Activity of TREK-2-like Channels in the Pyramidal Neurons of Rat Medial Prefrontal Cortex Depends on Cytoplasmic Calcium

Simple Summary The pyramidal neurons of rat prefrontal cortex express potassium channels identified as a non-canonical splice variant of the TREK-2 channel. The main function of TREK channels is to regulate the resting membrane potential. We showed that cytoplasmic Ca2+ upregulates the activity of TREK-2-like channels. Previous studies have indicated that the activation of TREK-2 channels is mediated by PI(4,5)P2, a polyanionic lipid in the inner leaflet of the plasma membrane. While TREK channels are believed to not be regulated by calcium, our work shows otherwise. We propose a model in which calcium ions enable the formation of PI(4,5)P2 nanoclusters, which stabilize active conformation of the channel. Abstract TREK-2-like channels in the pyramidal neurons of rat prefrontal cortex are characterized by a wide range of spontaneous activity—from very low to very high—independent of the membrane potential and the stimuli that are known to activate TREK-2 channels, such as temperature or membrane stretching. The aim of this study was to discover what factors are involved in high levels of TREK-2-like channel activity in these cells. Our research focused on the PI(4,5)P2-dependent mechanism of channel activity. Single-channel patch clamp recordings were performed on freshly dissociated pyramidal neurons of rat prefrontal cortexes in both the cell-attached and inside-out configurations. To evaluate the role of endogenous stimulants, the activity of the channels was recorded in the presence of a PI(4,5)P2 analogue (PI(4,5)P2DiC8) and Ca2+. Our research revealed that calcium ions are an important factor affecting TREK-2-like channel activity and kinetics. The observation that calcium participates in the activation of TREK-2-like channels is a new finding. We showed that PI(4,5)P2-dependent TREK-2 activity occurs when the conditions for PI(4,5)P2/Ca2+ nanocluster formation are met. We present a possible model explaining the mechanism of calcium action.


Introduction
The human prefrontal cortex is involved in a variety of cognitive functions [1]. The prefrontal cortex can be divided into two regions: the medial prefrontal cortex (mPFC) and the lateral prefrontal cortex [2]. Medial prefrontal cortex lesions leading to cognitive impairment have been associated with various human brain disorders, such as depression, anxiety disorders, schizophrenia, autism spectrum disorders, Alzheimer's disease, Parkinson's disease, and addiction [3]. Some of these pathological processes may involve two-pore domain potassium channels (K2P), which are thought to play a significant role in neuronal excitability and in the resting membrane potential [4].

Materials and Methods
The experimental procedures used in this study conform to institutional and international guidelines for the ethical use of animals in accordance with Directive 2010/63/EU of The European Parliament and of The Council of 22 September 2010 on the protection of animals used for scientific purposes. The methods used for sacrificing the animals were in accordance with Annex IV of the Directive. The experiments were performed on young, 20-day-old, male Wistar rats (WAG Cmd) obtained from a local animal house.

Immunofluorescence Staining
The anesthetized rats (sodium pentobarbital, 75 mg/kg, i.p.) were perfused with phosphate-buffered saline (PBS) and 4% paraformaldehyde in PBS (PFA). The brains were post fixed in PFA (4 • C) overnight, impregnated with sucrose (30% w/v in PBS, 4 • C), rapidly frozen in dry-ice-cold heptane, cut in cryotome (40 µm), and embedded and kept (−20 • C) in a cryoprotectant (30% glycerol, 30% ethylene glycol, and 0.02M PBS). For fluorescent staining, the cryoprotectant was washed with PBS and the brain slices were blocked in 5% normal goat serum in PBS with 0.01% Triton X-100 (NGST) and immersed overnight (4 • C) in rabbit anti-TREK2 primary antibody (Invitrogen, PA5-77608) solution in NGST. Next, the slices were washed with PBS with 0.01% Triton X-100 (PBST) and incubated overnight (4 • C) with goat anti-rabbit Alexa 568-conjugated secondary antibody (Invitrogen, A11011) solution in NGST. Furthermore, after washing, an analogical procedure was applied with a next pair of antibodies, i.e., mouse anti-NeuN primary antibody (Millipore, MAB377) and goat Alexa 488-conjugated anti-mouse secondary antibody (Invitrogen, A11001). Next, the slices were washed with PBST and mounted in Vectashield with a DAPI medium (Vector, catalogue number H-1200) [43]. Parallelly, the cerebellum tissue was processed in the same manner. The pattern of the signal in the cerebellum cortex, namely in the granular and molecular layers, was used to verify the specificity of the anti-TREK2 antibody. Signal of fluorescence was measured with Olympus Fluoview FV1000 confocal laser-scanning microscope and analysed with Fiji software [44]. The figures were prepared with Fiji and Office software.
