We fortuitously discovered PAPA while imaging an oligomeric protein labeled with two different JF dyes. U2OS cells expressing Halo-tagged NPM1 (a pentameric nucleolar protein; Heckert et al., 2022) were labeled with a low concentration of Janelia Fluor X 650 HaloTag ligand (JFX650-HTL; Grimm et al., 2021) to track single molecules, together with a higher concentration of Janelia Fluor 549 HaloTag ligand (JF549-HTL) to visualize nucleoli. When we alternately excited JFX650 with red light (639 nm) and JF549 with green light (561 nm), we noticed that some JFX650 molecules that had gone dark during red illumination suddenly reappeared after a brief, 7 ms pulse of green light (green vertical lines in Figure 1ai and green box in Figure 1b, Figure 1—video 1). Consistent with previous work (Grimm et al., 2015), we also observed reactivation of JFX650 by violet light, both with and without JF549-HTL (violet vertical lines in Figure 1ai,ii and violet box in Figure 1b). However, reactivation of JFX650 by green light required co-labeling with JF549 (compare Figure 1ai and ii), implying that reactivation results not from direct absorption of green light by dark-state JFX650 but indirectly due to excitation of JF549. Green illumination of cells labeled with JF549-HTL alone did not produce localizations in the JFX650 channel, demonstrating that this effect is not due to JF549 photochromism (Figure 1aiii).

Because double-labeling of NPM1-Halo pentamers is expected to bring JF549 and JFX650 close together (Figure 1ai, right panel), we asked whether proximity of the dyes is required for reactivation. To test this, we expressed fusions of Halo and SNAPf separated by either a short flexible linker (Halo-SNAPf) or a tandem P2A-T2A self-cleaving peptide (Halo-PT2A-SNAPf; Liu et al., 2017) in U2OS cells (Figure 1c); labeled cells with JF549-HTL and JFX650 SNAP tag ligand (JFX650-STL); and imaged JFX650 with red light interspersed with alternating short pulses of violet and green light. While violet reactivation was similar for both constructs, green reactivation was substantially greater for Halo-SNAPf than for Halo-PT2A-SNAPf, implying that proximity of the two dyes facilitates reactivation by green light (Figure 1c). Thus, we term this phenomenon proximity-assisted photoactivation (PAPA). We will call the dye that undergoes reactivation the ‘receiver’ and the dye whose excitation induces reactivation the ‘sender.’ Also, we will adopt the terms ‘shelving’ for conversion of the receiver into the dark state (Bretschneider et al., 2007; Grimm et al., 2015) and ‘direct reactivation’ (DR) for reactivation by violet light (Dempsey et al., 2009).

Conjugating JFX650 to SNAPf instead of Halo led to more efficient shelving in the dark state, as evidenced by a faster decline in fluorescence during red illumination and greater subsequent reactivation by violet light (Figure 1—figure supplement 1a). This accords with the previous observation that JF549 is more photostable when bound to Halo than when bound to SNAP (Presman et al., 2017). Ensemble and single-molecule kinetic measurements indicate that about 10% of JFX650-SNAPf molecules enter the dark state under our experimental conditions and can be reactivated by either DR or PAPA (Figure 1—figure supplements 1b and 3). DR by violet light precluded subsequent PAPA by green light, and vice versa, implying that both wavelengths reactivate the same dark state (Figure 1—figure supplement 1c and d). We tested other fluorophore pairs and found that PAPA occurred when tetramethylrhodamine (TMR), Janelia Fluor X 549 (JFX549), or Janelia Fluor 526 were used as the sender, or when JF646 or JFX646 were used as the receiver (Figure 1—figure supplement 2).

To investigate how PAPA depends on sender–receiver distance, we generated fusion transgenes in which Halo and SNAPf were separated by zero, one, three, five, or seven repeats of the titin I91 Ig domain (Scholl et al., 2016). The distance distribution between the two dyes was estimated for each fusion protein by simulating an ensemble of conformations using PyRosetta (Figure 2—figure supplement 1a, b; Chaudhury et al., 2010; Ferrie and Petersson, 2020). U2OS cells were stably transfected with each transgene, and fluorescence-activated cell sorting (FACS) was used to obtain pools of cells with similar low expression levels of each protein (Figure 2—figure supplement 1c and d; see Appendix 3, Supplementary note 1).

