A kinetic method for measuring agonist efficacy and ligand bias using high resolution biosensors and a kinetic data analysis framework

Abstract

The kinetics/dynamics of signaling are of increasing value for G-protein-coupled receptor therapeutic development, including spatiotemporal signaling and the kinetic context of biased agonism. Effective application of signaling kinetics to developing new therapeutics requires reliable kinetic assays and an analysis framework to extract kinetic pharmacological parameters. Here we describe a platform for measuring arrestin recruitment kinetics to GPCRs using a high quantum yield, genetically encoded fluorescent biosensor, and a data analysis framework to quantify the recruitment kinetics. The sensor enabled high temporal resolution measurement of arrestin recruitment to the angiotensin AT1 and vasopressin V2 receptors. The analysis quantified the initial rate of arrestin recruitment (kτ), a biologically-meaningful kinetic drug efficacy parameter, by fitting time course data using routine curve-fitting methods. Biased agonism was assessed by comparing kτ values for arrestin recruitment with those for Gq signaling via the AT1 receptor. The kτ ratio values were in good agreement with bias estimates from existing methods. This platform potentially improves and simplifies assessment of biased agonism because the same assay modality is used to compare pathways (potentially in the same cells), the analysis method is parsimonious and intuitive, and kinetic context is factored into the bias measurement.

Introduction

The kinetics/dynamics of G-protein-coupled receptor (GPCR) signaling is of increasing interest in elaborating the biology and therapeutic potential of these receptors1,2,3. The time frame of GPCR signal transduction is dependent on the signaling pathway, regulation of signaling mechanism, and location of the receptor in the cell (spatiotemporal signaling). Temporal dynamics of signaling are being elucidated and applied to develop new therapeutics. For example, the parathyroid hormone 1 (PTH1) receptor can signal persistently over time after partitioning into the endosomal compartment4. This effect was ligand dependent; PTH produced persistent signaling whereas PTH-related protein did not4. This behavior is potentially involved in the therapeutic mode of action; continuous administration of PTH1 receptor agonists results in bone loss, whereas intermittent administration results in net bone formation5. This kinetic effect was exploited in the development of new bone anabolic agents for treating osteoporosis6. Persistent signaling is potentially beneficial for other GPCR therapeutics1, for example sphingosine 1-phosphate receptor-1 agonists for treatment of multiple sclerosis7.

Of potential concern, the kinetics of signaling can affect measurement of biased agonism, by affecting classical measurements of agonist activity (potency and efficacy)3,8. Biased agonism is the capacity of a ligand to selectively activate one or more of multiple signaling pathways transduced by the GPCR9. This concept is of considerable current interest in the development of next-generation GPCR therapeutics because it enables selective targeting towards beneficial pathways and away from potentially deleterious ones10,11,12. For a series of dopamine receptor ligands, it was shown that the extent of bias was dependent on the time point at which the signaling responses were measured8. This complicates the interpretation of bias and its translation to in vivo efficacy because it isn’t straightforward to select the most appropriate time point for establishing structure-activity relationships and for predicting in vivo efficacy from in vitro bias measurements. Differences in assay timing might contribute to discrepancies of bias estimates reported in the literature. For example, aripiprazole has been reported to be an arrestin-biased ligand but the efficacy varies from 10 to 100% and the time point from 5 minutes to 20 hours13,14,15,16,17.

Quantifying the kinetics of signaling with useful drug parameters would aid the development of kinetically-optimized molecules, tuned, for example, to the optimum duration of signaling, timeframe of desensitization, and residence period in signaling compartments. This requires appropriately optimized kinetic assays and a data analysis platform for extracting drug parameter values from time course data. Biosensor assays have enabled high-throughput kinetic measurement of GPCR signal transduction because the same plate/well can be measured repeatedly over time18,19,20. The signaling molecule of interest interacts with an engineered protein, changing its optical properties, for example fluorescence intensity, which is detected in specialized plate readers. Previously we and others have developed genetically-encoded biosensors incorporating fluorescent proteins such as mNeonGreen that provide high-resolution kinetic data for G-protein-mediated signals (for example, cAMP21, diacylglycerol21 (DAG), and Ca2+22). Regarding the data analysis, drug activity metrics are required which quantify the kinetics in terms that can be applied in establishing structure-activity relationships23. We recently developed a data analysis framework for G-protein and downstream signaling that quantifies kinetics in terms of the initial rate of signaling24,25. This rate, analogous to the initial rate of enzyme activity, is the rate of signaling before it is impacted by regulation of signaling mechanisms such as receptor desensitization and signal decay25. This parameter, termed kτ, provides a biologically meaningful kinetic metric of ligand efficacy that has been applied to quantify ligand activity for G-protein activation and second-messenger generation24,25.

The goal of this study was to optimize and integrate the biosensor modality and the data analysis framework to create a unified platform suitable for robustly measuring and quantifying signaling kinetics and biased agonism for numerous GPCR pathways. This first required extending the framework described above to arrestin recruitment, since our biosensor and analysis technologies were developed only for G-protein signaling. Arrestin recruitment is an alternative pathway by which GPCRs modulate cellular activity26,27 and arrestin recruitment has been implicated in potentially beneficial and deleterious physiological processes. For example, arrestin recruitment by the angiotensin AT1 receptor improves the cardiac performance of ligands targeting the receptor in animal models28,29,30,31, whereas arrestin recruitment by the μ opioid receptor has been implicated in opioid side effects, including tolerance, reward and respiratory depression32,33,34,35. This has stimulated the development of ligands biased towards or away from the arrestin pathway9,11,36. Here we describe a novel arrestin biosensor, utilizing mNeonGreen, suitable for generating time course data with high enough temporal resolution for the arrestin recruitment kinetics to be measured accurately. We then extended the data analysis framework to incorporate arrestin recruitment to the receptor. Finally, we applied this unified platform to directly compare arrestin recruitment and G-protein signaling via the AT1 receptor, using near-identical experimental conditions and the same conceptual kinetic data analysis framework. This work demonstrated a novel approach for quantifying biased agonism in kinetic terms using a unified assay modality.

Results

In this study an experimental and analytical platform was developed to quantify the kinetics of arrestin recruitment in such a way as to enable direct comparison with the kinetics of downstream signaling. A genetically-encoded biosensor that converts the change in arrestin conformation upon receptor interaction to a change in fluorescence intensity made it possible to collect detailed recordings of the kinetics of arrestin recruitment, i.e. a large number of reads at closely-spaced time points. Robust arrestin responses were obtained for the angiotensin AT1 and vasopressin V2 receptors. The time course data, i.e. the change in fluorescence intensity over time, was then analyzed using a novel pharmacological analysis. This analysis quantifies the initial rate of arrestin recruitment to the receptor. The analysis was applied to responses activated by several agonists of the AT1 angiotensin receptor. Biased agonism was then assessed; the initial rate of arrestin recruitment was compared with the initial rate of downstream signaling measured using the same biosensor modality (DAG generation and Ca2+ mobilization). The resulting bias ratios were in good agreement with values obtained using conventional methods, validating the method.

Biosensor of arrestin-receptor interaction

Accurately quantifying signaling over time with an optical biosensor requires certain physical criteria. GPCR signaling is often rapid, for example the rise phase occurs within a few seconds for Ca2+ mobilization and within a few minutes for cAMP generation and arrestin recruitment. Consequently, in order to obtain sufficient data points, the read time, the time required to obtain sufficient signal, needs to be short, ideally <10 seconds. Second, a large number of time points are required to accurately define the curve shape and reliably fit the relevant equations to the time course data. This requires minimal photobleaching of the sensor. These criteria can be met with direct fluorescence sensors, owing to the high quantum yield21,22. This property enables short read times to be used because the signal per unit time is high. It also minimizes photobleaching because a short excitation time can be used.

We and others have developed fluorescent biosensors in which intrinsically fluorescent protein sensors have been incorporated. (Three examples used in this study are R-GECO22 for Ca2+, Downward DAG for DAG and cADDis for cAMP21). The protein sensors have been engineered to be conformationally-sensitive, such that interaction with the signaling molecule of interest changes the optical properties, enabling the interaction to be detected as a change of fluorescence intensity. Since the proteins are intrinsically fluorescent, no chemical tagging or substrate addition is necessary to generate the optical signal. Here this approach was used to develop a biosensor of receptor-arrestin interaction (Fig. 1a). Arrestin-3 (also known as β-arrestin2) and the fluorescent protein mNeonGreen37,38 were fused together such that the entire arrestin molecule was inserted into the critical seventh stave of mNeonGreen (see Methods).

Agonist application resulted in a robust change of fluorescence intensity of the arrestin sensor, for the angiotensin AT1 receptor (Fig. 1b) and V2 vasopressin receptor (Fig. 1e). The signal was normalized to baseline; specifically it was quantified as the fluorescence after agonist addition divided by that of the baseline signal before addition (ΔF/F). The robustness of the signal over time is a key determinant of utility for kinetic application of the sensor. Consequently, statistical analysis was conducted for the ΔF/F value at all time points measured. The angiotensin data was used for this purpose. The coefficient of variance (% CV) of the technical replicates (duplicates) is shown in Supplementary Fig. S1, for multiple concentrations of AngII spanning the effective concentration range. The % CV was less than 7% for all data points, and less than 5% in 98% of cases. This result indicates the signal is sufficiently robust to quantify the signal over the entire time course across the effective concentration range. Not surprisingly, the error was greatest when the signal was changing the most over time, i.e. on the linear part of the curve (Supplementary Fig. S1). Next we assessed the Z′ value over time to determine the ideal timeframe for a single time point measurement (Fig. 1c), the paradigm typically used for high throughput screening (HTS). Z′ is lowest on the rise phase of the time course, when the signal is changing the most over time and the magnitude of the signal is low relative to the plateau phase (Fig. 1c). At the plateau, the Z′ value was high and consistent over time. These findings indicate a time point at the plateau phase is ideal for HTS and that the signal for the AT1 receptor is potentially robust enough for HTS.

