Contribution of near-threshold currents to intrinsic oscillatory activity in rat medial entorhinal cortex layer II stellate cells

Abstract

The temporal lobe is well known for its oscillatory activity associated with exploration, navigation, and learning. Intrinsic membrane potential oscillations (MPOs) and resonance of stellate cells (SCs) in layer II of the entorhinal cortex are thought to contribute to network oscillations and thereby to the encoding of spatial information. Generation of both MPOs and resonance relies on the expression of specific voltage-dependent ion currents such as the hyperpolarization-activated cation current (I_H), the persistent sodium current (I_NaP), and the noninactivating muscarine-modulated potassium current (I_M). However, the differential contributions of these currents remain a matter of debate. We therefore examined how they modify neuronal excitability near threshold and generation of near-threshold MPOs and resonance in vitro. We found that resonance mainly relied on I_H and was reduced by I_H blockers and modulated by cAMP and an I_M enhancer but that neither of the currents exhibited full control over MPOs in these cells. As previously reported, I_H controlled a theta-frequency component of MPOs such that blockade of I_H resulted in fewer regular oscillations that retained low-frequency components and high peak amplitude. However, pharmacological inhibition and augmentation of I_M also affected MPO frequencies and amplitudes. In contrast to other cell types, inhibition of I_NaP did not result in suppression of MPOs but only in a moderation of their properties. We reproduced the experimentally observed effects in a single-compartment stochastic model of SCs, providing further insight into the interactions between different ionic conductances.

the entorhinal cortex (EC) plays an important role in the formation and retrieval of declarative (Squire and Zola-Morgan 1991) and spatial memories (Steffenach et al. 2005). As a key gateway in corticohippocampal communication, the EC receives inputs from the rhinal cortices and subicular regions and projects to the hippocampus as well as to the frontal cortex. The EC is known for its prominent oscillatory activity, and many individual neurons discharge in relation to the phase of hippocampal theta oscillations (Alonso and García-Austt 1987; Chrobak et al. 2000). The EC is also capable of sustaining theta oscillations in response to sensory stimulation or to pharmacological treatments enhancing cholinergic transmission (Chrobak et al. 2000; Gloveli et al. 1999; Klink and Alonso 1997; for review see Dickson et al. 2000a). The EC contains several types of neurons, including stellate cells (SCs) in layer II (Alonso and Llinás 1989; Dickson et al. 2000b; Klink and Alonso 1993), which display fluctuations of the membrane potential, usually in the theta-frequency range, termed membrane potential oscillations (MPOs) (Alonso and Llinás 1989). It is believed that intrinsic oscillatory properties of layer II SCs are crucial for the transmission of spatial information from the medial EC (mEC) to the dentate gyrus (Gloveli et al. 1997), although a clear relationship between in vitro intrinsic membrane potential fluctuations and in vivo network theta-frequency activity remains to be firmly established. This hypothesis is further supported by the existence of a dorsoventral gradient in the mEC, with SCs gradually changing their oscillatory frequency (Boehlen et al. 2010; Garden et al. 2008; Giocomo et al. 2007) in parallel to the size of their spatial receptive fields (Brun et al. 2008; Hafting et al. 2005).

Oscillatory phenomena in individual neurons, such as intrinsic MPOs and resonance, are often found together in particular cell types and are thought to rely on specific but varying underlying ionic mechanisms (for review see Hutcheon and Yarom 2000). According to established models, oscillatory behavior in SCs is thought to depend on the expression of voltage-gated ion channels giving rise to the H-current (I_H), the persistent sodium current (I_NaP) (Alonso and Llinás 1989; Dickson et al. 2000b; White et al. 1998), and possibly the M-current (I_M) (Heys et al. 2010; but see Heys and Hasselmo 2012). Some more recent findings suggest, however, that our understanding of the contributions of individual current to either MPOs or resonance could be incomplete. Genetic deletion of HCN1 channels, for instance, leads to a pronounced reduction of I_H without abolishing perithreshold MPOs (Nolan et al. 2007), and modeling work suggests that MPOs could be sustained without I_H (Dudman and Nolan 2009; White et al. 1998). Furthermore, I_H-dependent resonance decreases as SCs depolarize (Boehlen et al. 2010; Nolan et al. 2007), as expected for I_H activation characteristics and reversal potential. It is therefore tempting to speculate that near the action potential (AP) threshold, other ionic conductances may compensate for the reduced contribution of I_H to oscillatory activity in SCs. I_M represents one such alternative because it contributes to resonance in hippocampal pyramidal cells (Hu et al. 2002), but its contribution to MPOs and resonance in SCs is not yet precisely known. Finally, the essential role of I_NaP in sustaining oscillatory phenomena is well documented for many neurons (for review see Hutcheon and Yarom 2000). However, the majority of data in regard to SCs were obtained with the sodium channel blocker tetrodotoxin (TTX), which is per se not selective for persistent over transient sodium currents. TTX inhibits MPOs in SCs (Alonso and Llinás 1989). The predominant blockade of I_NaP and comparison with TTX should therefore help identify the specific contribution of I_NaP to resonance and MPOs in SCs.

For these reasons we examined the contributions of I_M, I_H, and I_NaP to the generation of MPOs and resonance in SCs of adult rats by using sharp microelectrode and whole cell patch-clamp recordings. Both widely used approaches have distinct disadvantages relevant to this study. In whole cell patch-clamp recordings the cytosol is dialyzed, potentially disrupting regulatory signaling cascades that control I_M, I_H, and I_NaP in intact cells. Sharp microelectrodes, on the other hand, introduce a nonspecific leak conductance, possibly affecting measurements of membrane time constants and input resistances (Spruston and Johnston 1992). Although some of the disadvantages associated with the whole cell patch-clamp configuration could be reduced by perforated patch clamp (Pastoll et al. 2012), considerable differences in measurements of, for instance, resting potentials and input resistances between sharp microelectrode and patch-clamp recordings remain (Boehlen et al. 2010; Pastoll et al. 2012). Therefore, data were obtained using both approaches in most cases to avoid potential biases introduced by the recording technique. The experimental results were complemented by simulations of MPOs in SC using a comprehensive single-compartment stochastic cell model (Dudman and Nolan 2009) with the addition of a stochastic I_M.

MATERIAL AND METHODS

Animals and slice preparation.

All protocols were approved and all experiments were performed according to regulations of the European Commission, the Berlin Animal Ethics Committee Berlin (T0068/02), and UK Home Office procedures. Slices were prepared and recorded from as described previously (Boehlen et al. 2009, 2010, 2011). In brief, Wistar rats (patch-clamp recordings, 5–8 wk; sharp microelectrode recordings, 10–14 wk) of either sex were anesthetized (ether or halothane), their brains were removed, and 400-μm slices were cut horizontally (vibratome, NVSLM1; Campden Instruments, Loughborough, UK). The slices were maintained submerged for at least 1 h at room temperature in a holding chamber containing artificial cerebrospinal fluid (ACSF) composed of (in mM) 129 NaCl, 21 NaHCO₃, 3 KCl, 1.6 CaCl₂, 1.8 MgSO₄, 1.25 NaH₂PO₄, and 10 glucose (saturated with 95% O₂-5% CO₂); pH was adjusted to 7.3 (KOH) before transfer to a recording chamber at 34 ± 1°C perfused at 1.8–2.4 ml/min.

Recording solutions.

Patch pipettes (5–7 MΩ, PC-10; Narishige, London, UK) were filled with an intracellular solution containing (in mM) 140 K-gluconate, 2 MgCl₂, 10 phosphocreatine, 2 Na₂ATP, 0.4 NaGTP, and 10 HEPES; pH was adjusted to 7.3 (KOH). Sharp glass micropipettes (75–85 MΩ) were filled with 2 M K-acetate. All pharmacological agents were applied via continuous bath perfusion: 8-bromoadenosine-3′,5′-cyclic monophosphate sodium salt (8-bromo-cAMP; 1 mM; Sigma-Aldrich), CsCl (Cs⁺; 1 mM; Sigma-Aldrich), 4-chlor-N-(6-chlor-pyridin-3-yl)-benzamid (ICAGEN-110381; 10 μM; Elbion, Radebeul, Germany), losigamone (200 μM; Dr. Willmar Schwabe Arzneimittel, Karlsruhe, Germany), [2-amino-4-(4-fluoro-benzylamino)-phenyl]-carbamic acid ethyl ester (retigabine; 1 μM; Elbion), TTX (0.1 μM; Tocris Bioscience, Bristol, UK), 10,10-bis(4-pyridinylmethyl)-9(10H)-anthracenone dihydrochloride (XE991; 10 μM; Tocris Bioscience), and 4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidinium chloride (ZD7288; 20 μM; Tocris Bioscience). ICAGEN-110381 and retigabine were first dissolved in DMSO and diluted in ACSF to their final concentration (final DMSO concentration ≤0.1%), whereas the other drugs were dissolved in water. In whole cell recordings excitatory and inhibitory synaptic transmission was blocked by supplementing the ACSF with the NMDA receptor antagonist dl-2-amino-5-phosphonovalerate (dl-APV; 60 μM), the AMPA/kainate receptor antagonist 6,7-dinitroquinoxaline-2,3-dione (DNQX; 10 μM), and the GABA receptor antagonists SR-95531 hydrobromide (5 μM) or bicuculline (5 μM). DNQX and SR-95531 hydrobromide were purchased from Tocris Bioscience. Riluzole, phenytoin, and dl-APV were obtained from Sigma-Aldrich.

Data acquisition and analyses.

