We present in this work a structural model of the open IKCa (KCa3.1) channel derived by homology modeling from the MthK channel structure, and used this model to compute the transmembrane potential profile along the channel pore. This analysis showed that the selectivity filter and the region extending from the channel inner cavity to the internal medium should respectively account for 81% and 16% of the transmembrane potential difference. We found however that the voltage dependence of the IKCa block by the quaternary ammonium ion TBA applied internally is compatible with an apparent electrical distance δ of 0.49 ± 0.02 (n = 6) for negative potentials. To reconcile this observation with the electrostatic potential profile predicted for the channel pore, we modeled the IKCa block by TBA assuming that the voltage dependence of the block is governed by both the difference in potential between the channel cavity and the internal medium, and the potential profile along the selectivity filter region through an effect on the filter ion occupancy states. The resulting model predicts that δ should be voltage dependent, being larger at negative than positive potentials. The model also indicates that raising the internal K+ concentration should decrease the value of δ measured at negative potentials independently of the external K+ concentration, whereas raising the external K+ concentration should minimally affect δ for concentrations >50 mM. All these predictions are born out by our current experimental results. Finally, we found that the substitutions V275C and V275A increased the voltage sensitivity of the TBA block, suggesting that TBA could move further into the pore, thus leading to stronger interactions between TBA and the ions in the selectivity filter. Globally, these results support a model whereby the voltage dependence of the TBA block in IKCa is mainly governed by the voltage dependence of the ion occupancy states of the selectivity filter.

## Introduction

Ca2+-activated potassium channels (K(Ca2+)) are present in most mammalian cell types, where their primary role is to establish a link between the various Ca2+-based second messenger systems and the electrical properties of the cells. Three main classes of Ca2+-activated potassium channels have been to date identified on the basis of their permeation properties and pharmacology (Vergara et al., 1998). These include the charybdotoxin- and iberiotoxin-sensitive KCa1.1 channels of large conductance (150–220 pS); the intermediate conductance (20–50 pS) IKCa channels (KCa3.1) inhibited by clotrimazole (Rittenhouse et al., 1997) and TRAM34 (Wulff et al., 2001), and the apamine-sensitive and -insensitive SK channels of small conductance (KCa2.1, KCa2.2, KCa2.3) (Kohler et al., 1996). In contrast to KCa1.1, the SK and IKCa channel gating process is voltage insensitive, and the Ca2+ sensitivity in both channels is conferred by the Ca2+-binding protein, calmodulin, constitutively bound to the channel proximal COOH-terminal regions (Khanna et al., 1999).

An important contribution to our understanding of the IKCa channel molecular identity came from the cloning of the hKCa4, hIK1, and hSK4 channels (Ishii et al., 1997; Joiner et al., 1997; Logsdon et al., 1997; Vandorpe et al., 1998; Warth et al., 1999). The IKCa channel is a tetrameric protein with each subunit comprising 427 amino acids organized in six transmembrane segments TM1–TM6 with a pore motif between segments 5 and 6. The three-dimensional (3D) structure of IKCa, however, remains unresolved. Docking simulations and binding studies using charybdotoxin analogues have revealed that the IKCa external vestibule is structurally similar to the external pore region of other charybdotoxin-sensitive channels, such as Kv1.2 and Kv1.6 (Rauer et al., 2000). Sequence and secondary structure alignments also suggest a structural similarity between the proximal COOH-terminal region of IKCa (residues 395–430) and the calmodulin-binding domain of rSK2 (unpublished data), the structure of which has been resolved by X-ray crystallography (Schumacher et al., 2001). More recently, work from our laboratory has led to the first molecular description of the open/closed IKCa pore region using an approach combining the substituted cysteine accessibility method (SCAM), computer-based homology modeling, and single channel recordings (Simoes et al., 2002). The proposed IKCa models showed the V275, T278, and V282 residues as lining the channel pore, with V275 and T278 contributing to the formation of a central inner cavity ∼10 Å wide. Fig. 1 presents the structures we propose for the open and closed IKCa obtained by homology modeling using the KcsA (Doyle et al., 1998) and MthK (Jiang et al., 2002a) channels as templates. Estimation of the distance between the α-carbons of corresponding residues along TM6 for subunits facing diagonally indicates a drastic widening of the pore starting at residue T278 upon channel opening. An analysis of the open channel structure reveals in addition that the inner vestibule exceeds 18 Å in diameter, suggesting that it should be wide enough to create a quasi isopotential continuum between the channel central cavity and the internal medium.

In this work we used the quaternary ammonium (QA) ion tetrabutylammonium (TBA) to investigate some of the structural features of the IKCa conduction pathway and probe the transmembrane potential profile within the IKCa open pore structure. QA ions are considered good blockers of K+ channels and have been extensively used to characterize channel inner architecture. One of the main features of the blocking properties of QA ions concerns the voltage dependence of the channel block. For instance, studies in which the QA ions TEA or TBA were applied internally showed that the electrical distances that account for the voltage sensitivity of the channel block ranged from 0.2 (Shaker and MaxiKCa) (Villarroel et al., 1988; Ding and Horn, 2002; Thompson and Begenisich, 2003a; Li and Aldrich, 2004) up to 0.9 (Kir1.1 and Kir2.1) (Spassova and Lu, 1998, 1999; Guo and Lu, 2001) depending on channel types. X-ray data for the TBA-closed KcsA complex support a binding site for TBA located in the central cavity (Zhou et al., 2001). Assuming an equivalent position for the binding site in the open channel, electrical distances from 0.2 to 0.9 could be indicative of pore structures where a significant fraction of the transmembrane potential drop occurs over the region extending from the channel central cavity to the internal medium. However, these values might be difficult to reconcile with an isopotential continuum between the channel central cavity and the internal medium, as suggested by the MthK channel structure. The blocking potency of internal QA ions also depends on the structural parameters controlling the accessibility of the ions to the interaction site. Notably, there are considerable variations in the entry rate of individual QA ions depending on channel types. For instance, the entry rate measured for TBA in zero current conditions was found to vary from 0.004 μM−1s−1 for the Kir1.1 and Kir2.1 inward rectifiers up to 0.55 μM−1s−1 for Shaker (Guo and Lu, 2001; Ding and Horn, 2002). These variations are likely to reflect gross differences in the channel inner vestibule geometry.

In this work, we measured the kinetics and the voltage dependence of the IKCa block by internal TBA. Our results confirm that the V275 residue is lining the channel central pore cavity and contributes to the architecture of the TBA interaction site. We also demonstrate that the voltage dependence of the IKCa block by TBA presents a complex pattern with an apparent electrical distance of 0.49 at negative potentials. Using the structure proposed for the open IKCa configuration and the recent model of Berneche and Roux (2003) describing the single file diffusion of K+ in the KcsA selectivity filter, we show that the observed dependence of the TBA block reflects the ion occupancy state of the selectivity filter rather than the actual potential difference between the channel inner cavity and the internal medium.

