. 2013 Jan;141(1):11–28. doi: 10.1085/jgp.201210860

Table 1.

Comparison of free-energy estimates of CNG and HCN channel obtained from dose–response curves, binding curves and kinetic models

Response	Free-energy estimation method		Free-energy estimate
			CNG		HCN
	Fitting function	Parameters	Parameter values	$Δ G_{C}$	Parameter values	$Δ G_{C}$
				kcal/mol		kcal/mol
DRC^a	$P_{O}^{\min} + \frac{P_{O}^{\max} - P_{O}^{\min}}{1 + {(x_{1 / 2} / x)}^{H}}$	$x_{1 / 2}$	1.65 µM	−7.7	0.54 µM	−8.3
DRC^a		H	1.9	−7.7	1.3	−8.3
BC^b	$\frac{1}{1 + {(x_{1 / 2} / x)}^{H}}$	$x_{1 / 2}$	2.3 µM	−7.5	0.54 µM	−8.4
BC^b	$\frac{1}{1 + {(x_{1 / 2} / x)}^{H}}$	H	0.75	−7.5	1.14	−8.4
BC^c	N_max RT ln x_m + C_F	x_m	2.42 µM	−29.4 (−30^d)	0.45 µM	−33.6 (−33.8^d)
		N_max	4		4
		C_F	0		−0.5 kcal/mol

The table lists the estimates of free-energy change of ligand-dependent activation of CNG channel and HCN channel (at −130 mV) calculated by different methods.

The simulated dose-response curve (DRC, relative open probability curve) is fitted with a Hill equation, normalized to account for nonzero open probabilities at zero ligand concentration, i.e., $P_{O}^{\min}$ (and non-unity open probabilities at saturating ligand concentrations, $P_{O}^{\max}$ ). $Δ G_{C}$ is calculated as RT lnx_1/2.

The simulated binding curve (BC) is fitted with the Hill equation, and ΔG_C is calculated as RT lnx_1/2.

From the simulated binding curve (BC), the median ligand concentration is extracted. C_F is the correction factor in Eq. 26 (informed by $P_{O}^{\min}$ and $P_{O}^{\max}$ ).

ΔG_C estimates of the net free-energy difference between the first closed state (C₀) and the last open state (O₅) ( $- R T \ln K_{C_{1} \to O_{5}}^{0}$ ) obtained from the kinetic model parameters (Fig. 4 A).