Dynamic tuneable G protein-coupled receptor monomer-dimer populations

G protein-coupled receptors (GPCRs) are the largest class of membrane receptors, playing a key role in the regulation of processes as varied as neurotransmission and immune response. Evidence for GPCR oligomerisation has been accumulating that challenges the idea that GPCRs function solely as monomeric receptors; however, GPCR oligomerisation remains controversial primarily due to the difficulties in comparing evidence from very different types of structural and dynamic data. Using a combination of single-molecule and ensemble FRET, double electron–electron resonance spectroscopy, and simulations, we show that dimerisation of the GPCR neurotensin receptor 1 is regulated by receptor density and is dynamically tuneable over the physiological range. We propose a “rolling dimer” interface model in which multiple dimer conformations co-exist and interconvert. These findings unite previous seemingly conflicting observations, provide a compelling mechanism for regulating receptor signalling, and act as a guide for future physiological studies.

To account for differences in sample size between the intensity distributions of the three samples (a-f), the data were bootstrapped 1,000 times, taking random samples of n = 1,000 for each of the three data sets. Four Gaussian mixture models composed of 1-4 components were fitted to each bootstrapped data sample, and the corresponding Bayesian information criterion (BIC) value was calculated to assess the relative likelihood of each of 8 the models. The highest BIC corresponds to the most probable model, and the absolute difference in BIC reflects the relative likelihood of the models, where differences larger than two can be seen as the most probable and less probable models was more than 10 in each case, suggesting very strong evidence for the most probable models relative to the other models.

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For  Table 6 -Estimation of lipid-to-protein ratio from sucrose density gradients.
The density ( "# ) of proteoliposome samples prepared for FRET and DEER experiments was estimated by running the samples on a sucrose density gradient from which the partial specific volume ( "# ) of the proteoliposomes was calculated. 42 The lipid-to-protein ratio (L:P, w/w) was estimated using %&'&() =0.986 mL g -1 and *+,-=0.735 mL g -1 . 43 The weight ratio was converted to a molar ratio assuming an average molecular weight of 650 g mol -1 for BPL.

Supplementary Note 1 -Equilibrium monomer-dimer distribution, rate of dimer formation, and calculation of kinetic parameters
The dynamic equilibrium monomer-dimer distribution was calculated from the initial two dimensional membrane density of donor and acceptor spots on initial frames of each video, prior to significant photobleaching. Frame one was discarded due to a triggering asynchrony between the laser shutter and camera resulting in under-illumination in the first frame. Trajectories existing within the next five frames were considered to represent the equilibrium visible donor and acceptor densities. Across 19 videos an average density of 0.072 and 0.0056 spots μm -2 was measured for visible monomer (donor) and dimer (acceptor) spots, respectively. The ratio of labelled species was then used to infer the total monomer and dimer species concentrations.
The probability of Cy3-Cy3 dimers is sufficiently low that we assume the total number of detectable Cy3-labelled receptors is represented by the total of equilibrium detected donor and acceptor spots, each comprising one Cy3-labelled receptor. With Cy3-labelled protein representing 0.182 of the total receptor species, total receptor density is approximated by equation (S1).
Receptor density = (A + D) x (1/(Cy3/(Cy3 + Cy5 + U))) (Eq. S1) Where A represents the visible equilibrium acceptor spot density, D represents the visible equilibrium donor acceptor spot density, with Cy3, Cy5, and U representing the relative proportions of Cy3labelled, Cy5-labelled and unlabelled protein, respectively. Cy3-Cy3 dimers were noted to be particularly rare representing ~3% of dimers and therefore ~0.27% of all species. This corresponds to approximately 0.98% of donor channel spots prior to photobleaching, in keeping with the intensity distribution measured for donor spots being adequately 23 described by a single log-normal distribution (Fig. 2).
The detection of trajectories in the acceptor channel represents the detection of Cy3-Cy5 dimers. At the start of imaging all initial detections are assumed to be attributable to pre-existing Cy3-Cy5 dimers present at the start of the experimental acquisition. Consequently, the first three frames are discarded (frame one due to underexposure) to account for detection of these Cy3-Cy5 dimers. Following this, subsequent detection of new acceptor trajectories can be attributed to the formation of new dimer species during the experiment, from which the rate of dimer formation can be extracted. An exponential decay ensues with a decreasing number of new trajectories detected with time, as predominantly donor, and to a lesser extent acceptor, fluorophores photobleach through the time course of the experiment (Fig. 3a,b). Fitting an exponential to this data enables extrapolation to conditions of zero photobleaching at the y-axis intercept providing the rate of Cy3-Cy5 dimer formation.