Patch-clamp recordings of the single-channel currents were performed in the cellattached or inside-out configurations at room temperature. A low-pass Bessel filter of 5 kHz was applied during the recordings. The data were digitized, added onto a computer, with sampling frequencies of 10 or 100 kHz. The extracellular control solution contained KCl (130 mM); EGTA (0.3 mM); HEPES (10 mM); glucose (10 mM); CaCl 2 (0-2 mM); and in some experiments, paxilline (1 µM, Sigma-Aldrich, Poznan, Poland). The control Biology 2021, 10, 1119 4 of 18 solution was then exchanged for the experimental solution containing the tested substances: arachidonic acid (Sigma-Aldrich), PIP2DiC8 (Echelon Biosciences, Salt Lake City, UT, USA), neomycin (Sigma-Aldrich), m-3M3FBS (EMD Millipore Corp. Darmstadt, Germany), and thapsigargin (Tocris, Bio-Techne, Warsaw, Poland). The tested substance was applied by changing the bath solution, i.e., by changing the contents of the entire recording chamber (~0.6 mL), which lasted from about 1 min to about 2 min. The rate of solution exchange was about 1 mL/minute. The concentration of Ca 2+ in these experimental solutions was as follows: with arachidonic acid, 0 Ca 2+ ; PIP2DiC8, 0 or 0.1 mM Ca 2+ ; m-3M3FBS, 0.1 or 1.7 mM Ca 2+ ; and thapsigargin, 1.7 mM Ca 2+ . The concentration of Ca 2+ was estimated based on the concentration of EGTA and CaCl 2 . The control solutions for these experiments contained corresponding amounts of Ca 2+ . The pipette solution contained K acetate (125 mM), KCl (5 mM), HEPES (10 mM), CaCl 2 (2 mM), LaCl 3 (2.5 µM), penitrem A (15 nM, Tocris), and charybdotoxin (100 nM, Alomone Labs, Jerusalem, Israel ), and the last two compounds were added to the block BK channel. A junction potential of 6 mV was not corrected during the experiments.
In some experiments, the cells were pre-treated with BAPTA-AM for about 30 min. P open corresponding to the probability of opening all channels in the patch was evaluated with Clampfit (pClamp 10.6, Molecular Devices, San Jose, CA, USA). The calculation for the probability did not take the number of ion channels into consideration. The threshold of the opening transition was set at one-half of the unitary current. Open dwell times were calculated by fitting the probability density function (the sum of two exponential terms [45]) to open time histograms with the use of Clampfit. τ oi corresponds to the time constant of the ith component, P corresponds to its normalized area. Openings shorter than 50 µs were not included in the histograms. All results are shown as means ± SEM. Nonparametric tests (unpaired Mann-Whitney test or paired Wilcoxon test) or the t-test with or without Welch's correction were used to make comparisons between the two groups. To compare the means of three groups, we used one-way ANOVA followed by multiple comparisons tests: Sidak's or Bonferroni's (parametric test), or Dunn's (nonparametric test). Statistical analyses were performed with GraphPad Prism 7.00.

Role of Calcium in TREK-2-Like Channel Activation
We already showed that pyramidal neurons in the medial prefrontal cortex of rats express high-conductance TREK-2-like channels [36,46]. The presence of TREK-2 channels in pyramidal neurons was confirmed by immunofluorescent staining of PFC slices ( Figure 1).
