In Vitro to in Vivo Translation of Allosteric Modulator Concentration-Effect Relationships: Implications for Drug Discovery

Abstract

Allosteric modulation of GPCRs represents an increasingly explored approach in drug development. Due to complex pharmacology, however, the relationship(s) between modulator properties determined in vitro with in vivo concentration-effect phenomena is frequently unclear. We investigated key pharmacological properties of a set of metabotropic glutamate receptor 5 (mGlu₅) positive allosteric modulators (PAMs) and their relevance to in vivo concentration–response relationships. These studies identified a significant relationship between in vitro PAM cooperativity (αβ), as well as the maximal response obtained from a simple in vitro PAM concentration–response experiment, with in vivo efficacy for reversal of amphetamine-induced hyperlocomotion. This correlation did not exist with PAM potency or affinity. Data across PAMs were then converged to calculate an in vivo concentration of glutamate putatively relevant to the mGlu₅ PAM mechanism of action. This work demonstrates the ability to merge in vitro pharmacology profiles with relevant behavioral outcomes and also provides a novel method to estimate neurotransmitter concentrations in vivo.

Small molecule allosteric modulation has emerged as an attractive strategy for development of novel pharmacotherapies targeting G protein-coupled receptors (GPCRs).¹ Modulators act by changing the affinity and/or efficacy of an endogenous orthosteric ligand. Advances in receptor theory have provided detailed mathematical models to describe allosteric ligand–receptor interactions.²⁻⁶ The operational model of allosterism (OMA) has proven particularly valuable for quantification of allosteric ligand properties using relatively simple and economical assays common to GPCR research.^2,4−8 Beyond incorporation of assay/system-specific parameters, including orthosteric ligand concentration ([A]), affinity (K_A), agonism (τ_A), maximal effect (E_M), and slope of the transducer function for occupancy-effect (n), global fitting of the OMA to data from in vitro studies enables determination of modulator-specific parameters: affinity for the unliganded receptor (K_B), composite affinity-efficacy cooperativity (αβ) with the orthosteric ligand, and intrinsic agonist activity (τ_B, if present). Additional data from equilibrium binding assays can also be used to separate composite cooperativity (αβ) into discrete affinity cooperativity (α) and efficacy cooperativity (β) parameters.² Such modeling approaches represent highly useful and widely recognized strategies for in vitro characterization of novel allosteric modulators.

Many drug discovery programs rely on determinations of modulator potency and efficacy from functional assays involving a modulator concentration–response curve (CRC) in the presence of a fixed concentration of orthosteric agonist.^1,3 Chemical optimization efforts then often focus on structure–activity relationships (SAR) using a single potency-based parameter (e.g., pEC₅₀/pIC₅₀ or EC₅₀/IC₅₀). Although this is useful for rank-ordering compounds and may be acceptable in certain contexts, it is generally not ideal for the optimization of allosteric modulators due to the diversity of primary properties (i.e., affinity and cooperativity factors, as well as pharmacological mode switches driven by synthetic chemical changes or metabolism and agonist probe dependence⁹) that may give rise to similar secondary properties (i.e., EC₅₀ and E_MAX) and may mask SAR more relevant to the desired in vivo effect profile. For instance, two modulators with distinct affinity and cooperativity properties (e.g., one with relatively high affinity and low cooperativity, the other with relatively low affinity and high cooperativity) may exhibit similar in vitro potencies yet display substantially different in vivo concentration-effect profiles due to their dissimilar molecular modulation properties. Such observations can preclude construction of reliable in vivo preclinical pharmacokinetic/pharmacodynamic (PK/PD) models, which often serve as the basis for projection of a clinically efficacious human dose level/schedule and must also capably account for frequently present species differences in modulator pharmacology. This approach also fails to account for the potential difference between the in vitro concentration of the orthosteric agonist ligand used in modulator profiling (e.g., fixed EC₂₀ for a PAM) and the in vivo concentration of the agonist in therapeutically relevant tissue(s). Thus, there exists a strong need for improved, holistic in vitro to in vivo translational approaches to GPCR allosteric modulator pharmacology.

Here, we probed data from an internal metabotropic glutamate receptor 5 (mGlu₅) positive allosteric modulator (PAM) development program at the Vanderbilt Center for Neuroscience Drug Discovery to determine the relationships between in vitro molecular pharmacological parameter(s), in vivo concentrations, and in vivo efficacy in an acute rodent neurobehavioral paradigm: reversal of amphetamine-induced hyperlocomotion (AHL), a preclinical predictor of antipsychotic efficacy. PAM concentrations in plasma and brain were quantified at the same time point from rat AHL studies employing a discrete dose range of each PAM. Measured and calculated concentrations (plasma total and unbound as well as brain total and unbound) were used to construct individual PAM CRCs. We then attempted to correlate the resulting in vivo EC₅₀ values with relevant in vitro parameters (EC₅₀, K_B, and αβ) to determine which modulator properties or profiles may govern in vivo efficacy; this approach was unsuccessful. However, by calculating the in vivo concentration of each PAM needed to reverse AHL to a specific degree (35%), we identified a significant correlation between AHL reversal and modulator cooperativity (composite log αβ) for all examined biophases. Additionally, this method revealed a significant correlation between the concentration of compound needed to reverse AHL and the maximal response (E_MAX) elicited in in vitro CRC experiments in the presence of an EC₂₀ concentration of glutamate. Finally, we used these data to predict the in vivo concentration of glutamate potentiated by the PAMs within the AHL paradigm, which converged to a common value. Overall, our data suggest that, at least for the mGlu₅ PAMs tested here, specific modulator properties influence efficacy in vivo and point to novel, refined methods that might be exploited during a lead optimization campaign.