Cells were labeled with a mixture of JF549-HTL and JFX650-STL and imaged as described above with red light interspersed with alternating pulses of violet light to induce DR and green light to induce PAPA. The ratio of the increase in fluorescence intensity in response to green and violet pulses (the ‘PAPA/DR ratio’) provides a normalized measure of PAPA efficiency, which corrects for cell-to-cell variability in the labeled protein concentration. For sufficiently short reactivation pulses, the PAPA/DR ratio increased linearly with the green pulse duration (with the violet pulse duration held constant), making it possible to measure relative rate constants by linear fitting (Figure 2a, b, left panel). In parallel, fluorescence lifetime imaging (FLIM) was used to measure FRET between JF549 and JFX650 for the same fusion proteins (Figure 2b, right panel; see Appendix 3, Supplementary note 2).

As predicted by our simulations (Figure 2—figure supplement 1b), FRET efficiency between JF549 and JFX650 declined sharply with increasing spacer length, from 0.271 ± 0.010 (95% CI) for the short linker to 0.124 ± 0.006 for a single Ig repeat and 0.020 ± 0.010 for three Ig repeats (Figure 2b, right panel). FRET was essentially undetectable for five or seven Ig repeats and for the PT2A self-cleaving peptide linker (Figure 2b, right panel). In contrast, PAPA was observed for the 3×, 5×, and 7× Ig linker constructs (Figure 2a and b). The rate of photoactivation by green light declined gradually with increasing linker length yet was distinguishable from the background rate of the PT2A self-cleaving linker. These results indicate that PAPA has a less stringent dependence on average inter-fluorophore distance than FRET.

Based on the above results, we reasoned that PAPA could be used to detect interaction of two different proteins labeled with SNAPf-JFX650 and Halo-JF549. As a test case, we monitored the rapamycin-inducible interaction of the proteins FRB and FKBP. U2OS cells expressing Halo-FRB and SNAPf-FKBP were labeled with JF549-HTL and JFX650-STL and imaged with alternating green and violet photostimulation as described above (Figure 3a, Figure 3—figure supplement 1a). Addition of rapamycin caused a dramatic increase in the ratio of PAPA (green reactivation) to DR (violet reactivation), consistent with ligand-induced dimerization of Halo-FRB and SNAPf-FKBP bringing together JF549 and JFX650 (Figure 3b and c, Figure 3—figure supplement 1b, Figure 3—video 1).

We next asked whether PAPA can be used to spotlight a subpopulation of receiver molecules close to sender molecules. As a simple test case, we analyzed defined mixtures of two proteins—one labeled with JFX650 only, and a second labeled with both JFX650 and JF549—and investigated whether PAPA could optically enrich the double-labeled component to distinguish its properties in single-molecule imaging.

First, we co-expressed SNAPf-tagged histone H2B (SNAPf-H2B), which is predominantly chromatin-bound, along with a Halo-SNAPf fusion with a nuclear localization sequence (Halo-SNAPf-3xNLS), which is mostly unbound (Figure 4a; Hansen et al., 2018; Heckert et al., 2022). Cells were incubated with JFX650-STL and JF549-HTL to label Halo-SNAPf-3xNLS with both JFX650 and JF549 and SNAPf-H2B with JFX650 alone (Figure 4a, Figure 4—figure supplement 1a). JFX650 fluorophores were thoroughly photobleached/shelved using a 10 s pulse of intense red light, after which JFX650 was imaged with red light interspersed with pulses of green and violet light. After localizing and tracking single molecules, we separated trajectories occurring after a green pulse (PAPA trajectories) from those occurring after a violet pulse (DR trajectories) and applied a recently developed Bayesian state array SPT (saSPT) algorithm (Heckert et al., 2022) to infer the underlying distribution of diffusion coefficients for each set of trajectories (its ‘diffusion spectrum’ for short). As predicted, diffusion spectra revealed two peaks, one corresponding to bound molecules (D = 0.01 µm²/s, the minimum value in the state array), and one corresponding to freely diffusing molecules (D = 8.3 µm²/s). PAPA trajectories were enriched for freely diffusing molecules compared to DR trajectories, as expected if PAPA selectively reactivates JF549/JFX650 double-labeled Halo-SNAPf-3xNLS molecules (Figure 4b). Next, PAPA and DR trajectories from individual cells were reanalyzed using a two-state model with bound (D = 0.01 µm²/s) and free (D = 8.3 µm²/s) states. Consistent with the ensemble analysis, PAPA trajectories had a lower bound fraction than DR trajectories in every cell (Figure 4c). The same trend is apparent from comparison of particle displacement histograms and raw trajectories (Figure 4—figure supplement 2a, b).

