Affinity for phosphatidylinositol 4,5-bisphosphate determines muscarinic agonist sensitivity of Kv7 K⁺ channels

A wide spectrum of ion channels and transporters are regulated by the plasma membrane abundance of the lipid phosphatidylinositol (PI) 4,5-bisphosphate (PIP₂). Upon stimulation of G_q/11-coupled receptors, activation of phospholipase Cβ hydrolyzes PIP₂, producing cytosolic inositol triphosphate (IP₃) and membrane-bound diacylglycerol, leading to three possible modes of action on ion channels: IP₃-mediated Ca²⁺_i signals, diacylglycerol-mediated activation of protein kinase C, and depletion of PIP₂ via consumption by PLC activity (Gamper and Shapiro, 2007). M-type K⁺ currents are produced by voltage-gated Kv7 (KCNQ) subunits in a variety of neuronal, muscle, and epithelial tissues, where they control excitability, action potentials, and K⁺ transport (Jentsch, 2000; Delmas and Brown, 2005; Mackie and Byron, 2008; Peroz et al., 2008). In the nervous system, most M channels are composed of Kv7.2/7.3 heteromers, but some channels also contain Kv7.5, and Kv7.2 or Kv7.3 homomers are also neuronally expressed (Wang et al., 1998; Cooper et al., 2001; Roche et al., 2002; Pan et al., 2006). In the inner ear and auditory cortex, Kv7.4 homomers dominate, and in the cardiovascular system, Kv7.1, Kv7.4, and Kv7.5 are expressed in various combinations (Kubisch et al., 1999; Kharkovets et al., 2000; Loussouarn et al., 2006; Mackie and Byron, 2008).

The term M current comes from its depression by muscarinic receptor stimulation in sympathetic neurons (Brown and Adams, 1980; Constanti and Brown, 1981). After intense study, a wide spectrum of evidence indicates that this muscarinic action arises from the need of M channels for membrane PIP₂ to be functional (Zhang et al., 2003; Li et al., 2005; Suh et al., 2006) and the depletion of PIP₂ abundance in neurons by muscarinic agonist (Suh and Hille, 2002; Ford et al., 2003; Winks et al., 2005). Furthermore, cellular modeling has been used to quantify this system, yielding a biophysically satisfying framework that produces sufficient changes in PIP₂ abundance upon receptor stimulation to account for the observed depression of M current, given known rates of lipid enzymes, reasonable estimates of channel/PIP₂ affinities and plausible densities of PIP₂ molecules, and the signaling molecules relevant to this G_q/11-mediated system (Suh et al., 2004; Horowitz et al., 2005).

Single-channel analysis of Kv7.2–7.5 channels has revealed widely divergent activities of the channels in intact cells that can be ascribed to widely differential apparent affinities for PIP₂. Whereas Kv7.3 homomers have a very high saturating open probability (P_o) and high PIP₂ apparent affinity, Kv7.2 and Kv7.4 homomers display dramatically lower values, and Kv7.2/7.3 heteromers have intermediate values for saturating P_o and PIP₂ apparent affinity, as one might expect for heteromeric channels containing subunits with divergent affinities (Li et al., 2005). We have recently localized the region of the channel that accounts for divergent P_o and PIP₂ apparent affinity to a highly basic interhelical linker domain in the C terminus that is critical for PIP₂ interactions (Hernandez et al., 2008). Kv7.3 homomers in particular possess several unique properties. Although they display much greater apparent affinity for PIP₂ and saturating P_o than the others (Li et al., 2004, 2005; Hernandez et al., 2008) and their unitary conductance is also the highest, the whole-cell currents from heterologously expressed Kv7.3 homomers are at least 20-fold lower. We have suggested this aspect to be the result of a high fraction of wild-type (WT) Kv7.3 channels being dormant, a condition wholly reversed by a single point mutation in the inner pore at the 315 position from an alanine to a hydrophilic threonine or serine (Zaika et al., 2008), and for many of the experiments shown here, we exploit the high expression of Kv7.3 (A315T) channels, which we will refer to as Kv7.3^T in this paper.

The widely divergent apparent affinity for PIP₂ of Kv7 channels predicts a corresponding divergence in sensitivity to stimulation of PLC-linked M₁ receptors because the degree of PIP₂ depletion should correlate with receptor stimulation, G_q/11 activation, and PLC activity. Thus, Kv7.3 is predicted to be relatively insensitive to muscarinic agonists, whereas Kv7.2 or Kv7.4 is predicted to be more sensitive. In addition, Kv7.2 mutants with decreased PIP₂ apparent affinity (Hernandez et al., 2008) should be more sensitive than WT channels, and increased tonic PIP₂ abundance should render channels less sensitive. In this study, we test these ideas on mammalian cells heterologously expressing various Kv7 channels and M₁ receptors and quantified agonist sensitivity as the dose–response relationship between muscarinic agonist concentration and Kv7-current inhibition. Furthermore, we modified a cellular model that simulates the G_q/11-mediated PLC signaling system, including PIP₂ metabolism and channel–PIP₂ interactions (Suh et al., 2004; Horowitz et al., 2005; Jensen et al., 2009), to model the relationship between receptor occupancy, PIP₂ affinity, and channel activity. The data and model are highly congruent, providing a satisfying biophysical basis for our observations.

