Probe dependency in the determination of ligand binding kinetics at a prototypical G protein-coupled receptor

Drug-target binding kinetics are suggested to be important parameters for the prediction of in vivo drug-efficacy. For G protein-coupled receptors (GPCRs), the binding kinetics of ligands are typically determined using association binding experiments in competition with radiolabelled probes, followed by analysis with the widely used competitive binding kinetics theory developed by Motulsky and Mahan. Despite this, the influence of the radioligand binding kinetics on the kinetic parameters derived for the ligands tested is often overlooked. To address this, binding rate constants for a series of histamine H1 receptor (H1R) antagonists were determined using radioligands with either slow (low koff) or fast (high koff) dissociation characteristics. A correlation was observed between the probe-specific datasets for the kinetic binding affinities, association rate constants and dissociation rate constants. However, the magnitude and accuracy of the binding rate constant-values was highly dependent on the used radioligand probe. Further analysis using recently developed fluorescent binding methods corroborates the finding that the Motulsky-Mahan methodology is limited by the employed assay conditions. The presented data suggest that kinetic parameters of GPCR ligands depend largely on the characteristics of the probe used and results should therefore be viewed within the experimental context and limitations of the applied methodology.

The pharmacodynamics of a drug are often related to the half-maximal modulation of target function (IC 50 , EC 50 ), which typically depends on the concentration required to obtain half-maximal target binding (K i , K d ). However, it is increasingly debated whether these pharmacological parameters provides sufficient information to predict the in vivo effectiveness of a ligand [1][2][3][4] . Drug-target binding kinetics have therefore received increased interest in the last decade, and the drug-target residence time has been linked to the in vivo efficacy of a number of important target classes, including the large family of membrane-bound G protein-coupled receptors (GPCRs) 3,[5][6][7][8][9] . Radioligand binding is routinely used to determine ligand binding affinity and kinetics to GPCR targets [10][11][12][13][14][15][16][17][18] . To determine the binding kinetics of unlabeled ligands, the competitive effect on the association binding of a GPCR radioligand is analyzed using the theoretical model derived by Motulsky and Mahan 19 . Despite the wide use of this methodology in the GPCR-field, it is not known to which extent the calculated binding rate constants of unlabeled ligands depend on the binding kinetics of the radiolabeled probe used.
The histamine H 1 receptor (H 1 R) is a prototypical Family A GPCR which is therapeutically targeted by several 2 nd generation antagonists in the treatment of allergic conditions such as allergic rhinitis and urticaria 20 . The therapeutic success of the 2 nd generation H 1 R antagonists is generally attributed to their reduced brain penetration compared to 1 st generation H 1 R antagonists, which results in a decrease of on-target side effects such as sedation. Interestingly, the binding kinetics of several H 1 R antagonists have been investigated using the Motulsky-Mahan methodology 13,[21][22][23][24] and were found to have a long residence time at the H 1 R 25 . In one study the prolonged residence time of levocetirizine was linked to the presence of a carboxylic acid group, which is a frequently occurring chemical moiety for 2 nd generation antihistamines 13 .
The success of the H 1 R as a drug target has resulted in a rich repertoire of antagonists that can bind the receptor, including different radiolabeled versions of commonly studied compounds 20,21,[25][26][27] . Several radioligands ([ 3

H]mepyramine, [ 3 H]levocetirizine and [ 3 H]olopatadine) have previously been characterized for their kinetic binding profile at the H 1 R. Interestingly, [ 3 H]mepyramine and [ 3 H]levocetirizine show similar binding affinities
at the H 1 R, but markedly different binding kinetics 21 . Recently, methodologies which utilize fluorescent ligands in place of radioligands have been introduced to characterize the binding kinetics of GPCR ligands and these newer methods have advantages over radioligand binding in terms of throughput and kinetic resolution 28 . Both bioluminescence (BRET 29 ) and time-resolved (HTRF 30 ) resonance energy transfer techniques have been applied to study binding kinetics at the H 1 R.