## Materials And Methods

### Cloning, Sequencing and Site-directed Mutagenesis of the IKCa Channel

IKCa channel cDNAs were obtained by RT-PCR from HeLa cells as described previously (Simoes et al., 2002). The resulting PCR product was identical to the sequences reported for the hKCa4 (GenBank/EMBL/DDBJ accession no. AF033021), hIK1 (AF022150), and hSK4 (AF000972) channels. Site-directed mutagenesis of IKCa channel was performed using the QuickChange Site-Directed Mutagenesis kit (Stratagene). Point mutations were obtained by using 25-mer mutated oligonucleotides with the wild-type IKCa as template. Mutations were confirmed by sequencing the entire coding region on both strands.

### Oocytes

Mature oocytes (stage V or VI) were obtained from Xenopus laevis frogs anesthetized with 3-aminobenzoic acid ethyl ester. The follicular layer was removed by incubating the oocytes in a Ca2+-free Barth's solution containing collagenase (1.6 mg/ml; Sigma-Aldrich) for 45 min. The composition of the Barth's solution was (in mM) 88 NaCl, 3 KCl, 0.82 MgSO4, 0.41 CaCl2, 0.33 Ca(NO3)2, and 5 HEPES (pH 7.6). Defolliculated oocytes were stored at 18°C in Barth's solution supplemented with 5% horse serum, 2.5 mM Na-pyruvate, 100 U/ml penicillin, 0.1 mg/ml kanamycin, and 0.1 mg/ml streptomycin. Oocytes were patched 3–5 d after coinjection of 0.92–9.2 ng of the cDNA coding for IKCa in pMT21 and 1.38 ng of cDNA coding for a green fluorescent protein that was used as a marker for nuclear injection.

Prior to patch clamping, defolliculated oocytes were kept in a hyperosmotic solution containing (in mM) 250 KCl, 1 MgSO4, 1 EGTA, 50 sucrose, and 10 HEPES buffered at pH 7.4 with KOH. The vitelline membrane was then peeled off using fine forceps, and the oocyte was transferred to a superfusion chamber for patch clamp measurements.

### Solutions

The bath and patch pipette solutions consisted of (in mM) 200 K2SO4, 1.8 MgCl2, 0.025 CaCl2, 25 HEPES, buffered at pH 7.4 with KOH. The use of sulfate salts prevented contributions from endogenous Ca2+-dependent chloride channels while enabling to chelate contaminant divalent cations such as Ba2+ (maximum free Ba2+ concentration: 0.5 nM in 200 mM K2SO4). Calcium-free solutions were prepared by omitting CaCl2 from the 200 mM K2SO4 solution and adding 1 mM EGTA. Solutions with different potassium concentrations were prepared using NMDG as replacing ion and titrated with H2SO4. Unless specified otherwise, potassium ion concentrations are expressed as potassium activities. Activity coefficients for the various K2SO4 solutions were obtained from literature (Robinson and Stokes, 1959). The potassium ion activity for each solution reads: 225 mM for the 400 mM K2SO4 solution; 140 mM for the 200 mM K2SO4 solution; 60 mM for the 50 mM K2SO4 solution; and 2 mM for the 1 mM K2SO4 solution. TBA was dissolved directly into the bath solution at the desired concentration. MTSET (Toronto Research Chemicals Inc.) was added into the recording saline directly before use. EBIO (Tocris Cookson Inc.) was first dissolved in DMSO and then diluted in the experimental solution.

### Rapid Solution Changes

Internal solution changes in inside-out recordings were performed using an RSC-160 rapid solution changer system (BioLogic). The bath solution could be fully exchanged within <30 ms as measured by the variation in patch pipette resistance when BaCl2 (10 mM)-containing patch electrodes were exposed to a 200 mM KCl plus 200 μM K2SO4 bath solution. Typically, Ca2+-free and TBA-containing bath solutions were perfused in successive 4-s periods, separated by 5-s washouts with the control solution.

### Patch Clamp Recordings

Single channel recordings were performed in the inside-out patch clamp configuration using a List EPC-7 amplifier (List Medical). Patch pipettes were pulled from borosilicate capillaries using a Narishige pipette puller (Model PP-83) and used uncoated. The resistance of the patch electrodes ranged from 4 to 6 mΩ. Data acquisition was performed using a TL-1 DMA interface (Axon Instruments) at a sampling rate of 1.0 kHz with filtering at 500 Hz. Experiments were performed at room temperature (22°C).

### TBA Protection Experiments

TBA protection experiments were performed by measuring the change in MTSET accessibility to cysteines engineered either at position 275 or 283 in the presence or absence of TBA in the internal solution. Basically, MTSET (5 mM) was applied for 1 s during single 2-s TBA application (5 mM). Each TBA application was followed by a 2-s washout period with the standard 200 K2SO4 solution (see Fig. 3). Control experiments performed without TBA were performed according to the same perfusion protocol.

### Data Analysis

Kinetics of intracellular TBA block were determined according to the following scheme:

where B is the concentration of the blocking agent, K12 and K21 the rates of channel opening and closing, respectively, K12B and K21B the rates of channel opening and closing with the channel in the blocked configuration, K3 the entry rate in μM−1s−1 of the blocking agent, and K4 the dissociation rate of the blocker (for example see Holmgren et al., 1997). K12 and K21 represent in this case the rates of opening and closing seen by the blocking agent averaged over all the channel states leading to observable transitions (see appendix in Garneau et al., 2003). It is assumed in Scheme 1

that the blocker cannot enter the channel when in the closed configuration. It follows from this scheme that the fraction of current block fB is given by

$\mathrm{f}_{\mathrm{B}}=\frac{\mathrm{I}_{\mathrm{B}}}{\mathrm{I}_{\mathrm{Max}}}=\frac{1}{\left(1+\frac{\mathrm{B}}{\mathrm{IC}_{50}}\right)}\mathrm{,}$
(1)

with IMax and IB the currents before and after application of the blocking agent and

$\mathrm{IC}_{50}=\frac{\mathrm{K}_{4}\mathrm{{\zeta}}}{\mathrm{K}_{3}}\mathrm{,}$
(2)

where ζ = PoB/Po with Po = K12/(K12 + K21) is the open probability of the channel before inhibition by the blocker (Ding and Horn, 2002), and PoB = K12B/(K12B + K21B) the probability that the channel will be in the open blocked configuration. If the binding of the blocker to the channel does not modify gating (ζ = 1), it follows from Eq. 2 that IC50 becomes independent of the channel open probability.

