Adaptive partitioning of a gene locus to the nuclear envelope in Saccharomyces cerevisiae is driven by polymer-polymer phase separation

Partitioning of active gene loci to the nuclear envelope (NE) is a mechanism by which organisms increase the speed of adaptation and metabolic robustness to fluctuating resources in the environment. In the yeast Saccharomyces cerevisiae, adaptation to nutrient depletion or other stresses, manifests as relocalization of active gene loci from nucleoplasm to the NE, resulting in more efficient transport and translation of mRNA. The mechanism by which this partitioning occurs remains a mystery. Here, we demonstrate that the yeast inositol depletion-responsive gene locus INO1 partitions to the nuclear envelope, driven by local histone acetylation-induced polymer-polymer phase separation from the nucleoplasmic phase. This demixing is consistent with recent evidence for chromatin phase separation by acetylation-mediated dissolution of multivalent histone association and fits a physical model where increased bending stiffness of acetylated chromatin polymer causes its phase separation from de-acetylated chromatin. Increased chromatin spring stiffness could explain nucleation of transcriptional machinery at active gene loci.

SAGA complex have been suggested to induce, or their deletion has been shown to prevent INO1 translocation 11,12 . However, so far, there are no direct evidence that these proteins are involved in physical tethering of the INO1 locus to the NE. Furthermore, 5' cis elements in the INO1 locus called Gene Recruitment Sequences (GRS) or "Zip Codes", have been shown to be essential to INO1 and now other loci translocations [11][12][13] . It has been proposed that GRSs could be anchoring sites for the tethering of gene loci to the NE via protein-DNA or proteinprotein interactions [11][12][13] . To date, however, evidence of interactions between GRSs and proteins at the NE have not been reported. Furthermore, studies of the statistical distributions of translocated genes among populations of cells, as well as gene tracking measurements, show that instead of being bound at the NE, as are, for instance, the NPC or Spindle Pole Body, activated gene loci are simply statistically more tightly distributed towards the NE 8,9,12,16 . These observations led us to postulate that active gene locus translocation could be the result of differential partitioning of active gene loci to the periphery by a local phase transition of the chromatin caused by histone acetylation and other modifications, resulting in increased rates of histone exchange and associated decompaction of the chromatin. Here we present evidence that the GRSs are sites of association of chromatin remodeling complexes, including HATs, which catalyze histone H3 acetylation. Consequently, there is an increase in H3 exchange between nucleosomes and nucleoplasm within and surrounding the activated INO1 locus. The resulting decompaction of chromatin causes phase separation of the INO1 locus from the compacted chromatin found in the nucleoplasm to the decompacted chromatin adjacent to the nuclear envelope.

Results
Translocation of the activated INO1 locus and decompaction of its chromatin were studied as follows: first, we obtained a yeast strain in which 128 LacO binding motifs are integrated into the gene and expression of the LacO binding protein LacI is fused to GFP 12 . Furthermore, reference markers for the nuclear envelope (Nup49-GFP) and nucleolus (Nop1-mCherry) are also expressed. This strain could then be used to monitor and compare the statistical distribution of INO1 in cells grown in the presence (inactive INO1) or absence (active INO1) of inositol (Fig. 1a, b). Next, we could monitor the phase transition of active chromatin based on the observation that the consequent decompaction of the chromatin, is reflected in changes in its mechanical properties and geometric organization 17,18 . These changes can be understood as follows: first, the persistence length (L p ) of DNA, as for all polymers, is the length over which a thermal perturbation would cause it to bend. The L p for naked DNA and transcriptionally active chromatin is smaller than that of chromatin on small lenght scales (5-50 nm versus 170-220 nm) [19][20][21][22][23] given that these forms of DNA have more degrees of freedom than compact, inactive chromatin 17,18 . Notably, the opposite is true over long length scales. This increase in degrees of freedom implies a higher number of configurations that can be explored per unit time by naked DNA or active chromatin, so its movements are more confined compared to chromatin. Consequently, chromatin behaves as an "entropic spring" of increasing spring stiffness as it transitions from compact to decompacted states 17,18 . The spring constant of a polymer such as chromatin (k s ) is inversely proportional to L p (Eq. (1)) and consequently k s is predicted to increase as chromatin decompacts. Furthermore, its trajectories through space are shorter, a characteristic that is determined from the radius of confinement (R c ) of the chromatin 17,18 . Such a model is highly simplified, but for our purposes, measuring these values for the INO1 gene locus would serve to quantify material properties of the chromatin and how these change under different conditions. Values for k s and R c can be determined from measurements of mean-square displacement (MSD) and localization coordinates of the GFP-labeled LacO array embedded in the INO1 gene locus 17 .
Deletion of GRS I and II prevents localization of active INO1 to the nuclear envelope The relocalization of the active INO1 locus to the nuclear periphery is prevented in strains in which the GRSI, and II of the INO1 locus are both deleted (hereafter referred to as the GRSI, IIΔ double mutant) 24 . To access the effects of GRS deletions on the statistical distribution of the INO1 locus in large populations of cells, we used a high-resolution computational approach that generates probabilistic maps of the locus distribution in the nucleus (Fig. 1a, b) 16 . Using the LacI-GFP-labeled LacO array as reporter for the INO1 locus and, Nop1-mCherry and Nup49-GFP as nucleolus and nuclear envelope reference markers, respectively, we mapped the distribution of the INO1 locus with respect to these landmarks for the wild type and single and double mutants of the GRS sites under repressing (+ inositol) and activating (− inositol) conditions. Consistent with previous studies, the repressed INO1 locus was distributed throughout the nucleoplasm, but the activated INO1 locus was mainly confined to a specific region in the vicinity of the NE (Fig. 1c, d) 12 . Single GRS deletion mutants reduced and the double mutant GRSI, IIΔ prevented partitioning of the active INO1 locus towards the NE, as reported previously ( Fig. 1e-g) 24 . The INO1 locus was distributed towards, but not fixed at the NE 12 . The effects of the mutants do not reflect changes in transcription of INO1 as disrupting transcription was previously shown to have no effect on INO1 relocalization 14 .
The activated INO1 locus shows a characteristic spatial distribution at the NE that perhaps reflects its position in the middle of the 3' arm of Chromosome X. NE localization of other activated gene loci also reflects their chromosome positions, including the GAL1-10 locus, which is located closer to the centromere region in Chromosome II and thus close to the Spindle Pole Body 16 and the HXK1 gene locus, located in a subtelomeric region of Chromosome VI, that is localized towards the NE whether active or repressed, but with a more compact distribution when activated 9 .

