A new, simple and robust radioligand binding method used to determine kinetic off-rate constants for unlabeled ligands. Application at α 2A - and α 2C -adrenoceptors

Kinetic on and off rate constants for many receptor ligands are dif ﬁ cult to determine with regular radioligand binding technique since only few of the ligands are available in labeled form. Here we developed a new and simple radioligand binding method for determining the kinetic off-rate constant for unlabeled ligands, using whole cells expressing α 2A - and α 2C -adrenoceptors. The new method involves pre-incubation with unlabeled ligand, centrifugation of microtiter plates in order to adhere the cells to the bottom surface, and then upside-down centrifugation of the plates for few sec-onds to wash away the non-bound fraction of the pre-incubated ligand. The ﬁ nal on-reaction assay for the radioligand is then started by quick addition of a relatively fast-associating radioligand to the cells. The curve obtained is de ﬁ ned by a fairly simple mathematical formula that re ﬂ ects the simultaneous dissociation of pre-incubated ligand and association of the radioligand. The method proved to produce highly reproducible results in determining the k off constants for various unlabeled ligands. The results show that the α 2C -selectivity of MK912 depends mainly on a very slow off-rate at the α 2C adrenoceptor subtype. Regarding the markedly α 2C - over α 2A -selective compound spiroxatrine, its much faster on-rate at α 2C - than α 2A -adrenoceptors explains much of its exceptional α 2C -selectivity. Several new techniques for determining the kinetic component of ligand-receptor interactions at molecular level are currently developing. As a reference, based on standard radioligand binding techniques, the present study describes a simple and robust experimental and mathematical procedure for determining k off constants of unlabeled drugs. & 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
In a recent review, the importance of quantitative data regarding drug interaction with receptors was highlighted (Bylund and Toews, 2014). It was pointed out that such interaction almost always follows well-defined mathematical relationships that are based on receptor theory. In the same special issue, the importance of drug-receptor theory in the field of pharmacology in biomedical research was highlighted (Kenakin and Williams, 2014). To date, almost all studies involved in determining the affinity of many ligands to a receptor have been performed at equilibrium. Thereby, the kinetic component of the ligand-receptor interaction becomes undervalued (Pollard, 2010;Hoffmann et al., 2015). The shortage of kinetic studies for unlabeled ligands is probably due to the difficulty of performing and analyzing such kinetic experiments, in which, when including a radioligand, four kinetic constants plus the time factor are participating simultaneously in the process. In the present study, we present an experimental method that reduces the complexity of the experimental data and consequently eases the mathematical analysis. The new radioligand binding experimental method was used to determine the kinetic off-rate constants for several unlabeled drugs at α 2A -and α 2C -adrenoceptors.
Previously, other studies have described different experimental and mathematical strategies for determining the kinetic constants for unlabeled small ligands acting at G protein-coupled receptors. For example, Motulsky and Mahan (1984) described the mathematics for analyzing the curves obtained after the simultaneous addition of radioligand and competitor, including four rate constants in the analysis. Another study presents a laboratory manual account for the full experimental procedure (Sykes et al., 2010). Yet another study addressed the same subject as the present study, i.e. the development of a simplified method for the determination of the off-rate k off constant of unlabeled ligands (Packeu et al., 2010). Both that study and the present study use an approach consisting of pre-incubating the receptor preparation with ligand, washing out free ligand molecules, adding radioligand and monitoring its binding after various times. However, the practical solutions and technical details differ widely (see Section 4). The methodology presented in the present study is rather robust, well suited for studies aiming at determining the off-rate constant for many unlabeled ligands at a receptor.
In a recent study, the K d value of the radioligand [ 3 H]-RX821002, and the K i values of seven competing drugs at the human α 2A -, α 2C -, and 4 chimeric α 2A -/α 2C -adrenoceptors were determined (Jahnsen and Uhlén, 2013). The results gave clues about what regions of the receptors are causing the subtype-selectivity for the ligands. In the present study, aiming at gathering more information about specific ligand-receptor interactions, the off-rate constants for [ 3 H]-RX821002 and 8 unlabeled drugs were determined at the human α 2A -and α 2C -adrenoceptors and at two chimeric α 2A -/α 2C -adrenoceptors. The mathematical differential equation formula used for fitting the data to the curves, described by Malany and coworkers (2009), is evaluated in some detail.

