Tuning the gate and the gear: The LRRC26 ($\mathit{\gamma }1$) subunit modulates intrinsic gating and voltage-sensor coupling of the BK channel

Abstract

Association of auxiliary subunits ($\beta 1–4$ and $\gamma 1–4$) with the pore-forming $\alpha$ subunit of the calcium-and voltage-activated potassium (BK) channel provides functional diversity. $\gamma 1$ promotes a significant leftward shift of the voltage activation curve, ensuring the adequate functioning of secretory glands, allowing the BK channel to release ${\text{K}}^{+}$at the cell’s resting ${\text{Ca}}^{2+}$ concentration. Given its physiological importance, it is crucial to elucidate the mechanisms of $\gamma 1$ action. However, structural and functional studies have yielded conflicting conclusions regarding the modulation of BK channels by $\gamma 1$. Here, using macroscopic, single-channel, and gating current measurements, we demonstrate that at zero mV $\gamma 1$ increases 92-fold the equilibrium constant that defines the closed-open transition by destabilizing the channel’s closed configuration and enhancing the coupling between the voltage sensor and the pore domain, without affecting voltage-sensor activation. These results suggest that $\gamma 1$ not only causes an increase in the energetic coupling between the voltage sensors and the pore but mainly enhances the channel opening reaction.

Teaser:

The $\gamma 1$ subunit favors the BK channel pore opening by destabilizing its closed configuration.

Introduction

Large-conductance calcium- and voltage-activated potassium channels (BK, MaxiK, Slo1, or ${\text{KCa}}_{1.1}$) are transmembrane proteins that transport with high selectivity ${\text{K}}^{+}$ over other ions (1) with a remarkably high unitary conductance compared to other ${\text{K}}^{+}$ channels (2, 3). The membrane potential and a wide range of intracellular Ca2+ concentrations independently modulate its activity (4, 5) allowing BK channels to have a pivotal role in many physiological processes such as action potential transmission and neurotransmitter release in nervous system (6–8) or vascular tone and contractility in smooth muscle (9, 10)

BK channels are homotetramers where each pore-forming ($\alpha$) subunit contains seven transmembrane segments (S0-S6) and an intracellular motif that mediates activation by intracellular ${\text{Ca}}^{2+}$. (8). They are modular proteins where every subunit contains a voltage-sensing domain, VSD (S0-S4), a pore domain, PD (S5-P-S6), and four carboxy-terminal domains (CTD) that associate to form a gating ring containing the ${\text{Ca}}^{2+}$-binding sites. (11). Even though a single gene codifies the BK $\alpha$ subunit – Slowpoke, Kcnmal – presents a great variety of channel phenotypes due to alternative splicing of pre-mRNA (12–14), metabolic regulation (15), and association with auxiliary subunits. The modulation of the BK channel, mediated by $\beta$-subunits ($\beta 1-\beta 4$), has been extensively studied due to its crucial role in the physiological functioning of tissues and organs, including the nervous system, smooth muscle, and kidney. (8, 16, 17). The discovery of the $\gamma$-subunits $(\gamma 1-\gamma 4)$ increased the diversity of BK channels (18, 19) and, more recently, the finding of LINGO1. Coexpression of the BK channel $\alpha$-subunit with LINGO results in rapidly inactivating ${\text{K}}^{+}$ currents (20).

Since the first electrophysiological characterization of BK channels, it was apparent that there is a wide range of BK channel ${\text{Ca}}^{2+}$ sensitivities (21). BK channels with high ${\text{Ca}}^{2+}$ sensitivity were identified in different cell types, such as mouse and rat inner hair cells (22), human glioma cells (23), mammalian salivary, lacrimal, and secretory epithelial glands, (24–27) and colon (28). Aldrich’s group showed that the high ${\text{Ca}}^{2+}$ sensitivity in LNCaP prostate cancer cells (29) was due to the presence of a BK auxiliary subunit, a leucine-rich repeat (LRR)-containing protein 26 (LRRC26; $\gamma 1$), which leftward-shifted BK voltage-activation curves around 140 mV compared to $\text{BK}\left(\alpha \right)$ alone in the absence of intracellular ${\text{Ca}}^{2+}$ (18, 19). The family of LRR is composed of three other paralogs $\gamma 2-\gamma 4$ (LRRC52, LRRC55, and LRRC38, respectively), which also modulate BK channels with a stoichiometry $\alpha :\gamma$ up to 1:1 (18, 19, 30). The four $\gamma$ subunits share a common structure: an N-terminal signal peptide, an extracellular LRR domain, a single transmembrane segment, and a short C-terminal containing a cluster of arginine residues (31, 32). $\gamma 2-\gamma 4$ subunits are also able to modulate the BK channel, albeit with less potency than $\gamma 1$ (19) due to sequence differences, particularly in TM and C-terminal (33).

The BK channel associated with $\gamma 1\left(\text{BK}\right(\alpha +\gamma 1\left)\right)$ complex appears to be expressed exclusively in secretory epithelial cells, where it plays a crucial role in ${\text{K}}^{+}$ secretion. The large leftward shift in the voltage axis promoted by the $\gamma 1$ subunit at cell resting ${\text{Ca}}^{2+}$ concentrations, (19) becomes crucial in the adequate functioning of secretory cells contained in the lacrimal gland, parotid gland, and colon (27). In cells of the lacrimal gland and parotid gland coming from $\gamma 1$ knockout mice, BK channels behave as channels containing only the $\alpha$-subunit (27). $\gamma 1$ has also been found in breast cancer cells and is a requisite to promote the cell malignant phenotype (34). Compared to $\beta$-subunits, which incrementally increase the probability of opening, a single $\gamma 1$ subunit can induce a complete gating shift (30, 35–37).

Recently, three independent groups have solved the structure of the $\text{BK}(\alpha +\gamma 1)$ channel complex (38–40). Two of these structures display the whole $\gamma 1$ subunit (38, 40), and the third structure contained the $\gamma 1$ transmembrane segment only (39). These structural studies confirmed that the complex has a stoichiometry of $\alpha :\gamma 1=1:1$ as previously inferred using electrophysiological and fluorescent techniques (30, 35). In the $\text{BK}(\alpha +\gamma 1)$ channel, the $\gamma 1$ transmembrane segment adopts a kink that interacts with S0-S3 and appears to be a critical structural element for the modulatory effects of the $\gamma 1$ subunit (41). The arginine cluster located at the C-terminal of the $\gamma 1$ is also crucial in determining the BK gating changes. By making chimeras in which the different domains of the different $\gamma$ subunits were exchanged, Li et al. (31) determined that the differential modulation of BK channels induced by the different $\gamma$ subunits was determined by their transmembrane domain and the positively charged C-terminal. On the other hand, the LRR domain regulates subunit trafficking, and its deletion produces BK channel in which the all-or-none effect is absent (42).