Deletion of GRSs prevents decompaction of the active INO1 locus
We measured differences in the mechanical spring stiffness of the INO1 locus in the repressed and activated states. To do this, we tracked the GFP-LacI-labeled LacO array in the INO1 locus for 1 min at intervals of 500 milliseconds and calculated MSD values in each case. The slope and plateaus of the MSD trajectories for the INO1 locus were markedly reduced under activating versus repressed conditions (Fig. 2a). In addition, loci closer to the NE appear to be excluded from the interior of the nucleoplasm as observed before for the GAL1-10 genes 8 , which also contain GRS sequences required for relocalization of the GAL1-10 loci to the NE 13 .
We then used established relationships between MSD statistics and R c and k s to calculate their values as follows: 17 R c could be calculated directly from the MSD plateaus (See Methods, Eq. (3)) 17,25 . R c could independently be determined from the standard deviation of spot positions, σ, and the average squared deviation from the mean position, , by applying the equipartition theorem (See Methods, Eq. (4)) 17,26,27 . The INO1 locus in wild type strains (Fig. 2b) and single GRS mutant cells (Fig. 2c, d) showed significantly larger R c for the repressed versus the activated state. The GRSI, IIΔ double deletion, however, resulted in no significant differences in R c between repressed and activated states (Fig. 2e). These results were also consistent with statistical distributions of loci in populations of cells, demonstrating that the observed changes in R c in single cells are pervasive in the population.
Using the equipartition theorem and standard deviation (σ) for the distribution of steps from the mean we calculated k s (See Methods, Eq. (5)) 17,26 . The k s of the INO1 loci significantly increased in cells with active versus repressed loci in both wild type (Fig. 2f) and the GRS single deletion strains (Fig. 2g, h), suggesting a stiffening of decompacted chromatin. There was no significant change in k s in the GRSI, IIΔ double deletion strain under activating conditions (Fig. 2i).
The active INO1 locus behaves as an elastic filament As discussed above, the increase in spring stiffness of decompacted chromatin reflects in a decrease in the rate and amplitude of INO1 locus expansion-contraction 17 . This behavior can be visualized with the LacI-GFP-labeled LacO array and quantified by fitting an ellipsoid function to the GFP signal imaged at super-resolution by Structured Illumination Microscopy and calculating the aspect ratio between long and short axes of the ellipsoid (Fig. 2j). Consistent with predicted behavior, the INO1 locus changes shape with higher frequencies and amplitudes in the repressed versus the activated states (Fig. 2k). These observations are also consistent with previous results in which a decrease in L p caused by H3 histone depletion resulted in a decrease in the rate and amplitude of expansion of the chromatin 17 .

