Correlation between structure and function in phosphatidylinositol lipid-dependent Kir2.2 gating

Inward rectifier K+(Kir) channels regulate cell membrane potential. Different Kir channels respond to unique ligands, but all are regulated by phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2). Using planar lipid bilayers we show that Kir2.2 exhibits bursts of openings separated by long quiescent inter-burst periods. Increasing PI(4,5)P2 concentration shortens the Kir2.2 inter-burst duration and lengthens the burst duration without affecting dwell times within a burst. From this, we propose that burst and inter-burst durations correspond to the CTD-docked and CTD-undocked conformations observed in the presence and absence of PI(4,5)P2 in atomic structures. We also studied the effect of different phosphatidylinositol lipids on Kir2.2 activation and conclude that the 5’ phosphate is essential to Kir2.2 pore opening. Other phosphatidylinositol lipids can compete with PI(4,5)P2 but cannot activate Kir2.2 without the 5’ phosphate. PI(4)P, which is directly interconvertible to and from PI(4,5)P2, might thus be a regulator of Kir channels in the plasma membrane.

Previous electrophysiological studies using inside-out patches from cell membranes showed that two different Kir channels, the KATP channel and a G protein-independent mutant of the GIRK channel, both gate in bursts, that is, intervals of rapid channel opening and closing were separated by long quiescent periods (Enkvetchakul et al., 2000;Jin et al., 2008). Furthermore, in the GIRK channel, PI(4,5)P2 influenced the duration of the burst periods (Jin et al., 2008). In the KATP channel, PI(4,5)P2 influenced the duration of quiescent periods, without changing the kinetics within the burst (Enkvetchakul et al., 2000). Two other Kir channels, Kir2.1 and Kir2.2, were studied following purification and reconstitution in lipid vesicles (D'Avanzo et al., 2010).
Using Rb + flux and patch clamp analysis these channels were found to be activated by PI(4,5)P2 and other phosphatidylinositol lipid derivatives in the absence of other regulatory molecules.
In this paper we present an analysis of the Kir2.2 channel gating response to phosphatidylinositol lipids using the planar lipid bilayer recording system. This system offers complete chemical control of lipid, solution and protein composition as well as free access to the solution bathing the surfaces of the membrane (Miller and Racker, 1976;Montal and Mueller, 1972;Wang et al., 2014). Given that we already have a detailed description of the structural changes that Kir2.2 undergoes upon binding of PI(4,5)P2 (Hansen et al., 2011;Tao et al., 2009), our goal here is to correlate PI(4,5)P2-dependent gating properties with the known structural changes. Furthermore, given our detailed chemical knowledge of the PI(4,5)P2 binding site on Kir2.2, we characterize and interpret the influence of different phosphatidylinositol lipid derivatives on channel gating.
Because both PI(4)P and PI(4,5)P2 contribute substantially to the pool of plasma membrane phosphatidylinositol lipids, their competition and interconversion might be relevant to Kir2.2 in vivo (Di Paolo and De Camilli, 2006;Hammond and Balla, 2015;Logothetis et al., 2015). Figure 1A shows a schematic of the planar lipid bilayer system used in this study (Miller and Racker, 1976;Montal and Mueller, 1972;Wang et al., 2014). A lipid bilayer with a defined composition separates the top and bottom chambers, each filled with electrolyte solution.