The mechanism by which this positively charged cluster modulates the BK channel function is under debate. Analysis of the electrophysiological results using the Horrigan-Aldrich (HA) allosteric model (43) (Fig. S1A) suggested that the presence of the $\gamma 1$ subunit mainly affects the coupling between the VSD and the PD (18). However, a recent structural study of the $\gamma 1$-containing BK channel, suggests that $\gamma 1$ stabilizes the active conformation of voltage and ${\text{Ca}}^{2+}$ sensors, as well as the strength of interaction between these two sensors (40). In particular, the intracellular interaction of the $\gamma 1$ arginine cluster with the RCK1 lobe suggested that the $\gamma 1$ modulates BK ${\text{Ca}}^{2+}$ and voltage activation (40). On the other hand, Redhardt et al. (39) hypothesized that the arginine cluster introduces an electrostatic positive bias on the internal aspect of the BK channel, stabilizing the active conformation of the VSD. A different view is put forward by Kallure et al. (38) which suggested that the arginine cluster present in the $\gamma 1$ C-terminal domain plays a role in the association between the $\gamma 1$ and $\alpha$ subunit. They pointed out that positively charged residues at the end of transmembrane segments interact with phospholipids, helping the membrane integration of the $\gamma 1$.

Due to the different interpretations of the structural data about the $\gamma 1$ mechanism of action and lacking functional conclusive evidence, this study aims to clarify $\gamma 1$ modulation using an electrophysiological approach along with the HA model, which includes measuring ionic and gating currents in multiple ${\text{Ca}}^{2+}$ conditions to determine which parameters in the allosteric gating model are affected by the $\gamma 1$ subunit. Our data indicates that while the $\gamma 1$ subunit increases the coupling between the VSD and the PD, its main effect is increasing the PD equilibrium constant ($L$; Fig. S1) by destabilizing the closed conformation.

Results

The $\gamma 1$ subunit does not alter the resting-active equilibrium of the voltage sensor

We expressed the BK $\alpha$ subunit in the presence and absence of $\gamma 1$ in Xenopus laevis oocytes. In both conditions, we observed robust ${\text{K}}^{+}$ currents in the absence of ${\text{Ca}}^{2+}$ (Fig. 1A–B). The plot of the normalized tail currents vs. voltage (G(V)) curves shows that, as previously found (18, 41) in the absence of ${\text{Ca}}^{2+}$, $\gamma 1$ produces a considerable leftward shift that amounts to −137 mV (Fig. 1C, see Table S1). This value is like those found previously using PC3 cells (-136 mV) or HEK cells (-147 mV) (18) and in Xenopus oocytes (-120 mV)(36). Fig. 1B also shows that the deactivation kinetics becomes slower in $\text{BK}(\alpha +\gamma 1)$ compared to $\text{BK}\left(\alpha \right)$ channels.

Figure 1. $\mathbf{\gamma }1$ subunit increases BK channel open probability without affecting the resting-active equilibrium of the voltage sensor.

Potassium currents recorded in inside-out membrane patches containing (A) $\text{BK}\left(\alpha \right)$ channels or (B) $\text{BK}(\alpha +\gamma 1)$ channels. Currents were recorded under symmetric 110 mM ${\text{K}}^{+}$ conditions and zero μM free internal ${\text{Ca}}^{2+}$. Inset: Voltage protocol used. (C) Normalized conductance versus voltage plots obtained from tail currents of $\text{BK}\left(\alpha \right)$ (blue, N = 9) and $\text{BK}(\alpha +\gamma 1)$ (purple, N = 8). Data were represented as mean ± SEM and fitted using the relation $\text{G}/\text{Gmax}=1/\left[1+\text{exp}\left(-{\text{z}}_{\text{G}}\text{F}\left(\text{V}-{\text{V}}_{0.5}\right)/\text{RT}\right)\right]$ where ${\text{z}}_{\text{G}}$ is the apparent gating valence, V the voltage, and ${\text{V}}_{0.5}$ the half-voltage. $\text{BK}\left(\alpha \right):{\text{z}}_{\text{G}}=0.85\pm 0.02$ and ${\text{V}}_{0.5}=218.3\pm 0.8\text{mV}$. $\text{BK}\left(\alpha +\gamma 1\right):{\text{z}}_{\text{G}}=1.37\pm 0.02\text{y}{\text{V}}_{0.5}=80.9\pm 0.3\text{mV}$. (D) Gating currents in inside-out membrane patches containing $\text{BK}\left(\alpha \right)$ channels and (E) $\text{BK}(\alpha +\gamma 1)$ channels, both recorded under conditions of zero μM free internal calcium. Inset: Voltage protocol used. (F) Normalized gating currents evoked by 1-ms pulses to 210 mV for $\text{BK}\left(\alpha \right)$ (blue) and $\text{BK}(\alpha +\gamma 1)$ (purple). Holding voltage −100 mV. A single exponential function was needed to fit the ON-gating currents of $\text{BK}\left(\alpha \right)$, and a double exponential function was needed to fit the ON-gating currents elicited by $\text{BK}(\alpha +\gamma 1)$. (G) Q(V) data obtained from the area under the fastest exponential function were plotted vs. voltage and fitted using a two-state model: $Q_{\mathit{\text{on}}}/Q_{\mathit{\text{on}}-\mathit{\text{max}}}=1/\left[1+\text{exp}\left(-{\text{z}}_{\text{Q}}\text{F}\left(\text{V}-{\text{V}}_{\text{H}}\right)/\text{RT}\right)\right]$. $\text{BK}\left(\alpha \right):{\text{z}}_{\text{Q}}=0.59\pm 0.04$ and ${\text{V}}_{\text{H}}=178\pm 0.4\text{mV}$ (N = 4), while for $\text{BK}(\alpha +\gamma 1):{\text{z}}_{\delta }=0.58\pm 0.04$ and ${\text{V}}_{\text{H}}=185\pm 1.5\text{mV}$ (N=5).

