Phosphatidylinositol-4,5-bisphosphate (PIP₂) regulation of strong inward rectifier Kir2.1 channels: multilevel positive cooperativity

Abstract

Inwardly rectifying potassium (Kir) channels are gated by the interaction of their cytoplasmic regions with membrane-bound phosphatidylinositol-4,5-bisphosphate (PIP₂). In the present study, we examined how PIP₂ interaction regulates channel availability and channel openings to various subconductance levels (sublevels) as well as the fully open state in the strong inward rectifier Kir2.1 channel. Various Kir2.1 channel constructs were expressed in Xenopus oocytes and single channel or macroscopic currents were recorded from inside-out patches. The wild-type (WT) channel rarely visited the subconductance levels under control conditions. However, upon reducing Kir2.1 channel interaction with PIP₂ by a variety of interventions, including PIP₂ antibodies, screening PIP₂ with neomycin, or mutating PIP₂ binding sites (e.g. K188Q), visitation to the sublevels was markedly increased before channels were converted to an unavailable mode in which they did not open. No channel activity was detected in channels with the double mutation K188A/R189A, a mutant which exhibits extremely weak interaction with PIP₂. By linking subunits together in tandem dimers or tetramers containing mixtures of WT and K188A/R189A subunits, we demonstrate that one functional PIP₂-interacting WT subunit is sufficient to convert channels from the unavailable to the available mode with a high open probability dominated by the fully open state, with similar kinetics as tetrameric WT channels. Occasional openings to sublevels become progressively less frequent as the number of WT subunits increases. Quantitative analysis reveals that the interaction of PIP₂ with WT subunits exerts strong positive cooperativity in both converting the channels from the unavailable to the available mode, and in promoting the fully open state over sublevels. We conclude that the interaction of PIP₂ with only one Kir2.1 subunit is sufficient for the channel to become available and to open to its full conductance state. Interaction with additional subunits exerts positive cooperativity at multiple levels to further enhance channel availability and promote the fully open state.

Kir channel activity depends on the interaction of the channel with phosphatidylinosital-4,5-bisphosphate (PIP₂) (Hilgemann et al. 2001). Many regulatory signals modulating channel activity are believed to act through the common mechanism of modifying the channel's affinity for PIP₂ (see Xie et al. 2007 for review): for example, protein kinase A (PKA) phosphorylation in Kir1.1 channels (Liou et al. 1999; Zeng et al. 2003), polyamines in strong rectifier Kir2.1 channels (Xie et al. 2005), G_βγ in Kir3 channels (Huang et al. 1998; Ho & Murrell-Lagnado, 1999; Zhang et al. 1999), and the sulphonylurea receptor SUR1 in Kir6.2 channels (Song & Ashcroft, 2001).

Single channel recordings revealed that the Kir2.1 channel enters an extra-long closed state when it undergoes rundown due to depleted membrane PIP₂ levels (Xiao et al. 2003). In this state, the channel is fully closed and remains in a distinct unavailable mode which can only be recovered by exogenous application of PIP₂ or MgATP. Another intriguing feature of Kir channels is the relationship between their PIP₂ affinity and the occurrence of subconductance levels (sublevels). In Kir1.1 channels, Leung et al. (2000) found that disruption of the PIP₂–channel interaction not only decreased single channel open probability (P_o), but also caused the appearance of sublevels. In Kir2.1 channels, Lopes et al. (2002) reported three types of single channels with different amplitudes and/or gating when they coexpressed WT subunits (1: 20) with R218Q, a mutant subunit with reduced PIP₂ affinity. They suggested that different WT/mutant stoichiometries resulted in different channel conductances and gating. In addition to disruption of PIP₂–channel interaction, sublevels have also been observed in Kir channels during (1) block by cationic ions such as Mg²⁺ or Ca²⁺ (Mazzanti et al. 1996; Oishi et al. 1998); (2) partial block of the internal channel pore with methanthiosulphonate (MTS) reagents (Lu et al. 1999a) or Tl⁺ (Lu et al. 2001b); and (3) conformational changes in the selectivity filter induced by backbone mutations in Kir2.1 (Lu et al. 2001a).

We speculated that the influence of PIP₂ on sublevels might provide insights into the molecular mechanisms by which PIP₂ regulates Kir2.1 channels. Since most previous studies were performed by expressing monomers to form Kir channels, there is currently limited information on how channel behaviour depends on the interaction of PIP₂ with individual subunits in tetrameric channels. Accordingly, in addition to expressing monomers, we examined the effects of disrupting the interaction of PIP₂ with Kir2.1 channels formed from tandem dimeric or tetrameric constructs, in which the number of subunits with intact PIP₂ binding sites was varied. We addressed the following questions: (1) Since Kir2.1 channels have at least one PIP₂ binding site per subunit, how many subunits must interact with PIP₂ for the channel to become available to open? (2) When the channel opens, do the sublevels correspond to the number of subunits interacting with PIP₂? (3) If not, how many subunits must interact with PIP₂ for the channel to enter the fully open state? (4) Is there cooperativity between the interaction of PIP₂ with subunits and channel gating?

Using inside-out patches from Xenopus oocytes expressing a variety of Kir2.1 constructs, we show that interaction of a single subunit with PIP₂ is sufficient to induce full openings, indicating that the first subunit–PIP₂ interaction shifts the channel from an unavailable to an available mode with high open probability (P_o). Interaction of PIP₂ with additional subunits exerts strong positive cooperativity in promoting the available mode. Once the channel is in the available mode, another level of positive cooperativity between subunits promotes the fully open state and minimizes the occurrence of sublevels, even when only a single subunit is interacting with PIP₂. However, interaction of additional subunits with PIP₂ further enhances this positive cooperativity, reducing the dwell time in sublevels even further.