Patch clamp experiments were performed on freshly dissociated pyramidal neurons from rat mPFC in "symmetrical" K + solutions. In such conditions, the cell membrane potential was close to 0 mV. In the cell-attached configuration, high-conductance potassium currents were observed in hyperpolarized and depolarized potentials (Figure 2A). In the cell-attached configuration in the presence of 1.7 mM Ca 2+ in the extracellular bath solution, P open was 0.989 ± 0.126 (n = 36) at 50 mV and 0.521 ± 0.087 (n = 28) at -50 mV (cells without TREK-2 like channel activity were excluded from the statistics). The channel was previously identified in our laboratory as a non-canonical splice variant of the TREK-2-like channel (first described by Gu et al. 2002) based on high conductance, weak rectification properties, membrane stretch, and temperature sensitivity and the inhibition by ruthenium red [36,47]. We confirmed that conductance depended on the membrane potential and magnesium presence in the pipette solution. In the cell-attached configuration, Mg 2+ present in the pipette solution reduced inward conductance from 221 ± 10 pS (n = 13, 0 mM Mg 2+ ) to 179 ± 7 pS (n = 23, 2 mM Mg 2+ ). The outward conductance decreased with increasing depolarization, but its value did not exceed that for inward currents. Figure 2A Patch clamp experiments were performed on freshly dissociated pyramidal neurons from rat mPFC in ''symmetrical" K+ solutions. In such conditions, the cell membrane potential was close to 0 mV. In the cell-attached configuration, high-conductance potassium currents were observed in hyperpolarized and depolarized potentials (Figure 2A). In the cell-attached configuration in the presence of 1.7 mM Ca2+ in the extracellular bath solution, Popen was 0.989  0.126 (n = 36) at 50 mV and 0.521  0.087 (n = 28) at -50 mV (cells without TREK-2 like channel activity were excluded from the statistics). The channel was previously identified in our laboratory as a non-canonical splice variant of the TREK-2like channel (first described by Gu et al. 2002) based on high conductance, weak rectification properties, membrane stretch, and temperature sensitivity and the inhibition by ruthenium red [36,47]. We confirmed that conductance depended on the membrane potential and magnesium presence in the pipette solution. In the cell-attached configuration, Mg2+ present in the pipette solution reduced inward conductance from 221  10 pS (n = 13, 0 mM Mg2+) to 179  7 pS (n = 23, 2 mM Mg2+). The outward conductance decreased with increasing depolarization, but its value did not exceed that for inward currents.  In many published studies, the high activity of TREK channels had to be induced by activating agents, whereas spontaneous activity of native TREK-2 channels was rarely reported [49]. Under our experimental conditions, high spontaneous activity of TREK-2-like channels was often observed. The spontaneous activity was observed with or without H89 pre-treatment. H89 was used to exclude the inhibitory effect of channel phosphorylation by kinase A [36]. TREK-2 is a thermo-and mechanosensitive channel controlled by various intracellular signalling pathways, including arachidonic acid (AA) and PI(4,5)P2. We confirmed on the excised patches that the activity of TREK-2-like channels was enhanced by the application of AA (10 µM) and PI(4,5)P2DiC8 (10 µM, a water-soluble analogue of PI(4,5)P2) to the cellular side of the patch ( Figure 3). Ion channels dependent on PI(4,5)P2 are inhibited by polycationic agents (e.g., neomycin), which act by screening the negative charges of PI(4,5)P2 [26,50,51]. We confirmed that neomycin (15 µg/mL) decreased the activity of TREK-2-like channels ( Figure 4) when applied to the cytoplasmic side of the membrane in excised patches. In many published studies, the high activity of TREK channels had to be induced by activating agents, whereas spontaneous activity of native TREK-2 channels was rarely reported [49]. Under our experimental conditions, high spontaneous activity of TREK-2-like channels was often observed. The spontaneous activity was observed with or without H89 pre-treatment. H89 was used to exclude the inhibitory effect of channel phosphorylation by kinase A [36]. TREK-2 is a thermo-and mechanosensitive channel controlled by various firmed on the excised patches that the activity of TREK-2-like channels was enhanced by the application of AA (10 μM) and PI(4,5)P2DiC8 (10 μM, a water-soluble analogue of PI(4,5)P2) to the cellular side of the patch (Figure 3). Ion channels dependent on PI(4,5)P2 are inhibited by polycationic agents (e.g., neomycin), which act by screening the negative charges of PI(4,5)P2 [26,50,51]. We confirmed that neomycin (15 μg/mL) decreased the activity of TREK-2-like channels ( Figure 4) when applied to the cytoplasmic side of the membrane in excised patches.   