Activation of the INO1 locus increases rates of exchange of histone H3
To test whether the changes in INO1 locus mechanical properties follow from an increase in histone exchange, we used a strain to probe changes in histone H3 nucleosome exchange in wild type and GRSI, IIΔ double mutant strains. In this strain histones H3 and H4 genes are deleted from the genome and replaced with both constitutively and inducible expressed copies (Fig. 3a) 28 . In a galactose inducible cassette, H3 is fused to a FLAG-tag, such that when expressed can be used to quantify newly synthesized H3 that is incorporated into nucleosomes at specific positions by Chromatin Immunoprecipitation followed by real time PCR (ChIP-qPCR) to measure nucleosome exchange in different chromatin regions under different conditions. To avoid the contribution of histone incorporation due to DNA replication, cells are also arrested in G1 by the addition of α-factor. We probed H3-FLAG incorporation in several regions in the in upstream (SNA3 and DAS1) and downstream (VPS35) genes to determine whether changes in histone exchange are confined to the INO1 locus ( Fig. 3b, Supplementary Fig. 1). ChIP-qPCR results with an anti-FLAG antibody showed higher incorporation of newly synthesized histone H3 at the INO1 promoter in cells under activated versus repressed conditions for the INO1 promoter and ORF regions (Fig. 3c). Results for repressed cells were consistent with genome-wide ChIP-chip data 28 , validating our method. For the GRSI, IIΔ double mutant, significant reductions in H3 exchange under activated conditions were observed in the INO1 locus promoter at the GRS I site and in the SNA3 promoter and coding sequence where GRS II is located but not in the INO1 ORF sequences (Fig. 3c). These results suggest that GRS I and II may be HAT and/or other chromatin remodeling complex association sites mediating H3 exchange in topologically adjacent nucleosomes. The fact that H3 exchange is not affected in the INO1 ORF sequence is consistent with the fact that there are other known remodeling enzymes that bind near this region. Thus, consistent with ours and previous results, an increase in nucleosome histone H3 exchange at the INO1 locus chromatin is associated with an increase in its spring stiffness reflecting decompaction of the chromatin 17 .
Depletion of yeast HATs prevents active INO1 locus partitioning to the nuclear envelope The increase in H3 exchange at the INO1 locus is consistent with histone post-translational modifications, and specifically lysine acetylation by histone acetyltransferases (HATs) 18,[28][29][30][31] . We therefore hypothesized that the GRSs could be association sites for HATs and other chromatin remodeling complexes that alter the rates of histonenucleosome exchange. Evidence for specific functions of HATs and histone deacetylases in controlling active INO1 partitioning towards the NE exists. For instance, the Rpd3(L) histone deacetylase blocks partitioning of the INO1 locus towards the NE and deletion of the gene encoding this deacetylase results in increased acetylation of nucleosome-associated histone complexes in the promoter of INO1 15 . Additionally, deleting subunits of the SAGA HAT complex decreases active INO1 locus partitioning to the NE 11 , also observed for the GAL loci 8 .
Since both GRS I & II, plus other unidentified GRS sites could be associated with HATs, we attempted to identify HATs associated with the INO1 locus by screening for loss of activated INO1 locus NE localization in cells in which an auxin-inducible degron (AID) coding sequence was integrated 3' to the ORFs of the 12 known yeast HAT catalytic subunits. The addition of auxin to growth medium then induces targeting of the HAT-AID degron fusion proteins for rapid proteasomal degradation (Fig. 4a) 32 . To induce fast degradation of each HAT-AID, cells were treated with 500 μM indole-3-acetic acid (IAA) for 1.5 h under inositol starvation (INO1 induction) conditions. This condition was sufficient to reduce the expression of each HAT-AID protein as observed by Western blot (Supplementary Fig. 2). After incubation, cells were immobilized on ConA-coated microtiter . Deletion of GCN5, coding for a subunit of the SAGA complex, has previously been shown to prevent active INO1 locus partitioning towards the NE 11 . The SAGA complex has also been implicated directly in the activation of INO1 through transcription factors that bind to the upstream activating sequence (UAS) sites close to the TATA box of INO1 33 . Rtt109 is not part of any known chromatin remodeling complex and has not been implicated in INO1 gene activation previously. This HAT acetylates lysine 56 on the histone H3 core domain (H3K56), a modification that has been globally observed on newly synthesized histones in S. cerevisiae and S. pombe [28][29][30][31]34 . Interestingly, H3K56 acetylation also correlates with higher histone exchange rates in global analyses of the S. cerevisiae genome 28 . Finally, Taf1 is a subunit of the large TFIID complex, a general transcription initiation factor for RNA polymerase II (Pol II). Taf1 has been shown to have histone acetyltransferase activity in in vitro assays, but its role in vivo is less well understood 35,36 .
We analyzed the effect of the depletion of each of these three HATs on a specific acetylation modification in the regions surrounding the INO1 locus including the GRS sites. The H3K14 acetylation is known to be catalyzed by Gcn5 [37][38][39][40] , and it has been observed in vitro that Taf1 also acetylates H3 K14 35 , although this is more controversial 36 . Rtt109 has been also observed to acetylate H3K14 in in vitro assays 41,42 . This modification was quantified by ChIP-qPCR on the INO1 locus and on proximal genes in the AID strains for each of the three HATs. Results are presented as the ratio between each modification and H3 levels in each region analyzed. The regions screened correspond to the same ones used when measuring the rate of incorporation of newly synthesized histones (Fig. 3).
The results obtained (Fig. 4h), show that there is a significant decrease in the H3K14ac/H3 ratio for the strain where Gcn5 was depleted compared to wild type in all regions analyzed. A significant decrease is also observed for the other two HATs, mainly for the regions close to the GRSII site, however not as significant as that for the Gcn5-AID strain. This result indicates that Gcn5 could be the dominant HAT for acetylation in these regions.
We quantified mRNA levels for these loci after depleting each of the HATs in the AID strains. We observed a decrease in INO1 mRNA levels for Gcn5-AID and Rtt109-AID depletion strains, and a decrease for SNA3 mRNA levels, in this case for all three HAT-AID strains, although more significantly for Gcn5-AID and Rtt109-AID strains ( Fig. 4i). For the DAS1 and VPS35 loci, there was no apparent difference in mRNA levels between all four strains (Fig. 4i). These results indicate that the transcription is affected for INO1 and the GRS containing upstream locus SNA3, when at least two of the three HATs are depleted. Previous results have shown that deleting the GRS sites cause a decrease in INO1 mRNA levels 11 .
To probe for HATs and other chromatin remodeling complexes proximal to specific GRSs, we developed a proximity-dependent biotinylation (BioID) approach, based on guide RNA (sgRNA)-directed catalytically dead (d)Cas9 (Fig. 5a) 43 . We created BirA*-dCas9 ligase fusions in different N-or C-terminal orientations and using short (12) or long (38) amino acid linkers. These constructions were used to provide for more or less steric constraint and flexibility and promiscuity of biotin labeling. The short linker was used in a previous BioID study in yeast (GSSGSSGSSGSS) 43 and the long sequence in a CasID study in mammalian cells (LERPPLCWISAEFHHTGLVDPSSVPSLSLNRGSGSGSG) 44 .
We transformed a wild type strain with the different plasmids encoding the BirA*-dCas9 constructs and four different sgRNAs targeting genomic sequences proximal to the GRS I site. We also generated control strains that were transformed with the BirA*-dCas9 constructs but not with sgRNAs (Supplementary Tables 1-3). Western blot confirmed the expression of the different fusion proteins generated ( Supplementary Fig. 5). Biotinylated proteins were pulled down on streptavidin-sepharose beads, bound proteins were trypsin digested, and resulting peptides were analyzed by tandem mass