Influence of C8-PI(4,5)P2 on the gating kinetics of Kir2.2
We next looked at how C8-PI(4,5)P2 influences the kinetics of Kir2.2 gating. Figure 2A shows a single-channel trace recorded in the presence of 3, 6 and 15 μM C8-PI(4,5)P2. The channel opens in bursts of activity separated by quiescent intervals. We see from this trace two processes that operate on very different timescales. The relatively fast process, occurring on the sub-second timescale, accounts for rapid channel opening and closing within a burst of activity ( Figure 1C). A second, longer closed dwell time exists because we see it in the raw trace ( Figure   2A), however, its frequency is too low to accumulate enough events during the recording, which is limited in duration owing to the phenomenon of channel disappearance over time. Figure 2F shows the connectivity diagram for two closed and one open state ( Figure 2F, 1). One linear kinetic sub-scheme, 2, is incompatible with the channel record because openings would not be interrupted by brief closures. The remaining two linear kinetic sub-schemes, 3 and 4, are compatible with the record, which cannot distinguish among them.
In the context of the compatible kinetic schemes, we next ask which transitions are affected by the concentration of C8-PI(4,5)P2? Given the low frequency of inter-burst intervals, confounded by channel disappearance over time, we resorted to studying bilayer membranes with several channels present at once. While this approach is not ideal, it provides a sufficient number of events to estimate the rate constants. Figure 3A shows a multi-channel membrane in the presence of 3, 6 and 15 μM C8-PI(4,5)P2. The 15 μM record was used to estimate the total number of channels in the membrane (see Methods), while 3 and 6 μM records were subject to kinetic analysis (Table 1) (Csanady, 2000). The analysis assumes that all channels are identical in their behavior. For most channel types we have studied, including Kir2.2, this assumption is only approximately true. There appeared to be a small fraction of outlier channels with lower or higher than average open probability, which undoubtedly contributed to the variation in rate constant values between different experiments. This limitation notwithstanding, Table 1 shows that C8-PI(4,5)P2 affects only the rate constants for transitions into and out of CLong. In detail, when C8-PI(4,5)P2 is increased, the burst periods lengthen and the quiescent periods shorten.
Consistent with the single-channel trace in Figure 2, rate constants for opening and closing within a burst are insensitive to C8-PI(4,5)P2 concentration: within a burst, only the mean number of transitions is affected by C8-PI(4,5)P2. Table 1 reports rate constant values for scheme 3, but scheme 4 ( Figure 2F) would yield a similar conclusion, that only rate constants into and out of CLong are sensitive to C8-PI(4,5)P2 concentration.
The functional analysis leads to the simple conclusion that only the slow kinetic process of transition between the burst and quiescent states is sensitive to C8-PI(4,5)P2. The structural studies show that the binding of C8-PI(4,5)P2 is associated with a large conformational change between the CTD-undocked and CTD-docked structures (Hansen et al., 2011;Niu et al., 2020;Tao et al., 2009). We thus propose that the slow gating transitions in the channel recordings correspond to CTD engagement and disengagement, and that when the CTD is engaged, the pore can open ( Figure 3B). The rapid gating transitions within a burst would then represent C8-PI(4,5)P2 -independent conformational changes that occur elsewhere along the ion conduction pathway. According to this model, the channel record provides a dynamic read-out of the CTD engagement and disengagement process, whose equilibrium is shifted by the C8-PI(4,5)P2 concentration.

Effect of phosphatidylinositol lipid derivatives on gating
Earlier studies have shown that phosphatidylinositol lipids with different phosphate substitutions can also interact with Kir channels, including Kir2.2 (Logothetis et al., 2015). Figure 4A shows a number of the chemical interactions between C8-PI(4,5)P2 and Kir2.2 derived from the crystal structure (Hansen et al., 2011). Individual membrane recordings using the planar bilayer system Kir2.2 can be activated in membrane patches from cells by C8-PI(4,5)P2 and C8-PI(3,4,5)P3, but not C8-PI(3,4)P2 (Rohacs et al., 2003). In the crystal structure of Kir2.2, the 5' phosphate forms ionized hydrogen bonds with several basic residues at and near the base of the inner helix, which forms the gate ( Figure 4A) (Hansen et al., 2011). This is compatible with the functional requirement of 5' phosphate to open Kir2.2 channel.
Do phosphatidylinositol lipids that do not activate Kir2.2 fail to bind altogether or do they bind but fail to open the gate? The data in Figure 5 suggest the latter, that certain phosphatidylinositol lipids inhibit Kir2.2 activation by competing with PI(4,5)P2 for its binding site. Following Kir2.2 activation by 6 μM C8-PI(4,5)P2, addition of 20 μM PI(3)P, PI(4)P or PI(3,4)P2 caused a pronounced reduction in current ( Figure 5 A-C). PI(3,5)P2, which itself activates Kir2.2 but to a lesser extent than PI(4,5)P2, also reduced current apparently by competition for the site ( Figure   5D). In membranes with a small number of channels we tried to determine how a competing lipid, C8-PI(4)P, influences the kinetics of gating ( Figure 5E and Table 2). Again, only the rate constants into and out of CLong are affected, as if addition of C8-PI(4)P mimics a reduction in the concentration of C8-PI(4,5)P2.