We next asked the question: Does the $\gamma 1$ subunit modify, and to what extent, the voltage sensor’s resting-active (R-A) equilibrium? We recall here that the equilibrium constant ($J$) defining the R-A equilibrium is given by (43):

$$J=J_0{e}^{\frac{\mathit{\text{zjFV}}}{RT}}=e^{\frac{zjF\left(V-V_H\right)}{RT}}$$ (1)

where $J_0$ is the equilibrium constant at zero $\text{mV}$, $z_J$ defines the voltage dependence of the voltage sensor activation, $V$ is the applied voltage, $V_H$ is the half activation voltage, and $F,R$, and $T$ have their usual meanings. The normalized total gating charge displaced during activation ($Q_{\mathit{\text{on}}}/Q_{\mathit{\text{on.max}}}$) relates to the equilibrium constant $J$ according to the relationship,

$$\frac{Q_{on}}{Q_{on.\text{max}}}=\frac{1}{1+J^{-1}}$$ (2)

We characterize the effect of the $\gamma 1$ subunit on the R-A equilibrium by measuring gating currents in the absence and the presence of $\gamma 1$ (Fig. 1D–E). It is apparent that the kinetics of the ON-gating current in $\text{BK}(\alpha +\gamma 1)$ has two exponential components, unlike $\text{BK}\left(\alpha \right)$ channels, which, as found previously (43–45) can be approximated to a single exponential function (Fig. 1F - Fig. S2). Moreover, the presence of $\gamma 1$ significantly slows down the OFF-gating current (Fig. 1F).

Integration over time of the fast component of the ON-gating currents shows that the presence of $\gamma 1$ do not alter significantly neither the parameter $z_J$ (0.58 ± 0.04 for $\text{BK}(\alpha +\gamma 1)$; 0.59 ± 0.04 for $\text{BK}\left(\alpha \right)$) nor $V_h$ (184.7 ± 1.5 mV for $\text{BK}(\alpha +\gamma 1)$; 178.4 ± 0.4 mV for $\text{BK}\left(\alpha \right)$) obtained when fitting the Q(V) data to Eq. 2 (Fig. 1G, see Table S1). Thus, this result shows that $\gamma 1$ modifies the voltage sensor’s R-A equilibrium marginally, promoting a 7-mV rightward shift of the Q(V) curve. A comparison of the G(V) and Q(V) curves in the presence of $\gamma 1$ reveals that 90% of the maximum conductance occurs when only ~20% of the voltage sensors are active. I.e., $\gamma 1$ allows the BK channel to open when fewer voltage sensors are activated. Since the fast component of the ON-gating current reflects the voltage sensor movement when the channels are in the closed state, Fig. 1G allows us to conclude that the $\gamma 1$ subunit promotes only a minor change in the equilibrium constant for voltage sensor activation, $J_0=exp\left(-z_{J}F{V}_h/RT\right)$ (Eq. 1, see Table S1).

The $\mathbf{\gamma }1$ subunit modulates the open-closed equilibrium

In the absence of ${\text{Ca}}^{2+}$, the allosteric model (Fig. S1A) predicts that the channel open probability ($P_o$) is given by (43):

$$P_o=\frac{1}{1+\frac{(1+J{)}^4}{L(1+JD{)}^4}}$$ (3)

where $L=L_0{e}^{z_{L}FV/RT}$, $L_0$ is the closed-to-open equilibrium constant at zero mV, $z_L$ is the voltage dependence for channel opening, and $D$ is the allosteric factor that couples the voltage sensor with the pore opening.

To have a complete description of the nature of the effect of $\gamma 1$ on $P_o$, in the absence of ${\text{Ca}}^{2+}$, we need to determine the parameters $L$ and $D$ in Eq. 3. Since the equilibrium constant $J$ (Eq.1) vanishes for very negative voltages, Eq. 3 tends $P_o\approx L\left(V\right)$. Therefore, we can obtain $L_0$ and $z_L$ by plotting ln($Po$) versus voltage when all the voltage sensors are at rest. This plot on a semilogarithmic scale is a straight line with a 0-volt intercept $L_o$, and the slope is $z_{L}F/RT$. To get $Po$, we detect single-channel activity at negative voltages in membrane patches containing a known number of channels $\left(N\right)$. Fig. 2A–B shows single-channel records obtained at two different voltages in the absence and presence of the $\gamma 1$ subunit, respectively, in membrane patches containing a few hundred channels. The presence of the $\gamma 1$ subunit allows the visualization of distinguishable opening events even at large negative voltages. We determined the product NPo using the Poisson distribution (Eqs. 7–8, see Methods) to fit the area under the peaks of an all-points histogram from long-time single-channel recordings (Fig. 2C–D–Fig. S3B). We estimate the number of channels in the membranes using nonstationary noise analysis of the activation currents (Fig. S3C; ^{43, 44}). Once $N$ is known, the $Po\left(V\right)$ data obtained by fitting the theoretical probability density function (PDF, Eq. 8, see Methods) to the experimental PDF (Fig. 2C–D) allow us to obtain $L_0$ by extrapolation of the $Po\left(V\right)$ data to 0 mV (Fig. 2E). $\gamma 1$ increases $L_0$ by 92-fold compared to the $L_0$ determined using channels formed by the $\alpha$ subunit alone (Fig. 2E, see Table S1). The value obtained for $L_0$ of the $\text{BK}\left(\alpha \right)$ channel is in reasonable agreement with that obtained previously by several groups (43, 48–51).

Figure 2. Unitary current analysis of BK in the presence of the $\mathbf{\gamma }1$ subunit reveals changes in the open-close equilibrium.

(A) Unitary recordings for hundreds of channels for $\text{BK}(\alpha +\gamma 1)$ and (B) $\text{BK}\left(\alpha \right)$ recorded in inside-out membrane patches at the indicated voltages and under symmetric 110 mM ${\text{K}}^{+}$ conditions and zero μM free internal ${\text{Ca}}^{2+}$. All-point histograms were constructed using 10–20 s of the single-channel recordings on the left, as shown in (C) $\text{BK}(\alpha +\gamma 1)$ and (D) $\text{BK}\left(\alpha \right)$. (E) Open probabilities at extreme negative voltages for $\text{BK}\left(\alpha \right)$ (blue, N = 5) and $\text{BK}\left(\alpha \right)+\gamma 1$ (purple, N = 11) were fitted to the straight-line $\text{ln}\left(\text{Po}\right)=\text{ln}\left(\text{Lo}\right)+{\text{z}}_{\text{L}}\text{FV}/\text{RT}$ with the following parameters for $\text{BK}\left(\alpha \right):{\text{L}}_0=4.9\cdot {10}^{-6}\pm 0.9\cdot {10}^{-6}y$ ${\text{z}}_{\text{L}}=0.36\pm 0.06$ while for $\text{BK}(\alpha +\gamma 1):{\text{L}}_0=4.5\cdot {10}^{-4}\pm 2.9\cdot {10}^{-4}\text{y}$ ${\text{z}}_{\text{L}}=0.74\pm 0.06$.