Phospholipase C cleaves PI(4,5)P2 to produce second messengers: IP3 and DAG. To further test whether the PI(4,5)P2-dependent pathway is involved in TREK-2-like channel Phospholipase C cleaves PI(4,5)P2 to produce second messengers: IP3 and DAG. To further test whether the PI(4,5)P2-dependent pathway is involved in TREK-2-like channel activity, we studied the effect of a phospholipase C activator m-3M3FBS. M-3M3FBS decreases the PI(4,5)P2 pool and activity of ion channels dependent on PI(4,5)P2 within a few hundred seconds [52,53]. We evaluated the changes in channel activity (P open ) over time in the presence of m-3M3FBS in a bath solution and compared them with changes in the activity in control conditions. P open in the control solution remained approximately unchanged during the recording period ( Figure 5), whereas the application of m-3M3FBS resulted in bimodal change in the channel activity. After~3 min in the presence of m-3M3FBS, P open increased, and then, after another period of~3 min, the activity of the channels significantly diminished. m-3M3FBS was shown to induce the release of Ca 2+ from intracellular stores [54]. When m-3M3FBS was used in the presence of thapsigargin (Th), no initial increase in P open was observed ( Figure 6). Thapsigargin blocks the ability of the cell to pump calcium into the endoplasmic reticula, which results in elevated cytosolic calcium and emptying of intracellular calcium stores. We observed that thapsigargin alone significantly increased the activity of TREK-2-like channels (P open ) when applied at high extracellular Ca 2+ concentrations (Figure 7). We concluded that the initial increase in P open induced by the application of m-3M3FBS is due to the increased level of cytoplasmic calcium, while the subsequent decrease in P open is due to the depletion of PI(4,5)P2. Therefore, we performed experiments to test the possibility that calcium increases the activity of TREK-2-like channels.    The impact of Ca2+ on the TREK-2 like channel activity was tested in the cell-attached and inside-out configurations. In the cell-attached configuration, Ca2+ applied extracellularly in the bath solution increased the Popen of TREK-2-like channels compared with experiments performed in the absence of Ca2+. The increase was statistically significant at 1.7 mM Ca2+ ( Figure 8B,C). A bath solution cannot directly affect the ion channel in the recorded patch in the cell-attached configuration, so the high activity of the TREK-2-like channel was a consequence of cytoplasmic factors. To test whether the effect depends on the intracellular calcium level, we measured the channel activity in the inside-out configuration. With 0 mM Ca2+, the TREK-2 like channels had low activity ( Figure 8A,D,E). The application of Ca2+ to the cytoplasmic side of the plasma membrane (0.1 mM or 1.7 mM) resulted in a significant increase in the mean Popen ( Figure 8A,D,E). The impact of Ca 2+ on the TREK-2 like channel activity was tested in the cell-attached and inside-out configurations. In the cell-attached configuration, Ca 2+ applied extracellularly in the bath solution increased the P open of TREK-2-like channels compared with experiments performed in the absence of Ca 2+ . The increase was statistically significant at 1.7 mM Ca 2+ (Figure 8B,C). A bath solution cannot directly affect the ion channel in the recorded patch in the cell-attached configuration, so the high activity of the TREK-2-like channel was a consequence of cytoplasmic factors. To test whether the effect depends on the intracellular calcium level, we measured the channel activity in the inside-out configuration. With 0 mM Ca 2+ , the TREK-2 like channels had low activity ( Figure 8A,D,E). The application of Ca 2+ to the cytoplasmic side of the plasma membrane (0.1 mM or 1.7 mM) resulted in a significant increase in the mean P open ( Figure 8A,D,E). Enhancement of the activity of TREK-2-like channels by PI(4,5)P2 required th ence of Ca2+ at the intracellular side of the plasma membrane (Figure 9). In the ments with no Ca2+, the activity of the recorded channels remained at very low when the inside-out patches were perfused with 10 μM PI(4,5)P2DiC8. The acti creased significantly when the 0.1 mM Ca2+ was added to the bath solution. Enhancement of the activity of TREK-2-like channels by PI(4,5)P2 required the presence of Ca 2+ at the intracellular side of the plasma membrane (Figure 9). In the experiments with no Ca 2+ , the activity of the recorded channels remained at very low levels when the inside-out patches were perfused with 10 µM PI(4,5)P2DiC8. The activity increased significantly when the 0.1 mM Ca 2+ was added to the bath solution.