Supplementary Note 2 -Quantifying False Positive Dimerisation Detections
We have previously demonstrated in single colour diffraction-limited experiments in droplet interface bilayers that interacting alpha hemolysin monomers co-localise for no longer than 5 ms where oligomerisation does not proceed to the stable heptameric state. 44 The individual monomer-monomer interaction of these membrane proteins is short-lived, despite their ability to ultimately form stable heptameric pores. The reported experiments find that heptamerisation is rare, but occurs rapidly (<5 ms) to produce a small number of stable heptamers in a high density monomeric population, with no intermediate oligomers persisting beyond the 5 ms timescale. Consequently, this benchmark provides strong evidence that the timescales of interaction for NTS1 monomers reported in this work (90+ ms) can reliably be attributed solely to bona fide and stable (although transient) protein-protein interaction and therefore dimerisation.
The contribution of chance (i.e. non-interacting), diffraction-limited co-localised trajectories to observed dimerisation events has been demonstrated to be negligible on these timescales in live cell single-molecule imaging. 45 In the well-controlled in vitro DIB system reported here we can have greater confidence that measured interactions are driven by molecular interaction alone, by virtue of making measurements in a minimal system with membrane diffusion unhindered by the cytoskeleton or other cellular features. Here we can extend the approach of Hern et al. 45 and experimentally determine the contribution of prolonged chance co-localised events by comparing trajectories in the continuously visualised Cy3 channel in multiple experiments. To this end we combine all measured Cy3-NTS1 trajectories from five separate experimental videos to provide an equivalent trajectory density to that of the non-visualised Cy5-labelled species. Every trajectory was then tested for spatial and temporal coincidence with all trajectories in a sixth Cy3-NTS1 video, serving as a set of donor trajectories. Coincidence was determined at different spatial proximities determining the number of chance co-localisations over different timescales and spatial distances. At a coincidence diameter of 200 nm, approximating to the proximity limit for determining diffraction-limited co-localisation, we find an equivalent to 15.1% of our measured dimer traces would be attributable to the chance colocalisation of two receptors within 200 nm over three or more consecutive frames. It is notable that these represent 3 frame (10.65%) and 4 frame (4.44%) events only, with no longer lasting coincident diffusion events detected ( Supplementary Fig. 5). This represents the false positive rate if determination of receptor-receptor interaction were made by diffraction-limited means at our reconstituted receptor density.
In the dimerisation experiments reported here, we use FRET to afford more than an order of magnitude greater spatial resolution in determining interaction compared to diffraction-limited colocalisation and have accepted only interactions persisting for longer than 90 ms (3 frames), providing a stringent threshold in attributing interaction for classification as NTS1 dimers. Since we employ FRET to determine receptor-receptor interaction, two receptors must be within the order of the Förster radius, in this case approximately 5 nm, to be detected as interacting and attributed as a dimer. At this length scale no coincident trajectories persisting for more than 3 frames (the employed cut-off) are observed ( Supplementary Fig. 5), demonstrating that chance coincident diffusion makes a negligible contribution to measured dimer trajectories. By plotting the relationship of coincidences persisting for a minimum of three frames against spatial radius defining coincidence, and fitting a decay curve, we estimate a maximum false positive detection rate of 0.04% in our single-molecule FRET experiments, confirming that co-diffusing, non-interacting, species do not significantly contribute to dimerisation detections in our population of 1,167 measured trajectories. These measurements are in good agreement with analytical solutions for receptor collision which indicate the rarity of co-occupation, even momentarily, of two receptors within a collision radius of each other (of comparable magnitude to the Förster radius). This is borne out by Monte Carlo simulations and the experimentally observed steep reduction in detected dimers with small reduction in receptor density ( Supplementary Fig. 4a), as a direct consequence of the decreasing probability of receptor collision.