Decompacted chromosome segments can undergo polymerpolymer phase separation
Our results provide biochemical evidence for the mechanism by which changes in material properties of the activated INO1 gene locus is initiated 17,19 . How then are these changes in material properties consistent with a phase transition that causes partitioning of the INO1 locus to the NE? Would a change in properties of a single gene locus towards the middle of a chromosome arm cause such narrow localization of the locus to the NE? Phase separation of segments of polymers or polymer-polymer phase separation (PPPS) have been predicted based on Flory-Huggins theory, in which self-interacting ligand molecules occupy multiple sites throughout the polymer 52 . Phase separation between two segments of the polymer will occur if the density of ligands decreases in one region. The high ligand occupancy region forms a dense phase through the high valency ligandligand interactions and the low-density segment forms an expanded, "dilute" phase.
Bead-spring models of chromatin provide the means to explore the physical properties of the chromatin fiber and to test hypotheses about mechanisms responsible for polymer, including DNA phase separation. For instance, as predicted by Flory-Huggins theory 53,54 , invoking dynamic chromosome cross-linkers (bound ligand) into a model of the yeast genome recapitulates the segregation and morphology of the nucleolus 55 . The physical basis for partitioning the INO1 gene locus extends beyond recruitment to the NE. The radius of confinement and mobility of the locus are decreased, indicating a change in the polymeric state that accompanies its migration to the NE. While we can readily identify transcriptionally active domains relative to DNA sequence, we are just starting to appreciate how gene activity manifests in structural changes at the chromosome level. Active genes can be sequestered into chromosome loops (topologically associated domains) or into membrane-less compartments 56,57 .
Although Flory-Huggins theory alone can explain segmental phase separation of a polymer as described above 52 , we also wanted to test if we could reproduce the dynamic behaviors of the INO1 locus observed experimentally and see whether segmental phase separation could occur by including parameters in our bead-spring model that are known to accompany changes in gene expression. One of these parameters is the persistence length of the chromatin fiber. As discussed above, persistence length (L p ) is the length scale over which the polymer tends to remain linear and resist bending (expected value of cosine of angle θ from the horizontal at length L over L p falls off exponentially according to Eq. (2)). For the large fraction of nontranscribed chromatin, persistence length measurements range in the hundreds of nanometers. In the case of transcribing gene loci or regions of reduced histone occupancy, these regions have a much shorter persistence length and therefore can explore a greater number of configurations [21][22][23] .
To simulate the experimental condition of active genes flanked by inactive genes, we tuned the model such that the midsection of beads representing active genes has the lowest bending stiffness, L p = 5 nm, flanked by sections of inactive chromatin with L p = 250 nm. The MSD of the 5 nm L p segment was considerably reduced relative to the 250 nm L p segment (Fig. 6a), recapitulating our experimental observations (Fig. 2). Likewise, the increase in k s and reduced R c of the 5 nm L p segment further reflect our experimental results (Fig. 6b, c). The 5 nm L p chain collapsed into a much smaller area compared to the 250 nm L p segments, due to the increase in number of entropic states that they can explore. Consequently, the 5 nm L p region appears spherical compared to the ellipsoid shape of the 250 nm L p due to their increased randomness, and hence increased shape symmetry. The result is that the 250 nm L p segments showed increased frequencies and amplitudes of expansion-contraction compared to the 5 nm L p (Fig. 6d). These behaviors reflect our experimental observations of compression/expansion of the INO1 locus in repressed versus activated states (Fig. 2k). Finally, simulations of chain dynamics reveal phase separation of the 5 and 250 nm L p segments modeling the phase separation observed in the analytical model and in our experimental results for the active INO1 locus (Supplementary Movie 1).
We can reproduce segmental changes in dynamics and phase separation of a model polymer, we cannot explain the dynamics itself, which are known to be driven by active, ATP-dependent processes that remain obscure, but which we model as Brownian dynamics with tuning of temperature 58,59 .

Discussion
Our results for INO1 locus chromatin can now be put into molecular terms to explain the partitioning of the active gene to the NE. Recent evidence suggests that liquid-liquid phase separation (LLPS) of histones combines with PPPS of chromatin to form condensates, a potentially important mechanism by which the spatiotemporal organization of the genome can be regulated 56,57 . Specifically, acetylationdeacetylation of the histone tails in nucleosomal arrays has been shown to underlie PPPS in which deacetylated histones induce formation of a protein-DNA condensate and acetylation causes its dissolution 56 . We propose that the disruption of histone interactions that occurs due to acetylation in the active INO1 locus causes it to "dissolve" out of the dense nucleoplasmic chromatin phase into the less dense chromatin phase adjacent to the NE, as predicted previously for a single copolymer chain 52 .
The increased spring stiffness of the active INO1 locus we observed in experiments and simulations also have implications for LLPS of proteins associated with sub-compartmentalization of different processes in the nucleus. The contribution of PPPS to formation of chromatin-containing condensates has been considered both theoretically 60 and most recently, demonstrated both in vivo and in vitro 61,62 . Quail et al. recently showed that LLPS of a transcription factor required it to be bound to DNA in a tension-dependent manner. They presented evidence to support the postulate that less dense DNA forms an ideal template for nucleating LLPS of the bound protein and that protein-DNA co-condensation is associated with the difference in chemical potential of the DNA, as reflected in its difference in spring stiffness. Shin et al. observed that light-activated condensates in the nucleus selectively formed in regions of lowdensity chromatin as observed in vitro 61,62 . Ribosomal DNA (rDNA) is another example of this phenomenon. rDNA is essential for the phase separation of the nucleolus 63 . When rDNA was made discontinuous (rDNA genes were expressed from individual plasmids versus genome repeats), nucleolus formation was disrupted upon transcriptional inactivation 63 . That is, rDNA is a PPPS that relies on transcription to remain phase separated from the bulk genome. Thus, combined protein-DNA LLPS-PPPS of chromatin could facilitate the nucleation of co-condensates that have been associated with transcription and its regulation 64,65 , heterochromatin formation 66,67 , nucleolus assembly 68 and DNA repair 69 .
The work done to sub-compartmentalize the INO1 and other active gene loci could also be driven by PPPS. Partitioning of the repressed locus into the nucleoplasm phase is driven by transduction of the chemical potential of PPPS into mechanical work on the noncondensed DNA 62 . The work done in sub-compartmentalizing the active INO1 locus to the nuclear periphery is simply equal and opposite to that driving condensation. It is also possible that the INO1 chromatin could nucleate LLPS of associated proteins combined with PPPS, resulting in a DNA-protein condensate.
The polymer modeling provides critical insight into mechanisms of translocation of an active locus. The means by which the subcompartment comes to reside at the nuclear periphery is that it is seeking the most thermodynamically favored state. Chains with selfsimilar properties tend to segregate as mixing of two chains is thermodynamically disfavored in a confined space, such as the nucleus 55,70 . In the case of the nucleus, segregation of dissimilar chains leads to their migration to the furthest distance from each other, which is the outer edge of the nucleus at the nuclear envelope.
Finally, the ability to partition the genome into discrete domains that transition between physical states, either through multivalent binding of DNA-associated proteins (dense and deformable) or disruption of histone association (dilute but less deformable active subcompartments) could lead to architectural changes that can be understood from the material properties of the components, as we have demonstrated in this study.