Plastic ware
The drug MK912 sticks to polystyrene (PS) surfaces, but not to polypropylene (PP) (Uhlén et al., 1994). Therefore, MK912 was dissolved, diluted, and assayed in PP tubes and PP microtiter plates. In other cases, PS microplates were used, since PS plates are transparent, enabling casual observation of the cells in a microscope. For upside down centrifugation, Greiner 96-well flat bottom microtiter plates (polystyrene # 655101; polypropylene # 655201) were fit upside down into slightly trimmed bottom parts of Finntip filter 200 μl yellow tip boxes (# 94052300) from Thermo Fisher Scientific Oy, Vantaa, Finland, and then centrifuged.

Cell culture
The HEK293 cells were grown in standard tissue culture plastic material at 37°C, 95% air, 5% CO 2 , in Dulbecco's modified Eagle's medium (DMEM), supplemented with 9% fetal calf serum and 100 U/ml penicillin and 0.1 mg/ml streptomycin. Cells were subcultured every 3-4 days, by detachment with 0.5 mg/ml trypsin and 0.2 mg/ml EDTA.

Transient expression
The HEK293 cells were transiently transfected with the receptor constructs. 1.2 μg of plasmid DNA was diluted in 245 μl of OptiMEM, and 6 μl of Lipofectamine was diluted in 245 μl of Op-tiMEM. 5 min later these two solutions were mixed. After 30 min of incubation, the complex was added to HEK293 cells in 25 cm 2 culture dishes in a total volume of 2.8 ml of OptiMEM. After transfection, the cells were further cultured for 48 h.

Cell preparation
Cells transfected with receptor constructs were detached from 25 cm 2 culture dishes with 8 ml of isotonic 50 mM Tris, 1.5 mM EDTA, 100 mM NaCl, pH 7.5. Each cell suspension was centrifuged at 400 g for 3 min, and the cell pellets were re-suspended in 4 ml of binding buffer (50 mM Tris, 100 mM NaCl, pH 7.5). Cell clumps were thoroughly dispersed by pipetting up and down many times with a 1-ml pipette. The suspensions were further diluted (12 times for α 2A , 6 times for CppA, and 3 times for α 2C and AppC) in order to obtain about 0.1 nM receptor concentration in the preincubation assays.
2.8. [ 3 H]-RX821002 binding to whole cells, for obtaining the k off and k on constants for the radioligand For the radioligand bound to a receptor, the k off value is easily measured in radioligand binding experiments by blocking the onreaction with a high concentration of an antagonist (LR ¼LR eq *exp -k°ff*t ). In order to determine the k off constant for [ 3 H]-RX821002 at the 4 tested receptors, 125 μl of cell suspension aliquots were mixed with 25 μl radioligand in the binding assays. After 60 min of incubation, one microplate row, with assays representing the binding equilibrium at T 0 , was filtered. To the remaining assays, 150 μl of 20; μM atipamezole was added, and then, after various times the assays were filtered.
The on-rate constant (k on ) is somewhat more complicated to measure, since the experimental on-reaction curve also involves the k off value, the formula being LR ¼LR eq *(1-exp -(kon*L þ koff)*t ).
Anyhow, knowing the k off value, it is rather straightforward to establish the k on value from an on-reaction curve. In principle 125 μl of cell suspension were mixed with 25 μl radioligand in the binding assays, and after various times the assays were filtered. The filtering was performed on Whatman GF/C filters, using a Brandel cell harvester. Radioactivity retained on the filters was counted in a Beckman β-scintillation counter. Curves were fitted using GraphPad Prism. The k off and k on constants obtained from these experiments are presented in Table 1, and the curves are shown in Fig. 1A-B.
2.9. Experimental design developed for the determination of k off constants for unlabeled drugs In order to facilitate the mathematical analysis, we developed an experimental design where the impact of the on-reaction for the competitors was almost eliminated, and therefore the on-rate could be approximated to zero. Using whole cells in suspension, the cell surface receptors were pre-incubated for 1 h in 96-wells microtiter plates (see paragraph 2.3) with a high (19xK i ) concentration of an antagonist in order to obtain 95% saturation of antagonist binding to the receptors. The assay volume was 150 μl.
Then, the microtiter plates were centrifuged at 3000 rpm (1110 g) for 3 min. This attached the HEK 293 cells with antagonist-blocked receptors to the bottom surface. The microplate was then centrifuged upside-down at 600 rpm (44 g) for 10 s to remove the H]-RX821002) was added rather forcefully to the cells. Thereby, most of the HEK293 cells became re-suspended, due to that cell attachment was weak since attachment of the cells had been achieved just by the previous centrifugation in the calcium free buffer. This step also defines T 0 in the on-reaction for the radioligand as well as T 0 in the off-reaction for the antagonist. Thereafter, the assays were filtered at different time points. The first filtration was performed after 30 s, then after 2, 6, 15, 36 and 72 min. At T 0 the on-rate for the binding of [ 3 H]-RX821002 to receptors will be very small, since there are very few free receptors available. Depending on the off-reaction for the antagonist more receptors become available for [ 3 H]-RX821002 to bind to. The off-reaction of the unlabeled ligand is easily inferred from the delay imposed on the on-reaction curve of the radioligand. In practice, from each one-day experiment we obtained the k off constants of 4 ligands at 2 different receptors, with n¼ 1. This equals the k off constants of 8 ligands at 4 different receptors after 12 one-day experiments, with n ¼3. Some advice on the application of the experimental method is provided in supplement 1.

