Allosteric analysis of α₁β₃γ_2L γ-aminobutyric acid type A (GABA_A) receptor direct activation by etomidate and naphthalene–etomidate. (A) Allosteric model for receptor activation. C and O are the closed and open states, respectively. CL_n and OL_n are the liganded closed and open states, respectively, and n is the number of ligand (etomidate or naphthalene–etomidate) binding sites. L₀ is the open state:closed state ratio in the absence of any modulatory ligands. Kd_closed and Kd_open are the ligand microscopic dissociation constants in the closed and open states, respectively. (B) GABA_A receptor open state probability (P_open) as a function of etomidate or naphthalene–etomidate concentration. The inset shows the naphthalene–etomidate data on an expanded vertical axis. The curves are fits of the data sets to equation 3 yielding respective Kd_closed and Kd_open values of 0.23 μM (95% CI, 0.15 to 0.31 μM) and 44 μM (95% CI, 26 to 62 μM) for etomidate and 6.2 μM and 27 μM for naphthalene–etomidate. For etomidate and naphthalene–etomidate, the number of binding sites (n) was assumed to be 2 and 4, respectively. L₀ was constrained at 40,000 for both fits.