Human Kv7.2, Kv7.3, and Kv7.4 (GenBank/EMBL/DDBJ accession nos. AF110020, AF071478, and AF105202, respectively) were provided by D. McKinnon (Kv7.2; State University of New York at Stony Brook, Stony Brook, NY) and T. Jentsch (Kv7.3 and Kv7.4; Zentrum fur Molekulare Neurobiologie, Hamburg, Germany). Plasmids were subcloned into pcDNA3.1 using standard techniques. Mouse type 1α PI(4)P5-kinase (PIP 5-kinase) was provided by L. Pott (Ruhr-University, Bochum, Germany; Bender et al., 2002). Mutations were made by PCR using the QuikChange method (Agilent Technologies) and verified by sequencing. The Kv7.3 (A315T) mutant (Kv7.3^T) and all Kv7.2 mutants were made by site-directed mutagenesis using standard techniques and verified by dye-termination sequencing.

Chinese hamster ovary (CHO) cells were used for electrophysiological analysis as described previously (Gamper et al., 2005). Cells were grown in 100-mm tissue culture dishes (Falcon; BD) in Dulbecco's modified Eagle's medium with 10% heat-inactivated fetal bovine serum and 0.1% penicillin and streptomycin in a humidified incubator at 37°C (5% CO₂) and passaged every 3–4 d. Cells were discarded after ∼30 passages. For transfection, cells were plated onto poly-l-lysine–coated coverslip chips and transfected 24 h later with Polyfect reagent (QIAGEN) according to the instructions of the manufacturer. For electrophysiological experiments, cells were used 48–96 h after transfection. As a marker for successfully transfected cells, cDNA encoding green fluorescent protein was cotransfected together with the cDNAs of the genes of interest. We found that >95% of green fluorescing cells expressed Kv7 currents in control experiments.

Pipettes were pulled from borosilicate glass capillaries (1B150F-4; World Precision Instruments) using a Flaming/Brown micropipette puller (P-97; Sutter Instrument Co.) and had resistances of 1–2 MΩ when filled with internal solution and measured in standard bath solution. Membrane current was measured with pipette and membrane capacitance cancellation and was sampled at 5 ms and filtered at 1 kHz by an amplifier (EPC-9) and PULSE software (HEKA/Instrutech). In all experiments, the perforated-patch method of recording was used with 200–600 µg/ml amphotericin B in the pipette (Rae et al., 1991). Amphotericin was prepared as a stock solution as 60 mg/ml in DMSO. In these experiments, the access resistance was typically 10 MΩ 5–10 min after seal formation. Cells were placed in a 500-µl perfusion chamber through which solution flowed at 1–2 ml/min. Inflow to the chamber was by gravity from several reservoirs, selectable by activation of solenoid valves (Warner Scientific). Bath solution exchange was complete by <30 s. Experiments were performed at room temperature. The amplitude of the Kv7 current was usually defined as the holding current at 0 mV. In some cells, a more precise measurement was the XE991-sensitive current at the holding potential of 0 mV. CHO cells had negligible endogenous macroscopic K⁺ currents under our experimental conditions, and 10 µM XE991 completely blocked the K⁺ current in Kv7-transfected CHO cells but had no effect on currents in nontransfected cells (Gamper et al., 2005). Dose–response data of channel current inhibition versus [oxotremorine-M] ([oxo-M]) were fit using Prism software (version 5.01; GraphPad Software, Inc.) for Windows by nonlinear regression using a Hill equation of the form

where Inhib is the fractional inhibition of the Kv7 current, Inhib_max is the maximal inhibition, x is [oxo-M], x_half is the [oxo-M] at which inhibition = 50% of maximal inhibition, and n is the Hill coefficient, which we constrained to the value of one. All results are reported as mean ± SEM.

The external Ringer's solution used to record Kv7 currents in CHO cells contained 160 mM NaCl, 5 mM KCl, 2 mM CaCl₂, 1 mM MgCl₂, and 10 mM HEPES, pH 7.4, with NaOH. The pipette solution contained 160 mM KCl, 5 mM MgCl₂, 5 mM HEPES, and 10 mM EGTA, pH 7.4, with KOH and added amphotericin B (200–600 µg/ml). Reagents were obtained as follows: Dulbecco's modified Eagle's medium, fetal bovine serum, penicillin, and streptomycin were purchased from Invitrogen; amphotericin B was obtained from Sigma-Aldrich. XE991 was purchased from Tocris.