The blocker effective exit rate, K4Poζ, can be obtained by measuring the rate at which the macroscopic current recovers after removal of the blocker. According to the Scheme 1, current recovery after removal of the blocker is given by

$\mathrm{I}\left(\mathrm{t}\right)=\mathrm{I}_{\mathrm{Max}}+\mathrm{A1e}^{\mathrm{{-}}\left(\mathrm{K}_{12}+\mathrm{K}_{21}\right)\mathrm{t}}+\mathrm{A2e}^{\mathrm{{-}{\omega}1t}}+\mathrm{A3e}^{\mathrm{{-}{\omega}2t}}\mathrm{,}$
(3)

where A1, A2, and A3 are constants and ω1 and ω2 transitions rates such that

$\mathrm{{\omega}}1+\mathrm{{\omega}}2=\mathrm{K}_{4}+\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}$
(4)
$\mathrm{{\omega}}1\mathrm{{\omega}}2=\mathrm{K}_{4}\mathrm{K}_{12}^{\mathrm{B}}\mathrm{.}$
(5)

In conditions where the dissociation rate is slow (K12B + K21B >> K4), ω1 and ω2 can be approximated as

$\mathrm{{\omega}}1{\cong}\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}$
(6)

and

$\mathrm{{\omega}2}{\cong}\mathrm{K}_{4}\frac{\mathrm{K}_{12}^{\mathrm{B}}}{\left(\mathrm{K}_{12}^{\mathrm{B}}+\mathrm{K}_{21}^{\mathrm{B}}\right)}\mathrm{.}$
(7)

Assuming in addition that K12 + K21 >> K4, Eq. 3 reduces to a single exponential with a time constant τon given by

$\mathrm{{\tau}}_{\mathrm{on}}=\frac{1}{\mathrm{{\omega}2}}=\frac{1}{\mathrm{K}_{4}\mathrm{Po{\zeta}}}\mathrm{.}$
(8)

It follows from Eq. 2 that the effective entry rate of the blocker can now be obtained from

$\mathrm{K}_{3}\mathrm{Po}=\frac{1}{\mathrm{{\tau}}_{\mathrm{on}}\mathrm{IC}_{50}}\mathrm{.}$
(9)

In the present study, IB and IMax were estimated using the QuB package (Qin et al., 1996, 1997). The time constant τon was obtained from the time course of the current recovery after TBA removal fitted to a single exponential function using the Origin 6.1 software (Origin; Microcal Software Inc.). IC50 values were computed by fitting the TBA dose–response inhibition curves to Eq. 1 using the logistic function in Origin 6.1. The analytic solution of the kinetic scheme presented in Fig. 6 A and model-based simulations were generated with the Mathematica 4.1 software (Wolfram Research Inc.).

In conditions where single channel events could be recorded, the single channel conductance was estimated from current amplitude histograms as described previously (Morier and Sauvé, 1994). For multichannel recordings, Po was determined from noise analysis by measuring the ratio

$\frac{\mathrm{{\sigma}}^{2}}{\mathrm{{<}I>}}=\left(1{-}\mathrm{Po}\right)\mathrm{Io}$
(10)

as a function of the applied voltage V with σ2 the steady-state current variance, <I> the current mean value, and Io the channel unitary current. Po was computed as

$\mathrm{Po}=1{-}\frac{\mathrm{{\Lambda}}_{\mathrm{noise}}}{\mathrm{{\Lambda}}_{\mathrm{single\ channel}}}\mathrm{,}$
(11)

where Λnoise is the conductance derived from the plot of σ2/<I> as a function of V and Λ single channel the unitary channel conductance.

### Statistical Analysis

Statistical significance was analyzed using unpaired Student's t test. P < 0.01 was considered statistically significant.

### Homology Modeling

Automated homology modeling was performed with Modeller V6.1 (Sali and Blundell, 1993) and involved the generation of 50 models of the IKCa channel pore using the MthK and KcsA channel structures as templates (Protein Data Bank entry 1LNQ). Energy minimization was carried on the model with the lowest objective function (roughly related to the energy of the model) using CHARMm.

### Electrostatic Energy Profile

The atomic structure of the IKCa model was inserted in a 25-Å-thick membrane represented as a continuum medium with a dielectric constant of 2. No electrolyte was included in the bulk solution and in the potassium channel central cavity, but a 17-Å diameter cylindrical aqueous pore with a dielectric constant of 80 was added along the pore axis (z). The electrostatic contribution to the free energy needed to transfer a K+ from the bulk solution to a position z along the channel pore was calculated as

$\mathrm{{\Delta}{\Delta}G}_{\mathrm{elec,i(z)}}=\left(\mathrm{{\Delta}G}_{\mathrm{i(z)-c}}{-}\mathrm{{\Delta}G}_{\mathrm{c}}{-}\mathrm{{\Delta}G}_{\mathrm{i(z)}}\right)\mathrm{,}$
(12)

where ΔGi(z)-c is the electrostatic energy of the channel with an ion at the position z with x = y = 0, ΔGc is the electrostatic energy of the channel with no ion, and ΔGi(z) the electrostatic energy of the K+ ion in the bulk solution. The finite-difference calculations were performed using the PBEQ module of the biomolecular simulation program CHARMm (for example see Roux, 1997). The numerical calculations were performed using a standard relaxation algorithm (Warwicker and Watson, 1982). The complete system was mapped onto a cubic grid, and the Poisson equation solved numerically. The total electrostatic potential was calculated at each point of the grid by solving the finite difference Poisson equation. Calculations were performed in two steps, first using spacing of 1.0 Å (130 points, with periodic boundary conditions in the membrane plane), followed by more precise calculations around the main region with a grid spacing of 0.5 Å. A hydrogen minimization procedure was performed between each ion position.

## Results

### Block of IKCa Wild Type by TBA

TBA has been documented to block the pore of a wide variety of K+ channels by entering the open channel from the cytoplasmic side up to the channel inner cavity. Experiments were conducted to characterize the effects of TBA on wild-type IKCa channels expressed in Xenopus laevis oocytes. Fig. 2 A shows representative inside-out current traces in which TBA was applied internally at a constant membrane potential of −60 mV. As seen, application of TBA at concentrations ranging from 50 to 800 μM caused a dose-dependent inhibition of the IKCa current that was fully reversible after washout of the QA ion. In addition, the time course of the current recovery after TBA washout is shown to be accounted for by a single exponential (see Eqs. 38). The dose–response curve for current inhibition measured at −60 mV is presented in Fig. 2 B. Data points could be well fitted to Eq. 1 with IC50 equal to 192 ± 7 μM (n = 12), indicating a bimolecular reaction involving one inhibitor per ion channel as hypothesized in the kinetic Scheme 1.