We tested whether the arrestin sensor could be multiplexed with sensors of G-protein signaling, i.e. that the signals could be detected in the same well. The green arrestin sensor could be combined with the red diacylglycerol sensor (Fig. 1d, AT1 receptor) and red cAMP sensor (Fig. 1e, V2 receptor). This capability allows direct comparison of the kinetics of arrestin recruitment and G-protein signaling. For both the AT1 receptor and V2 receptor, the recruitment of arrestin occurs within the timeframe of the attenuation of the G-protein-mediated signal (decline of the DAG signal (Fig. 1d) and approach to plateau of cAMP concentration (Fig. 1e)). This finding is consistent with arrestin recruitment regulating (attenuating) G-protein signaling via these receptors.

Some receptors interact more transiently with arrestin than the AT1 and V2 receptors, for example the β2-adrenoceptor39. The interaction of the arrestin sensor with the β2-adrenoceptor was tested, in response to a maximally-stimulating concentration of isoproterenol (10 μM). The magnitude of the response was smaller (Supplementary Fig. S2); the ΔF/F value was reduced to 0.84 in this experiment, compared to a reduction to 0.56 for the AT1 receptor in the experiment in Fig. 1b. This finding is consistent with weaker coupling of the arrestin sensor with the β2-adrenoceptor compared with AT1 and V2 receptors.

Time course and concentration-dependence of arrestin recruitment by the angiotensin AT1 receptor

We next characterized the arrestin recruitment kinetics of the AT1 receptor, examining the shape of the time course and the concentration-response characteristics. For the full agonist and endogenous ligand AngII, arrestin was initially recruited rapidly at a maximally-effective concentration (32 μM), starting within 1 minute of application (Fig. 2a). The recruitment leveled off then reached a plateau within five minutes (Fig. 2a). The plateau was stable for the remainder of the measurement period (for example, 20 min, Fig. 2a), indicating a steady-state had been obtained. By visual inspection, this profile appeared to conform to the familiar association exponential curve. The data were fit to this equation using Prism 8.0:

$$y=Plateau\times (1-{e}^{-{k}_{obs}.t})$$

where Plateau is the response at the asymptote (at infinite time) and kobs the rate constant. Data were fit well by this equation (R2 correlation coefficient > 0.99 in all cases). The t1/2, calculated from kobs (t1/2 = 0.693/kobs) was 45 ± 3 sec at 32 μM (Supplementary Table S1). For lower, sub maximally-effective concentrations, e.g. 10 nM, the initial recruitment was slower, manifest as a shallower initial rise, and the plateau was lower (Fig. 2a). Data for lower concentrations were also fit well by the association exponential equation (Fig. 2a, R2 > 0.95 in all cases). The concentration-dependence of the Plateau and kobs parameter values is shown in Supplementary Fig. S3 - both Plateau and kobs increased as the AngII concentration was increased.

A known partial agonist for arrestin recruitment was then tested, [sarcosine1, Ile4, Ile8]AngII (SII)40. Superficially, visual inspection of the plots suggests little difference between SII and AngII at the maximally-effective concentration of 32 μM (Fig. 2a,b). However, the ability to accurately quantify the kinetics of the response indicated an appreciable difference in the rate of arrestin recruitment; the t1/2 of SII calculated from kobs was 84 ± 21 sec, approximately twice that of AngII (45 sec) (Supplementary Table S1). This indicated SII recruits arrestin more slowly than AngII, providing a kinetic perspective on its partial agonist activity. By contrast, at the plateau, there was no appreciable difference between SII and AngII (compare 32 μM data in Fig. 2a,b, Supplementary Table S1). This finding indicates that if arrestin recruitment was measured at a single time point on the plateau, the difference of activity between the peptides would not have been detected; SII would have appeared to be a full agonist. Only by measuring the rate of arrestin recruitment was the partial agonist activity revealed.

Pharmacological analysis model of receptor-arrestin interaction kinetics

Applying kinetics to development of new ligands in pharmacological discovery requires the extraction of simple drug parameters from time course data. The time course of arrestin recruitment conformed to an association exponential curve for the AT1 receptor (see above) and the V2 receptor (Fig. 1e). A number of empirical drug parameters can be obtained from these data, such as the t1/2, plateau, AUC, or the signal at a single time point. An alternative and biologically meaningful parameter is the initial rate of signaling, analogous to the initial rate of enzyme activity24,25. We recently discovered this parameter can be easily obtainable from signaling kinetic data using a kinetic pharmacological framework of GPCR signaling (Fig. 3)25. This approach is based on the principles of enzyme kinetic data analysis. An enzyme converts a substrate into a product (Fig. 3a). By analogy, a GPCR converts a precursor of the signal into the signal (Fig. 3b), for example, conversion of inactive G-protein to active G-protein. For enzymes, the initial rate of activity is the rate before it becomes limited by regulation mechanisms and depletion of the substrate. By analogy, the initial rate of GPCR signaling is the rate before signaling regulation mechanisms limit the signal (Fig. 3c)25. The canonical short-term regulation of signaling mechanisms are receptor desensitization, and degradation of the signal (e.g. hydrolysis of GTP bound to G-protein or clearance of cytoplasmic Ca2+). The response can also become limited by depletion of the precursor of the signal, e.g. depletion of Ca2+ from intracellular stores. The initial rate is defined by the law of mass action, being a function of the interacting components and a microscopic rate constant. For enzymes the initial rate is [E]TOT[S]TOTkCAT (product of total enzyme, total substrate, and the catalytic rate constant). By analogy, for GPCR signaling, the initial rate is EP(TOT)[R]TOTkE, where EP(TOT) is the total precursor, [R]TOT the total receptor concentration, and kE a rate constant termed the transduction rate constant24,25. This is the initial rate of signaling by the ligand-bound receptor and is termed kτ. This parameter can be easily estimated by curve fitting25.

Here we developed a pharmacological analysis that can be applied to measure the initial rate of arrestin recruitment, the direct analogue of the initial rate of signaling described above. The mechanism of arrestin recruitment is known. Agonist-bound GPCR is phosphorylated by kinase enzymes41,42 and the phosphorylated receptor binds arrestin43,44. This mechanism is represented as follows:

$$RA+N\mathop{\mathop{\rightleftharpoons }\limits^{{k}_{N}}}\limits_{{k}_{-N}}NRA$$

Arrestin (N) interacts with ligand-bound receptor (RA), governed by the rate constant kN. (In most cases the rate-limiting step in arrestin recruitment is receptor phosphorylation so in these cases kN is the rate constant for receptor phosphorylation). Arrestin dissociates from the ligand-receptor complex, governed by the arrestin-receptor dissociation rate constant k-N. In the Appendix an equation was derived that describes the level of ligand-receptor-arrestin complex ([NRA]) over time after the addition of ligand (Eq. (3)):

$${[NRA]}_{t}=\frac{{\rho }_{A}{k}_{\tau }}{{k}_{obs}}(1-{e}^{-{k}_{obs}t})$$

where ρA is fractional receptor occupancy by ligand and kobs the observed rate constant.

The validity of the model was assessed by comparing data simulated using the model with experimental data. In agreement with experimental data, the simulated arrestin recruitment conforms to an association exponential curve (Supplementary Fig. S4a). This is because Eq. (3) is of the form of the association exponential equation (Appendix). (It is noteworthy that once recruitment reaches a plateau then the signal remains unchanged for several minutes even though the arrestin-receptor complex interacts with internalization machinery. One possible explanation is that the interaction with the internalization machinery does not appreciably alter the fluorescence intensity of the sensor). The concentration-response was simulated (Supplementary Fig. S4a) and the resulting kobs and Plateau value of the association exponential fit determined (Supplementary Fig. S4b,c). Increasing the agonist concentration increased Plateau and kobs, with both effects approaching a limit at maximally-effective agonist concentrations (Supplementary Fig. S4). This profile was in agreement with the experimental concentration-response data for the AT1 receptor (Supplementary Fig. S3). We also simulated the change of EC50 over time, which showed that EC50 decreases over time (Supplementary Fig. S4e), in agreement with experimental data (Supplementary Table S2).

kτ for arrestin recruitment by the ligand-bound receptor is a measurable parameter in the model. This parameter is [N]TOT[R]TOTkN, where [N]TOT is total arrestin concentration. It emerges that this parameter can be quantified using the Plateau and kobs parameters from the fit to the association exponential equation (Appendix). Specifically, kτ is equal to the Plateau value multiplied by the kobs value at a maximally-stimulating concentration of ligand. This can be determined using either a full concentration response (Supplementary Fig. S5) or just a maximally-stimulating concentration (Supplementary Fig. S6), as described below.

Quantifying arrestin recruitment kinetics for the angiotensin AT1 receptor - concentra-tion- response

The angiotensin AT1 receptor is a prototypical GPCR in the study of arrestin recruitment and biased signaling. The receptor for angiotensin II (AngII), the AT1 receptor, regulates blood pressure and consequently is a target for antihypertensive drugs (the sartan antagonists)45. Biased ligands at the AT1 receptor that selectively promote arrestin recruitment while blocking G-protein signaling can elicit increased cardiac performance compared with unbiased ligands, potentially beneficial for treating cardiovascular disorders28,29,30,31.