A kinetic model was implemented in the Virtual Cell modeling and simulation framework (www.vcell.org). From within Virtual Cell, the model can be accessed by any user under Shared Models/bfalken/Hernandez Falkenburger Shapiro 2009. The rate constants and equations that constitute the model and initial values for the parameters are listed in Tables S1–S3. The model is a simplified adaptation of a model describing PIP₂ metabolism and Kv7.2/7.3 current by Hille and co-workers (Suh et al., 2004; Horowitz et al., 2005). Basal levels of PIP₂ were assumed to be 5,000 molecules/µm² based on the results of earlier modeling that well accounted for the onset and recovery rates of muscarinic suppression of Kv7.2/7.3 current (Suh et al., 2004) and from the calculated membrane-bound fraction of the PIP₂/IP₃-binding PH-PLCδ1 probe (Horowitz et al., 2005). Xu et al. (2003) used a value of 4,000/um² based on biochemical assays, but the exact number does not affect the conclusions drawn from the modeling (Fig. S1). Our model has only one invariant reaction rate for PIP₂ synthesis (syn) that lumps together activity of phosphatidylinositol (PI) 4-kinase and PIP 5-kinase. Syn prevents PIP₂ levels from falling to zero during application of muscarinic agonist (oxo-M) and mediates PIP₂ recovery after washout of agonist. The rates of receptor-independent steady-state PIP₂ degradation via PIP₂ phosphatase and basal PLC activities were lumped together (deg), whose value was chosen to keep PIP₂ levels stable at rest. The model simulates extracellular concentrations of oxo-M with a 10-s time constant for solution exchange, as determined by calibration experiments. For dose–response curves, oxo-M was modeled as applied for 100 s to ensure that steady state was reached as in the experiments. PLC is activated by muscarinic receptor agonist with an EC₅₀ of 1.6 µM, a value chosen to allow significant PIP₂ changes over the entire oxo-M concentration range, which is the prerequisite to observe changes in Kv7 currents. The time constant for PLC activation was taken from fluorescence resonance energy transfer (FRET) measurements of PLC binding to G_αq (Jensen et al., 2009).

The amplitudes of Kv7 currents were implemented in two steps: PIP₂ binding to Kv7-channel subunits and generation of current by four Kv7 subunits. The K_A values for PIP₂ binding were 500 µm⁻² Kv7.2 (WT), 75 µm⁻² Kv7.3^T, 2,500 µm⁻² Kv7.4, 10⁶ µm⁻² Kv7.2 (EEE), 75 µm⁻² Kv7.2 (R463E), and 5,000 µm⁻² Kv7.2 (R463Q). By analogy to the Hodgkin and Huxley term n⁴, which combines the sensing state of four voltage sensors to determine the voltage-dependent open probability of the entire channel, we calculated the PIP₂-dependent open probability of the entire channel as the product of the PIP₂ saturation of the four channel subunits (Table S2). For the heteromeric channels consisting of WT or mutant Kv7.2 and 7.3 subunits, we assumed the channel tetramers to consist of two subunits of each type, which is sufficient for our purposes here. Because the PIP₂ saturation of Kv7.3^T subunits does not change much in response to oxo-M, the changes in Kv7.2/7.3 current are predominantly governed by the PIP₂ occupancy of the Kv7.2 subunits with an exponent of 2 and a K_A of 500. This implementation is thus similar to the earlier models (Suh et al., 2004; Horowitz et al., 2005), which used a K_A of 1,000 µm⁻² for the entire Kv7.2/7.3 channel and an exponent of 1.8.

To get a sense of how the model works, we varied several parameters over a wide range and modeled the results (Fig. S1). We first modeled the effects of varying the K_A value of a subunit for PIP₂ on the dose–response relationship between muscarinic agonist and current inhibition for a homomeric channel (Fig. S1 A). When the model used values of K_A that varied from 75 to 2,400, two trends were evident. At the high end of the range (i.e., low-affinity subunits), a change in the K_A mostly results in a shift of the dose–response curve, with little impact on the maximum inhibition. However, at the low end of the range (i.e., high-affinity channels), a change in the K_A results in little displacement of the dose–response curve (quantified by the EC₅₀) but a big effect on the maximum inhibition. This can be understood in that maximum PLC activity does not reduce the PIP₂ abundance to zero but rather to a steady-state value that reflects the equilibrium between PLC-mediated consumption and PIP₂ synthesis. Thus, for the high-affinity channels whose overall n⁴ affinity is near those steady-state values, the predominant effect of altering K_A in the low range is a change in maximal inhibition. However, for the low-affinity channels, the subunit occupancy at maximal [oxo-M], which is very low, will change little when K_A is altered in this high range. Thus, the predominant effect is a shift in the dose–response curve, as the amount of PLC activity needed for the same degree of PIP₂ unbinding changes accordingly. Fig. S1 B shows a similar analysis for a heteromeric channel in which two subunits are Kv7.2 and the other two have K_A values over the same wide range. One can see that the same principles apply but to a lesser extent, as expected from the invariant affinity of the Kv7.2 subunits that buffer the overall response.

PIP₂ abundance has been suggested to vary considerably among cell types. For a given cell, this value reflects the equilibrium between tonic PIP₂ synthesis by PI kinases (syn in our model) and degradation by tonic PIP₂ phosphatases and basal PLC activity (deg in our model). In Fig. S1 C, we model the effect on the dose–response curve for Kv7.2/3 heteromers of doubling the tonic PIP₂ abundance to 10,000 µm⁻² by doubling the value of syn. In Fig. S1 D, we model the effect of the same maneuver on the relationship between [oxo-M] and PIP₂ abundance. It can be seen that there are some modest changes: the curve in Fig. S1 C is a little shifted to the left and the maximal inhibition is a little less, and the curve in Fig. S1 D has a steeper fall toward a steady-state value that is a little larger.