To exclude the possibility that enrichment of unbound molecules arose from a systematic bias in our method, we repeated the experiment with the reciprocal mixture of Halo-SNAPf-H2B and SNAPf-3xNLS (Figure 4d). As expected, the opposite trend was observed: PAPA trajectories were enriched in bound molecules compared to DR trajectories, both across an ensemble of cells and at the single-cell level (Figure 4e and f, Figure 4—figure supplement 2c and d). As a further control, we analyzed cells expressing JF549-HTL/JFX650-STL double-labeled Halo-SNAPf-3xNLS or Halo-SNAPf-H2B alone. As expected, PAPA and DR trajectories displayed virtually identical diffusion spectra for these individual components (Figure 4—figure supplement 3a–f).

To test whether PAPA can also distinguish a mixture of diffusing components, we co-expressed fast-diffusing cytosolic Halo-SNAPf with a SNAPf-tagged synthetic protein that forms large, slowly diffusing 60-mers (Hsia et al., 2016; Figure 4g). As expected, diffusion spectra had two peaks corresponding to slow-diffusing (SNAPf-60-mer) and fast-diffusing (Halo-SNAPf) components (Figure 4h). Compared to DR trajectories (violet curve), PAPA trajectories (green curve) were strongly enriched in the fast-diffusing subpopulation, consistent with selective reactivation of the double-labeled Halo-SNAPf protein by green light (Figure 4h). The same trend was observed in single-cell reanalysis, displacement histograms, and raw trajectories (Figure 4i, Figure 4—figure supplement 2e and f). The enrichment of the fast-diffusing population was not absolute as a slow-diffusing shoulder peak was still observed among PAPA trajectories (Figure 4h, green curve; see ‘Discussion’). As before, swapping SNAPf and Halo-SNAPf labels yielded the opposite trend, both at the ensemble and single-cell level (Figure 4j–l, Figure 4—figure supplement 2g and h, Figure 4—video 1). Enrichment of the 60-mer peak by PAPA is especially pronounced in this case (compare green and violet curves in Figure 4k), which may reflect reactivation of a receiver molecule by any of several neighboring sender molecules within a 60-mer.

To estimate the fold enrichment of double-labeled molecules by PAPA, the curves shown in Figure 4 were fitted to a linear combination of the distributions for individual components. For Halo-SNAPf-3xNLS + SNAPf-H2B, the best fit was obtained for DR trajectories with a mixture of 53% Halo-SNAPf-3xNLS and 47% SNAPf-H2B, while the best fit for PAPA trajectories was obtained with 91% Halo-SNAPf-3xNLS and 9% SNAPf-H2B (Figure 4—figure supplement 4a). The estimated ratio of Halo-SNAPf-3xNLS to SNAPf-H2B thus increases from 0.53/0.47 ≈ 1.1 among DR trajectories to 0.91/0.09 ≈ 10 among PAPA trajectories, an approximately ninefold enrichment of double-labeled molecules by PAPA. Similar calculations showed that PAPA enriched Halo-SNAPf-H2B over SNAPf-3xNLS by 3.7-fold (Figure 4—figure supplement 4b), Halo-SNAPf over SNAPf-60mer by 7.6-fold (Figure 4—figure supplement 4c), and Halo-SNAPf-60mer over SNAPf by 37-fold (Figure 4—figure supplement 4d).

Taken together, these results demonstrate that PAPA can be used to enrich a subpopulation of molecules in which a receiver fluorophore (e.g., JFX650) is in proximity to a sender fluorophore (e.g., JF549), thereby revealing the distinct properties of this subpopulation at both the ensemble and single-cell level. While this enrichment was substantial—between 3.7- and 37-fold for different defined mixtures—it was not absolute, and thus it is crucial not to misinterpret PAPA trajectories as a pure sample of interacting molecules (see ‘Discussion’ and Appendix 2).