Discussion
These results build on previous studies showing that PI(4,5)P2 is necessary and sufficient to open Kir2.2 (D'Avanzo et al., 2010). They also build on earlier characterizations of phosphatidylinositol lipid specificity in the activation of Kir channels in general (Logothetis et al., 2015). The present study advances our understanding by analyzing the phosphatidylinositol lipid-dependent gating of Kir2.2 in the compositionally-defined lipid bilayer system. It also presents a mechanistic model derived by correlating C8-PI(4,5)P2-dependent changes in the atomic structure of Kir2.2 with C8-PI(4,5)P2-dependent changes in the kinetics of gating. The accuracy of the kinetic data is limited for reasons described above. Nevertheless, the conclusion that C8-PI(4,5)P2 influences only the relatively slow transitions that govern exchange between the burst and quiescent periods is robust. In the model we connect the large conformational change observed in structural studies -C8-PI(4,5)P2-mediated engagement between the CTD and TMD -with the burst-quiescent period interconversions. This idea is depicted in cartoon form in Figure 3B. In the CTD-docked conformation, the pore opens and closes rapidly in a C8-PI(4,5)P2-independent manner. Other Kir channels also exhibit burst kinetics (Enkvetchakul et al., 2000;Jin et al., 2008) and in KATP, ATP-independent gating within burst periods has been attributed to processes inside the selectivity filter (Proks et al., 2001). The basis for rapid gating in Kir2.2 is still unknown.
A G protein-independent GIRK channel was found to exhibit a more complex dependence on PI(4,5)P2 than we describe here for Kir2.2 (Jin et al., 2008). In the mutant GIRK channel, in addition to influencing the burst (but not the inter-burst) duration, multiple open states were deduced and attributed to different degrees of PI(4,5)P2 occupation. In Kir2.2 we observe only a single open state and can only say the following regarding the functional stoichiometry of PI(4,5)P2 activation. That the quiescent periods shorten with increasing PI(4,5)P2 concentration indicates that at least one bound PI(4,5)P2 molecule is required to enter a burst. That the burst periods lengthen with increasing PI(4,5)P2 concentration indicates that after a sufficient number of PI(4,5)P2 molecules have bound to enter a burst, at least one more can still bind ( Figure 3B).
If this were not the case, then the burst duration would be independent of the PI(4,5)P2 concentration. In conclusion, somewhere between 1 and 3 PI(4,5)P2 molecules would seem to be required to stabilize the structure underlying the burst state, which we propose is the CTDdocked state. We know from the structures that 4 PI(4,5)P2 molecules can bind to the CTDdocked conformation, but if the model is correct, fewer than 4 can support the CTD-docked conformation.
The requirement of a 5' phosphate to achieve channel opening seems compatible with the crystal structure of Kir2.2 with PI(4,5)P2 bound because the 5' phosphate interacts directly with amino acids on the inner helix, which forms the gate. PI(4,5)P2 also makes other interactions with the channel so it is understandable that a phosphatidylinositol lipid without the 5' phosphate would still bind to the site. This is undoubtedly why PI(4)P, for example, competes with PI(4,5)P2 for the phosphatidylinositol lipid binding site on the channel. PI(4)P as a competing lipid is particularly interesting because it, along with PI(4,5)P2, is abundant in the plasma membrane (Hammond and Balla, 2015). Moreover, PI(4)P is a precursor in the synthesis of PI(4,5)P2 and dephosphorylation of PI(4,5)P2 generates PI(4)P (Di Paolo and De Camilli, 2006;Hammond and Balla, 2015;Logothetis et al., 2015). Because PI(4,5)P2 activates and PI(4)P competitively inhibits, changes in lipid metabolism could give rise to a very steep change in the level of Kir2.2 activity.

Cloning, expression, and purification
A synthetic gene fragment (Bio Basic, Inc.) encoding residues 38 to 369 of chicken Kir2.2 (cKir2.2) channel (GI:118097849) was subcloned into a modified pEG BacMam vector with a Cterminal green fluorescent protein (GFP)-1D4 tag linked by a preScission protease site (Goehring et al., 2014). This construct was used in all experiments in this study.
Bacmid containing cKir2.2 gene was generated according to the manufacturer's instructions (Invitrogen) by transforming the cKir2.2 pEG BacMam construct into E. coli DH10Bac cells.
The bacmid was then transfected into Spodoptera frugiperda Sf9 cells to produce baculoviruses using Cellfectin II (Invitrogen). After two rounds of amplification, P3 viruses were added to HEK293S GnTIcells (ATCC) in a 1:10 (v:v) ratio for protein expression. Suspension cultures of HEK293S GnTIcells were grown in Freestyle 293 media (GIBCO) supplemented with 2% FBS (GIBCO) at 37°C to a density around 1.5-3x10 6 cells/ml. After incubating the infected cell for 20 hours at 37°C, 10 mM sodium butyrate was added and the temperature was changed to 30°C. Cells were harvested ~40 hours after changing the temperature (Goehring et al., 2014).
The lipid mixture was rotated for 30 min and sonicated again till clear. Equal volume of protein (at 2 mg/ml and 0.2 mg/ml) and lipid (at 20 mg/ml) were mixed, resulting in protein: lipid (w:w) ratios of 1:10 and 1:100 respectively. The mixture was incubated at 4°C for 1 hour and then dialyzed against 2L reconstitution buffer for 2 days, exchanging buffer every 12 hours. Biobeads was added to the reconstitution buffer for the last 12 hours. The resulting proteoliposomes were frozen with liquid nitrogen and stored at −80°C.

