As an initial test case for studying T2NR interactions, we focused on the heterodimeric partners RARα and RXRα, which are endogenously expressed alongside various other T2NRs in U2OS cells, a well-established cancer cell line for SMT (Hansen et al., 2017; McSwiggen et al., 2019; Figure 1A, Appendix 2—table 1). Using CRISPR/Cas9-mediated genome editing, we generated clonal lines with homozygous knock-in (KI) of HaloTag at the N-terminus of RXRα and the C-terminus of RARα (Heckert et al., 2022b; Los et al., 2008; Figure 1—figure supplement 1A). Western blotting confirmed that RARα and RXRα were tagged appropriately and expressed at similar levels to the untagged proteins (Figure 1B), while co-immunoprecipitation (co-IP) experiments verified that Halo-tagged RARα and RXRα heterodimerize normally as expected (Figure 1—figure supplement 1B). In addition, we confirmed using luciferase assays that the RAR ligand, all-trans retinoic acid (atRA), activated retinoic acid responsive element (RARE)-driven gene expression in wild-type and homozygously edited clones, confirming the normal transactivation function of the tagged proteins (Figure 1—figure supplement 1C). Confocal live-cell imaging of cells stained with Janelia Fluor X 549 (JFX549) Halo ligand displayed normal nuclear localization of both Halo-tagged RARα and RXRα (Figure 1—figure supplement 1D).

To evaluate how RARα and RXRα explore the nuclear environment and interact with chromatin, we used fSMT with a recently developed Bayesian analysis method, SASPT (Heckert et al., 2022b), to infer the underlying distribution of diffusion coefficients within the molecular population, yielding a ‘diffusion spectrum’ (Figure 1C and D). From these diffusion spectra we can extract quantitative parameters of subpopulations (peaks) such as mean diffusion coefficients and fractional occupancy, allowing us to measure the chromatin-bound fraction (f_bound) in live cells (Figure 1C and D). To benchmark our SMT measurements, we first compared the diffusion spectra of RARα-Halo and Halo-RXRα to that of H2B-Halo (which as expected is largely chromatin-bound) and Halo-3×NLS (which is mostly unbound). We observed that RARα and RXRα both exhibit a clearly separated slow diffusing population (<0.15 μm²/s) along with a faster mobile population (1–10 μm²/s) (Figure 1C). The former we classify as ‘bound’ since it represents molecules diffusing at a rate indistinguishable from that of Halo-H2B (chromatin motion). The proportion of molecules diffusing at <0.15 μm²/s is henceforth designated as f_bound. In comparison with Halo H2B (f_bound = 75.5 ± 0.7%) and Halo-NLS (f_bound = 10 ± 0.9%), RARα and RXRα have intermediate levels of chromatin binding (f_bound of 50 ± 3.0% and 38 ± 3.5%, respectively) (Figure 1D). The f_bound was reproducible between three clonal cell lines of RARα (49 ± 1%, 47 ± 1%, 53 ± 1%) and RXRα (36 ± 1%, 36 ± 1%, 42 ± 1%). Finally, although recent studies have reported an increase in chromatin interaction upon agonist treatment (Brazda et al., 2014; Brazda et al., 2011; Rehó et al., 2023; Rehó et al., 2020), we did not observe a significant change in f_bound of RARα and RXRα upon atRA treatment, nor did atRA treatment appear to alter the fast-moving populations of RARα and RXRα (Figure 1—figure supplement 3A and B). These results are consistent with the classic model in which dimerization and chromatin binding of T2NRs are ligand independent.

Chromatin binding by an individual TF within a dimerization network is predicted to be sensitive to its expression level (Klumpe et al., 2023). To test how the expression levels of RARα and RXRα affect f_bound, we overexpressed Halo fusions from stably integrated transgenes in U2OS cells (Figure 2A). After confirming transgene expression by western blotting (Figure 2A), we compared the abundance of endogenous and exogenous Halo-tagged RARα and RXRα using flow cytometry (Cattoglio et al., 2019; Figure 2—figure supplement 1A). Average cellular abundance of endogenous RARα and RXRα obtained from biological replicates of each homozygous clone were similar (Figure 2B). In contrast, expression of exogenous RARα-Halo was approximately four times that of the endogenous protein, while expression of Halo-RXRα was nearly twenty times that of endogenous RXRα (Figure 2B). Chromatin binding of overexpressed RARα was reduced by approximately half compared to endogenous (f_bound = 27 ± 0.72%) (Figure 2C, Figure 2—figure supplement 1B), while that of overexpressed RXRα was decreased even more dramatically to 11 ± 0.75% - a value barely above the f_bound of the Halo-NLS control (Figure 2C, Figure 2—figure supplement 1B). Using nuclear fluorescence intensity as a rough proxy for protein concentration in individual cells, we observed a negative correlation in single cells between TF concentration and f_bound (Figure 2—figure supplement 1C). These results imply that chromatin binding of both RARα and RXRα in U2OS cells is saturable - i.e., the total number of chromatin-bound molecules does not increase indefinitely with expression level but is in some way limited.