Due to the wide range of radioactive and fluorescently labelled ligands available for H 1 R, we used this GPCR as a model system to investigate if the measured binding rate constants of unlabeled ligands are influenced by the binding kinetics of the employed labelled probe. To this end, [ 3 H]mepyramine and [ 3 H]levocetirizine were used to characterize the binding kinetics of a set of unlabeled H 1 R ligands by the Motulsky-Mahan methodology. This was followed by the determination of the binding kinetics of H 1 R ligands via competitive association binding using two different non-radioactive H 1 R binding assays (BRET-based 29 or HTRF based 30 approaches). The k on and K i values, obtained from kinetic and steady-state experiments, respectively, were correlated between the various datasets employing either fluorescent ligands or radioligands as probes. However, it was found that k off -values are in part dependent on the used assay methodology. Therefore, both probe-dependent and assay-dependent factors are important contributors to the accurate determination of binding kinetics of unlabeled ligands.
oxepin-2-yl)acetic acid hydrochloride (150 mg, 0.40 mmol), ethanol (3 mL, 0.40 mmol) and 4-toluenesulfonic acid (23 mg, 0.12 mmol) were stirred at reflux under Dean-Stark conditions for 2 h. Triethylamine (73 µL, 0.52 mmol) was added and the mixture evaporated under reduced pressure, the residue was partitioned between water (5 mL) and ethyl acetate (15 mL). The organic phase was washed with NaHCO 3 (satd. aq, 5 mL), brine (5 mL), dried (MgSO 4 ), filtered and evaporated to give ethyl  (3 mL) was added and the mixture heated to reflux for 2 h. The mixture was purified by preparative HPLC (Waters XBridge Prep C18 OBD column, 5 µ silica, 19 mm diameter, 100 mm length), using decreasingly polar mixtures of water (containing 0.1% TFA) and MeCN as eluents. Fractions containing the desired compound were combined, concentrated under vacuum, adjusted to pH 9 with NaHCO 3 , extracted with DCM (2 × 20 mL), then further purified by flash silica chromatography, elution gradient 0 to 6% NH 3 -MeOH Cell culture. Human embryonic kidney cells transformed with large T antigen (HEK293T) and stably expressing Nluc-H 1 were generated as described elsewhere 29 , as is the transient transfection of these HEK293T cells with the N-terminally HA-tagged H 1 R 31 . Both native and transfected HEK293T cells were maintained in Dulbecco's Modified Eagles medium supplemented with 10% fetal calf serum at 37 °C, 5% CO 2 . Cell pellets of transiently transfected HEK293T cells were prepared and stored at −20 °C until used in radioligand binding experiments, as previously described 31 . Frozen aliquots of TagLite ® cells expressing the Tb-labeled SNAP-H 1 R were acquired from Cisbio.

Radioligand binding assays.
Radioligand binding experiments were performed as described before with minor alterations as summarized below 31 (10-15 nM) was pre-incubated with cell homogenate for 2 h (0.5-3 mg/well), after which a saturating concentration mianserin (10 µM) was added for various incubation times (triplicate binding reactions per time point). Non-specific binding was determined by the presence of mianserin (10 µM) during the pre-incubation step. Dissociation experiments were performed at both 37 °C and 25 °C.
Binding reactions were terminated using a cell harvester (Perkin Elmer) by rapid filtration and wash steps over PEI-coated GF/C filter plates. Filter bound radioligand was then quantified by scintillation counting using Microscint-O and a Wallac Microbeta counter (Perkin Elmer).