Results

Distinct in Vitro Pharmacology Profiles Are Present within a Set of mGlu₅ PAMs

The structures of the 10 mGlu₅ PAMs used in these studies are shown in Figure 1a. For each compound, we performed potency determinations in human embryonic kidney (HEK293A) cells expressing the rat mGlu_5a receptor (Figure 1b,c, Table 1). In these experiments, the compound was applied to rat mGlu₅ cells that had been loaded with the calcium indicator dye, Fluo-4 AM. After 2 min, a concentration of glutamate that elicits an approximately 20% maximal response was added (EC₂₀). The ability of each compound to potentiate the glutamate EC₂₀-induced calcium mobilization response was calculated and normalized to the response elicited by a maximal concentration of glutamate (1 mM). In the absence of glutamate, none of the 10 PAMs exhibited intrinsic agonism in this assay (data not shown).

Figure 1.

Modulator potency curves for enhancement of glutamate stimulation of mGlu₅ iCa²⁺mobilization. (a) Structures of a validation set of 10 mGlu₅ PAMs. (b, c) Modulation of glutamate stimulation of iCa²⁺ mobilization in HEK cells expressing the rat mGlu_5a. Increasing concentrations of indicated modulator were added prior to a concentration of glutamate that elicits a 20% maximal response (b, c). The glutamate control curve is shown in gray squares. Data were normalized to the maximal glutamate (1 mM) response and fit with a 4-parameter logistic equation. Data are mean ± s.e.m. of three independent determinations performed in triplicate.

Table 1. In Vitro Pharmacological Properties of mGlu₅ PAMs. Data are Mean ± s.e.m. from Three to Six Independent Experiments.

compound ID	rat pEC50a (EC50, nM)	%Glu maxb	pKBc (KB, μM)	log αβd (αβ)	log τAe (τA)	nf	basalg	Emh
VU0419832	6.94 ± 0.07 (114)	76.2 ± 1.7	5.93 ± 0.02 (1.2)	0.99 ± 0.07 (9.7)	0.31 ± 0.03 (2.0)	1.7 ± 0.3	1.1 ± 0.2	96.0 ± 1.1
VU0455651	7.78 ± 0.03 (16.8)	75.9 ± 0.3	6.96 ± 0.13 (0.11)	0.97 ± 0.12 (9.2)	0.27 ± 0.01 (1.9)	1.9 ± 0.3	1.4 ± 0.4	97.1 ± 1.1
VU0464075	6.94 ± 0.02 (115)	61.8 ± 1.8	6.40 ± 0.04 (0.40)	0.58 ± 0.04 (3.8)	0.32 ± 0.02 (2.1)	2.1 ± 0.2	1.8 ± 0.2	97.3 ± 0.5
VU0447256	6.91 ± 0.03 (123)	71.9 ± 2.0	6.09 ± 0.03 (0.81)	0.70 ± 0.03 (5.1)	0.24 ± 0.11 (1.8)	2.4 ± 0.3	1.9 ± 0.3	96.6 ± 2.3
VU0415133	6.74 ± 0.01 (181)	73.3 ± 1.0	6.14 ± 0.20 (0.72)	0.76 ± 0.04 (5.7)	0.29 ± 0.04 (1.9)	2.1 ± 0.2	2.5 ± 0.5	98.7 ± 1.5
VU0409551	6.65 ± 0.01 (224)	74.1 ± 1.0	5.13 ± 0.12 (7.4)	0.97 ± 0.10 (9.4)	0.33 ± 0.02 (2.2)	2.2 ± 0.2	1.7 ± 0.4	97.6 ± 1.9
VU0462807	6.63 ± 0.04 (236)	64.9 ± 0.4	5.99 ± 0.05 (1.0)	0.64 ± 0.07 (4.3)	0.30 ± 0.02 (2.0)	2.0 ± 0.2	1.6 ± 0.3	97.2 ± 1.4
VU0464042	6.58 ± 0.07 (264)	71.5 ± 0.7	5.90 ± 0.05 (1.3)	0.76 ± 0.05 (5.7)	0.29 ± 0.01 (2.0)	2.1 ± 0.2	2.0 ± 0.3	97.9 ± 1.5
VU0405372	6.34 ± 0.04 (456)	48.3 ± 2.9	5.70 ± 0.10 (2.0)	0.32 ± 0.04 (2.1)	0.40 ± 0.02 (2.5)	2.1 ± 0.2	1.5 ± 0.2	95.9 ± 0.7
VU0408899	5.37 ± 0.07 (4200)	79.4 ± 3.0	4.94 ± 0.04 (12)	0.78 ± 0.05 (6.1)	0.36 ± 0.01 (2.3)	2.3 ± 0.2	1.5 ± 0.3	97.2 ± 0.7

^aNegative logarithm of the modulator concentration required to induce half-maximal potentiation of an EC₂₀ glutamate response derived from curve fits in Figure 1.

^bMaximal level of potentiation of EC₂₀ glutamate in the presence of indicated PAM, expressed as a percentage of the response to 1 mM glutamate.