Pattern of TREK-2-Like Channel Activity
Two modes of activity were characteristic for TREK-2-like channels. The TREK-2-like channel activity occurred either as bursts of well-resolved openings or as flickering activity with very fast closure kinetics. The two modes of activity had different voltage dependences: while well-resolved bursts of long openings were very often observed during depolarization, flickering was promoted by hyperpolarization ( Figure 10). Flickering often preceded the loss of activity. However, strong hyperpolarization facilitated the transition from the flickering state to the state of typical activity (Figure 2A: −75 mV). With increased hyperpolarization, the frequency of the flickering increased in each studied patch ( Figure 10B). The flickering state depended on the level of cytosolic Ca2+ ( Figure  11). In the absence of Ca2+ secured by BAPTA-AM, no flickering activity was present in any of the recorded patches ( Figure 11B, n = 6). In contrast, with thapsigargin in the bath solution, the flickering was predominant ( Figure 11A, n= 15).

Pattern of TREK-2-Like Channel Activity
Two modes of activity were characteristic for TREK-2-like channels. The TREK-2like channel activity occurred either as bursts of well-resolved openings or as flickering activity with very fast closure kinetics. The two modes of activity had different voltage dependences: while well-resolved bursts of long openings were very often observed during depolarization, flickering was promoted by hyperpolarization ( Figure 10). Flickering often preceded the loss of activity. However, strong hyperpolarization facilitated the transition from the flickering state to the state of typical activity (Figure 2A: −75 mV). With increased hyperpolarization, the frequency of the flickering increased in each studied patch ( Figure 10B). The flickering state depended on the level of cytosolic Ca 2+ (Figure 11). In the absence of Ca 2+ secured by BAPTA-AM, no flickering activity was present in any of the recorded patches ( Figure 11B, n = 6). In contrast, with thapsigargin in the bath solution, the flickering was predominant ( Figure 11A, n= 15).

Pattern of TREK-2-Like Channel Activity
Two modes of activity were characteristic for TREK-2-like channels. The TREK-2-like channel activity occurred either as bursts of well-resolved openings or as flickering activity with very fast closure kinetics. The two modes of activity had different voltage dependences: while well-resolved bursts of long openings were very often observed during depolarization, flickering was promoted by hyperpolarization ( Figure 10). Flickering often preceded the loss of activity. However, strong hyperpolarization facilitated the transition from the flickering state to the state of typical activity (Figure 2A: −75 mV). With increased hyperpolarization, the frequency of the flickering increased in each studied patch ( Figure 10B). The flickering state depended on the level of cytosolic Ca2+ ( Figure  11). In the absence of Ca2+ secured by BAPTA-AM, no flickering activity was present in any of the recorded patches ( Figure 11B, n = 6). In contrast, with thapsigargin in the bath solution, the flickering was predominant ( Figure 11A, n= 15).

Discussion
The main goal of this study was to understand how TREK-2-like channels in mPFC pyramidal neurons activate spontaneously in the absence of exogenous stimuli. We reasoned that the activity of the high-conductance potassium channel, preferentially representing the activity of a non-canonical splice variant of the TREK-2 channel [36], occurs at a substantial expense of the cell's energy and thus needs to be strictly regulated. All TREK channels are subject to complex regulation. The activation mechanisms of TREK channels are numerous and include mechanical, thermal, and chemical stimulation [18]. The mechanisms of TREK channel activation suggest that they play a neuroprotective role in ischemia of the central nervous system [55,56]. In such conditions, the stimuli activating TREK channels accumulate as arachidonic acid, and lysophospholipids are released in the ischemic focus, swelling occurs, and cell membranes are stretched as a consequence [20,57]. Activated by these stimuli, the TREK channels induce hyperpolarization of neuronal membranes, which contributes to a decrease in the energy demand of the neuron under unfavourable conditions. The activity of TREK channels is, therefore, an important element of neuronal bioenergetics.