HtRF binding assays. HTRF based binding assays were performed as described before 30  NanoBRet binding assays. For NanoBRET assays, HEK293Tcells stably expressing Nluc-H 1 were seeded 24 h before experimentation in white Thermo Scientific 96-well microplates in normal growth medium. For saturation and competition experiments, the medium was removed and replaced with HEPES-buffered saline solution (HBSS; 25 mM HEPES, 10 mM glucose, 146 mM NaCl, 5 mM KCl, 1 mM MgSO 4 , 2 mM sodium pyruvate, 1.3 mM CaCl 2 ) with the required concentration of AV082 and competing ligand. Cells were then incubated for 1 h at 37 °C (no CO 2 ). The Nluc substrate furimazine (Promega) was then added to each well at a final concentration of 10 µM and allowed to equilibrate for 5 min prior to measurement of fluorescence and luminescence. For association kinetic and competitive association kinetic experiments, medium was replaced by HBSS containing furimazine (10 µM) and incubated at room temperature in the dark for 15 min to allow the luminescence signal to reach equilibrium. For association kinetic experiments, the required concentration of AV082 in the presence and absence of doxepin (10 µM) was then added simultaneously. Immediately after, all wells of the microplate were read once per minute for 60 min. For competitive association experiments, AV082 (10 nM) was added simultaneously with the required concentration of unlabeled ligand or doxepin (10 µM) and read once per minute for 60 min. For all experiments fluorescence and luminescence was read sequentially using the PHERAstar FS plate reader (BMG Labtech) at room temperature. Filtered light emissions were measured at 460 nm (80-nm bandpass) and at >610 nm (longpass) and the raw BRET ratio was calculated by dividing the >610-nm emission by the 460-nm emission.
Data analysis. Analysis of saturation binding experiments, competition binding experiments and association binding experiments are fully described elsewhere [29][30][31] . The kinetic experiments were analyzed by GraphPad Prism (GraphPad Software, Inc., La Jolla, CA, USA) using non-linear regression of the data to pharmacological models that assume a one-step binding of the ligand to the receptor.
Competitive association -Motulsky-Mahan model (2019)  www.nature.com/scientificreports www.nature.com/scientificreports/ The baseline signal was subtracted from the total signal obtained in competitive association experiments. In the case of radioligand binding experiments and NanoBRET experiments equation (1) was employed to fit the data. In the case of HTRF experiments the adapted equation (2) is used to account for the observed signal drift (using k drift as a fitting constant). RL* is the baseline corrected signal that corresponds to the level of receptor binding by the labeled ligands. B max is the theoretical RL* in the case that all receptors would be occupied by the labeled ligand. [L*] and [I] stand for the concentrations labeled ligand and unlabeled ligand, respectively. Association rate constants are denoted by k 1 or k 3 and the dissociation rate constants by k 2 or k 4 for labeled ligand or cold ligand respectively. For the kinetics of competitive binding model, binding rate constants of the labeled ligands are required to fit the binding rate constants of the unlabeled ligand. The relative error was calculated for k 3 and k 4 values by dividing the reported error of the non-linear regression (SE) by the fitted mean value.
Dissociation experiments. Non-specific binding was subtracted from the total bound radioligand and the resulting specific radioligand binding over time was analyzed with a one-phase dissociation model (Graphpad prism: 'Dissociation -One phase exponential decay'). When the radioligand was not fully dissociated within the timespan of the experiment, the final steady-state radioligand binding was constrained to baseline during analysis.

Results
Characterization of radioligand probes. To explore how the binding kinetics of a radioligand affects the Motulsky-Mahan analysis of radioligand association in competition with unlabeled GPCR ligands, three different radioligands and two fluorescence-based probes for the H 1 R were investigated in this study. In addition to the widely used and commercially available [ 3 H]mepyramine (fast off rate), radiolabeled versions of the 2 nd generation antihistamine radioligands olopatadine and levocetirizine (slow off rate) 21,33 were synthesized as described in the method section and structures are depicted in Fig. 2  www.nature.com/scientificreports www.nature.com/scientificreports/ binding rate constants (pK d,kin = k off /k on ) were in good agreement with equilibrium dissociation constants determined by saturation binding experiments (pK d ) ( Table 1).
The k off values of the radioligand probes were verified by radioligand displacement experiments, in which pre-bound radioligand is forced to dissociate by a high concentration of the unlabeled competitor mianserin (Supplementary Fig. 1 Fig. 1c). To accelerate the association and dissociation of the radioligands and, thereby obtain a more robust quantification of the binding kinetics for the three radioligands, experiments were also performed at 37 °C ( Supplementary  Fig. 1 Table 2). However, even at 37 °C there was still limited dissociation of [ 3 H]olopatadine within the 6 h time span. Interestingly, at 37 °C the association of [ 3 H]olopatadine was not described well by a mono-exponential increase in binding as expected for a one-step binding mechanism. Consequently, [ 3 H] olopatadine was therefore excluded as probe, as the Motulsky-Mahan model that is used to describe competitive association ligand binding is based a one-step binding mechanism.