Crystallization of the bacterial channel KcsA in the presence of TBA has provided direct evidence for TBA binding in the channel central cavity (Zhou et al., 2001). An analysis of the TBA binding site in the closed KcsA structure indicates that the external Van der Waals surface of TBA is in close contact with the T75 and I100 pore lining residues. The 3D model of the closed IKCa we derived through homology modeling using the KcsA channel as template suggests a structural equivalence between I100 in KcsA and V275 in IKCa (Simoes et al., 2002). This prediction was confirmed by SCAM experiments where the V275C mutant channel in the open state was strongly inhibited by the positively charged MTSET reagent applied internally (Simoes et al., 2002). Fig. 1 shows a superimposed representation of the proposed IKCa channel model structures in the closed and open configurations. The structure of the open channel was obtained by homology modeling with MthK as template (see materials and methods). In the open configuration, the residue V275 is predicted to be lining the IKCa channel central cavity. In contrast, the A283 residue is expected to be located in the channel inner vestibule at the entrance of the cavity region. Notably, internal application of MTSET to the A283C mutant, resulted in an increase in channel activity, coupled to a partial inhibition of the single channel currents (Simoes et al., 2002).

To identify the TBA binding site in the IKCa channel, inside-out experiments were undertaken to evaluate the ability of TBA to protect cysteines engineered either at position 275 or 283 against a chemical modification by the MTSET reagent (see materials and methods). An example of a TBA protection experiment with the V275C channel is presented in Fig. 3 A. As seen, 5 mM TBA completely and reversibly blocked the V275C currents. The change in MTSET accessibility due to the presence of TBA is summarized in Fig. 3 B. These results show an eightfold increase in the time constant for MTSET-induced inhibition from 18 ± 1 s (n = 2) in the absence of TBA, to 147 ± 5 s (n = 4) with TBA. This observation indicates that TBA had access to a site close enough to V275 as to interfere with the accessibility of MTSET to the cysteine at position 275, in agreement with the structural data of the KcsA + TBA complex (Zhou et al., 2001). In contrast, the results in Fig. 3 C show that TBA failed to affect the time course of the stimulatory action of MTSET on the A283C channel, indicating that the TBA binding site is located closer to the cavity region than to the inner vestibule.

### TBA Block and IKCa Channel Open Probability

The analytical expression presented in Eq. 2 predicts that the concentration for half inhibition, IC50, should depend on the parameter ζ = PoB/Po, which accounts for the change in open probability due to the presence of TBA in the channel cavity (see materials and methods). As a result, IC50 measurements should be independent of the channel open probability, provided the channel gating behavior is not affected by the binding of TBA to its site (ζ = 1). This hypothesis was tested by modifying the channel open probability using the IKCa opener EBIO. An example of inside-out recording illustrating the effects of EBIO applied internally is presented in Fig. 4 A. As seen, the addition of internal EBIO led to a substantial increase in the current mean value and variance. Noise analysis performed on the recordings before and after the addition of 100 μM EBIO to the internal medium revealed an increase in the channel open probability Po from 0.17 ± 0.08 (n = 6) to 0.50 ± 0.09 (n = 6) (see Eq. 11 and Fig. 4 D). The effect of EBIO (100 μM) on the dose response curve of the IKCa block by TBA is illustrated in Fig. 4 B. Our results show a significant decrease of the IC50 value from 298 ± 20 μM (n = 11) in the absence of EBIO to 192 ± 7 μM (n = 12) in EBIO conditions (P < 0.0001). These results indicate that the presence of TBA in the channel cavity affects gating.

### Voltage Dependence of the TBA Block

Fig. 5 A summarizes the effect of voltage on the TBA dose–response curve for voltages ranging from −30 to −120 mV, measured in EBIO conditions. As seen, negative membrane voltages resulted in a rightward shift of the TBA dose–response curve. The variation in IC50 as a function of voltage is presented in Fig. 5 B. Clearly, the voltage dependence of the TBA block shows a complex behavior with a stronger voltage dependence at negative than at positive potentials. In the former case, the data could be approximated to a single exponential function of the form IC50 = IC50(0) exp(−δVq/KT), where δ is the fraction of the transmembrane potential through which internal TBA moves to reach its site (Woodhull, 1973), V the applied voltage, q, K, and T the electrical charge, the Boltzmann constant, and the temperature, respectively. Estimations of the electrical distance δ within the voltage range −120 to −30 mV led to a value of 0.49 ± 0.02 (n = 6).

### Channel Gating and TBA Block

According to Scheme 1, it is hypothesized that TBA can be trapped inside the channel cavity upon closing. The effect of changing the channel open probability on the voltage dependence of the TBA entry and exit rates was thus investigated using EBIO as stimulating agent. As seen in Fig. 5 (C and D), stimulation by EBIO increased the effective entry (PoK3) and exit (Po ζ K4) rates 3.8-fold and 2.7-fold, respectively, over the whole voltage range with no significant change in the voltage dependence of the TBA block. The observation that the TBA exit rate depends on the channel open probability supports the linear kinetic scheme proposed in Scheme 1 and suggests that TBA can be trapped in the cavity upon channel closing. This proposal is also supported by the results presented in Fig. 5 D, where the unbiased entry rates K3 (diamonds) could be estimated from the effective entry rates PoK3 measured either in the absence or presence of EBIO, using Po values equal to 0.13 and 0.49 in control and EBIO conditions, respectively. The latter values are well within the Po range estimated by noise analysis (Fig. 4 D). Finally, the data in Fig. 5 C show that the TBA exit rate decreased an e-fold factor per 85 mV over the voltage range −120 to 0 mV for an electrical distance δ = 0.29. In contrast, the effective entry rate Po K3 increased with an e-fold factor per 150 mV over the same voltage range for a δ value corresponding to 0.16. Interestingly, the apparent electrical distances δ obtained for the kinetic parameters of TBA block (δentry + δexit = 0.45) are in good agreement with the equilibrium δ = 0.49 obtained from the changes in IC50 as a function of voltage.

### Modeling of the Voltage Dependence of the TBA Block

According to electrostatic potential calculations based on the MthK crystal structure, the channel cavity and the cytoplasmic medium should form a continuous isopotential region (Jiang et al., 2002b). This property reflects in essence the broad opening of the vestibule predicted by the MthK structure (Fig. 1). Fig. 6 B presents the membrane potential profile obtained by solving the Poisson-Boltzmann equation for the TM5-pore-TM6 region derived by homology modeling for the wild-type IKCa (Fig. 1). These calculations indicate that the potential difference between the cavity (z = 0) and the cytoplasmic medium accounts for <16% of the potential applied across the membrane with 81% of the voltage drop restricted to the selectivity filter. In turn, the difference in potential between adjacent sites within the selectivity filter ([S2-S1], [S3-S2], [S4-S3]) should represent 23% of the membrane potential compared with 12% between the S0 and S1 binding sites and 3% between the cavity (S5) and the S4 site. Finally, there should be no difference in potential between the external binding site S0 and the external solution. On the basis of the proposed model for the open IKCa channel, it is clear that a simple model whereby the voltage dependence of the TBA block arises from the difference in potential between the internal medium and the TBA binding site cannot account for an electrical distance δ of 0.49 as observed experimentally (Fig. 5 B).