For patch-clamp recordings, cells were visualized using an upright microscope equipped with a ×40 water-immersion objective. Recordings were obtained from layer II SCs in the mEC using a Multiclamp 700B amplifier (Axon Instruments, Foster City, CA). Signals were filtered at 3 kHz for current-clamp recordings and at 10 kHz for voltage-clamp recordings, digitized at a sampling frequency of 10–100 kHz, and acquired using Clampex 9.0 software (Molecular Devices, Sunnyvale, CA). Bridge balance was set using the “Auto” function of the Multiclamp 700B and verified several times during the recording session. The liquid junction potential was not compensated for. For sharp microelectrode recordings data were amplified (NeroData IR 183; National Instruments), low-pass filtered at 3 kHz, and digitized with an input-output card (DAQ card Al16E4; National Instruments) at a sampling rate of 8 kHz. LabView (National Instruments) was used for the generation of stimuli and data acquisition.

SCs obtained by patch-clamp recordings fulfilling the following criteria were considered acceptable for further analysis: a stable membrane potential less than −50 mV, input resistance >20 MΩ, overshooting APs and an access resistance <25 MΩ. The input and access resistances were calculated from the current response to 200-ms-long voltage steps of −10 mV at a holding potential of −60 mV. The average access resistance of all analyzed cells was 15.9 ± 0.6 MΩ (n = 51). To reduce variability caused by the ventral-dorsal gradient of cell properties, all recordings were obtained in the middle of mEC: 3.6–4.6 mm (interaural) from the ventral surface.

The same experimental conditions using potassium-based intracellular solutions (see above) were used for characterization of I_NaP inhibitors in voltage clamp (see Figs. 5 and 6) to ensure that results are comparable to data obtained in current-clamp mode and to enable cell type identification based on electrophysiological properties. We purposefully avoided any changes in recording temperature, recording solution, and additions of other inhibitors (for a detailed discussion of experimental conditions see Hu et al. 2002). The measured I_NaP kinetic values may therefore deviate from those previously published (Magistretti and Alonso, 1999).

Fig. 5.

Pharmacological modulation of persistent sodium current (I_NaP) near spike threshold. A: sample current responses to voltage steps from a holding potential of −70 mV to −80 to −40 mV in control, after application of losigamone (200 μM) and subsequent addition of TTX (1 μM) to fully block sodium channels. The current levels at −40 mV before and after application of losigamone are indicated by the dashed line. The positive shift is consistent with the blockade of a persistent inward current by losigamone. B: the change of the current profile induced by losigamone (n = 6) and losigamone + TTX (n = 5) compared with control was determined for each voltage. It was significantly affected by losigamone near spike threshold (−45 and −40 mV, P = 0.024, paired Student's t-test throughout), and further addition of TTX only had an insignificant effect (P = 0.17, n = 5). C: 10 μM riluzole also affected near-threshold currents (P = 0.032, n = 5), and addition of TTX had no significant effect (P = 0.28, n = 3). D: similarly, 100 μM phenytoin modified currents near threshold (P = 0.025, n = 5), as did addition of TTX (P = 0.032, n = 5). E: to compare the 3 substances, their effects on near-threshold currents are expressed as percentages of the effect of TTX. Losigamone inhibited 82 ± 6.0% (n = 5) of TTX-sensitive currents, riluzole inhibited 71.8 ± 18.8% (n = 3), and phenytoin inhibited 43.3 ± 6.3% (n = 4). Values are means ± SE. F: modulation of transiently active sodium channels was investigated by recording and analyzing the first action current evoked by a step voltage command. Sample action currents are shown in control conditions and after sequential application of losigamone (200 μM) and then losigamone + TTX (1 μM). Action currents were not significantly reduced by losigamone (P = 0.26, n = 6, paired Student's t-test) but were fully blocked by TTX, indicating that transiently active sodium channels are largely unaffected by losigamone.

Fig. 6.

Characterization of I_NaP. A: in SCs a prominent I_NaP could be evoked by delivering slow voltage ramps (30 mV/s). The ramp-induced current was partially blocked by losigamone and blocked by TTX. B: application of the I_NaP inhibitors losigamone, phenytoin, and riluzole shifted activation of voltage ramp-induced currents to more positive potentials. Values are means ± SE. C: we calculated the predicted window current for each cell as a product of activation of fast sodium current (dashed line; V_1/2 = 19.7 mV, k = −3.2) and steady-state inactivation (dotted line: V_1/2 = 58.2 mV, k = 5.0). The values were not different from those previously reported for SCs (Magistretti and Alonso 1999). G_NaTW, transient sodium current window conductance. D: TTX-sensitive currents (activation curve is shown as black dashed line; V_1/2 = 42.2 mV, k = −3.9) were different from a window current. In contrast, the current remaining after application of losigamone sodium current (black solid line; losigamone-TTX) was in the range predicted for the window current (gray solid line). Cell capacitance was evaluated from hyperpolarizing pulses at −50, −60 mV from on and off transients. The area under an individual transient was integrated. The total cell capacitance determined in this way ranged from 9–13 pF and was not different from that previously reported (Eder and Heinemann 1994). The average cell capacitance was 11.7 ± 2.3 pF (n = 10). The cell surface area was then estimated by assuming a specific membrane capacitance of 1 pF/cm². G_NaP, persistent sodium current window conductance. E: sodium channel-dependent noise was estimated from 1-s-long depolarizing pulses as the standard deviation of the steady-state current at the end of the pulse and displayed as a function of membrane voltage for control cells (open circles) and in the presence of losigamone (gray circles) and TTX (black triangles). F: application of losigamone reduced current noise in the voltage range where MPOs normally occur. Values are means ± SE.

Off-line data analyses were performed using Clampfit (Molecular Devices, Sunnyvale, CA), Excel (Microsoft, Redmond, WA), and custom software written in Matlab (version 7.4; The MathWorks). The discharge behavior, membrane time constant, rheobase, sag potential, time course of the sag potential (sag-tau), and AP parameters, including analysis of afterpotentials, were estimated from the response of the cell to a square current pulse of 500 ms ranging from −400 to 400 pA in 10-pA steps (for details see Boehlen et al. 2010). The AP parameters were estimated from the first spike elicited by the rheobase stimulus. The intrinsic resonance of SCs was studied using a sinusoidal current injection (5 repetitions) with constant peak-to-peak amplitude and linearly increasing frequency (0–20 Hz, 30 s) at different membrane potentials (hyperpolarized, ∼ −76 mV; resting; depolarized, approximately −52 mV) as described previously (Boehlen et al. 2010; Hutcheon and Yarom 2000; Puil et al. 1986). The input frequency corresponding to the highest impedance was defined as the resonance frequency. The amplitude (Q value) of the resonance was determined as the ratio of the peak impedance to the impedance at zero frequency, and the D value as the ratio of the impedance at zero frequency to the impedance at 20 Hz.

The dominant frequency of MPOs at near-threshold (evoked by constant current injection) was determined from at least 2 s of data and defined as the frequency with the highest power in the windowed Fourier power spectra (a running window of 950 ms was smoothed by a Hanning function, with a window overlap of 500 ms) between 1 and 15 Hz (for details see Erchova et al. 2004). This method, although useful for extracting information about frequencies, ignores phase relationship between different components and does not provide accurate information regarding time-frequency localization, because it imposes a time window and aliases high- and low-frequency components that do not fall within the frequency range of the window. Temporal autocorrelation analysis of MPOs improves analysis of periodic signals that deviate in shape from an ideal sinusoid and preserves information on phase relationship between frequency components. The normalized autocorrelogram was calculated from the same data set as before (with a 1-s window and 1.25-ms bin width, mean value of the signal subtracted). The time interval between the central and first peak was used as an estimate for the dominant frequency that was, however, very close to the values estimated from the power spectra. The ratio between the magnitudes of the first and second side peaks was called “relative decay” λ and served as a measure for the internal coherence of oscillations (Stenkamp et al. 2001). In autocorrelation analyses “white” noise in the signal is revealed as a sharp narrow peak at zero lag, whereas “colored” noise manifests itself in a broad central peak and sometimes in additional valleys (also see Dodson et al. 2011).

We defined the MPO amplitude as a measure of how far a neuron's membrane potential deviated from the baseline. In general the amplitude of complex oscillatory signal is a function of all its frequencies components and their phase relationship; its estimation from the power spectra and autocorrelations is not straightforward. For these reasons we quantified MPO amplitudes by calculating the standard deviation of the membrane voltage, termed average MPO amplitude, and the maximum MPO amplitude, i.e., the difference between maximum voltage and the baseline within the analyzed period. Although these conservative measures are potentially contaminated by a small amount of instrumental and other noise (recording baseline, standard deviation 0.09 ± 0.0091 mV, n = 12), they do not make assumptions about the temporal structure of the underlying signal. We also provide the quantitative values for the amplitude of the dominant frequency peak in the power spectra. Examples of how MPO frequency spectra and autocorrelation functions are affected by pharmacological interventions are given in figures and quantified in the text.

Statistical data are reported as means ± SE, with n being the number of neurons studied. Paired data were tested for statistical significance using the paired Student's t-test. Otherwise, ANOVA with post hoc Tukey's honestly significant difference was used unless stated differently (Origin 6.0; OriginLab, Northampton, MA).

RESULTS

Recordings were obtained from layer II SCs in the mEC under whole cell patch-clamp conditions (n = 66) and with sharp microelectrodes (n = 26). Measurements obtained using sharp microelectrodes had in general lower input resistance and faster time constants compared with patch-clamp recordings. The basic cell characteristics before and after pharmacological manipulations are summarized in Tables 1–3.

Table 1.