We fitted the $P_o$ data in the whole voltage range to Eq. 3, allowing $D$ to vary freely while restricting the value of $J_0$ and $z_J$ to those obtained from fitting the Q(V) data to Eq. 2, and $L$ to the values obtained of $L_0$ and $z_L$ extracted from Fig. 2E. Fig. 3A shows that the increase in $L_0$ by the presence of $\gamma 1$, is accompanied by an increase in the allosteric factor $D$ describing the coupling between the voltage sensor and the pore opening from 25.6 to 84.4 (see Table S1), which is smaller than the one reported earlier ($D=412$; (17)). Thus, our results show that the leftward shift in the G(V) curve induced by the $\gamma 1$ is due to the increase in the VSD-PD coupling, accompanied by an appreciable enhancement of $Po$ due to the increase in $L_0$. Quantitatively, the reduction in the energy necessary to open the channel is defined as $\Delta \Delta G=-RT\left(ln{L}_{0_{BK\left(\alpha +\gamma 1\right)}}-ln{L}_{0_{BK\left(\alpha +\gamma 1\right)}}\right)=-2.6\text{kcal}/\text{mol}$. In contrast, the reduction in VSD-PD coupling energy is defined as $\Delta \Delta G=-RT\left(ln{D}_{BK\left(\alpha +\gamma 1\right)}-\right.\left.ln{D}_{BK\left(\alpha \right)}\right)=-0.7\text{kcal}/\text{mol}$ per voltage sensor activation. Notably, we found that a 2-fold increase in $z_L$, from 0.36 to 0.74, accompanies the significant rise in $L_0$ due to the presence of $\gamma 1$ (Table S1). Due to the lack of knowledge about the molecular nature of the voltage dependence of the closed-pen reaction, it is difficult to propose a hypothesis about the origin of the increase in $z_L$. However, given that the transmembrane helix of $\gamma 1$ is kinked and tightly packed against the BK voltage-sensor (38–40), the subunit may be stabilizing a BK channel conformation that modifies the electric field where the charges or dipoles that produce the voltage dependence of $L$ are displaced.

Figure 3. Voltage dependence of the $\mathbf{B}\mathbf{K}(\mathit{\alpha }+\mathbf{\gamma }1)$ channel open probability and ${\mathbf{K}}^{+}$ current kinetics.

(A) ${\text{P}}_{\text{o}}$ over the whole range of voltages for $\text{BK}\left(\alpha \right)$ (blue, N = 5) and $\text{BK}(\alpha +\gamma 1)$ (purple, N = 11–7). Data were fitted using Eq. 3, leaving only D as a free parameter, with J and L obtained from the results shown in Figs. 1, 2, and Table S1. $\text{BK}\left(\alpha \right):\text{D}=25.6\pm 4.9$, while $\text{BK}(\alpha +\gamma 1):\text{D}=84.4\pm 6.4$. (B) Time constant $\left(\tau \right)$ - voltage data for $\text{BK}\left(\alpha \right)$ (blue, N = 3–4) and $\text{BK}(\alpha +\gamma 1)$ channels (purple, N = 3–8). At extreme negative voltages, $\tau$ was adjusted to the straight line: $\text{ln}\left({\gamma }_0\right)=\text{ln}{\left({\gamma }_{0,0}\right)}_{+}\text{z}\gamma \text{FV}/\text{RT}$ for ${\text{C}}_0-{\text{O}}_0$ transition, where ${\gamma }_{\mathrm{0,0}}$ is the backwards rate at zero mV and ${\text{z}}_{\delta }$ the rate voltage dependence. For $\text{BK}\left(\alpha \right):{\gamma }_{\mathrm{0,0}}=3590\pm 69\left({\text{s}}^{-1}\right)$ and ${\text{z}}_{\gamma }=0.136\pm 0.002$, while $\text{BK}(\alpha +\gamma 1):{\gamma }_{\mathrm{0,0}}=675\pm 41\left({\text{s}}^{-1}\right)$ and ${\text{z}}_{\gamma }=0.212\pm 0.005$.

In the absence of ${\text{Ca}}^{2+}$ and assuming that the resting-active transition of the voltage sensors is in equilibrium with respect to the closed-open reaction, the time constant-voltage curve, $\tau \left(V\right)$, is given by the relation (kinetics scheme in Fig. S1B;⁴⁹):

$$\tau \left(V\right)=\frac{1}{\sum _i\left({\delta }_{i}p{C}_i+{\gamma }_{i}p{o}_i\right)}$$ (5)

where the subindex $i=1,2,3,4$ is the number of voltage sensors activated and ${\delta }_i$ and ${\gamma }_{\text{i}}$ are the voltage-dependent forward and backwards rate constants of the individual ${\text{C}}_{\text{i}}-{\text{O}}_{\text{i}}$ transitions, respectively, and $p{C}_i$ and $p{O}_i$ are the conditional occupancies of the closed and open states, respectively. Notice that at very negative voltages, the ${\text{C}}_0-{\text{O}}_0$ transition determines $\tau \left(\text{V}\right)$, i.e., $\tau \left(V\right)={\gamma }_0^{-1}$. At zero mV, ${\gamma }_{\mathrm{0,0}}$ decreases 5-fold in the presence of the $\gamma 1$ subunit (see Table S2) and the voltage dependence ${\text{z}}_{\gamma }$, increases from 0.136 for $\text{BK}\left(\alpha \right)$ to 0.212 for $\text{BK}(\alpha +\gamma 1)$ suggesting that the $\gamma 1$ subunit affects the O-C transition explaining the slowing down of the deactivation kinetics and a 29 % of the increase in the voltage dependence of $L$ (Fig. 3B–Fig. S4–S5). Since $L_0={\delta }_{\mathrm{0,0}}/{\gamma }_{\mathrm{0,0}}$, knowing $L_0$ and ${\gamma }_{\mathrm{0,0}}$, we can calculate ${\delta }_{\mathrm{0,0}}$. The $\gamma 1$ subunit increases the forward rate constant ${\delta }_{\mathrm{0,0}}$ by 17-fold compared to the ${\delta }_{\mathrm{0,0}}$ obtained for the $\text{BK}\left(\alpha \right)$ channels (see Table S2). This result also corroborates those of Yan and Aldrich (18), who found a decrease in ${\gamma }_{\mathrm{0,0}}$ of about 4-fold, albeit with no change in ${\text{z}}_{\gamma }$. Overall, our results allow us to conclude that, in the absence of ${\text{Ca}}^{2+}$, the main effect of $\gamma 1$ is to modulate the C-O equilibrium, primarily by destabilizing the closed configuration of the BK channel, thereby facilitating the opening reaction.