A minimal kinetic scheme describing the blocking action of TBA within the channel pore is shown in Fig. 6 A. A similar model has already been described by Heginbotham and Kutluay (2004). In many respects, this model incorporates some of the features of models previously proposed to account for the effect of external and internal permeant ions on the Kir1.1 and Shaker channels (Spassova and Lu, 1998, 1999; Thompson and Begenisich, 2003a,b). The model in Fig. 6 A includes the essential features of the single file diffusion process in the selectivity filter recently described for the KcsA channel for K+ ion concentrations within the range of our experimental conditions (K+ ion activity of 140 mM) (Berneche and Roux, 2003). In the unblocked mode, K+ ion efflux is seen as a sequence of changes in the ion occupancy state of the pore with [S3,S1] ↔ [S5,S3,S1] ↔ [S4,S2,S0] ↔ [S4,S2] and back to [S3,S1]. The sites referred to as S0 and S5 are located outside the selectivity filter and correspond to the channel external K+ binding site and central cavity, respectively. The model also considers the possibility of a K+ ion in S5 with S4 occupied (states [S5,S4,S2] and [S5,S4,S2,S0]). An interaction factor termed “f” has in this case been introduced to account for the change in K+ entry and exit rates ki and ke due to the presence of a K+ ion in S4. The rates describing the transitions [S5,S3,S1] ↔ [S5,S4,S2] and [S3,S1] ↔ [S4,S2] become in this case related, so that k3/k4 = f2 (k1/k2). Fig. 6 C presents the free energy profiles calculated for a K+ ion along the pore axis for the [S4,S2] and [S3,S1] filter configurations. These calculations predict a maximum difference of 1.8 kcal/M between the [S5,S4,S2] and [S5,S3,S1] configurations, for an f factor corresponding approximately to 0.22.

Calculations were first performed to determine to what extent the model proposed in Fig. 6 A accounts for the channel current/voltage characteristics. The continuous line in Fig. 4 C represents the prediction of the model. Best results were obtained assuming a K+ binding affinity in S0 (kx/ko) and S5 (ke(0)/ki(0)) of 45 mM and 70 mM, respectively, with a ratio k1(0)/k2(0) of 0.3. The difference between the [S4,S2] ↔ [S3,S1] transition rates k1(0) and k2(0) accounts for most of the channel rectification, and may be related to the fast blocking action of divalent cations such as Ca2+ at a site close to S4 (Soh and Park, 2002). In these calculations, the fraction of potential drop between the cavity and the external medium α was set to 0.84 as suggested by the potential profile presented in Fig. 6 B. Clearly the model in Fig. 6 A in which the voltage dependence of the rate constants is determined according to Fig. 6 B, satisfactory describes the channel current–voltage relationship (Fig. 4 C).

The blocking action of TBA was next modeled assuming that the blocking agent cannot enter S5 (channel cavity) when the site is already occupied by a K+ ion ([S5,S3,S1], [S5,S4,S2], and [S5,S4,S2, S0]). Again, the presence of TBA in S5 is likely to affect the transition [B,S3,S1] ↔ [B,S4,S2] by shifting the equilibrium toward the [S3,S1] filter configuration. If the location of TBA binding site corresponds to S5, the transition [B,S3,S1] ↔ [B,S4,S2] should be such that kB1/kB2 = k3/k4. Strong interactions between TBA and the K+ ions in the selectivity filter have already been postulated (French and Shoukimas, 1981) but never derived from structural considerations (Guo and Lu, 2001; Thompson and Begenisich, 2003b). In the model for TBA block proposed in Fig. 6 A, the entry rate of TBA is assumed to depend on the actual ion occupancy state of the pore with entry rates KB31 = KB31(0)exp(0.5(1 − β)Vq/KT), KB32 = KB32(0)exp(0.5(1 − β)Vq/KT), and KB33 = KB33(0)exp(0.5(1 − β)Vq/KT), when the pore is in state [S4,S2], [S4,S2,S0], and [S3,S1], respectively (for example see MacKinnon and Miller, 1988; Thompson and Begenisich, 2003a). The parameter β refers to the fraction of the potential that is applied between the TBA binding site and the external medium. In conditions where the TBA binding site corresponds exactly to the channel central cavity, we have β = α ≅ 0.84 (Fig. 6 B). As the ion occupancy in these sites can be considered in equilibrium relative to the entry and exit rates of TBA, the average number of transitions between the unblocked and the blocked pore configuration can be expressed as

\begin{eqnarray*}&&\mathrm{{<}K}_{\mathrm{B}}3\mathrm{>}=\mathrm{e}^{\left(0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\left[\mathrm{K}_{\mathrm{B}}\mathrm{31(0)P}\left[\mathrm{S4,S2}\right]\right.\ \\&&\left.\ +\right.\ \\&&\left.\ \mathrm{K}_{\mathrm{B}}\mathrm{32(0)P}\left[\mathrm{S4,S2,S0}\right]+\mathrm{K}_{\mathrm{B}}\mathrm{33(0)P}\left[\mathrm{S3,S1}\right]\right]\mathrm{,}\end{eqnarray*}
(13)

where P[S3,S1], P[S4,S2], and P[S4,S2,S0] are the probabilities for the unblocked channel selectivity filter to be in the [S3,S1], [S4,S2], or [S4,S2,S0] configurations, respectively. The variations in P[S3,S1], P[S4,S2], and P[S4,S2,S0] computed as a function of voltage are presented in Fig. 7 A. As seen, the probability of the [S4,S2] state is highly favored at negative potentials, whereas positive potentials increase the probability of the [S4,S2,S0] filter state. For potentials ranging from −100 to −30 mV, the probability of the state [S3,S1] appeared to vary within <15%. This analysis shows that the voltage dependence of the entry rate <KB3> predicted by Eq. 13, is expected to vary as a function of voltage in a complex manner.