Effects of the H-current blocker ZD7288, Cs⁺, and 8-bromo-cAMP on somatic passive and active properties in layer II stellate cells

Cell Properties	Control (Patch)	ZD7288 (Patch)	Control (Sharp)	Cs+ (Sharp)	Control (Sharp)	8-Bromo-cAMP (Sharp)
RMP, mV	−61.4 ± 0.9	−76.1 ± 1.7‡ (9)	−65.8 ± 0.5	−68.8 ± 1.1* (8)	−64.6 ± 0.8	−61.9 ± 0.7* (7)
Rinput, MΩ	53.1 ± 5.1	123.6 ± 10.2‡ (9)	31.7 ± 4.1	40.3 ± 4.7* (8)	31.9 ± 4.8	27.7 ± 4.9† (7)
Time constant at −100 pA, ms	11.7 ± 0.8	20.9 ± 1.6‡ (9)	11.9 ± 1.1	12.9 ± 1.3 (8)	10.6 ± 0.6	11.5 ± 0.8
Voltage threshold, mV	−43.1 ± 0.4	−40.9 ± 0.6† (9)	−54.3 ± 0.8	−54.9 ± 1.6 (8)	−53.9 ± 1.0	−49.6 ± 1.5* (7)
Rheobase, pA	181.1 ± 24.5	235.6 ± 29.0 (9)	172.8 ± 28.7	233.5 ± 26.0 (8)	186.7 ± 33.9	283.7 ± 54.6† (7)
Spike latency, ms	111.6 ± 29.0	321.2 ± 41.8† (9)	18.1 ± 1.3	13.0 ± 1.4* (8)	20.7 ± 3.3	13.16 ± 2.1
Sag-tau, ms	23.4 ± 2.9	nd	21.2 ± 1.4	40.1 ± 4.2† (8)	21.4 ± 2.0	17.8 ± 2.6† (7)
Sag ratio at −400 pA	0.07 ± 0.01	0.95 ± 0.01‡ (9)	0.065 ± 0.03	0.96 ± 0.01‡ (8)	0.08 ± 0.02	0.08 ± 0.03 (7)
Sag ratio at −200 pA	0.7 ± 0.1	0.98 ± 0.15‡ (9)
fAHP amplitude, mV	−7.6 ± 0.8	−3.9 ± 1.1 (9)	−10.0 ± 0.6	11.0 ± 0.6 (8)	−9.4 ± 0.4	−10.4 ± 0.7 (7)
DAP amplitude, mV	1.3 ± 0.3	0.2 ± 0.1† (9)	0.6 ± 0.4	1.7 ± 1.5 (2)	0.7 ± 0.4	2.7 ± 0.5 (3)
mAHP amplitude, mV	−10.0 ± 0.6	−10.7 ± 0.6‡ (9)	−5.7 ± 1.2	−5.5 ± 0.7	−4.6 ± 0.4	−4.7 ± 0.7
mAHP amplitude DAP, mV	−3.3 ± 0.6	−4.5 ± 1.0 (6)
mAHP duration, ms	71 ± 13	133 ± 27* (6)	26.2 ± 1.5	21.6 ± 0.6 (8)	26.7 ± 2.4	20.2 ± 2.4* (7)
AP amplitude. mV	75.4 ± 2.8	67.0 ± 3.7† (5)	72.1 ± 1.0	70.6 ± 1.0	71.7 ± 1.0	69.7 ± 1.0
AP time to peak, ms	0.58 ± 0.02	0.54 ± 0.02 (5)
AP half-width, ms	0.70 ± 0.03	0.82 ± 0.06* (5)
AP voltage peak, mV	32.2 ± 2.6	26.0 ± 3.8* (5)
No. of spikes
At 100 pA	0.1 ± 0.1	0 ± 0 (9)	0.0 ± 0.0	0.0 ± 0.0	0.0 ± 0.0	0.0 ± 0.0
At 200 Pa	3.3 ± 0.9	0.6 ± 0.3* (9)	0.4 ± 0.3	0.4 ± 0.3	0.0 ± 0.0	0.0 ± 0.0
At 300 pA	7.7 ± 1.5	3.6 ± 0.7* (9)	2.0 ± 0.5	1.2 ± 0.4	1.3 ± 0.3	0.3 ± 0.3
At 400 pA	11.4 ± 1.5	6.0 ± 0.9† (9)	4.0 ± 0.6	3.4 ± 0.6	3.0 ± 0.6	0.7 ± 0.7

Values are means ± SE (n = no. of observations) for effects of the H-current blocker ZD7288 (20 μM), cesium (Cs⁺; 1 mM), and the second messenger cyclic adenosine monophosphate (8-bromo-cAMP; 1 mM) on somatic passive and active properties in layer II stellate cells. Data were obtained using either whole cell patch-clamp (patch) or sharp microelectrode (sharp) recording techniques. AP, action potential; DAP, depolarizing afterpotential; fAHP, fast afterhyperpolarization; mAHP, medium afterhyperpolarization; R_input, input resistance; RMP, resting membrane potential; sag, depolarization after an initial hyperpolarization.

^*P < 0.05;

^†P < 0.01;

^‡P < 0.001; nd, not detectable.

Table 2.

Effects of the persistent sodium blocker losigamone and tetrodotoxin on somatic passive and active properties in layer II stellate cells

Cell Properties	Control (Patch)	Losigamone (Patch)	Control (Sharp)	TTX (Sharp)
RMP, mV	−58.8 ± 0.6	−58.0 ± 1.0 (11)	−65.0 ± 0.9	−64.9 ± 0.8 (5)
Rinput, MΩ	−47.1 ± 2.7	−47.0 ± 3.2 (11)	29.4 ± 3.4	26.0 ± 2.6 (5)
Time constant at −100 pA, ms	11.5 ± 0.7	13.9 ± 1.1† (11)	8.3 ± 1.5	9.1 ± 0.6 (5)
Voltage threshold, mV	−42.1 ± 0.8	−36.3 ± 1.4† (11)	−52.4 ± 0.7	—
Rheobase, pA	166.4 ± 19.2	248.2 ± 30.0† (11)	170.0 ± 33.5	—
Spike latency, ms	58.3 ± 5.8	48.6 ± 6.5 (11)	28.6 ± 2.9	—
fAHP amplitude, mV	−7.0 ± 0.5	−7.3 ± 0.6 (11)	−9.2 ± 1.0	—
DAP amplitude, mV	1.7 ± 0.4	0.9 ± 0.3* (11)	1.3 ± 0.2	—
mAHP amplitude, mV	−8.8 ± 0.4	−8.6 ± 0.9 (11)	−7.4 ± 1.3	—
mAHP amplitude DAP, mV	−3.6 ± 0.3	−2.3 ± 0.5† (11)	−2.34 ± 0.2	—
mAHP duration, ms	70.0 ± 7.5	58.8 ± 10.2 (11)	32.3 ± 2.9	—
AP amplitude, mV	75.7 ± 1.8	69.4 ± 2* (8)	73.4 ± 1.4	—
AP time to peak, ms	0.65 ± 0.03	0.62 ± 0.01 (8)	—	—
AP half-width, ms	0.77 ± 0.03	0.80 ± 0.03 (8)	—	—
AP voltage peak, mV	32.8 ± 2.1	30.7 ± 2.3 (8)	—	—
No. of spikes
At 100 pA	0.3 ± 0.2	0 ± 0 (11)	0.4 ± 0.3	—
At 200 pA	3.3 ± 0.9	0.6 ± 0.4† (11)	1.2 ± 0.4	—
At 300 pA	7.4 ± 1.0	1.8 ± 0.5‡ (11)	2.2 ± 0.4	—
At 400 pA	10.9 ± 0.8	2.9 ± 0.6‡ (11)	4.8 ± 0.9	—

Values are means ± SE (n = no. of observations) for effects of the persistent sodium blocker losigamone (200 μM) and tetrodotoxin (TTX; 0.1 μM) on somatic passive and active properties in layer II stellate cells.

^*P < 0.05;

^†P < 0.01;

^‡P < 0.001.

Table 3.

Effects of the Kv7/KCNQ/M-channel activators ICAGEN-110381 and retigabine and Kv7/KCNQ/M-channel blocker XE991 on somatic passive and active properties in layer II stellate cells

