(a) Schemes IA and IB represent the canonical models of cooperativity, where a direct interaction between the open pore and the activated voltage-sensor mediates coupling of the two structural domains. Scheme II represents alternate model of voltage-sensor-pore coupling, where the closed pore interacts with the resting voltage-sensor and the open pore interacts with the activated voltage-sensor.

*K*_{1} and

*K*_{2} are the intrinsic activation constants of the voltage-sensor and the pore and

*θ* is the coupling parameter. The intrinsic activation constants can be expressed as:

and

where

and

represent the contribution of chemical interactions to the activation process of the voltage-sensor and the pore, respectively.

(b) and (c) The probabilities of voltage-sensor activation and pore opening when the three thermodynamic parameters are modified in Scheme IA. The expressions for

*P*_{VA} and

*P*_{PO} from Scheme I ( and ) were fitted to the WT F–V and G–V curves respectively, to obtain the values for the different parameters:

, z

_{1} = 3.494,

, z

_{2}= 4.219,

*θ* = 999.916.

and

*θ* were varied over 10 orders of magnitude and the response to these changes on the

*P*_{VA} values at −50mV and

*P*_{PO} values at −20mV were plotted in (b) and (c) respectively.

(d) and (e) The probabilities of voltage-sensor activation and pore opening when the three thermodynamic parameters are modified in Scheme IB. The initial thermodynamic parameters

, z

_{1}= 0.936,

, z

_{2}= 3.914,

*θ* = 1003.561 were obtained by fitting the expressions for

*P*_{VA} and

*P*_{PO} in Scheme IB (Eqs. 3 and 4) to the WT F–V and G–V curves respectively.

and

*θ* were varied over 10 orders of magnitude and the response to these changes on the

*P*_{VA} values at −50mV and

*P*_{PO} values at −20mV were plotted in (d) and (e) respectively.

(f) and (g) The probabilities of voltage-sensor activation and pore opening when the three thermodynamic parameters are modified in Scheme II. The expressions for

*P*_{VA} and

*P*_{PO} from Scheme II (Eqs. 3 and 4) were fitted to the WT F–V and G–V curves respectively, to obtain the values for the different parameters:

, z

_{1}= 0.949,

, z

_{2}= 3.905, θ= 999.913.

and

*θ* were varied over 10 orders of magnitude and the response to these changes on the

*P*_{VA} values at −50mV and

*P*_{PO} values at −20mV were plotted in (d) and (e) respectively.

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