Our research shows that the activity of TREK-2-like channels is dependent on cytoplasmic Ca2+. We rejected the possibility that Ca2+ alone is able to activate the channel because, in the presence of the PLC activator, Popen decreased ( Figure 5). The PLC activator diminishes the PI(4,5)P2 pool [46] and increases the cytoplasmic Ca2+ concentration, but the Ca2+ increase was insufficient to maintain the channel activity. TREK-2 channels are dependent on PI(4,5)P2; we therefore focused on the mechanism of TREK-2-like channel activation based on its interaction with PI(4,5)P2 [29,32,33,40]. In particular, we considered possible mechanisms involving both Ca2+ and PI(4,5)P2. When considering such mechanisms, it should be noted that multivalent cations, including Ca2+, interact with PI(4,5)P2, allowing them to self-aggregate. This leads to the formation of negatively charged domains, nanometer-scale PI(4,5)P2 clusters, where PI(4,5)P2 molecules are bridged by calcium ions. Calcium-induced PI(4,5)P2 clustering was studied by FRET, atomic force, and electron microscopy as well as by infrared spectroscopy and other methods [58][59][60].

Discussion
The main goal of this study was to understand how TREK-2-like channels in mPFC pyramidal neurons activate spontaneously in the absence of exogenous stimuli. We reasoned that the activity of the high-conductance potassium channel, preferentially representing the activity of a non-canonical splice variant of the TREK-2 channel [36], occurs at a substantial expense of the cell's energy and thus needs to be strictly regulated. All TREK channels are subject to complex regulation. The activation mechanisms of TREK channels are numerous and include mechanical, thermal, and chemical stimulation [18]. The mechanisms of TREK channel activation suggest that they play a neuroprotective role in ischemia of the central nervous system [55,56]. In such conditions, the stimuli activating TREK channels accumulate as arachidonic acid, and lysophospholipids are released in the ischemic focus, swelling occurs, and cell membranes are stretched as a consequence [20,57]. Activated by these stimuli, the TREK channels induce hyperpolarization of neuronal membranes, which contributes to a decrease in the energy demand of the neuron under unfavourable conditions. The activity of TREK channels is, therefore, an important element of neuronal bioenergetics.
Our research shows that the activity of TREK-2-like channels is dependent on cytoplasmic Ca 2+ . We rejected the possibility that Ca 2+ alone is able to activate the channel because, in the presence of the PLC activator, P open decreased ( Figure 5). The PLC activator diminishes the PI(4,5)P2 pool [46] and increases the cytoplasmic Ca 2+ concentration, but the Ca 2+ increase was insufficient to maintain the channel activity. TREK-2 channels are dependent on PI(4,5)P2; we therefore focused on the mechanism of TREK-2-like channel activation based on its interaction with PI(4,5)P2 [29,32,33,40]. In particular, we considered possible mechanisms involving both Ca 2+ and PI(4,5)P2. When considering such mechanisms, it should be noted that multivalent cations, including Ca 2+ , interact with PI(4,5)P2, allowing them to self-aggregate. This leads to the formation of negatively charged domains, nanometer-scale PI(4,5)P2 clusters, where PI(4,5)P2 molecules are bridged by calcium ions. Calcium-induced PI(4,5)P2 clustering was studied by FRET, atomic force, and electron microscopy as well as by infrared spectroscopy and other methods [58][59][60].