Cell properties	Control	ICA	Control	RTG	Control	XE991
RMP, mV	−59.0 ± 0.9	−60.0 ± 1.4* (11)	−57.6 ± 1.1	−60.8 ± 1.4† (8)	−60.4 ± 0.8	−57.6 ± 1.0† (10)
Rinput, MΩ	50.5 ± 3.5	42.3 ± 2.2* (12)	50.5 ± 2.7	52.8 ± 3.3 (8)	48.3 ± 3.9	45.7 ± 3.9 (10)
Time constant at −100 pA, ms	13.4 ± 1.0	13.9 ± 1 (11)	12.5 ± 1.0	10.8 ± 1.4† (8)	12.3 ± 0.5	14.0 ± 0.7† (10)
Voltage threshold, mV	−42.2 ± 0.9	−37.1 ± 1.3‡ (12)	−42.5 ± 0.6	−37.7 ± 2.4 (8)	−43.4 ± 0.6	−41.3 ± 1.1 (10)
Rheobase, pA	153.3 ± 19.2	330.2 ± 29.9‡ (12)	135.0 ± 11.5	271.3 ± 42.3† (8)	155.0 ± 19.7	163.0 ± 23.4 (10)
Spike latency, ms	60.1 ± 3.7	51.8 ± 4.7 (11)	69.1 ± 10.7	59.3 ± 17.5† (8)	59.7 ± 5.5	118.6 ± 23.0* (10)
fAHP amplitude, mV	−7.2 ± 0.6	−7.0 ± 0.8 (12)	−6.9 ± 0.7	−7.5 ± 0.3 (6)	−7.0 ± 0.4	−4.0 ± 0.4‡ (10)
DAP amplitude, mV	1.6 ± 0.3	0.6 ± 0.3‡ (12)	2.4 ± 0.5	1.5 ± 0.2 (6)	1.5 ± 0.3	0.6 ± 0.2‡ (10)
mAHP amplitude (mV)	−8.6 ± 0.4	−10.7 ± 0.7† (12)	−8.9 ± 0.5	−9.6 ± 0.8 (7)	−8.6 ± 0.5	−7.8 ± 0.7 (10)
mAHP amplitude DAP, mV	−3.7 ± 0.5	−3.9 ± 0.9 (12)	−4.4 ± 0.3	−3.5 ± 2.0 (6)	−3.8 ± 0.5	−4.4 ± 0.4 (10)
mAHP duration, ms	75.7 ± 9.5	121.14 ± 26.1 (8)	80.6 ± 16.3	109.6 ± 67.9 (3)	71.3 ± 8.5	113.9 ± 12.7* (7)
AP amplitude, mV	72.8 ± 2.4	68.3 ± 2.2* (12)	73.7 ± 1.0	65.9 ± 1.1† (7)	79.2 ± 2.4	73.9 ± 2.2 (7)
AP time to peak, ms	0.67 ± 0.02	0.68 ± 0.04 (12)	0.65 ± 0.02	0.72 ± 0.01† (7)	0.66 ± 0.02	0.73 ± 0.04 (7)
AP half-width, ms	0.86 ± 0.02	0.94 ± 0.04* (12)	0.89 ± 0.02	0.94 ± 0.03* (7)	0.84 ± 0.02	0.93 ± 0.02 (7)
AP voltage peak, mV	30.5 ± 2.0	31.4 ± 1.8 (12)	30.8 ± 2.0	26.2 ± 1.4* (7)	36.1 ± 2.4	32.3 ± 2.5 (7)
No. of spikes
At 100 pA	0.7 ± 0.4	0 ± 0 (12)	0.4 ± 0.3	0 ± 0 (8)	0.4 ± 0.4	0.7 ± 0.5 (10)
At 200 pA	3.6 ± 0.9	0.1 ± 0.1† (12)	3.8 ± 0.9	1.0 ± 0.7* (8)	4.3 ± 1.1	4.4 ± 1.2 (10)
At 300 pA	6.8 ± 1.0	0.8 ± 0.3‡ (12)	8.4 ± 0.6	2.6 ± 1.1† (8)	8.9 ± 1.4	7.9 ± 1.4 (10)
At 400 pA	10.2 ± 1.0	1.5 ± 0.5‡ (11)	11.4 ± 0.6	4.0 ± 1.7† (8)	12.4 ± 1.4	10.9 ± 1.3 (10)

Values are means ± SE (n = no. of observations) for effects of the Kv7/KCNQ/M-channel activators ICAGEN-110381 (ICA; 10 μM) and retigabine (RTG; 1 μM) and the Kv7/KCNQ/M-channel blocker XE991 (10 μM) on somatic passive and active properties in layer II stellate cells. All data were obtained using the patch-clamp technique.

^*P < 0.05;

^†P < 0.01;

^‡P < 0.001.

To establish the baseline for the pharmacological manipulations, we first investigated voltage-dependent resonance and MPO properties of SCs and compared the results from sharp microelectrode and patch-clamp recordings. Membrane resonance was tested at three levels of membrane potential [on average −76, −63 (resting), and −52 mV] and quantified using the following parameters: input impedance (Z₀), resonance frequency, resonance strength (Q value), attenuation at 20 Hz (D value), and bandwidth.

The resonance frequency was slightly larger when measured with sharp microelectrodes (P < 0.001) and decreased on depolarization in both patch-clamp (7.5 ± 0.2, 5.7 ± 0.1, and 3.9 ± 0.1 Hz, n = 49) and sharp microelectrode recordings (10.8 ± 2.1, 10.1 ± 2.1, and 9.8 ± 2.2 Hz, n = 23). The input impedance was lower when measured with sharp microelectrode (P < 0.001) and increased steadily on depolarization (P < 0.001; patch: 33.6 ± 1.5 to 53.9 ± 2.0 to 89.0 ± 3.6 MΩ; sharp: 28.0 ± 6.3 to 30.5 ± 7.0 to 37.9 ± 6.4 MΩ). In both cases the resonance peak became sharper on depolarization (P < 0.001; bandwidth; patch: 18.1 ± 0.4, 10.7 ± 0.3, and 6.1 ± 0.3 Hz; sharp: 15.3 ± 0.3, 10.1 ± 0.4, and 7.3 ± 0.3 Hz). Most resonance parameters were voltage dependent, and changes were consistent between both recording techniques. The exception was the Q value, which increased with depolarization for the sharp microelectrode recordings (P < 0.05; 1.35 ± 0.12, 1.49 ± 0.28, and 1.58 ± 0.27) and decreased for patch recordings (P < 0.001; 1.64 ± 0.03, 1.46 ± 0.02, and 1.30 ± 0.02), and the D value, which decreased in patch-clamp recordings (P < 0.001; 1.00 ± 0.02, 0.62 ± 0.02, and 0.37 ± 0.01) but not in sharp microelectrode recordings. Taking into account that both Q and D values are ratio-based values and depend on the value of impedance, we attributed these differences to the smaller impedance typical for the sharp microelectrode recordings.

MPOs were recorded near spike threshold (approximately −52 mV) and characterized using both spectral and autocorrelation analysis. MPOs recorded with sharp microelectrodes had larger peak amplitudes and higher frequencies (P < 0.001). The average frequency and peak amplitude values were 3.5 ± 1.0 Hz (n = 39) and 1.4 ± 0.2 mV (n = 39) for patch-clamp recordings and 9.2 ± 2.1 Hz (n = 21) and 2.3 ± 0.6 mV (n = 21) for sharp microelectrode recordings. The size of the dominant frequency peak in spectral analyses did not differ between recording techniques and ranged from 0.12 to 0.45 mV²/Hz. The average amplitude values and temporal stability of oscillations (λ) were similar for patch-clamp (0.5 ± 0.2 mV, λ = 0.34 ± 0.07) and sharp microelectrode recordings (0.6 ± 0.1 mV, λ = 0.24 ± 0.03). Overall, the control values were similar to those previously reported (Boehlen et al. 2010; Erchova et al. 2004).

Modulation of the H-current.

Experimental evidence suggests that hyperpolarization-activated cation currents (I_H) shape the excitability of SCs. It has been demonstrated that I_H influences both frequency and strength of MPOs in SCs (Dickson et al. 2000b; Giocomo and Hasselmo 2008; Haas et al. 2007; Nolan et al. 2007). Also, the sag time constant (Boehlen et al. 2010; Giocomo et al. 2007) and the I_H amplitude (Garden et al. 2008) change along the dorsal-ventral axis of the mEC alongside changes of the resonance frequency (Boehlen et al. 2010; Giocomo et al. 2007).

We further investigated the contribution of I_H to near-threshold excitability using the relatively specific HCN channel blocker ZD7288 (20 μM, patch-clamp recordings, n = 9; 100 μM, sharp microelectrode recordings, n = 3), the nonspecific blocker CsCl (Cs⁺, 1 mM, sharp microelectrode recordings, n = 8), and the nonspecific modulator 8-bromo-cAMP (1 mM, sharp microelectrode recordings, n = 7). The effects of all pharmacological agents on cell excitability are summarized in Table 1. In brief, both ZD7288 and Cs⁺ hyperpolarized the cell, increased its time constant, removed negative sag potentials, and reduced depolarization-induced overshoot (Figs. 1A and 2A). As a result, injection of the control rheobase current did not elicit a spike in ZD7288 (Fig. 1A). In a subset of experiments the reduction of the resting membrane potential (RMP) by ZD7288 was then compensated for by an additional constant current injection to restore the original control RMP (ORMP; Fig. 1A). In this case injection of the control rheobase current elicited a spike train, and the average current to evoke a single spike at ORMP was reduced to 94.8 ± 18.7 pA (n = 8, P < 0.05). The net effect of I_H therefore likely depends on the balance between changes of RMP and input resistance, similar to that in hippocampal interneurons (Maccaferri and McBain 1996).

Fig. 1.

The hyperpolarization-activated cation current (I_H) blocker ZD7288 (20 μM) profoundly affects both excitability and resonance properties of entorhinal cortex (EC) layer II stellate cells (SCs) (patch-clamp recordings). A: sample voltage responses to 500-ms-long constant current pulses of −400 pA and of the rheobase current under control conditions (left), after bath application of ZD7288 at the new resting membrane potential (RMP; middle; original rheobase current does not elicit a spike), and in ZD7288 at the original RMP (ORMP; right; original rheobase current elicits a spike train). The baselines were aligned, and the RMP for each recording is given. B: sample recordings of the voltage responses to a ZAP [impedance (Z) amplitude profile] stimulus at 3 different membrane potentials before (top) and after (middle) ZD7288 treatment. Note the change in stimulus amplitude at depolarized membrane potential (left). C: example of an SC resonance profile before (black line) and after ZD7288 application (gray line) at 3 levels of membrane depolarization. D: quantitative analyses of input impedance (Z₀; left), resonance frequency (F_res; middle), and resonance amplitude (Q value; right) before (filled circles) and after (open circles) ZD7288 treatment. Open triangles in the input impedance plot (left) represent normalized impedance values. Hyper, hyperpolarization, n = 9; RMP, n = 9; Depo, depolarization, n = 7. Values are means ± SE. *P < 0.05; ***P < 0.001.

Fig. 2.