Quantifying the binding characteristics of unlabeled H1R antagonist. A chemically diverse set of unlabeled H 1 R ligands (structures are depicted in Supplementary Fig. 2), including reference molecules with known differences in their H 1 R binding kinetics, was selected for characterization of their H 1 R binding kinetics using either [ 3 H]mepyramine or [ 3 H]levocetirizine 13,23,31 . To guide the design of competitive association experiments, binding affinities (K i ) of the unlabeled ligands were first determined by equilibrium competition binding.  www.nature.com/scientificreports www.nature.com/scientificreports/ Cell homogenates were therefore co-incubated with [ 3 H]mepyramine and increasing concentrations of the unlabeled ligands (Supplementary Fig. 3). Binding affinities (K i ) for H 1 R were calculated from the determined IC 50 values using the Cheng-Prusoff equation 34 and are depicted in Supplementary Table 3.
The binding rate constants of the unlabeled ligands at the H 1 R were determined by competitive association binding experiments, in which H 1 R binding of the radioligand probes is quantified over time in the absence or presence of unlabeled ligands at three different concentrations. Concentrations of unlabeled ligand were varied ten-fold between the lowest and highest used concentration which was within an equipotent range of 1-100 times the respective K i of the ligands at the H 1 R. From the resulting radioligand association binding curves, the binding rate constants of unlabeled ligands can be determined by Motulsky-Mahan analysis (Fig. 4, Table 2) 19 . As each time point requires a new binding reaction, the kinetic resolution for quantifying radioligand binding is limited  Table 2 and Supplementary Table 2.    Fig. 4. a pK d,kin = k off /k on. b Values were reported before except for (S)fexofenadine, (R) fexofenadine and (S)cetirizine 23 . c RT = residence time = 1/k off.
www.nature.com/scientificreports www.nature.com/scientificreports/ and dependent on the number of parallel incubations. Therefore, incubation times were adjusted for the individual radioligands to best capture their kinetic profile. For the rapidly binding radioligand [ 3 H]mepyramine a relatively short 80 min incubation time was chosen (Fig. 4a-c), whereas a 360 min incubation time was employed for the slowly binding probe [ 3 H]levocetirizine (Fig. 4d-f). The association of the radiolabeled probes to the H 1 R in the presence and absence of three competing unlabeled ligands with (from left to right) fast, intermediate, and slow binding kinetics, is depicted in Fig. 4 and covers the diversity in binding kinetics observed within the full set of unlabeled ligands. Binding of [ 3 H]mepyramine in the presence of unlabeled mepyramine leads to a gradual increase in radioligand binding until binding equilibrium has been established after approximately 10 min (Fig. 4a). In the presence of doxepin and levocetirizine there is first a transient overshoot in the binding of [ 3 H] mepyramine which results from the relatively slow dissociation (lower k off value) of both unlabeled ligands compared to the rapid binding of [ 3 H]mepyramine (Fig. 4b,c). Conversely, since [ 3 H]levocetirizine binds much slower than [ 3 H]mepyramine (Fig. 3d,e), no overshoot pattern is observed for [ 3 H]levocetirizine binding to the H 1 R in the presence of the same three unlabeled ligands (Fig. 4d-f). The selected time points and length of incubation depended on the employed radioligand (Fig. 4), which might also affect the resulting binding rate constants in competitive association experiments. Probe dependent differences in binding characteristics. The observed association binding data of both radioligands (Fig. 4a-f) agreed well with the fitted non-linear regression lines based on the Motulsky-Mahan model from which binding rate constants (k on and k off ) of the unlabeled ligands could be calculated (Table 2). Thus, two datasets were obtained with the binding rate constants of