Methods

Molecular biology and preparation of oocytes

The Kir2.1 cDNA (Kubo et al. 1993) was generously provided by Dr Lily Y. Jan. ‘Quickchange’ mutagenesis (Stratagene, La Jolla, CA, USA) was used to construct individual mutants such as K188Q and K188A/R189A. In order to construct tandem structure K188A/R189A–WT, the ‘Quickchange’ mutagenic protocol was used to insert an EcoR1 site at the 5′ open reading frame (ORF) of the wild-type and 3′ ORF of the mutant (K188A/R189A) Kir2.1 sequences. Linkage via the EcoR1 sites generated a GGGGEFGGG (single letter amino acid code) sequence between the Kir2.1 repeat sequences. Other tandem dimeric constructs including WT–K188A/R189A, K188A/R189A–K188A/R189A or WT–WT were constructed using the same protocol. To make the tetrameric oligomer: a HindIII site was inserted into the tandem dimers, at the 5′ end (ORF) of Kir 2.1 carrying a 3-EcoRI restriction site, and a HindIII site inserted at the 3′ ORF of a Kir2.1 sequence carrying an EcoR1 site at the 5′ end. Linkage via the HindIII site generated another tandem construct separated by AGGKLGGA, which can be inserted into the tandem construct carrying the EcoRI site in its middle. The final construct therefore resembles 2.1 Eco 2.1 Hind 2.1 Eco 2.1, where 2.1 can either be wild-type or mutant sequences. We therefore can obtain tetrameric channels with any number of mutant and WT subunits. The strategy of constructing dimeric and tetrameric channels has been used in Kir channels extensively (Lu et al. 1999b; Cho et al. 2000; Kono et al. 2000; Zingman et al. 2002; Lin et al. 2003; Matsuda et al. 2003). The cRNAs were synthesized using T7 polymerase (Ambion Inc.)

Oocytes (stage IV–V) were isolated by partial ovariectomy from mature female Xenopus anaesthetized with 0.1% tricaine. All of the frogs were humanely killed at the end of the oocyte collection. The use and care of the animals in these experiments were approved by the Chancellor's Animal Research Committee at UCLA. The oocytes were then defolliculated by treatment for 1 h with 1 mg ml⁻¹ collagenase (TypeII, Life Technologies) in Barth's solution containing (mm): 88 NaCl, 1 KCl, 2.4 NaHCO₃, 0.3 Ca(N₂O₆).4H₂O, 0.41 CaCl₂, 0.82 MgSO₄, 15 Hepes; and 50 mg ml⁻¹ gentamicin and 10 mg ml⁻¹ Baytril; pH 7.6. The day after collagenase treatment, selected oocytes were pressure-injected with ∼50 nl RNA (1–100 ng ml⁻¹). Oocytes were maintained at 18°C in Barth's solution and electrophysiological studies were conducted 1–3 days later. The vitelline membrane was removed immediately before the patch clamp recording.

Electrophysiology and data analysis

Macroscopic currents were recorded from excised inside-out giant patches of RNA-injected oocytes with an Axopatch 200A amplifier (Axon Instruments) at room temperature. Patch electrodes were pulled from thin-wall borosilicate glass (Garner Glass Co., Claremont, CA, USA) and had a tip diameter of 20–30 μm after fire polishing. The patch electrode solution contained (mm): 85 KCl, 1.8 CaCl₂, 5 K₂HPO₄, 5 KH₂PO₄, pH 7.2 with KOH. The standard bath solution contained (mm): 85 KCl, 5 EDTA, 5 K₂HPO₄, 5 KH₂PO₄, pH adjusted to the desired level with KOH. Chemicals were purchased from Sigma (St Louis, MO, USA). Continuous current traces were elicited by voltage ramps from −100 to +100 mV at 0.4 mV ms⁻¹. The currents were measured at −100 mV. The leak current corrections were made in most of the patches by subtracting current after complete rundown. Data were filtered with an 8-pole Bessel filter (Frequency Devices) at 1 kHz and digitized at 2 kHz via a DigiData 1200 interface (Axon Instruments).

Single channel activity was recorded from inside-out patches excised from oocytes injected with WT and mutant channel RNA. Patch electrodes were pulled from thick-wall borosilicate glass (Warner Instrument Corp.) and had a resistance of 5–8 MΩ when filled with the pipette solution. Electrodes were coated near their tips with Sylgard (Dow Corning Co.) or N,N-dimethyltrimethylsilylamine (Fluka) to reduce electrical capacitance. The patch electrode solution contained (mm): 140 KCl, 1.8 CaCl₂, 5 K₂HPO₄, 5 KH₂PO₄, pH 7.2 with KOH. The standard bath solution contained (mm): 140 KCl, 5 EDTA, 5 K₂HPO₄, 5 KH₂PO₄, pH adjusted to the desired level with KOH. The rundown of channel activity was delayed by treating inside-out patches with 2 mm MgATP in the EDTA-free bath solution. Data were filtered at 2–5 kHz and digitized at 5–10 kHz. Data acquisition and analysis were carried out using pCLAMP8 or 9 software (Axon Instruments). The all-point histograms were constructed with a bin width of 0.1 pA from data records of ∼10 s. Dwell-time distributions were constructed and fitted with one or two exponential functions.

All experiments were conducted at room temperature (20–24°C). Data are presented as mean ±s.d. The paired or unpaired Student's t test was conducted with P value < 0.05 being considered as statistically significant.

Simulation of single channel data with kinetic models

Simulation and fitting of single channel data was carried out with the QuB software (The State University of New York at Buffalo). Briefly, pCLAMP data files were firstly exported as .ldt files and then imported into the QuB data window. After generation of the model, the data were idealized by using Idl function and the segmental k-means (SKM) method. The model optimization was carried out by using the Maximum Interval Likelihood rate estimation (MIL) function with setting of the initial values for the rate constants. Simulated single channel events were then generated based on the estimated rate constant values, using the Simulate (SIM) function and compared with the experimental data to establish the validity of the kinetic model.

Abbreviations

Kir channel, inwardly rectifying potassium channel; PIP₂, phosphatidylinositol-4,5-bisphosphate; WT, wild-type; M, double mutant K188A/R189A subunit; WT4, channel containing four wild-type monomers or linked tetramer; WT₃M₁, WT–K188A/R189A–WT–WT tetramer, WT₂M₂, K188A/R189A–WT dimer or WT–K188A/R189A–K188A/R189A–WT tetramer; WT₁M₃, K188A/R189A–K188A/R189A–K188A/R189A–WT tetramer; M4, channel containing K188A/R189A monomers or linked tetramer.