In the blocked configuration, the exit rate of the blocking agent is assumed to depend similarly upon the ion occupancy state of the channel filter with exit rates KB41 = KB41(0)exp(−0.5(1 − β)Vq/KT), KB42 = KB42(0)exp(−0.5(1 − β)Vq/KT), and KB43 = KB43(0)exp(−0.5(1 − β)Vq/KT) when the pore is in state [B,S4,S2], [B,S4,S2,S0], and [B,S3,S1], respectively. The average exit rate <KB4> then reads

\begin{eqnarray*}&&\mathrm{{<}K}_{\mathrm{B}}4\mathrm{>}=\mathrm{e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\left[\mathrm{K}_{\mathrm{B}}4\mathrm{1(0)P}\left[\mathrm{B,}S\mathrm{4,S2}\right]\right.\ \\&&\left.\ +\mathrm{K}_{\mathrm{B}}\mathrm{42(0)P}\left[\mathrm{B,S4,S2,S0}\right]+\mathrm{K}_{\mathrm{B}}\mathrm{43(0)P}\left[\mathrm{B,S3,S1}\right]\right]\mathrm{,}\end{eqnarray*}
(14)

where P[B,S4,S2], P[B,S4,S2,S0], and P[B,S3,S1] are the probabilities for the filter to be in the [B,S4,S2], [B,S4,S2,S0], and [B,S3,S1] configuration for the blocked channel. In conditions where KB41(0) ≅ KB42(0) = Kout, the mean rate of transitions <KB4> reduces to

\begin{eqnarray*}&&\mathrm{{<}K}_{\mathrm{B}}4\mathrm{>}=\\&&\frac{\mathrm{K}_{\mathrm{out}}\mathrm{e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}}{\left(1+\mathrm{Kb}\right)}+\frac{\mathrm{K}_{\mathrm{B}}\mathrm{43(0)e}^{\left(\mathrm{{-}}0.5\left(1{-}\mathrm{{\beta}}\right){\mathrm{Vq}}/{\mathrm{KT}}\right)}\mathrm{Kb}}{\left(1+\mathrm{Kb}\right)}\end{eqnarray*}
(15)

with

$\mathrm{Kb}=\mathrm{Ke}\left(1+\frac{\mathrm{Co}}{\mathrm{Ko}}\right)\mathrm{,}$
(16)

where Co is the external potassium ion concentration, Ke = [kB1(0)/kB2(0)]exp(−0.46 Vq/KT) and Ko = kX/kO the affinity of the external site (S0) for K+. It is important to notice that if the blocker exit rate were assumed to be independent of the ion occupancy state of the filter (KB41(0) ≅ KB42(0) ≅ KB43(0) = Kout), the voltage dependence of <KB4> would become 0.5(1 − β) with β = 0.84. This would correspond to an e-fold change in <KB4> per 310 mV, which was never observed experimentally.

The continuous line in Fig. 5 C shows the predicted voltage dependence of the exit rate for the wild-type IKCa channel as computed from Eq. 14. Calculations were performed using the values of k3, k4, kx, and ko obtained by curve fitting the model to the channel I/V curve with in addition kB1= k3 and kB2 = k4. Data points could be best accounted for with KB41(0), KB42(0), and KB43(0) equal to 2.9 s−1, 10.4 s−1, and 0.63 s−1 in control conditions and 8 s−1, 28 s−1, and 1.7 s−1 in the presence of EBIO, respectively. Clearly, the model presented in Fig. 6 A can account for the voltage dependence of the TBA exit rate. The continuous line in Fig. 5 B shows the predicted voltage dependence of IC50 for voltages ranging from −150 to +150 mV. IC50 values were computed as the ratio of <KB4>/<KB3> with KB31(0), KB32(0), and KB33(0) as unique adjustable parameters. Best results were obtained with KB31(0), KB32(0), and KB33(0) equal to 0.022 s−1μM−1, 0.07 s−1μM−1, and 0.1 s−1μM−1 in the presence of EBIO and 0.006 s−1μM−1, 0.02 s−1μM−1, and 0.026 s−1μM−1 in control conditions, respectively. As seen, the model presented in Fig. 6 A successfully predicts a voltage dependence with δ = 0.49 over the voltage range −150 to −30 mV, despite a potential profile where only 16% of the transmembrane potential is effectively applied between the channel cavity and the cytoplasmic medium. Globally these results indicate that the voltage dependence of the internal TBA block reflects for the most part an interaction of TBA with the K+ ions in the selectivity filter with a limited contribution coming from the difference in potential between the internal medium and the TBA binding site.

### Effect of the External K+ Concentration on IKCa Blockade by TBA

One of the main features of the model presented in Fig. 6 A concerns the effect of the internal and external K+ concentrations on the kinetics of the TBA block. Eq. 16 predicts for instance that the exit rate <KB4> should be a function of the external K+ ion concentration (Co) with <KB4> increasing at higher Co values. Fig. 7 B shows the voltage dependence of the TBA blockade for external K+ ion activities ranging from 60 to 225 mM. As seen, increasing Co resulted, as expected, in a voltage-dependent increase in IC50. For instance, the IC50 measured at −90 mV for a K+ ion activity of 60 mM was estimated at 203 ± 9 μM (n = 4) as compared with 437 ± 26 μM (n = 4) in 225 mM external K+ ion conditions. Increasing Co resulted also in a variation of the apparent electrical distance δ obtained by curve fitting the data points to IC50 = IC50(0)exp(−δVq/KT) for −150 mV < V < −30 mV. This analysis led to δ values of 0.44 ± 0.01 (n = 4), 0.49 ± 0.02 (n = 6), and 0.52 ± 0.03 (n = 4) for 60, 140, and 225 mM external K+, respectively. These results indicated that the apparent voltage dependence of the TBA block not only depends on the structural parameters underlying the transmembrane potential profile but also on the parameters that control ion flux.

The predictions of the model described in Fig. 6 A are shown in Fig. 7 B as continuous lines. The proposed model is seen to successfully account for the voltage dependence of IC50 over the K+ activity range considered. Fig. 8 A presents a 3D plot of the expected variation in δ as a function of the external and internal K+ activities. The electrical distance δ was computed by fitting the predictions of the model for a given set of internal and external K+ activities to an equation of the form IC50 = IC50(0)exp(−δVq/KT) for −150 mV < V < −30 mV. This analysis revealed that increasing external K+ activity up to 50 mM results in a systematic increase in δ independently of the internal K+ activity. For external K+ activities >50 mM, the predicted voltage dependence of the TBA block is exclusively a function of the internal K+ level. For instance, with an internal K+ ion activity of 140 mM, the electrical distance δ was estimated at 0.44, 0.47, and 0.46 in 60, 140, and 225 mM external K+, respectively. This is well within the values measured experimentally, despite the fact that the results in Fig. 7 B point toward a stronger increase in δ at high external K+ activities.