unlabeled ligands that were determined by using either [ 3 H]mepyramine or [ 3 H]levocetirizine as competitive probe. The measured binding rate constants correlated well between datasets as is depicted in Fig. 5a (k on values: R 2 = 0.80, P < 0.001) and in Fig. 5b (k off values: R 2 = 0.77, P = 0.002). However, the regression lines (solid lines) deviate from unity (dashed line) and some unlabeled ligands showed larger differences in binding kinetics between the two datasets than others. For example, more than 10-fold differences in the k on and k off values were observed for VUF14454 and VUF14544 between both datasets (with the K d,kin , calculated as the k off /k on , deviating less than 2-fold). The differences in the k on values between datasets were largest for ligands with a relatively high k off value (Table 2). Additionally, a probe-dependent difference for the range in k off values was observed, with [ 3 H]mepyramine discriminating unlabeled ligands over a range with higher k off -values (Fig. 5b, logk off −2.2 and 0.1) and [ 3 H]levocetirizine discriminating unlabeled ligands over a range with lower k off -values (Fig. 5b, logk off −3.2 and −0.7). These data suggest that the [ 3 H]mepyramine-based assay better distinguishes fast dissociating unlabeled ligands(high k off values), whereas the [ 3 H]levocetirizine-based assay better distinguishes slow dissociating unlabeled ligands (low k off values). From the determined binding rate constants, the binding affinity (pK d,kin = k off /k on ) and the residence time (RT = 1/k off ), a proposed metric to relate binding kinetics to in vivo drug efficacy 3,5-9 , were calculated ( Table 2). The pK d,kin values correspond well with the respective pK i values (Fig. 5c), with a good correlation for both the [ 3 H]mepyramine-dataset (R 2 = 0.93, P < 0.0001) and [ 3 H]levocetirizine-dataset (R 2 = 0.87, P < 0.0001). Furthermore, the pK d,kin values correlate nicely between the probe specific datasets as well (R 2 = 0.87, P < 0.0001, data not shown). Since the K d,kin value is directly derived from the binding rate constants (k off /k on ), these correlations highlight the reciprocal changes in k on -and k off values in both binding assays and suggests that the ratio between the binding rate constants (e.g., reflected by the steady state level of radioligand binding, Fig. 4) is more robustly determined by the Motulsky-Mahan model than the binding rate constants themselves.
To investigate the accuracy of the obtained k on and k off values, the relative errors of the fitted binding rate constants were calculated for each individual experiment for both data sets. The relative errors of the k on and the k off values were plotted against the corresponding mean k off value for each individual competitive association www.nature.com/scientificreports www.nature.com/scientificreports/ experiment, as depicted in Fig. 6. It is shown that the relative error on the determined binding rate constants depends on the fitted mean k off values of unlabeled ligands at the H 1 R (Fig. 6). For both binding-rate-constants a decrease in accuracy, i.e. an increase in the relative error, is observed for unlabeled ligands with high mean k off -values at the H 1 R (Fig. 6a,b) as is apparent for, e.g., −logk off values > −1. Additionally, an increase in the relative error on the k off -values (Fig. 6b), but not on the k on -values (Fig. 6a), is observed for unlabeled ligands with low mean k off -values as is apparent for, e.g., −logk off values < −2. Interestingly, Fig. 6 clearly shows a probe-dependent accuracy for the determination of the k on and the k off -values of unlabeled ligands. The k on value for H 1 R binding is generally more accurate when determined in a [ 3 H]mepyramine binding experiment (blue curve, Fig. 6a), whereas the k off value is more accurate for the [ 3 H]levocetirizine dataset in the case of unlabeled ligands with a logk off < −2 and less accurate for ligands with a logk off > −2 (red curve, Fig. 6b).

