Chowdhury S , Chanda B .

GM084140 NIGMS NIH HHS , R01 GM084140-05 NIGMS NIH HHS , R01 GM084140 NIGMS NIH HHS

	Figure 1. Free energy measures from a QV curve. (A) A hypothetical normalized QV curve. The vertical dashed line is the V = 0 axis. The shaded area is the integral ∫01V dQ−f (Q−f=Q−/Qmax), which equals ΔG−C/Qmax. The integral is negative on the left of the V = 0 axis and positive on the right, as indicated by the − and + signs. (B) The same QV curve with the median voltage of charge movement (Vm) marked by the vertical dashed lines. The areas on either side of the Vm axis are equal and are both positive. (C) The QV curve intersected by the V = 0 and V = Vm axes. The area of the shaded rectangle is equal to the sum of the two areas shaded in A, taking their respective signs into consideration.
	Figure 2. QV curves of the Shaker potassium channel and the rNaV1.4 channel. Normalized QV curves for Sh-IR W434F and NaV1.4. Each curve is a mean of independent measurements from five oocytes. The normalized QV curve for the ILT mutant was simulated according to the kinetic model proposed by Ledwell and Aldrich (1999).
	Figure 3. Effect of an intermediate voltage-independent step on the free energy estimates. (A) A six-state linear model of activation of a voltage-dependent ion channel with five closed state and a single final open state. The voltage dependence of the equilibrium constants is given by Ki=Ki0exp(ziFVβ) (i = 1, 2, 3, 4, or 5), where Ki0 is the chemical component of the equilibrium constant Ki and zi is its voltage dependence. The third step (shown in bold) is voltage independent, and thus z3 = 0. ΔG−C is the sum of the chemical free energy change of each of the steps and will equal −RTln∏i=15Ki0. (B) QmaxFVm is plotted against ΔG−C for different values of log K30 (−5 to 5) and two values of z2 (closed squares, z2 = 5; and open triangles, z2 = 0). The remaining parameters of the model were arbitrarily chosen as K10 = 1, K20 = 75, K40 = 25, K50 = 5, z1 = 2, z3 = 0, z4 = 2.5, and z5 = 1. (C and D) Variation of ΔG−C (C) and Vm (D) with changing values of z2 (0–5) and log K30.
	Figure 4. Effect of terminal voltage-independent steps on the free energy estimates. (A) Two six-state linear schemes of voltage-dependent activation of a channel. In both schemes, except for the final transition (in bold), all other steps are voltage dependent. Scheme II has one open state, whereas scheme II has two open states. The voltage dependence of each of the equilibrium parameters in schemes II and III is defined similar to those in scheme I (Fig. 3 A). For schemes II and III, z5 = 0. (B) Results of the numerical simulations performed using scheme II. K30 = 10, z2 = 1.5, z3 = 1, and z5 = 0. The remaining parameters were same as those in scheme I (Fig. 3 A). K50 was varied from 0.001 to 2,097.15. The relation between the free energy difference between the initial and final states, ΔG−C (−RTln∏i=15Ki0), and the free energy change in the ensemble, QmaxFVm (closed symbols) and −RTlnPOmax (open symbols), for different values of K50. Adding QmaxFVm and the correction factor, −RTlnPOmax, gives ΔG−C, as depicted by the dashed line. (C) POmax values calculated at different values of K50 for scheme II (A).
	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.
	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.

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