TSPO ligand residence time: a new parameter to predict compound neurosteroidogenic efficacy

The pharmacological activation of the cholesterol-binding Translocator Protein (TSPO) leads to an increase of endogenous steroids and neurosteroids determining benefic pleiotropic effects in several pathological conditions, including anxiety disorders. The relatively poor relationship between TSPO ligand binding affinities and steroidogenic efficacies prompted us to investigate the time (Residence Time, RT) that a number of compounds with phenylindolylglyoxylamide structure (PIGAs) spends in contact with the target. Here, given the poor availability of TSPO ligand kinetic parameters, a kinetic radioligand binding assay was set up and validated for RT determination using a theoretical mathematical model successfully applied to other ligand-target systems. TSPO ligand RT was quantified and the obtained results showed a positive correlation between the period for which a drug interacts with TSPO and the compound ability to stimulate steroidogenesis. Specifically, the TSPO ligand RT significantly fitted both with steroidogenic efficacy (Emax) and with area under the dose-response curve, a parameter combining drug potency and efficacy. A positive relation between RT and anxiolytic activity of three compounds was evidenced. In conclusion, RT could be a relevant parameter to predict the steroidogenic efficacy and the in vivo anxiolytic action of new TSPO ligands.

The 18 kDa Translocator Protein (TSPO) is an outer mitochondrial membrane high affinity cholesterol-and drug-binding protein abundant in steroid-producing tissues, including gonads, adrenal, and brain 1 . Previous pharmacological, biochemical and genetic studies, as well as in vivo experiments, have provided several lines of evidence demonstrating that TSPO is a key member of the multiprotein complex transduceosome, as it participates to the cholesterol translocation into mitochondria, which is considered the rate-limiting step of steroidogenesis 2 .
However, one of the most recurrently issue concerning TSPO ligands consists in the lack of correlation between the binding affinity and the in vitro efficacy, including steroidogenic efficacy 21 . This phenomenon has limited not only the identification of lead compounds during the traditional affinity-based drug discovery processes, but also questioned the specificity of the observed effects [22][23][24] . Recent studies have shown that the affinity of a ligand for its target could not directly define its biological action effectiveness, that it may instead be related to the period for which a drug interacts with its target defined as 'Residence Time' (RT) 25,26 .
In the present work, it was investigated whether the RT could be a crucial measure to estimate the steroidogenic efficacy of a TSPO ligand. To this aim, a number of our previous reported TSPO ligands, belonging to phenylindolylglyoxylamides (PIGAs) was selected based on their different abilities to stimulate in vitro steroidogenesis [27][28][29] ,  Table 1. Among such selected TSPO compounds, three presented in vivo anxiolytic effects 28,30,31 .
As a first step, given the poor availability of kinetic parameters for TSPO ligands, a kinetic radioligand binding assay was set up and validated for TSPO ligand RT determination by the use of the theoretical mathematical PK11195 Table 2). The k off determination was obtained by: (i) pre-labelling of TSPO to equilibrium with one [ 3 H]PK11195 concentration (approximately 10 × K d ) that provides high initial TSPO occupancy; (ii) inducing radioligand dissociation by addition of TSPO-saturating concentration (about 1000 × K d ) of unlabeled competing compound PK11195. Then, the dissociation time-course was analyzed using an exponential function. An example of [ 3 H]PK11195 dissociation kinetic curve is shown in Fig. 1A; [ 3 H]PK11195 dissociation was monophasic and gave a half-life of radioligand-TSPO complex (t 1/2 ) of 23 min, which when applied to Equation 1 (see Materials and Methods section) gave a k off of 0.030 ± 0.002 min −1 . The RT value, which is the reciprocal of k off , was 33 ± 4 min ( Table 2).
To determine [ 3 H]PK11195 k on , a family of association kinetic curves using a range of radioligand concentrations were constructed. Each association curve was monitored until equilibrium. In Fig. 1B  In this case, the slope of the line should equate to the association rate and extrapolation of the plot to the Y-intercept (at x = 0) should equal the dissociation rate 39 . When the k ob values were plotted against radioligand concentration, the data were consistent with a straight line (r 2 = 0.98), indicating that binding of [ 3 H]PK11195 to TSPO was consistent with the law of mass action (Fig. 1C). The obtained values were k on = 8.30 ± 0.64 × 10 6 M −1 min −1 and k off = 0.030 ± 0.002 min −1 (Fig. 1C and Table 2). The kinetically derived K d (3.61 ± 0.21 nM; kinetic K d = k off /k on ) was in good agreement with the value obtained from [ 3 H]PK11195 saturation experiments (equilibrium K d = 3.60 ± 0.41) ( Table 2).