Cross-comparison between fluorescent-ligand and radioligand binding experiments. Recently,
promising advances using resonance energy transfer techniques have been made in the use of fluorescent ligands as probes to characterize the binding kinetics of unlabeled ligands to GPCRs such as the H 1 R 29,30 . Since the binding of a fluorescent ligand can be measured continuously using a HTRF or NanoBRET-based approach, the kinetic resolution and throughput of such assays are much higher than conventional radioligand binding kinetics experiments. The availability of these assays for H 1 R, allows them to be compared to traditional radioligand binding assays for measuring the binding kinetics of unlabeled ligands. We initially sought to characterize the binding kinetics of the fluorescent probes in both the NanoBRET and HTRF assays. For the NanoBRET binding assay a BODIPY630/650-labeled mepyramine analog which emits in the red range (AV082; formally described as compound 10 in Stoddart et al. 29 and depicted in Fig. 2) is used as fluorescent probe and is used with HEK293T cells expressing H 1 R tagged on the N-terminus with NanoLuc which are grown in a mono-layer. For the HTRF binding assay, a commercially available fluorescent analog of mepyramine (structure unknown) which emits light in the green range (Gmep) was employed alongside TagLite ® cells expressing an N-terminally SNAP-tagged H 1 R and labelled with terbium cryptate. Characterization of both fluorescent probes was as previously described (Table 1) 29,30 . Although the relative large size of the attached fluorophore is likely to affect the binding properties of the unlabeled ligand 29 , the k off value for the binding of mepyramine-analogs AV082 and Gmep to the H 1 R resembled those of [ 3 H]mepyramine (<2-fold difference), albeit with differences in their k on values (2-100 fold) ( Table 1).
Both non-radioactive assays were used to characterize the H 1 R binding properties of the set of unlabeled ligands depicted in Supplementary Fig. 2. Equilibrium competition binding experiments were performed to obtain pK i values of the unlabeled ligands as described before 29,30 (Supplementary Fig. 3, Supplementary Table 3) and ligands were further characterized in kinetic competition association experiments (Fig. 7, Supplementary Table 4). For the binding of AV082 measured by NanoBRET, in line with the competitive association experiments using [ 3 H]mepyramine (Fig. 7a-c), an overshoot was apparent when co-incubated with doxepin and levocetirizine but not with mepyramine. Kinetic binding rate constants were determined by fitting the NanoBRET signal over time to the Motulsky-Mahan model.
For the competitive association experiments with Gmep ( Fig. 7d-f), a signal drift was observed in the absence of unlabeled ligand. To allow robust fitting of the HTRF signal (including the signal drift), an additional one-phase decay function was incorporated into the Motulsky-Mahan model, as described before 30 . Despite the Figure 6. Accuracy of the measured binding rate constants depend on the fitted mean k off of unlabeled ligands at the H 1 R at 25 °C. The accuracy in which the Motulsky-Mahan model fitted the k on (a) and k off (b) by nonlinear regression was examined for the different experimental conditions that were employed in this study. To compare the accuracy of the fitted mean k on and k off values over a broad range, the relative magnitude of the error (SE), as derived from non-linear regression, was calculated for each individual replicate experiment and pooled for all ligands. The relative error was calculated by normalizing the SE by the mean (relative error = SE/ mean). Subsequently, the relative error for the k on and k off were plotted against the corresponding mean k off determined from the same competitive association curve. www.nature.com/scientificreports www.nature.com/scientificreports/ signal drift, an overshoot in Gmep binding is apparent in competition association experiments with unlabeled ligands with slow binding kinetics. After an initial rapid increase of Gmep binding, the HTRF-signal decreases much faster when co-incubated with 25 nM or 250 nM levocetirizine than in the absence of any competitor (Fig. 7f). In contrast, in the presence of mepyramine (Fig. 7d), the HTRF-signal never decreased faster than was observed for Gmep in the absence of unlabeled ligand.
A comparison of the binding constants that were obtained with [ 3 H]mepyramine binding (x-axis) and the two fluorescent binding assays (y-axis) are depicted in Fig. 8a-c and Supplementary Table 3. Interestingly, a good correlation was observed between assays for the relative binding affinities (pK i ) ( Fig. 8a; (AV082: R 2 = 0.88, P < 0.0001; Gmep: R 2 = 0.94, P < 0.0001) and logk on values ( Fig. 8b; AV082: R 2 = 0.84, P < 0.0001; Gmep: R 2 = 0.92, P < 0.0001). Although, the use of AV082 in probe-displacement experiments resulted additionally in a log-unit lower pK i -values compared to values obtained in the orthogonal assays (Fig. 8a). Moreover, the  www.nature.com/scientificreports www.nature.com/scientificreports/ logk off values determined with Gmep as probe (HTRF assay) also correlated with those determined using [ 3 H] mepyramine as probe ( Fig. 8c; R 2 = 0.96, P < 0.0001). However, when employing AV082 (NanoBRET assay) in competitive association experiments, the relative differences in the k off values between the unlabeled ligands differ from those observed in the orthogonal assays (Fig. 8c). Since both the K i -values and k on values correlate between orthogonal assays, the k off can be calculated (K i × k on ) for the NanoBRET assay in order to estimate the relative differences in the k off between unlabeled ligands. As expected, these calculated values correlate better with the observed values in the orthogonal assays ( Supplementary Fig. 4).