As a proof-of-concept biological application, we tested whether PAPA could be used to detect ligand-induced self-association of mammalian androgen receptor (AR) and distinguish the properties of AR monomers and dimers/oligomers. First, we stably co-expressed SNAPf and Halo fusions of mouse AR in U2OS cells (which express very little endogenous AR [Dellal et al., 2020]), labeled the two proteins with a mixture of JFX650-STL and JF549-HTL (Figure 5—figure supplement 1a), and measured the PAPA/DR ratio by quantifying changes in JFX650 fluorescence intensity in response to alternating green and violet stimulation as described above. As expected, treatment with the androgen dihydrotestosterone (DHT) led to an increase in the ratio of PAPA to DR over the course of several minutes (Figure 5b, Figure 5—figure supplement 1b), consistent with the two fluorophores being brought together by ligand-induced interaction between SNAPf-mAR and Halo-mAR.

Next, we combined PAPA with single-molecule imaging to assess how self-association influences diffusion and chromatin binding by AR. Consistent with previous biochemical and live-cell imaging experiments, addition of DHT caused an increase in the overall bound fraction of AR (Figure 5c and d; Schaufele et al., 2005; van Royen et al., 2007; van Royen et al., 2012). Strikingly, PAPA trajectories had a higher bound fraction than DR trajectories, both before and after addition of DHT (Figure 5c, d). This is consistent with an increase in the affinity of AR for specific DNA sequence motifs upon self-association. Moreover, PAPA revealed that a subset of AR molecules self-associated and bound chromatin with elevated affinity even prior to addition of exogenous androgen. Thus, PAPA can be applied to monitor regulation of a biologically important protein–protein interaction in live cells, discern its effect on chromatin binding, and reveal the existence of molecular subpopulations.

U2OS cells were grown in Dulbecco’s modified Eagle’s medium (DMEM) with 4.5 g/l glucose (Thermo Fisher #10566016), 10% fetal bovine serum (FBS), and 100 U/ml penicillin-streptomycin (Thermo Fisher #15140122) at 37°C and 5% CO₂. Phenol red-containing medium was used for propagation of cells, while phenol red-free medium (Thermo Fisher #21063029) was used to minimize fluorescence background in imaging experiments.

Ig linkers were subcloned from a previously described plasmid containing repeats of the titin I91 Ig domain, which were codon-shuffled to prevent recombination (Scholl et al., 2016). The various Halo and SNAPf fusion constructs described in this article were generated by PCR and isothermal assembly, and all constructs were completely sequenced before use. Two-component expression plasmids included a codon-shuffled SNAPf-3xNLS-T2A-P2A cassette that was ordered as a gBlock from Integrated DNA Technologies (IDT). All plasmid sequences are available at https://gitlab.com/tgwgraham/papa_paper_plasmids, copy archived at swh:1:rev:984803582c0023a9fe975ec6d41be3d723c2737b; Graham, 2022a.

To generate stable lines by PiggyBac integration, U2OS cells from a confluent 10 cm plate were trypsinized, resuspended in DMEM, and divided between two 15 ml conical tubes. Cells were centrifuged for 2 min at 200 × g, and the medium was aspirated and replaced with 100 µl of Lonza Kit V transfection reagent (82 µl of Kit V solution and 18 µl of Supplement I; Cat# VCA-1003) containing 1 µg of the donor plasmid and 1 µg of Super PiggyBac transposase plasmid. The cell suspension was transferred to an electroporation cuvette and electroporated using program X-001 on an Amaxa Nucleofector II (Lonza). Cells in the cuvette were mixed with 300 µl of DMEM, and 100 µl of the cell suspension was diluted in 10 ml of DMEM in a 10 cm plate. After allowing cells to grow for 1–2 days, selection was initiated by adding puromycin to a final concentration of 1 µg/ml.

To generate clonal cell lines of Halo-mAR + SNAPf-mAR and FKBP-SNAPf-3xNLS + FRB-Halo-3xNLS, a polyclonal pool of stably transfected cells from a 10 cm plate was labeled with a mixture of 50 nM JF549 SNAP tag ligand and 50 nM JFX650 HaloTag ligand, and FACS was used to sort single cells expressing both proteins into separate wells of a 96-well plate. For pTG800 (3xFlag-Halo-SNAPf-3xNLS-T2A-P2A-H2B-SNAPf-3xNLS), single-cell clones were obtained by limiting dilution into 96-well plates. Polyclonal pools of stably transfected cells were used for the other two-component and one-component experiments in Figure 4 and Figure 4—figure supplements 1–4.