We next assessed how overexpression of RARα and RXRα affects f_bound of the endogenous proteins by stable integration of SNAP-tagged RARα or RXRα transgenes in Halo-KI RARα and RXRα cell lines (Figure 2D). As controls, we also stably integrated transgenes expressing SNAP-NLS or a SNAP-tagged dimerization-incompetent RARα (RARα^RR) (Bourguet et al., 2000; Zhu et al., 1999; Figure 2D). We validated disruption of the RARα^RR-RXRα interaction using Rosetta modeling (Shringari et al., 2020) and co-IP (Figure 2—figure supplement 2A). Using flow cytometry, fluorescent gels, and western blots, we first assessed if transgene expression alters expression of endogenous Halo-tagged RARα and RXRα (Figure 2E, Figure 2—figure supplement 2B–D). While no drastic changes in the cellular abundance of KI Halo-tagged RARα or RXRα was observed in the presence of SNAP, SNAP-RXRα, or RARα^RR-SNAP proteins, the abundance of KI Halo-tagged RARα was approximately halved when RARα-SNAP was overexpressed (Figure 2E, Figure 2—figure supplement 2B). This is likely distinct from previously reported ligand-dependent RARα degradation (Tsai et al., 2023; Zhu et al., 1999) (see Discussion).

We then carried out a series of fSMT experiments to understand how f_bound of the endogenous RARα or RXRα is altered when its binding partner is present in excess (Figure 2—figure supplement 4A and B). Surprisingly, we found that the f_bound of endogenous RARα-Halo (47 ± 1%) was largely unchanged upon expression of RXRα-SNAP (49 ± 1%), consistent with the control SNAP (47 ± 1%) (Figure 2F, Figure 2—figure supplement 4B), implying that RARα f_bound is not limited by the availability of RXR. In contrast, RARα-SNAP expression significantly decreased chromatin binding of endogenous RARα-Halo to 29 ± 5% (Figure 2F, Figure 2—figure supplement 4B). However, overexpression of mutant RARα^RR-SNAP did not change the f_bound of endogenous RARα (43 ± 4%) (Figure 2F, Figure 2—figure supplement 4B), suggesting that heterodimerization with RXRα is required for this effect.

In the reciprocal experiment with endogenous Halo-RXRα, the initial f_bound (35 ± 1%) was barely altered by overexpression of SNAP (38 ± 1%) or RARα^RR-SNAP (35 ± 1%). As expected, overexpression of SNAP-RXRα reduced the f_bound of endogenous Halo-RXRα to 16 ± 2%. In contrast to RARα, however, overexpression of RARα-SNAP increased the f_bound of endogenous Halo-RXRα to 56 ± 1%. This result suggests that endogenous RXRα chromatin binding is limited by the availability of RAR (Figure 2F, Figure 2—figure supplement 4B), and not due to limiting amounts of the universal dimer core partner RXR as would be expected based on current models in the literature.

While it may seem paradoxical that RAR is limiting for RXR binding, given the similar number of molecules of endogenous RARα and RXRα per cell (Figure 2B), this is likely due to the presence of other endogenous RXR paralogs (see Appendix 2—table 1 and Discussion). It is also probable that some fraction of RXR binding to chromatin arises from other T2NRs that can produce chromatin binding-competent dimers with RXR (Figure 1A, Appendix 2—table 1, and Discussion). Notwithstanding these complexities, the results of the above SMT measurements in the presence of varying amounts of partner TFs allow us to infer that endogenous RXRα is likely in excess while RXR partners are limiting in U2OS cells.

The above results support a model in which the total RXR pool (including all paralogs) is in stoichiometric excess of its partners in U2OS cells. To more directly monitor RXR-RAR interactions, we employed a recently developed SMT assay by our lab, PAPA (Graham et al., 2022). PAPA detects protein-protein interactions by using excitation of a ‘sender’ fluorophore with green light to reactivate a nearby ‘receiver’ fluorophore from a dark state (Graham et al., 2022; Figure 3A). As an internal control, violet light is used to induce direct reactivation (DR) of receiver fluorophores independent of their proximity to the sender (Figure 3A). See Appendix 1 for a more detailed description of the steps involved in a PAPA-SMT experiment.