^cNegative logarithm of the equilibrium dissociation constant of indicated allosteric modulator, estimated by application of the OMA to functional interaction studies with glutamate (Supplemental Figure 1).

^dComposite cooperativity factor describing the magnitude and direction of the allosteric interaction between indicated modulator and glutamate for iCa²⁺ mobilization.

^eCoupling efficiency of glutamate for iCa²⁺ mobilization in HEK293A-mGlu₅ (rat) cells.

^fNonlinear transducer function that links agonist occupancy to response.

^gBasal response of HEK293A-mGlu₅ (rat) cells for iCa²⁺ mobilization in response to vehicle.

^hMaximum possible system response, expressed as a percentage of the response to 1 mM glutamate.

PAM potency curves are commonly used within discovery programs to efficiently screen for positive modulator activity, with modulator pEC₅₀’s and E_MAX used to interpret SAR. However, both pEC₅₀ and E_MAX derived from such curves represent composite values that are influenced by the orthosteric agonist concentration and system coupling efficiency,⁸ as well as modulator-specific parameters: cooperativity (αβ), affinity (K_B) and intrinsic efficacy (τ_B). To demonstrate this point, we simulated the influence of a pure PAM on an orthosteric agonist functional response (Figure 2a) and modeled the resulting potency and E_MAX values in the presence of an EC₂₀ concentration of agonist (Figure 2b,c). As can be seen from the simulations, cooperativity influences both potency and E_MAX, whereas modulator affinity influences PAM potency alone. We previously demonstrated that an operational model of allosterism can be directly applied to PAM potency curves to estimate modulator K_B and αβ.⁸ However, given the potential for both system and ligand-dependent factors to influence these estimates as simulated in Figure 2, we further profiled each compound using “progressive fold-shift” experiments. In these studies, an escalating range of compound concentrations was applied two min prior to increasing concentrations of glutamate, generating a full glutamate CRC at each concentration of PAM (Supplemental Figure 1, Table 1). Data were fitted using an operational model of allosterism as described in Supplementary Methods to calculate a composite cooperativity value (log αβ) and PAM affinity (logK_B).⁸ As can be seen in Table 1, these compounds exhibited a range of in vitro potencies, cooperativities, and affinities.

Figure 2.

Simulating allosteric modulation of functional responses and the impact of different operational parameters on modulator potency curves. For all simulations, the orthosteric agonist was defined by pK_A = 6, log τ_A = 1, where basal = 0, E_m = 100, and n = 1. In these simulations, the maximum response to orthosteric agonist approaches the system E_m. The parameters governing the allosteric modulator are noted in the figure for each simulation; in all instances, affinity modulation was neutral (log α = 0) and allosteric agonism was negligible (log τ_B = −100). (a) Simulating the effect of a pure PAM with different degrees of efficacy cooperativity on the concentration–response curve to an orthosteric agonist. (b) From the simulations in panel a, we plotted the PAM potency at the EC₂₀ orthosteric agonist response. (c) We performed similar simulations where log β values were held constant (equal to 1), but the modulator affinity (pK_B) was changed to show the impact on PAM potency.

In Vivo EC₅₀ of mGlu₅ PAMs To Reverse Amphetamine-Induced Hyperlocomotion in Rodents Does Not Correlate with in Vitro Modulator Properties

mGlu₅ PAMs exhibit efficacy in reversing amphetamine-induced hyperlocomotion (AHL) in rodents,¹⁰⁻¹³ a model that has predictive validity for typical and atypical antipsychotics in schizophrenia, a long-standing proposed indication for mGlu₅ PAMs. During the course of our mGlu₅ PAM discovery program, we profiled the compound activity using dose–response analysis in the AHL model (Supplementary Figures 2 and 3). At the end of each AHL study (1.5 h post-administration of test compound), brain and plasma samples were collected and subjected to bioanalysis by LC–MS/MS to quantitate compound concentration (Supplemental Figure 4). We plotted the total and unbound (using fraction unbound values determined in vitro) brain and plasma concentrations measured at each dose at the same time point after administration (Figure 3a and Supplemental Figure 5). We then fitted these data using nonlinear regression to determine the in vivo EC₅₀ (black horizontal line) for total brain (black vertical line), unbound brain (blue vertical line), total plasma (green vertical line), and unbound plasma concentrations (red vertical line, Figure 3a, Supplemental Figure 5, Table 2, and Supplemental Tables 1–3). We subsequently used these in vivo EC₅₀ values to perform correlations with the in vitro-derived parameters: potency, affinity, and cooperativity. As shown in Figure 3b–d (total brain) and Supplemental Table 4 (unbound brain, total plasma, and unbound plasma), there was no significant correlation of in vivo EC₅₀ of the compounds to reverse AHL and modulator properties calculated in vitro.

Figure 3.

mGlu₅ PAMs exhibit dose-dependent reversal of AHL that correlates with increasing total and unbound exposure in brain and plasma. (a) % AHL reversal was calculated based on the total number of beam breaks (Supplemental Figures 2 and 3) from n = 5–13. Brain and plasma concentrations were determined at the conclusion of each experiment via LC–MS/MS (Supplemental Figure 4). Log [compound] was plotted versus the % AHL reversal, and data (all are mean ± s.e.m.) were fitted using a three-parameter logistical equation. EC₅₀ values (horizontal black dotted line) in each of the four matrices (total brain, black vertical dashed line; unbound brain, blue vertical dashed line; total plasma, green vertical dashed line; and unbound plasma, red vertical dashed line) were calculated (Table 2 and Supplemental Tables 1–3). (b–d) Correlations are shown for the calculated EC₅₀ value versus the in vitro potency (pEC₅₀, b), the unliganded affinity (log K_B, c), and cooperativity (log αβ, d). R² and p values for each regression line are listed in Supplemental Table 4.