For the experiments in Figure 2 and Figure 2—figure supplement 1, FACS was used to obtain polyclonal pools of U2OS cells expressing a low level of each Halo-linker-SNAPf construct. Confluent 10 cm plates of cells were stained with 50 nM each of JF549-STL and JFX650-HTL, and cells were sorted using the same intensity gate in the JFX650-Halo channel. Cells expressing pTG820 (Halo-3x Ig-SNAPf) and pTG828 (Halo-5x Ig-SNAPf) were sorted on a different day using the intensity of the previously sorted pTG747/U2OS pool to define a gate in the JFX650-Halo channel.

Cells in either 10 cm plates or 6-well plates were labeled with 500 nM of the indicated HTL or STL ligand for 1 hr at 37°C, washed twice with 1× PBS, trypsinized, and resuspended in DMEM. Cells were counted using a Countess 3 FL cell counter (Invitrogen), pelleted by centrifugation for 2 min at 200 × g, and frozen at –80°C. Lysates were prepared by addition of 1 ml (for 10 cm plates) or 200 µl (for 6-well plates) of SDS lysis buffer without dye (Cattoglio et al., 2019). Each lysate was passed through a 26-gauge needle 10 times to reduce its viscosity.

Custom 8-well, 1.5 mm combs for SDS-PAGE were 3D-printed using an AnyCubic Photon 3D printer (model files available at https://gitlab.com/tgwgraham/gel-combs; copy archived at swh:1:rev:7d5a083eec963534c1bf54632e5e3fb7606e5518; Graham, 2022b). For the gels in Figure 2—figure supplement 1c and d, samples of cell lysate corresponding to 100,000 cells were separated on a 10% SDS-PAGE gel, which was imaged on a Pharos FX imager (Bio-Rad) using the ‘low-intensity’ setting in the Cy3 channel. Cell lysate corresponding to 60,000 cells was loaded per lane of the gels in Figure 3—figure supplement 1, Figure 4—figure supplement 1, and Figure 5—figure supplement 1. The gel in Figure 4—figure supplement 1a was imaged on a Pharos FX imager (Bio-Rad) using the ‘low-intensity’ setting in the Cy5 channel. The gels in Figure 3—figure supplement 1a, Figure 4—figure supplement 1b, and Figure 5—figure supplement 1a were imaged in the 700 nm channel on an Odyssey imager (LI-COR) at 169 µm resolution with the ‘medium’ quality setting and a z-offset of 0.5 mm. Precision Plus Protein All Blue Prestained Protein Standards (Bio-Rad #1610373) were used as molecular weight standards for all gels.

One day prior to imaging, 25 mm No. 1.5H glass coverslips (Marienfeld, #0117650) were immersed in isopropanol, transferred with forceps to 6-well plates, and aspirated thoroughly to remove all traces of isopropanol. Cells were trypsinized, counted using a Countess 3 FL cell counter (Invitrogen), centrifuged for 2 min at 200 × g, resuspended in phenol red-free DMEM, and plated at a density of 5 × 10⁵ cells per well. Just prior to imaging, cells were incubated with Janelia Fluor HaloTag and SNAP tag ligands in phenol red-free DMEM for 15 min at 37°C, washed twice with 1× phosphate-buffered saline, and destained for at least 15 min in phenol red-free DMEM. The following dye concentrations were used for staining:

Coverslips were mounted in a stainless steel Attofluor Cell Chamber (Thermo Fisher #A7816) and covered with 1 ml of phenol red-free DMEM with 10% FBS and penicillin/streptomycin. Cells were imaged using HILO illumination on the microscope described in detail in Hansen et al., 2018. Laser power densities used for imaging were approximately 52 W/cm² for 405 nm (violet), 100 W/cm² for 561 nm (green), and 2.3 kW/cm² for 639 nm (red). Fluorescence emission was filtered through a Semrock 676/37 bandpass filter.

For the experiments in Appendix 1—figure 1, a Di02-R635 dichroic (Semrock) was used to separate JF549 and JFX650 emission, which were filtered through 593/40 and 676/37 bandpass filters, respectively, and imaged on separate cameras.