Strains and plasmids
The LMY52 strain 12 was used as a control for the statistical mapping and for the gene tracking experiments (provided by Jason Brickner, Northwestern University, USA) (Supplementary Table 1). This strain contains a cassette of 128 repeats of the Lac operator binding site (LacO) into the INO1 locus and expresses a GFP-Lac repressor (LacI), which binds to the LacO repeats. This strain also expresses the Nuclear Pore Complex (NPC) protein Nup49 fused to GFP and the nucleolar protein Nop1 fused to mCherry as reference markers for the NE and the nucleolus, respectively. GRS I and II deletion mutants used for the statistical mapping and for the gene tracking experiments were generated in the LMY52 strain by employing a CRISPR-Cas9 based strategy developed by and with reagents provided by Tom Ellis at Imperial College London, UK (Shaw   Table 1) was used as control to measure the incorporation of newly synthesized histone H3 into nucleosomes (provided by Amine Nourani, Université Laval, Canada). In this strain, endogenous genes for histones H3 and H4 are deleted and expressed in two different ways: 1, constitutively from a plasmid, under the control of their own promoter, and 2, from another region in the genome under the control of the GAL1-10 promoter, with H3 fused to a FLAG tag. This allows to measure incorporation of newly synthesized H3-FLAG into nucleosomes following galactose induction. GRS I and II (GRSI, IIΔ) deletion mutants (Supplementary Table 1) were generated in the YAN1001 by the CRISPR-Cas9 strategy described above.
To measure the effect of rapid depletion of different HATs on active INO1 localization to the NE, 12 known yeast HAT catalytic subunits were tagged with a degron peptide IAA17 (71/116) that targets the protein for proteasomal degradation in the presence of the plant hormone auxin 32 . First, the TIR1 gene that mediates the auxin-IAA degradation was integrated into the genome of the LMY52 strain by transformation with the Yeast Integrating plasmid YIp204-PADH1-atTIR1-9myc (Addgene #99532, Supplementary Table 2). This strain was used as background to tag each HAT 3' to the coding sequence to produce C-terminal fusion products with a cassette containing the IAA17 degron sequence as well as six FLAG epitopes amplified from a plasmid generated in a previous study (pHyg-AID * -6FLAG, Supplementary Table 2) 32 . These FLAG tags allowed us to verify the efficiency of degradation by Western Blot.
BirA*-dCas9 fusions to identify candidate GRS-binding proteins and specifically, histone acetyl transferases (HATs), were generated based on a previously described Proximity-dependent Biotin Identification (BioID) strategy that was successful in S. cerevisiae 43 . The BirA* ligase sequence was provided in a plasmid vector by Oliver Valerius at Georg-August-University, Germany (Supplementary Table 2). dCas9 mutant was first obtained in one of the Cas9-sgRNA expression vectors (pWS174) to introduce the mutations D10A and H840A resulting in a catalytically dead (d)Cas9. Then, by linearizing this vector at the selected fusion site and using the GeneArt Seamless Cloning and Assembly kit (ThermoFisher Scientific), the sequence encoding for BirA* with specific linker sequences (linker 1: GSSGSSGSSGSS or linker 2: LERPPLCWISAEFHHTGLVDPSSVPSLSLNRGSGSGSG) were fused 5' or 3' to the dCas9 gene to produce N-terminal or C-terminal fusion products, respectively. Once we obtained the desired BirA*-dCas9 expression vectors, the same procedure was performed as described above for CRISPR/Cas9 genome editing by transforming both BirA*-dCas9 and sgRNA linearized cassettes into the LMY52 strain to obtain the strains used in this approach (Supplementary Table 1), this time without the need of using any donor DNA sequence. We also transformed the LMY52 strain with the different BirA*-dCas9 expression vectors alone with empty sgRNA cassettes as negative controls for non-targeted biotinylation of proteins.

Statistical mapping of the INO1 locus
Statistical mapping of the INO1 locus was performed as previously described 12 . Briefly, overnight cultures in synthetic, defined medium (SDC) without inositol or SDC containing 100 µM of inositol were diluted to 10 6 cells/mL and after two generations cells were immobilized on Concanavalin A-coated well slides 73 . Images were acquired with a Zeiss Axio Observer Z1 Yokogawa spinning disk confocal microscope using a 100× 1.40 NA oil objective. Z-stacks with a slice spacing of 250 nm were taken at an acquisition time of 50 ms for GFP (50%, 3 mW 488 nm excitation), and 100 ms for mCherry (50%, 3.3 mW 561 nm excitation). Images were processed by nucloc software modified to display probability density maps as percentiles using a kernel density estimate 74 .

