs the position of chain x(s), where s is the arc length, is from Keizer et al. 30 h vx vt = k v 2 x vs 2 + fðt; sÞ; (Equation 18)
where h is the friction coefficient, k is a coefficient for the stiffness of the chain, f(t,s) is the force on the chain. The condensate only interacts with the locus while all other parts of chain are ''phantom'' that do not chemically interact with other components in this system, hence the capillary force only acts on the locus, which is approximated as a point located at s = 0, that is, f(t,s) = F(t)d(s), where F is the capillary force defined in Equation 10. Consistent with previous simulations, we omitted the thermal noise for simplicity, focusing only on the capillary force. Suppose the chain is infinitely long and initially straight, and using subscript i=1,2 to denote the two loci, then the analytical solution to Equation 18 at the position of the locus r i (t) = x(t,s = 0) is
This dynamic applies to both telomere loci which are assumed to be located on two independent polymer chains. From Equation 19, we find that for infinitely long polymer chains, only one parameter is needed to describe its dynamics and the time scale of relaxation for the Rouse model t rs,i satisfies R 0 $ jF i j ðt rs;i =ð4ph i k i ÞÞ 1=2 , hence we define
(Equation 20)
Similar to previous sections, we start from the state where the Corelet droplet has merged and study the effect of t rs /t d on the evolution of the distance between the telomere loci, as shown in Figure S4K. As the resistance of the polymer chain increases (t rs /t d increases), the displacement of the locus decreases. For large resistances (t rs /t d R 0.01), the telomeres detach from the condensate and recoil at about t/t d =1.4. For small resistances (t rs /t d R 0.1), the telomeres merge (Figure S4K). When the telomeres detach and the capillary force vanishes, the recoil dynamics at long times follows jrðtÞ À rð0Þj $ t À 1=2 (Figure S4L). In Figure S4M, we show the evolution of capillary force F on the telomere loci in the direction toward each other over time. During condensate dissolution, the pull force increases, and note that for small resistance, the capillary force remains after the condensate has dissolved since adhesion force between the loci is necessary to keep them in place while the polymer chains relax (Figure S4M). Over the range of Rouse polymer relaxation time t rs , the model predicts a spread of recoil dynamics similar to the Jeffreys model, so a Rouse polymer is not inconsistent with the observed range of viscous and elastic recoil recoveries in our experimental data (Figures 4G and 4H).
A simulation of the Cajal body in Figure S4J uses Equation 2 without the interaction kernel. Parameters are chosen to match the observed length and time scales in Figure S2F. We also perform an additional control simulation comparing the telomere (using Equation 9) and the Cajal body Equation 2 with the only difference being whether the interaction kernel is included. The Coilin construct forms a ring at the interface between the condensate and the buffer (Figure S4J inset), similar to experimental results (Figure S2G).
Specifically, we perform simulations with all the parameters identical to the 'base case simulation' section except for the sizes of the condensates and domain and the average composition to better reflect the experimental observation in Figure S2F. The average compositions are f A + f B + f AB = 0.104, f C = 0.03 The domain size is changed to L/l = 50. Initially, the radii of the two Cajal bodies are 2.3l. Their centers are located in the same way as the 'base case simulation' section, while the distance is d 0 /l = 33. The illumination region is again {|r| % d 0 /2}. When the two condensates merge into a single droplet, the radius of the merged droplet is 8l. Note that while the single condensate size is different from R 0 in the 'base case simulation' section, t r and t d are still defined using R 0 = 9l as the characteristic length scale.
In Figure S4J, we compare the telomere (with interaction kernel) and Cajal bodies (without interaction kernel) using the same exact parameters, average composition, and length scales as defined above.
Time series images of chromatin locus movement were registered to correct for whole cell movement in FIJI (ImageJ 1.52p) 85 using HyperStackReg, 92 Rigid Body translation. A line was drawn across the activation region and kymographs were created using the MultiKymograph plugin.