The slow gating charge movement reveals that the $\mathbf{\gamma }1$ subunit allows BK channel activation from deeper closed states

The kinetic scheme in Fig. S1A predicts that the increase in $D$ and $L$ induced by the presence of the $\gamma 1$ should modify the kinetics of the OFF-gating charge (${\text{Q}}_{\text{OFF}}$), as it increases the open-closed equilibrium, allowing the channel to enter open states from deeper closed states. In other words, channels can open with fewer active voltage sensors. Fig. S6A shows OFF-gating currents in response to voltage pulse protocols of increasing duration for the $\text{BK}\left(\alpha \right)$ channel, designed to characterize their kinetics by integrating the total ${\text{Q}}_{\text{OFF}}$. As found previously, as the duration of the depolarizing pulse increases, a slow component develops in the ${\text{Q}}_{\text{OFF}}$ vs pulse length in $\text{BK}\left(\alpha \right)$ channels until reaching a constant value ($Q_{ss}$; Fig. S6B; ^{41, 50}). The $Q_{ss}$ data obtained using a pulse duration of 25 ms is plotted vs. voltage in Fig. S6C and fitted using Eq. 2 with a $z_J=0.54$ and a $V_H=145\text{mV}$.

Fig. 4A, shows how a slow component in the gating current records develops as a function of the ON voltage pulse duration in $\text{BK}(\alpha +\gamma 1)$ channels (Fig. 4A). Fig. 4B shows the time course data of the ${\text{Q}}_{\text{OFF}}$ obtained from the gating currents, fitted using a double exponential function at the indicated voltages. Fig. 4C shows the ${\text{Q}}_{\text{ss}}\left(\text{V}\right)$ data obtained with a 25-ms pulse duration plotted against voltage. The ${\text{Q}}_{\text{ss}}\left(\text{V}\right)$ curve is shifted to the left by 74mV compared to the Q(V) curve obtained by time-integrating the fast component of the ON-gating current (Fig. 1G) and approaches the G(V) curve (purple open points; Fig. 1C). As a comparison, we show in Fig. 4C the G(V) and Qss(V) curves for the $\text{BK}\left(\alpha \right)$ channel, noting that the Qss is shifted to the left with respect to the G(V) curve. The results shown in Fig. 4C demonstrate that the $\gamma 1$ subunit increases the probability that the channels will open at voltages where voltage sensors are not activated by enhancing the closed-open equilibrium.

Figure 4. The $\mathbf{\gamma }1$ subunit enables BK channels to open when only a subset of voltage sensors is active.

(A) Representative records of gating currents of $\text{BK}(\alpha +\gamma 1)$ channels, evoked at 200 mV, with different pulse length durations (from 0.05 ms to 25 ms). The total OFF-gating charge (${\text{Q}}_{\text{off}}$) was determined by integrating numerically the OFF-gating current over 0.25 ms. (B) $\text{BK}(\alpha +\gamma 1)$ ${\text{Q}}_{\text{off}}$ was normalized by ${\text{Q}}_{\text{off,max}}$ at 0, 40, 80, 120, 160, and 200 mV, plotted against time (the length for each depolarization pulse; purple filled circle). Data as mean ± SEM, (N = 4), and each dataset was fitted to a biexponential function (see Methods) for every voltage. (C) Normalized steady state OFF charge (${\text{Q}}_{\text{ss}}$) of $\text{BK}(\alpha +\gamma 1)$ from experiments like in (B) (N = 4) and from $\text{BK}\left(\alpha \right)$ (N = 4, from Fig. S6). For comparison, G(V) data from $\text{BK}\left(\alpha \right)$ and $\text{BK}(\alpha +\gamma 1)$ from Fig.1C were plotted. ${\text{Q}}_{\text{ss}}$ were fitted to a two-state model $Q_{\mathit{\text{ss}}}/Q_{ss,-\mathit{\text{max}}}=1/\left[1+\text{exp}\left(-{\text{z}}_{\text{Qss}}\text{F}\left(\text{V}-{\text{V}}_{0.5}\right)/\text{RT}\right)\right]$ with the following parameters: ${\text{V}}_{0.5}=147\pm 3\text{mV}$ and ${\text{z}}_{\text{Qss}}=0.54\pm 0.02$ for $\text{BK}\left(\alpha \right)$, while a ${\text{V}}_{0.5}=111\pm 11\text{mV}$ and ${\text{z}}_{\text{Qss}}=0.6\pm 0.1$ for $\text{BK}(\alpha +\gamma 1)$.

The $\mathbf{\gamma }1$ subunit does not affect the BK channel ${\mathbf{C}\mathbf{a}}^{2+}$-sensitivity

We next determined the ${\text{Ca}}^{2+}$-dependent activation of $\text{BK}(\alpha +\gamma 1)$ channels with robust ${\text{K}}^{+}$ current recordings at multiple ${\text{Ca}}^{2+}$ conditions (Fig. 5A–D). Fig. 5E shows a family of G(V) curves obtained from tail currents at various ${\text{Ca}}^{2+}$ concentrations, ranging from 0.01 μM to 1 mM (see Table S3). The leftward shift of the G(V) curve ($\Delta {\text{V}}_{0.5}$) in the whole ${\text{Ca}}^{2+}$ concentration range is −240 mV, which compares well with that we have obtained previously for the BK channel in the absence of $\gamma 1$ (shaded zone in Fig. 5E; −219 mV (54) and −247 mV (48)). Corroborating the results from Yan and Aldrich (-210 mV), these findings suggest that $\gamma 1$ does not affect the BK channel ${\text{Ca}}^{2+}$ activation. However, we can make a more quantitative comparison by fitting Gibbs free energy values ($\Delta G$) obtained from the ${\text{V}}_{0.5}$ at different ${\text{Ca}}^{2+}$ concentration data ($\Delta G_{C{a}^{2+}}=z_{G}F{V}_{0.5}$) and the relation (55, 56):