Particle tracking of the INO1 locus
To track the INO1 locus in live yeast cells, LMY52 and GRS I or II mutant strains containing the gene tagged with the LacO array and expressing GFP-LacI as well as the NE tagged with Nup49-GFP were used. Images of the cells were also recorded on a Zeiss spinning disk Axio Observer Z1 confocal microscope at an acquisition time of 50 ms (50%, 3 mW 488 nm excitation) for 1 min at an interval of 500 ms. To check for possible stage-drift the GFP signal was also imaged in fixed cells.
Images of GFP foci corresponding to the INO1 locus were automatically tracked using the WaveTracer tool in MetaMorph software 75 . The algorithm segments circular objects with a particular size and intensity cut-off and then calculates the centroid position for each object in each frame through Gaussian fitting. For each locus monitored, the software quantifies the movement and calculates mean squared displacement (MSD). Only cells whose MSD curves exhibited a linear slope were included in subsequent analysis.
To calculate the radius of confinement, the MSD plateau values were used in each case since the plateau reached is proportional to the square of R c , as previously described (Eq. (3)) 17,25 .
Effective spring constants (k s ) for the INO1 locus in repressed versus activated conditions were determined by using the equipartition theorem to measure the standard deviation (σ) of each step from the mean position to calculate k s (Eq. (5)) 17,26 .
Statistical differences for R c and effective k s in strains grown under different conditions were determined by Student's t tests.
To analyze the rate and amplitude of INO1 locus expansion-contraction, the GFP array was also acquired at the same frequency as mentioned before but using a Zeiss Elyra PS.1 system. SIM images were acquired in this case with a 63× 1.40 NA oil objective in the GFP channel Article https://doi.org/10.1038/s41467-023-36391-6 (15 %, 20 mW 488 nm HR diode laser), exposure time 24 ms and 3 rotations. Each locus was then fitted to an ellipsoid function to quantify the ratio between long and short axes by using the Fiji software 76 .

Chromatin polymer simulations
An elastic worm-like chain consisting of 201 beads (masses) connected by linear springs was sectored into three equal segments: two flanking segments composed of beads 1-67 and 135-201, and one middle segment with beads 68-134. Initially the chain was homogenized with L p for all segments set to 250 nm (in n = 5 randomly seeded simulations). In the experimental condition we lowered the L p for the middle segment to 5 nm (in n = 6, randomly seeded simulations) by adjusting the value of hinge force on the beads. Whenever three beads (or two springs) are not colinear, hinge forces act to restore the positions of the beads to lie on a line (see Fig. 6e, f). Hinge forces are based on the Euler-Bernoulli formula (Eq. (6)), where E is Young's modulus, proportional to a polymer's bending stiffness, and is linearly related to the persistence length (for more details see methods Lawrimore et al. 77 ). In our approach the Young's modulus (E) in Eq. (6) is varied only in calculation of bending stiffness, and does not affect the tensile stiffness of individual DNA springs. Hinge forces were manually set to constant L p = 250 nm for the flanking segments, and set to either L p = 250 nm and L p = 5 nm for the variable middle segment.
In the simulations we obtained 35,000 timepoints of bead position data (x t , y t , z t ) for a duration of 70 ms at 2 μsec resolution. With a working estimate of cellular nuclear viscosity of 141 Pa 78 the model's parameters reflected a fluid environment set to 0.01 Pa allowing a 14,100X speedup of physical time for the simulation. An equilibration time corresponding to 25% of the total trajectories was set to allow for meaningful chain configurations from its starting linear conformation. Second, to eliminate the effects of drift on the entire chain, we considered individual bead positions relative to bead number 55 within the invariable portion of the chain (L p 250 nm segments) throughout our analyses. Positions of a center of mass of a 26-bead long subsegment (beads 90-115) within the middle segment representing a fluorescent segment (virtual LacO array segment), were tracked for each of 15,000 time intervals (t values) amounting to 35 ms of simulation time (equivalent to 423 s of real time), and MSD was computed for each independent experiment in MATLAB with computespotmsd.m (Eq. (7)). Average MSD with standard error bars for a spot (26-bead subsegment) within L p 250 (n = 5) compared to spot within L p 5 nm (n = 6) chain segments are displayed in Fig. 6a.
We computed R c , for the simulated with Eq. (4) 17 . we compared spatial confinements of L p 250 nm (n = 5) to L p 5 nm segments (n = 6). Effective spring constants were estimated by using the standard deviations obtained from simulation's spot positions, σ, as in Eq. (5).
We used principal component analysis to estimate 2D shapes of simulated fluorescent spots (26-beads) to obtain their aspect ratios. Given averaged bead position data at 38 regularly spaced time intervals we used MATLAB aspect_ratio.m to calculate the aspect ratio for the point cloud representing the fluorescent spot (26-bead subsegment) by taking the square root of the ratio of the first principal component's scaling factor over the second.