Registered time series images of chromatin locus repositioning were cropped to a region containing the relevant telomeres, then loaded into the TrackMate plug-in Tinevez et al. 93 in FIJI. Telomeres were identified in the miRFP670 channel with the LoG detector, with an estimated blob diameter of 0.7 microns and no initial thresholding. Spots were filtered by quality to eliminate background. Tracks were generated using Simple LAP tracker with max linking distance 1 micron, gap-closing max distance 1 micron and gap-closing max frame gap 0 frames. Tracks of the relevant telomeres were identified and the XY distance (d) between them calculated for each time point d =
Detachment probability Constructs with FUS N point mutants (FUS N 3YS , FUS N 5YS , FUS N 9YS , FUS N 15YS , FUS N
) fused to miRFP670-TRF1 were created, expressed in living U2OS cells along with Corelet components, and imaged using the Optogenetic Stimulation protocol as described above. ROIs were aimed at singular telomere loci to observe how a single locus-condensate pair would behave during condensate dissolution during the de-activation sequence. Chromatin-condensate pairs were classified as 'attached' if the condensate dissolved towards the locus or 'detached' if the condensate dissolved concentrically, away from the telomere.
Estimating number of IDR-IDR interactions at the chromatin-condensate interface Previously, we have measured the diameter of telomeres in U2OS cells by super-resolution STED microscopy to be on the order of 100-150 nm (data not shown), in agreement with published estimates of telomere sizes in different cell lines. [94][95][96][97][98][99] The surface area of an average telomere would then be 4p(0.075mm) 2 = 0.071mm 2 . We estimate from our images that usually less than half of the surface of the telomere is in contact with the Corelet condensate, so the interfacial area between the chromatin and condensate is up to 0.035 mm 2 . Each FUS N -SspB-decorated ferritin ''core'' particle has a radius of 20 nm, 42 so a surface area of 0.005 mm 2 . Assuming packed spherical core particles coating the condensate-telomere interface, we estimate that approximately (0.035/0.0025) = 14 cores interact with the available surface of the telomere. Every core has binding sites up to 24 FUS N IDRs distributed on its surface, up to half of which (12) are in an orientation to interact with the locus-tethered IDRs at any time. These experiments represent a bulk of approximately 14 3 12 = 168 condensate IDRs interacting with a similar number of chromatin-tethered IDRs providing the interfacial force between a chromatin locus and condensate.
Probability of detachment of single FUS N 15YS -miRFP670-TRF1-marked locus from its attached condensate was separated into bins by strain (0 -1) and by velocity (0 -1.0 microns/min). Images were processed in FIJI, using Trackmate to identify the XY position of the locus of interest using the miRFP670 channel and XY position of the condensate centroid using the FUS N WT -mCherry-SspB channel.
Strain was defined as (d 0 -d d )/d 0 where d 0 is the initial distance between the chromatin locus centroid and condensate centroid during the first frame of deactivation, when force application begins, and d d is their distance at the moment of measurement. Examples which stay attached experienced all possible strains between 0 and 1. Detachment velocity was defined as the linear slope of locus displacement over time for the 10 -30 seconds before detachment; loci that did not detach were counted as 'attached' in the bin within their highest recorded velocity.
Symmetric/asymmetric locus movement characterization All images were analyzed using FIJI for the image pre-processing steps and Python 3.7.10 for image processing and analysis. During pre-processing, each nucleus was corrected for whole cell movement using HyperStackReg, and set to a contrast level sufficient for segmentation in Python. In Python, the last frame of the activation sequence from the mCherry and miRFP670 channels were used to segment nuclei and telomeres respectively, and repositioned telomeres from the last frame of the de-activation sequence were segmented, then binary nuclear masks were processed with the Canny Edge Detection method to identify the nuclear and nucleolar peripheries from the FUS N IDR -mCherry-SspB channel. The nucleoli are detectable in this channel as dark spots within the nucleus due to exclusion of the construct from nucleolar regions. The distance from all nuclear and nucleolar edges to telomere centroids in both frames were calculated, and the edge bearing the shortest distance from each telomere was called out and characterized as the point of 'nearest periphery.' This information was then used to find the actual distance between the closest edge and telomere
Statistics were performed using GraphPad PRISM version 9.1.0 software (GraphPad). Statistical significance of detachment probabilities in Figures 2 and S2 were calculated using a Chi-squared test for trend; p value and size of n are noted in figure legends and captions accordingly. Statistical significance of asymmetric locus movement as a function of locus position was calculated using one-way ANOVA with multiple comparisons, number of replicates, and size of n are noted in the figure legends and captions accordingly.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Cell 187, 5282-5297, September 19, 2024 Article
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