We applied PAPA-SMT to cell lines expressing SNAP-tagged RARα and RXRα transgenes in the background of Halo-tagged endogenous RXRα or RARα, respectively (Figure 3B). As controls, we also imaged SNAP-3×NLS and RARα^RR-SNAP, which are not expected to interact with Halo-RARα or RXRα. First, we plotted the number of single-molecule localizations reactivated by green and violet light in each cell (Figure 3B). As expected, a low level of background reactivation by green light was observed for SNAP negative control, reflecting the baseline probability that an unbound SNAP molecule will at some low level be close enough to Halo to observe PAPA (Figure 3B, orange points) (Graham et al., 2022). Violet light-induced DR and green light-induced PAPA were linearly correlated as expected, since both are proportional to the number of receiver molecules. However, a greater PAPA signal was seen for the Halo-RXRα → RARα-SNAP and RARα-Halo → SNAP-RXRα combinations than for the negative control, consistent with direct protein-protein interactions (Figure 3B). The relation between DR and PAPA was sublinear (Figure 3B, left and middle panel, see residuals of the linear fit in Figure 3—figure supplement 1B), consistent with saturation of binding to the Halo-tagged component. In contrast, the ratio of PAPA to DR for Halo-RXRα → RARα^RR-SNAP was similar to the SNAP negative control, confirming that PAPA signal depends on a functional RAR-RXR interaction interface (Figure 3B, right panel).

Next, we compared the diffusion spectra of molecules reactivated by DR and PAPA (Figure 3C). For both Halo-RXRα → RARα-SNAP and RARα-Halo → SNAP-RXRα combinations, PAPA trajectories had a substantially higher chromatin-bound fraction than DR trajectories, indicating that a greater proportion of SNAP-tagged RARα/RXRα binds chromatin when it is in complex with its Halo-tagged partner. Only a slight shift in bound fraction was seen for RARα^RR-SNAP (f_bound,DR = 7.5 ± 0.6%; f_bound,PAPA = 11.1 ± 0.8%), comparable to that seen for the SNAP negative control (f_bound,DR = 7.1 ± 0.5% and f_bound,PAPA = 11.2 ± 0.9% for Halo-RXRα; f_bound,DR = 7.3 ± 0.4% and f_bound,PAPA = 9.3±0.7 for RARα-Halo) (see Discussion), confirming that RARα^RR fails to form chromatin binding-competent heterodimers with RXR.

The enrichment of chromatin-bound molecules in the PAPA-reactivated population of both RAR and RXR is consistent with heterodimerization mediating chromatin binding, that is further validated by the low f_bound of the dimerization-incompetent mutant.

U2OS cells were grown in Dulbecco’s modified Eagle’s medium (DMEM) with 4.5 g/l glucose supplemented with 10% fetal bovine serum (FBS) (HyClone, Logan UT, Cat. #AE28209315), 1 mM sodium pyruvate (Thermo Fisher 11360070), L-glutamine (Sigma #G3126-100G), GlutaMAX (Thermo Fisher #35050061), and 100 U/ml penicillin-streptomycin (Thermo Fisher #15140122) at 37°C and 5% CO₂. Cells were subcultured at a ratio of 1:4 to 1:10 every 2–4 days for no longer than 30 passages. Regular mycoplasma testing was performed using polymerase chain reaction (PCR). Phenol containing media was used for regular cell culture and phenol red-free DMEM (Thermo Fisher #21063029) supplemented with 10% FBS and 100 U/ml penicillin-streptomycin was used for imaging.