Modulation of I_H by Cs⁺ (1 mM) and 8-bromo-cAMP (cAMP; 1 mM) has opposite effects on SC excitability and impedance profiles (sharp microelectrode recordings). A: sample voltage responses to 500-ms-long constant current pulses from −400 to 100 pA above rheobase in 100-pA steps under control conditions (left) and after application of Cs⁺ (middle) or cAMP (right). B: sample recordings of the voltage responses to a ZAP stimulus of 50 pA (not shown) at 3 different membrane potentials before (left) and after application of Cs⁺ (middle) or cAMP (right). C: example of an SC resonance profile before (black line) and after Cs⁺ (dashed line) or cAMP (dotted line) treatment. D: quantitative analyses of input impedance (left), resonance frequency (middle), and resonance amplitude (right) before (filled circles) and after Cs⁺ (filled inverted triangles, n = 7) and cAMP treatment (open triangles, n = 8). Values are means ± SE. *P < 0.05; **P < 0.01; ***P < 0.001.

The afterhyperpolarization (AHP) following spikes that constrains the firing rate and contributes to spike clustering in SCs relies on a number of ionic currents, including I_H (Nolan et al. 2007). Both ZD7288 and Cs⁺ had profound effects on spike shape and the AHP. The spike amplitude was reduced, and its half-duration was increased without a change of rise time of the spike itself. The amplitude of the fast AHP (fAHP) was reduced, whereas the medium AHP (mAHP) amplitude remained stable, although its duration increased almost twofold.

ZD7288 and Cs⁺ both largely reduced resonance of SCs at all membrane potentials in both patch-clamp and sharp microelectrode recordings (Figs. 1, B–D, and 2, B–D) and reduced the frequency and amplitude of subthreshold MPOs (Fig. 3, A–F). When Cs⁺ was used to block I_H in sharp microelectrode recordings, its effect was less prominent compared with that of ZD7288, which is in line with the observation of a 70% block of I_H by Cs⁺ (Richter et al. 2000).

Fig. 3.

Modulation of I_H profoundly affects but does not completely abolish membrane potential oscillations (MPOs) in EC layer II SCs. A: representative 2-s-long MPO traces recorded near rheobase (patch-clamp recordings, top) before (left) and after ZD7288 application (right), and corresponding autocorrelation functions (bottom). B: spectral analysis of MPOs shown in A before (left) and after ZD7288 application (right). C: representative 2-s-long MPO traces recorded by sharp microelectrode near rheobase (top), before (left) and after ZD7288 application (right), and corresponding autocorrelation functions (bottom). Note increase in ZD7288 concentration. D: spectral analyses of MPOs shown in B before (left) and after ZD7288 application (right). The dashed line represents additional application of losigamone. E: representative 2-s-long MPO traces recorded with sharp microelectrode near rheobase (top) before (left) and after Cs⁺ application (right) and corresponding autocorrelation functions (bottom). F: spectral analyses of MPOs shown in E before (left) and after Cs⁺ application (right). G: representative 2-s-long MPO traces recorded by sharp microelectrode near rheobase (top) before (left) and after 8-bromo-cAMP application (right) and corresponding autocorrelation functions (bottom). H: spectral analyses of MPOs shown in G before (left) and after 8-bromo-cAMP application (right). I–K: quantitative summary of the modulators' effects on MPO frequency (I) and average (std; J) and maximum amplitude (max; K). Values are means ± SE; n.s., not significant. *P < 0.05; **P < 0.01; ***P < 0.001.

Although I_H blockade was highly efficient in inhibiting SC membrane resonance, MPOs were reduced in amplitude but still detectable after application of ZD7288 (Fig. 3, A–D). The average frequency of MPOs decreased from 4.4 ± 0.4 to 2.2 ± 0.4 Hz in patch-clamp recordings and from 8.3 ± 1.4 to 2.5 ± 0.5 Hz in sharp microelectrode recordings. The average MPO amplitude decreased (from 0.58 ± 0.2 to 0.40 ± 0.1 mV in patch-clamp recordings and from 0.84 ± 0.1 to 0.31 ± 0.1 mV in sharp microelectrode recordings; Fig. 3, A and C). The amplitude of the dominant frequency peak in the spectra was halved by ZD7288 (from 0.37 ± 0.03 to 0.17 ± 0.02 mV²/Hz, P < 0.05), and the value of λ was reduced (P < 0.05) by 0.05–0.1, indicating that remaining membrane oscillations also lost their prominent theta-frequency component and regularity. The maximum membrane voltage deviation from the baseline was also reduced, but to a lesser degree, from 1.2 ± 0.6 to 1.0 ± 0.5 mV in patch-clamp recordings and from 2.4 ± 0.6 to 1.5 ± 0.6 mV in sharp microelectrode recordings (note the larger concentration of ZD7288 for sharp microelectrode recordings).

Cs⁺ had a similar but more variable effect (Fig. 3, E and F), reducing the frequency and amplitude of MPOs [from 10.8 ± 1.4 Hz, 0.50 ± 0.1 mV (average) and 2.2 ± 0.4 mV (maximum) to 3.0 ± 1.2 Hz, 0.32 ± 0.1 mV (average) and 1.1 ± 0.2 mV (maximum)]. The dominant frequency peak decreased from 0.34 ± 0.03 to 0.07 ± 0.01 mV²/Hz, and λ from 0.24 ± 0.03 to 0.07 ± 0.02.

Given that HCN channels are regulated by cAMP, we attempted to modulate I_H in SCs. cAMP binds to a COOH-terminal cyclic nucleotide-binding domain and shifts the voltage-dependent activation of HCN channels to more depolarized potentials, thereby enhancing channel opening (DiFrancesco and Tortora 1991; Wainger et al. 2001). Bath application of a membrane-permeable cAMP analog (8-bromo-cAMP) has been previously reported to increase I_H amplitude in SCs (Richter et al. 2000). Consistent with an enhancement of I_H, 8-bromo-cAMP depolarized the cell and decreased the input resistance, membrane time constant, and sag decay time constant (Fig. 2A and Table 1). The overall cellular excitability was reduced: both rheobase (from 186.7 ± 33.9 to 283.7 ± 54.6 pA, P < 0.01) and voltage threshold increased (by 4.3 ± 1.5 mV, P < 0.05). Whereas blockade of I_H resulted in longer mAHP duration, an augmentation of I_H by 8-bromo-cAMP application shortened mAHPs, confirming that I_H is involved in shaping the AHP.

8-Bromo-cAMP treatment also increased the resonance frequency at all tested membrane potentials without significant changes in Q value (Fig. 2, B–D, hyperpolarized: from 11 ± 0.7 to 12.9 ± 0.5 Hz, P < 0.001; RMP: from 10.5 ± 0.5 to 12.3 ± 0.5 Hz, P < 0.05; and depolarized: from 10.2 ± 0.6 to 11.5 ± 0.6 Hz, P < 0.05, n = 7). As suggested by changes in cell excitability, more current was necessary to induce MPOs (increased from 177 ± 31 to 275 ± 54 pA, P < 0.01; Fig. 3, G and H); MPOs had higher frequency (from 9.1 ± 0.6 to 11.0 ± 0.7 Hz, P < 0.01, n = 7) and lower average amplitude (from 0.63 ± 0.4 to 0.52 ± 0.4 mV, P < 0.05). The size of the dominant frequency peak was reduced from 0.31 ± 0.02 to 0.16 ± 0.02 mV²/Hz (P < 0.05), and λ decreased from 0.24 ± 0.02 to 0.18 ± 0.01 (P < 0.05), indicating that, despite augmentation of I_H, the theta component of oscillations became weaker and MPOs became less regular. We attribute this effect to the possible action of cAMP on other channels in SCs (Khawaja et al. 2007). Despite reduced average amplitudes, the maximum positive excursion of membrane voltage was similar to that in control conditions (see Fig. 3, I–K, for a summary). These data suggest that whereas frequency of resonance and MPOs were primarily mediated by HCN channels in SCs, the amplitude of MPO was regulated via complex interaction of several channel types.

Modulation of sodium currents by TTX and losigamone.

MPOs in SCs depend on TTX-sensitive sodium currents (Alonso and Llinás, 1989). Further studies have suggested that the noninactivating, i.e., persistent (for review see Crill 1996), sodium current (I_NaP) supports MPOs in SCs (Burton et al. 2008; Dorval and White 2005; White et al. 1998). To unequivocally ascribe a mechanism to I_NaP, it would require, for instance, clear pharmacological dissection of transient sodium currents (I_NaT) and I_NaP, which has proven to be challenging. However, a few substances such as riluzole, phenytoin, and losigamone inhibit predominantly and dose-dependently I_NaP over I_NaT (Draguhn et al. 1997; Gebhardt et al. 2001; Segal and Douglas 1997; Urbani and Belluzzi 2000). We therefore tested whether TTX and losigamone represent potent modulators of MPOs and resonance in SCs and to what extent their effects overlap.

First of all we ensured that bath application of TTX (0.1 μM, n = 5) blocked both spike and MPO generation in SCs (Figs. 4A and 8A). TTX application also modified resonance of SCs (Fig. 4, B–D) at RMP and at depolarized membrane potentials. A reduction of the input impedance (from 30.7 ± 2.4 to 25.4 ± 2.4 MΩ, P < 0.05 at RMP, and from 36.4 ± 2.3 to 27.6 ± 2.7 MΩ, P < 0.05 near threshold) and impedance at resonance frequency (from 40.3 ± 3.6 to 31.8 ± 4.1 MΩ, P < 0.05 at RMP, and from 56.0 ± 5.6 to 37.2 ± 4.5 MΩ, P < 0.05) was observed without significant changes of other resonance parameters (Fig. 4, C and D).

Fig. 4.