We used the kτ method to quantify the kinetics of arrestin recruitment of five AT1 receptor ligands with known varying degrees of arrestin recruitment and bias. The method for quantifying kτ is as follows (illustrated schematically in Supplementary Fig. S5). First, the time course data for the effective concentrations (10 nM–32 μM for AngII) were fit to the association exponential equation (Fig. 2a). From these fits the fitted parameter values were taken for Plateau and kobs. These values were then multiplied together. The resulting Plateau x kobs values were then plotted against the ligand concentration, as shown in Fig. 2c. The resulting plot was a sigmoid curve (consistent with the theoretical prediction of the model (Supplementary Fig. S4d)). The data were then fit to the sigmoid curve equation, for example the “log(agonist) vs. response–Variable slope” equation in Prism46. From this fit kτ was obtained - it is the value of the asymptote. More precisely, kτ is the Plateau x kobs value for a maximally-effective concentration of ligand. The theoretical basis for this calculation is shown in Appendix, “Defining the initial rate of arrestin recruitment and identifying in the equations.” The fitted value for kτ for AngII was 0.41 ± 0.03 normalized fluorescence units (NFU) per min (Table 1).

We next evaluated four synthetic AT1 receptor ligands, SII, TRV120055, TRV120045 and TRV12002640,47. (For clarity, the name of the last three compounds is abbreviated to TRV055, TRV045 and TRV026). These compounds were developed in SAR campaigns aiming to identify biased ligands for the AT1 receptor. Three of these compounds, SII, TRV045 and TRV026, have been reported to be biased for arrestin recruitment over G-protein signaling. It is important to note that the compounds are not specific for arrestin recruitment – they do possess G-protein activating activity48,49, as shown in numerous studies of SII50,51,52.

Applying the kinetic analysis method to the SII data gave the Plateau x kobs vs ligand concentration data in Fig. 2c. Fitting the sigmoid curve equation to these data gave a kτ value of 0.20 NFU per min (Table 1). This value is approximately half that of AngII (0.41 NFU per min). This means the initial rate of arrestin recruitment by the SII-receptor complex is approximately half that of the AngII-receptor complex. Note this provides a biologically meaningful kinetic scaling of the partial agonist activity of SII for arrestin recruitment. The degree of partial agonism can be quantified conventionally, by dividing kτ of SII by that of AngII. This gave a normalized kτ value of 48% for SII (Table 1).

This method was applied to the remaining three ligands. In all cases the time course data conformed to the kinetic model, being well-fitted by the association exponential equation (Supplementary Fig. S7) with the Plateau and kobs values being dependent on agonist concentration (Supplementary Fig. S3). Applying the kinetic analysis method gave the sigmoid curves in Fig. 2c and the kτ values in Table 1. TRV055 and TRV045 are effectively full agonists for recruiting arrestin at the initial rate (kτ 93% and 89%, respectively, of that of AngII). The efficacy of TRV026 (62%) was intermediate between that of TRV055 and SII (Fig. 2c, Table 1).

The analysis also provides an estimate of ligand affinity for the receptor, KA. This is given by the L50 of the Plateau x kobs vs concentration sigmoid curve (Appendix, Supplementary Fig. S5, L50 being the concentration of ligand yielding a Plateau x kobs value half that produced by maximally-stimulating concentrations). With the exception of SII, the affinity of the ligands was similar (120–300 nM, Table 1). The affinity of SII was lower (1,100 nM, Table 1).

It is instructive to compare the pharmacology determined by the initial rate with the response at specific time points, the approach used in endpoint assays of arrestin recruitment. Fig. 4 and Supplementary Table S2 show the arrestin concentration-response curve at two different time points, 1 minute (on the rise-phase of the time course) and 20 minutes (representing the plateau phase) for the five ligands. The profile was notably different at the two time points. At 1 minute, the partial agonism of TRV045 and SII was evident from the lower maximal response (Fig. 4a). At 20 minutes, TRV045 was a full agonist and the maximal response of SII was increased close to that of the full agonists (Fig. 4b). In addition, the potency of the compounds increased over time; from 1 minute to 20 minutes, the EC50 decreased 3-fold for SII to 8-fold for TRV045 (Supplementary Table S2). (This reduction of EC50 over time is consistent with the kinetic model, see Supplementary Fig. S4e.) The pharmacological profile at 1 minute, on the rise phase, closely matched that defined by the initial rate kinetic method (Supplementary Table S2). This was anticipated, since at the 1 minute time point the response was on the linear, initial rate portion of the time course (Fig. 2a,b). The data for single time points were also fit to the operational model for the partial agonist SII, as described in Methods and the legend to Fig. 4. This analysis showed the parameter estimates were time dependent, particularly for the transducer ratio τ (1.8 at 1 min and 7.1 at 20 min) (Fig. 4). The agonist affinity estimate decreased slightly from 1 min to 20 min (from 1,200 nM to 530 nM).

Quantifying arrestin recruitment kinetics for the angiotensin AT1 receptor - single concentration

A simplified method is feasible for measuring kτ (see Supplementary Fig. S6). All that is required is a time course of response measurement at a single, maximally-stimulating concentration of ligand (maximally-stimulating at all time points). In Fig. 5a the data for the maximally-effective concentration of the AT1 receptor peptides is presented (32 μM). The data were fit to the association exponential equation to determine Plateau and kobs. kτ was then calculated - it is the Plateau multiplied by kobs for a maximally-stimulating concentration of ligand, as explained in the Appendix. The kτ values for the five ligands tested are shown in Table 2 and are in good agreement with the values determined using the concentration-response method (Table 1). Comparing the multiple concentration and single concentration methods, the single-concentration method provides the benefit of a smaller experiment whereas the multiple concentration method likely provides a more accurate estimate of kτ because it is defined as the asymptote of the curve for multiple concentrations rather than the value for a single concentration.

Application to quantifying biased agonism

Biased agonism quantification relates the capacity of a ligand to activate one pathway relative to one or more other pathways9,10,11,12. Numerous methods and scales have been developed and successfully applied8,47,53,54,55,56,57,58,59. One approach is to compare ligand efficacy, i.e. the capacity of the agonist-occupied receptor to generate the signal. kτ provides such an efficacy value, being the initial rate of signal generation by the agonist-occupied receptor. Here kτ is used to assess signaling bias of the AT1 receptor ligands described above. These ligands have been reported to vary in their bias, with SII, TRV026 and TRV045 being arrestin biased47,48,49 and TRV 055 being unbiased relative to AngII47. In this study, G-protein signaling and arrestin recruitment was measured using the same fluorescent biosensor assay modality, enabling near-identical conditions to be employed in comparing the pathways. The Gq pathway was quantified at the level of diacylglycerol using the Red Downward DAG sensor21 (Fig. 5b), and, one step downstream, Ca2+ mobilization measured using the R-GECO sensor22 (Fig. 5c).

The arrestin, DAG and Ca2+ data are shown in Fig. 5, for a maximally-stimulating concentration of the five ligands (32 μM). It is immediately obvious that curve shapes are different for the pathways - an association exponential curve defines arrestin recruitment (Fig. 5a) and a rise-and-fall curve defines DAG and Ca2+ signaling (Fig. 5b,c). The kinetic analysis method was designed to handle this scenario - the initial rate can be extracted from different curve shapes24,25. The initial rate of arrestin recruitment was quantified as described above, by multiplying the rate constant by the plateau of the association exponential fit, and the resulting kτ values are in Table 2. For DAG and Ca2+, a rise-and-fall exponential equation was applied:

$$y=\frac{C}{{k}_{obs1}-{k}_{obs2}}({e}^{-{k}_{obs2}t}-{e}^{-{k}_{obs1}t})$$

kτ is equal to the value of C in this equation24,25. The equation assumes two regulation mechanisms are in operation, corresponding to the two exponent terms. (These are most likely receptor desensitization and response degradation for DAG, and precursor depletion and response degradation for the shorter-term Ca2+ response25). The fitted kτ values for DAG and Ca2+ are shown in Table 2. For DAG, no response was detectable for TRV045, TRV026 and SII. Responses to these peptides were observed for Ca2+, one step downstream and so potentially more sensitive to small effects owing to signal amplification.

The next step in the bias calculation is normalization to a reference agonist. AngII was used for this purpose, being a full agonist and the endogenous ligand. The resulting normalized kτ values are shown in Table 2. A qualitative assessment of bias can be made with these values. All ligands appreciably stimulate arrestin recruitment (by ≥49%, Table 2). By contrast, only weak activation of the Gq pathway was detected for three of the ligands (TRV045, TRV026 and SII); DAG was not detectable, and only a weak maximal effect was observed in the more amplified Ca2+ signal (12–30%, Table 2). This finding suggests the ligands are biased for arrestin recruitment over Gq signaling.

The final, quantitative step in the bias  assessment is the bias ratio calculation. This was done by dividing the normalized kτ value for arrestin recruitment by that for Ca2+. By definition, the ratio for the reference ligand AngII was 1.0 (Table 2). Three ligands were arrestin-biased, evidenced by their arrestin/Ca2+ kτ ratio being greater than 1 (3.1, 3.0 and 4.2 for TRV045, TRV026 and SII, Table 2). One ligand was unbiased, relative to AngII (TRV055, Table 2). These results are consistent with the known bias profiles of these ligands47,48,49. For example, SII is an established arrestin-biased AT1 receptor ligand, and TRV055 is known as a balanced ligand (relative to AngII). In Fig. 6, the bias factor from the kτ ratio was compared with the bias factor calculated previously using a validated method, the operational model approach47. The bias profile across the four ligands tested was similar; TRV 055 was similar to AngII, whereas TRV045 and TRV026 were arrestin-biased and the degree of bias was similar for both ligands (Fig. 6).