Stable cell lines expressing the exogenous gene products (Appendix 2—table 2) were generated by PiggyBac transposition and antibiotic selection. Gibson assembly was used to clone genes of interest into a PiggyBac vector containing a puromycin or neomycin resistant gene. Plasmids were purified by Zymo midiprep kit (Zymo D4200) and all cloning was confirmed by Sanger sequencing. Cells were transfected by nucleofection using the Lonza Cell line Nucleofector Kit V (Lonza, Basel, Switzerland, #VVCA1003) and the Amaxa Nucleofector II device. For each transfection cells were plated 1–2 days before nucleofection in a six-well plate until they reach 70–90% confluency. Cells were trypsinized, resuspended in DMEM media, and centrifuged at 200×g for 2 min before the media was aspirated. Cells were then resuspended in 100 µl Lonza transfection reagent (82 μl Kit V solution+16 μl of Supplement #VVCA1003) containing 0.4 μg of SuperPiggyBac transposon vector and 0.8 μg of donor PiggyBac plasmid and transferred to an electroporation cuvette. Cells were electroporated using program X-001 on the Amaxa Nucleofector II (Lonza). Transfected cells were cultured in DMEM growth media without any antibiotics for 24–48 hr and then selected for 10 days with 1 μg/ml puromycin (Thermo Fisher #A1113803) or 1 mg/ml neomycin (G418 Sulfate, Thermo Fisher #10131027). After selection polyclonal cell lines were maintained in the selection media containing required antibiotics.

For ligand treatment, 100 μM atRA stock was prepared by dissolving atRA powder (CAS No: 302794, Sigma-Aldrich #R2625) in dimethyl sulfoxide (DMSO) (Sigma-Aldrich #D2650) and was diluted 1:100,000 or 1:1000 in growth media to final concentration of 1 nM or 100 nM respectively. The same volume of DMSO used for 100 nM atRA treatment (0.1%) is used for the control group as a condition without atRA treatment. Cells were treated 24 hr in either atRA or DMSO alone before imaging.

KI cell lines were generated as previously described (Hansen et al., 2017) with some modifications. Halo-tagging of endogenous RARα was described in our previously published work (Heckert et al., 2022b) which we have further validated for the current study. For Halo-tagging we designed sgRNAs using CRISPOR web tool (Concordet and Haeussler, 2018). Since exon 1 of RXRα is very short (only 9 aa) we chose to gene edit at the start of exon 2 for a successful tagging. sgRNAs were cloned into the Cas9 plasmid (a gift from Frank Xie) under the U6 promoter (Zhang Lab) with an mVenus reporter gene under the PGK promoter. Repair vectors were cloned in a basic pUC57 backbone for N-terminal tagging and pBluescript II SK (+) (pBSKII+) backbone for C-terminal tagging, with 500 bp left and right homology arms on either side of the Halo-tag sequence. Two guide/repair for N-terminal and three guide/repair vector pairs for C-terminal were attempted; only-N-terminal clones were ultimately recovered. Each sgRNA/donor pair were transfected to approximately 1 million early passage U2OS cells, at 1:3 ratio of sgRNA/donor (total 5 μg DNA) and plated in a six-well plate. 48 hr after transfection, Venus-positive cells were FACS sorted and cultured for another 7–10 days. Then, Halo-positive cells (stained with TMR) were sorted individually into single wells of 96-well plates and cultured for another 12–14 days. Clones were expanded and genotyped using PCR. PCR was done using one primer upstream of the left homologous arm and the other primer downstream of the right homologous arm. Another PCR with either external primer paired with a corresponding internal primer located in the Halo-tag coding region was done for further validation. Homozygous clones with the correct genotype (V5-Halo-RXRα clones C10, D6, and D9) were confirmed by Sanger sequencing and western blotting.

The following antibodies were used for western blotting: mouse monoclonal anti-RARα [H1920] (Abcam, #ab41934) diluted at 1:400, rabbit monoclonal anti-RXRα [EPR7106] (Abcam, #ab125001) diluted at 1:500, rabbit polyclonal anti-RXRα (Proteintech, #212181AP), mouse monoclonal anti-V5 tag (Thermo Fisher, #R960-25) diluted at 1:5000, mouse monoclonal anti-FLAG [M2] (Sigma-Aldrich, #F1804) diluted at 1:5000, mouse monoclonal anti-Halo (Promega, #G9211) diluted at 1:500, mouse monoclonal anti-TBP (Abcam, #ab51841) diluted at 1:5000, rabbit polyclonal anti-Centrin 2 (Proteintech, # 158771AP) diluted at 1:1000, goat polyclonal anti-mouse IgG light chain specific (Jackson ImmunoResearch, # 115035174) diluted at 1:10,000, mouse monoclonal anti-rabbit IgG light chain specific (Jackson ImmunoResearch, #211032171) diluted at 1:10,000.

The following antibodies were used for co-IP: rabbit polyclonal anti-V5 (Abcam, # ab9116) for immunoprecipitation, mouse monoclonal anti-FLAG [M2] (Sigma-Aldrich, #F1804) diluted at 1:5000 and mouse monoclonal anti-V5 tag (Thermo Fisher, #R960-25) diluted at 1:5000 for blotting.

