Figure 5.
Figure 5. Influence of latent charge movement and cooperativity on inferred energetics. (A) A 10-state MWC cooperative scheme of voltage-dependent ion channel activation. The channel comprises four identical voltage-sensing modules and one pore domain, each capable of existing in two conformations. States Ci and Oi differ in the conformational status of the pore domain, whereas the different Cis and Ois differ among each other in the number of activated voltage-sensing modules (i = 0, 1,…, 4). Activation of the each of the voltage sensors facilitates the opening transition of the pore and vice versa. The number alongside each state indicates its multiplicity. The voltage dependence of the equilibrium constant for activation of the pore and voltage sensors follows the relation Ki=Ki0exp(ziFVβ) (i = V, P). (B) Plot of QmaxFVm against ΔG−C for different values of θ (varied between 5 and 80) and two values of zV (open triangles, zV = 1; closed squares, zV = 3). The other model parameters were chosen to be KV0 = 20, KP0 = 10−5, and zP = 1.5. Different values of zV lead to different latent charge movement. (C) Plot of QmaxFVm and −RTlnPOmax against ΔG−C for different values of θ (varied between 5 and 80) when zP = 0. The arrow shows the value of θ and POmax beyond which ΔG−C and QmaxFVm deviate. For these simulations, KV0 = 20, KP0 = 10−5, and zV = 3. POmin in each case was ∼0. Adding QmaxFVm and the correction factor, −RTlnPOmax, gives ΔG−C, as depicted by the dashed line. (D) Plot of QmaxFVm and −RTln(1−POmin) against ΔG−C for different values of KP0 (varied between 10−5 and 50) when zP = 0. The arrow shows the value of KP0 and POmin below which ΔG−C and QmaxFVm deviate. For these simulations, KV0 = 20, θ = 20, and zV = 3. POmax in each case was ∼1. Adding QmaxFVm and the correction factor, −RTln(1−POmin), givesΔG−C, as depicted by the dashed line.

Influence of latent charge movement and cooperativity on inferred energetics. (A) A 10-state MWC cooperative scheme of voltage-dependent ion channel activation. The channel comprises four identical voltage-sensing modules and one pore domain, each capable of existing in two conformations. States Ci and Oi differ in the conformational status of the pore domain, whereas the different Cis and Ois differ among each other in the number of activated voltage-sensing modules (i = 0, 1,…, 4). Activation of the each of the voltage sensors facilitates the opening transition of the pore and vice versa. The number alongside each state indicates its multiplicity. The voltage dependence of the equilibrium constant for activation of the pore and voltage sensors follows the relation Ki=Ki0exp(ziFVβ) (i = V, P). (B) Plot of QmaxFVm against ΔG−C for different values of θ (varied between 5 and 80) and two values of zV (open triangles, zV = 1; closed squares, zV = 3). The other model parameters were chosen to be KV0 = 20, KP0 = 10−5, and zP = 1.5. Different values of zV lead to different latent charge movement. (C) Plot of QmaxFVm and −RTlnPOmax against ΔG−C for different values of θ (varied between 5 and 80) when zP = 0. The arrow shows the value of θ and POmax beyond which ΔG−C and QmaxFVm deviate. For these simulations, KV0 = 20, KP0 = 10−5, and zV = 3. POmin in each case was ∼0. Adding QmaxFVm and the correction factor, −RTlnPOmax, gives ΔG−C, as depicted by the dashed line. (D) Plot of QmaxFVm and −RTln(1−POmin) against ΔG−C for different values of KP0 (varied between 10−5 and 50) when zP = 0. The arrow shows the value of KP0 and POmin below which ΔG−C and QmaxFVm deviate. For these simulations, KV0 = 20, θ = 20, and zV = 3. POmax in each case was ∼1. Adding QmaxFVm and the correction factor, −RTln(1−POmin)⁠, givesΔG−C⁠, as depicted by the dashed line.

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