ChIP experiments
Cell cultures and crosslinking. ChIP experiments were performed in four biological replicates. YAN1001 or the corresponding GRS mutant strains were inoculated on 100 mL SDC + 2% glucose with or without 100 µM inositol medium and incubated until they reached OD 600 0.2-0.3. Cells were recovered by centrifugation and switched to 100 mL medium with 2% raffinose and incubated overnight. In the morning, cell cycle was arrested with 5 mM α-factor for 3.5 h and inositol was added again to 100 µM inositol final concentration to the repressed cells. Efficient G1 arrest (at least 90% of cells) was confirmed by microscope as percentage of cells with shmoo morphology. Cells were collected by centrifugation at 2000 × g, 5 min switched to 2% galactose medium and incubated for 1 h. At every step, OD 600 cells were grown only long enough to reach values of <0.5, to avoid losing the repressed phenotype.
After 1 hour incubation in galactose, cells were crosslinked with 1 % formaldehyde for 30 min with gentle rotation at room temperature. To quench formaldehyde, 2.5 M glycine was added to a final concentration of 125 mM. Crosslinked cells were recovered by centrifugation and washed twice with 25 mL ice cold 1X Tris-buffered saline (TBS: 20 mM Tris, 150 mM NaCl, pH 7.6). Pellets were resuspended in the remaining liquid and transferred to 1.5 mL tubes. Cells were harvested by centrifugation at 2000 × g, 4°C, 5 min, immediately frozen in liquid nitrogen and stored at −80°C until processed.
Chromatin immunoprecipitation (ChIP) and quantitative PCR (qPCR). Immunoprecipitation assays were performed as previously described 79 with slight modifications. Cells were resuspended in 700 µL of lysis buffer (50 mM HEPES-KOH pH 7.5, 140 mM NaCl, 1 mM EDTA, 1% Triton X-100, 0.1% Na-deoxycholate, 1 mM PMSF, 1 mM Benzamidine, 10 μg/mL Aprotinin, 1 μg/mL Leupeptin, 1 μg/mL Pepstatin) and mechanically lysed with glass bead beating. Cells were spun at 5000 × g for 10 s and supernatants were transferred to new tubes. Cells were sonicated in a Sonic dismembrator Model 100 equipped with a micro probe (Fisher Scientific), 4 × 20 s at output of 7 Watts, with a 1-minute break between sonication cycles. Supernatants containing solubilized chromatin fragments were recovered by centrifugation at 16,000 × g, 5 min and transferred to new tubes. An aliquot of 5 µL (1 %) per sample of this whole-cell extract was kept at −20°C to be used as input sample, which represents the amount of chromatin used in the ChIP, usually 1% of starting chromatin. 500 µL of the remaining material was used for immunoprecipitation (IP). For each IP sample, 50 µL of Dynabeads™ Pan Mouse IgG (ThermoFisher Scientific) pre-coupled to 5 µg of mouse Monoclonal Anti-FLAG M2 antibody (Sigma) was added to the 500 µL of chromatin sample and incubated overnight at 4°C.
The immunoprecipitated DNA and DNA from 1% of the Input samples were analyzed by quantitative PCR on a ViiA 7 Real-Time PCR System (Thermo Fisher Scientific) using the PowerUp™ SYBR™ Green Master (Thermo Fisher Scientific). The amount of newly synthesized FLAG-H3 incorporated at the nucleosomes was calculated as the percent of Input using the following formula: 100*2ˆ(Ct Input −6.644-Ct IP ), Ct being the value where the PCR curve crosses the threshold line above background levels of detection. Subtracting 6.644 from Ct Input allows to adjust for the fact that 1 % of Input was used. In this case since the starting input fraction is 1%, then a dilution factor of 100 or 6.644 cycles (log 2 of 100) is subtracted from the Ct value of diluted input. Primer sequences for the regions analyzed are described in Supplementary Table 4.
HATs depletion using an auxin degron system All 12 HAT-AID fusion strains (Supplementary Table 1) were generated to rapidly deplete specific HAT activity and the wild type cells were cultured in SDC medium without inositol until OD 600 0.3. At this point, cultures were split in two and auxin (I2886, Sigma-Aldrich) was added to one of the tubes for each sample to a final concentration of 500 μM. Cells were incubated with auxin for 1 h 30 min followed by immobilization on ConA-coated Nunc 96 well Optical-Bottom plates (164588, ThermoFisher). Imaging and nucloc analysis were performed as previously described 12 for the Statistical Mapping of the INO1 locus wild type and the GRS mutants. Western Blots were performed on HAT-AID fusion strains to verify the degradation of the corresponding HAT once the auxin was added to growth medium.
ChIP-qPCR experiments for H3K14ac and H3 in the AID strains were performed in three biological replicates similarly as described before for the H3-FLAG with modifications for the sample preparation and the IP procedures. In this case, cells were grown under the same conditions as described for the AID experiments before crosslinking. For the IP protocols, 50 μL of Dynabeads™ Protein G beads (Thermo-Fisher Scientific) pre-coupled to 2 µL of rabbit anti-H3K14ac (Millipore) or 2 µg of rabbit anti-H3 (Abcam) were used per IP sample.

Reverse transcriptase real-time quantitative PCR (RT-qPCR)
Cells were prepared under the same conditions described before for AID and inositol starvation. Total RNA was isolated from yeast cells using TRIzol reagent (Invitrogen) following manufacturer's instructions. Approximately 2 µg of total RNA was reverse transcribed using All-In-One 5X RT MasterMix (abm). qPCR reactions were performed using FastStart Essential DNA Green Master (Roche Diagnostics) and gene expression levels for INO1 and proximal loci (Supplementary Table 4) were determined with LightCycler 96 (software version 1.1). All assays were performed in biological triplicates.