### Effect of the Internal K+ Concentration on IKCa Blockade by TBA

Fig. 7 C presents the effect of internal K+ (Ci) on the IKCa blockade by TBA. Reducing Ci appeared to facilitate the blocking action of internal TBA, as expected for a system where the presence of a K+ ion in S5 prevents the entry of TBA in the cavity. For instance, the TBA concentration for half inhibition at −30 mV decreased from 113 ± 5 μM (n = 6) in 140 mM, to 53 ± 10 μM (n = 3) in 2 mM internal K+ conditions. The voltage dependence of the TBA block in low (2 mM) and high (140 mM) internal K+ is also illustrated in Fig. 7 C. Clearly, the voltage sensitivity of the block over the voltage range −150 to −30 mV is increased by lowering internal concentration of K+, with an electrical distance δ equal to 0.54 ± 0.01 (n = 3) in 2 mM internal/140 mM external K+ conditions, as compared with 0.49 ± 0.02 (n = 6) in symmetrical 140 mM/140 mM K+, respectively. The predictions of the model proposed in Fig. 6 A are represented as continuous lines (Fig. 7 C). The model was found to satisfactorily account for the variation in the voltage dependence of IC50 as a function of Ci, and correctly predict that decreasing Ci should lead to a decrease in δ independently of Co (Fig. 8 A). In 140 mM external K+ for instance, the model predicts an apparent electrical distance δ of 0.56 in 2 mM internal K+, which is in accordance with the electrical distance observed experimentally.

### Effect of V275 Mutations on the Voltage Dependence of the TBA Block

The results by Zhou et al. (2001) and the observations in Fig. 3 strongly suggest that the TBA interaction site is located in close proximity of the cavity lining residue V275. On this basis, we hypothesized that a shift of the TBA position relative to the selectivity filter, obtained by mutating V275, might affect the voltage dependence of the TBA block through an effect on the interactions between the blocking agent and the ions in the selectivity filter. Examples of reversible current block measured at increasing doses of TBA for the V275A, V275L, and V275C mutants are illustrated in Fig. 9 A. The resulting TBA–current inhibition dose–response curves measured at −60 mV in symmetrical 140 mM K+ + 100 μM internal EBIO conditions are presented in Fig. 9 B. First of all, we observed that mutating the V275 residue had an effect on TBA affinity: the mutation V275C shifted the dose–response curve toward smaller concentrations from an IC50 of 192 ± 7 μM (n = 12) for wild type to 18 ± 2 μM (n = 4) for the V275C channel. In contrast, the V275A and V275L substitutions caused an increase of the IC50 value to 262 ± 29 μM (n = 6) and 607 ± 54 μM (n = 3), respectively. Notably, the substitution V275L was also found to decrease the channel conductance for inward currents by 50% with a unitary conductance of 21 ± 2 pS (n = 2) for voltages negative to −50 mV (unpublished data). The voltage dependence of the TBA block for the V275C, V275A, and V275L mutant channels is illustrated in Fig. 9 C. For voltages ranging from −150 to −30 mV, estimations of the equivalent electrical distance δ led to 0.50 ± 0.03 (n = 3), 0.72 ± 0.03 (n = 2), and 0.7 ± 0.06 (n = 3) for the V275L, V275C, and V275A mutants, respectively. Clearly, the extent of the changes in TBA binding affinity did not correlate with the changes in electrical distance.

## Discussion

In this study, we showed that the transmembrane potential profile computed from a model structure of the open IKCa channel derived from MthK is compatible with the voltage dependence of the channel block by internal TBA. Since the 3D structure of IKCa has not yet been solved, we cannot rule out the possibility that the open IKCa structure might differ from MthK. However, we showed in this work that a functional model that incorporates an interaction mechanism between TBA and the ions in the selectivity filter, together with transmembrane potential and free energy profiles derived from a MthK-like structure, can globally account for the complex behavior of IKCa block by TBA. In addition, evidence is presented that the voltage dependence of the TBA block can be modified by mutating the cavity lining V275 residue, suggesting that TBA position relative to the selectivity filter is important to the voltage dependence of the block. Finally, our data indicate that a model of TBA block derived from a MthK-like structure absolutely requires TBA to interact with the ions in the selectivity filter.

### TBA Block in K+ Selective Channels

Quaternary alkylammonium ions have been used as probes to investigate the pore structure of a number of K+ selective channels. It is generally agreed that the mechanism of channel block by ammonium ion from the cytoplasmic side involves an entry step into the open channel up to the channel central cavity where it binds without passing through the selectivity filter. The blocking action of QA ions is thus likely to reflect the internal structure of specific classes of K+ channels. For instance, TBA was shown to block the inward rectifiers Kir2.1 and Kir1.1 at IC50(0) of 40 and 2 mM, respectively, with fractional electrical distances ≥1.0 arguing for an inner vestibule with single file diffusion properties (Guo and Lu, 2001). These values differ from the results reported in the present work with an IC50(0) of 70 μM and a fractional electrical distance at negative potentials δ of 0.49. Furthermore, the TBA entry rate for the Kir2.1 and Kir1.1 channels in zero current conditions (0 mV) was estimated at 0.004 μM−1s−1 compared with 0.07 μM−1s−1 in the present case. Clearly the inner pore region of IKCa seems to be less restrictive to TBA flow than that observed in Kir1.1 and Kir2.1. Fractional electrical distances ranging from 0.2 to 0.3 were reported for the voltage-gated Shaker and calcium-activated KCa1.1 channels, suggesting a weaker voltage dependence of the TBA block relative to IKCa (Villarroel et al., 1988; Choi et al., 1993; Ding and Horn, 2002; Thompson and Begenisich, 2003a; Li and Aldrich, 2004). However, the voltage sensitivity in both cases was measured at positive potentials in contrast to the protocols used in this work, where δ was estimated at negative potentials only. Fig. 8 B presents a 3D plot of the electrical distance δ computed from the model in Fig. 6 A for positive voltages within 0 to +90 mV as a function of internal and external potassium activities. As seen, the electrical distance δ appeared significantly smaller when computed for positive than negative potentials over the entire external and internal potassium concentration range. For instance, the plot in Fig. 8 B shows that δ increases monotonically as a function of external potassium with a value of 0.24 in 150 mM internal/5 mM external K+ and 0.32 in symmetrical 150 mM K+ conditions. These values are well in agreement with the results obtained for Shaker and KCa1.1 and confirm that the apparent electrical distance associated with the TBA blocking mechanism is voltage variable. Furthermore, the results in Fig. 8 B indicate that increasing the internal potassium ion activity should lead to an increase in δ, as reported for the Shaker channel (Thompson and Begenisich, 2003a). The fact that the electrical distance varied as a function of the applied potential truly reflects a strong interaction between TBA and the ions in the selectivity filter. Finally, our results provide evidence for a regulation of the TBA block by internal and external K+. In contrast to Shaker, competition by internal K+ was apparent even in the absence of an external blocking agent such as TEA, suggesting a higher ion occupancy of S5 in IKCa compared with Shaker (Thompson and Begenisich, 2003a).