For western blots, cells growing in six-well or 10 cm plates at 80–90% confluency were scraped and pelleted in ice-cold phosphate-buffered saline (PBS) containing protease inhibitors. Cell pellets were resuspended using 500–1000 μl hypotonic buffer (100 mM NaCl, 25 mM HEPES, 1 mM MgCl₂, 0.2 mM EDTA, 0.5% NP-40 alternative) containing protease inhibitors - 1× aprotinin (Sigma, #A6279, diluted 1:1000), 1 mM benzamidine (Sigma, #B6506), 0.25 mM PMSF (Sigma #11359061001), and 1× cOmplete EDTA-free Protease Inhibitor Cocktail (Sigma, #5056489001) along with 125 U/ml of benzonase (Novagen, EMD Millipore #71205-3). Resuspended cells were gently rocked at 4°C for at least 2 hr after which 5 M NaCl was added. Cells were left rocking for extra 30 min at 4°C and then centrifuged at max speed at 4°C. Supernatants were quantified using Bradford and 15–20 μg was loaded on 8% Bis-Tris SDS gel. Wet transfer to 0.45 μm nitrocellulose membrane (Thermo Fisher #45004031) was performed in a transfer buffer (15 mM Tris-HCl, 20 mM glycine, 20% methanol) for 60–80 min at 100 V, 4°C. Membranes were blocked in 10% non-fat milk in 0.1% TBS-Tween (TBS-T) for 1 hr at room temperature (RT) with agitation. Membranes were then blotted overnight with shaking at 4°C with primary antibodies diluted in TBS-T with 5% non-fat milk. After 5×5 min washes in 0.1% TBS-T, membranes were incubated at RT with HRP-conjugated light chain secondary antibodies diluted 1:10,000 in TBS-T with 5% non-fat milk, for 1 hr with agitation. After 5×5 min washes in 0.1% TBS-T, membranes were incubated for 2 min in freshly prepared Perkin Elmer LLC Western Lightning Plus-ECL, enhanced Chemiluminescence Substrate (Thermo Fisher, #509049326). Finally, membranes were imaged with Bio-Rad Chemidoc Imaging System (Bio-Rad, Model No: Universal Hood III).

pGL3-RARE luciferase, a reporter containing firefly luciferase driven by SV40 promoter with three RAREs, a gift from T Michael Underhill (Addgene plasmid 13456; addgene:13458; RRID:Addgene_13458; Hoffman et al., 2006) was used for luciferase assays. A pRL-SV40 vector (Promega #E2261) expressing Renilla luciferase with SV40 promoter was used as a control to normalize luciferase activity. Cells were plated on six-well plate at least 48 hr before being co-transfected with 200 ng pGL3-RARE-luciferase and 10 ng Renilla luciferase vector, using TransIT-2020 Transfection Reagent (Mirus Bio, #MIR5404). A day after transfection, cells were treated with 100 nM atRA or 0.1% DMSO (control). Luciferase assay was performed the next day, using Dual-Luciferase Reporter Assay System (Promega, #E1910) according to the manufacturer’s protocol, on the Glomax Luminometer (Promega). The relative luciferase activity was calculated by normalizing firefly luciferase activity to the Renilla luciferase activity to control for transfection efficiency.

For co-IP experiments, Cos7 cells were plated to 2×15 cm dishes for each condition, at 60–70% confluency. DNA Lipofectamine 3000 (Thermo Fisher #L3000015) was used to co-transfect the cells with plasmids expressing RARα-Halo-3×FLAG and RXRα-V5 or V5-Halo-RXRα and RARα-3×FLAG or RARα^RR-Halo-3×FLAG and RXRα-V5. According to the manufacturer’s instructions, 500 μl Opti-MEM medium (Thermo Fisher #31985062) was combined with 20 μl P3000 reagent and the plasmids for each condition. To control for the ratio of transfected DNA to the reagents, total transfected DNA mass was kept at 10 μg for each condition using empty pBSK vector (Addgene # 212205). 500 μl Opti-MEM medium containing 20 μl Lipofectamine 3000 reagent was subsequently added to the plasmid containing mixture and incubated at RT for 15 min, after brief pipetting to mix the solutions. The mixture was then divided equally to the cells plated in 2×15 cm dishes. COS7 cells were cultured in DMEM media with 4.5 g/l glucose supplemented with 10% FBS, 1 mM sodium pyruvate, L-glutamine, GlutaMAX, and 100 U/ml penicillin-streptomycin and maintained at 37°C and 5% CO₂.