Formulas used for the curve fitting
The differential equation developed by Malany et al. (2009) describes the on-reaction curve for the radioligand when the receptors have been pre-incubated with a competitor as described above. In their analysis it is assumed that all receptors are blocked by the pre-incubated competing drug at the time of addition of the radioligand, and that the free concentration of competitor, left from the pre-incubation or derived from subsequently dissociated bound competitor, is negligible. Under these conditions, the binding curve is defined by Eq. (1): The first part of the equation above, i.e. RL¼ B max *(k1*L)/ (k1*L þ k2)*(1 À exp -(k1*L þ k2)*t ), describes the association binding curve for the radioligand in the absence of a competitor. Within this part, the term k1*L/(k1*L þ k 2 ) describes occupancy based on the rate constants, while (1 À exp -(k1*L þ k2)*t ) describes the association rate.
The second part of the equation, i.e. ((k 1 *L)/(k 1 *L þk 2 -k 4 ))* (B max *(exp À (k1*L þ k2)*t -exp -k4*t )), describes the factor to be subtracted from the first part due to the pre-bound competitor. This factor always has a negative value, lowering the on-rate of the radioligand, especially at early time points of the reaction. It is this part that makes Eq. (1) a differential equation (see Supplements 3A-B for details).
The formula actually used in the present study (Eq. (2), below) is a slight modification of Eq. (1), and describes the on-reaction curve for the radioligand when initially only 95% of the receptors are blocked. This level of blockade occurs after pre-incubation with the competing drug at a concentration 19 times its K i value. The explicit writing of Eq. (2)   The curve fitting becomes fairly easy. The on-rate constant of the radioligand k 1 is detectable in the control curve, and is then set constant for all curves in that particular experiment (exemplified in Fig. 1(C)-F). The off-rate constant of the radioligand k 2 was obtained in earlier experiments, and is also set constant. The concentration of the radioligand L can be approximated to [L] E [L] added , or can be calculated precisely as [L]¼[L] added - [LR]. Since very little competitor is present in the final radioligand binding assay almost no receptors are blocked by competitor at the final equilibrium, and LR eq can be approximated as being shared among the control curve and all the other curves in that experiment. It can be noted that the competitor's k on constant, k 3 , is absent from the formula, since the on-reaction of the competitor is negligible due to the low concentration of the competitor after the washout of free competitor, and due to the blocking effect by the radioligand and the large 300 μl final assay volume. The remaining rate constant, i.e. the searched for k off constant for the competing drugs, k 4 , should be well detectable using our experimental set-up. The best applicability is for drugs where the t 1/2 of the drug is longer than the duration of time before the first measurement, which in our case was 30 s Each experiment aimed at determining the k off constant of unlabeled drugs included six curves, whereof one duplicate control curve for determining the on-rate constant of the radioligand in that particular experiment. After calculating k 1 from the control curves, k 1 and k 2 were set constant in the full 6-curve analysis (2 control curves and 4 curves obtained after preincubation with antagonists), and the B max value was set shared for the 6 curves. Except the shared B max value, the only constant the mathematical analysis had to define was the k off constant of the pre-incubated unlabeled drugs, i.e. the k 4 constants. Eq. (2) describes the curves obtained by the herein described experimental design, and under these conditions Eq. (2) is fully sufficient, and easier to use than the full 4 kinetic constant analysis described by Motulsky and Mahan (1984). The main limitation of our method is that only drugs with half-lives in the range 1 À 60 min were readily analyzable, i.e. drugs with k off constants between 0.693 min À 1 and 0.012 min À 1 (t 1/2 ¼ln2/k 4 ). At the fast dissociation rate extreme, the dissociation rate was hard to detect for competitors having k 4 values higher than 1.386 min À 1 , i.e. when it takes less than half a min for the pre-incubated drug to dissociate from half of the receptors.
Pre-incubating with not more than 19 fold the K i values of the unlabeled compounds seems to avoid the problem of residual presence of competitors in the final assays (such "contamination" was seen with higher doses in pilot experiments). Using ligand pre-incubation concentrations at 19X their K i values, all curves in the experiments approached the shared B eq after 72 min, except the curves with MK912. However, even for MK912 the analysis indicated that the residual blocking of [ 3 H]-RX821002 binding by pre-incubated MK912, at the α 2C -and AppC-adrenoceptors, at 72 min, was due to not yet dissociated molecules, since the drug was continuously dissociating for up to 3 h in experiments with extended incubation times (not shown). In addition, pilot experiments performed at 37°C showed that all MK912 eventually dissociated from pre-incubated α 2C -adrenoceptors, In a study resembling the present study, Packeu et al. (2010) used plated cultured cells in their approach to determine the offrate constant of unlabeled ligands. They introduced the term "twostep" procedure, involving a pre-incubation step with unlabeled ligand. The main technical differences between their study and our study are that we started with cell suspensions instead of plated cells, and we removed free ligand by upside-down centrifugation instead of aspiration. Using cell suspensions is very convenient, especially when many drugs are to be tested, since the cell solutions are homogeneous and can be diluted at will, and there is no delay between plating of the cells and performing the kinetic experiment. Un-binding of the pre-incubated ligand, as well as binding of the radioligand, occur at cells which to a large extent had become re-suspended by the forceful addition of the diluting radioligand solution. This allows good diffusion accessibility for the ligands. In addition, our mathematics is even more reductive than that of Packeu and coworkers, since we use just one concentration of pre-incubated competitor, while they constructed dose-response curves. Our on-reaction curves represent the same type of curves that are present in their Figure 4C.