Tables S1, S2, and S3 present information on model parameters, the formulations describing the Kv7 currents, and initial values of the parameters, respectively. Fig. S1 characterizes the basic behavior of the model, as described in the Materials and methods section.

We studied CHO cells transfected with various Kv7 channels and M₁ muscarinic receptors under perforated-patch whole-cell voltage clamp. The inhibition of the current was quantified over a range of concentrations of the muscarinic agonist oxo-M. Our first experiments evaluated the muscarinic agonist sensitivity of WT Kv7.2/7.3 heteromers under control conditions and in cells in which tonic PIP₂ abundance was artificially increased. In control, the Kv7.2/7.3 current was inhibited by oxo-M in a concentration-dependent manner (Fig. 1, A and C) with an EC₅₀ of 0.44 ± 0.08 µM (n = 5–7) and a maximal current inhibition of 74 ± 3% (Fig. 1 B, open circles). The EC₅₀ value is comparable with that obtained previously in sympathetic neurons (0.30–0.68 µM; Bernheim et al., 1992; Haley et al., 2000; Winks et al., 2005), in which most M channels are thought to be Kv7.2/7.3 heteromers (Wang et al., 1998), but somewhat higher than that found in tsA-201 cells expressing the same channels and M₁ receptors (0.10–0.12 µM; Suh et al., 2004; Jensen et al., 2009). Likewise, the maximal inhibition is well within the range of that reported in sympathetic neurons (61–93%; Beech et al., 1991; Bernheim et al., 1992; Cruzblanca et al., 1998; Haley et al., 2000; Winks et al., 2005; Robbins et al., 2006; Zaika et al., 2007) but is on the low end of that reported in mammalian expression systems (79–95%; Selyanko et al., 2000; Shapiro et al., 2000; Gamper et al., 2003; Suh et al., 2004, 2006; Horowitz et al., 2005). We suspect that the precise values of both parameters will depend on the specific density of receptors or PLC molecules for each type of native, or heterologously transfected, cell.

PIP₂ is synthesized by sequential phosphorylation of PI by PI4- and PIP 5-kinases. Tonic PIP₂ levels have been experimentally increased by overexpression of PIP 5-kinase (Bender et al., 2002). In studies on M/Kv7 channels, the resulting effects were increases in unitary P_o at the single-channel level and current amplitude at the whole-cell level and a decrease in receptor-mediated suppression (Li et al., 2005; Winks et al., 2005; Suh et al., 2006). In general accord with those findings, we found overexpression of PIP 5-kinase to shift the oxo-M concentration dependence of Kv7.2/7.3-current suppression by threefold to higher concentrations (EC₅₀ = 1.2 ± 0.08 µM, n = 5–7) but without any significant change in the maximal current inhibition (73 ± 4%; Fig. 1 B, open circles). These results are consistent with greater activity of molecules in the G_q/11 signaling pathway being required in the cells transfected with PIP 5-kinase relative to the activity required to reduce PIP₂ abundance in control cells to the level needed for a given amount of current inhibition. In our model, an increase in syn by 1.7-fold is required to produce our observed effect on the EC₅₀ value, which is a little less than the twofold increase whose effect we modeled (Fig. S1, C and D). Our modeling also predicts a significant decrease in Inhib_max, which we did not observe. The relatively mild effects observed of PIP 5-kinase transfection, compared with previous studies, are probably caused either by less expression of PIP 5-kinase molecules than before or by a higher level of tonic PIP₂ abundance in the membrane in the present studies.

Our previous work indicates the apparent affinity of PIP₂ for Kv7.3 homomers to be high and that of Kv7.2 or Kv7.4 homomers to be much lower, with Kv7.2/7.3 heteromers being intermediate (Li et al., 2005; Hernandez et al., 2008). To ask whether the sensitivity to muscarinic suppression of Kv7 channels correlates with differences in apparent PIP₂ affinity, we quantified the dose–response relationship of muscarinic agonist and current suppression for Kv7.3 and Kv7.4 homomers. Many laboratories report only tiny Kv7.3 homomeric currents in heterologous systems (Etxeberria et al., 2004; Schenzer et al., 2005; Zaika et al., 2008), which would preclude the dose–response analysis desired here. Thus, for the Kv7.3 experiments, we used the A315T pore mutant, which displays large whole-cell currents that enable such analysis, with no changes in the unitary P_o of the channel at saturating voltages, indicating that the A315T mutation does not alter the high PIP₂ apparent affinity of Kv7.3 subunits (Zaika et al., 2008). We will call this mutant Kv7.3^T in this paper. Compared with Kv7.2/7.3 heteromers, the most dramatic difference for Kv7.3^T homomers was the strongly reduced maximal inhibition of the current at high oxo-M concentrations. Thus, at 10 µM oxo-M, the Kv7.3^T current was suppressed by only 39 ± 3% (n = 5–7; Fig. 2, A and C), whereas there was only a slight shift of the oxo-M dose–response curve to higher concentrations (EC₅₀ = 1.0 ± 0.76 µM, n = 5–7; Fig. 2 B). As discussed below, these data suggest that at supramaximal concentrations of muscarinic agonist, the equilibrium between PLC-mediated consumption and synthesis of PIP₂ results in a PIP₂ abundance at which most high-affinity Kv7.3^T channels are still bound by PIP₂ molecules. This hypothesis is further explored in the modeling to follow.