Blockade of sodium channels by tetrodotoxin (TTX; 0.1 μM) abolishes spike generation and decreases resonance amplitude at resting and depolarized potentials in EC layer II SCs. A: sample voltage responses to 200-ms-long constant current pulses from −400 pA in 100-pA steps under control conditions (top) and after application of TTX (bottom). B: sample recordings of the voltage responses to a ZAP stimulus of 50 pA (not shown) at 3 different membrane potentials before (left) and after application of TTX (right). C: example of an SC resonance profile before (black line) and after TTX (gray line) treatment. D: quantitative analyses of input impedance (left), resonance frequency (middle), and resonance amplitude (right) before (filled circles) and after TTX treatment (open circles). Values are means ± SE; n = 5. *P < 0.05.

Fig. 8.

Modulation of I_NaP affects MPOs in EC layer II SCs. A: representative 2-s-long MPO traces recorded by sharp microelectrode near rheobase (top) before (left) and after TTX application (right), and corresponding autocorrelation functions (bottom). B: spectral analyses of MPOs shown in A before (left) and after TTX application (right). C: representative 2-s-long MPO traces recorded with sharp microelectrode near rheobase (top), before (left) and after losigamone application (right), and corresponding autocorrelation functions (bottom). D: spectral analyses of MPOs shown in B before (left) and after losigamone application (right). E: representative 2-s-long MPO traces near rheobase (patch-clamp recordings, top) before (left) and after losigamone application (right), and corresponding autocorrelation functions (bottom). Note an increase in losigamone concentration. The second trace for losigamone application was recorded at the same level of depolarization as control (− 51 mV). F: spectral analyses of MPOs shown in E before (left) and after losigamone application (right). The gray line in plot at right represents spectra for the MPOs at the same depolarization level as control. G–I: quantitative summary of modulators' effects on MPO frequency (G) and on MPO average (H) and maximum amplitude (I). Values are means ± SE. *P < 0.05; **P < 0.01.

In voltage-clamp experiments (see materials and methods), bath application of losigamone at a concentration of 200 μM inhibited 10 ± 10% of I_NaT but 82 ± 6% of I_NaP (n = 6 and 5, Fig. 5, also for the effect of phenytoin and riluzole). These values are comparable to the previously reported ∼85% inhibition of I_NaP by riluzole or ∼43% by phenytoin in comparable voltage ranges in cortical neurons (Urbani and Belluzzi 2000; Yue et al. 2005) and are consistent with a blockade of I_NaP by losigamone as previously reported (Gebhardt et al. 2001). All blockers shifted the activation curve of I_NaP toward positive potentials (Fig. 6B). The dynamics of the persistent sodium current remaining after application of losigamone were consistent with a sodium window current (Fig. 6, C and D). Interestingly, activation of the I_NaP-associated current noise was much faster than activation of I_NaP itself (Fig. 6F), and losigamone-induced reduction in current noise was the most pronounced in the voltage range where MPOs normally occur (Fig. 6G).

Losigamone altered SC excitability (Fig. 7A, Table 2) and induced a reversible reduction of the AP discharge rate without changing the AP amplitude or duration. Both the current and voltage thresholds for AP generation were increased. The rheobase increased from 166.4 ± 19.2 to 248.2 ± 30.0 pA (n = 8, P < 0.01), and the voltage threshold shifted by 5.9 ± 1.3 mV (n = 8, P < 0.01) toward more positive potentials. The input impedance was reduced at RMP (from 54.6 ± 4 to 49 ± 4 MΩ, n = 12, P < 0.05) and near threshold (from 91.0 ± 6.6 to 78.8 ± 6.9 MΩ, n = 9, P < 0.01) by losigamone, similar to the effect of TTX (Fig. 7, B–D). Resonance frequency, Q value, D value, and bandwidth were not affected. These data suggest that I_NaP has a profound effect on AP threshold and AP generation but has little effect on membrane resonance in SCs.

Fig. 7.

I_NaP blockade by losigamone (200 μM) profoundly affects excitability but not the resonance properties of EC layer II SCs (patch-clamp recordings). A: sample voltage responses (top) to 500-ms-long constant current pulses (bottom) under control conditions (left), after bath-applied losigamone (middle), and after washout (right). B: sample recordings of the voltage responses to a ZAP stimulus (bottom) at 3 different membrane potentials before (top) and after (middle) losigamone treatment. Please note the change in stimulus amplitude at depolarized membrane potential (left). C: example of a resonance profile before (black line) and after losigamone application (gray line) at 3 levels of membrane depolarization. D: quantitative analyses of input impedance (left), resonance frequency (middle), and resonance amplitude (right) before (filled circles) and after (open circles) losigamone treatment. Values are means ± SE; Hyper, n = 10; RMP, n = 12; Depo, n = 9. *P < 0.05; **P < 0.01.

Observing subthreshold MPOs in the presence of losigamone required an increase of the current injection to depolarize SCs by 123.9 ± 36.4 pA (n = 11, P < 0.001) to a more positive membrane potential (from −46.3 ± 1.2 to −37.1 ± 2.4 mV, P < 0.001) compared with controls (Fig. 8, C and E). However, low-amplitude membrane oscillations were also present at potentials similar to control (Fig. 8E). In this control voltage range the MPO frequency was not altered, but MPO amplitudes were significantly reduced (average amplitude from 0.5 ± 0.1 to 0.3 ± 0.1 mV, P < 0.001, and maximum amplitude from 1.2 ± 0.2 to 0.6 ± 0.2 mV, P < 0.001). However, in the presence of losigamone the firing threshold shifted upward, allowing cells to depolarize further before starting to spike. At more depolarized near-threshold potentials, MPOs reappeared. The effect was most prominent in our patch-clamp recordings, where the amplitude of MPOs at depolarized potential was not statistically different from the control. The frequency of these MPOs increased from 3.0 ± 0.3 to 4.0 ± 0.5 Hz (P < 0.01), and the shape of the power spectra (a single dominant peak in most of the cells compared with multipeak spectra before drug application) and autocorrelation function (with λ being almost doubled in some cells after application of losigamone) suggested somewhat more regular “sinusoidal” shape oscillations compared with control cases (Fig. 8, E and F). We attributed these effects to different voltage-dependent properties of ionic conductances generating MPOs at depolarized potentials. Our data, hence, suggest that though I_NaP contributes to the MPO generation in SCs, MPOs may also persist in its absence supported by the transient sodium currents at more positive potentials. In this context I_NaP did not control MPOs amplitude directly but rather defined the voltage range in which sub- and perithreshold MPOs occurred.

Modulation of the M-current.

The low-threshold, slowly activating and deactivating, and noninactivating M-current (I_M) is an important determinant of neuronal excitability and response patterns in many cell types (Brown and Adams 1980; Gu et al. 2005; Halliwell and Adams, 1982; Peters et al. 2005; Yoshida and Alonso 2007). I_M is slowly activated when the neuron is depolarized toward the threshold, hyperpolarizes the membrane, and thus reduces membrane excitability. I_M also participates in the generation of near-threshold resonance in hippocampal pyramidal cells (Hu et al. 2002, 2007; Peters et al. 2005) and SCs (Heys et al. 2010; but see Heys and Hasselmo 2012). MPOs in SCs were found to be sensitive to carbachol, an agonist of the muscarine receptor that controls I_M (Gloveli et al. 1999; Klink and Alonso 1997) but not to the I_M blocker linopirdine (Yoshida and Alonso 2007). We therefore investigated whether pharmacological I_M inhibition and augmentation shape the generation of resonance and MPOs in SCs differentially.

In our experiments inhibition of I_M by XE991 (n = 10) produced an upward shift in the RMP by 2.8 ± 1.0 mV (P < 0.01, Fig. 9A), indicating that I_M is present and plays a role in controlling the RMP. However, the input resistance and current and voltage thresholds for spike generations were not significantly affected. Overall, the block of I_M did not profoundly alter SC excitability or spike amplitude and shape (Table 3). An increase of the membrane time constant from 12.3 ± 0.5 to 14 ± 0.7 ms (n = 10, P < 0.01) is probably responsible for the longer latency of the first AP at rheobase (118.6 ± 23.0 ms compared with 59.7 ± 5.5 ms in controls, n = 10, P < 0.05). It is noteworthy that the amplitude of the fAHP and the duration of the mAHP were significantly reduced by XE991 (fAHP: from −7 ± 0.4 to −4 ± 0.4 mV, n = 10, P < 0.001; mAHP: from 71.3 ± 8.5 to 113.9 ± 12.7 ms, n = 7, P < 0.05). In line with previous reports (Heys et al. 2010), resonance was only weakly affected by I_M blockade in these cells. At depolarized membrane potentials the resonance frequency decreased in 6 of 9 cells (not significant; Fig. 9D), whereas XE991 reduced the impedance at resonance frequency (107.1 ± 10.7 to 85.6 ± 11.7 MΩ, n = 8, P < 0.01), resulting in a reduction of the Q value (from 1.35 ± 0.06 to 1.21 ± 0.03, n = 8, P < 0.05) without affecting D value or bandwidth.

Fig. 9.

Muscarine-modulated potassium current (I_M) controls excitability and could modulate resonance properties in EC layer II SCs. A: sample voltage responses (top) to 500-ms-long constant current pulses (bottom) under control conditions (left) and after application of XE991 (right). B: sample voltage responses (top) to 500-ms-long constant current pulses (bottom) under control conditions (left) and after application of ICA (right). C: sample recordings of the voltage responses to a ZAP stimulus of 50 pA (unless indicated otherwise) at 2 different membrane potentials before (top) and after application of XE991 (bottom). D: a representative resonance profile before (black line) and after XE991 (gray line) treatment. E: sample recordings of the voltage responses to a ZAP stimulus of 50 pA at 2 different membrane potentials before (top) and after application of ICA (bottom). F: example of an SC resonance profile before (black line) and after ICA (gray line) treatment. G: quantitative analyses of input impedance (left), resonance frequency (middle), and resonance amplitude (right) before (filled circles) and after XE991 (open circles). Values are means ± SE; Hyper, n = 11; RMP, n = 10; Depo, n = 9. *P < 0.05. H: quantitative analyses of input impedance (left), resonance frequency (middle), and resonance amplitude (right) before (filled circles) and after ICA (open circles) or retigabine (open triangles). Values are means ± SE; Hyper, n = 12; RMP, n = 10; Depo, n = 8. *P < 0.05; **P < 0.01.