Cells were collected from plates 48 hr after transfection by scraping in ice-cold 1× PBS with protease inhibitors (1× aprotinin, 0.25 mM PMSF, 1 mM benzamidine, and 1× cOmplete EDTA-free Protease Inhibitor Cocktail). Collected cells were pelleted, flash-frozen in liquid nitrogen, and stored at –80°C. On the day of co-IP experiments, cell pellets were thawed on ice, resuspended to 700 μl of cell lysis buffer (10 mM HEPES pH 7.9, 10 mM KCl, 3 mM MgCl₂, 340 mM sucrose [1.16gr], and 10% glycerol) with freshly added 10% Triton X-100. Cells were rocked at 4°C for 8 min to allow lysis and centrifuged for 3 min at 3000×g. The cytoplasmic fraction was removed, and the nuclear pellets were resuspended in 1 ml hypotonic buffer (100 mM NaCl, 25 mM HEPES, 1 mM MgCl₂, 0.2 mM EDTA, 0.5% NP-40 alternative) containing protease inhibitors and 1 μl benzonase. After rocking for 2–3 hr at 4°C, the salt concentration was adjusted to 0.2 M NaCl final and the lysates were rocked for another 30 min at 4°C. Supernatant was removed after centrifugation at maximum speed at 4°C for 20 min and quantified by Bradford. Typically, 1 mg of protein was diluted in 1 ml 0.2 mM co-IP buffer (200 mM NaCl, 25 mM HEPES, 1 mM MgCl₂, 0.2 mM EDTA, 0.5% NP-40 alternative) with protease inhibitors and cleared for 2 hr at 4°C with magnetic Protein G Dynabeads (Thermo Fisher, #10009D) before overnight immunoprecipitation with 1 μg per 250 μg of proteins of either normal serum IgGs or specific antibodies as listed above. Some precleared lysates were kept overnight at 4°C as input. Magnetic Protein G Dynabeads were also precleared overnight with 0.5% BSA at 4°C. Next day the precleared Protein G dynabeads were added to the antibody containing samples and incubated at 4°C for 2 hr. Samples were briefly spun down and placed in a magnetic rack at 4°C for 5 min to remove the co-IP supernatant. After extensive washes with the co-IP buffer, the proteins were eluted from the beads by boiling for 10 min in 1× SDS-loading buffer and analyzed by SDS-PAGE and western blot.

Cells were grown in six-well dishes. On the day of the experiment, cells were labeled with 500 nM Halo-TMR for 30 min, followed by one quick wash with 1× PBS and 15 min wash in dye-free DMEM before trypsinization. Cells were pelleted after centrifugation, resuspended in fresh medium, filtered through 40 μm filtration unit, and placed on ice until fluorescence read out by Flow Cytometry (within 30 min). Using an LSR Fortessa (BD Biosciences) flow cytometer, live cells were gated using forward and side scattering and TMR fluorescence emission readout was filtered using 610/20 band pass filter after excitation with 561 nm laser. Mean fluorescence intensity of the samples and absolute abundance were calculated as described in Cattoglio et al., 2019, using a previously quantified Halo-CTCF cell line as a standard (Cattoglio et al., 2019).

For confocal imaging ~50,000 cells were plated in tissue culture-treated 96-well microplate (Perkin Elmer, #6055300) a day before imaging. Cells were labeled with Halo and/SNAP for 1 hr and incubated in dye-free media for 20 min after a quick 1× PBS wash to remove any free dye. Phenol-free media containing Hoechst (1 μM) was added to the cells and incubated for 1 hr before proceeding with imaging.

For SMT, 25 mm circular No. 1.5H precision coverglass (Marienfield, Germany, 0117650) were sonicated in ethanol for 10 min, plasma cleaned then stored in 100% isopropanol until use. ~250,000 U2OS cells were plated on sonicated, and plasma cleaned coverglass placed in six-well plates. For ligand treatment, cells were treated with DMSO (control, 0.1%), 1 nM atRA or 100 nM atRA, a day after plating cells in the coverslip and a day before imaging. After ~24–48 hr, cells were incubated with 100 nM PA-JFX549 dye in regular culture media for 30 min, followed by 4×30 min incubations with dye-free culture media at 37°C. A quick 2× PBS wash was interspersed between each 30 min dye-free media incubation. After the final wash, coverslips with plated cells facing upward were transferred to Attofluor Cell Chambers (Thermo Fisher, # A7816), and phenol-free media added for imaging. For Halo-tagged RARα and RXRα homozygous clones that were stably integrated with SNAP-tagged RARα, RXRα, or control transgenes under EF1α promoter; cells were double-labeled with 100 nM HaloTag ligand (HTL) PA-JFX549 and SNAP tag ligand (STL) 50 nM SF-650 simultaneously. The 30 min labeling step was followed by the same wash steps to remove free dye as described above, before transferring the coverslips to Attofluor Cell Chambers and imaging.