Our results indicate that PI(4,5)P2-dependent TREK-2 activity occurs when there are conditions for PI(4,5)P2/Ca 2+ nanocluster formation: TREK-2-like channel activity significantly increased when the presence of PI(4,5)P2 and Ca 2+ was secured ( Figure 9) and decreased in the presence of a PLC activator, polycations (such as neomycin), and BAPTA-AM (Figures 4 and 11B). We, therefore, speculate that the mechanism of calcium action is to enable the formation of PIP2 nanoclusters and that such calcium-induced nanoclusters facilitate the interaction of the TREK-2-like channel with the membrane, which results in channel activation ( Figure 12). Our finding that 100 µM Ca 2+ is sufficient to induce high activity in TREK-2-like channels (Figure 8) is important in view of the observation that, at Ca 2+ levels of 100 µM, PI(4,5)P2 is highly clustered [58]. Many channels appear to be both activated and inhibited by PI(4,5)P2, including TREK-1, TRPV1, K v , HCN, Ca v , and TRP [61]. However, to our knowledge, the involvement of PI(4,5)P2/Ca 2+ nanoclusters in the activation of ion channels has not been demonstrated so far; therefore, our research suggests a novel pathway for channel activation, which should, however, be confirmed by more detailed research. The observation that calcium participates in the activation of TREK-2-like channels is a new finding. openings had reduced amplitudes ( Figure 10B). The activity of TREK-2-like channels in the burst mode increased with depolarization (Figure 2), whereas in the flickering mode, it increased with hyperpolarization ( Figure 10B). The depolarization-induced increase in Popen of bursts could possibly be due to the interaction of calcium with the membrane, facilitated by depolarization. We speculate that the voltage dependence of the TREK-2like channel activity in burst mode is due to the electrostatic attraction of Ca2+ to the membrane when the membrane is depolarized and thus to the voltage-dependent PI(4,5)P2/Ca2+ nanocluster formation. Although they do not have a canonical voltagesensing domain, TREK channels show voltage-dependent activity [69]. The reason for this voltage dependency has been attributed to the voltage-dependent movement of K+ within the selectivity filter [70] or to the interaction of the C-terminus domain with the membrane [69]. Our suggestion that the voltage dependence of TREK-2 channel activity is due to the voltage dependence of nanocluster formation is a new contribution to studies on this phenomenon and agrees with the results of Maingret et al. [69]. Flickering (fast openings) occurred only under conditions of elevated calcium. Since flickering often preceded the loss of activity, we suggest that the flickering corresponds to a partially desensitized channel state, which precedes the state of full channel desensitization. Strong hyperpolarization (usually −75 mV) facilitated the transition from the flickering state to the state of typical activity (bursts,), suggesting that a partially desensitized channel can recover from desensitization during hyperpolarization. Desensitization of TREK-2 channels has not been previously reported. However, the PI(4,5)P2-induced inhibition of TREK-2 channels observed at elevated PI(4,5)P2 concentrations could possibly be another manifestation of channel desensitization [38].
Calcium-induced activation of TREK-2-like channels may be physiologically important in pathophysiological transient cellular hypercalcemia. It may reveal a novel calcium-dependent mechanism that prevents the neuron from becoming deleteriously overactive, e.g., it could prevent epileptiform activity [71,72] or activity in other pathological conditions

Conclusions
mPFC pyramidal neurons express high-conductance potassium channels with the characteristics of two-pore domain TREK-2 channels. These channels are regulated by Ca 2+ is an important intracellular second messenger involved in many signalling pathways. Below, we explain why we rejected other possible mechanisms of calcium action on the channel. Possible pathways for calcium interaction with ion channels include DAG kinase and PKC. Both kinases have been shown to be Ca-dependent [62,63]. The phosphorylation of DAG by DAG kinase leads to the production of phosphatidic acid, which is an activator of TREK channels. However, this pathway, while possible in cellattached experiments, is unlikely in inside-out experiments. We also reject the possibility that Ca 2+ acts via PKC activation because TREK-2 phosphorylation results in channel inhibition, which is in contrast with our experiments in which calcium presence resulted in increased channel activity.