### TBA Block and IKCa Gating

The present work also provides evidence for a reduction of the TBA IC50(0) by EBIO. EBIO has been documented to modulate SK and IKCa channels by stabilizing the interactions between Ca2+-calmodulin and the channel α subunit (Pedarzani et al., 2001; von Hahn et al., 2001). An EBIO-dependent increase in Po could be detected by noise analysis at 25 μM internal Ca2+ but not in nominally Ca2+-free conditions (unpublished data). Our results would thus support a model whereby EBIO can activate IKCa at saturating Ca2+ concentrations, in contrast to other reports (Pedersen et al., 1999; Syme et al., 2000; Pedarzani et al., 2001). The observation that EBIO led to a decrease in IC50(0) indicates that the IKCa opener affected Po and PoB differently, with the ratio ζ (PoB/Po) becoming smaller after EBIO stimulation (see Eq. 2). One possible explanation would consist in PoB being higher than Po in the absence of EBIO, so that PoB would be relatively less affected by EBIO than Po. In support of this proposal is the observation of a 2.7-fold increase in PoB for a 3.8-fold increase in PoK3 in EBIO conditions (Fig. 5 C). Notably, the measured 3.8-fold increase in PoK3 elicited by EBIO fully correlates the Po increase estimated by noise analysis. These observations suggest therefore that the presence of TBA in the channel cavity affects the channel kinetic parameters as to either destabilize the channel closed configuration or stabilize the channel open state, or both. These results would be consistent with a model whereby TBA is trapped in the channel central cavity upon channel closing. Such a behavior would support a gating model where the TM6 helix bundle crossing in the closed configuration is small enough to constrict TBA flow from the channel central cavity to the internal medium. We cannot however rule out the possibility that the state dependency of the TBA block might result from a variation upon channel closing in the interactions between TBA and the pore residues involved in TBA binding. Such a mechanism would lead to a state-dependent kinetics of TBA block, without a trapping mechanism involving the TM6 bundle crossing (Li and Aldrich, 2004).

### Mutations of V275 and Voltage Dependence

The present work shows that the voltage dependence of the TBA block is modified by mutating the cavity lining residue V275. Our results indicate for instance that the fractional distance δ measured over the voltage range −150 to −30 mV is increased from 0.49 to 0.70 by substituting the Val at 275 by either a Cys or an Ala, whereas the mutation V275L left δ unchanged. Mutating the V275 residue was also found to affect the binding affinity of the TBA receptor, but this effect appeared uncorrelated with the associated changes in δ. For instance, both V275C and V275A led to a δ value of 0.7 despite an IC50(0) for the V275C mutant 20 times smaller than for V275A. Similarly, the V275L mutation caused a threefold increase in IC50(0) relative to wild type without a significant change in δ. We cannot rule out, however, that part of the observed effects on IC50(0) may be related to a modification of the channel open probability, as indicated by our EBIO results. These observations differ somehow from the results obtained on Shaker, where changing the affinity of the external TEA receptor was reported to affect the voltage dependence of the TEA block (Heginbotham and MacKinnon, 1992). It was concluded in this case that the substitution Y499T moved the TEA binding site further into the pore.

The electrostatic free energy profiles presented in Fig. 6 C, predict that the magnitude of the interactions between TBA and the ions in the selectivity filter should be highly sensitive to the position of TBA within the channel cavity (−3 Å < z <3 Å). In contrast, the results in Fig. 6 B show that a shift in TBA position over the same distance range should minimally affect the potential difference between the TBA binding site and the internal medium ([1 − β]). Fig. 10 presents the expected variation in electrical distance for TBA block at negative potentials calculated on the basis of the transmembrane potential and energy profiles illustrated in Fig. 6 (B and C). As seen, the electrical distance δ increased from 0.30 to 0.62 for z varying from −3 to 3 Å . In contrast, 1 − β changed from 0.12 to 0.18 over the same distance range. Clearly the proposed model for TBA block predicts an increase in δ measured at negative potentials that far exceeds the associated change in electrical distance 1 − β. The fact that the V275C and V275A mutations resulted in a TBA block with a stronger voltage dependence suggests, therefore, that the substitution of the Val at 275 (volume 140 Å3) by residues of smaller sizes (108 Å3 for Cys and 88 Å3 for Ala) enabled TBA to penetrate further into the pore, closer to the selectivity filter. It is possible that the substitutions V275C and V275A allowed TBA to move closer to the T250 residue located at the entrance of the channel selectivity filter. Notably, the crystal structure reported by Zhou et al. (2001) predicts that T250 and V275 should be close to TBA, potentially contributing to the formation of the TBA binding site. Mutating the Val at 275 to a larger residue such as Leu (166 Å3) did not seem to modify the position of the TBA relative to the selectivity filter, as the electrical distance δ remained unchanged. Our model could not, however, account for electrical distances >0.65, the electrostatic energy profiles illustrated in Fig. 6 C becoming less accurate for large interaction energies (z > 3 Å). Furthermore, we cannot rule out additional effects on the pore structure due to mutations at position 275 as the V275 residue is adjacent to the alleged TM6 gating hinge at G274. Finally, the observation that the V275L mutant showed a 50% smaller unitary conductance further demonstrated the importance of the 275 residue to the formation of the central cavity. In fact, the model in Fig. 6 A indicates that the 50% decrease in conductance with the V275L mutant can be ascribed to a decrease in the equilibrium constant k5(0)/k6(0), which accounts for the transitions of a K+ ion between S4 and the channel cavity. Globally, these results support the model proposed in Fig. 6 A, where most of the voltage dependence of the TBA block is due to the blocking agent sensing the ion occupancy state of the selectivity filter.

### Conclusion

The data presented in this work show that the electrical distance δ, which describes the voltage dependence of blocking agents such as TBA, is voltage variable and does not simply reflect the actual difference in potential between the blocker binding site and the internal medium. Our results rather support a model where the voltage dependence of charged blockers is controlled to a large extent by the ion occupancy state of the selectivity filter.

## Acknowledgments

We thank Dr. Benoit Roux for stimulating discussions and for providing a copy of the manuscript on the intracellular TEA block of the KcsA potassium channel prior to publication. We also acknowledge the work of Ms. Julie Verner for expert oocyte preparation.

This work was supported by grants from the Canadian Institutes of Health Research (MOP 7769), from the Canadian Heart and Stroke Foundation, and from the Canadian Cystic Fibrosis Foundation.

Olaf S. Andersen served as editor.

Abbreviations used in this paper: EBIO, 1-ethyl-2-benzimidazolinone; MTS, methanethiosulfonate; MTSET, [2-(trimethylammonium) ethyl]methanethiosulfonate bromide; NMDG, N-methyl-d-glucamine; QA, quaternary ammonium; SCAM, substituted cysteine accessibility method; TBA, tetrabutylammonium.

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