Experimental methodology
The concept behind the present study was to practically eliminate the on-reaction of the competitors at the stage after the preincubation. Thereby, we arrive at a simpler mathematical formula. At the start of the present project, such an elimination of the onreaction seemed straightforward in theory, but technically it turned out to be more difficult than anticipated. In series of pilot experiments we tried in vain an experimental setup where membrane preparations expressing the α 2A -adrenoceptors were pre-incubated with competitors. After the pre-incubation, excess competitor was washed away by centrifugation at high speed (38,000 g), and the supernatant discarded. However, re-suspension of the pellets took too long time, and no reproducible results were obtained. Therefore, we turned to whole cell preparations.
[ 3 H]-RX821002 does not enter whole cells, and thereby it labels plasma membrane receptors from the extracellular side only (Jahnsen and Uhlén, 2012). Whole HEK293 cells (150 μl suspension) pre-incubated with competitors (19xK i ) in a microtiter-plate can be centrifuged at 3000 rpm (1110 g) for three min, attaching the cells to the bottom surface. Then, turning the microplate upside-down and centrifuging at 600 rpm (44 g) for 10 s removes essentially all medium into the attached waste container. Immediately after the centrifugation process, 300 μl of [ 3 H]-RX821002 was quickly and rather forcefully added to the cells. This action resulted in the re-suspension of most of the cells in one step. Assuming pre-bound competitor does not start to dissociate from the receptors until the addition of the diluting buffer, including the radioligand, the on-reaction for [ 3 H]-RX821002 and the off-reaction for the pre-bound competitor start simultaneously.