Cells were imaged at a rate of 7.48 ms/frame. Different experiments employed variations of an illumination sequence with alternating pulses of 639 nm red (R), 561 nm green (G), and 405 nm violet (V) light synchronized to the camera. We use these abbreviations below and indicate the duration of the light pulse in brackets. For instance, ‘250 R [2 ms]’ denotes 250 frames with a 2 ms pulse of red 639 nm illumination per frame. Red illumination was restricted to one 2 ms stroboscopic pulse per frame in single-molecule tracking to reduce the motion blur of moving molecules (Hansen et al., 2018). The green and violet pulse durations were adjusted in different experiments to maintain a trackable density of localizations after each pulse.

For ensemble PAPA experiments (Figure 1c, Figure 2a and b, Figure 3b and c, Figure 5b, Figure 1—figure supplements 1–2, Figure 3—figure supplement 1b, Figure 5—figure supplement 1b, and Appendix 2—figure 1), custom MATLAB code was used to sum the total intensity of all pixels in the field of view at each frame. Frame-by-frame intensity across multiple movies was averaged to obtain ‘sawtooth’ plots of intensity vs. frame number (Figure 1c and Figure 1—figure supplement 1a,c,and d, Figure 1—figure supplement 2, Figure 3—figure supplement 1b, and Figure 5—figure supplement 1b). The PAPA/DR ratio was calculated for Figure 2a and b, Figure 3b and c, Figure 5b, and Appendix 2—figure 1 by dividing the mean increase in fluorescence intensity induced by green and violet pulses. For Figure 2a and b, which used an illumination sequence with fewer frames per cycle, the initial green and violet pulse were omitted from the averages to avoid the transient photobleaching/shelving phase at the beginning of each movie.

To measure direct reactivation of JFX650-SNAPf as a function of 405 nm illumination time (Figure 1—figure supplement 1b), cells expressing Halo-SNAPf-3xNLS (pTG747) were stained with 5 nM JFX650 STL and 50 nM JF549 HTL and imaged at 7.48 ms/frame using a five-phase protocol: (1) 20 frames with 1 ms pulses of 639 nm (intensity measurement before bleaching/shelving), (2) 400 frames with 7 ms pulses of 639 nm (bleaching/shelving), (3) 20 frames with 1 ms pulses of 639 nm (intensity measurement after bleaching/shelving), (4) N frames with 7 ms pulses of 405 nm (reactivation), and (5) 20 frames with 1 ms pulses of 639 nm (intensity measurement after reactivation). The total pixel intensity was summed for all 20 frames in phases (1), (3), and (5), and the fractional reactivation was calculated by subtracting the increase in signal between (3) and (5) by the initial drop in signal between (1) and (3). The number of violet frames in phase 4, N, was varied as indicated by the values on the horizontal axis of Figure 1—figure supplement 1b. The data were fitted to a single-exponential model.

To monitor reactivation of single immobilized JFX650 fluorophores, U2OS cells expressing H2B-Halo-SNAPf were labeled for 15 min with 50 pM of JFX650 STL, either with or without 50 nM JF549 HTL. Cells were imaged at 7.48 ms/frame with five cycles of 100 frames of 639 nm illumination, 10 frames of either 561 nm or 405 nm illumination, and another 100 frames of 639 nm illumination. Individual, well-separated JFX650 fluorophores (≥8 pixels apart) were identified in the first frame of each movie, and each fluorophore was scored as fluorescent in subsequent frames if a localization was detected within 4 pixels of its initial position.

Fluorescence lifetime was measured on a Zeiss LSM 980 confocal microscope equipped with a Becker & Hickl SPC-150NX TCSPC module. Cells were labeled with a mixture of 50 nM JFX650-HTL and 50 nM JF549-STL for 1 hr at 37°C, or with 50 nM JF549-STL alone as a no-FRET control. After briefly washing twice with 1× PBS, cells were destained for at least 15 min prior to imaging. JF549 was excited using a 562 nm laser, and fluorescence emission was filtered through a Semrock 593/40 bandpass filter. Signal was acquired for 10 s over a 256 × 256 px region centered on each cell nucleus. Raw data were imported into SPCImage (Becker & Hickl) and fitted to a single-exponential model without binning pixels. Decay constants and total fluorescence intensities for each pixel were exported in .csv format. Custom MATLAB code was used to define nuclear masks by intensity thresholding and determine the mean fluorescence lifetime within the nucleus. FRET efficiency was calculated using the formula E_FRET = 1 – τ/τ₀, where τ is the fluorescence lifetime of the sample and τ₀ is the fluorescence lifetime of cells stained with JF549-STL donor only.