RT Determination: TSPO ligand k off and k on by competition kinetic association assays. With the predetermined k on (k 1 ) and k off (k 2 ) values of [ 3 H]PK11195 from 'traditional' kinetic association and dissociation experiments, k on (k 3 ) and k off (k 4 ) of an unlabeled ligand could be determined by fitting the kinetic parameters into the model of 'Kinetics of competitive binding' described in Materials and Methods section. This method is based on a framework developed by Motulsky and Mahan 32 , where an unlabeled competitor is added simultaneously with a radioligand to the receptor preparation of interest. Then, the experimentally derived rate of specific radioligand binding can be modelled to provide the association and dissociation rates of the unlabeled compound.
As a first step, the competition association assay was performed using unlabeled PK11195. Three different concentrations of PK11195 were tested to ensure that the rate parameters calculated were independent of ligand concentration ( Fig. 2A). The k on (k 3 ) and k off (k 4 ) values determined in this assay were 9.20 ± 0.71 × 10 6 M −1 min −1 and 0.034 ± 0.004 min −1 , respectively ( Table 2; PK11195 RT = 29 ± 3 min), which corresponded rather well to the kinetics rates determined by 'traditional' association and dissociation experiments (Table 2). Moreover, the kinetically derived K d obtained from the competition association assay for unlabeled PK11195 was similar to K i obtained from displacement experiments and K d derived from saturation experiments ( Table 2). Taken together, these findings proved that the competition association assay could be applied to determine the binding kinetics of an unlabeled TSPO ligand.
The competition association assay approach has been shown to be highly accurate in determining the binding kinetics at several targets [33][34][35] . However, when the kinetics of multiple compounds need to be determined, the standard model is laborious and time consuming because it implies the use of three concentrations of each unlabeled ligand. Recently, it has been demonstrated that the use of one concentration of unlabeled ligand is able to yield an accurate determination of kinetic rates of unlabeled ligands at their receptor, too 34 . These findings prompted us to modify the three-concentration-dependent assay into a one-concentration-based method. The data analyzed at three-fold K i of unlabeled PK11195 showed a comparable result (k on = 9.30 ± 0.94 × 10 6 M −1 min −1 and K off = 0.029 ± 0.003 min −1 ; RT = 34 ± 3 min) (Fig. 2B) to that generated in a standard (three-concentration-dependent) competition association experiment (Table 2). This result indicates that this simplified method is strong enough to quantify the binding kinetics, which eventually enables testing in a faster medium-throughput format, yet without loss of accuracy.
By using the 'simplified' competition kinetic association assay, the TSPO ligands, including the classical ones Ro5-4864 and PIGA compounds (Table 1) were tested at three-fold respective K i concentration and data were  (Table 2). Competition association assay results demonstrated two patterns of [ 3 H]PK11195 binding in dependence of the competing ligand used. In general, if the competitor dissociates from its target faster than the radioligand, the specific binding of the radioligand will approach its equilibrium time slowly and monotonically. However, when the competitor dissociates slower, the association curve of the radioligand will consist of two phases, starting with a typical "overshoot" and then a decline until a new equilibrium is reached. The results obtained are consistent with a rapid (PIGA719, PIGA720, PIGA745, PIGA835, PIGA925, PIGA1214, Ro5-4864) and a slow (PIGA823, PIGA839 (M-PIGA), PIGA1128, PIGA1138) dissociation rate of the ligands from TSPO. Representative curves for rapid dissociating (PIGA1214) and slow dissociating (PIGA1138) TSPO ligands were shown in Fig. 3A,B, respectively.
To validate the rate constants, the kinetically derived K d were compared with K i obtained from equilibrium competition binding experiments. Notably, an excellent correlation (r 2 = 0.999, p < 0.0001; Fig. 3C) was observed between K i determined in equilibrium-binding studies and K d values derived from the competition association assays ( Table 2). This further proved that the simplified model is able to quantify the association and dissociation rates of unlabeled TSPO ligands accurately.