Results

Single channel gating of WT Kir2.1 channels under control conditions

Figure 1A illustrates typical single channel behaviour of WT Kir2.1 channels in recordings from an inside-out patch at various holding potentials. The average unitary current–voltage (i–V) relation from 10 patches is shown in Fig. 1B, with the unitary conductance (g) averaging 29.1 ± 1.6 pS. Single channel transitions between the closed and fully open states at a holding potential of −100 mV were analysed in detail. Channels exhibited a typically high P_o of 0.90 ± 0.03 (n = 5). The open-time distribution was well fitted by a single exponential, and the closed-time distribution was well fitted by the sum of two exponential components. These indicate that there are minimally one open state, with open time constant τ_o, and two closed states, with closed time constants τ_c1 and τ_c2 (Fig. 1D and E, Table 1). Under control conditions, sublevels were rarely observed in WT patches, typically showing very brief transitions to to of the fully open level. Due to the low frequency and short dwell times of the sublevels, however, extra peaks corresponding to sublevels were not apparent in the amplitude histogram (Fig. 1C, histogram).

Figure 1. Single channel gating of WT Kir2.1 channels.

A, representative single channel currents recorded at various holding potentials as indicated. B, single channel current–voltage (i–V) relationship. C, all-point histogram of the current trace recorded at a holding potential of −100 mV. D, open and E, closed time distributions of single channel activity at holding potential of −100 mV. The open time distribution was well fitted by a single exponential with a time constant (τ_o) of 79.4 ms. The closed time distribution was well fitted by two exponential components with time constants τ_c1= 7.9 ms and τ_c2= 0.65 ms, respectively, in this particular patch.

Table 1.

Single channel gating kinetics of Kir 2.1 WT and various channel constructs at −100 mV

Constructs	Po	τo (ms)	τc1 (ms)	τc2 (ms)
WT4 (n = 5)	0.90 ± 0.01	71.5 ± 15.5	9.4 ± 2.4	0.72 ± 0.12
WT3M1 (n = 6)	0.91 ± 0.02*	78.4 ± 12.7*	10.3 ± 1.6*	0.57 ± 0.11*
WT2M2 (n = 4)	0.91 ± 0.03*	67.0 ± 11.5*	13.3 ± 2.6*	0.75 ± 0.12*
WT1M3 (n = 4)	0.87 ± 0.03*	61.2 ± 8.6*	14.2 ± 2.8*	0.69 ± 0.12*
K188Q (n = 5)	0.90 ± 0.02*	82.9 ± 12.4*	13.4 ± 0.9*	0.82 ± 0.14*

Channel constructs are indicated in Abbreviations in Methods. The data were obtained under control condition in the absence of DA12.

^*P > 0.05 compared to values in WT₄ channel.

PIP₂ dually regulates channel availability and conductance sublevels

To examine how PIP₂ affects single channel properties, we inhibited channel–PIP₂ interaction using three interventions: (1) application of neomycin; (2) application of PIP₂ antibody; and (3) mutation of putative PIP₂ binding residues. Neomycin, a polycation that binds PIP₂ (Arbuzova et al. 2000), has been shown to reduce Kir channel activity by screening PIP₂ molecules (Schulze et al. 2003; Ribalet et al. 2005; Xie et al. 2005). The effects of neomycin on single channel currents are shown in Fig. 2A. In this patch, two channels opened with high P_o under control conditions (Fig. 2Aa). After application of 100 μm neomycin, one of the channels closed immediately. The remaining channel remained functional, but exhibited frequent sublevels, as shown in Fig. 2Ab. The most frequently observed sublevel was of the fully open level, while other sublevels, such as , were rare. This channel then also closed and did not reopen during continued neomycin application (Fig. 2Ac). K₂ATP had no effect on the channel activity after neomycin (Fig. 2Ad), while MgATP rescued channel activity with normal kinetics and unitary amplitude without sublevels (Fig. 2Ae). Recovery of normal channel activity after MgATP but not K₂ATP in the continued presence of neomycin (1) excludes the possibility that neomycin directly caused the sublevels by partially blocking the ion-conducting pathway (like Mg); (2) suggests that PIP₂ synthesis, not ATP complexation, recovers channel activity and suppresses sublevels. Thus, neomycin induces both sublevels and long-lasting full closure in Kir2.1 channels by disrupting their interaction with PIP₂.

Figure 2. Screening of PIP₂ by neomycin or PIP₂-antibody inhibits Kir2.1 single channel activity by inducing sublevels and full closure.

A, effect of neomycin (Neo). a, two channels with high P_o under control conditions. b, In the presence of 100 μm Neo, one channel closed and the other showed various sublevels. c, both channels then ceased activity. The traces in the presence of Neo were selected before each channel completely ran down. d, K₂ATP had no effect on the channel activity after neomycin. e, channel activity with normal kinetics and unitary amplitude was recovered by MgATP, presumably via synthesis of PIP₂. B, effect of PIP₂-antibody (PIP₂-Ab). There were 3 channels under control conditions, and PIP₂-Ab caused all three to close abruptly. Three segments in the presence of PIP₂-Ab are expanded, showing sublevels (arrows) preceding complete closure of each channel.

It has been previously shown that anti-PIP₂ antibodies can bind PIP₂ and inhibit macroscopic current in Kir channels (Huang et al. 1997; Zhang et al. 1999). Similar to neomycin, we found that treatment of patches with PIP₂ antibody induced sublevels as well as full closure (Fig. 2B). In this patch, there were three channels with high open probability under control conditions. Application of PIP₂-Ab caused channels to lose function one by one. Note that multiple sublevels (arrows) were observed before each channel closed completely, especially when only one active channel remained in the patch, as shown in the expanded traces.

Multiple positively charged residues located in N- and C-termini are critical for the interaction of PIP₂ with Kir channels (Fan & Makielski, 1997; Huang et al. 1998; Shyng et al. 2000; Lopes et al. 2002; Schulze et al. 2003), such that neutralization of these putative PIP₂ binding residues reduces channel activity. For example, mutant K188Q channels exhibit very small macroscopic currents and low PIP₂ affinity as gauged by high sensitivity to neomycin (Schulze et al. 2003; Xie et al. 2005). Consistent with weakened PIP₂ affinity, these channels are minimally activated by either MgATP (2 mm) or PIP₂ (10 μm), although high activity can be unmasked by adding long polyamines, such as diamine10 (DA10) and diamine12 (DA12) which strengthen the channels' interaction with PIP₂ (Schulze et al. 2003; Xie et al. 2005). Although the majority of K188Q channels in the patch were inactive under control conditions, the few spontaneously active channels showed a high open probability with single current amplitude and open–close transition kinetics similar to WT channels (Fig. 3 and Table 1). Unlike WT Kir2.1 channels, however, multiple sublevels, at and of full amplitude, occurred frequently in 5 out of 7 patches studied. In some of the patches, gradual stepwise transitions between sublevels from the closed to fully open state, or vice versa, were observed (Fig. 3B, bottom panel).