On average, MPOs appeared in a similar voltage range and with the same amplitude and regularity (λ as in control), although a subset of cells needed more depolarization to generate MPOs (Fig. 10A). However, the frequency of MPOs was reduced in 7 of 9 cells and on average from 3.2 ± 0.3 to 2.6 ± 0.3 Hz (n = 9, P < 0.05), suggesting that I_M may influence the frequency of MPOs.

Fig. 10.

I_M controls frequency and magnitude of MPOs in EC layer II SCs. A: representative 2-s-long MPO traces near rheobase (patch-clamp recordings, top) before (left) and after XE991 application (right), and corresponding autocorrelation functions (bottom). B: spectral analyses of MPOs shown in A before (left) and after XE991 application (right). C: representative 2-s-long MPO traces near rheobase (patch-clamp recordings, top) before (left) and after retigabine application (right), and corresponding autocorrelation functions (bottom). D: spectral analyses of MPOs shown in C before (left) and after losigamone application (right). E: representative 2-s-long MPOs traces recorded by patch electrode near rheobase (top) before (left) and after ICA application (right), and corresponding autocorrelation functions (bottom). F: spectral analyses of MPOs shown in E before (left) and after ICA application (right). G–I: quantitative summary of modulators' effects on MPO frequency (G) and on MPO average (H) and maximum amplitude (I). Values are means ± SE. *P < 0.05; **P < 0.01; ***P < 0.001.

It is conceivable that augmentation of I_M could further reveal a modulatory role of I_M. To examine this hypothesis, we used two different types of the M-channel activators (also potential antiepileptic drug) ICAGEN-110381 (ICA; 10 μM; Boehlen et al. 2012) and retigabine (RTG; 1 μM) that may differ in subunit specificity.

The effect of RTG on neuronal excitability has been previously described in detail (Hetka et al. 1999; Vervaeke et al. 2006; ; Yue and Yaari 2004), and our results are in line with these reports (Table 3). Both I_M activators dampened SC excitability by reducing the RMP and elevating current and voltage threshold for AP generation (for ICA, see Fig. 9B). The input impedance decreased following application of ICA from 50.5 ± 3.5 to 42.3 ± 2.2 MΩ (P < 0.05), but not after RTG treatment. Both activators reduced spike amplitudes (this was stronger for RTG) and increased spike duration. In addition, ICA also enhanced mAHP amplitudes from −8.6 ± 0.4 to −10.7 ± 0.7 mV (n = 12, P < 0.01) and duration from 75.7 ± 9.5 to 121.14 ± 26.1 ms. Both ICA and RTG increased the resonance frequency near threshold (ICA: from 3.9 ± 0.3 to 4.5 ± 0.2 Hz, n = 9, P < 0.05; RTG: from 4.0 ± 0.4 to 4.8 ± 0.6 Hz, n = 6, P < 0.05) without altering the corresponding Q value (Fig. 9, E–H). The D value near threshold increased (ICA: from 0.38 ± 0.04 to 0.53 ± 0.03, P < 0.01; RTG: from 0.36 ± 0.03 to 0.57 ± 0.08, P < 0.01) due to changes in input impedance.

The current threshold for appearance of MPOs (Fig. 10, C and E) increased with ICA and RTG by 149 ± 19 and by 131 ± 14 pA (P < 0.01), respectively. Both substances reduced average MPO amplitudes (by 0.20 ± 0.12 mV for ICA, P < 0.05; by 0.22 ± 0.09 mV for RTG, P < 0.0 5) and maximum MPO amplitude (by 0.62 ± 0.22 mV for ICA, P < 0.01; by 0.53 ± 0.15 mV for RTG, P < 0.001). The amplitude of the dominant spectral peak decreased almost twofold (from 0.38 ± 0.03 to 0.18 ± 0.02 mV²/Hz), and λ decreased (from 0.32 ± 0.2 to 0.26 ± 0.2) for both substances. The MPO frequency was increased by both drugs, but the effect reached statistical significance only for RTG (P < 0.05, Fig. 10G).

Together these experiments indicate that I_M is present in SCs and has the potential to modulate SC excitability and oscillatory behavior if upregulated by endogenous mechanisms.

Modeling the contribution of near-threshold currents to intrinsic oscillatory activity.

We next modeled oscillatory activity of SCs to complement our experimental findings, thereby also illustrating some methodological issues related to the characterization of MPOs. Given the stochastic nature of membrane fluctuations in SCs, we choose a single-compartment stochastic model previously developed (Dudman and Nolan 2009). To simplify comparisons with previously published results, we kept cell geometry and activation dynamics of ionic currents similar to those of the original model. In addition, stochastic KCNQ2/3 channels based on a five-state kinetic model (Selyanko and Brown 1999) were implemented and readjusted (ratio of different conductances and in some cases time constants) to fit our experimental data (see appendix for further details). We adjusted the model parameters to reproduce the excitability of a control cell and then tested the resulting model in the conditions that mimic our pharmacological experiments. In particular, we focused on the role of I_H, I_NaP, and I_M in modifying the cellular responses to external oscillatory drives (resonance measurements) and their contribution to MPOs. The effects of channel blockers were reproduced by removing the corresponding conductances from the model, and the effect of retigabine was modeled by alteration of the kinetics of the I_M current as described (Schwake et al. 2000; Tatulian et al. 2001).

We modeled our cell based on an experimentally recorded cell from the central part of mEC. The cell produced rebound spikes when hyperpolarized and exhibited MPOs on depolarization (Fig. 11A). The resonance frequency of the modeled cell was set to 6.1 Hz at rest (Fig. 11B). The temporal dynamics of resonance at hyperpolarized levels was set by the ratio of fast vs. slow components of HCN channels; the Q value was set by the total number of HCN channels. The frequency of resonance on depolarization was adjusted by the addition of I_M. The resulting model produced stochastic MPOs with noisy spectra and average frequency of 5.5 Hz (Fig. 11C).

Fig. 11.

Stochastic modeling of SC dynamics near threshold. From left to right data show voltage responses to 500-ms-long current pulses near rheobase; resonance profiles at different levels of membrane depolarization; and 2-s-long MPOs near rheobase (top), with autocorrelation (bottom) and Fourier spectra. A–C: full model response. A: constant current injection (I_inj) −800, 200, and 250 pA; half mAHP duration, 36.5 ms; maximum mAHP amplitude (mAHP_max), 12.4 mV. B: resonance frequency: Hyper, 6.7 Hz; RMP, 6.1 Hz; and Depo, 5.7 Hz. C: MPO amplitude: std, 0.57 mV; max, 2.3 mV; frequency, 5.5 Hz. D–F: omitted sodium currents. D: I_inj, 300 and 400 pA. E: resonance frequency as in B. F: MPO amplitudes are reduced: std, 0.21 mV, max, 0.4 mV; frequency, 2.9 Hz. G–I: omitted I_NaP. G: I_inj 370 and 400 pA. H: resonance frequency: Hyper, 6.7 Hz; RMP, 6.1 Hz; Depo, 6.6 Hz. I: MPOs similar to control: std, 0.4 mV; max, 1.8 mV; frequency, 4.7 Hz. J–L: omitted I_H. J: I_inj −200, −100, 370, and 400 pA; half mAHP duration, 39.4 ms; mAHP_max, 11.1 mV. K: resonance is abolished at and below RMP; Depo, 4.2 Hz. L: MPO frequency is reduced: std, 0.56 mV; max, 2.1 mV; frequency, 2.7 Hz. M–O: omitted I_M. M: I_Inj 200 and 220 pA; half mAHP duration, 33.8 ms; mAHP_max, 11.0 mV. N: resonance frequency decreased 4.9 Hz (Depo). O: MPOs are similar to control: std, 0.54 mV; max, 1.8 mV; frequency, 4.5 Hz. P–R: enhanced I_M. P: I_Inj 270 and 300 pA; half mAHP duration, 41.2 ms; mAHP_max, 12.0 mV. Q: resonance frequency increased to 8.9 Hz (Depo). R: MPO amplitudes are reduced; std, 0.4 mV; max, 0.9 mV; frequency, 9.6 Hz.

It is common practice in experimental studies to smooth noisy spectra to obtain meaningful single-frequency estimates. In our experience, however, the choice of smoothing kernel may affect the final results. To allow direct comparison with experimental data, we used the same parameters as for experimental data analyses.

The model reproduced the main effects of our pharmacological manipulations, such as changes in the threshold and the AHP, as well as in resonance and MPOs (Fig. 11, D–R), similarly to the original model (Dudman and Nolan 2009). Our results also indicate that very similar oscillatory traces can be obtained with different combinations and ratios of ionic conductances. As expected, removing sodium channels from the model (Fig. 11, D–F) abolished APs and drastically reduced the amplitude of MPOs; however, removing I_NaP (Fig. 11, G–I) had only a small effect on MPO amplitudes, confirming experimental data (average amplitude reduced from 0.57 to 0.5 mV and peak amplitude from 2.3 to 1.7 mV). Blockade of I_H (Fig. 11, J–L) did not abolish MPOs, but their spectra became noisier and shifted toward lower frequencies. As expected, absence of I_M (Fig. 11, M–O) caused a small shift of MPO frequency toward lower values, and an increase of I_M (Fig. 11, P–R) resulted in a small reduction of oscillation amplitudes (standard; from 0.57 to 0.44) and a shift of MPO frequency toward higher values. To summarize, our results show that in SCs, MPOs are robust and none of the near-threshold currents that contribute to MPO generation (I_H, I_M, or I_NaP) had an exclusive control over MPO amplitudes. This is in good agreement with our experimental findings.