In contrast, lower affinity Kv7.4 homomers displayed an inhibition of ∼75% at 1 µM oxo-M (Fig. 3, A and C), a concentration that produced only ∼19% inhibition of the Kv7.3^T current (Fig. 2, B and C), and ∼48% inhibition of the Kv7.2/7.3 current (Fig. 3 B, dashed line). Analyzed over a wide range of agonist concentrations, the dose dependence of Kv7.4-current suppression by oxo-M was shifted to lower concentrations by approximately sevenfold (EC₅₀ = 66 ± 8 nM, n = 3–4) compared with Kv7.2/7.3 channels and by 15-fold compared with Kv7.3^T channels. Interestingly, there was no significant difference from Kv7.2/7.3 channels with regard to maximal suppression (81 ± 6%; Fig. 3 B). Thus, the activity of molecules in the G_q/11 signaling pathway required to reduce PIP₂ levels enough to cause unbinding of PIP₂ from low apparent affinity Kv7.4 channels must be significantly less than the activity required to cause PIP₂ unbinding from higher affinity Kv7.2/7.3 channels or highest affinity Kv7.3^T channels. These ideas are also tested in our modeling below.

We have localized the primary binding site of PIP₂ to M channels to a C-terminal domain that consists of a cluster of conserved basic amino acids within a seven–β-sheet barrel motif common to other PIP₂-binding domains (Hernandez et al., 2008). Interestingly, that study found mutation of two conserved basic residues in Kv7.2 (R463 and R467) within the cationic cluster to display opposite effects on PIP₂ apparent affinity that depended on the nature (charge reversal vs. charge neutralization) of the substituted residues, observations explained by molecular modeling and docking simulations (Hernandez et al., 2008). To ask whether muscarinic agonist sensitivity correlates with the observed changes in PIP₂ apparent affinity of one such Kv7.2 mutant pair, we studied R463E and R463Q, which were previously shown to have a much higher and lower apparent affinity for PIP₂, respectively (Hernandez et al., 2008). However, because cells transfected with those mutants display only small whole-cell currents (Hernandez et al., 2008), we studied the oxo-M concentration dependence for inhibition of R463E and R463Q mutant subunits coexpressed with Kv7.3^T (Fig. 4). For Kv7.2 (R463E)/7.3^T, the muscarinic sensitivity was sharply reduced, manifested by a reduction in the maximal inhibition of the current to 27 ± 3% and a slight shift of the EC₅₀ to higher concentrations (0.58 ± 0.07 µM, n = 3–4), compared with Kv7.2/7.3 (Fig. 4, A and B). In contrast, mutation of R463 to the noncharged glutamine shifted the dose dependence of Kv7.2 (R463Q)/7.3^T channels to lower concentrations by fourfold (Fig. 4, A and B). For those heteromers, the EC₅₀ was reduced to 0.12 ± 0.08 µM with a maximal inhibition of 79 ± 6% (n = 3–4). We then investigated the effect on muscarinic sensitivity of incorporation into the channels of the Kv7.2 K452E/R459E/R461E triple mutant (EEE), in which the charges of three conserved basic residues important for PIP₂ interactions in the putative PIP₂-binding domain are simultaneously reversed, causing a profound reduction in single-channel open probability and presumed PIP₂ affinity (Hernandez et al., 2008). For the Kv7.2 (EEE)/7.3^T heteromer, the muscarinic sensitivity was indeed strongly increased, with the EC₅₀ reduced to 32 ± 4 nM (n = 3–4) and a maximal current inhibition of 83 ± 3% (n = 3–4; Fig. 4 B, circles). This shift of the oxo-M dose–response relation, as measured by the change in EC₅₀, represents a 14-fold and 18-fold increase in muscarinic sensitivity relative to the higher affinity Kv7.2/7.3 and Kv7.2 (R463E)/7.3^T channels, respectively, and even a fourfold increase when compared with Kv7.2 (R463Q)/7.3^T channels (Fig. 4). Thus, the currents from Kv7.2 (EEE)/7.3^T mutant channels were inhibited by ∼60% at 0.1 µM oxo-M, a concentration that produced an inhibition of Kv7.2 (R463Q)/7.3^T channels of only ∼30% (Fig. 4 C). In summary, our results suggest that sensitivity to muscarinic agonist via G_q/11-coupled M₁ receptors, PLC activity, and consumption of PIP₂ correlates well with apparent PIP₂ affinity across the family of homomeric and heteromeric M-type channels both for WT Kv7 variants and for the Kv7.2 mutants. They also suggest that the PIP₂ affinity of one type of subunit in a heteromer has strong effects on the overall PIP₂ affinity and subsequent muscarinic sensitivity of the overall tetrameric channel. Thus, PIP₂ binding to all subunits in the tetramer is likely to be required for the channel to be activatable by voltage.