Experimental k off and k on values for [ 3 H]-RX821002
at the α 2A -, α 2C -, and two chimeric α 2 -adrenoceptors In Fig. 1(A) is shown the on-rate curves for [ 3 H]-RX821002, obtained at whole cells expressing α 2A , α 2C , and two chimeric α 2adrenoceptors. The curves represent the binding of [ 3 H]-RX821002 at various time points after adding the radioligand. The association t 1/2 values at the various receptors were in the range 0.5-3 min Fig. 1(B) shows the off-rate curves for [ 3 H]-RX821002 from its equilibrium binding state. The procedure was to add an excess of atipamezole after a 60 min of pre-incubation with [ 3 H]-RX821002, and then filtering at various time points. The dissociation t 1/2 values at different receptors were in the range 3-6 min. Among the α 2A -, α 2C -and chimeric α 2 -adrenoceptors, the on-rate constant (k on ) of [ 3 H]-RX821002 was highest at the α 2C -and AppC-receptors, while the off-rate constant (k off ) was highest at the α 2Cand CppA-receptors (Table 1). The calculated K d values, i.e. the k off / k on ratios, were 2.06 nM at the α 2A -, 1.26 nM at the α 2C -adrenoceptors, 0.38 nM at the AppC receptor and 4.90 nM at the CppA receptor. The order of these values corresponds to the corresponding K d values determined by equilibrium binding (Jahnsen and Uhlén, 2013). The kinetically determined K d values are slightly higher than the K d values determined at equilibrium, an effect likely induced by the high concentration of blocking competitor added in the off-rate experiments (see Vauquelin and van Liefde, 2012).

Experimental k off values and calculated k on values for unlabeled
ligands at the α 2A -, α 2C -, and two chimeric α 2 -adrenoceptors Fig. 1(C)-(F) show the on-rate curves for [ 3 H]-RX821002 after pre-incubation with competitors. Displaying the curves in a semilogarithmic plot, the curves are shifted to the right as compared to the antagonist-free control time-curve, though not in parallel since the blocking effect of the pre-incubated ligands is largest at early time points. The binding curves, which are influenced by the offrates of the competitors, look quite similar among the α 2A -and CppA-receptors, and so are the binding curves among the α 2Cand AppC-receptors. This implies the C-terminal half of these receptors has the largest subtype-selective influence on the offrate of the ligands, confirming that the C-terminal half of these receptors is the main determinant for the receptor's drug selectivity (Jahnsen and Uhlén, 2013).  Table 2 with the K i values of the ligands yields the calculated k on values (k on ¼ k off /K i ). The K i values of RS79948-197 and yohimbine were obtained in the present study, while the K i -values of all the other tested compounds had already been determined in our previous study (Jahnsen and Uhlén, 2013  The calculated k on constants are shown in Table 3. As can be seen in Table 3, the ligand with the lowest calculated k on value was yohimbine at the α 2A -adrenoceptor (k on ¼0.0152 nM À 1 min À 1 ).
The ligand with the highest calculated k on value was atipamezole at the AppC receptor (k on ¼1.671 nM À 1 min À 1 ). Table 4 shows the α 2C /α 2A selectivity ratios of six ligands, regarding k off constants, k on constants, and affinities. The drugs with lowest k off ratio between α 2C /α 2A were spiroxatrine and MK912. This contributes to their α 2C -selectivity. The drug with the highest k on ratio between α 2C /α 2A was spiroxatrine. The high on-rate and slow off-rate for spiroxatrine at the α 2C -adrenoceptor makes spiroxatrine markedly α 2C -selective.
The results show that the α 2C -over α 2A -adrenoceptor selectivity of MK912 depends mainly on a very low off-rate for MK912 at the α 2C -adrenoceptor. On the other hand, the α 2C -over α 2A -selectivity of spiroxatrine depends both on its high on-rate as well as on its low off-rate at the α 2C -adrenoceptor. Atipamezole showed very high off-rate at the α 2A -and α 2C -adrenoceptors, but still shows high affinity thanks to its concomitant very high on-rate (see Fig. 2(A)-(B)).