The experiments showing that exogenous PI(4,5)P2 increases the activity of TREK-2 channels [26] could suggest that Ca 2+ acts via the stimulation of PI(4,5)P2 synthesis. The increase in the PI(4,5)P2 pool was observed after the stimulation of G q/11 -coupled muscarinic receptors [64]. The synthesis of PI(4,5)P2 involves two phosphatidylinositol kinases: (PI) 4-kinase and (PIP) 5-kinase. Ca 2+ stimulates (PI) 4-kinase indirectly via calmodulin-like neuronal calcium sensor 1 [65]. We cannot exclude that the increase in the PI(4,5)P2 pool by elevated cytoplasmic calcium could contribute to the observed increase in TREK-2-like channel activity in the experiments performed in a cell-attached configuration. However, we exclude such a possibility in inside-out experiments due to the fact that they were performed in the absence of ATP, which is a substrate for PI phosphorylation.
The calcium dependence of TREK-2 channel activity has not yet been reported in published studies. The effect of calcium on TREK-2 channels has been investigated in heterologous expressing systems using CHO cells, and those authors did not observe any significant effect of Ca 2+ in inside-out patches [66]. In contrast with these data, our research concerns the high-conductance channel, possibly representing the non-canonical splice variant of TREK-2, with a conductance much greater than that of the canonical isoform described in cited research [5]. Whether the effect of calcium on TREK-2-like channels is a specific feature of pyramidal neurons of mPFC or is a common feature of other cells requires further research, in particular, whether an isoform of the channel is crucial needs to be clarified.
Pyramidal mPFC neurons express the classic high-conductance potassium channel dependent on calcium (K BK ) [67]. To eliminate the possibility that the observed activity involves K BK channels, two blockers of these channels were used simultaneously (charybdotoxin or paxilline and penitrem A). Additionally, TREK-2-like channels and K BK channels have distinct kinetics. K BK channels are strongly voltage-dependent, and even at high calcium concentrations, a large difference in activity between the hyperpolarized and depolarized potentials is present [68]. TREK-2-like channels are weakly voltage-dependent, and their activity at hyperpolarized potentials is often of similar intensity as at depolarized potentials ( Figure 2).
The gating of TREK-2-like channels was polymodal. The activity of TREK-2-like channels occurred either as bursts of well-defined openings and closings or as rapid openings, the opening times of which were at the limit of the apparatus resolution; hence, some openings had reduced amplitudes ( Figure 10B). The activity of TREK-2-like channels in the burst mode increased with depolarization (Figure 2), whereas in the flickering mode, it increased with hyperpolarization ( Figure 10B). The depolarization-induced increase in P open of bursts could possibly be due to the interaction of calcium with the membrane, facilitated by depolarization. We speculate that the voltage dependence of the TREK-2-like channel activity in burst mode is due to the electrostatic attraction of Ca 2+ to the membrane when the membrane is depolarized and thus to the voltage-dependent PI(4,5)P2/Ca 2+ nanocluster formation. Although they do not have a canonical voltage-sensing domain, TREK channels show voltage-dependent activity [69]. The reason for this voltage dependency has been attributed to the voltage-dependent movement of K + within the selectivity filter [70] or to the interaction of the C-terminus domain with the membrane [69]. Our suggestion that the voltage dependence of TREK-2 channel activity is due to the voltage dependence of nanocluster formation is a new contribution to studies on this phenomenon and agrees with the results of Maingret et al. [69].
Flickering (fast openings) occurred only under conditions of elevated calcium. Since flickering often preceded the loss of activity, we suggest that the flickering corresponds to a partially desensitized channel state, which precedes the state of full channel desensitization. Strong hyperpolarization (usually −75 mV) facilitated the transition from the flickering state to the state of typical activity (bursts,), suggesting that a partially desensitized channel can recover from desensitization during hyperpolarization. Desensitization of TREK-2 channels has not been previously reported. However, the PI(4,5)P2-induced inhibition of TREK-2 channels observed at elevated PI(4,5)P2 concentrations could possibly be another manifestation of channel desensitization [38].
Calcium-induced activation of TREK-2-like channels may be physiologically important in pathophysiological transient cellular hypercalcemia. It may reveal a novel calciumdependent mechanism that prevents the neuron from becoming deleteriously overactive, e.g., it could prevent epileptiform activity [71,72] or activity in other pathological conditions

Conclusions
mPFC pyramidal neurons express high-conductance potassium channels with the characteristics of two-pore domain TREK-2 channels. These channels are regulated by various physical and chemical factors. Our research indicates that cytoplasmic calcium is