For PAPA-SMT experiments, polyclonal U2OS cells stably expressing SNAP-tagged RARα or RXRα under EF1α promoter within the endogenous Halo-tagged RARα and RXRα homozygous clones were used. ~400,000 polyclonal cells were plated in glass-bottom dishes (MatTEK P35G-1.5–20-C) and stained overnight with 50 nM JFX549 HTL and 5 nM JFX650 STL in phenol red-free DMEM (Thermo Fisher #21063029). Next day, cells were briefly rinsed twice with 1× PBS, incubated twice for 30 min in phenol red-free DMEM to remove free dye, and exchanged into fresh phenol red-free medium more before imaging.

For confocal imaging, endogenously Halo-tagged cells were labeled with Halo ligand JFX549 (100 nM) and Hoechst (1.6 μM); endogenously Halo-tagged cells overexpressing SNAP-tagged proteins were labeled with Halo ligand JFX549 (100 nM), SNAP ligand SF650 (25 nM), and Hoechst (1.6 μM). Imaging was performed at the UC Berkeley High Throughput Screening facility on a Perkin Elmer Opera Phenix equipped with 37°C and 5% CO₂, using a built-in ×40 water immersion objective.

All SMT experiments were performed using a custom-built microscope as previously described (Hansen et al., 2017). Briefly, a Nikon TI microscope was equipped with a ×100/NA 1.49 oil immersion total internal reflection fluorescence (TIRF) objective (Nikon apochromat CFI Apo TIRF 100× Oil), a motorized mirror, a perfect Focus system, an EM-CCD camera (Andor iXon Ultra 897), laser launch with 405 nm (140 mW, OBIS, Coherent), 488 nm, 561 nm, and 639 nm (1W, Genesis Coherent) laser lines, an incubation chamber maintaining a humidified atmosphere with 5% CO₂ at 37°C. All microscope, camera, and hardware components were controlled through the NIS-Elements software (Nikon).

For tracking endogenous as well as overexpressed Halo-tagged proteins, PA-JFX549 labeled cells were excited with 561 nm laser at 2.3 kW/cm² with single band-pass emission filter (Semrock 593/40 nm for PA-JFX549). All imaging was performed using highly inclined optical sheet (HILO) illumination (Tokunaga et al., 2008). Low laser power (2–3%) was used to locate and focus cell nuclei. Region of interest (ROI) of random size but with maximum possible area was selected to fit into the interior of the nuclei. Before tracking, 100 frames of continuous illumination with 549 laser (laser power 5%) at 80 ms per frame was recorded to later calculate mean intensity of each nuclei. After partial pre-bleaching (only for overexpressed Halo-tagged proteins), movies were taken with 1 ms pulses of full power of 561 nm illumination at the beginning of frame interval with camera exposure of 7 ms/frame, while the 405 nm laser (67 W/cm²) was pulsed during ~447 μs camera transition time. Total of 30,000 frames were collected. 405 nm intensity was manually tuned to maintain low density (1–5 molecules fluorescent particles per frame).

For tracking experiments with endogenous Halo-tagged proteins in the presence of transgenic SNAP protein products, cells were dual-labeled with both PA-JFX549 and STL-SF650. Before tracking cells were excited with a 639 nm laser at 88 W/cm² and single band-pass emission filter set to Semrock 676/37 nm. Low laser power (2–3%) was used to locate and focus cell nuclei. As before, ROI of random size but with maximum possible area was selected to fit into the interior of the nuclei. The emission filter was switched to Semrock 593/40 nm band-pass filter for PA-JFX549, keeping the TIRF angle, stage XYZ position, and ROI the same. Cells were then excited with 549 nm and single molecules were tracked for 30,000 frames as described above.

Note, we estimated that to calculate f_bound of RARα and RXRα with minimal bias and variation, we need to analyze at least 10,000 pooled trajectories from n≥20 cells (Figure 1—figure supplement 1E). Therefore, all analyses of fSMT to calculate f_bound or f_bound % presented in this paper are done accordingly. At least 8–10 movies were collected for each sample as one technical replicate on a given day. Two technical replicates on 2 separate days were collected to produce the reported results. As observed previously for SMT experiments (McSwiggen et al., 2024), the variance within collected data was largely due to cell-to-cell variance (Figure 1—figure supplement 1E).