These results indicate bias can be calculated simply and in kinetic terms using a common data analysis framework, the kτ method, for G-protein signaling and arrestin recruitment. The application of a common detection modality for arrestin and G-protein (the genetically-encoded sensors) also provides a unified technical platform that simplifies the interpretation of bias.

Discussion

Arrestin recruitment to GPCRs is the first step in a pathway that mediates myriad GPCR responses26,27 that are often selectively activated over G-protein pathways by biased agonists 10,15,36,48,49. Here we developed a method of quantifying arrestin-receptor interaction that takes into account the kinetics, i.e. the time course, of the response. We developed an improved kinetic arrestin assay. Present assays include endpoint assays, requiring a plate for every time point, or employ bioluminscent resonance energy transfer-based sensors that often require read times too long to accommodate the rapid changes of arrestin recruitment typically observed for GPCRs. A data analysis framework was developed to analyze time course data to quantify arrestin recruitment in kinetic terms, specifically the initial rate of recruitment. The resulting values can be directly compared with the initial rate of signaling through other pathways, enabling straightforward assessment of biased agonism. Application of this approach to biased agonists of the AT1 angiotensin receptor provided bias estimates similar to literature values, suggesting the method can be applied generally to quantify biased agonism.

The arrestin sensor is a genetically-encoded arrestin protein modified to incorporate the intrinsically-fluorescent protein mNeonGreen37,38. The fluorescent protein is incorporated in such a way as to render the fluorescence emission conformationally-sensitive, such that interaction with the GPCR results in a decrease of fluorescence intensity. The sensor was designed to meet criteria necessary for application to drug discovery. The high quantum yield provides a large enough signal for detection in plate readers and enables short excitation times to be used, which minimizes photobleaching21. BacMam provides consistent receptor and biosensor expression, minimizing cell to cell and well to well variability. Importantly the BacMam delivery can adjust to optimize expression levels. The Z-score was high enough for the AT1 and V2 receptors for application to HTS and lead optimization. Minimal steps are required for the assay; once the cells are prepared, the only reagent addition step is the application of agonist. The absence of subsequent detection reagent additions improves workflow and likely contributes to the high Z-score. The disadvantage of the sensor for HTS is that fluorescent compounds can potentially interfere with the assay because direct fluorescence excitation-emission is employed, requiring a follow-up assay to test for compound fluorescence. This is likely less of an issue in lead optimization, by which time fluorescent molecules, usually undesirable, have been disregarded. The sensor also possesses desirable pharmacological properties that simplify the analysis and interpretation of data in lead optimization, specifically, 1) The unmodified receptor can be used, providing estimates of authentic rather than forced coupling to arrestin. 2) The detection of the interaction is at the level of the receptor interaction itself, rather than downstream (for example, activation of transcription factors or phosphorylation of extracellular signal-regulated kinase). As a result, there is no receptor reserve, simplifying interpretation of ligand efficacy for arrestin recruitment; the maximal response to ligand is equal to the efficacy of the ligand. The sensor is ideal for kinetic measurements. The short excitation time enables a short time interval between data points of the time course (e.g. 9 sec, Fig. 1d). The high reproducibility provides robust data at early time points, when the change of signal is small but the value of the data point to defining the kinetics is high (Fig. 1c, Supplementary Fig. S1). Finally, two or more pathways can be quantified using the same modality (and in the case of multiplexing, in the same cells, Fig. 1d,e), ideal for assessing biased agonism. This avoids complications arising from the use of different assay systems for the pathways being compared, for example different biological material (e.g. membranes for GTPγS binding and cells for arrestin recruitment), different time points, buffer conditions, temperatures and so on.

A data analysis framework was required to translate the arrestin time course data into a useful pharmacological parameter. Previously we have quantified G-protein signaling kinetics using the initial rate of signaling, which we termed kτ24,25. Here this concept was extended to arrestin recruitment. (This was necessary because the original mechanism described generation of a downstream signal, whereas the arrestin sensor signal reports direct receptor-effector interaction.) The resulting analysis quantifies the initial rate of arrestin recruitment, i.e. the same parameter as that used previously for G-protein signaling. kτ is reasonably straightforward to measure from time course data, using either a full concentration-response (Fig. 2c, Supplementary Fig. S5) or at a single maximally-effective concentration (Fig. 5a, Supplementary Fig. S6). Time course data are fitted to the association exponential equation, fitted values of Plateau and kobs obtained, then these values multiplied together. kτ is Plateau x kobs at a maximally-effective ligand concentration.

The kτ parameter has certain benefits as a pharmacological parameter. First, it takes into account the kinetics of signaling, being a rate. In simple terms, kτ is the same at all time points. This avoids the problem of time-dependence of ligand efficacy values that can occur when using a single time point assay3,4,8. Second, the initial rate is biologically meaningful; it describes the response generation (arrestin recruitment or G-protein signaling) by the receptor before the response becomes modulated by regulation of signaling mechanisms (e.g. dissociation of arrestin, and degradation of second messengers). For this reason kτ is potentially more intuitive to use in interpreting and translating ligand efficacy than more abstract pharmacological parameters such as τ in the operational model. However, the kτ method is relatively new and so not established. Currently unexplored is the impact of receptor reserve on kτ estimates of downstream signaling. The current theoretical framework assumes kτ incorporates receptor reserve24 but the extent to which this is sufficient to explain experimental data remains to be determined.

This analysis was applied to biased agonism assessment using the AT1 receptor (Fig. 5, Table 2). Bias between arrestin and Gq-mediated signaling was quantified using the kτ method for five ligands. Bias was quantified as the ratio between the kτ value, normalized to that of AngII, for arrestin and Ca2+. The resulting bias estimates were in good agreement with those from previous studies (Fig. 6)47, validating the method. The analysis clearly showed that the ligands described as arrestin-biased, such as SII, do possess G-protein activating activity, being partial agonists. The sensor and analysis platform provides an ideal system for measuring biased agonism. Technical differences between signaling assay readouts are minimized because the same assay conditions are employed for arrestin and G-protein signaling measurements - the only difference is the sensor introduced into the cells the day before assay. [Though not used in this study, the sensors can be multiplexed, which eliminates assay condition differences completely (Fig. 1d,e)]. The use of the kinetic paradigm and kτ eliminates the time dependence of biased agonism estimates that can result from the use of endpoint assays and single time point data analysis8. The unified data analysis framework enables arrestin and G-protein signaling to be directly compared using the same parameter (initial rate of arrestin recruitment or signal generation). The new analysis simplifies the determination of the bias factor. The current analysis methods are quite complex8,47,53,54,55,56,57,58,59, involving multiple calculations and in some cases advanced curve fitting (such as simultaneous fitting of multiple ligand concentration-response curves). The calculations of the kτ method are simple to perform, requiring a single bias calculation (the kτ ratio) and employing basic, familiar curve fitting. Finally, the bias scale is more straightforward; the bias scales of existing methods are abstract, whereas the kτ ratio is a more biologically meaningful parameter, being the ratio of the initial rate of the responses being compared.

In summary, in this study we describe a platform that utilizes the kinetics of response to quantify arrestin recruitment and G-protein-mediated signaling. This provides a universal analysis framework employing the initial rate of activity that simplifies quantification and interpretation of ligand activity and biased agonism. This method can be employed by drug discovery scientists to improve the identification, optimization and development of new therapeutics.

Methods

Sensor design

The design goals for a new arrestin-3 (β-arrestin2) sensor were: 1) it needed to be bright enough for detection on automated fluorescence plate readers, 2) it needed to use a single fluorescent protein so that other portions of the visible spectrum were available for other colored sensors and multiplex recordings, and 3) the change in fluorescence in response to GPCR activation has to be large enough to produce signal-to-noise ratios of >60.

Using the arrestin-3 structures as our guide, we designed a series of constructs in which the entire arrestin-3 was inserted into the middle of the seventh stave of β-sheet in the barrel of mNeonGreen, directly adjacent to the chromophore37,38. The goal was to convert the change in arrestin-3 shape when it binds a phosphorylated receptor into a change in the chromophore environment resulting in a change in fluorescence intensity. The first biosensors that positioned analyte binding domains in this position used a circularly permuted version of the fluorescent protein, and include the GCaMP and GECO Ca2+ sensors, the upward and downward DAG sensors, and the caDDis cAMP sensor21,22. More recently it has become clearer that if the termini of the analyte binding domain are close to one another, then the entire binding domain can be inserted into the 7th stave of the fluorescent protein without having to circularly permute the fluorescent protein60.

The initial constructs were screened for responses on a fluorescence microscope with time lapse imaging, and drugs were added to the well by hand. HEK 293 T cells were transiently transfected with the sensor prototypes as well the AT1 angiotensin receptor. The receptor was then activated with the addition of 30 μM AngII, and the sensor was monitored for changes in fluorescence. After identifying a functional prototype, mutagenic PCR was used to randomly mutagenize two to three amino acids at a time at the fusion junction/s, producing random libraries of thousands of mutants. These mutants were then screened in a high throughout format on a fluorescence plate reader for AT1 receptor activation-dependent changes in fluorescence intensity.