Affinity range for applicability of the experimental method
The dissociation of MK912, RS79948-197, spiroxatrine, yohimbine, and RX821002 had t 1/2 values above one min at the receptors. These ligands produced a clear delay of [ 3 H]-RX821002 binding. Atipamezole, BRL44408, and chlorpromazine had t 1/2 values near or below one min at the receptors, and the calculated k off values for these drugs are therefore less adequate. Nevertheless, it is clear that chlorpromazine dissociates quickly from all the tested receptors. As a rule of thumb, the methodology enabled clear detection of the off-rate constant for unlabeled ligands with K i values in the range 200 pM-10 nM. The drug with lowest affinity where k off still was detectable was spiroxatrine at α 2A , where the K i value was 24 nM, and the k off value 0.64 min À 1 (Table 3). This is a fairly low k off value, and low off-rate, for such a low-affinity drug, so the low affinity seems to be caused by a corresponding low k on value. The drug with highest affinity that still dissociated completely within 72 min was RX821002 at AppC, where the K i value was 0.24 nM and the k off value 0.082 min À 1 (Table 3). Since, RX821002 had rather high on-and off-rates, the half-life of bound RX821002 was fairly short despite its high affinity, namely about 8 min (t 1/2 ¼ln2/k off ).

Discussion
4.1. A radioligand binding experimental design for determining the Table 2. Experimental k off dissociation rate constants for pre-incubated ligands, determined at native α 2A -and α 2C -adrenoceptors and at two chimeric receptors. Shown are the k off 7 StdP values (unit min À 1 ), and number of experiments. The k off values in Table 2 are also presented graphically in Fig. 2 Table 3. Calculated k on association rate constants (nM À 1 min À 1 ) for the pre-incubated ligands at native α 2A -and α 2C -adrenoceptors and at two chimeric receptors. The formula used is k on ¼ k off /K i . The k off values were taken from Table 2. The K i values were taken from Jahnsen and Uhlen, 2013, except for RS79948-197 and yohimbine where the K i values were obtained in the present study. The calculated k on values in Table 3 are also presented graphically in Fig. 2 Table 4.
Ratio of α 2C -over α 2A -selectivity for 7 ligands, regarding dissociation rates, association rates, and affinities. In the second column is shown the calculated α 2C /α 2A k off values ratio. In the third column is shown the calculated α 2C /α 2A k on values ratio. These ratios were calculated from data presented in the previous tables. In the fourth column are shown the α 2C -over α 2A -selectivity of the ligands, calculated from the k on value ratios in column 3 divided with the k off value ratios in column 2.
The same α 2C -over α 2A -selectivity value is extractable from the K i values, since the k on values were derived by calculation from the ligand's k off and K i values.