Figure 3. Full openings and multiple sublevels in K188Q, a mutant channel with weak PIP₂ binding.

A, single channel current recorded at various holding potentials and single channel i–V relationship. B, full openings and various sublevels with long dwell times recorded from a K188Q mutant single channel. The patch was held at −100 mV. Bottom trace illustrates slow open-to-closed state transitions via continuous sublevel changes shows noted in this channel.

These experiments reveal that reducing channel–PIP₂ interaction exerts dual effects on the single channel gating, promoting both sublevels as well as long-lasting full channel closure (unavailable mode). Thus, PIP₂ plays a key role in regulating both Kir2.1 channel availability and its ability to open fully.

Regulation of channel availability by PIP₂: first level of positive cooperativity between channel subunits

Like K188, R189 has also been shown to regulate PIP₂ affinity in Kir2.1 channels (Lopes et al. 2002). We confirmed that the double mutant K188A/R189A traffics normally to the cell membrane by linking the double mutant to green fluorescent protein (GFP) (K188A/R189A–GFP). Cells expressing K188A/R189A–GFP channels showed strong surface membrane labelling, similar to the WT–GFP channels (data not shown). However, in 10 patches tested, no macroscopic or single channel currents were detected from either giant or standard inside-out patches, even in the presence of PIP₂ and long diamines (Figs 4A and 5A), suggesting that channel–PIP₂ interaction was disrupted sufficiently to trap the channels in an unavailable mode in which channel openings were eliminated altogether.

Figure 4. Loss of channel activity in the double mutation K188A/R189A with low PIP₂ binding affinity, and progressive rescue by adding back WT subunits in a tandem tetrameric channel to increase PIP₂ affinity.

A, continuous macroscopic current traces recorded from inside-out giant patches (electrode diameter ∼20 μm) in channels with the various stoichiometries as indicated. Currents were elicited by voltage ramps from −100 to +100 mV at 0.4 mV ms⁻¹. Short chain PIP₂, diC₈-PIP₂, in various concentrations was applied as indicated by the bars under the traces. DA12 (100 μm) + diC₈-PIP₂ (100 μm) was used to maximally activate channel activity. The application of MgATP activated an outward current in some patches (e.g. the patch expressing M₄), probably due to activation of an endogenous Ca²⁺- or Mg²⁺-sensitive Cl⁻ current known to be present in Xenopus oocytes (Weber et al. 1995). B, concentration–activation curves for each channel construct. The activation by diC₈-PIP₂ was expressed as I/I_max, where I_max is the maximum current activated by diC₈-PIP₂+ DA12.The mean EC₅₀ values are indicated. C, effects of neomycin in WT₄ and WT₁M₃ constructs. Current at −100 mV was recorded during application of neomycin at various concentrations indicated by the horizontal bars. D, neomycin dose–response curves for WT₄ and WT₁M₃ constructs. The mean EC₅₀ values are indicated.

Figure 5. Channel availability measurement in various tandem tetrameric channel constructs.

A, macroscopic current–voltage relations recorded from inside-out giant patches in channels with the various stoichiometries as indicted. Continuous current traces were elicited by voltage ramps from −100 to +100 mV at 0.4 mV ms⁻¹. The patches were pre-treated with 2 mm MgATP (ctl) before application of 100 μm diamine 12 (DA12) to strengthen the channel–PIP₂ interaction. B, the observed available probability (P_A) values for various channel constructs calculated as I_ctl/I_DA12, in which I_ctl represents control current level at −100 mV, and I_DA12 the current level after application of 100 μm DA12 pre-treated with 2 mm MgATP. C, in a patch containing few channels, the application of PIP₂ plus DA12 (horizontal bar) caused unavailable channels to open reversibly.

To determine whether channel activity could be rescued by incorporating one or more WT subunits into K188A/R189A channels, we performed studies on tandem dimeric and tandem tetrameric constructs containing mixtures of WT and mutant (M) K188A/R189A subunits. We measured macroscopic currents from giant patches to determine the apparent PIP₂ affinity of each construct with short chain PIP₂, diC8-PIP₂ (Fig. 4). We have demonstrated in our previous study (Xie et al. 2005) that long polyamines, such as DA12, interact with the channel membrane pore region (including negatively charged D172) and stabilize the bundle crossing in its open configuration. This allosteric effect enhances the interaction of the channel cytoplasmic region (including K188, R189) with PIP₂ at the cytoplasmic side of the membrane and thus increases PIP₂ affinity. Therefore, to activate channels maximally (I_max), we used the combination of 100 μm diC₈-PIP₂+ 100 μm DA12, since when channel PIP₂ binding affinity is decreased, even saturating levels of PIP₂ alone cannot fully activate channel activity (Xie et al. 2005) and higher concentrations (200 μm diC₈-PIP₂+ 100 μm DA12) did not further increase current level. As shown in Fig. 4A and B, the apparent PIP₂ affinity strongly depended on the number of PIP₂ interacting subunits. WT₄ showed highest PIP₂ affinity with a mean EC₅₀ value of 1.9 ± 0.3 μm while WT₃M₁, WT₂M₂ and WT₁M₃ had lower PIP₂ affinities, with EC₅₀ values of 10.7 ± 1.6, 79.6 ± 7.6 and 387.7 ± 84.2 μm (n = 4 for each group), respectively. These results suggest that the affinity of PIP₂ is shifted to a lower level (rightward) when the number of mutant subunit increases. In the presence of 100 μm DA12, all the constructs tended to be fully activated by 100 μm PIP₂ and the differences in the affinity for PIP₂ among the different constructs were minimized. The Hill coefficient values for the four constructs were 1.21 ± 0.16 (WT₄), 0.78 ± 0.08 (WT₃M₁), 0.75 ± 0.14 (WT₂M₂) and 0.65 ± 0.15 (WT₁M₃), respectively.

Consistent with short-chain PIP₂ data, we observed that decreasing the number of WT subunits progressively increased the neomycin sensitivity of the channels. Figure 4C and D shows representative data in WT₄ and WT₁M₃ channels. The neomycin concentration causing 50% inhibition of current (IC₅₀) averaged 33.5 ± 5.1 μm in WT₄ channels, and 6.4 ± 2.4 μm in WT₁M₃ channels (P < 0.05).