Table 2. Total Brain Curve Fits.

compound ID	AHL pEC50 (EC50, μM)	R2 of curve fit	span/2b (% reversal at pEC50)	pCBr total at 35% reversalc (μM)
VU0419832	5.80 ± 0.22 (1.6)	0.575	50	6.06 (0.9)
VU0455651	5.91 ± 0.49 (1.2)	0.466	50	6.18 (0.67)
VU0464075	6.20 ± 0.25 (0.63)	0.501	23.1	5.71 (1.9)
VU0447256	5.13 ± 0.32 (7.5)	0.462	35.1	5.13 (7.4)
VU0415133	5.83 ± 0.22 (1.5)	0.653	33.5	5.79 (1.6)
VU0409551	5.64 ± 0.16 (2.4)	0.705	49.1	5.89 (1.3)
VU0462807	6.11 ± 0.28 (0.78)	0.442	31.2	6.01 (0.99)
VU0464042	5.11 ± 0.21 (7.8)	0.594	43.6	5.28 (5.2)
VU0405372d	5.00 ± 0.51 (9.9)	0.272	22.7	4.48 (33.2)
VU0408899	6.82 ± 0.26 (0.15)	0.588	36.2	6.85 (0.14)

^aCurve shown in Figure 3 and Supplemental Figure 3.

^bThe span was calculated as the distance between the bottom and top of the curve fit and divided by 2 to calculate % reversal at the determined pEC₅₀ concentration. Top was constrained between 0 and 100, for which 100% reversal was defined as the locomotor response for rats treated with vehicle/vehicle. Therefore Span/2 values equal to 50 represent curve fits for which the top plateau was not completely defined by the doses used.

^cTotal brain concentration (C_Br Total) at a constant 35% AHL reversal.

^dFor VU0405372, the response to 56.6 mg/kg gave a lower % reversal than both 30 and 100 mg/kg doses. To enable curve fitting, these data were excluded from the fit.

The Concentration of mGlu₅ PAM Needed to Induce a 35% Reversal of AHL Correlates with in Vitro Cooperativity but Not Potency or Affinity

The EC₅₀ value derived from the in vivo data curve fits results in a distinct level of “percent reversal” at the determined EC₅₀ for each compound (Table 2 and Supplemental Tables 1–3). Indeed, for multiple compounds, there was an incomplete definition of the sigmoidal concentration–response curve fit, requiring extrapolation of the maximal response due to the limited doses administered in the AHL paradigm. The lower confidence observed for some of these curve fits may contribute to the low correlation observed with the various pharmacological parameters. However, rather than relying on individual EC₅₀ values, another way to compare activity of compounds in vivo would be to compare the concentration needed to induce the same level of response in the pharmacodynamic assay (dashed horizontal red line in Figure 3 and Supplemental Figure 5). For this comparison, we chose a reversal level of 35%, as all compounds reversed AHL to at least this magnitude, but this level was also submaximal for all compounds. For example, at the highest dose tested for VU0405372, the maximal degree of reversal observed was 39%. As shown in Figure 3 and Supplemental Figure 5, the horizontal red lines depicting 35% reversal are below the determined EC₅₀ value for some compounds (VU0419832, VU0455651, VU0409551, VU0464042) and equal to, or above, the determined EC₅₀ value for others (VU0464075, VU0447256, VU0415133, VU0462807, VU0405372, and VU0408899). Upon obtaining these “35% reversal concentrations” (Table 2 and Supplemental Tables 1–3), we correlated these concentrations with the in vitro pEC₅₀, pK_B, and log αβ values (Table 1). As with the EC₅₀ studies, we did not observe a significant correlation of the PAM concentrations that induce a reversal level of 35% with in vitro potency or unliganded pK_B (calculated) in any matrix (Supplemental Figure 6 and Table 4). This was not surprising for in vitro potency values given that this parameter is a composite that is influenced by multiple system and ligand dependent factors as simulated in Figure 2. In contrast, there was a significant correlation with the cooperativity (log αβ) values for this set of 10 mGlu₅ PAMs for all matrices (Figure 4a–d, Table 3).

Figure 4.

The concentration needed to reverse AHL by 35% [AHL₃₅] is significantly correlated with the in vitro determined cooperativity (a–d) and% maximal glutamate response (e–h) across all matrices. Values are listed in Table 2 and Supplemental Tables 1–3. In each panel the red data point corresponds to VU0360172. The reported R² and p values on these graphs exclude VU0360172. When VU0360172 is included in the regression analyses of log αβ, for total brain R² = 0.447 and p = 0.0244; for unbound brain R² = 0.360 and p = 0.051; for total plasma R² = 0.502 and p = 0.0146; for unbound plasma R² = 0.373 and p = 0.0459. Including VU0360172 for analyses of PAM E_MAX values, for total brain R² = 0.580 and p = 0.0065; for unbound brain R² = 0.405 and p = 0.035; for total plasma R² = 0.619 and p = 0.0041; for unbound plasma R² = 0.372 and p = 0.047.