Ligand
Ratio of dissociation rates (k off α 2C / k off α 2A) Ratio of association rates (k on α 2C / k on α 2A) α 2C -over α 2A -selectivity (k on ratio / k off ratio) Cut-offs were set at k off ¼1.386 min À 1 and k on ¼1.386 nM À 1 min À 1 . At higher k off values half of the dissociation occurs in less than 30 s, and therefore determination of off-rate constants above this value is less accurate.
kinetic off-rate constants for unlabeled drugs at α 2 -adrenoceptors The major aim of the present study was to develop a simple radioligand binding experimental design for determining the kinetic off-rate constants for unlabeled drugs. Previous radioligand binding studies, including in-depth mathematical analysis, have been performed, characterizing the kinetics of competitive binding at β-adrenoceptors (Motulsky and Mahan, 1984), muscarinic receptors (Schreiber et al., 1985;Dowling and Charlton, 2006), D 2 dopamine and CB 1 cannabinoid receptors (Packeu et al., 2010), and adenosine A 1 receptors (Sykes et al., 2010;Guo et al., 2013;Xia et al., 2016). Most of the methods used in these studies have limitations, either due to high complexity or due to narrow applicability. In an all-at-once assay, several factors ([C], [CR], [R], [L] and [LR]) are varying simultaneously, and four different kinetic constants are involved (k 1 , k 2 , k 3 , k 4 ) (see Motulsky and Mahan, 1984). Using a two-step method, as in the present study, the only unknown kinetic constant in the final on-rate curve for the radioligand is the k off constant of the unlabeled competitor (k 4 ). Thus, the on-rate constant for the radioligand (k 1 ) is set constant with the value obtained from the control curve. The off-rate constant for the radioligand (k 2 ) is known from previous experiments (Table 1). The on-rate constant for the competitor (k 3 ) becomes redundant by the efficient washing-out of the competitor.
The results confirm that the experimental concept works, the wet-lab methodology essentially consisting of pre-incubation of receptors at whole cells with competitor, then quick washout by upside-down centrifugation, followed by performing the on-reaction for the radioligand. In the analysis, the k off constant of the unlabeled competitor was calculated by fairly simple curve fitting mathematics (Eq. (2)), derived from the differential equation (Eq. (1)) of Malany et al. (2009). Our results show that spiroxatrine associates slowly and dissociates rapidly at the α 2A -and the CppAreceptors. Conversely, at the α 2C -and AppC-adrenoceptors, spiroxatrine associates rapidly and dissociates slowly. This pattern constitutes the α 2C -and AppC-selectivity of spiroxatrine. Regarding MK912, the off-kinetics experiments showed that MK912 dissociated very slowly from α 2C and AppC. In PET studies it has been shown that [ 11 C]MK-912 washed out problematically slow from the brain (Shiue et al., 1998). A contributing reason for this slow washout might be the low off-rate of MK912 at α 2C -adrenoceptors, as shown in the present study.

Kinetic parameters of ligand-receptor interactions
There are two established methodologies for studying the kinetic component of ligand-receptor interactions, namely radioligand binding and surface plasmon resonance, while several fluorescence-based methods were classified as in development [Hoffmann et al., 2015]. However, it is not until just recently that surface plasmon resonance technique (Biacore) has been used for determining the kinetic constants for small molecules interacting with G protein-coupled receptors (Rich et al., 2011). This technique still is laborious in the preparation of receptor-coated sensor chips and it is more difficult to analyze the binding kinetics for small molecules than for larger molecules. A different but technically advanced method is currently developed, namely a single molecule nanoscopic method for tip-attached peptides, enabling detection of the contact force between the ligand and receptor, i.e. measuring the required off-kinetic energy (Alsteens et al., 2015). To large extent, the off-kinetic energy determines the residence time for a ligand at a receptor. Copeland and coworkers defined the term residence time to refer to the temporal duration of the binary receptor-ligand complex, and stated that the residence time is affected by the dissociation rate (see Copeland, 2016). According to Copeland et al. (2006) the residence time (τ) is defined by τ¼1/ k off , making residence time proportionally 1.443 times longer than dissociation half-life defined by t 1/2 ¼ ln2/k off . Thus, in mass action kinetics, residence time and dissociation half-life are interchangeable. These two time-constants do not fully define ligand affinity or receptor occupancy, which according to the law of mass action are dependent on both the on-and off-rates. However, at the individual receptor level, the residence time of a ligand might influence its biological effect, so the quantitative assessment of this parameter has a role in the overall evaluation of receptor-ligand interactions in pharmacology (Tummino and Copeland, 2008;Guo et al., 2014;Hothersall et al., 2016;Vauquelin, 2015). Intuitively, residence time can be mistaken for the temporal presence of the ligand-receptor complex, i.e. receptor occupancy Â B max Â time ((mol/liter)xmin), which is visualized as an area under the curve. However, residence time in the simplest model (Hothersall et al., 2016) is just a time point (min) at the dissociation curve. In binding kinetics experiments, the temporal presence of the ligand-receptor complex becomes larger with faster on-rate or slower off-rate, while residence time only is influenced by the off-rate. In our experiments, the observed k off values reflect detachment and dissociation from the receptor, i.e. the freeing of the receptor from pre-bound competitor. This rate is somewhat modified by immediate re-binding of the ligand to the original receptor, i.e. by a local un-binding -re-binding process (see Vauquelin, 2016 in press). Thus, our observed k off value represents dissociation of the ligand all the way out of the receptor (Fig. 3), which may resemble a true situation at individual receptors.