Supplementary Note 3 -Calculation of collision frequency and estimation of productivity
Dimer formation is a stochastic event initiated by the chance collision of two diffusing receptors in the bilayer. At the single-molecule level concentrations studied, such collisions are relatively infrequent and this is reflected in the frame-to-frame variability in detected dimer arrival events (Fig. 3a,b). With

Supplementary Note 4 -Estimation of error
Our single-molecule FRET experiments provide a time-limited glimpse into the dynamic equilibrium of NTS1 dimerisation. Since we are monitoring short-lived (t 1/2 = 1.205 s), stochastic events, occurring at low frequency and low concentration (0.0813 μm 2 s -1 ), measurement variation is expected from video to video, in addition to experimental variation due to differences in reconstitution efficiency between bilayers. To characterise this variance in equilibrium data each video file was analysed individually, in addition to combining all videos for analysis, in accordance with the data analysis procedure detailed above. The error in dissociation constant  Fig. 4b).

Supplementary Note 5 -Estimation of smFRET distance measurements
The inter-label distance in Cy3-Cy5 NTS1 dimers was estimated from acceptor intensity distributions of both the dimer species and a monomeric doubly labelled mutant ( Supplementary Fig. 11). A Cy3-Cy5 Förster radius (R0) of 54 Å was adopted following previously reported values. 48 For the doubly labelled mutant NTS1 a Cy3-Cy5 distance of r = 1.5 nm was ascribed based on the crystal structure of NTS1. 49 FRET efficiency (E) is therefore defined by equation (S9).
At a distance of 1.5 nm, E = 0.9995 = ~1. Consequently, we assume 100% energy transfer in the case of the doubly labelled mutant, where a median single-molecule acceptor intensity of 146.4 counts is measured (Fig. 2) as a result of donor excitation and energy transfer. Here, we reverse the sensitised acceptor emission approach typically used to estimate distances based on the quantification of donor emission quenched by FRET. Since this is anti-correlated with acceptor emission to define E, we assess the distance-dependent decrease in energy transfer via acceptor intensity decrease compared to that at a known distance corresponding to E = 1. For dimeric Cy3 and Cy5 labelled NTS1 a median single-molecule acceptor intensity of 91.7 counts is measured (Fig. 2), corresponding to 0.63 of the emission observed at ~100% efficient energy transfer of the doubly labelled mutant. Consequently, an energy transfer efficiency of 0.63 is calculated to correspond to an approximate Cy3-Cy5 distance of 5 nm, in close agreement to that obtained by ensemble FRET measurements. Additionally, a subpopulation of high acceptor intensity dimers is observed (Fig. 2). Here, the Gaussian centre intensity of 148 counts corresponds closely to the intensity measured in the high efficiency doubly labelled construct with known dye-dye separation of ~1.5 nm. This distance corresponds to the spacing between two neighbouring transmembrane helices in single receptor. A comparable distance may be anticipated between interfacial transmembrane helices of a dimer complex, indicative of a subpopulation of dimers with short TM4-4 separation and a larger population with longer TM4-4 distances, approaching the Förster radius for the Cy3-Cy5 label pair. Estimation of TM4-4 separation from FRET efficiency (E) data (Fig. 4) yielded comparable results, with an average dimer TM4-4 Cy3-Cy5 distance of 5.3 nm.

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The use of narrow band emission filters, whilst reducing total photon detection, eliminated detectable emission bleed between donor and acceptor channels. Cross-excitation of acceptor by the illumination laser was not detectable at the single-molecule level in the described imaging setup and consequently was considered negligible. It should be noted that donor and acceptor dye orientation also affect energy transfer efficiency. This may be indistinguishable from small changes in distances.
However, changes in fluorescent energy transfer are indicative of a conformational change, with large changes in efficiency, as we observe here with the two dimer population states, likely involving significant changes in dye distances due to bona fide conformational changes, given the short linker length.