Figure 5A and B further compares macroscopic current levels under control conditions and after maximal activation. Immediately after patch excision, the patches were treated with 2 mm MgATP for > 1 min to generate high membrane levels of PIP₂. A voltage ramp from −100 to +100 mV was applied to measure basal channel activity, and then repeated during exposure to 100 μm DA12 to enhance channel–PIP₂ interaction and maximally activate all channels in the patch. Similar to K188A/R189A monomers, the tandem tetrameric construct containing four K188A/R189A subunits (M₄ channels) did not show channel activity before or after DA12 treatment, consistent with an extremely low PIP₂ affinity. Current levels in channels formed from tandem dimeric or tetrameric constructs containing at least one WT subunit were enhanced by application of DA12 (100 μm). The enhancement of the current depended on the number of WT subunits in the tetrameric channel: it was greatest in channels with a single WT subunit (WT₁M₃ channels); intermediate in channels with two or three WT subunits, and least in channels with four WT subunits (WT₄ channels) (Fig. 5A). The findings indicate that with high ambient basal PIP₂ levels in the membrane (i.e. after treatment with 2 mm MgATP), WT₄ channels in which all four subunits are capable of interacting with the PIP₂ are nearly all active (defined here as the available mode). As the number of subunits with PIP₂ interaction sites (WT) decreases, fewer and fewer channels remain in the available mode, unless PIP₂ affinity is increased by exposure to long diamines. Nevertheless, channels with only a single WT subunit (WT₁M₃) can still be active, especially if the PIP₂ affinity of this channel is enhanced by the application of long diamines.

The conclusion that PIP₂ promotes the available mode was confirmed in the WT₁M₃ channel as shown in Fig. 5C. Increasing channel–PIP₂ interaction by direct exposure to PIP₂ (combined with DA12) increased the number of active channels, e.g. from one to four in this specific patch. Please notice this result was obtained in the WT₁M₃ channel which showed much lower PIP₂ affinity, and both PIP₂ and DA12 were necessary for the maximal activation. The fast reversibility was mostly probably due to the washout of DA12 causing an immediate reduction in channel–PIP₂ interaction, rather than PIP₂ depletion per se.

After pretreatment with MgATP (for > 1 min) to synthesize PIP₂ in the membrane, DA12 (100 μm) maximally increased channel activities in all channel constructs, since application of PIP₂ or diC8-PIP₂ in the presence of DA12 did not further increase the currents, suggesting a conversion of all channels into the available mode. Even for channels with a single WT subunit, MgATP pretreatment + DA12 was sufficient to convert all channels in the membrane to the available mode. If this assumption is accurate, then the observed available probability (P_A) for various channel constructs can be calculated as a ratio of the basal current to that after maximal activation (I_ctl/I_DA12) (Fig. 5B and Table 2, 2nd row). For WT₁M₃ channels, this would correspond to a predicted P_A of 0.21 for a single PIP₂ interacting subunit. If all four subunits bind PIP₂ independently (i.e. neutral cooperativity), then the probability of no subunits binding PIP₂ (P_NB, equivalent to the channel being in the unavailable mode) should be (0.79)⁴ for WT₄ channels, respectively. Thus, the predicted P_A= (1 −P_NB) for the WT₄ channel should give the value of 0.61, assuming neutral cooperativity. However, this value is much lower than the experimentally observed P_A value of 0.97, which was calculated from the I_ctl/I_DA12 ratio. These observations indicate that the multiple PIP₂ interaction sites must exert positive cooperativity to promote the available mode as each additional subunit interacts with PIP₂.

Table 2.

Positive cooperativity ratios for PIP₂ binding subunits regulating channel available probability P_A

	WT1M3 (n = 9)	WT2M2 (n = 7)	WT3M1 (n = 8)	WT4 (n = 6)
Predicted PA for neutral cooperativity	0.21	0.38	0.51	0.61
Observed PA (Ictl/IDA12)	0.21 ± 0.05	0.47 ± 0.04	0.70 ± 0.05	0.97 ± 0.02

Regulation of sublevels by PIP₂: a second level of positive cooperativity

In addition to regulating channel availability, the findings in the first section show that PIP₂ also regulates transitions between sublevels. One possibility is that sublevels correspond to the number of subunits that are interacting with PIP₂, as has been suggested in voltage-gated Kv2.1 channels (Chapman & VanDongen, 2005). However, this possibility is ruled out for Kir2.1 channels by our observation that in the tetramer WT₁M₃ with a single WT subunit, the predominant open state, even under basal conditions in the absence of exogenous PIP₂ or long diamines, was the fully open state with same single channel conductance as in WT₄ channels. Figure 6 and Table 1 show that the typical transitions in all the tandem tetrameric and dimeric channels exhibited WT-like open–close kinetics and with a similar unitary conductance of the fully open state. Figure 6B shows an example in the WT₁M₃ channel. More frequent sublevels were observed in WT₃M₁ channel than in WT₂M₂ or WT₄ channels. However, level was still the most commonly observed sublevel.

Figure 6. Single channel kinetics in various tandem tetrameric and dimeric constructs with different numbers of mutant K188A/R189A subunits.

A, single channel traces recorded from tandem dimeric WT₂M₂ channels and B, tandem tetrameric WT₁M₃ channels at holding potentials as indicated. The data were obtained under control conditions in the absence of DA12. Note sublevels with long dwell times in WT₁M₃ channels, although the fully opening state remained dominant. All-points histograms for each construct are shown in for WT₂M₂ (C) and for WT₁M₃ (D), respectivewly; E, single channel current–voltage relations for the two constructs. F, single channel cord conductances at −100 mV measured in the various constructs. The number of patches in each group are indicated above each bar.

For all the constructs tested, the most frequently sublevel visited was of the fully open state. Transitions to other sublevels such as and of full opening level were rare, precluding detailed quantitative analysis of their kinetics. Therefore, to analyse the kinetics quantitatively, we considered only the sublevel and the fully open state.

Figure 6B illustrates that the sublevels were accessible from both the fully open state and closed state. The closed-to-sublevel transitions shared similar kinetics to the closed–full open state transitions. We calculated the sublevel probability (P_s, the fraction of time spent at the sublevel) by measuring the area under the all-point histogram for the sublevel, and taking the ratio of this area (A_s) to the total area under the all-point histogram (A). (Similar values were obtained from the ratio of the dwell time for the sublevel using the QuB software program.) In WT₁M₃ channels, sublevels were observed in 6/7 patches with mean P_s= 0.13 ± 0.06; in WT₂M₂, sublevels occurred in 6/14 patches with P_s= 0.05 ± 0.02; and in WT₃M₁ and WT₄, sublevels had too low a P_s to quantify reliably. Thus, sublevels occurred more frequently as the number of PIP₂-interacting subunits decreased.

