(A) Representative whole-cell currents recorded, at the indicated voltages, from HEK293T cells transiently expressing wt, the single mutants R154A, E478A and the double mutant R154A-E478A. (B) Mean tail current activation curves of wt (black), R154A (orange), E478A (green) and R154A-E478A (magenta). Lines show data fit to a Boltzmann function (Materials and methods) providing half activation potential (V1/2) and inverse slope factor (k) values reported in Supplementary file 1A. Values are shown as mean ± SEM. Scale bar is 200 pA x 500 ms. (C), Mutant cycle analysis (Chowdhury et al., 2014) scheme for the R154 and E478 pair with each corner box colored as the G/V curves in (B) from which k and V1/2 values were derived by fitting a Boltzmann curve (Supplementary file 1A). The free energy difference between the open and closed states of the channel, ΔGapp = (RT/k)V1/2, are as follow: −9.8 ± 1.1,–8.5 ± 0.8,–9.2 ± 1.3,–9.8 ± 1.5 for wt, R154A, E478A and R154A-E478A, respectively. The perturbation energy upon mutation, ΔGp = Δ(RT/k)V1/2, is indicated along each path. The magnitude of non-additivity ΔΔG was calculated as reported in Material and methods. ΔGapp, ΔGp and ΔΔG are in kcal/mol.