Discussion
In GPCR drug discovery, drug-receptor binding kinetics are often quantified using competition association experiments with a radioligand probe. Despite the increased use of this methodology, it is unclear whether the kinetic properties of the probe influence the obtained kinetic binding parameters of unlabeled ligands. Therefore, in this study we employed two radioligand probes, that differ in their H 1 R binding kinetics ([ 3 H]mepyramine and [ 3 H]levocetirizine), to measure the binding rate constants of a diverse set of unlabeled antagonists. The analysis shows that the k on and k off values obtained with each probe correlate between both probe-specific datasets (Fig. 5a,b). However, large differences in the binding rate constants are observed for some compounds, e.g., VUF14454 and VUF14544. Moreover, although more than 10-fold differences in the k off are observed among (S)-cetirizine, triprolidine, mepyramine, VUF14454, VUF14493 and VUF14544 when using [ 3 H]mepyramine as probe, no difference is observed when the k off are measured for the same set of unlabeled ligands with [ 3 H] levocetirizine as probe. The comparison of these two datasets therefore suggests a probe-dependent limit to discriminate binding rate constants of unlabeled ligands. A related probe-dependent effect is apparent in the relative errors of the determined k on (Fig. 6a) and k off values (Fig. 6b) of the unlabeled ligands. In our competitive binding experiments, only the binding of the probe can be directly observed. When unlabeled ligands reach a binding equilibrium rapidly, before noticeable binding of the probe, binding kinetics of these unlabeled ligands is masked by the slow onset of probe binding at each time point. Since the onset of a receptor-binding equilibrium is faster with increasing k off of the respective ligands 19 , it seems logical that at some point, when the unlabeled ligands have an increasingly high k off compared to that of the probe, kinetic binding of the unlabeled ligands can no longer be distinguished. This is in line with the observation that the relative error in the fitted binding rate constants increases when the corresponding mean k off value (i.e. from the same competitive association curve) increases (Fig. 6). Moreover, a pronounced increase in the relative error is observed when the unlabeled ligands dissociate faster than the respective radioligand (k off unlabeled > k off radioligand, see arrows Fig. 6a,b). This implies that [ 3 H] mepyramine, which has a 100-fold higher k off than [ 3 H]levocetirizine, is better suited to discriminate the binding kinetics of fast dissociating (high k off ) unlabeled ligands at the H 1 R. Moreover, in our dataset the k on (Fig. 7a) and k off (Fig. 7b) are fitted with a higher accuracy using [ 3 H]mepyramine as probe for unlabeled ligands with a residence time less than 100 min (log k off > −2).
In contrast to the determined k on -values, which show a growing inaccuracy upon increases of the linked k off -value (Fig. 6a), the k off -values are increasingly inaccurate at the lower end of the spectrum as well, i.e. both with low k off as well as high k off values (Fig. 6b). Interestingly, a probe dependent difference in inaccuracy in these determinations is again apparent. However, for slowly binding unlabeled ligands (residence time of more than 100 min; fitted log k off < −2) a moderately better accuracy is obtained when using [ 3 H]levocetirizine (and not [ 3 H]mepyramine) as probe in competition association experiments (Fig. 6b).
Taken together, analysis of the competitive association radioligand binding data show probe-dependent differences in the measured binding rate constants of unlabeled ligands, which result (at least to some extent) from the accuracy with which these binding rate constants can be fitted to the competitive association curves of the radioligand probes. Considering that the accuracy of the measured binding rate constants decreased most extensively for unlabeled ligands that bind the receptor faster than the probe (k off unlabeled > k off radioligand), it is recommended to use a fast binding probe for the GPCR of interest (like [ 3 H]mepyramine for the H 1 R).