We used a simplified version (Fig. 5 A) of a more comprehensive kinetic model developed previously (Suh et al., 2004) to show that our experimental findings can be explained by the basic principles of G_q/11 signaling and channels regulated by PIP₂ abundance, which we assume to tonically be 5,000 molecules/µm² of plasma membrane.. In our model here, Kv7.2, 7.3, and 7.4 subunits or mutant Kv7.2 subunits possess distinct affinities for PIP₂, quantified as the K_A for PIP₂ binding, which was empirically determined to best fit the data. For Kv7.2–7.4, the K_A values were 500, 75, and 2,500, and for the Kv7.2 mutants R463E, R463Q, and the EEE mutant, they were 75, 5,000, and 10⁶, respectively. The model supposes binding of one PIP₂ to one Kv7 subunit. Because each channel is composed of four subunits, the current of a Kv7 channel is proportional to the product of the fractional PIP₂ saturation of four subunits (see Materials and methods and Table S2). We assumed heteromeric Kv7.2/7.3 channels to consist of two Kv7.2 (WT or mutant) and two Kv7.3 subunits, which is reasonable for our purposes here. For homomeric channels, current was modeled as being proportional to the fourth power of PIP₂-bound subunits. This implementation differs from the model by Suh et al. (2004) in which PIP₂ bound to a channel particle instead of to a subunit particle, which did not allow “mixing” of Kv7.2 and 7.3 subunits to form a heteromeric channel. Thus, we first determined the affinity of homomeric channels to determine the affinity of each type of WT subunit and then adjusted the affinity of WT or mutant Kv7.2 subunits to reproduce the dose–response relationships observed experimentally with Kv7.2/7.3 heteromers. Our model reflects the affinity of PIP₂ for Kv7.2, 7.3, and 7.4 subunits to be intermediate, high, and low, respectively, and the R463E and R463Q mutants of Kv7.2 to give that subunit high (similar to Kv7.3) and low (similar to Kv7.4) affinities for PIP₂, respectively. Finally, in our model, the EEE mutant possesses a profoundly low PIP₂ affinity, which is in accord with the very low affinity predicted in our earlier docking simulations and seen in single-channel patches (Hernandez et al., 2008).

The first important observation is the relationship between PIP₂ density and concentration of receptor agonist (Fig. 5 B). The activation of PLC by oxo-M was informed by measurements of muscarinic agonist–induced changes in FRET between Gα_q and PLC (Jensen et al., 2009) and adjusted to produce significant changes in PIP₂ density over the entire range of oxo-M concentrations in which current inhibition was observed. Steady-state PIP₂ density reflects the equilibrium between consumption by PLC and synthesis by PI kinases, with half-maximal PIP₂ reduction at ∼0.2 µM oxo-M (Fig. 5 B). PIP₂ synthesis during oxo-M application is greater than zero (and in fact stimulated as compared with baseline values; Gamper et al. 2004). PLC activity saturates at a finite value, as there are a finite number of PLC molecules that can be activated. As a consequence, there is a defined, nonzero minimum level for PIP₂ in the presence of maximal oxo-M concentrations (∼500 µm⁻² in Fig. 5 B). As a consequence, the inhibition of all Kv7 channels will saturate at high [oxo-M] (Fig. 5 C). Inhib_max is predicted to diverge between Kv7 channels, depending on their affinity for PIP₂. Low-affinity channels will have lost virtually all their bound PIP₂ molecules at minimal PIP₂ densities, whereas a substantial proportion of high-affinity channels will retain their bound PIP₂. The small maximum inhibition of Kv7.3 current at supramaximal oxo-M is thus explained by the fact that, because of their high PIP₂ affinity, they retain much of their bound PIP₂ even at maximal PLC activity (Fig. 5 C, dashed line). Another consequence of the high affinity of Kv7.3 for PIP₂ is that the channel is relatively PIP₂ saturated at rest, and the predicted relationship between PIP₂ abundance and Kv7.3 current is relatively flat at resting PIP₂ densities (Fig. 5 D, dashed line). Low concentrations of oxo-M are therefore predicted to have virtually no effect on Kv7.3 current, in accord with the data. Conversely, Kv7.4 has a low affinity for PIP₂, and the PIP₂ concentration curve for Kv7.4 is relatively steep in the area of resting PIP₂ (Fig. 5 D, dotted line). This results in strong current reduction even by small changes of PIP₂ abundance and augmented inhibition at saturating [oxo-M]. Current inhibition thus requires only little oxo-M, low activation of receptors, G_q/11, and PLC, explaining the left-shifted concentration curve as compared with Kv7.2/7.3 channels (Fig. 5 C, dotted line). The comparison between values for EC₅₀ and maximal inhibition for the data and model values for Kv7.3, 7.4, and 7.2/7.3 channels are nicely in accord (Table I), providing satisfying support for our thinking.