BacMam production and titer

BacMam was produced following the methods described previously21. To establish BacMam titers, we quantified viral genes per mL using quantitative PCR. Samples are diluted 1:10 in Triton X-100, and then exposed to two freeze/thaw cycles of 5 minutes in a dry ice/ethanol bath and 2 minutes in a 42 °C water bath. Samples are then diluted 1:50 in TE buffer in preparation for use as a qPCR template. qPCR is performed using the SYBR Select Master Mix (Applied Biosystems, Waltham, MA) in a Rotor-Gene Q thermocycler (Qiagen, Germantown, MD). PCR primers are specific to the VSVG gene (Forward Primer 5' GCAAGCATTGGGGAGTCAGAC 3', Reverse Primer 5' CTGGCTGCAGCAAAGAGATC 3'). Viral stocks are tested monthly and are typically stable for 12 months when stored at 4 °C and protected from light. While viral genes/mL is a reliable, consistent measurement of viral concentration, the efficiency by which a viral stock successfully transduces mammalian cells varies by cell type, the promoter used to drive expression, and the means by which transduction is detected.

Molecular biology

The cDNA for the AT1 angiotensin receptor and V2 vasopressin receptor were obtained from the cDNA Resource Center (Bloomsburg University, Bloomsburg, PA). The cDNA encoding the arrestin-3 sensor, Red DAG sensor, R-GECO sensor, Red cADDis sensor, and the receptors were cloned into the same vector which put them under the transcriptional control of a CMV promoter.

Cell culture and viral transduction

HEK 293 T cells were cultured in Eagle’s minimum essential media (EMEM) supplemented with 10% fetal bovine serum (FBS) and penicillin-streptomycin at 37 °C in 5% CO2. For BacMam transduction, cells were resuspended in media at a density of 52,000 cells per 100 μL. 100 μL of this suspension was combined with BacMam containing the arrestin-3, Red Downward DAG, Red Upward cADDis, and/or R-GECO sensors and the indicated receptors, 2 mM sodium butyrate, and EMEM in a final volume of 150 μL. For each experiment 4.24 × 108 viral genes of arrestin virus were added to each well. For multiplex experiments, 4.79 × 108 viral genes of the Red DAG sensor or 6.18 × 108. Viral genes of the Red cADDis (cAMP) sensor were added with the arrestin sensor. For experiments with the R-GECO sensor, 8.46 × 108 viral genes were added to each well. The viruses carrying the AT1 and V2 receptors were added such that 2.12 × 108 and 3.04 × 108 viral genes went into each well, respectively. For the β2-adrenoceptor experiment, 4.28 × 108 viral genes for the receptor and 2.13 × 108 viral genes of GPCR kinase 2 were added to each well. The cell/transduction mixture was then seeded into 96-well plates and incubated for ~24 hours at 37 °C in 5% CO2. Thirty minutes prior to fluorescence plate reader or imaging experiments, the media in each well was replaced with 150 μL of Dulbecco’s phosphate buffered saline (DPBS) supplemented with Ca2+ (0.9 mM) and Mg2+ (0.5 mM).

Fluorescence plate reader experiments were performed on the BioTek Synergy Mx (BioTek, Winooski, VT) and BMG CLARIOstar (BMG Labtech, Cary, NC) in 96 well plates. On the Biotek Synergy Mx plate reader, green fluorescence detection was recorded using 488/20 nm excitation and 525/20 nm fluorescence emission, while red fluorescence detection was recorded using 565/20 nm excitation wavelength and 603/20 nm fluorescence emission. On the BMG CLARIOstar plate reader, green fluorescence detection was recorded using 488/14 nm excitation wavelength and 535/30 nm fluorescence emission, while red fluorescence detection was recorded using 566/18 nm excitation wavelength and 620/40 nm fluorescence emission. Drug was added manually with a multichannel pipette in a volume of 50 µL at the indicated time points. While all of the data reported here came from cells in 96 well plates, we and others have been successful using this assay in the 384 well format.

Drug compounds

Vasopressin was obtained from Cayman Chemical (Ann Arbor, MI). Angiotensin II and SII (Sar1, Ile4,8]-Angiotensin II)40 were obtained from Genscript (Piscataway, NJ) and MyBioSource (San Diego, CA), respectively. Trevena peptides TRV120026, TRV120045, and TRV12005547 were synthesized by Genscript. For clarity, the ligand names are abbreviated to TRV026, TRV045 and TRV055. All working concentration of drugs were dissolved in DPBS and added manually to the HEK 293 T cells at the indicated concentrations and time points.

Data analysis

Fluorescence data were normalized to baseline. Specifically, baseline fluorescence i.e. prior to the addition of compound, was measured over at least 5 time points and the average baseline value calculated. The fluorescence value in the well subsequent to the addition of compound or vehicle was divided by the average baseline value for that well, giving the baseline-normalized fluorescence value (Δ F/F). For fitting of the model equations, in which stimulation of signaling was analyzed, downward sensor data were first normalized to be upward (arrestin sensor data in Fig. 2a,b, Fig. 4, Fig. 5a and Supplementary Fig. S7, and DAG sensor data in Fig. 5b)). This was done by subtracting the baseline-normalized value from unity (1 − ΔF/F). This approach enabled a unified presentation and analysis of stimulation of signaling data.

Curve fitting was performed using Prism 8.1 (Graphpad Software, San Diego, CA). Time course data were fit to exponential equations. The time course data included the baseline phase and the equation incorporated a parameter which represents baseline fluorescence (“y0” or “Baseline” - see below). For downward responses data were fit to the “Plateau followed by one phase decay” equation built into Prism61:

$$y={\rm{i}}{\rm{f}}(x < x0,y0,Plateau+(y0-Plateau){e}^{-K.(x-x0)})$$

where y0 is the baseline signal, x0 the time of initiation of the signal, Plateau is the signal at the plateau (formally the asymptote as time approaches infinity) and K the observed rate constant in units of time−1. For upward responses data were fit to the “Plateau followed by one phase association” equation built into Prism62:

$$y={\rm{i}}{\rm{f}}(x < x0,y0,y0+(Plateau-y0)(1-{e}^{-K.(x-x0)}))$$

For the rise-and-fall DAG response (Fig. 5b) data were fit to a user-defined bi-exponential equation24:

$$y={\rm{i}}{\rm{f}}(x < x0,Baseline,Baseline+\frac{C}{{K}_{1}-{K}_{2}}({e}^{-{K}_{2}(x-x0)}-{e}^{-{K}_{1}(x-x0)}))$$

where “Baseline” is the baseline signal (response before addition of ligand), C a fitting constant, and K1 and K2 rate constants for the two exponential phases in units of time−1. This is the general form of the two component signaling model24,25. The calcium response also conformed to a rise-and-fall curve but the baseline response drifted downwards slightly (Fig. 5c). Specifically, the plateau at late time points was slightly lower than the baseline fluorescence prior to the addition of ligand. This drift was incorporated by introducing a drift parameter into the bi-exponential equation:

$$y={\rm{i}}{\rm{f}}(x < x0,Baseline+Drift\times x,Baseline+Drift\times x0+Drift\times (x-x0)+\frac{C}{{K}_{1}-{K}_{2}}({e}^{-{K}_{2}(x-x0)}-{e}^{-{K}_{1}(x-x0)}))$$

In all the analyses, x0, the time of initiation of the signal, was allowed to vary in the analysis (as opposed to being held constant) to accommodate slight differences between wells in the time of addition of ligand.

Concentration-response data were fit to a sigmoid curve equation, the “Log(agonist) vs. response–Variable slope” equation in Prism46:

$$y=Bottom+\frac{Top-Bottom}{1+{10}^{({\rm{L}}{\rm{o}}{\rm{g}}{L}_{50}-x)\times HillSlope}}$$

The “Bottom” parameter was constrained to zero in the case of the kτ analysis, in which the Plateau x kobs value is plotted against the agonist concentration. (Note in the Prism formulation, L50 is written as EC50. The EC50 term is not used here because it has an explicit pharmacological definition63).

SII concentration-response data for single time points were fit to the operational model of agonism64, using the following equation entered as a user-defined equation in Prism:

$$y=\frac{{E}_{m}{\rho }_{A}\tau }{1+{\rho }_{A}\tau }$$
$${\rho }_{A}=\frac{{[A]}^{n}}{{{K}_{A}}^{n}+{[A]}^{n}}$$

where Em is the maximal response of the system, τ the transducer ratio, [A] the ligand concentration, KAthe agonist affinity (specifically the agonist equilibrium dissociation constant) and n the agonist binding slope factor. In the analysis it was assumed Em was equal to the maximal response to AngII at the time point under study and so this value was entered as a constant as the “Top” value for AngII from the fit to the sigmoid curve equation.

Technical replicates in the data sets were considered separate points in the curve fitting analysis.

Appendix: Arrestin Recruitment Mechanism and Equations

GPCRs interact with arrestin and this interaction can be detected directly using optical biosensors. In this study the biosensor was a conformationally-sensitive mNeonGreen-tagged arrestin in which the optical properties changed upon binding to the GPCR. The interaction can be described as a straightforward bimolecular interaction between the two proteins, as indicated in the following scheme:

$$RA+N\mathop{\mathop{\rightleftharpoons }\limits^{{k}_{N}}}\limits_{{k}_{-N}}NRA$$

N is arrestin, R is receptor and A is the ligand. RA is receptor-ligand complex and NRA the ternary complex of arrestin, receptor and ligand. kN is the association rate constant for receptor-arrestin association. The value of this parameter is most likely determined by the rate of receptor phosphorylation since this is the rate-limiting step in receptor-arrestin association. k-N is the arrestin-receptor dissociation rate constant. KA is the affinity constant for ligand binding to the receptor (more precisely, the equilibrium dissociation constant). It is assumed that ligand binding is at equilibrium with the receptor, that the unbound receptor (R) does not bind arrestin, and that ligand dissociation from the ternary complex NRA is much slower than that from the binary complex RA.