Table 3. Linear Regression Fits Correlating the PAM Concentration for 35% AHL Reversal with Indicated in Vitro Pharmacological Parameters.

	pEC50			pKB			log αβ			Glu max
	slope	R2	p	slope	R2	p	slope	R2	p	slope	R2	p
total brain	–0.152 ± 0.322	0.0269	0.6510	–0.144 ± 0312	0.0261	0.6560	0.206 ± 0.086	0.4210	*0.0424	10.57 ± 3.32	0.5595	*0.0128
unbound brain	–0.193 ± 0.365	0.0336	0.6123	–0.355 ± 0.336	0.1224	0.3217	0.236 ± 0.097	0.4258	*0.0408	10.85 ± 4.19	0.4567	*0.0319
total plasma	–0.126 ± 0.367	0.0145	0.7407	–0.175 ± 0.351	0.0301	0.6316	0.238 ± 0.095	0.4376	*0.0372	12.25 ± 3.62	0.5882	*0.0096
unbound plasma	0.040 ± 0.376	0.0014	0.9176	–0.119 ± 0.360	0.0134	0.7499	0.247 ± 0.095	0.4554	*0.0323	10.67 ± 4.33	0.4318	*0.0390

^*Notes significant (p<0.05).

The Concentration of mGlu₅ PAM Needed To Induce a 35% Reversal of AHL also Correlates with in Vitro Maximal Response for Potentiation

In a chemical optimization structure–activity relationship campaign for PAMs, a compound CRC in the presence of a low orthosteric agonist concentration (e.g., giving 10–20% of maximal response) is commonly generated to initially triage compounds, as generating multiconcentration progressive fold shift data can be time-consuming and cost-prohibitive. Given that differences in αβ can influence the maximal response obtained in a modulator CRC determination with an EC₂₀ of agonist (Figure 2b), we next assessed whether maximal responses for PAMs could be used instead of αβ to predict in vivo efficacy (% glutamate maximum (Glu Max) values are shown in Table 1(8)). Indeed, when we plotted the concentration needed for AHL reversal with the maximal response obtained in our modulator CRC, we found significant correlation for total and unbound levels in both plasma and brain (Figure 4e–h, Table 3). We next sought to ascertain if αβ and E_MAX correlated with in vivo efficacy for an earlier, structurally distinct, “pure PAM”, VU0360172. Our previous report demonstrated that VU0360172 reversed AHL by ∼37% when dosed at 10 mg/kg i.p.,¹² reaching total brain and plasma concentrations of 5.1 μM and 10.2 μM (with 98.9% plasma protein bound and 97.1% brain homogenate bound), respectively. Inclusion of VU0360172 data in these analyses retained significant correlations with αβ (Figure 4, red symbol), but not E_MAX (data not shown). We reasoned that the lack of correlation with E_MAX when VU0360172 may be due to the use of different detection methods for iCa²⁺ mobilization assays, as well as observations that VU0360172 can elicit allosteric agonist activity in some assays.^14,15 Therefore, we re-evaluated VU0360172 in the same cell line and assay system used here. We observed no agonism as well as no significant change in potency (pEC₅₀ of 7.47 ± 0.13, ref (12) versus 7.44 ± 0.29, mean ± s.e.m., unpaired t test, p = 0.0016 n = 3) but a significant difference in the maximal response (86.9 ± 2.7, ref (12), versus 61.1 ± 2.1, mean ± s.e.m., unpaired t test, p = 0.002, n = 3). When these new data were included into the correlation, a significant relationship between E_Max and AHL efficacy was now observed. This suggests that the correlation of in vitro parameters may require consistent profiling in the same cell background to afford the highest likelihood of developing a relationship between in vivo efficacy and in vitro properties. Overall, these data suggest that, at least for the compounds tested here, efficacy in the AHL model for mGlu₅ PAMs is primarily driven by cooperativity, where compounds with the highest cooperativity require lower PAM concentrations to achieve the same amount of efficacy in AHL. Further, for this target and in vivo model, rank-ordering pure PAMs by E_MAX responses derived from primary concentration–response data performed in the same cell line and assay can provide valuable information for a chemical optimization campaign without requiring extensive operational modeling analysis.

Employment of a Range of Allosteric Modulators Can Be Used To Predict in Vivo Endogenous Agonist Concentrations

A final question we asked with these data relates to the orthosteric agonist concentration that is present for potentiation in vivo. This can be an important point for multiple reasons, such as validating a true PAM mechanism in vivo, understanding how potential changes in endogenous agonist (i.e., glutamate) levels that occur within a specific disease context might impact allosteric modulator efficacy, and selecting the most relevant fixed agonist concentration for in vitro PAM CRCs to drive chemical optimization. Thus, we returned to the progressive fold shift data performed in vitro (Supplemental Figure 1) and calculated the responses induced by different PAM concentrations in the presence of EC₂₀, EC₃₀, EC₄₀, EC₅₀, EC₆₀, EC₇₀, and EC₈₀ glutamate concentrations. These data were then transformed into concentration–response curves for each compound, and the concentration of each PAM required to induce a 35% response in vivo was interpolated or extrapolated from these curve fits (Figure 5a, Supplemental Figure 7). These data are, in essence, the predicted glutamate-response relationship for the in vivo efficacious concentration of each PAM (Figure 5b, Supplemental Figure 8). We hypothesized that these concentration–response relationships may reflect the relevant concentration of glutamate being potentiated in vivo. When averaged across the four matrices, for 8 of the 10 compounds tested, the glutamate EC₅₀ values derived from these studies (Figure 5c) were not significantly different. For the two PAMs that did not meet this criterion, we note that the glutamate concentrations were derived from fits for which the unbound brain and plasma data were extrapolated, which may contribute to lower estimates. In addition, VU0408899 also showed greater variability with respect to in vivo concentrations across individual animals than the other compounds. These studies predict that an in vivo glutamate EC₅₀ of approximately 100 nM is relevant for the AHL mechanism and suggest that use of a range of allosteric modulators may be useful for establishing a hypothesis to predict in vivo endogenous agonist concentrations.

