PMC

(a) Restricted Boltzmann Machines as a realization of the Boltzmann Machine Equation in Equation (); and (b) Matrix Product States as a realization of the Born Machine Equation in Equation ().

The G/V curves of the rSlo3 channel are best described by a two‐component Boltzmann equation. (a–c) A set of steady‐state currents in inside‐out configuration at different pH (from pH 6.5–9.0) were measured and converted to relative conductance by normalizing conductance to maximal conductance measured at pH 9.0 with highest voltage (averaged from six patches). The curves fitted by Boltzmann equations are shown in red lines. The poorly fitted parts are labelled in purple circles. (a) G/V curves of the rSlo3 channel were fitted by a single‐component Boltzmann equation with a fixed maximal conductance measured at highest voltage in pH 9.0. (b) G/V curves of therSlo3 channel were fitted by a single‐component Boltzmann equation with a free maximal conductance without restriction. (c) The G/V curves of the rSlo3 channel were best fitted by a two‐component Boltzmann equation. (d) The voltage of half activation (V_h) was plotted as a function of pH value. The V_h values were calculated based on Boltzmann fits in which G _max was restricted to maximal conductance measured at pH 9.0. (e) V_h values were plotted as a function of pH values. The V_h values were calculated by a single‐component Boltzmann equation fit in which the G_max was not constrained. (f) V_h values estimated by two Boltzmann components fits were plotted as functions of pH values

(R)-Roscovitine enhances VDI of channels containing L-DI. Inactivation was measured as the I_Post/I_Pre ratio using the three-pulse protocol described in the legend to . Control (CNTL, gray circles), 100 μm (R)-roscovitine (R-Rosc, black squares), and washout (WO, gray triangles) data from −120 to peak inactivation were fitted using a single Boltzmann equation (smooth lines) to yield V½ and slope as described in the legend to . The activation-voltage relationship in control (right axis, open circles) is superimposed here for comparison with the voltage dependence of inactivation. The activation-voltage relationship was fitted by a single Boltzmann function (smooth lines), and the relationship was normalized to the maximum current from that fit. (R)-Roscovitine enhanced VDI of LLLL (A), LLNN (C), LLNL (E), LLLN (F), LN*LL (G), and LN*NN (H) channels but did not affect NNNN (B) and NLLL (D) channels. For LLLL channels (A), the Boltzmann parameters for inactivation were V½ = −19.6, −15.3, and −16.4; slope = −13.6, −19.1, and −18.7; maximum inactivation = 0.23, 0.67, and 0.27 for control, (R)-roscovitine, and washout, respectively, whereas those parameters for activation were V½ = 15.0 and slope = 15.6. For NNNN channels (B), the Boltzmann parameters for inactivation were V½ = −24.1, −24.7, and −28.6; slope = −13.9, −14.5, and −15.6; maximum inactivation = 0.48, 0.47, and 0.45 for control, (R)-roscovitine, and washout, respectively, whereas those for activation were V½ = 21.0 and slope = 12.6. For LLNN channels (C), the Boltzmann parameters for inactivation were V½ = 1.4, 0.8, and 0.6 mV; slope = −6.8, −10.0, and −5.0; maximum inactivation = 0.15, 0.6, and 0.15 for control, (R)-roscovitine, and washout, respectively, whereas those parameters for activation were V½ = −17.7 mV and slope = 9.6. It was not possible to accurately describe the inactivation data from the NLLL chimera (D) using the Boltzmann equation, but for activation, the Boltzmann parameters were V½ = 18.7 and slope = 21.7. For LLNL channels (E), the Boltzmann parameters for inactivation were V½ = −43.5, −51.8, and −45.8 mV; slope = −9.8, −13.3, and −9.5; maximum inactivation = 0.6, 0.81, and 0.58 for control, (R)-roscovitine, and washout, respectively, whereas those for activation were V½ = −9.2 mV and slope = 18.1. For LLLN channels (F), inactivation in control was too small to allow for Boltzmann fitting. However, the Boltzmann parameters for activation were V½ = 41.7 mV and slope = 19. For LN*LL channels (G), the Boltzmann parameters for inactivation were V½ = −79.1, −48.5, and −60.8 mV; slope = −9.1, −11.2, and −9.0; maximum inactivation = 0.07, 0.30, and 0.09 for control, (R)-roscovitine, and washout, respectively, whereas those parameters for activation were V½ = −21.7 mV and slope = 12.5. For LN*NN channels (H), the Boltzmann parameters for inactivation were V½ = −2.4, −12.1, and −2.5 mV; slope = −4.9, −5.2, and −7.1; maximum inactivation = 0.07, 0.29, and 0.09 for control, (R)-roscovitine, and washout, respectively, whereas those parameters for activation were V½ = 6.5 mV and slope = 11.6.

F-V relationships of Ci-VSP WT and mutants with G214C-TMRM from representative experimental data of three individual cells (black circles) were fitted by single (gray broken line) or two components of Boltzmann distribution (black lines), respectively. Red and blue lines show individual two components fitted by the sum of two Boltzmann distributions. In WT and L284F, experimental data were not well fitted by single Boltzmann distribution and better fitted by two components of Boltzmann distribution. On the other hand, the equation of single Boltzmann distribution was sufficient to fit the curve of L284Q (See also ).