Equations defining the change of signal (arrestin-receptor complex, NRA) over time were derived. From these equations the initial rate of arrestin recruitment by the ligand-bound receptor (kτ) emerged as a readily-measurable parameter. Two scenarios regarding stoichiometry were formularized – receptor excess over arrestin (the most likely scenario in this study) and arrestin excess over receptor. Both formulations yield kτ, and kτ is measured in the same way for both scenarios. Here the equations for arrestin-receptor complex are solved for the two scenarios, then the identity of the initial rate in the equations demonstrated, and finally the method for measuring the initial rate (kτ) presented.

Receptor excess over arrestin

In this scenario it is assumed receptor is in sufficient excess over arrestin that the arrestin-receptor complex does not appreciably deplete the concentration of receptor. The differential equation defining the change of receptor-arrestin complex over time is,

$$\frac{d[NRA]}{dt}=[RA][N]{k}_{N}-[NRA]{k}_{-N}$$

In this case the units of kN are receptor units−1.min−1. [RA] can be expressed as a function of the total receptor concentration, as follows. First, since we assume [NRA] does not appreciably deplete the total receptor concentration, the conservation of mass equation for the receptor can be written as,

$${[R]}_{TOT}\approx [R]+[RA]$$

Next, [R] is substituted in this equation. Since ligand-receptor binding is at equilibrium, [R] can be defined as,

$$[R]=\frac{[RA]{K}_{A}}{[A]}$$

Substituting and rearranging gives the desired expression for [RA]:

$$[RA]={\rho }_{A}{[R]}_{TOT}$$

where ρA is fractional occupancy of receptor by A, defined by,

$${\rho }_{A}=\frac{[A]}{{K}_{A}+[A]}$$

Substituting into the differential equation for [NRA] gives,

$$\frac{d[NRA]}{dt}={\rho }_{A}[N]{[R]}_{TOT}{k}_{N}-[NRA]{k}_{-N}$$

Next the [N] term is substituted with an expression for the total concentration of arrestin. In this scenario, the conservation of mass equation for arrestin is:

$${[N]}_{TOT}=[N]+[NRA]$$

Solving for [N] and substituting into the differential equation gives,

$$\frac{d[NRA]}{dt}={\rho }_{A}{[R]}_{TOT}{[N]}_{TOT}{k}_{N}-[NRA]{k}_{obs1}$$

where,

$${k}_{obs1}={\rho }_{A}{[R]}_{TOT}{k}_{N}+{k}_{-N}$$

Integrating gives the desired equation defining [NRA] over time, Eq. (1):

$${[NRA]}_{t}=\frac{{\rho }_{A}{[N]}_{TOT}{[R]}_{TOT}{k}_{N}}{{k}_{obs1}}(1-{e}^{-{k}_{obs1}t})$$
(1)

Arrestin excess over receptor

In this scenario it is assumed arrestin is in sufficient excess over receptor that the arrestin-receptor complex does not appreciably deplete the concentration of arrestin. The differential equation defining the change of receptor-arrestin complex over time is the same as for the receptor excess assumption given above:

$$\frac{d[NRA]}{dt}=[RA][N]{k}_{N}-[NRA]{k}_{-N}$$

In this case the units of kN are arrestin units−1.min−1. Since N is in excess over R, the free concentration of N is approximately equal to the total concentration of N, [N]TOT. Consequently, the differential equation can be written as,

$$\frac{d[NRA]}{dt}={[N]}_{TOT}[RA]{k}_{N}-[NRA]{k}_{-N}$$

Next, [RA] in this equation can be expressed as a function of [R]TOT. The conservation of mass equation is,

$${[R]}_{TOT}=[R]+[RA]+[NRA]$$

This equation can be rearranged and solved for [RA], utilizing the expression [R] = [RA]KA/[A]:

$$[RA]={\rho }_{A}{[R]}_{TOT}-{\rho }_{A}[NRA]$$

Substituting into the differential equation and rearranging gives,

$$\frac{d[NRA]}{dt}={\rho }_{A}{[R]}_{TOT}{[N]}_{TOT}{k}_{N}-[NRA]{k}_{obs2}$$

where,

$${k}_{obs2}={\rho }_{A}{[N]}_{TOT}{k}_{N}+{k}_{-N}$$

Integrating gives the desired equation defining [NRA] over time, Eq. (2):

$${[NRA]}_{t}=\frac{{\rho }_{A}{[N]}_{TOT}{[R]}_{TOT}{k}_{N}}{{k}_{obs2}}(1-{e}^{-{k}_{obs2}t})$$
(2)

Defining the initial rate of arrestin recruitment and identifying it in the equations

The initial rate of arrestin interaction with the receptor is that before depletion of arrestin or receptor by formation of the NRA ternary complex, and before breakdown of the complex. This rate is defined as,

$$Initial\,rate={[N]}_{TOT}{[R]}_{TOT}{k}_{N}$$

This parameter is a direct analogue of the initial rate of signaling in the kinetic signaling model, the equation for which is,

$$Initial\,rate={E}_{P(TOT)}{[R]}_{TOT}{k}_{E}$$

where EP(TOT) is total concentration of precursor and kE the response generation rate constant. In order to standardize the nomenclature between arrestin recruitment and the signaling models kτ is used as the term for the initial rate of arrestin recruitment as well as that for signaling:

$${k}_{\tau }={[N]}_{TOT}{[R]}_{TOT}{k}_{N}$$

It is evident by visual inspection that this term, [N]TOT[R]TOTkN is present in the numerator of the equations for arrestin recruitment over time, Eqs. (1) and (2), reproduced here for convenience:

$${[NRA]}_{t}=\frac{{\rho }_{A}{[N]}_{TOT}{[R]}_{TOT}{k}_{N}}{{k}_{obs1}}(1-{e}^{-{k}_{obs1}t})$$
$${[NRA]}_{t}=\frac{{\rho }_{A}{[N]}_{TOT}{[R]}_{TOT}{k}_{N}}{{k}_{obs2}}(1-{e}^{-{k}_{obs2}t})$$

Substituting kτ for [N]TOT[R]TOTkN gives the equation used to analyze the time course data, Eq. (3):

$${[NRA]}_{t}=\frac{{\rho }_{A}{k}_{\tau }}{{k}_{obs}}(1-{e}^{-{k}_{obs}t})$$
(3)

where,

$${k}_{obs}={k}_{obs1,2}$$

Estimating the initial rate by curve fitting

Here it is shown that kτ can be measured by combining parameters from a familiar curve fitting procedure, either from a concentration-response experiment or from an experiment employing a saturating concentration of ligand (Supplementary Figs. S5 and S6, respectively). The equations for both the receptor and arrestin excess assumptions (Eqs. (1) and (2), respectively) take the form of the familiar exponential association equation:

$${y}_{t}=Plateau\times (1-{e}^{-{k}_{obs}.t})$$

where Plateau is the asymptote, the value of y as time approaches infinity, and kobs the observed rate constant. (This is the “One phase association” equation in GraphPad Prism65). By comparing with Eqs. (1) and (2), it can be seen that the parameters are defined as,

$$Plateau=\frac{{\rho }_{A}{k}_{\tau }}{{k}_{obs}}$$

Combining these parameters, by multiplying them together, yields kτ multiplied by ρA (the fractional receptor occupancy by ligand):

$$Plateau\times {k}_{obs}={\rho }_{A}{k}_{\tau }$$

Note that this expression is the same regardless of the excess scenario. It is instructive now to expand the ρA term:

$$Plateau\times {k}_{obs}=\frac{[A]}{[A]+{K}_{A}}{k}_{\tau }$$

When the ligand concentration is maximally effective for recruiting arrestin, we assume [A] is in large excess over KA. Under this condition, the equation reduces to,

$${[Plateau\times {k}_{obs}]}_{[A]\gg {K}_{A}}={k}_{\tau }$$

This means that kτ for arrestin recruitment can be measured by multiplying the plateau by the rate constant for a maximally effective concentration of ligand. This can be done either using a single, maximally stimulating concentration (Supplementary Fig. S6, Fig. 5a) or by plotting the Plateau × kobs vs [A] (Supplementary Fig. S5, Fig. 2c). In the latter method, the data are analyzed using a sigmoid dose-response equation and in this case kτ is the fitted maximum Plateau × kobs value of the curve and KA is the [A]50 concentration, i.e. the value of [A] giving 50% of the maximal Plateau × kobs value.

Global analysis of time course data for multiple agonist concentrations

An alternative method for analyzing the data is global fitting of the time course data for multiple concentrations of agonist simultaneously. This can be done by fitting data globally to Eq. (3). This requires handling of the kobs term since it is dependent on the concentration of ligand. The definition of kobs is dependent on whether receptor or arrestin are in excess, the equation for which is, respectively,

$${k}_{obs1}={\rho }_{A}{[R]}_{TOT}{k}_{N}+{k}_{-N}$$
$${k}_{obs2}={\rho }_{A}{[N]}_{TOT}{k}_{N}+{k}_{-N}$$

These equations reduce to a common form:

$${k}_{obs1,2}={\rho }_{A}C+{k}_{-N}$$

where C is a fitting constant, defining [R]TOTkN if receptor is in excess and [N]TOTkN if arrestin is in excess.

It is also useful to introduce a slope term (n) to accommodate experimental variability in the precision of serial dilution of the agonist, or biological processes that can deviate the agonist concentration range in the vicinity of the receptor from the concentration range added to the assay. This is done by raising the agonist concentration and agonist affinity terms to the power of the slope factor.