$$\Delta G_{C{a}^{2+}}=\Delta G_0+4RT\left\{ln\left[\frac{1+\frac{\left[Ca\right]i}{K_D}}{1+\frac{\left[Ca\right]i}{C{K}_D}}\right]\right\}$$ (6)

where $\Delta G_0$ is the free energy at zero ${\text{Ca}}^{2+}$, $R$ and $T$ have their usual meaning, $\left[Ca\right]i$ is the internal ${\text{Ca}}^{2+}$ concentration, $K_D$ the ${\text{Ca}}^{2+}$ binding constant to the closed channel, and $C$ is the CTD-PD coupling factor. Eq. 6 assumes one binding affinity ($K_D$) that includes RCK1 and RCK2 binding sites, and that there is no interaction between voltage and calcium sensor, i.e., allosteric factor E = 1. The best fit of the ${\text{V}}_{0.5}-{\text{Ca}}^{2+}$ concentration data to Eq. 6 gives no significant differences in $K_D$, and $C$ values for $\text{BK}\left(\alpha \right)$ and $\text{BK}(\alpha +\gamma 1)$ which are very similar to that reported in the literature for the $\text{BK}\left(\alpha \right)$ channel (41, 45, 51),(41, 45, 51), (see Table S4). Thus, we confirm previous results that claimed $\gamma 1$ does not considerable affect the BK channel ${\text{Ca}}^{2+}$ sensitivity (17), in opposition to recent findings suggesting a decrease in ${\text{Ca}}^{2+}$ sensitivity and an increase in CTD-PD coupling factor $C$ (39).

Figure 5. $\mathbf{\gamma }1$ subunit modulation of ${\mathbf{C}\mathbf{a}}^{2+}$-sensitivity.

Representative ionic currents recorded in inside-out configuration under symmetric 110 mM ${\text{K}}^{+}$ conditions and (A) 0.01 μM ${\text{Ca}}^{2+}$, (B) 0.8 μM ${\text{Ca}}^{2+}$, (C) 300 μM ${\text{Ca}}^{2+}$, or (D) 1 mM ${\text{Ca}}^{2+}$ for patches containing $\text{BK}(\alpha +\gamma 1)$ channels. (E) Normalized conductance versus voltage plots (G(V)) constructed from tail currents for intracellular ${\text{Ca}}^{2+}$ conditions in the range of 0.01 μM −1mM were adjusted to a two-state model (see Table S3). (F) $\Delta \text{G}$ versus calcium concentration plot for $\text{BK}(\alpha +\gamma 1)$ channels (purple) and $\text{BK}\left(\alpha \right)$ (blue). The data were fitted using Eq. 6. for $\text{BK}\left(\alpha +\gamma 1\right):{\text{K}}_{\text{D}}=0.3\pm 0.2\mu \text{M}$ and $\text{C}=11.3\pm 1.1$ and $\text{BK}\left(\alpha \right):{\text{K}}_{\text{D}}=1.0\pm 0.5\mu \text{M}$ and $\text{C}=11.5\pm 4.1$.

Discussion

The Horrigan-Aldrich Allosteric Model Provides a Mechanistic Understanding of $\mathbf{\gamma }1$ Action

Yan & Aldrich (18) concluded that $\gamma 1$ modulates BK channels through a significant increase in the coupling between the VSD and channel opening (allosteric factor $D;$ Fig. S1A). An increase in $D$ from 21 to 412 was enough to explain the leftward shift in the BK voltage activation curve. However, by determining the voltage sensor and pore equilibria, respectively, $J$ and $L$, we greatly restricted the degrees of freedom of the fit to the H-A model (only $D$ in our case). On the other hand, Redhardt et al. (39) proposed a mechanism by which $\gamma 1$ stabilizes the active state of $\text{BK}\left(\alpha \right)$ VSD. Moreover, the impact of $\gamma 1$ on the BK ${\text{Ca}}^{2+}$ sensitivity is under debate. While Yan & Aldrich (18) proposed that this was not affected by $\gamma 1$, Yamanouchi et al. (40) results indicate that $\gamma 1$ weakens the $\text{BK}\left(\alpha \right)$ channel ${\text{Ca}}^{2+}$ sensitivity, while favoring the active conformation of RCK1 ${\text{Ca}}^{2+}$ binding site. All this evidence points to a controversial subject that has not yet landed into a common answer to the question: how $\gamma 1$ operates molecularly to modulate the function of $\text{BK}\left(\alpha \right)$ channels? Motivated by the previous question, we used the Horrigan-Aldrich allosteric gating model. (18, 43) to assess the mechanism by which $\gamma 1$ subunit produces BK channels to be able to activate at negative potentials in the absence of ${\text{Ca}}^{2+}$ (18, 43).

Notably, our results show that the closed-open equilibrium is greatly affected by $\gamma 1$, which increases $L_0$ by more than 90-fold and interestingly, augments $z_L$, accounting for BK channel voltage-dependent activation regardless of VSD activation. Increasing $L_0$ orders of magnitude have been described previously in point mutants of BK (57), however in these mutants the voltage dependence remained unaltered. This effect, produced by the $\gamma 1$ subunit suggests a novel mechanism of action involving the modification of the electric field presumably around the pore domain. The increase in $L_0$ is partially due to a 5-fold decrease in the closing rate constant $\left({\gamma }_0\right)$ but mainly caused by a 17-fold increase in the forward rate constant (${\delta }_0$) of the closed-open reaction. Our results and the fitting of the ${\text{P}}_{\text{o}}\left(\text{V}\right)$ data using the allosteric model indicate that the increase in $D$ is smaller than that obtained by Yan and Aldrich (18), and are not consistent with their proposal that $L$ was unaffected by the $\gamma 1$ subunit. Still, their results show a 4-fold decrease in ${\delta }_0$, an observation not discussed in their study. Regardless of these differences, in our results, the effect of the $\gamma 1$ on the allosteric factor $D$ is at a lesser scale, increasing from 26 in the $\text{BK}\left(\alpha \right)$ to 84 in $\text{BK}(\alpha +\gamma 1)$ channels. However, even if we consider that D = 400 in $\text{BK}(\alpha +\gamma 1)$ as reported by Yan and Aldrich (18), the reduction in VSD-PD coupling energy per voltage sensor activation (1.7 kcal/mol) is still smaller than the reduction in the energy necessary to open the channel promoted by the $\gamma 1$ subunit (2.8 kcal/mol).