Figure 5.

Extrapolation of glutamate concentrations from combined in vitro and in vivo data. (a) From progressive fold shift interactions with glutamate (Supplemental Figure 1), the data were transformed to plot the concentration of glutamate versus the PAM concentration. The PAM concentration required to reverse AHL by 35% is indicated by the vertical lines for each of the four matrices (solid black, total brain; dotted black, total plasma; blue, unbound brain; red, unbound plasma). (b) For each matrix, a glutamate concentration–response curve was generated for the 35% reversal concentration (as shown for VU0419832); the EC₅₀ of these curves for each PAM were then averaged for the four matrices and are plotted in panel c. One way ANOVA with a Tukey’s post hoc test on averaged pEC₅₀ values showed VU0408899 was significantly different (p < 0.05) from VU0455651, VU0447256, VU0464042, whereas VU0409551 was significantly different from VU0447256 and VU0464042.

Discussion

Pharmacologists are often faced with the challenges of “which in vitro parameter is the most important for predicting in vivo efficacy, and how do we best screen and optimize for it?” While many drug discovery programs rely on modulator potency in the presence of a fixed, low concentration of agonist to drive modulator structure–activity relationships,¹ it is not clear that this experimental design results in a meaningful interpretation of the in vivo situation. In our own experience, it often does not, suggesting that there are components of the allosteric mechanism that warrant further investigation. The molecular and analytical techniques used to characterize allosteric modulators have expanded in scope, allowing quantification of modulator affinity, cooperativity, and intrinsic activity. Consideration of these factors is increasingly being applied in GPCR allosteric modulator discovery campaigns to dissect structure–activity relationships for the individual components that govern efficacy in vitro.¹⁴⁻¹⁹ Qualitative understanding of the importance or role of individual modulator parameters might emerge over time from simple “trial and error”. While such broad observations may prove useful and positively impact the direction or focus of a discovery/optimization program, there remains a need for more rigorous assessment of in vitro molecular pharmacological properties that underscores allosteric modulator in vivo activity. Of the 10 mGlu₅ PAMs depicted here, we found a significant correlation of modulator cooperativity and maximal potentiation response (with glutamate) with in vivo efficacy in rat AHL, which extended to another structurally distinct PAM, VU0360172.^12,20 This correlation did not exist with PAM potency, highlighting the inherent issues with using PAM EC₅₀ values, which are influenced by system, orthosteric agonist, and allosteric modulator properties,¹ as a decision point for compound progression.

Correlations were performed with different in vivo matrices: total and unbound plasma levels as well as total and unbound brain levels. Several matrices were examined with the assumption that a principally linear relationship in one or more matrices, with some degree of uniform bias (i.e., systemic over- or underprediction of in vivo potency from in vitro potency by an empirical factor), would be anticipated. This approach can be used to identify the most-relevant matrix (i.e., biophase) that “drives” in vivo activity (e.g., “unbound plasma-driven efficacy”). Our most robust correlations with log αβ were observed with total brain and total plasma levels. We interpret this to be important from several standpoints. For example, allosteric modulators are generally highly lipophilic, which can often result in difficulties in calculating accurate unbound concentrations relevant to engagement of the target (which itself may be present in a deep tissue biophase). Additionally, each modulator has specific molecular pharmacological properties. The correlation with both total and unbound plasma, as well as total and unbound brain concentrations, with cooperativity and/or maximal potentiation is relevant as dose projection is often determined from plasma levels and, for CNS targets, an understanding of a compound’s ability to penetrate the blood brain barrier (i.e., brain:plasma K_p; K_p,uu). Observations of total brain tissue concentrations “driving” in vivo efficacy may also arise from persistent signaling by internalized GPCR-ligand(s) complex (i.e., “endosomal GPCR signaling”)²¹ or acting via intracellularly located receptors.²² In such scenarios, total concentrations, versus unbound levels, may better approximate the “effective” concentration due to the receptor-bound compound being sequestered within the tissue’s intracellular compartments. However, this possibility would be predicted to be more likely for target receptors with high expression levels and with compounds exhibiting relatively low to moderate brain distribution.