dCas9-BioID assays
Cell cultures and streptavidin affinity purification. The protocol for biotinylated proteins purification was modified from Opitz et al. 43 . LMY52 wild type and LMY52-BirA*-dCas9 with or without sgRNA mutants generated (Supplementary Table 3) were inoculated in 4 L of SDC medium without inositol plus D-biotin (B4639, Sigma-Aldrich) added to final concentration of 10 μM. Cells were grown to OD 600 of 0.8 and harvested by filtration using a Kontes™ Ultra-Ware™ Microfiltration Assembly with Fritted Glass Support (90 mm) and MF-Milli-pore™ Membrane Filters, 0.45 µm pore size (HAWP0900 Millipore). Pellets were immediately frozen in liquid nitrogen and kept at −80°C. Cell lysis was performed under cryogenic conditions using solid phase milling in a planetary ball mill (Retsch PM 100) producing a fine cell grindate 80 . Grindate samples were stored at −80°C until processed. Biotinylated proteins were purified using streptavidin-sepharose beads (GE Healthcare, 17-5113-01). For each sample, 0.7 g of crude extract was resuspended in 6.3 mL of buffer A: commercial buffer W (100 mM Tris-Cl, 150 M NaCl, pH 8, 2-1003-100, IBA) containing 0.1 % SDS, 0.5 % Sodium Deoxycholate, and protease inhibitors mixture (cOmplete™, Mini, EDTA-free Protease Inhibitor Cocktail, 11836170001, Roche). Samples were homogenized with a vortex agitator, polytron (PT1200E, for 30 s, one time), and incubated at 65°C for 5 min in a water bath. Subsequent clarification was performed by two rounds of centrifugation at 2465 × g, 4°C, 5 min, and 20,292 × g, 4°C, 20 min, respectively. Triplicates for each sample were prepared; clear extracts were incubated with 30 µL of beads previously equilibrated with buffer A. Samples with beads were incubated for 3 hours at 4°C with gentle mixing (VWR® Nutating Mixer). Beads were washed with buffer A and transferred to 1.5 mL Protein LoBind tubes (Eppendorf, 0030108422) and three consecutive washes with buffer A were performed, followed by four quick washes with 50 mM Ammonium Bicarbonate pH 8 (ABC). 30 µL of 50 mM ABC pH 8 containing 6 mM fresh DTT were added to each tube followed by 30 min incubation at 37°C with gentle agitation in a ThermoMixer (Eppendorf) at 350 rpm. Samples were spun quickly and 5μL IAA 126 mM dissolved in ABC 50 mM pH 8 were added to each tube and incubated for another 30 min in the dark at room temperature. Tubes were quickly spun again and 5 µL Trypsin/LysC Mix (Promega, V5073) dissolved in ABC 50 mM pH 8 at 200 ng/µL were added to each one. Samples were digested on-beads overnight at 37°C, 350 rpm. The next day, after a quick spin, 60 µL of MS grade H 2 O were added to the beads, mixed, and centrifuged at low speed (1 min, 400 × g). Eighty (80) µL of the peptides digests were transferred to new labeled Protein LoBind tubes before adding formic acid (FA) to a final concentration of 4% v/v. The peptides were dried in a SpeedVac at room temperature and then stored at −80°C.
Mass spectrometry and data analysis. Samples were resuspended in 11 µL of 2 % acetonitrile (ACN) and 1 % FA containing 0.5X of iRT standard peptides (Biognosys, Ki-3002-1), of which, 2 µL of each sample was further diluted 1/5 in the same buffer. Diluted samples were loaded (2.5 µL each) at 450 nL/min on a 17 cm × 75 µm i.d. PicoFrit fused silica capillary column (New Objective), packed in-house with Jupiter 5 µm C18 300 Å (Phenomenex). The column was mounted in an Easy-nLC II system (Proxeon Biosystems) and coupled to an Orbitrap Fusion mass spectrometer (ThermoFisher Scientific) equipped with a Nanospray Flex Ion source (Proxeon Biosystems). Peptides were eluted at a flow rate of 250 nL/min on 2-slope gradient made with 0.2% FA in water (buffer A) and 0.2% FA in 100% ACN (buffer B). Concentration of buffer B first increased from 2% to 36% over 105 minutes, and from 36 % to 80 % over 12 minutes. The mass spectrometer was operated in dataindependent acquisition mode. Full MS scans in the range of 400-1000 m/z range were acquired in the Orbitrap at a resolution of 120 K. Each full scan was followed by 25 MS2 acquisition windows with 24 m/z increments and 0.5 m/z overlaps, covering each full scan. Matching MS2 m/z window precursor ions were fragmented by HCD at a 30% collision energy and acquired in the Orbitrap at a 30 K resolution. Both MS and MS2 AGC target were set to 4e5 with maximum fill times of 60 ms. The lock mass option (lock mass: m/z 371.101233) was used for internal calibration. MS RAW files were analyzed with Spectronaut v15.1.210713 (Biognosys) by directDIA. The Fasta database was downloaded from Uniprot and consisted of all Saccharomyces cerevisiae S288c verified nuclear proteins entries (1749). Considered peptide length for Pulsar search was 6-52 amino acids with two missed cleavages tolerance, using the semi-specific Trypsin/P rules. Carbamidomethylation of cysteines was set as fixed modifications while oxidation of methionines, protein N-termini acetylation, biotinylation of lysines and protein N-termini as well as phosphorylation (STY) were set as variable modifications, with a maximum of five. Peptide spectrum match, peptides, and protein group FDR were set at 0.01. Machine learning was applied per run and both precursor and protein were identified at a Qvalue cutoff of 0.01. Proteins were quantified at the MS2 level on stripped peptide median quantities. Unique peptides were used for quantification. Only proteins for which values from all biological triplicates were measured in the sgRNA-BirA*-dCas9 were kept for quantification, and no values were imputed during the analysis. The resulting protein datasets were crosschecked with a list of chromatin and transcription related proteins obtained from Uniprot (Supplementary Data 5). The protein list and associated ontologies was built from searches using the keyword chromatin (461 reviewed entries), and transcription (1211 reviewed entries) in S. cerevisiae. After merging both lists and removing duplicates, 1320 entries remained (Supplementary Table 6). A two-sided unpaired Student's t-test with equal variance was used to help in the evaluation of significant protein enrichment from sgRNA-BirA*-dCas9 triplicates. Analyses of evidence for association of chromatin remodeling subunits with nuclear protein complexes was performed for all significant candidates with definitions of subunit compositions of protein complexes taken from the Saccharomyces Genome Database (SGD) 81 and UniProt 82 , and proteinprotein interactions were identified in The Biological General Repository for Interaction Datasets (BioGrid) 83 . For representation clarity, proteins having a log2 fold change above 2.5 were limited at the 2.5 value on MA plots (Fig. 5). We removed two sgRNA-BirA*-dCas9 samples out of a total of 4 because they did not reveal significant fold changes for many or most of the candidates that were identified in the samples kept for further analysis. Both MA and box plots were made in RStudio (v2022.07.2) using the ggplot2 package (v3.3.6). Data are available via ProteomeXchange with identifier PXD029913.

Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability
Mass spectrometric data are publicly available via ProteomeXchange. Project accession: PXD029913. The data supporting the results presented in this work are available in the main article and the supplementary information. Any additional information is available upon request from the corresponding author. Source data are provided with this paper.