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. 2016 Apr 27;6:25158. doi: 10.1038/srep25158

Table 1. Prism equations for calculating receptor agonist and modulator equi-response and equi-occupancy selectivity 2D plots.

Selectivity Definitions Prism-based equations
Modulator equi-response selectivity Equation (4): The ratio of modulator 1 concentration for receptor 1 in assay 1 over either modulator 2 concentration for receptor 1 in assay 1, or modulator 1 concentration for receptor 2 or in assay 2, yielding the same level of functional response by said agonist and modulator A = 10^X; for Fig. 2a (replace with B1 = 10^X; for Fig. 2b)
Kapp1 = (KA1 + A)*KB1 + (KA1 + aa1*A)*B1
Eapp1 = (chi1*KA1 + tauA1*A)*KB1 + (tauB1*KA1 + aa1*bb1*tauA1*A)*B1
P = (Kapp1/Eapp1)^(n1/n2)
Selectivity = B1*[P*RR*(tauB2*KA2 + aa2*bb2*tauA2*A)-(KA2 + aa2*A)]/{[KA2 + A-P*RR*(chi2*KA2 + tauA2*A)*KB2]}
Y = IF(Selectivity >0,Selectivity,0)
Agonist equi-response selectivity Equation (6): The ratio of agonist 1 concentration for receptor 1 in assay 1 over either agonist 2 concentration for receptor 1 in assay 1, or agonist 1 concentration for receptor 2 or in assay 2, yielding the same level of functional response by said agonist and modulator B = 10^X; for Fig. 2c (replace with A1 = 10^X; for Fig. 2d)
Kapp1 = (KA1 + A1)*KB1 + (KA1 + aa1*A1)*B
Eapp1 = (chi1*KA1 + tauA1*A1)*KB1 + (tauB1*KA1 + aa1*bb1*tauA1*A1)*B
P = (Kapp1/Eapp1)^(n1/n2)
Selectivity = A1*[P*RR*(KB2*tauA2 + aa2*bb2*tauA2*B)-(KB2 + aa2*B)]/[KA2*(KB2 + B)-P*RR*KA2*(chi2*KB2 + tauB2*B)]
Y = IF(Selectivity >0,Selectivity,0)
Modulator equi-occupancy selectivity Equation (13): The ratio of modulator 1 concentration for receptor 1 in assay 1 over either modulator 2 concentration for receptor 1 in assay 1, or modulator 1 concentration for receptor 2 or in assay 2, yielding the same level of receptor occupancy by said agonist B1 = 10^X; for Fig. 4a
P1 = (1 + tauA1)/KA1 + aa1*B1*(1 + bb1*tauA1)/KA1/KB1
P2 = 1 + chi1 + B1/KB1*(1 + tauB1)
Selectivity = B1*[P2*aa2/KA2*(1 + bb2*tauA2*RR)-P1*(1 + tauB2*RR)]/KB2/[P1*(1 + chi2*RR)-P2*(1 + tauA2*RR)/KA2]
Y = IF(Selectivity >0,Selectivity,0)
Agonist equi-occupancy selectivity Equation (15): The ratio of agonist 1 concentration for receptor 1 in assay 1 over either agonist 2 concentration for receptor 1 in assay 1, or agonist 1 concentration for receptor 2 or in assay 2, yielding the same level of receptor occupancy by said agonist B = 10^X; for Fig. 4b
Top = (1 + chi1 + B/KB1*(1 + tauB1))*(1 + tauA2*RR + aa2*B/KB2*(1 + bb2*tauA2*RR))
Bottom = KA2/KA1*(1 + tauA1 + aa1*B/KB1*(1 + bb1*tauA1))*(1 + chi2*RR + B/KB2*(1 + tauB2*RR))
Selectivity = Top/Bottom
Y = IF(Selectivity >0,Selectivity,0)