The chimeric AppC and CppA receptors
The chimeras were designed in order to evaluate whether the first transmembrane helix of the α 2A -adrenoceptor is indirectly interacting with the second extracellular loop of the receptor, hypothetically inducing slow on-rate (or fast off-rate) for bulky drugs like chlorpromazine, rauwolscine and spiroxatrine at the α 2A -subtype, and thereby induce α 2C -over α 2A -selectivity (Laurila et al., 2011). Our results could not confirm any hypothetical interaction between TM1 and extracellular loop 2 in the α 2A -adrenoceptor, such that bulky drugs would associate slowly and/or dissociate rapidly at the α 2A -but not at all of the α 2C -, AppC and CppA-receptors. That complete pattern was in fact not observed for any of the four successfully tested bulky ligands MK912, RS79948-197, spiroxatrine or yohimbine. For example, the specifically slow on-rate of spiroxatrine was shared among the α 2A -and the CppA-receptors, even though the CppA-receptor has its first transmembrane helix from the α 2C -adrenoceptor. However, a general observation was that most of the tested ligands had slower on-rates at the α 2A -as compared to at the α 2C -adrenoceptor ( Fig. 2(B)).

Off-rate detection range between too fast and too slow off-rates for the pre-incubated ligands
Among the herein tested drugs the detection range corresponded to drugs with K i values in the range 0.2 À 10 nM. Drugs with K i values above 10 nM tended to have too high off-rate for the k off constant to be detectable. The fact that low affinity drugs usually have high off-rates is obvious from the formula K i ¼k off / k on . However, for analysis of drug binding to receptors there are plenty of substances with K i values in the range 0.2 À 10 nM, and among them some may show unexpected on-or off-rates at various receptors.

Kinetic ligand-receptor interactions
In the present study we show that the on-reaction rate may vary substantially among different drugs as well as for any drug at two different receptors ( Table 2). The results implies that the onrate for a ligand is dependent on diffusion, positioning at the receptor, and attachment to the binding site, while the off-rate is dependent on detachment and diffusion away from the binding site. The physical bond forces at the binding site constitute the main factor in determining the dissociation half-life and affinity of a ligand for the receptor, but the on-and off-movements of the ligand may also play a role for its affinity. Thus, in a recent molecular dynamics simulation and experimental study it was demonstrated that even receptor features with little contribution to affinity may prove critical to the dissociation process (Guo et al., 2016). The fact that some drugs, like spiroxatrine, have a higher k on constant at the α 2C -than at the α 2A -adrenoceptor seems to indicate that the α 2A -and α 2C -adrenoceptors interact differentially with spiroxatrine at the entrance process for the drug. RS79948 and yohimbine moved slowly in and out of the binding site at all tested receptors, while RX821002 and atipamezole moved fast in and out. Notably, MK912 dissociates extremely slowly from the α 2C -adrenoceptor subtype. Finally, at the α 2C -adrenoceptor subtype, spiroxatrine enters the binding site fast, but dissociates slowly, explaining its α 2C -selectivity. In Fig. 3 we present a model where the movements of the ligand are separated from the physical bonds between ligand and binding site. The model is meant to illustrate a theoretical separation between on one hand the movements of the ligand into and out of the binding site, and on the other hand the physical binding force keeping the ligand attached at the binding site. The model gives an idea about what is defining the affinity of a reversible drug for the receptor, and may help theorists refine in silico receptor models. For example, the affinity of a prospective ligand could be optimized, by creating a new molecular structure, having a higher on-rate.