TSPO ligand steroidogenic efficacy. The steroidogenic efficacy of TSPO ligands was measured in terms of pregnenolone production in C6 glioma cells following exposure with increasing ligand concentrations for a fixed incubation time. For each TSPO ligand, potency (EC 50 value) was derived by sigmoidal concentration-dependent curve and efficacy (E max value, relative to the highest tested concentration of TSPO ligand) was calculated with respect to control (DMSO-treated sample), corresponding to basal pregnenolone production. In Fig. 4, the curves of TSPO ligand-stimulated pregnenolone production are shown. The EC 50 and E max values are detailed in Table 3. Specifically, among all tested TSPO ligands, M-PIGA, PIGA823 and PIGA1138 had the highest efficacy. The majority of the tested TSPO ligands showed efficacy to stimulate pregnenolone production ranging from 140% up to 179% (basal value was set to 100%). Correlation between RT and steroidogenesis efficacy. In Fig. 5, correlation analyses are reported between the TSPO ligand-mediated steroidogenic potency or efficacy and either binding affinity (K i ) or Residence Time (RT). The steroidogenic potency of TSPO ligands correlated with the logarithm of K i (Pearson r = 0.6553; P = 0.0207; r 2 = 0.4295) (Fig. 5A), in agreement with previous reported data [40][41][42] , but not with RT (Pearson r = 0.08962; P = 0.7818; r 2 = 0.0803) (Fig. 5B). The steroidogenic efficacy of TSPO ligands did not significantly correlate with K i (Pearson r = − 0.3489; P = 0.2663; r 2 = 0.1217) (Fig. 5C). Conversely, a highly significant correlation was observed between steroidogenic efficacy and RT (Pearson r = 0.8526; P = 0.0004; r 2 = 0.7270) (Fig. 5D). Correlation analyses were also performed between the logarithm of K i or RT and the area under the dose-response curve (AUC), a value that combines potency and efficacy of a drug into a single parameter 43 . When the relationship    between AUC and the logarithm of K i was analyzed, no correlation was found (Pearson r = − 0.3308; P = 0.2937; r 2 = 0.1094) (Fig. 5E). On the contrary, the AUC values significantly correlates with logarithm of RT (Pearson r = 0.7563; P = 0.0044; r 2 = 0.5720) (Fig. 5F).

Discussion
The TSPO drug discovery has followed the traditional thermodynamic equilibrium constant (K d or K i ) paradigm to identify lead compounds. However, binding kinetics parameters, especially the Residence Time of a drug on its target, are becoming critical predictors for in vivo drug efficacy 25,26 . In the present manuscript, accurate kinetic parameters for TSPO ligands were obtained by the use of the mathematical model of Motulsky and Mahan 32 that has been shown to be highly accurate in determining the binding kinetics of unlabeled ligands at several targets [33][34][35] . This mathematical model has overcame the high cost of compound radiolabeling in order to measure directly the association and dissociation rates of a drug to the target 44 . For binding kinetics determination, classical TSPO   47 . Notably, the steroidogenic efficacy of TSPO ligands did not correlated with the compound binding affinity 21 , suggesting the limitation of a SAR affinity-based strategy. Herein, a highly significant positive correlation between the efficacy to stimulate in vitro steroidogenesis of TSPO ligands and their kinetic parameter RT was found. Remarkably, the efficacy did not correlate with the thermodynamic equilibrium constant K i of the TSPO ligands. Taken together, these results indicate that the key factor for robust steroidogenic TSPO ligand efficacy is not the binding affinity per se, but rather the time the compound spends on the target. Such this novel concept for TSPO ligands suggests the importance of using the RT parameter rather than the constant K i during the in vitro characterization of TSPO compounds in relation to their steroidogenic activity.
The results discussed thus far allow us to outline a preliminary efficacy-based SAR for the interaction of PIGAs with TSPO. Data in Table 2 suggest a cooperative effect between the size of the substituents on the amide nitrogen and the lipophilicity of the aryl group at the 2-indole position. In particular, high retention times and high efficacy seem to derive from the presence of an highly lipophilic moiety at the 2-position (C 6 H 4 -4-CH 3 , C 6 H 4 -4-Cl, naphth-2-yl), combined with at least one of the two N-alkyl groups with a number of carbon atoms in the 1-3 range (PIGA839, PIGA823, PIGA1138).