PAPA-SMT imaging was performed using the same custom-built microscope described above using an automated system (Graham et al., 2024; Walther et al., 2024). Briefly, the microscope described above was programmed using Python and NIS Elements macro language code to raster in a grid over the coverslip surface, acquire an image in the JFX650 channel, identify cell nuclei, reposition the stage to center it on a target nucleus, resize the imaging ROI to fit the nucleus, pre-bleach JFX650 with red light (639 nm) for 5 s, and finally perform a PAPA-SMT illumination sequence. The illumination sequence consisted of 5 cycles of the following, at a frame rate of 7.48 ms/frame:

Laser power densities were approximately 67 W/cm² for 405 nm, 190 W/cm² for 561 nm, and 2.3 kW/cm² for 639 nm. This illumination sequence includes non-stroboscopic illumination periods to bleach fluorophores or place them back in the dark state (steps 1 and 5), and it records only the frames immediately before and after the PAPA and DR pulses. This is done to decrease file sizes and speed up subsequent analysis compared to our previous protocol (Graham et al., 2022).

All SMT movies were processed using the open-source software package quot (Heckert and Fan, 2022). For SMT dataset quot package was run on each collected SMT movie using the following settings: [filter] start = 0; method = ‘identity’; chunk_size = 100; [detect] method = ‘llr’; k=1.0; w=15, t=18; [localize] method = ‘ls_int_gaussian’, window size = 9; sigma = 1.2; ridge = 0.0001; max_iter = 20; damp = 0.3; camera_gain = 109.0; camera_bg = 470.0; [track] method = ‘euclidean’; pixel_size_μm=0.160; frame interval = 0.00748; search radius = 1; max_blinks = 0; min_IO = 0; scale - 7.0. The first 500 or 1000 frames of each movie were removed due to high localization density. To confirm that all movies were sufficiently sparse to avoid misconnections, a maximum number of 5 localizations per frame was maintained (although most frames had 1 or less). To infer the distribution of diffusion coefficients from experimentally observed trajectories, we used the state array method, which is publicly available at https://github.com/alecheckert/saspt (Heckert et al., 2022a; Heckert et al., 2022b). The following settings were used: likelihood_type = ‘rbme’; pixel_size_μm=0.16; frame_interval = 0.00747; focal depth = 0.7; start_frame = 500 or 1000 frames. RBME likelihood for individual cells and occupations as the mean of the posterior distribution over state occupations marginalized on diffusion coefficient is reported. For SMT movies in Figure 2—figure supplement 1C, mean intensity of each cell was calculated using the mean gray value tool in FIJI. Mean gray value of each frame (total 100 frames) of the pre-bleaching 80 ms movie was measured. Average mean gray value over the 100 frames is reported as mean intensity for each cell.

For PAPA-SMT quot package was run on each collected SMT movie using the following settings: [filter] start = 0; method = ‘identity’; chunk_size = 100; [detect] method = ‘llr’; k=1.2; w=15, t=18; [localize] method = ‘ls_int_gaussian’, window size = 9; sigma = 1.2; ridge = 0.0001; max_iter = 10; damp = 0.3; camera_gain = 109.0; camera_bg = 470.0; [track] method = ‘conservative’; pixel_size_μm=0.160; frame interval = 0.00748; search radius = 1; max_blinks = 0; min_IO = 0; scale - 7.0. Trajectories were sorted based on whether they occurred before or after green (561 nm; PAPA) or violet (405 nm; DR) reactivation pulses, and state array analysis (Heckert et al., 2022b) was applied to each set of trajectories. For Figure 3C, reactivation by PAPA and DR for each cell were quantified by calculating the difference in total number of localizations before and after reactivation pulses.

To derive a measure of error for SMT and SMT-PAPA, we performed bootstrapping analysis on all SMT datasets. For each dataset, a random sample of size n, where n is the total number of cells in the dataset, was drawn 100 times. The mean and standard deviation (stdev) from this analysis is reported.

Two-tailed p-values were calculated based on a normal distribution (Scipy function, scipy.stats.norm.sf) with mean equal to the difference between sample means and variance equal to the sum of the variances from bootstrap sampling (for SMT and SMT-PAPA) or biological replicates (for absolute abundance calculation of molecules from flow cytometry assay). The Šidák correction was applied to correct for multiple hypothesis testing within each experiment.