Markov model quantitatively simulating single channel sublevel kinetics

We constructed a Markovian model (Fig. 7 and Scheme 1) to account for the following observations: (1) interaction of a single Kir2.1 subunit with PIP₂ is sufficient to induce full openings shifting the channel from the unavailable to available mode with an intrinsically high P_o; (2) once the channel is in the available mode, positive cooperativity between subunits promotes the fully open state and minimizes the occurrence of sublevels; (3) interaction of additional subunits with PIP₂ further enhances this positive cooperativity, reducing the dwell time in sublevels even further. We based Fig. 7 on the emerging idea from recent functional and structural studies (see Discussion) that two distinct gates control the behaviour of Kir channels (Proks et al. 2001; So et al. 2001; Phillips & Nichols, 2003). We assume that when the channel is in the available mode, open–closed transitions are mediated by gating of an ‘upper gate’, putatively located at the selectivity filter. Both availability and sublevel behaviour of the channel, on the other hand, are controlled by the interaction of PIP₂ with cytoplasmic regions that regulate a ‘lower gate’ (LG), which may relate to conformational changes in the M₂ bundle crossing and/or G-loop of the cytoplasmic pore (Xiao et al. 2003). Schematically, the four subunits each contribute a component of the LG, which opens fully when all four components are in the UP position, and closes fully when all four are in the DOWN position. In the absence of PIP₂, or in a mutant channel with no PIP₂ interaction sites (i.e. K188A/R189A), all subunits remain in the DOWN position such that the channel is unavailable to open. However, interaction of any single subunit with PIP₂‘tethers’ that subunit ‘up’ against the membrane, facilitating the UP position with high probability. In addition, when one subunit is tethered by PIP₂, strong positive cooperativity between the subunits favour other subunits entering the UP position with slightly lower, but still high, probability even when they are themselves not directly interacting with PIP₂ (Fig. 7A). A recent crystal structure study (Nishida et al. 2007), suggesting that PIP₂ binding may open the apex of the cytoplasmic pore (G-loop) through a rigid-body movement to an Upper position, fits well with our proposed scheme. We further assume that the sublevels correspond to the number of subunits in the UP position. When one subunit is UP, the LG opens partially ( sublevel), and with two UP, three UP and four UP, the conductance progressively increases from to (or ) to the fully open levels, respectively (Fig. 7B). This model accounts for the observation that tetrameric WT₁M₃ channels, with only a single PIP₂ interacting subunit, exhibit the same fully open state as well as the various sublevels observed as WT₄ channels. Because of strong positive cooperativity between subunits, when a single subunit is tethered by PIP₂, all four subunits favour the UP position, rarely visiting the substate (3 UP) and almost never visiting the (2 UP) and (1 UP) sublevels.

Figure 7. Putative channel conformational changes corresponding to single channel sublevels – a cartoon image.

A, longitudinal section through the channel showing subunits I and III only. When no subunits are interacting with membrane PIP₂ (red circles), the cytoplasmic lower gate (LG) portion of all subunits reside in the DOWN position (a) and the channel is UNAVAILABLE to open. To become AVAILABLE to open, at least one subunit must interact with PIP₂ at K188/R189, causing the lower gate (LG) portion of that subunit to move to the UP position, and exerting positive cooperativity on the LG portions of the other subunits to move into the UP position. Once in the AVAILABLE mode, the selectivity filter (SF) in the transmembrane pore controls open–close gatings. The single channel conductance corresponds to the number to LG portions in the UP position, with 1, 2, 3 and 4 UP corresponding to the or , and fully open levels, respectively, as indicated by the dashed lines through the pore region. Thus, with only one subunit tethered to PIP₂, strong coupling allows other subunits to enter the UP position favouring the fully open state. B, schematic representation of a cross-section through the lower gate region, in which each subunits contribution to the lower gate is indicated by a circle, which can be either in the UP (U) or DOWN (D) position. When DOWN, that subunit's component of the lower gate partially occludes the ion-conducting pathway. Thus, with 4 DOWN, the channel is closed, and with 1, 2, 3 or 4 UP, the LG progressively opens corresponding to the (or ), and full conductance levels, respectively. Thus, the sublevels correspond to the number of subunits in the UP position.

In the Markov model, we represent a channel in the available mode with one open and two closed states (Sakmann & Trube, 1984) (box in Scheme 1), reflecting the observed ‘upper gate’ gating kinetics with a single open time and two closed times (see Table 1). The values of the rate constants (α, β, δ, γ) were then obtained by fitting to the mean open and closed times for the fully open state. To account for sublevels, we linked the fully open state (O₁) to series of partially open states (), leading to a closed state (C_n) representing the unavailable mode (Scheme 1). We assumed that the rate constants (α, β, δ) were identical for the sublevel transitions.

Since only the sublevel was observed frequently enough for quantitative analysis, Scheme 1 was further simplified to Scheme 2. Here we assume a high degree of positive cooperativity between the transitions to the fully open state, so that all the sublevels can be condensed into a single O_s state, whose open probability P_s quantitatively matches that of the state in Scheme 1.

The transition from C_n to O_s, controlling channel availability, was assumed to be PIP₂ sensitive, whereas the transitions between O_s and O₁ were modulated by the number of subunits interacting with PIP₂. The main effect on sublevels of decreasing the number of WT subunits in tetrameric channels was attributed to a decrease in the equilibrium coefficient K₁ = k₁/k₋₁, giving the mutant channel more opportunity to reside in the O_s state. When the single channel data were fitted to Scheme 2 to obtain the rate constants both for gating by the ‘upper gate’ (α, β, δ, γ) and ‘lower gate’ (k₁ and k₋₁) mediating transitions between the sublevel state O_s and fully open state O₁, we found that for modelling transition of the channel into the available mode, k_n and k_−n could be set within a wide range as long as k_n/k_−n > 20 and k_−n < k₁. Figure 8 shows that with these constraints, simulated single channel traces using QuB software closely matched the experimental recordings from both WT₄ and WT₁M₃ channels. Table 3 lists the average rate constants obtained for the various tetrameric constructs. For the k₁ and k₋₁ values shown in Table 3, the probability of WT₁M₃ channels residing in the sublevel state is P_s = k₋₁/(k₁+k₋₁) = 0.11, similar to the observed value of 0.13. For WT₂M₂ channels, the changes in k₁ and k₋₁ cause P_s to fall to 0.04, similar to the experimental value of 0.05. For either WT₃M₁ and WT₄ channels, k₁ and k₋₁ were chosen to predict very short dwell times (1/k₁) and extremely low P_s values [k₋₁/(k₁+k₋₁)], consistent with experimental finding that sublevels were too infrequent to quantify in these channels.

