An Insight into the Potassium Currents of hERG and Their Simulation

Figure 1. Schematic picture of two opposite subunits of a peculiar hERG open conformation [3], simplified by removing the S1–S3 helices of each voltage sensing domain and replacing them with an hourglass symbolizing two hydrophilic vestibules separated by the gating pore. The cylinders denote α-helices, whereas the curved lines connecting the cylinders denote intra- or extracellular loops. The two small red circles symbolize an inward potassium current. Extracellular fluid at the top, intracellular medium at the bottom.

Figure 2. Schematic picture of the transverse section of the hERG K+ channel, illustrating a gating cycle of its consecutive conformational states by arranging them in a circle: selectivity filter at the top, activation gate (the bundle crossing) at the bottom. States C/O, O/O, and O/I are indicated at the bottom of each transverse section. Transition rates are indicated by the words “fast” and “slow” along the gating cycle. The endogenous blocker is denoted in grey.

Figure 3. Plot of the steady-state activation curve, i.e., the open probability (red curve), the damping factor (blue straight line), the product of the two at each transmembrane potential (green curve), and the experimental points of the bell-shaped curve in Figure 1c of [8] upon ascribing a 0.30 value to its highest point on the vertical scale normalized to unity. Unfortunately, Piper et al. [8] did not show this bell-shaped curve together with the corresponding steady-state activation curve on the same vertical scale, unlike [1] and [24]. The damping factor does not strictly refer to the open probability scale, although it takes values between about 0 and 0.8 on this scale for transmembrane potential values ϕ varying from +40 to −40 mV.

Figure 4. Schematic of the arrangement of the four subunits (I)–(IV) of a Shaker or hERG potassium channel around the central pore during the stepwise opening of the channel. The six disks on top of each of the four subunits denote the six α-helices, with the S4 helices in yellow and the other five helices in light brown. More precisely, during the first opening step of the channel, the S4 helix of subunit I moves outward and is represented as a yellow cylinder, while the three other S4 helices are still in the ‘in’ position. Following the direction of the red arrows, all four S4 α-helices move outwards step by step, and the K+ outward current, represented as a progressively longer outward blue arrow, increases accordingly.

Figure 5. Experimental K+ outward I-t curves taken from Figure 5b (left) of [8] (a) and those calculated from Equation (10) (b) with kNkR2 = 1 × 1012 s−3 at +30 mV (black), +10 mV (red), −10 mV (green), −30 mV (blue), and −50 mV (cyan). The calculated curves are moderately close to those calculated by Piper et al. in Figure 5b (right) of [8], since they are both based on the same experimental steady-state activation curve.

Figure 6. Experimental K+ inward I-t curves taken from Figure 5b (left) of [8] (a) and calculated from Equation (15) (b) with kNkR2 = 1 × 1012 s−3 and kh = 1 at +30 mV (black), +10 mV (red), −10 mV (green), −30 mV (blue), and −50 mV (cyan). The calculated curves (b) are quite close to those calculated by Piper et al. in Figure 5b (right) of [8], since they are both based on the same ‘open probability of the inward K+ current’.

Figure 7. Gating current estimated from the time derivative of S and elicited by a 300 ms long square wave pulse from −110 to −10 mV and vice versa. The potential values on the gating current denote the final potential of the square wave pulse.