Supplementary Note 6 -Single-molecule acceptor intensity threshold analysis
Acceptor intensity fluctuation giving rise to two observed dimer acceptor intensity state populations ( Fig. 2) was investigated by implementing an intensity threshold crossing algorithm for all acceptor trajectories. The relative contribution of the high-and low-FRET populations was used to inform a conservative threshold to define population switching events (Fig. 4). This was favoured over a more simple mid-point assignment to reduce the probability of assigning false positive events, accepting the implicit trade-off in greater rejection of bona fide population switching events. A threshold of 166.5 counts was assigned ( Fig. 4d and Supplementary Fig. 8). Intensities above this threshold represent 42% of high-FRET state spot intensities and just 0.95% of the low-intensity population. Dimer acceptor (Cy5) trajectories were analysed for crossing this defined population threshold, and the dwell-time spent in either high-or low-intensity states prior to either a successive threshold crossing, or trajectory termination by either dimer dissociation or photobleaching, was measured. Cumulative probability plots display the fraction of the observations (on the y-axis) below a given dwell-time given on the x-axis (Fig. 4e). NTS1 dimers were seen to exhibit a greater dwell-time in low-intensity conformation state(s) (Fig. 4e, top panel) than in a high-intensity state (Fig. 4e, bottom panel), in accordance with the relative mixing proportions of the two-component intensity distributions. This is likely indicative of a more stable dimer conformation of lower FRET efficiency, with forays into higher intensity conformations before rapid switching again to a lower intensity conformation (Fig. 4e).
However, it should be noted that the high intensity threshold employed to describe high state events will likely over-report high-state to low-state transitions as a result of acceptor intensity fluctuations within the log-normal distribution of the high-intensity population state. Such a trade-off is unavoidable given the broad nature and overlap of the two population intensity distributions, but is offset by the increased confidence in assigning high-state events. Cumulative lifetime probability of low acceptor intensity states (Fig. 4e, top panel)  However, the acceptor lifetime histogram also shows an otherwise unanticipated initial increase in 31 probability towards longer trajectory observations, to a probability maximum at 150 ms.
( Supplementary Fig. 11c) A monotonically decreasing lifetime probability is expected for photobleaching-limited observations (as per donor histogram, Supplementary Fig. 11b). Acceptor lifetime probability is observed to be non-monotonic, with a further, more rapid, decay process contributing to a lifetime peak at 150 ms. At this timescale we can rule out incidental collisions and the possibility of any systematic error due to misdetection of acceptor spots, or inaccurate trajectory linking (which would display a monotonically decreasing probability of successively longer tracks).
The observation of longer (180+ ms) trajectories displaying a decaying observation probability, on the order of donor photobleaching, is consistent with the simultaneous presence of longer surviving dimer species where photobleaching largely limits observation times.