To measure whether PAPA precludes DR and vice versa (Figure 1—figure supplement 1c and d), we first labeled cells expressing Halo-SNAPf-3xNLS (pTG747) with 5 nM JFX650 STL and 50 nM JF549. We then imaged at 7.48 ms/frame in three phases: (1) 500 frames of 639 nm light (7 ms pulses), alternating with unrecorded frames with either no illumination (black curves) or 7 ms pulses of 405 nm (violet curves) or 561 nm (green curves) illumination; (2) 20 frames with 7 ms pulses of 405 nm light (Figure 1—figure supplement 1c) or 561 nm light (Figure 1—figure supplement 1d); and (3) 100 frames of 639 nm light (7 ms pulses). Fluorescence intensity traces were prepared as described in ‘Analysis of ensemble PAPA experiments‘ above.

Particles were localized and tracked using the quot package (https://github.com/alecheckert/quot; Heckert, 2022) with default settings. Custom MATLAB code (https://gitlab.com/tgwgraham/papacode_v1; Graham, 2022c) was used to extract all trajectory segments occurring within the first 30 frames after pulses of 405 nm light (DR trajectories) and 561 nm light (PAPA trajectories). PAPA and DR trajectories were then separately analyzed using a Bayesian ‘fixed-state sampler’ algorithm (https://github.com/alecheckert/spagl; Heckert et al., 2022), which estimates the posterior probability distribution over a fixed array of diffusion coefficients. To allow a side-by-side comparison of the distributions for PAPA and DR trajectories, the same number of trajectories was included in the analysis for each. To this end, trajectories were randomly subsampled without replacement from whichever condition, PAPA or DR, had more trajectories. The fraction bound was calculated in Figure 4c and f and Figure 4—figure supplement 3c and f by reanalyzing the data using a reduced two-state model with diffusion coefficients 0.01 and 8.3 µm²/s. The fraction slow-diffusing was calculated in Figure 4i and l and Figure 4—figure supplement 3i by fitting to a three-state model with diffusion coefficients 0.01, 2.1, and 13.2 µm²/s (Figure 4i) or 0.01, 1.3, and 15.8 µm²/s (Figure 4l, Figure 4—figure supplement 3i). Fraction bound for androgen receptor (Figure 5—figure supplement 1c) was calculated by fitting to a two-state model with diffusion coefficients 0.01 and 4.4 µm²/s. Diffusion coefficients used in the reduced models correspond to the local maxima of the ensemble distributions (Figures 4b, e, h, k, 5c and d). Displacement histograms in Figure 4—figure supplement 2b,d,f,and h were tabulated using custom code in MATLAB.

A more streamlined and user-friendly Python module for PAPA-SPT analysis, employing an updated version of the SASPT analysis software, will be maintained at https://gitlab.com/tgwgraham/papacode_v2 (copy archived at swh:1:rev:77dbcca3d4ca2833a5d051d495d52444ba34ac27; Graham, 2022a).

Inter-fluorophore distances were computed from simulated structural ensembles of each linker construct generated using PyRosetta. Crystal structures of Halo (PDB: 6u32), SNAPf (PDB: 6y8p), and titin Ig (PDB: 1tit) were used to model structured regions. Regions lacking density were filled in using RosettaRemodel, and co-crystalized fluorophores bound to Halo and SNAPf were used to estimate inter-fluorophore distance (Huang et al., 2011). After filling in missing residues, each structure was minimized using the FastRelax protocol, and starting structures were generated by concatenating structured regions using linkers corresponding to those used in experimental constructs. Ensembles were generated using an adapted version of the FastFloppyTail method used for sampling disordered protein regions, in which only residues comprising the inter-domain linkers were allowed to move (Ferrie and Petersson, 2020). The adapted version of the FastFloppyTail algorithm features the addition of the BackrubMover, to allow for motion within a large loop present in SNAPf and facilitate more complete sampling (Smith and Kortemme, 2008). After application of the adapted FastFloppyTail protocol, resultant structures were minimized using FastRelax. Each ensemble consisted of 100 structures from which inter-fluorophore distances were computed. Scripts used to generate these ensembles along with the input structures and resultant ensembles can be found at https://github.com/jferrie3/FusionProteinEnsemble, (copy archived at swh:1:rev:9a8ffe946a20d8efb6c4eb531b22dd96e7431e28; Ferrie, 2022).