Electrophysiology
The bilayer experiments were performed as previously described with minor modifications (Ruta et al., 2003;Wang et al., 2014). A piece of polyethylene terephthalate transparency film separates the two chambers of a polyoxymethylene block which are filled with buffer containing 10 mM potassium phosphate pH 7.4, 150 mM KCl and 2 mM Mg 2+ .
A 20 mg/ml decane lipid mixture (w:w:w 2:1:1) of 1,2-dioleoyl-sn-glycero-3phosphoethanolamine (DOPE) : 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) : 1palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine (POPS) (Avanti) was pre-painted over a ∼100 μm hole on the transparency film. Voltage was controlled with an Axopatch 200B amplifier in whole-cell mode. The analog current signal was low-pass filtered at 1 kHz (Bessel) and digitized at 10 kHz with a Digidata 1322A digitizer. Digitized data were recorded on a computer using the software pClamp (Molecular Devices, Sunnyvale, CA). Experiments were performed at room temperature. For macroscopic current recordings, data reduction with a reduction factor of 100 and 5 Hz Gaussian low-pass filter was applied for plotting purpose. For single-channel recordings, a 300 Hz Gaussian low-pass filter was applied to the expanded trace ( Figure 2A, inset), or data reduction with a reduction factor of 200 was applied to the whole single-channel recording for plotting.

Kinetic analysis
Recordings containing 1-9 channels were idealized through half-amplitude threshold crossing and analyzed using Clampfit software (Molecular Devices).
For single-channel recordings, open or closed dwell time distributions for events within the burst were fitted to an exponential probability density function. Models with different term numbers were compared and the best model was selected (Horn, 1987).
Multi-channel recordings were analyzed as described . Eventlists were fitted using a three-state linear scheme. Dead time was 0.27 ms. Channel numbers used in the multi-channel kinetic analysis were estimated using the maximum number of observed open channel levels (from 15 μM C8-PI(4,5)P2 recordings). Rate constants between all states (k12, k21, k23 and k32) were obtained by simultaneous fit to the dwell-time histograms of all conductance levels (Csanady, 2000). The mean number of short closures per burst, mean burst and inter-burst duration were then calculated based on the rate constants --mean number of short closures per burst = 1 + k23 / k21, mean inter-burst duration = 1 / k12, and mean burst duration = (1 / k21) (1+ k23 / k32).

Estimation of the channel number used in multi-channel kinetic analysis
To evaluate the validity of using the maximum number of observed open channel levels (from 15 μM C8-PI(4,5)P2 recordings) as the channel number (N) in the multi-channel kinetic analysis, we ask what is the probability of observing N channels at least once during the duration of the record? This probability is a function of N, the rate constants, and the initial condition. This probability is given by the integral of the first passage time probability density function for the appearance of the right-most state for the scheme, for N = 8, shown here: This scheme, with the rate constants weighted as shown, models a membrane with N = 8 identical channels. The quiescent state of each channel is denoted as Cclose and the burst is denoted as Copen. The left-most state represents the membrane with 8 closed channels. The rightmost state represents the membrane with 8 open (i.e. burst channels).
Using Mathematica (Wolfram), we estimate that the mean first passage time is 268 s and that the probability of observing 8 channels at least once during the duration of the record (10 min) is 0.9. Given the 10% chance that we cannot see all 8 channels open within 10 min an the problem of channel disappearance over time, it is possible that we have underestimated the channel number. We therefore ask, if we assign the incorrect value for N, will our conclusion that C8-PI(4,5)P2 affects only the burst and inter-burst periods be wrong? Using recording 3 (Table 1), in which we have assigned N = 4 on the basis of direct observation we re-analyzed the record for N  (Table 3). The value of N had little influence on the determination of kinetic values within the burst and had a small influence on k21 and mean burst duration. The main affect was on k12 and mean inter-burst duration. But importantly, when C8-PI(4,5)P2 is increased, the burst periods lengthen and the quiescent periods shorten. Thus, our general conclusion that C8-PI(4,5)P2 concentrations influence the transitions between the burst and inter-burst states holds even if we have underestimated N.