The resulting equation for globally analyzing the data is Eq. (4),

$${[NRA]}_{t}=\frac{{\rho }_{A,n}{k}_{\tau }}{{\rho }_{A,n}C+{k}_{-N}}(1-{e}^{-({\rho }_{A,n}C+{k}_{-N})t})$$

where,

$${\rho }_{A,n}=\frac{{[A]}^{n}}{{{K}_{A}}^{n}+{[A]}^{n}}$$
(4)

Assessing whether receptor or arrestin is in excess

In principal the component that is in excess can be determined by varying the level of receptor or arrestin and measuring the observed rate constant, kobs. The rate constant value is dependent on receptor concentration if receptor is in excess and arrestin concentration if arrestin is in excess. This is because kobsis defined as ρA[R]TOTkN + kN when receptor is in excess and ρA[N]TOTkN + kN when arrestin is in excess.

References

1. 1.

Hothersall, J. D., Brown, A. J., Dale, I. & Rawlins, P. Can residence time offer a useful strategy to target agonist drugs for sustained GPCR responses? Drug. Discov. Today 21, 90–96, https://doi.org/10.1016/j.drudis.2015.07.015 (2016).

2. 2.

Grundmann, M. & Kostenis, E. Temporal Bias: Time-Encoded Dynamic GPCR Signaling. Trends Pharmacol. Sci. 38, 1110–1124, https://doi.org/10.1016/j.tips.2017.09.004 (2017).

3. 3.

Lane, J. R., May, L. T., Parton, R. G., Sexton, P. M. & Christopoulos, A. A kinetic view of GPCR allostery and biased agonism. Nat. Chem. Biol. 13, 929–937, https://doi.org/10.1038/nchembio.2431 (2017).

4. 4.

Ferrandon, S. et al. Sustained cyclic AMP production by parathyroid hormone receptor endocytosis. Nat. Chem. Biol. 5, 734–742, https://doi.org/10.1038/nchembio.206 (2009).

5. 5.

Tay, D., Cremers, S. & Bilezikian, J. P. Optimal dosing and delivery of parathyroid hormone and its analogues for osteoporosis and hypoparathyroidism - translating the pharmacology. Br. J. Clin. Pharmacol. 84, 252–267, https://doi.org/10.1111/bcp.13455 (2018).

6. 6.

Miller, P. D. et al. Effect of Abaloparatide vs Placebo on New Vertebral Fractures in Postmenopausal Women With Osteoporosis: A Randomized Clinical Trial. JAMA 316, 722–733, https://doi.org/10.1001/jama.2016.11136 (2016).

7. 7.

Mullershausen, F. et al. Persistent signaling induced by FTY720-phosphate is mediated by internalized S1P1 receptors. Nat. Chem. Biol. 5, 428–434, https://doi.org/10.1038/nchembio.173 (2009).

8. 8.

Klein Herenbrink, C. et al. The role of kinetic context in apparent biased agonism at GPCRs. Nat. Commun. 7, 10842, https://doi.org/10.1038/ncomms10842 (2016).

9. 9.

Kenakin, T. Biased Receptor Signaling in Drug Discovery. Pharmacol. Rev. 71, 267–315, https://doi.org/10.1124/pr.118.016790 (2019).

10. 10.

Whalen, E. J., Rajagopal, S. & Lefkowitz, R. J. Therapeutic potential of beta-arrestin- and G protein-biased agonists. Trends Mol. Med. 17, 126–139, https://doi.org/10.1016/j.molmed.2010.11.004 (2011).

11. 11.

Violin, J. D., Crombie, A. L., Soergel, D. G. & Lark, M. W. Biased ligands at G-protein-coupled receptors: promise and progress. Trends Pharmacol. Sci. 35, 308–316, https://doi.org/10.1016/j.tips.2014.04.007 (2014).

12. 12.

Kenakin, T. & Christopoulos, A. Signalling bias in new drug discovery: detection, quantification and therapeutic impact. Nat. Rev. Drug. Discov. 12, 205–216, https://doi.org/10.1038/nrd3954 (2013).

13. 13.

Allen, J. A. et al. Discovery of beta-arrestin-biased dopamine D2 ligands for probing signal transduction pathways essential for antipsychotic efficacy. Proc. Natl Acad. Sci. USA 108, 18488–18493, https://doi.org/10.1073/pnas.1104807108 (2011).

14. 14.

Chen, X. et al. Discovery of G Protein-Biased D2 Dopamine Receptor Partial Agonists. J. Med. Chem. 59, 10601–10618, https://doi.org/10.1021/acs.jmedchem.6b01208 (2016).

15. 15.

Chen, X. et al. Structure-functional selectivity relationship studies of beta-arrestin-biased dopamine D(2) receptor agonists. J. Med. Chem. 55, 7141–7153, https://doi.org/10.1021/jm300603y (2012).

16. 16.

Klewe, I. V. et al. Recruitment of beta-arrestin2 to the dopamine D2 receptor: insights into anti-psychotic and anti-parkinsonian drug receptor signaling. Neuropharmacol. 54, 1215–1222, https://doi.org/10.1016/j.neuropharm.2008.03.015 (2008).

17. 17.

Masri, B. et al. Antagonism of dopamine D2 receptor/beta-arrestin 2 interaction is a common property of clinically effective antipsychotics. Proc. Natl Acad. Sci. USA 105, 13656–13661, https://doi.org/10.1073/pnas.0803522105 (2008).

18. 18.

Lohse, M. J., Nuber, S. & Hoffmann, C. Fluorescence/bioluminescence resonance energy transfer techniques to study G-protein-coupled receptor activation and signaling. Pharmacol. Rev. 64, 299–336, https://doi.org/10.1124/pr.110.004309 (2012).

19. 19.

Marullo, S. & Bouvier, M. Resonance energy transfer approaches in molecular pharmacology and beyond. Trends Pharmacol. Sci. 28, 362–365, https://doi.org/10.1016/j.tips.2007.06.007 (2007).

20. 20.

Halls, M. L. & Canals, M. Genetically Encoded FRET Biosensors to Illuminate Compartmentalised GPCR Signalling. Trends Pharmacol. Sci. 39, 148–157, https://doi.org/10.1016/j.tips.2017.09.005 (2018).

21. 21.

Tewson, P. H., Martinka, S., Shaner, N. C., Hughes, T. E. & Quinn, A. M. New DAG and cAMP Sensors Optimized for Live-Cell Assays in Automated Laboratories. J. Biomol. Screen. 21, 298–305, https://doi.org/10.1177/1087057115618608 (2016).

22. 22.

Zhao, Y. et al. An expanded palette of genetically encoded Ca(2)(+) indicators. Sci. 333, 1888–1891, https://doi.org/10.1126/science.1208592 (2011).

23. 23.

Kenakin, T. Quantifying biological activity in chemical terms: a pharmacology primer to describe drug effect. ACS Chem. Biol. 4, 249–260, https://doi.org/10.1021/cb800299s (2009).

24. 24.

Hoare, S. R. J., Pierre, N., Moya, A. G. & Larson, B. Kinetic operational models of agonism for G-protein-coupled receptors. J. Theor. Biol. 446, 168–204, https://doi.org/10.1016/j.jtbi.2018.02.014 (2018).

25. 25.

Hoare, S. R. J., Tewson, P. H., Quinn, A. M., Hughes, T. E. & Bridge, L. J. Analyzing kinetic signaling data for G-protein-coupled receptors. BiorXiv https://www.biorxiv.org/content/10.1101/2020.01.20.913319v1 (2019).

26. 26.

Peterson, Y. K. & Luttrell, L. M. The Diverse Roles of Arrestin Scaffolds in G Protein-Coupled Receptor Signaling. Pharmacol. Rev. 69, 256–297, https://doi.org/10.1124/pr.116.013367 (2017).

27. 27.

Schmid, C. L. & Bohn, L. M. Physiological and pharmacological implications of beta-arrestin regulation. Pharmacol. Ther. 121, 285–293, https://doi.org/10.1016/j.pharmthera.2008.11.005 (2009).

28. 28.

Violin, J. D. et al. Selectively engaging beta-arrestins at the angiotensin II type 1 receptor reduces blood pressure and increases cardiac performance. J. Pharmacol. Exp. Ther. 335, 572–579, https://doi.org/10.1124/jpet.110.173005 (2010).

29. 29.

Boerrigter, G. et al. Cardiorenal actions of TRV120027, a novel ss-arrestin-biased ligand at the angiotensin II type I receptor, in healthy and heart failure canines: a novel therapeutic strategy for acute heart failure. Circ. Heart Fail. 4, 770–778, https://doi.org/10.1161/CIRCHEARTFAILURE.111.962571 (2011).

30. 30.

Boerrigter, G., Soergel, D. G., Violin, J. D., Lark, M. W. & Burnett, J. C. Jr. TRV120027, a novel beta-arrestin biased ligand at the angiotensin II type I receptor, unloads the heart and maintains renal function when added to furosemide in experimental heart failure. Circ. Heart Fail. 5, 627–634, https://doi.org/10.1161/CIRCHEARTFAILURE.112.969220 (2012).

31. 31.

Ryba, D. M. et al. Long-Term Biased beta-Arrestin Signaling Improves Cardiac Structure and Function in Dilated Cardiomyopathy. Circulation 135, 1056–1070, https://doi.org/10.1161/CIRCULATIONAHA.116.024482 (2017).

32. 32.

Bohn, L. M., Gainetdinov, R. R., Lin, F. T., Lefkowitz, R. J. & Caron, M. G. Mu-opioid receptor desensitization by beta-arrestin-2 determines morphine tolerance but not dependence. Nat. 408, 720–723, https://doi.org/10.1038/35047086 (2000).

33. 33.

Bohn, L. M. et al. Enhanced rewarding properties of morphine, but not cocaine, in beta(arrestin)-2 knock-out mice. J. Neurosci. 23, 10265–10273 (2003).

34. 34.