For a given target and allosteric compound mechanism of action it is necessary to deconvolute the critical parameter/s that are predictive of in vivo efficacy. While we found a correlation between parameters measured in an in vitro calcium assay and in vivo activity, this may not be the case for all in vitro assays, between structurally distinct modulators, among different in vivo behavioral assessments, or between compounds with distinct pharmacokinetic properties (note that here exposure was only determined at a single time point). In these studies, we used a calcium mobilization assay to measure activity of mGlu₅ PAMs; in this case, this in vitro assay gave a readout that was correlative to in vivo efficacy. However, this may not be the case for other in vitro assays that may be chosen for compound profiling. Indeed, certain mGlu₅ PAMs have different degrees of positive cooperativity with the same agonist depending on the measure of mGlu₅ activity.²³⁻²⁵ Additionally, even when interacting at the same site,¹² distinct modulators can differentially stabilize receptor conformations. More structurally diverse analogues may also engage completely unique sites on the receptor or have distinct residence times.^25,26 These differences in receptor engagement can induce signal bias downstream of mGlu₅ activation, which can lead to differential efficacy or side effect profiles in vivo.^13,27 This is critically important for mGlu₅ PAMs as it relates to their pro-convulsive and neurotoxic effects. While it has been argued for mGlu₅ that low levels of potentiation (i.e., < 3-fold shift of glutamate CRC) are needed to avoid adverse effects,²⁸ other parameters may be equally important. Indeed, VU0409551 exhibits robust cooperativity and a unique biased agonism profile in vitro, and yet does not induce neurotoxic effects or seizures at very high in vivo exposures in rodents.¹³ In contrast to other mGlu₅ PAMs, VU0409551 does not induce coupling of mGlu₅ to NMDA receptor currents,¹³ and we hypothesize that this property contributes to its safety margin. These results are consistent with the interpretation that NMDA receptor current potentiation is not responsible for efficacy in AHL. However, had potentiation of NMDA receptor activity been a primary screening assay for mGlu₅ PAMs, compounds with favorable safety and efficacy profiles, such as VU0409551, would have been eliminated from further consideration. For this reason, building a data set throughout a program to correlate pharmacokinetic and pharmacodynamic relationships for a series of ligands is crucial, and back-translating this information into the primary assay used for compound assessment would be anticipated to allow integration of the most predictive in vitro assays to assist in prioritizing chemistry and driving SAR. Moreover, clear understanding of in vitro to in vivo concentration–response relationships/mechanisms for a given series of compounds in a particular animal model is vital to maximize the probability of accurate translation to higher species for which predictions often require adjustment for species differences in a candidate drug’s pharmacology.

Here, we found that the maximal potentiation response elicited by an mGlu₅ PAM in an in vitro potency experiment could be used as a proxy for αβ and correlated with efficacy in rat AHL. There are two important caveats here that are evident from our simulations (Figure 2). PAM E_max values from a titration assay and cooperativity will only correlate in cases (1) for which there is no intrinsic agonist efficacy and (2) when the system max does not impose a limit on the maximal level of potentiation observed. Indeed, for all PAMs tested, the maximal degree of potentiation achieved was lower than the maximal response elicited by glutamate. There are many examples of in vitro assays in which the maximal response induced in the presence of PAM is higher than the response elicited by a maximal concentration of agonist, defined as the E_MAX (i.e., the maximal response induced by agonist in the assay), versus the E_m (i.e., the maximal system response), particularly when chimeric or promiscuous G proteins are used to couple a G_i/o-coupled GPCR to various signaling pathways (e.g., see ref (29)). Further, for mGlu₅ allosteric modulators, cooperativity with glutamate is primarily mediated by efficacy (β) rather than affinity (α) modulation.^8,30 Additionally, in the current study employing this cell line and assay, we did not observe allosteric agonist activity. Indeed, mGlu₅ PAM-agonist activity and biased agonism has been linked to adverse effect liability,^23,28,31 as well as potential to induce acute desensitization,³² all of which may influence apparent E_MAX. With increased pharmacological complexity due to the system or ligands under investigation, using E_MAX rather than an operationally determined αβ value may not retain the same predictive ability as was observed here.

An additional note relates to the in vivo assay and time points chosen for compound profiling. In the studies here, we have established that cooperativity appears to drive in vivo efficacy in rat AHL (on an in vivo PAM concentration-normalized basis). However, cooperativity alone may NOT underlie adverse effect liability for mGlu₅ PAMs, or, potentially, efficacy in a distinct in vivo readout. This divergence in efficacy versus safety margins may be particularly important for the continued development of mGlu₅ PAMs, for which recent reports of on-target adverse effect liability have dampened enthusiasm for an otherwise promising target in the treatment of schizophrenia, cognitive impairments, and autism-associated disorders such as Rett syndrome.³⁴⁻³⁸ We have not determined the elimination half-life of each compound or the kinetics following oral administration at all doses used. Therefore, the concentrations measured at 1.5 h may not represent the maximum concentrations reached during the study, and concentrations of each compound are likely to change in a compound-specific manner over the AHL time-course. However, our goal was to provide a method that could be integrated efficiently into a chemical optimization screening campaign, and the main objective was to correlate efficacy with in vitro parameters. For this reason, these studies were designed to take a “snapshot” approach regarding exposure from the AHL study to determine if such correlations could be made. Additional pharmacokinetic/pharmacodynamic studies, with complete time-course measurements, would provide further information and refinement to our studies.

