TABLE 5

Comparison of parameters describing mGlu₅ allosteric interactions analyzed with different allosteric models

mGlu₅ allosteric interactions with glutamate in Ca²⁺_i mobilization assays were analyzed with the original operational model of agonism and allosterism (eq. 3) or the operational model of allosterism with cooperative agonist binding (eq. 4) to determine modulator affinity, glutamate or modulator efficacy, respectively), cooperativity, transducer or binding slopes, and maximum system response.

Parameter	Glutamate vs. MPEP^{^a}		Glutamate vs. M-5MPEP^{^a}		Glutamate vs. VU-29^{^b}		Glutamate vs. DPFE^{^b}
Parameter	eq. 3	eq. 4	eq. 3	eq. 4	eq. 3	eq. 4	eq. 3	eq. 4
pK_A [K_A (µM)]	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}	6.2 (0.6)^{^c}
pK_B [K_B (µM)]	7.9 ± 0.1 (0.01)	8.4 ± 0.1 (0.004)	6.8 ± 0.2 (0.2)	6.8 ± 0.2 (0.2)	6.7 ± 0.2 (0.2)	6.7 ± 0.2 (0.2)	6.0 ± 0.3 (1.0)	5.6 ± 0.1 (2.5)
Log τ_A (τ_A)	0.7 ± 0.1 (5.0)	1.0 ± 0.2 (10)	0.6 ± 0.1 (3.9)	0.6 ± 0.2 (4.0)	0.7 ± 0.03 (5.0)	0.7 ± 0.1 (5.0)	0.6 ± 0.1 (4.0)	0.8 ± 0.1 (6.3)
Log τ_B (τ_B)	n.a. (0)	n.a. (0)	n.a. (0)	n.a. (0)	n.a. (0)	n.a. (0)	−0.2 ± 0.1 (0.6)	−0.4 ± 0.1 (0.4)
Log αβ (αβ)	−100 (∼0)^{^d}	−100 (∼0)^{^d}	−0.5 ± 0.1 (0.3)	−0.8 ± 0.2 (0.2)	0.3 ± 0.03 (2.0)	0.3 ± 0.04 (0.2)	0.6 ± 0.1 (4.0)	1.1 ± 0.1 (13)
n	1.7 ± 0.2^{^e}	1.5 ± 0.2^{^e}	2.0 ± 0.2^{^e}	1.6 ± 0.2^{^e}	1.3 ± 0.1^{^e}	1.2 ± 0.1^{^e}	2.5 ± 0.7^{^e}	1.3 ± 0.1^{^e}
E_m (% glutamate)	106 ± 6.0	111 ± 6.0	107 ± 6.0	123 ± 1.0	108 ± 3.0	111 ± 3.0	107 ± 2.0	105 ± 2.0

Dfd, degrees of freedom denominator; Dfn, degrees of freedom numerator; E_m, maximum system response; Log αβ (αβ), modulator cooperativity; Log τ_A (τ_A), glutamate efficacy; Log τ_B (τ_B), modulator efficacy; n, transducer or binding slope; n.a., no agonist activity [log τ_B fixed to −100 (τ_B 0)]; pK_A (K_A), agonist affinity; pK_B (K_B), modulator affinity.
↵^a Values derived by fitting previously reported experimental data (Sengmany et al., 2019).
↵^b Values derived by fitting previously reported experimental data (Sengmany et al., 2017).
↵^c The pK_A value was fixed to that determined in radioligand binding assays (Mutel et al., 2000).
↵^d The log αβ value was fixed to −100 due to complete inhibition of glutamate-mediated stimulation of Ca²⁺_i mobilization, reflecting high negative cooperativity.
↵^e An F test determined that data were fitted best when the transducer or binding slopes were different from unity. The F data used to test the hypothesis that n differed from 1 were the following: eq. 3 MPEP P = 0.0003, F [(Dfn, Dfd) 13.46 (1, 149)]; eq. 3 M-5MPEP P = 0.0007, F [(Dfn, Dfd) 11.96 (1, 126)]; eq. 3 VU-29 P = 0.0015, F [(Dfn, Dfd) 10.45 (1, 144)]; eq. 3 DPFE P = 0.0062, F [(Dfn, Dfd) 7.587 (1, 294)]; eq. 4 MPEP P = 0.0002, F [(Dfn, Dfd) 14.33 (1, 149)]; eq. 4 M-5MPEP P < 0.0001, F [(Dfn, Dfd) 22.26 (1, 126)]; eq. 4 VU-29 P = 0.0003, F [(Dfn, Dfd) 13.97 (1, 144)]; and eq. 4 DPFE P < 0.0001, F [(Dfn, Dfd) 24.13 (1, 294)].