Raehal, K. M., Walker, J. K. & Bohn, L. M. Morphine side effects in beta-arrestin 2 knockout mice. J. Pharmacol. Exp. Ther. 314, 1195–1201, https://doi.org/10.1124/jpet.105.087254 (2005).

35. 35.

Bu, H., Liu, X., Tian, X., Yang, H. & Gao, F. Enhancement of morphine analgesia and prevention of morphine tolerance by downregulation of beta-arrestin 2 with antigene RNAs in mice. Int. J. Neurosci. 125, 56–65, https://doi.org/10.3109/00207454.2014.896913 (2015).

36. 36.

Violin, J. D. & Lefkowitz, R. J. Beta-arrestin-biased ligands at seven-transmembrane receptors. Trends Pharmacol. Sci. 28, 416–422, https://doi.org/10.1016/j.tips.2007.06.006 (2007).

37. 37.

Clavel, D. et al. Structural analysis of the bright monomeric yellow-green fluorescent protein mNeonGreen obtained by directed evolution. Acta Crystallogr. D. Struct. Biol. 72, 1298–1307, https://doi.org/10.1107/S2059798316018623 (2016).

38. 38.

Shaner, N. C. et al. A bright monomeric green fluorescent protein derived from Branchiostoma lanceolatum. Nat. Methods 10, 407–409, https://doi.org/10.1038/nmeth.2413 (2013).

39. 39.

Moore, C. A., Milano, S. K. & Benovic, J. L. Regulation of receptor trafficking by GRKs and arrestins. Annu. Rev. Physiol. 69, 451–482, https://doi.org/10.1146/annurev.physiol.69.022405.154712 (2007).

40. 40.

Holloway, A. C. et al. Side-chain substitutions within angiotensin II reveal different requirements for signaling, internalization, and phosphorylation of type 1A angiotensin receptors. Mol. Pharmacol. 61, 768–777, https://doi.org/10.1124/mol.61.4.768 (2002).

41. 41.

Inglese, J., Freedman, N. J., Koch, W. J. & Lefkowitz, R. J. Structure and mechanism of the G protein-coupled receptor kinases. J. Biol. Chem. 268, 23735–23738 (1993).

42. 42.

Stadel, J. M. et al. Catecholamine-induced desensitization of turkey erythrocyte adenylate cyclase is associated with phosphorylation of the beta-adrenergic receptor. Proc. Natl Acad. Sci. USA 80, 3173–3177 (1983).

43. 43.

Krupnick, J. G. & Benovic, J. L. The role of receptor kinases and arrestins in G protein-coupled receptor regulation. Annu. Rev. Pharmacol. Toxicol. 38, 289–319, https://doi.org/10.1146/annurev.pharmtox.38.1.289 (1998).

44. 44.

Lohse, M. J., Benovic, J. L., Codina, J., Caron, M. G. & Lefkowitz, R. J. Beta-Arrestin: a protein that regulates beta-adrenergic receptor function. Sci. 248, 1547–1550 (1990).

45. 45.

Alexander, W. et al. Angiotensin receptors: AT1 receptor. www.guidetopharmacology.org/GRAC/ObjectDisplayForward?objectId=34.

46. 46.

Motulsky, H. J. Equation: log(agonist) vs. response–Variable slope. www.graphpad.com/guides/prism/8/curve-fitting/index.htm?reg_dr_stim_variable.htm, (2019).

47. 47.

Rajagopal, S. et al. Quantifying ligand bias at seven-transmembrane receptors. Mol. Pharmacol. 80, 367–377, https://doi.org/10.1124/mol.111.072801 (2011).

48. 48.

Namkung, Y. et al. Functional selectivity profiling of the angiotensin II type 1 receptor using pathway-wide BRET signaling sensors. Sci Signal 11, doi:10.1126/scisignal.aat1631 (2018).

49. 49.

Wei, H. et al. Independent beta-arrestin 2 and G protein-mediated pathways for angiotensin II activation of extracellular signal-regulated kinases 1 and 2. Proc. Natl Acad. Sci. USA 100, 10782–10787, https://doi.org/10.1073/pnas.1834556100 (2003).

50. 50.

Sauliere, A. et al. Deciphering biased-agonism complexity reveals a new active AT1 receptor entity. Nat. Chem. Biol. 8, 622–630, https://doi.org/10.1038/nchembio.961 (2012).

51. 51.

Grundmann, M. et al. Lack of beta-arrestin signaling in the absence of active G proteins. Nat. Commun. 9, 341, https://doi.org/10.1038/s41467-017-02661-3 (2018).

52. 52.

Strachan, R. T. et al. Divergent transducer-specific molecular efficacies generate biased agonism at a G protein-coupled receptor (GPCR). J. Biol. Chem. 289, 14211–14224, https://doi.org/10.1074/jbc.M114.548131 (2014).

53. 53.

Schmid, C. L. et al. Bias Factor and Therapeutic Window Correlate to Predict Safer Opioid Analgesics. Cell 171, 1165–1175 e1113, https://doi.org/10.1016/j.cell.2017.10.035 (2017).

54. 54.

Ehlert, F. J. On the analysis of ligand-directed signaling at G protein-coupled receptors. Naunyn Schmiedebergs Arch. Pharmacol. 377, 549–577, https://doi.org/10.1007/s00210-008-0260-4 (2008).

55. 55.

Hall, D. A. & Giraldo, J. A method for the quantification of biased signalling at constitutively active receptors. Br. J. Pharmacol. 175, 2046–2062, https://doi.org/10.1111/bph.14190 (2018).

56. 56.

Gregory, K. J., Hall, N. E., Tobin, A. B., Sexton, P. M. & Christopoulos, A. Identification of orthosteric and allosteric site mutations in M2 muscarinic acetylcholine receptors that contribute to ligand-selective signaling bias. J. Biol. Chem. 285, 7459–7474, https://doi.org/10.1074/jbc.M109.094011 (2010).

57. 57.

Evans, B. A. et al. Quantification of functional selectivity at the human alpha(1A)-adrenoceptor. Mol. Pharmacol. 79, 298–307, https://doi.org/10.1124/mol.110.067454 (2011).

58. 58.

McPherson, J. et al. mu-opioid receptors: correlation of agonist efficacy for signalling with ability to activate internalization. Mol. Pharmacol. 78, 756–766, https://doi.org/10.1124/mol.110.066613 (2010).

59. 59.

Kenakin, T., Watson, C., Muniz-Medina, V., Christopoulos, A. & Novick, S. A simple method for quantifying functional selectivity and agonist bias. ACS Chem. Neurosci. 3, 193–203, https://doi.org/10.1021/cn200111m (2012).

60. 60.

Odaka, H., Arai, S., Inoue, T. & Kitaguchi, T. Genetically-encoded yellow fluorescent cAMP indicator with an expanded dynamic range for dual-color imaging. PLoS One 9, e100252, https://doi.org/10.1371/journal.pone.0100252 (2014).

61. 61.

Motulsky, H. J. Equation: Plateau followed by one phase decay. www.graphpad.com/guides/prism/8/curve-fitting/reg_exponential_decay_plateau.htm?q=decay+plateau, (2019).

62. 62.

Motulsky, H. J. How to: Plateau followed by one phase association. www.graphpad.com/guides/prism/8/curve-fitting/reg_exponential_plateau_then_association.htm?q=association (2019).

63. 63.

Neubig, R. R., Spedding, M., Kenakin, T. & Christopoulos, A. International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification. XXXVIII. Update on terms and symbols in quantitative pharmacology. Pharmacol. Rev. 55, 597–606, https://doi.org/10.1124/pr.55.4.4 (2003).

64. 64.

Black, J. W. & Leff, P. Operational models of pharmacological agonism. Proc. R. Soc. Lond. B Biol. Sci. 220, 141–162 (1983).

65. 65.

Motulsky, H. J. Equation: One phase association. www.graphpad.com/guides/prism/8/curve-fitting/index.htm?reg_exponential_association.htm (2019).

Acknowledgements

Research reported in this publication was supported by National Institute of General Medical Sciences, National Institutes of Health under award number R44GM125390 and National Institute of Neurologic Disorders and Stroke, National Institutes of Health R44NS082222. This content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Author information

Authors

Contributions

S.R.J.H. designed the data analysis framework, designed experiments and analyzed data. P.H.T. designed and executed experiments and analyzed data. A.M.Q. and T.E.H. designed experiments and conceived the study. All authors wrote the manuscript.

Corresponding authors

Correspondence to Sam R. J. Hoare or Thomas E. Hughes.

Ethics declarations

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

Hoare, S.R.J., Tewson, P.H., Quinn, A.M. et al. A kinetic method for measuring agonist efficacy and ligand bias using high resolution biosensors and a kinetic data analysis framework. Sci Rep 10, 1766 (2020). https://doi.org/10.1038/s41598-020-58421-9

• Accepted:

• Published:

• Novel mathematical and computational models of G protein–coupled receptor signalling

• Sabrina Carvalho
• , Abigail Pearce

Current Opinion in Endocrine and Metabolic Research (2021)

• A cellular perspective of bias at G protein‐coupled receptors

• Thomas J. Fernandez
• , Monica De Maria

Protein Science (2020)

• β-arrestin-based biosensors – tools to explore structural determinants of metabolic functions?

• Edda Sofie Fabienne Matthees
• , Raphael Silvanus Haider
•  & Carsten Hoffmann

Current Opinion in Endocrine and Metabolic Research (2020)

• Analyzing kinetic signaling data for G-protein-coupled receptors

• Sam R. J. Hoare
• , Paul H. Tewson
• , Anne Marie Quinn
• , Thomas E. Hughes
•  & Lloyd J. Bridge

Scientific Reports (2020)