Figure 8. Recorded and simulated single channel traces using scheme 2.

Representative single channel traces recorded from WT₁M₃ channels (left) and simulated current traces using Scheme 2 (right). Real and simulated amplitude histograms are shown below. The rate constants obtained from fitting: α= 8.6, β= 86.0, γ= 3.2, δ= 1470, k₁= 26.0, k₋₁= 4.0. B, representative single channel traces recorded from WT₄ channels (left) and simulated using Scheme 2 (right). Real and simulated amplitude histograms are shown below. The rate constants obtained from fitting: α= 3.4, β= 67.0, γ= 4.0, δ= 1052, k₁= 500, k₋₁= 3.0. C, direct application of PIP₂ reduced sublevel probability. Single channel traces recorded from WT₁M₃ channel at a holding potential of −100 mV in an inside-out patch under control conditions (left) and in the presence of 10 μm PIP₂ (right). All-point histograms for each condition are shown in the lower panels.

Table 3.

Rate constants (1/s) obtained from fitting the experimental data with the proposed schematic model (Scheme 2) with the QuB software

Constructs	k1	k−1	α	β	γ	δ
WT4	737.5 ± 37.5	2.8 ± 0.6	8.4 ± 2.4	131.8 ± 43.6	11.3 ± 6.3	1557 ± 332
WT2M2	73.5 ± 15.4	3.1 ± 0.5	7.3 ± 1.6	82.8 ± 13.9	9.2 ± 2.0	1463 ± 278
WT1M3	31.2 ± 4.6	3.7 ± 0.5	6.9 ± 1.2	98.8 ± 13.3	7.7 ± 2.1	1694 ± 361

k_n/k_−n > 20 andk_−n < k₁.

In WT₁M₃ channels, we also found that P_s decreased when the patch was directly exposed to 10 μm PIP₂ (Fig. 8C). Thus, although PIP₂ and DA12 had no effect on open–close gating kinetics or the unitary conductance of the fully open state, they reduced sublevel probability in WT₁M₃ channels. These results indicate that sublevel probability is controlled both by number and affinity of PIP₂ interaction sites in the channel as well as PIP₂ levels in the membrane. The latter factor may account for the variability in P_s between patches for the same channel construct. For instance, in WT₁M₃, in 1/7 patches did not exhibit sublevels, implicating a high ambient membrane PIP₂ level in that patch. Consistent with the experimental data, increasing the concentration of PIP₂ by ∼10-fold (overall k₁) in the simulation also decreased sublevel visitations.

Sakmann and Trube (Sakmann & Trube, 1984) suggested another model C₁↔ C₂↔ O that also fitted the kinetic properties of the cardiac inwardly rectifying K channels well. We also tested this model by incorporating it into Scheme 2 and could fit the experimental data equally well. Considering there is no clear structural evidence that two closed states are sequentially connected, we preferred to use the model with two parallel closed states.

Discussion

The major findings of the present study are: (1) PIP₂ has dual effects on Kir2.1 channels, modulating both channel availability and the probability of visiting sublevels. Reducing Kir2.1 channel interaction with PIP₂ by a variety of interventions, such as PIP₂ antibodies, screening PIP₂ with neomycin, or mutating known PIP₂ binding sites such as K188 and/or R189 promoted both sublevels and long-lasted channel closure into an unavailable mode. Conversely, enhancing channel–PIP₂ interaction by direct application of PIP₂ and long polyamines increased channel availability and reduced sublevel probability; (2) At least one subunit must interact with PIP₂ for the tetrameric channel to exit the unavailable mode and enter the available mode. As the number of PIP₂-interacting subunits in tandem tetramers or dimers increased, strong positive cooperativity between these subunits progressively stabilized the channel in the available mode; (3) Once the interaction of a single subunit with PIP₂ placed the channel in the available mode, the channel favoured the fully open state rather than sublevels, reflecting a strong inherent second level of positive cooperativity between subunits. Sublevels therefore do not directly correspond to number of channel subunits interacting with PIP₂. When additional subunits do interact with PIP₂, their effect is to strengthen the inherent positive cooperativity between subunits, decreasing sublevel probability further in favour of the fully open state. In summary, our findings are consistent with a model in which PIP₂ binding to a single subunit suffices to induce a transition from an unavailable mode to an available mode. Once in the available mode, strong positive cooperativity between subunits promotes the fully open state with high probability, which is further enhanced when additional subunits interact with PIP₂. Thus, PIP₂ acts by enhancing positive cooperativity at multiple levels which reinforce Kir2.1 subunit interactions to promote available, fully open channels.

A remaining question is how many PIP₂ molecules bind to each individual PIP₂-interacting subunit. In the present study, we found that the interaction of a single subunit with PIP₂ is sufficient for the Kir2.1 channel to transition readily to the fully open state. One PIP₂ molecule per subunit seems a reasonable guess, since the two positively charged residues which we have mutated, K188 and R189, are located together and are likely to contribute to a single PIP₂ binding site. However, other PIP₂ binding sites in the channel are also likely to modulate sublevel probability (see below).

It is well known that polyamines block outward current through Kir channels and contribute to inward rectification. Therefore, one can wonder if polyamines could also cause discrete subconductance levels. We previously showed that polyamines decreased inward Kir2.1 channel unitary conductance in a continuous manner, probably by a charge screening effect (Xie et al. 2002). However, we did not observe obvious discrete subconductance levels in the presence of polyamines.

Regulation of channel availability by PIP₂

Although we cannot exclude the possibility that the K188A/R189A mutation may directly affect the lower gate to generate a non-functional channel in the M₄ construct, the results shown in Figs 4 and 5 suggest it is most likely that disrupting channel–PIP₂ interactions in one or more subunit causes the channel to progressively enter an unavailable mode, in which the channels still reside in the membrane but do not open. Evidence for a distinct unavailable mode is observed with decreasing membrane PIP₂ levels (due to spontaneous degradation, screening or PIP₂ antibodies) when the channel suddenly enters a super-long closed state, rather than undergoing a gradual decrease in open time (Xiao et al. 2003) (also see Fig. 2). Under these conditions, normal channel gating with high P_o could only be recovered by exogenous application of PIP₂ or MgATP (Xiao et al. 2003).