The resting-active equilibrium of the VSD is not affected by the $\mathbf{\gamma }1$ subunit

The present results appear to be incompatible with the mechanism proposed by Redhardt et al. (39), who suggested that the positive charges (arginines) contained in $\gamma 1$ C-terminal stabilize the VSD active configuration through long-range electrostatic interactions. An electrostatic bias imposed by the internal arginine cluster of $\gamma 1$ should affect the resting and active equilibrium of the voltage sensors, thereby shifting the Q(V) curves towards negative voltages. The fact that the gating charge activation curve is not affected by $\gamma 1$ when the channels are closed discards the possibility that a long-range electrostatic effect is involved in the mode of action of $\gamma 1$. Moreover, the fact that $\gamma 1$ does not affect the resting-active equilibrium between closed states does not support the proposal that $\gamma 1$ increases the probability of opening at negative potential by locking the active configuration of the VSD through the conformational changes in the S3 transmembrane segment (40). In Fig. 1, we demonstrate that $\gamma 1$ does not stabilize the VSD active configuration when the channels are closed and that the BK channel reaches its maximum open probability when fewer than 20% of the voltage sensors are in their active configuration. In other words, the data indicate that $\gamma 1$ increases $D$ to stabilize the VSD active configuration when the channels are open. The HA allosteric gating model gives a parsimonious explanation of these results. By increasing the equilibrium constant that defines the closed-open equilibrium ($L$) and the coupling between the voltage sensor and pore opening ($D$), $\gamma 1$ alters the primary activation pathway (see Fig. S1B).

${\mathbf{C}\mathbf{a}}^{2+}$ sensitivity and physiological implications of the $\mathbf{B}\mathbf{K}(\mathit{\alpha }+\mathit{\gamma }1)$ complex

Regarding ${\text{Ca}}^{2+}$-dependent activation, Yan & Aldrich (18) previously suggested that $\gamma 1$ does not modify the BK channel ${\text{Ca}}^{2+}$ sensitivity. However, Yamanouchi et al. (40) found a decrease in BK channel ${\text{Ca}}^{2+}$ sensitivity induced by $\gamma 1$ and suggested that the interaction between the RCK1 domain and the $\gamma 1$ arginine cluster promoted and increase in the RCK-PD coupling factor $C$. Nonetheless, our experiments at multiple ${\text{Ca}}^{2+}$ concentrations, showing a slight increase in ${\text{Ca}}^{2+}$ affinity and no alteration in coupling factor $C$, indicate that there is no effect in CTD-PD coupling nor ${\text{Ca}}^{2+}$ affinity decrease due to $\gamma 1$ subunit. The increase in ${\text{Ca}}^{2+}$ affinity is nothing but a result of an energetic bias that the $\gamma 1$ subunit imposes in the voltage-dependent activation curves, which is more noticeable when calculating and comparing the difference in $\mathbf{\Delta }\mathit{G}$ between saturating ${\text{Ca}}^{2+}$ and free ${\text{Ca}}^{2+}$ conditions ($\mathbf{\Delta }\mathbf{\Delta }\mathit{G}$; see Table S4), which is the same in the presence of the $\gamma 1$ subunit. Therefore, the $\gamma 1$ subunit positions $\text{BK}(\alpha +\gamma 1)$ within the activation window at resting intracellular ${\text{Ca}}^{2+}$, providing a mechanistic basis for robust physiological ${\text{K}}^{+}$ fluxes (see Fig. 5E).

Towards a structural and mechanistic understanding of $\mathbf{\gamma }1$ modulation of the BK channel

Our data are in line with Kallure et al.(38) proposal based on the $\text{BK}(\alpha +\gamma 1)$ structure, which posits that the $\gamma 1$ transmembrane domain kink promotes a stabilization of the voltage sensor domain helices (S0-S3), which favors the active configuration of S4 by primarily affecting VSD-PD communication (38). However, the main departure of previous interpretations of the modulatory effects of the $\gamma 1$, is that $\gamma 1$ mainly increases the channel open probability by destabilizing the closed state and not by increasing the allosteric coupling factor $D$. This kink may also be involved in the increase of PD voltage-dependence $z_L$, most likely reducing the electric field fraction that charges must traverse to open the channel.

Molecular modeling (58–60) and structural studies (61, 62) demonstrate that the open-closed transition implies a rotation and an approximation of the S6 transmembrane helices, making the BK channel’s internal vestibule more hydrophobic and decreasing the pore radius. These structural characteristics of the closed conformation led to the hydrophobic gating hypothesis (58–60). The closed BK channel structure also shows the appearance of membrane-facing fenestrations (61–64). Molecular simulations indicate that lipids can bind to the membrane-facing fenestrations and access the inner pore cavity, thereby increasing its hydrophobicity (65). The $\gamma 1$ subunit transmembrane domain kink may destabilize the closed configuration by introducing a “brake” to the configurational changes that lead to the closed state. However, to answer this question, a well-resolved structure of the closed $\text{BK}(\alpha +\gamma 1)$ channel and molecular modeling will allow us to compare the stability of the closed channel configuration with that of the $\text{BK}\left(\alpha \right)$ channel.

Materials and Methods

Molecular Biology and Channel Expression

Xenopus laevis oocytes were utilized as the heterologous expression system for $\text{BK}\left(\alpha \right)$ and $\text{BK}(\alpha +\gamma 1)$ expression. The $\alpha$ subunit of the human BK channel (GenBank: U11058) was gift of L. Toro from the University of California, Los Angeles. The cDNA for hSlo1 was subcloned into the pBSTA vector. The mutant 2D2A (D362A/D367A) for the RCK1 ${\text{Ca}}^{2+}$-binding site (Xia et al., 2002) and the 5D5A mutant for the RCK2 ${\text{Ca}}^{2+}$-binding site, also known as the calcium bowl (D894A/D895A/D896A/D897A/D898A; (66), were kindly provided by M. Holmgren from the National Institutes of Health in Bethesda, MD. Dr. Jiusheng Yan from the University of Texas MD Anderson Cancer Center in Houston, TX, and Dr. Richard Aldrich from the University of Texas at Austin, TX provided the cDNA coding for the human $\gamma 1$ subunit (LRRC26). The cRNA was checked and sequenced. The restriction enzyme NotI was used to digest the cDNA. The linearized DNA was transcribed using the mMESSAGE mMACHINE T7 transcription kit (Ambion, Austin, TX, USA). The RNA obtained was quantified using a Nanodrop, which measured the 260/280 and 260/230 ratios to determine purity, and agarose gel electrophoresis to assess quality. Finally, Xenopus laevis oocytes were injected with 50 ng of cRNA for $\text{BK}\left(\alpha \right)$, and when injected with $\gamma 1$ in a ratio of $\left[\text{RNA}\gamma 1\right]:\left[\text{RNA}\alpha \right]=5$, they were incubated in an ND96 solution (in mM: 96 NaCl, 2 KCl, 1.8 ${\text{CaCl}}_2$, 1 ${\text{MgCl}}_2$, 5 HEPES, pH 7.4) at 18°C for 1–4 days before electrophysiological recordings.