From a therapeutic perspective, this new concept paves the way to identify TSPO drugs with promising pharmacological activities, including anxiolytic effects. Scientific community has directed particular interest to TSPO ligands for the treatment of anxiety-related disorders, as they have shown fast-acting anxiolytic properties without the typical side-effects of benzodiazepine-based regimes 15,48,49 . Differently to benzodiazepines, which act as direct modulators of the GABA A receptor, TSPO ligands generally enhance GABAergic neurotransmission via the promotion of neurosteroidogenesis without direct effects at the GABA A receptor 17 . Neurosteroids, especially the 3-alpha-reduced steroids, are potent positive allosteric modulators of GABA A receptor 17 . Consistent with such evidences, previous our data 30 50 . In addition, PK11195 has been used to antagonize anxiolytic effects exerted by other TSPO ligands (high steroidogenic efficacy, such as FGIN-1-27, FGIN-1-44 and YL-IPA08) 4,6,19 . These retrospective assessments suggested that a long RT predicts the anxiolytic activity of a TSPO ligand. Moreover, RT is a better efficacy predictive measure than the thermodynamic equilibrium constant K d or K i . Indeed, PK11195, PIGA823 and PIGA839 (M-PIGA) showed comparable K i values (PK11195: K i = 3.60 nM; PIGA823 K i = 3.30 nM; PIGA839 (M-PIGA) K i = 5.50 nM), irrespective to their in vivo activity. Consistent with our data, it has been recently demonstrated discrepancy between the K i of known anxiolytic TSPO ligands (Etifoxine and XBD173) and the enhancement of neurosteroid synthesis 21 . Specifically, Etifoxine, which is already clinically approved for the treatment of anxiety-related disorders, is more potent to stimulate neurosteroidogenesis than XBD173, although its binding affinity to TSPO was approximately 140 fold lower than XBD173. These findings have suggested that the efficacy of such TSPO ligands to stimulate neurosteroid synthesis, thereby leading to anxiolytic effects, cannot be concluded from their binding affinity to TSPO.
In conclusion, the present results indicate that the Residence Time is a better parameter to estimate the steroidogenic effectiveness of a TSPO ligand compared to the equilibrium thermodynamic parameters, corroborating the importance of the drug-target interaction dynamics in predicting the drug efficacy. These findings, in combination with the future availability of a RT database, open the way to optimize TSPO ligands as promising therapeutic tools.
[ 3 H]PK11195 binding saturation assays. Membranes from rat kidneys were prepared as described previously 51 . All the experimental procedures were carried out following the guidelines of the European Community Council Directive 86-609 and have been approved by the Committee for animal experimentation of the University of Pisa. The resulting membrane pellets were aliquoted and frozen at -20 °C. For all radioligand binding assays, an aliquot of membranes was thawed, suspended in assay buffer (AB, Tris-HCl 50 mM, pH 7.4) and homogenized using Ultraturrax. In cell membrane homogenate, protein content was measured by the Bradford method 52 using the Bio-Rad Protein Assay reagent.
Membrane homogenates (30 μ g of proteins) were incubated with increasing [ 3 H]PK11195 concentrations (0.1-20 nM; Specific Activity, 85.7 μ Ci/nmol) in the final volume of 500 μ l of AB for 90 min at 0 °C. Non-specific [ 3 H]PK11195 binding was obtained in the presence of 1 μ M PK11195 (solubilized with ethanol); the solvent concentration was less than 1% and did not interfere with specific [ 3 H]PK11195 binding. After incubation time, samples were filtered rapidly under vacuum through GF/C glass fiber filters. After being washed three times with 3 ml of AB, radioactivity trapped on the filter was measured by liquid scintillation counter (TopCount; PerkinElmer Life and Analytical Sciences; 65% counting efficiency).