Supplementary Note 7 -Reconstitution orientation
In the presented work we do not have experimental control over the reconstitution orientation of NTS1 in the artificial membrane. NTS1 reconstitution in liposomes using the same methods as used in this study has previously been reported by our laboratory to yield symmetric reconstitution with ~50/50 distribution of both orientations. 43 The reconstitution orientation in the droplet interface bilayers (DIBs) used in our single-molecule work is unknown. This leads to a number of theoretically possible scenarios: 1) Reconstitution is asymmetric (i.e. all monomers are inserted in the same orientation); 2) Reconstitution is symmetric (i.e. monomers are inserted in random orientations), and antiparallel dimers do not from; 3) Reconstitution is symmetric, and antiparallel dimers can form.
In scenario #1 our analysis would not be affected.
In scenario #2, our reconstitution efficiency would effectively be off by a factor 2, since each receptor will only be able to interact with half of the receptors present. This would mean that our measured/derived parameters would (only) be underestimated by a factor of 2 In scenario #3, in theory, any measured parameter would represent a population-weighted average of the parallel and the non-physiological antiparallel dimers. However, we would not expect to observe a large part of any hypothetical antiparallel dimers via FRET because the inter-label distance would be too large to give rise to efficient energy transfer for most hypothetical antiparallel dimer configurations.
Whilst, we cannot definitively exclude any of the three aforementioned scenarios, the observed dimer half-life (1.2 s) is consistent with previous reports on other GPCR dimers (~0.1-5 s). 45,50,51 Additionally, the observed TM4-4 distance of ~5.0 nm for the low FRET state and shorter distance (~1.5 nm) for the high-FRET state are too short to both originate from antiparallel dimers, for which we would expect a minimal distance of ~4-7 nm. Thus, neither the high-FRET state observed in smFRET, nor the short distances observed by DEER, could originate from an antiparallel dimer. Furthermore, the smFRET threshold crossing analysis (presented in Fig. 4) showed that individual dimers sample both the low-and high-FRET states, i.e. show interconversion between these states. Both these states must thus originate from a parallel dimer to be able to interconvert, validating our conclusion that the physiologically relevant dimer samples multiple interfaces.
In addition, the relative proportion of low-and high-FRET states identified from the FRET efficiency histogram (80/20, Fig. 4c) is very similar to that identified from the dimer acceptor fluorescence intensity distribution (84/16, Fig. 2a). Notably, FRET efficiencies were only calculated from a subset of long-lived dimers (to be able to extract meaningful acceptor trajectories) and are thus more likely to include contributions from the high-FRET state. Thus, the FRET efficiency histogram is biased towards trajectories containing transitions between low-and high-FRET states, which, as argued above, cannot originate from antiparallel dimers. The dimer acceptor fluorescence intensity histogram does not have this bias and also includes shorter traces that are more likely to only sample the low FRET states. If hypothetical antiparallel dimers with long, but observable inter-label distances were present in significant proportions, this would be reflected in a much higher low FRET population in the acceptor fluorescence intensity distribution histogram compared to the FRET efficiency histogram, which we do not observe.
Taken collectively, while we cannot exclude the possibility of random insertion in the bilayer, and the formation of antiparallel dimers with the data at hand, we consider it reasonable to conclude that any effect must be modest. values. 52 Radio-ligand binding assays 53 showed that spin labelling with MTSL also did not affect ligand-binding, with 100 ± 20% activity retained (n = 6, for TM5-6 cysteine mutants). G protein (Gα i1 ) binding to cysteine mutants labelled with Alexa Fluor 488 on TM4 (T186C) or TM6 (V307C), showed slightly lower, but comparable binding affinity to WT-NTS1, labelled using the native cysteines ( Supplementary Fig. 3). Although it cannot be excluded that the intracellular position of the relatively large fluorophores in the mutants interferes with the G protein interaction, addition of GTPγS (nonhydrolysable analogue of GTP) lowered the binding affinity by at least one order of magnitude ( Supplementary Fig. 3b,d,f), suggesting G protein does bind specifically to both the WT and mutant receptors. Similar affinity values for the NTS1-G protein interaction have been previously reported; Gα i1 was shown to bind to WT-NTS1 in nanodiscs of various lipid compositions with a K d of ~100-600 nM 54 , and in radioactivity assays detergent-solubilised NTS1 was shown to catalyses GTP exchange at the Gα q β 1 γ 2 heterotrimer with an apparent EC 50 of ~145 nM. 55