Electrophysiology

All recordings were conducted using the patch-clamp technique in the inside-out configuration. For ${\text{K}}^{+}$ ionic currents (${\text{I}}_{\text{K}}$), we used symmetrical solutions composed of mM: K-MeS 110 (KOH 108 and KCl 2), HEPES 10, and 5 EGTA for the ‘ free’ ${\text{Ca}}^{2+}$ ‘ solution (~0.8 nM, based on the presence of ~10 μM contaminant $\left[{\text{Ca}}^{2+}\right]$ (67), adjusted to pH 7.4). For test solutions at different ${\text{Ca}}^{2+}$ concentrations (0.03 – 1000 μM), ${\text{CaCl}}_2$ was added to achieve the desired free $\left[{\text{Ca}}^{2+}\right]$, and 5 mM EGTA (0.1–0.5 μM) or HEDTA (0.8–10 μM) was used as a calcium buffer. No ${\text{Ca}}^{2+}$ chelator was used for ≥100 μM ${\text{Ca}}^{2+}$ solutions, and the free ${\text{Ca}}^{2+}$ concentration was estimated using the WinMaxChelator Software and verified with a ${\text{Ca}}^{2+}$ electrode (Hanna Instruments). All experiments were performed at room temperature (20–22°C). Potassium currents at different ${\text{Ca}}^{2+}$ concentrations in the same oocyte were obtained by excising the patch and washing it with an appropriate internal solution using at least 10 times the chamber volume. Pipettes for macroscopic and gating currents were fabricated using borosilicate capillary glass (1B150F-4, World Precision Instruments, Sarasota, FL, USA) and pulled using a horizontal puller (Sutter Instrument) and fire-polished (Narishige, London, UK). The pipettes for macro patches were designed to achieve a pipette resistance in the range of $0.5-1.5\text{M}\Omega$. Data were acquired using an Axopatch 200B (Molecular Devices). Voltage commands and current outputs were filtered at 20 kHz using an 8-pole Bessel low-pass (Frequency Devices). For current recordings, we sampled using a 16-bit A/D converter (Digidata 1550B; Molecular Devices), sampling at a rate of 250 kHz.

For gating currents (${\text{I}}_{\text{g}}$), a solution containing (mM): X-MeS 110, HEPES 10, and EGTA 1, adjusted to pH 7.4, where X = N-methyl-D-glucamine (NMDG) in the bath solution was used. To avoid ionic currents through $\text{BK}(\alpha +\gamma 1)$ channels were blocked using 2 μM paxilline. In the pipette solution X = tetraethylammonium (TEA). The voltage and current were filtered analogically using an 8-pole Bessel low-pass filter (Frequency Devices, Ottawa, IL, USA) at 10 kHz, through a 16-bit analog-to-digital converter (Digidata 1550B, Axon Instruments) with a sampling frequency of 500 kHz. The gating currents were measured using giant patches with $0.5-<1\text{M}\Omega$ pipettes. In the case of $\text{BK}(\alpha +\gamma 1)$ channels the gating charge was estimated by fitting the gating current time course using of two exponentials of which only the fast component was considered when calculating the gating charge.

Determination of the open probability (${\mathit{P}}_{\mathit{o}}$)

For $Po$ determination, macro-patches containing hundreds of channels were used. Tail current analysis was used to determine $Po$ values > 0.01. For Po < 0.01 values, membranes with many channels and measurements of single-channel currents at large hyperpolarization were used. Nonstationary noise analysis (46, 47) was used to calculate the number of channels $\left(N\right)$ in the patch and the unitary current ($i$). The average current and variance of isochrones were obtained from 200 current relaxation records in response to a depolarizing voltage pulse or during the tail after depolarization. After channel counting, membrane current was acquired for 5–30 s at Vm values ranging from 60 to −220 mV, voltages where the instantaneous current corresponds to a few open channels. To determine the open channel probability ($NPo$), we generated all-point histograms of the number of times a given current, $I$, was observed. The ordinate values of the histogram were divided by the integral over the current axis to obtain an experimental probability density function, PDF. The PDF is modeled as a sum of 10 normal Gaussian functions (Eq.7) weighted by coefficients, $Pk$, obtained from Poisson’s distribution (Eq. 8) where the expected number of open channels is $NPo$

$$PDF=\sum _{k=0}^9\frac{P_k}{{\sigma }_k\sqrt{2\pi }}{e}^{\frac{(I-ki{)}^2}{2{\sigma }_k^2}}$$ (7)

$$P_k=\frac{{\left(N{P}_O\right)}^k}{k!}{e}^{-N{P}_O}$$ (8)

where $P_k$ is the probability of having $k$ open channels. The mean value of each Gaussian is the amplitude of $k$ unitary currents, $i$, while the noise of one open channel defines the corresponding variance:

$$\sigma (\text{k}>0)={\sigma }_{\text{open}}\surd \text{k}$$

For recordings showing two or more simultaneous open channels, the variance of the closed channel, $\sigma (\text{k}=0)$, was empirically found to be 0.75 times the variance of the open channel, ${\sigma }_{\text{open}}$. This restriction was applied to fit the model, where only single channels were detected. We also adjusted the unitary current, $i$, to resemble the instantaneous I/V relationship from tail currents in deactivation protocols. At extremely negative potentials, where single-channel openings are very brief, the acquisition filter distorts the shape of normal histograms between Gaussian peaks (68). Because in this condition, the model PDF lies below the experimental data points between the two Gaussian peaks, we corrected the NPo as the area under the $k=1$ Gaussian, plus the area between the model and experimental PDFs divided by 2. By previously subtracting the baseline, the free parameters of the Poisson-Gauss fit are $NPo$ and ${\sigma }_{\text{open}}$.

Funding Statement

FONDECYT Regular #1230265 (R.L.)

ANID Millennium Science Initiative Program P09-022F (R.L.)

National Institute Award RO1GM030376 (R.L.)

PhD ANID fellowship #21202097 (F.E.)

Data and materials availability:

All data are available in the main text or the supplementary materials.