Figure 6. Influence of inactivation on... | Rockefeller University Press

Figure 6.

$Figure 6. Influence of inactivation on the median estimate of free energy change. (A) An eight-state model for an inactivating channel. The encircled states represent the initial reference state (VRPCIR, red) and the final state (VAPOIA, black) of the system. In the final state, all of the units of the system are in their activated/open conformations, whereas in the reference state, all are in their resting/closed conformations. The equilibrium constants are assumed to have an exponential voltage dependence, Ki=Ki0exp(ziFVβ), (i = 1, 2,…, 12). (B) An equivalent nested coupled model of inactivation. The conformational transitions in each of the structural units are Ki=Ki0exp(ziFVβ), where i is V, P, or inact. The pairwise coupling parameters, θVP, θPI, and θIV, denote the voltage-independent coupling between units V and P, P and I, and I and V, respectively. The parameters of the cubic model can be related to those of the nested model. For instance, K10 = Kinact and K11 = KinactθPIθIV. (C) Plot of QmaxFVm against ΔG−C for different values of Kinact0 (varied between 0.0001 and 0.0256) and two values of zinact. The remaining parameters were arbitrarily chosen to be KV0 = 75, KP0 = 1, θVP = 5, θPI = 8, θIV = 100, zV = 3, and zP = 1. Here, ΔG−C=−RTlnKVRPCIR→VAPOIA0=−RTln(K10K20K110)=−RTln(KV0KP0Kinact0θVPθPIθIV). (D) Maximum fraction of inactivated channels at depolarizing voltages for different values of Kinact0.$

Influence of inactivation on the median estimate of free energy change. (A) An eight-state model for an inactivating channel. The encircled states represent the initial reference state (V_RP_CI_R, red) and the final state (V_AP_OI_A, black) of the system. In the final state, all of the units of the system are in their activated/open conformations, whereas in the reference state, all are in their resting/closed conformations. The equilibrium constants are assumed to have an exponential voltage dependence, $K_{i} = K_{i}^{0} \exp (z_{i} F V β),$ (i = 1, 2,…, 12). (B) An equivalent nested coupled model of inactivation. The conformational transitions in each of the structural units are $K_{i} = K_{i}^{0} \exp (z_{i} F V β),$ where i is V, P, or inact. The pairwise coupling parameters, θ_VP, θ_PI, and θ_IV, denote the voltage-independent coupling between units V and P, P and I, and I and V, respectively. The parameters of the cubic model can be related to those of the nested model. For instance, K₁₀ = K_inact and K₁₁ = K_inactθ_PIθ_IV. (C) Plot of Q_maxFV_m against $Δ {\bar{G}}_{C}$ for different values of $K_{i n a c t}^{0}$ (varied between 0.0001 and 0.0256) and two values of z_inact. The remaining parameters were arbitrarily chosen to be $K_{V}^{0}$ = 75, $K_{P}^{0}$ = 1, θ_VP = 5, θ_PI = 8, θ_IV = 100, z_V = 3, and z_P = 1. Here, $Δ {\bar{G}}_{C} = - R T \ln K_{V_{R} P_{C} I_{R} \to V_{A} P_{O} I_{A}}^{0} = - R T \ln (K_{1}^{0} K_{2}^{0} K_{11}^{0}) = - R T \ln (K_{V}^{0} K_{P}^{0} K_{i n a c t}^{0} θ_{V P} θ_{P I} θ_{I V}) .$ (D) Maximum fraction of inactivated channels at depolarizing voltages for different values of $K_{i n a c t}^{0} .$

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