[ 3 H]PK11195 binding displacement assays. Membrane homogenates (20 μ g of proteins) were incubated with increasing concentrations of unlabeled TSPO ligand and 1 nM [ 3 H]PK11195 (Specific Activity, 85.7 μ Ci/nmol) in the same above described conditions. The inhibitory constant (K i ) determination was performed for PK11195 and additional compounds, including Ro5-4864 (Sigma-Aldrich Milano, Italy) and PIGA ligands 27-29 . [ 3 H]PK11195 binding 'traditional' kinetics assays. The  Unlabeled TSPO ligand competition kinetic association assays. The unlabeled TSPO ligand kinetic parameters were assessed using the theoretical model of Motulsky and Mahan 32 . Unlike methods in which one compound is pre-equilibrated with the receptor, this approach involves the simultaneous addition of both radioligand and competitor to receptor preparation, so that at t = 0 all receptors are unoccupied. [ 3 H]PK11195 (approximately 30 nM; SA, 21.4 μ Ci/nmol) was added simultaneously with unlabeled compound to membrane homogenates (30 μ g of proteins) in a final volume of 500 μ l AB. The degree of bound to TSPO was assessed at multiple time points by filtration harvesting and liquid scintillation counting, as above described. The assay was performed using concentration of PK11195 corresponding to one-, three-and ten-fold its K i . For 'simplified' competition kinetic association assays, the experiments were performed using concentration of unlabeled TSPO ligands corresponding to three-fold their K i . Pregnenolone measurement. Pregnenolone assessment was performed using rat C6 glioma cells as an in vitro steroidogenic model, as previously described 29 . C6 cells were cultured in Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum, 2 M L-glutamine, penicillin at 100 U/mL, and streptomycin at 100 μ g/mL. Cell cultures were maintained in a humidified atmosphere of 5% CO 2 and 95% air at 37 °C. Before the measurement of pregnenolone production, the cells (seeded in 96-well plates at a density of ∼ 10 5 cells/well) were washed 2 times with a salt medium, consisting of 140 mM NaCl, 5 mM KCl, 1.8 mM CaCl 2 , 1 mM MgSO 4 , 10 mM glucose, and 10 mM N-2-hydroxyethylpiperazine-N′ -2-ethanesulfonic acid(HEPES)-NaOH (pH 7.4) plus 0.1% bovine serum albumin. For the measurement of pregnenolone secreted into the medium, the further metabolism of pregnenolone was blocked by the addition of trilostane (25 μ M) and SU10603 (10 μ M) (inhibitors of 3β -hydroxysteroid dehydrogenase and 17α -hydroxylase, respectively) to the salt medium. The addition of PK11195, Ro5-4864 or PIGAs to the C6 cells was accomplished by complete change of the salt medium to a medium containing increasing concentrations of the compounds (ranging from 0 to 100 μ M). The final concentration of vehicle (DMSO or ethanol) was constant for all of the samples and did not exceed 0.5% (v/v), a concentration that did not affect steroid production on its own. At the end of the incubation periods (2 hours), the cell medium was collected and the amount of pregnenolone secreted into the medium was quantified by an enzyme immunoassay, under the conditions recommended by the supplier. Cross-reactivity with other steroids was typically less than 1% Scientific RepoRts | 6:18164 | DOI: 10.1038/srep18164 and cross-reactivity with progesterone is 6%. The sensitivity of the assay was 0.05 ng/ml. Unknown samples were compared with concurrently run standards of pregnenolone using a one-site competition model (calibrator curve). Data analysis. All experiments were analyzed by either linear or non linear regression using Prism 5.0 (GraphPad Software Inc., San Diego, CA). Equilibrium K d and maximum binding sites (B max ) values of [ 3 H] PK11195 at TSPO were obtained by computational analysis of saturation curves. Competition displacement binding were fitted to sigmoidal (variable slope) curves. The concentration of test compounds that inhibited [ 3 H]PK11195 binding to kidney membranes by 50% (IC 50 values) obtained from the inhibition curves were converted to K i values using the method of Cheng and Prusoff 53 . [ 3 H]PK11195 dissociation data were fitted to a one-phase exponential decay function and the t 1/2 value obtained was transformed into a k off rate using the Equation: [ 3 H]PK11195 association data were fitted to a single phase exponential association function to calculate an observed rate constant k ob . Association and dissociation rates for unlabeled TSPO ligands were calculated by fitting the data in the competition association model using the 'kinetics of competitive binding' assay, defining the amount of radioligand bound to receptor ([RL]) as a function of time 32 :