Table 8. Summary of thermodynamic... | Rockefeller University Press

Table 8.

Summary of thermodynamic methods applied to Schemes 2–5

Quantity	Global analysis	Local (Hill) analysis
Equilibrium curve	Q-V (Q = N〈q〉)	G-V (G = N〈g〉)
Canonical relation	$〈 q 〉 = - \frac{\partial Φ}{\partial V}$	$G / G_{\max} = - k T \frac{\partial \ln Z}{\partial η_{L}}$ ^a
“Bridge” equation	Φ = −kTlnZ	η_L (= ΔG_L − Δq_LV) = −kTlnL^b
Work function	$W_{C [q]} = - \int_{V (-)}^{V (+)} V \frac{d 〈 q 〉}{d V} d V$	$W_{H [g]} = k T (\frac{G}{G_{\max} - G})$
CPF ratios	$\frac{Z_{O A}}{Z_{C R}}$ = 〈CE〉_μ	${(\frac{Z_{O}}{Z_{C}})}_{V (\pm)}$ = 〈C〉_μ , ${(\frac{Z_{O}}{Z_{C}})}_{μ (\pm)}$ = 〈D〉_V^c
Allosteric energies	^μΔW_C_[q] = −4(ΔW_C + ΔW_E) = −Δq_T^μΔV_M	^μΔW_H_[g]V(±) = −4ΔW_C
		^VΔ(W_H_[g] + η_L)_μ_(±) = −4ΔW_D^d

Quantity	Global analysis	Local (Hill) analysis
Equilibrium curve	Q-V (Q = N〈q〉)	G-V (G = N〈g〉)
Canonical relation	$〈 q 〉 = - \frac{\partial Φ}{\partial V}$	$G / G_{\max} = - k T \frac{\partial \ln Z}{\partial η_{L}}$ a
“Bridge” equation	Φ = −kTlnZ	η_L (= ΔG_L − Δq_LV) = −kTlnLb
Work function	$W_{C [q]} = - \int_{V (-)}^{V (+)} V \frac{d 〈 q 〉}{d V} d V$	$W_{H [g]} = k T (\frac{G}{G_{\max} - G})$
CPF ratios	$\frac{Z_{O A}}{Z_{C R}}$ = 〈CE〉_μ	${(\frac{Z_{O}}{Z_{C}})}_{V (\pm)}$ = 〈C〉_μ , ${(\frac{Z_{O}}{Z_{C}})}_{μ (\pm)}$ = 〈D〉_Vc
Allosteric energies	^μΔW_C_[q] = −4(ΔW_C + ΔW_E) = −Δq_T^μΔV_M	^μΔW_H_[g]V(±) = −4ΔW_C
		^VΔ(W_H_[g] + η_L)_μ_(±) = −4ΔW_Dd

Some of the local equations for Scheme 5 differ from those of the other schemes as a result of the tetrameric pore structure. The following equations become relevant at extreme voltages, where Scheme 5 deviates from Scheme 4 (Fig. 12, C and D):

Canonical relation: $G / G_{\max} = - k T \frac{\partial \ln Z}{\partial η_{P}} .$

“Bridge” equation: η_P (= η_L/4) = −kTlnP.

$\frac{Z_{P}}{4 Z - Z_{P}} = \frac{\frac{4 x_{1}}{B} Z_{C}^{3} Z_{O} + \frac{2 (x_{2 t} + 2 x_{2 c} B_{1})}{B^{2}} Z_{C}^{2} Z_{O}^{2} P + \frac{4 x_{3} B_{1} B_{2}}{B^{3}} Z_{C} Z_{O}^{3} P^{2} + Z_{O}^{4} P^{3}}{Z_{C}^{4} + \frac{4 (1 - x_{1}) Z_{C}^{3} Z_{O}}{B} P + \frac{2 [(1 - x_{2 t}) + 2 (1 - x_{2 c}) B_{1}]}{B^{2}} Z_{C}^{2} Z_{O}^{2} P^{2} + \frac{4 (1 - x_{3}) B_{1} B_{2} Z_{C} Z_{O}^{3}}{B^{3}} P^{3}} .$

Allosteric energies: ^μΔW_H_[g]V(±) = −ΔW_C and ^VΔ(W_H_[g] + η_P)_μ_(±) = −(ΔW_D + ΔW_B₃ + ΔW_B₄) + kTln[16x₁(1−x₃)].

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