To avoid that the kinetics of the probe will mask the binding kinetics of the unlabeled ligands, the k off of the probe should ideally be higher than that of the unlabeled ligands. In radioligand binding experiments, the bound radioligand should not dissociate during the wash steps. A minimum residence time is therefore required and the k off should probably not go beyond 1 min −1 (at room temperature). For probes in fluorescent binding experiments, which do not require wash steps, probes could be designed to have a very high k off . There are not yet sufficient structure-kinetics-relationships available that allow clear cut optimization of the k off . However, reducing the binding affinity sufficiently will in most cases increase the k off 35 . Introducing subtle steric clashes in the binding pocket 22 might therefore be a way to fine-tune the k off of fluorescent probes.
Comparing the binding kinetics of unlabeled H 1 R antagonists determined in experiments using the fluorescently labelled H 1 R probes AV082 and Gmep with those obtained using [ 3 H]mepyramine, again reveals that the determined pK i values and the binding rate constants are highly correlated (Fig. 8). This might be explained (partially) by the fact that all three H 1 R probes have quite similar k off values (Table 1). In fact, the correlations for the measured binding rate constants were stronger when comparing the different assays (Fig. 8a,b) than when comparing the datasets obtained with the different radioligands (Fig. 6a,b). The notable exception were the k off -values determined with AV082 competition association binding experiments (measured by NanoBRET), which deviated only slightly among unlabeled ligands, suggesting again a probe-dependent limitation for discriminating the binding kinetics of unlabeled ligands. However, this effect is most likely not explained by the binding kinetics of the H 1 R probe as the binding rate constants of AV082 and [ 3 H]mepyramine differed only <3-fold. Assay-dependent differences might therefore also underlie the observed disconnect between k off values. It has been described that the measurement of drug-target binding kinetics can be additionally convoluted in pharmacological assays by rebinding 36,37 , the mechanism of ligand binding 38,39 , and the differences in local ligand concentration 40 , all of which cannot be accounted for during this analysis. Interestingly, in silico docking suggests that the hydrophobic fluorophore of large fluorescent ligands, like AV082, can protrude out of the GPCR 7TM pocket and might incorporate in the membrane 29 , which is distinct from the binding mode of [ 3 H]mepyramine, which is deeply buried within the transmembrane region of the H 1 R 41-43 . One can speculate that the simple one-step binding mechanism that is the conceptual basis of the Motulsky-Mahan model for probe binding to the H 1 R, is not a valid approximation in the case of AV082. Besides the probe, the extracellular N-terminal tag of the employed H 1 R was different between the NanoBRET-based detection of AV082 binding and the HTRF-based detection of Gmep binding to the H 1 R protein. Moreover, since AV082 was the only probe that was employed in binding experiments on adherent living cells, the extracellular environment might shape a unique exosite that promotes ligand-rebinding. For example, the epithelial layer of human lungs in organ bath perfusion experiments proved crucial for the insurmountable antagonism of the H 1 R imposed by azelastine 44 . Since the insurmountable antagonism depends on the length of the receptor-occupancy by azelastine 23,44,45 , the extracellular environment may in some cases contribute to the observed ligand binding kinetics.
In conclusion, the Motulsky-Mahan approach is a useful approach to quantify the binding rate constants of unlabeled GPCR ligands, especially with the high throughput and kinetic resolution that can be obtained with fluorescent ligand binding experiments. However, it should be taken into account that probe-dependent and assay-dependent factors can have an impact on the measured binding kinetics of the unlabeled ligands. It is recommended to use orthogonal approaches to confirm the binding kinetics of a set of reference compounds, for example, by studying the kinetics by which ligands functionally modulate GPCR activity. Previously, we found the ligand binding kinetics at the H 1 R of a set of H 1 R antagonists to correlate well with their kinetic effects on functional H 1 R responses 23,31 . Furthermore, the use of benchmark ligands will also allow comparison between different methodologies and will allow the selection of the best method to reach highest confidence for discriminating the target-binding kinetics of unlabeled ligands by the Motulsky-Mahan method. Considering that the Motulsky-Mahan model is by far the most frequently used way to derive the residence time of GPCR ligands, this study provides important considerations for the study of drug-target binding kinetics at GPCRs.

Data Availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.