Table 1. Estimation of free energy... | Rockefeller University Press

Table 1.

Estimation of free energy change from QV

Fitting function	Parameters	Sh-IR W434F		Na_V1.4
		Values	$Δ {\bar{G}}_{C}$	Values	$Δ {\bar{G}}_{C}$
$\frac{1}{1 + \exp {z F (V_{1 / 2} - V) β}}$ ^a	V_1/2	−45.9	−3.2	−56.5	−1.82
$\frac{1}{1 + \exp {z F (V_{1 / 2} - V) β}}$ ^a	z	3.03	−3.2	1.4	−1.82
$\frac{1}{{[1 + \exp {z F (V_{1 / 2} - V) β}]}^{4}}$ ^b	V_1/2	−64.6	−13.93	−97.15	−9.63
$\frac{1}{{[1 + \exp {z F (V_{1 / 2} - V) β}]}^{4}}$ ^b	z	2.35	−13.93	1.08	−9.63
$\frac{1}{(z_{1} + z_{2})} (\frac{z_{1}}{1 + \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β}} + \frac{z_{2}}{1 + \exp {z_{2} F (V_{1 / 2}^{(2)} - V) β}})$ ^c	V_1/2⁽¹⁾	−58.2	−7.07	−71.6	−3.92
	z₁	1.99		1.1
	V_1/2⁽²⁾	−42.4		−49.64
	z₂	4.5		1.85
$\frac{1}{z_{1} + z_{2}} (\frac{z_{1} \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β} + (z_{1} + z_{2}) \exp [{z_{1} V_{1 / 2}^{(1)} + z_{2} V_{1 / 2}^{(2)} - (z_{1} + z_{2}) V} F β]}{1 + \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β} + \exp [{z_{1} V_{1 / 2}^{(1)} + z_{2} V_{1 / 2}^{(2)} - (z_{1} + z_{2}) V} F β]})$ ^d	V_1/2⁽¹⁾	−56.64	−6.44	−71.02	−3.62
	z₁	2.02		1.15
	V_1/2⁽²⁾	−42.6		−48.23
	z₂	3.89		1.58
$F \int_{0}^{Q_{\max}} V d Q = Q_{\max} F V_{m}$ ^e	V_m	−46.81	−14.63	−56.28	−16.5
$F \int_{0}^{Q_{\max}} V d Q = Q_{\max} F V_{m}$ ^e	Q_max	13.6	−14.63	12.8	−16.5

Fitting function	Parameters	Sh-IR W434F		Na_V1.4
		Values	$Δ {\bar{G}}_{C}$	Values	$Δ {\bar{G}}_{C}$
$\frac{1}{1 + \exp {z F (V_{1 / 2} - V) β}}$ ^a	V_1/2	−45.9	−3.2	−56.5	−1.82
$\frac{1}{1 + \exp {z F (V_{1 / 2} - V) β}}$ ^a	z	3.03	−3.2	1.4	−1.82
$\frac{1}{{[1 + \exp {z F (V_{1 / 2} - V) β}]}^{4}}$ ^b	V_1/2	−64.6	−13.93	−97.15	−9.63
$\frac{1}{{[1 + \exp {z F (V_{1 / 2} - V) β}]}^{4}}$ ^b	z	2.35	−13.93	1.08	−9.63
$\frac{1}{(z_{1} + z_{2})} (\frac{z_{1}}{1 + \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β}} + \frac{z_{2}}{1 + \exp {z_{2} F (V_{1 / 2}^{(2)} - V) β}})$ ^c	V_1/2⁽¹⁾	−58.2	−7.07	−71.6	−3.92
	z₁	1.99		1.1
	V_1/2⁽²⁾	−42.4		−49.64
	z₂	4.5		1.85
$\frac{1}{z_{1} + z_{2}} (\frac{z_{1} \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β} + (z_{1} + z_{2}) \exp [{z_{1} V_{1 / 2}^{(1)} + z_{2} V_{1 / 2}^{(2)} - (z_{1} + z_{2}) V} F β]}{1 + \exp {z_{1} F (V_{1 / 2}^{(1)} - V) β} + \exp [{z_{1} V_{1 / 2}^{(1)} + z_{2} V_{1 / 2}^{(2)} - (z_{1} + z_{2}) V} F β]})$ ^d	V_1/2⁽¹⁾	−56.64	−6.44	−71.02	−3.62
	z₁	2.02		1.15
	V_1/2⁽²⁾	−42.6		−48.23
	z₂	3.89		1.58
$F \int_{0}^{Q_{\max}} V d Q = Q_{\max} F V_{m}$ ^e	V_m	−46.81	−14.63	−56.28	−16.5
$F \int_{0}^{Q_{\max}} V d Q = Q_{\max} F V_{m}$ ^e	Q_max	13.6	−14.63	12.8	−16.5

The table lists the different functions used to fit the QV curve and the values of the corresponding parameters derived from the fits to the QV curves of the Sh-IR W434F and Na_V1.4 channels. V_1/2 parameters have units in millivolts, and z parameters have units of electronic charges. The free energy changes calculated from each of the fits are also listed (kcal/mol).

A two-state model and the fitting function is a Boltzmann function.

A model where the channel activates in four independent single-step transitions; the fitting function is the fourth power of the Boltzmann function and $Δ {\bar{G}}_{C} = 4 z F V_{1 / 2} .$

A model where the channel activates via two energetically independent steps; the fitting function is the sum of two Boltzmann terms and $Δ {\bar{G}}_{C} = z_{1} F V_{1 / 2}^{(1)} + z_{2} F V_{1 / 2}^{(2)} .$

A three-state model where the channel activates in two sequential steps; $Δ {\bar{G}}_{C} = z_{1} F V_{1 / 2}^{(1)} + z_{2} F V_{1 / 2}^{(2)} .$

The free energy change calculated via the median method of channel activation. The Q_max values for each channel was obtained from previously published literature (Schoppa et al., 1992; Hirschberg et al., 1995; Aggarwal and MacKinnon, 1996; Seoh et al., 1996).

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