Supplementary Note 9 -Ensemble FRET data analysis
For FRET samples (containing both donor and acceptor), and acceptor-only samples emission spectra with excitation at the donor (490 nm) and acceptor (555 nm) wavelength were recorded (over 495-600, and 560-600 nm, respectively). For donor-only samples only the emission spectrum with excitation at the donor wavelength was recorded. A background sample consisting of empty liposomes was also prepared and measured to correct for any background fluorescence and 34 scattering effects in the sample spectra. The FRET data was processed as described by Goddard et al. 56 First, the background spectrum (empty liposomes) was subtracted from all spectra. Spectra were smoothed using Savitzky-Golay filtering (10 nm window, 2nd order polynomial) using OriginPro 8.5 to minimise noise artefacts in the determination of spectral maxima. Then, the FRET spectrum (mixed sample at donor excitation) was corrected for bleedthrough by subtracting the donor-only spectrum, scaled to the donor peak in the FRET spectrum, and the uncorrected FRET ratio (A) was then 15.2% and 81.7% of the maximum extinction coefficients, respectively. The apparent FRET efficiency was further corrected for the donor-to-acceptor ratio (`b) in the FRET samples (see Methods).

Supplementary Note 10 -Estimation of lipid-to-protein ratio for ensemble experiments
Discontinuous sucrose-density gradients (5-35% w/v sucrose in 50 mM Tris-HCl pH 7.4, 50 mM NaCl, 1 mM EDTA, with 5% sucrose steps) were run of liposome-reconstituted NTS1 to estimate the lipid-toprotein ratio after reconstitution. NTS1 proteoliposomes were layered on top of the gradients, which were centrifuged overnight in a swing-out rotor (SW41, Beckman Coultier) at 28,500 rpm (~100,000 g). The sucrose gradient was then fractionated and the presence of reconstituted receptor verified by SDS-PAGE analysis. The position of the proteoliposome band on the gradient was used to estimate the density and thus the lipid-to-protein (L:P) ratio of the samples as described by Goddard et al. 42 The observed density for three separate gradients for the FRET samples, and four for the DEER samples was averaged. The FRET samples ran as a single band, while for the DEER samples a second band corresponding to empty liposomes was observed (as verified by SDS-nPAGE analysis).
The final L:P ratios were substantially lower than the initial ratios used in the reconstitution, with estimated ratios of 840±20 (6,000:1 initial) and 410±10 (1,500:1 initial) for the FRET and DEER samples, respectively (Supplementary Table 6). The origin hereof is unclear, but it has been observed previously for detergent-mediated reconstitution of NTS1 43 , and could in part be due to absorption of lipids by the hydrophobic Bio-Beads used in the reconstitution procedure 57 , and due to not all liposomes incorporating protein (as a band corresponding to empty liposomes was seen on the sucrose gradients of NTS1 DEER samples). Assuming the vesicle radius to be 500 Å (as unilamellar liposomes were created by extrusion through 100 nm filters), and the internal radius as 460 Å (subtracting a bilayer thickness of 40 Å), the total surface area of the liposome bilayer is estimated at 5.8x10 6 Å 2 (including both surfaces of the bilayer). Using the total area ( p ), the number of receptor molecules ( r ) per vesicle can be estimated from p = s s + 2 r r (Eq. S14) and with lipid-to-protein ratio = s r (Eq. S15) it follows that r = p ( s + 2 r ) (Eq. S16) where r and s are the surface area of the receptor and the lipid molecules, which were taken to be 71.1 Å 2 (area of a POPC molecule 58 ) and 1350 Å 2 (protein size estimated from crystal structure ~30x45 Å 5 ), and s is the number of lipids. Thus, the number of receptors per vesicle was estimated to be 90 ± 20 and 180 ± 40, corresponding to a receptor density of 1.6 ± 0.3 x10 3 and 3.1 ± 0.6 x10 3 molecules per μm 2 for the FRET and DEER samples, respectively (Supplementary Table 6). This is similar to receptor densities reported in the literature for cell studies based on heterologous overexpression of the β 2 -adrenergic receptor 59 , but is similarly well above expected physiological densities of ~6000 copies per cell (~2 molecules per μm 2 ). 50 However, the BRET efficiency due to β 2 -adrenergic receptor dimerisation in the cell-based study was constant over the same density range as used here, suggesting that bystander BRET (or FRET) due to crowding is minimal under these conditions. 59 Indeed, a previous FRET study on NTS1 under similar conditions did not see dependence of the apparent FRET efficiency on the lipid-to-protein ratio (at this order of magnitude). 43