Based on crystal structural and functional studies, two regions have been proposed to control gating in Kir channels, an ‘upper gate’ due to stochastic switching between different conformational states of the selectivity filter, and a ‘lower gate’ involving larger conformational changes in the M₂ bundle crossing and/or G-loop of the cytoplasmic pore (Xiao et al. 2003). Recent structural studies (Pegan et al. 2005; Nishida et al. 2007) have suggested that the G-loop is too narrow for K⁺ ions to permeate in the absence of PIP₂ binding, and that the electrostatic interaction between cytoplasmic regions and membrane-bound PIP₂ provides the energy to keep the lower gate in the open conformation. Conversely, Yang's group (Xiao et al. 2003) has suggested that although the lower gate region of the pore narrows when PIP₂ unbinds from the cytoplasmic domain, the constriction at bundle crossing may not by itself fully close the channel, but is instead coupled to closure of the selectivity filter. Supporting this assumption, Yang's group has demonstrated that backbone mutations in the selectivity filter (Lu et al. 2001a) or partial blockage of the inner pore (Lu et al. 1999a, 2001b) cause sublevels to appear. In addition, there is also a possibility that the slow (C₁) transition gating may be controlled by or located at the lower gate, as suggested by Proks et al. in the Kir6.2 channel (Proks et al. 2001; So et al. 2001; Phillips & Nichols, 2003).

Although the precise molecular mechanisms by which PIP₂ gates Kir2.1 channels remain to be elucidated, it is well established that there are allosteric links between PIP₂ binding and channel gating. PIP₂-dependent channel opening has been shown to involve conformational changes in the M₂ bundle crossing and G-loop regions, where the ‘lower gate’ may reside. Based on these studies, we favour the hypothesis that the interactions of PIP₂ with Kir2.1 primarily regulate a lower gate near the M₂ bundle crossing or G-loop (Fig. 7). Recent studies of human Kir2.1 genetic defects causing Andersen's Syndrome (Pegan et al. 2006; Ma et al. 2007) have revealed that several mutations are located in close proximity to the G-loop and may disrupt intra-subunit (R218–T309, R218–V302) or inter-subunit (E303–R312) salt bridges or polar interactions. These interactions are thought to be required to stabilize the G-loop in a functional state permitting ion permeation. Some of these residues are either PIP₂ binding sites (e.g. R218) or allosterically affect PIP₂ gating (V302, T309). Mechanistically, PIP₂ binding to the inner leaflet-facing cytoplasmic portions of the channel may be critical for properly aligning the side chains of the residues for efficient salt bridge formation. Thus, disruption of PIP₂–channel interactions may cause channels to become non-functional due to loss of intra- or inter-subunit interactions important for maintenance of tetramer structure. Conversely, facilitation of these intra- or inter-subunit interactions by PIP₂ may be the underlying explanation for the positive cooperativity. Our finding that single channel gating kinetics of the sublevel are similar to those of the fully open conductance level (Figs 3B and 8B) supports the concept that the same gate regulates open–closed transitions within the fully open or sublevel states (i.e. the vertically orientated rate constants in Schemes 1 and 2), independently from a PIP₂-sensitive gate which regulates transitions between the fully open state, sublevels and the long-lasting closed state (the horizontally orientated rate constants in Schemes 1 and 2).

Regulation of sublevels by PIP₂

Leung et al. (2000) showed that disruption of PIP₂–channel interaction not only decreased single channel P_o, but induced sublevels in the Kir1.1 channels. In Kir2.1 channels, Lopes et al. (2002) identified three types of single channels with different amplitudes and/or gating when they coexpressed WT and the PIP₂-insensitive R218Q mutant. They suggested that the different channel conductances and gating behaviours represented different WT/mutant subunit stoichiometries. The present study is the first to show definitively how the number of PIP₂-interacting subunits in a Kir channel affects gating and sublevels. A similar approach was previously used in the voltage-gated potassium channel, Kv2.1, which also exhibits sublevels (Chapman & VanDongen, 2005). By constructing tandem dimers that linked two Kv2.1 channel subunits with different activation voltage thresholds, Chapman et al. (1997) reported that heteromeric pore conformations produced sublevels correlating with the voltage gate status of the individual subunits. Considering the general similarity in channel pore structure (Doyle et al. 1998; Jiang et al. 2003; Kuo et al. 2003; Pegan et al. 2005), we originally hypothesized that the Kir2.1 channel might also display stepwise sublevels depending on how many of the channel's four subunits were strongly bound to PIP₂. If this were the case, then we would predict that WT₁M₃ channels, with only a single subunit capable of interacting with PIP₂, would exhibit only the sublevel. However, our finding that WT₁M₃ channels exhibited all of the sublevels as well as the fully open state excluded this possibility. Thus, the interaction of PIP₂ with additional subunits was not required for full channel opening, but rather enhanced the inherent positive cooperativity between subunits to promote the fully open state. This conclusion is supported by the single channel kinetics data listed in Table 1, demonstrating there is no significant difference in P_o, t_o and t_c between WT₄ and other channel constructs. Thus the different levels of macroscopic current are related to channel availability, i.e. the number of channels available to open in the patches. By adding positive cooperativity to the Markov model, these features were readily simulated with reasonable quantitative accuracy (Fig. 8).

Besides K188 and R189, several other positively charged residues (e.g. R67 in N-terminus; R218 and R312 in C-terminus) have also been demonstrated to affect PIP₂ sensitivity in activating Kir channels. However, the K188A/K189A double mutant (M₄) experiments suggest that the K188/R189 PIP₂ binding site is absolutely required to convert the channel to the available mode; the other PIP₂ binding sites are not sufficient, even in the presence of PIP₂ and DA12 (Figs 4 and 5). Nevertheless, although they are not essential for the channel to enter the available mode, interaction of these additional PIP₂ binding sites appears to further increase the positive cooperativity between the subunits to favour the fully open state when the channel is in the available mode. This would explain why application of exogenous PIP₂ further suppressed sublevels in the WT₁M₃ mutant channels, in which only one subunit contains the critical K188/K189 site (Fig. 8C). This modulatory effect of additional PIP₂ binding sites would also explain why P_s varies from patch to patch in each construct.