The next set of modeling has to do with the behavior of the Kv7.2 mutants. Again, we assumed a 1:1 stoichiometry in the channel tetramers made from coexpressed Kv7.2 mutant subunits and Kv7.3 subunits, with current proportional to the sequential product of four PIP₂-bound subunits. We assume that the changes in muscarinic sensitivity for the higher or lower PIP₂ affinity Kv7.2 mutants studied here can be ascribed to the same biophysical principles as for the WT channels. In the model, the best fit for the data from Kv7.2 (R463E) and (R463Q) subunits were with PIP₂ affinities similar to that of Kv7.3 or Kv7.4 subunits, respectively, and the PIP₂ affinity needed for the Kv7.2 (EEE) mutant had to be made extremely low. Thus, for Kv7.2 (R463E)/Kv7.3 channels, the relationship between current inhibition and [oxo-M] is predicted to be flat at low [oxo-M] with relatively low inhibition at saturating [oxo-M], which is in accord with the data, like that of Kv7.3 homomers. Conversely, for Kv7.2 (R463Q)/7.3 channels, the relationship between current inhibition and [oxo-M] is predicted to be relatively steep at low [oxo-M], resulting in strong current reduction by small changes in PIP₂ abundance and augmented inhibition at saturating [oxo-M], all similar to the response of Kv7.4 homomers. In the model, the oxo-M sensitivity of Kv7.2 (EEE)/Kv7.3 channels is only slightly greater than that for Kv7.2 (R463Q)/Kv7.3 channels, but this is actually predicted by the dominance of PIP₂ binding to the Kv7.3 subunits in the tetramer and is again very similar to the data. Note that at intermediate oxo-M concentrations for both the data and the model, the difference in the response of Kv7.2 (R463Q)/Kv7.3 and Kv7.2 (EEE)/Kv7.3 channels is most significant. In the Discussion, we compare the current experimental and model data with our previous molecular docking simulations.

Two related types of single-channel experiments have suggested that the family of Kv7 channels possesses divergent apparent affinities for PIP₂. The first are cell-attached patch recordings in which channel P_o at saturating voltages varied widely, consistent with the tonic PIP₂ abundance supporting a divergent level of channel opening. The second are inside-out patch data in which P_o measured over a wide range of concentrations of a water-soluble PIP₂ analogue revealed a parallel differential PIP₂ apparent affinity (Hernandez et al., 2008). These results predicted a corresponding divergent dose–response relationship between PLC-linked receptor agonist and Kv7-channel inhibition. That prediction was verified here. A main result of this work is that the effect of alterations in PIP₂ affinity on the sensitivity of the channels to muscarinic agonist depends on whether the channels have a relatively low or high apparent affinity for PIP₂. For the former, reductions in PIP₂ affinity do not much affect the Inhib_max because it is already quite high but rather shift the dose–response relation of [oxo-M] versus inhibition to lower concentrations. Conversely, for the latter, reductions in affinity do not much change the EC₅₀ of the dose–response relation, but rather the large effect is an increase in Inhib_max. Thus, the current from Kv7 channels does not generally go to zero upon maximal stimulation of M₁ receptors, but rather Inhib_max depends on the equilibrium between PLC-mediated hydrolysis and PIP₂ synthesis and the affinity of the particular channel. All of these phenomena are well simulated by our model incorporating PIP₂ metabolism, receptor-mediated PLC activation, and channels regulated by PIP₂ binding with quantifiable affinities. What adds impact to our results is that agonist-dependent PIP₂ depletion or creation is highly receptor and cell dependent. Thus, PIP₂ binding/unbinding is hypothesized to often occur not via PIP₂ depletion but rather via alteration of the PIP₂ affinity of PIP₂-regulated channels by myriad signaling molecules (Gβγ, Ca²⁺/calmodulin, pH, Na⁺, PKC, PKA, etc.; Gamper and Shapiro, 2007). Therefore, the changes of PIP₂ affinity by mutagenesis or change of subunit composition in these experiments somewhat mimic this physiological mechanism of lipid signaling. For example, whereas Kv7.3 homomers are only slightly inhibited at maximal depletion of PIP₂ by PLC, a reduction in the channel's affinity for PIP₂ will put its K_A in the range where such physiological depletions will have a much stronger effect on the currents. In addition, the strong subunit dependence of muscarinic agonist sensitivity predicts that transcriptional control of subunit expression in distinct regions of the nervous system will have profound consequences for muscarinic receptor control over neuronal excitability.