If a strong, linear relationship is observed between PAM in vitro and in vivo potencies from a given matrix (e.g., total brain concentrations), we predict that these data may conceptually be used to crudely estimate the relevant orthosteric agonist (e.g., endogenous glutamate) concentration present in vivo (i.e., “tone” in the brain regions/circuitry underlying the pharmacodynamic effect(s)). Here we interpolated or extrapolated the concentration of each PAM needed to induce a fixed in vitro response of each modulator and then calculated the predicted glutamate concentration available for potentiation. Predicted glutamate concentrations were remarkably similar across 8 of the 10 PAMs tested. We note that VU0408899 appears to be an outlier in these studies, and exclusion of this compound would tighten the predicted EC₅₀ glutamate concentration even further. Whether this relates to structural differences between VU0408899 versus the other compounds (and/or presence of pharmacologically active metabolites that may be confounding the analysis) remains to be determined, but these data support the idea that it may be possible to predict endogenous agonist tone by using a range of allosteric modulators.

In summary, we have shown that, for the series of mGlu₅ PAMs depicted here, we observe a significant correlation between in vitro cooperativity, as well as maximum potentiation, with in vivo measured concentration levels and in vivo efficacy in an antipsychotic paradigm. Additionally, we propose a mechanism to estimate in vivo concentrations of the endogenous agonist relevant to specific behavioral paradigms. As allosteric modulator programs become more prominent in drug discovery organizations, it is anticipated that building similar data sets for other targets and other pharmacodynamic paradigms (or animal species) will greatly inform efforts to develop safe and effective therapeutics.

Materials and Methods

Compounds

d-Amphetamine hemisulfate was obtained from Sigma-Aldrich. All mGlu₅ PAMs were synthesized in house at Vanderbilt University, and detailed methods can be found in the following papers or patents: VU0419372/WO 2012092539; VU0408899,³⁹ VU0409551,¹⁰ VU0415133/WO 2012078817; VU0419832/WO 2012083224;⁴⁰ VU0447256/US 20130345203; VU0455651/WO 2012083224; VU0462807;⁴¹ VU0464042/US 20130345204; VU0464075/US 20130345204; VU0360172 (N-cyclobutyl-6-[2-(3-fluorophenyl)ethynyl]-3-pyridinecarboxamide).⁴²

In Vitro Pharmacology

Detailed methods regarding cell culture and in vitro pharmacology/curve fitting are provided in the Supplemental Methods section.

Animal Care and Housing

All in vivo studies were carried out using adult male Sprague–Dawley rats (Harlan, Indianapolis, IN). Animals were group-housed under a 12/12 h light-dark cycle (lights on at 6 AM) with food and water available ad libitum. All animal experiments were approved by the Vanderbilt University Animal Care and Use Committee, and experimental procedures conformed to guidelines established by the National Research Council Guide for the Care and Use of Laboratory Animals.

Locomotor Activity Studies in Rats

Open field activity was tested using a SmartFrame Open Field System (Kinder Scientific, San Diego, CA) with a 16 × 16 array of infrared photo beams located 2.5 cm above the floor of the chamber as previously described.^9,18 Rats were habituated in an open field for 30 min; vehicle (20% β-cyclodextrin/80% in sterile water), or test compound prepared in vehicle, was administered orally in rats in a volume of 10 mL/kg (doses ranged from 1–56.6 mg/kg). Thirty minutes post-dosing, amphetamine, dissolved in sterile water and administered at a dose of 0.75 mg/kg, was administered subcutaneously at 1 mL/kg. Locomotor activity was recorded for an additional 60 min. Total locomotor activity was calculated as the total number of beam breaks from the time of amphetamine administration [t = 60 min] to the end of the experiment [t = 120 min], where total beam breaks from vehicle treated animals in parallel experiments defined 100% reversal of the amphetamine-induced hyperactivity (defined as 0% reversal).

PK Experiments and Exposure Determinations

Measurement of in vivo total plasma and total brain concentrations of test compounds was performed via quantitative LC–MS/MS bioanalysis of terminal (1.5 h postadministration of each test compound) samples from rat AHL studies essentially according to methods described previously.^10,27,43In vivo unbound plasma and unbound brain concentrations for each compound were determined by multiplication of the measured total plasma and total concentrations by each compound’s fraction unbound in plasma (fu_plasma) and in brain (fu_brain), respectively, which were obtained via in vitro rat plasma protein and rat brain homogenate binding assays using equilibrium dialysis methods described previously.^10,27,43

Glossary

Abbreviations

AHL

amphetamine-induced hyperlocomotion

CRC

concentration–response curve

GPCR

G protein-coupled receptor

mGlu₅

metabotropic glutamate receptor 5

OMA

operational model of allosterism

PK/PD

pharmacokinetic/pharmacodynamic

PAM

positive allosteric modulator

SAR

structure–activity relationship

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsptsci.9b00062.

• Detailed methods; unbound brain curve fits; total and unbound plasma curve fits; linear regression fits; additional figures supporting the text; supplemental references (PDF)

Author Contributions

This project arose out of an idea proposed by T.M.B. and C.M.N. K.J.G., R.G.G., M.J.N., and C.M.N. performed/interpreted molecular pharmacology data and simulations using the operational model of allosterism. S.R.R. and C.W.L. supervised chemical synthesis. C.J.K. performed and supervised the AHL experiments and sample collection. T.M.B. analyzed samples for compound exposure. K.J.G. and C.M.N. performed the correlation analyses and glutamate extrapolation with input from T.M.B., M.J.N., and R.G.G. P.J.C. provided discussion of analysis and funding support. K.J.G., T.M.B., R.G.G., and C.M.N. wrote the paper with input from all authors.

The authors declare no competing financial interest.