The cellular modeling makes predictions for the values of EC₅₀ and Inhib_max for muscarinic suppression of the Kv7 subunits that we studied. Those predicted and experimental values are compared in Table I. For clarity, we will use Kv7.2/7.3 heteromers as the baseline to compare with the others in this discussion. Several trends are clearly in accord between the two sets of values. First, they both show high-affinity channels (Kv7.3^T and Kv7.2 (R463E)/Kv7.3^T) to have sharply reduced Inhib_max but only slightly increased EC₅₀ values. Second, they both show low-affinity channels (Kv7.4, Kv7.2 (R463Q)/Kv7.3^T, and Kv7.2 (EEE)/Kv7.3^T) to manifest strongly decreased EC₅₀ values. The model also predicts the significant current remaining after maximal receptor stimulation for intermediate affinity channels, which is in accord with the experimental observations. However, a clear discrepancy is the near complete elimination of the current by low-affinity channels predicted by the model, which we did not observe in the data. An explanation may be the existence of “protected” pools of PIP₂ (perhaps sequestered by MARCKS [myristoylated alanine-rich C-kinase substrate] proteins or other PIP₂-sequestering moieties; Gambhir et al., 2004; McLaughlin et al., 2005; Milosevic et al., 2005) that cannot be consumed by PLC, preventing Kv7-channel activity from ever going to zero. Alternatively, the CHO cells that we use for our heterologous expression system may be endowed with receptor-mediated stimulation of PIP₂ synthesis, as has been demonstrated in neurons (Xu et al., 2003; Gamper et al., 2004; Loew, 2007). Lastly, there may be feedback acceleration of the activity of PI kinases tied to PIP₂ levels (Hilgemann et al., 2001). Both of these factors may prevent PIP₂ levels from being as depleted as in our modeling, which does not incorporate any feedback alteration in the rate of PIP₂ synthesis. We cannot know for sure whether the stoichiometry of subunits in the coexpression of the Kv7.2 mutants with Kv7.3^T is as nearly 1:1 as we assume, which would bias the data if more Kv7.3^T subunits were in the tetramers. However, this caveat does not apply for Kv7.4 homomers, which also manifested a more complete suppression of the current in the model than in the data.

We should also comment on the variance in dose–response relationships described in the literature for muscarinic suppression of M current and of PIP₂ depletion. Steady-state PIP₂ densities achieved at various concentrations of G_q/11-coupled receptor agonists are expected to be very much dependent on the experimental paradigm and cell type used; for example, whether the receptors are endogenous or heterologously expressed or whether PI kinases are stimulated by receptor stimulation. Jensen et al. (2009) recently determined an oxo-M dose–response curve for PIP₂ densities using the PH-PLCδ1 FRET probe in which the EC₅₀ for oxo-M–mediated depletion of PIP₂ was found to be ∼10-fold lower than in the present modeling results (Fig. 5 B). Although PH-PLCδ1 probe expression can affect phosphoinositide levels and metabolism (Xu et al., 2003; Gamper et al., 2004), the oxo-M dose–response curve for Kv7.2/7.3 inhibition was also shifted by about fourfold in cells not expressing the probe. We suspect the differences could result from lower levels of endogenous G proteins or PLC molecules in CHO cells as compared with tsA-201 cells or reflect a higher activity of PI kinases. In addition, much work indicates receptor-mediated stimulation of PI-kinases, which is concurrent with activation of PLC (Zhao et al., 2001; Koizumi et al., 2002; Rajebhosale et al., 2003; Xu et al., 2003; Gamper et al., 2004; Winks et al., 2005; Zheng et al., 2005; Balla and Balla, 2006). Thus, differential stimulation of PI-kinases across cell types could easily account for the differences seen in agonist sensitivity and efficacy toward ion channel targets.

In this study, the K_A values for binding of PIP₂ to Kv7.2, 7.3, 7.4, 7.2 (R463E), 7.2 (R463Q), and 7.2 (EEE) subunits were modeled to be 500, 75, 2,500, 75, 5,000, and 10⁶, respectively. Using the classical relationship between equilibrium constant and free energy of ΔG = −RTln(K_A), those affinities correspond to differences in free energy relative to Kv7.2 of 4.7 (Kv7.3), −4.0 (Kv7.4), 4.7 (Kv7.2 R463E), −5.7 (Kv7.2 R463Q), and −18.9 (Kv7.2 EEE) kJ/M. In our docking simulations between the channels’ putative PIP₂-binding domains and the PIP₂ analogue, GPMI-P₂, the differences in affinity energies were found, relative to Kv7.2, to be 2.2 (Kv7.3), 3.8 (Kv7.2 R463E), −5.7 (Kv7.2 R463Q), and −11.2 (Kv7.2 EEE) kJ/M (docking with Kv7.4 was not modeled; Hernandez et al., 2008). Although there are quantitative differences between the present modeling results and the previous docking simulations, there is qualitative agreement that lends credence to the docking simulations and adds to an internally consistent body of data and modeling across single-channel patches, receptor-mediated modulation in intact cells, homology/docking modeling, and the model simulations. Clearly, the next step will be to perform biochemical affinity measurements for the PIP₂-binding domains of the various M-type channels to test whether our conclusions from signaling cascades translate into quantitative measurements of physical molecular interactions.

We thank P. Reed for expert technical assistance and B. Hille for discussions.

This work was supported by National Institutes of Health grant R01 NS043394 (to M.S. Shapiro), American Heart Association grant-in-aid 0755071Y (to M.S. Shapiro), and the Human Frontier Science Program (to B. Falkenburger).

Lawrence G. Palmer served as editor.