DISCUSSION

In this study we analyzed near-threshold intrinsic membrane potential fluctuations (MPOs) and resonance in SCs and examined the contributions of I_H, I_M, and I_NaP in detail. The results suggest that all investigated currents support generation of MPOs in SCs, but none of them exclusively controls amplitude or frequency of MPOs. We contribute new experimental evidence for a critical role of I_H and I_M in determining key aspects of SC excitability and frequency of oscillatory behavior and suggest a novel role for I_NaP in determining the voltage range in which MPOs occur.

SCs display age-dependent I_NaP (Burton et al. 2008; Klink and Alonso 1993), and its crucial role in supporting subthreshold oscillations has been suggested on the basis of experiments using the sodium channel blocker TTX and modeling (Burton et al. 2008; Klink and Alonso 1993; Magistretti and Alonso 1999; White et al. 1998). TTX, however, lacks specificity for I_NaP. We therefore used the more specific blocker losigamone, an antiepileptic drug that preferentially blocks I_NaP in cultured neurons (Gebhardt et al. 2001) and SCs, as demonstrated here. Losigamone inhibited MPOs at control subthreshold potentials similarly to the previously reported inhibition of MPOs by riluzole (Dorval and White 2005). However, MPOs reappeared at more positive, new near-threshold membrane potentials, arguing that sodium windows currents could also support MPOs. The effect was more pronounced in patch-clamp recordings where the amplitudes of MPOs at this new, more depolarized, threshold were comparable with the amplitudes of MPOs in control cells. The discrepancy between recording techniques might be attributed to the presence of nonspecific depolarizing current in sharp microelectrode recording that prompted spike generation at lower membrane potentials compared with patch-clamp recordings.

It was previously suggested (Dorval and White 2005) that noise generated by I_NaP-associated sodium channels rather than the current itself may be crucial for near-threshold MPO generation, because the authors were unable to rescue SC MPOs blocked by riluzole by injecting an average I_NaP current using dynamic clamp. In our experiments we also observed significant reduction in near-threshold channel noise associated with losigamone application (Fig. 6) that would be consistent with the above hypothesis. Another hypothesis (proposed by Hu et al. 2002) suggests that I_NaP may help to spread locally imposed (in our case somatic) depolarization further out into the dendrites, creating a “spatial plateau depolarization.” The I_NaP blockers thus restrict this depolarization to the soma, causing electrophysiological recordings to be more spatially localized and specific to soma. In our study, application of losigamone had a substantial, previously unreported, effect on SC excitability consistent with I_NaP's role in promoting spike initiation, repetitive firing, and bursting (Harvey et al. 2006; Lee and Heckman 2001; Urbani and Belluzzi 2000; Wu et al. 2005; Yue et al. 2005) and thus being dominant in the axon initial segment (Astman et al. 2006; Osorio et al. 2010).

Although I_NaP is known to be present in SCs dendrites (Magistretti et al. 1999), an inhomogeneous distribution of I_NaP across SC segments, similar to the compartmentalization of conductances reported for CA1 pyramidal cells (Hu et al. 2009; Magee 1998; Narayanan and Johnston 2007), remains a potential explanation for relatively little contribution of I_NaP to somatic membrane resonance in SCs in comparison, for example, to frontal cortex neurons (Gutfreund et al. 1995; Hutcheon et al. 1996).

The notion that SC excitability is modulated by I_M is further supported by the presented findings. Although inhibition of I_M affected SC excitability, AP generation, resonance, and MPOs only moderately compared with, for instance, hippocampal pyramidal cells (Hu et al. 2007; Peters et al. 2005; Yue and Yaari 2004), activators of I_M had a robust effect on SC excitability. This suggests that KCNQ channels, which give rise to I_M, are present in SCs but possibly not recruited, at least under resting conditions, which potentially reflects the cholinergic tone, the dorsoventral position of the recorded SC, and/or intracellular Ca²⁺ levels (Brown and Adams 1980; Heys et al. 2010; Linley et al. 2012). Carbachol-induced deactivation of I_M has been shown to enhance MPOs via membrane depolarization while reducing the MPO frequency (Klink and Alonso 1997), and carbachol also decreased the resonance of SCs (Heys et al. 2010). Both findings are consistent with the data presented here. However, carbachol was also shown to inhibit I_NaP in neocortical cells (Mittmann and Alzheimer 1998) and possibly I_H in SCs (Heys et al. 2010), complicating the mechanistic interpretation of carbachol-induced modulation of MPOs and resonance. Nonetheless, it appears safe to argue that I_M is potentially a strong modulator of SC function with its specific contribution set by, for instance, the cholinergic tone (Gloveli et al. 1999; Klink and Alonso 1997).

The role of I_H in setting SC excitability and determining resonance and oscillatory SC properties has been thoroughly investigated in the past, and results of our study are in good agreement with the literature (Boehlen et al. 2010; Giocomo et al. 2007; Giocomo and Hasselmo 2009; Heys et al. 2010; Nolan et al. 2007; Shay et al., 2012). We report that delivery of an exogenous cAMP analog can increase the resonance frequency of SCs, highlighting that acute modulation of I_H will have an immediate dynamic effect on SC temporal integration. The key role of I_H in sustaining near-threshold and perithreshold MPOs in SCs is less clear. Early reports found a robust modulation of perithreshold MPOs in SCs by the relatively specific I_H inhibitor ZD7288 (Dickson et al. 2000b; Fransen et al. 2004). However, when HCN1 channels were genetically deleted and most of I_H was lost, perithreshold MPOs were reported to persist (Nolan et al. 2007). This apparent discrepancy could in principle arise from differences in terminology and the assumptions made about the temporal structure of the underlying signal, thus affecting analysis (Dodson et al. 2011), or simply differences of the position of the SCs studied along the dorsoventral axis (Giocomo and Hasselmo 2009). In our study ZD7288 reduced the average amplitude of near-threshold MPOs and changed the temporal structure of oscillations without completely abolishing them. The perithreshold MPOs also persisted in the presence of I_H blockers. The variability of MPOs among cells and our experiments with I_H modulators are in line with the idea that MPOs scale with the amount of I_H available but are at odds with the hypothesis that I_H has exclusive control over generation of MPOs near threshold.

Taking into account that frequency preferences change gradually in populations of SCs in accordance with the size of their receptive fields (Giocomo et al. 2007) and that grid field spacing (Barry et al. 2007) itself changes as a function of the novelty of an environment, it is conceivable that frequency preferences of the cells may be dynamically regulated, as suggested by oscillatory interference models (Burgess et al. 2007; Giocomo et al. 2007; Hasselmo et al. 2010). This effect could be achieved, for example, via suppression of I_M current via cholinergic modulation (Heys et al. 2010), by signaling cascades that ultimately set the activity of the cyclic nucleotide-producing cyclase and in turn modulate I_H, or by mechanisms that alter alternative splicing or subunit composition of sodium channels and thus may alter the prevalence of I_NaP (Fletcher et al. 2011; Osorio et al. 2010).

When comparing SCs with other types of cells with prominent resonance or MPOs in the EC, such as layer V pyramidal cells (Schmitz et al. 1998), the less abundant non-SC layer II cells or layer III pyramidal cells (Alonso and Klink 1993; Gloveli et al. 1999; Yoshida and Alonso 2007) or parasubicular neurons (Glasgow and Chapman 2008), all seem to have very similar sets of conductances, but the apparent contribution of each to MPOs and resonance varies largely. Although variable conductance densities and their modulation could account for these observations, the spatial distribution of channels within individual cells requires consideration. In hippocampal CA1 pyramidal cells, the density of I_H, for example, increases in dendrites with distance to the soma (Magee 1998) along with enhanced resonance (Hu et al. 2009; Narayanan and Johnston 2007). Similarly, KCNQ channels and the resulting I_M appear to be primarily localized in the axonal initial segment, soma, and proximal dendrites (Chung et al. 2006; Hu et al. 2007; Shah et al. 2008), where they determine excitability and resonance properties (Hu et al. 2007, 2009; Shah et al. 2008). Dissecting these spatial inhomogeneities and their impact on the mechanisms that govern both MPOs and resonance will represent a major challenge.

GRANTS

This research was supported by German Research Foundation (DFG) Grant He 1128/17-1, the Bernstein Center for Computational Neurosciences Berlin with funding from the German Federal Ministry of Education and Research (BMBF) and DFG Research Training Grant GRK 1123 (A. Boehlen and U. Heineman), the Hertie Foundation (U. Heineman), the Royal Society of Edinburgh/Lloyds TSB (I. Erchova), the Engineering and Physical Sciences Research Council/Medical Research Council-funded Doctoral Training Center in Neuroinformatics and Computational Neuroscience (I. Erchova), the North Rhine-Westphalia Rückkehrerprogramm (C. Henneberger), and a University College London Excellence Fellowship (C. Henneberger).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

A.B., U.H., and I.E. conception and design of research; A.B., C.H., and I.E. performed experiments; A.B., C.H., and I.E. analyzed data; A.B., C.H., U.H., and I.E. interpreted results of experiments; A.B., C.H., U.H., and I.E. prepared figures; A.B., C.H., U.H., and I.E. drafted manuscript; A.B., C.H., U.H., and I.E. edited and revised manuscript; A.B., C.H., U.H., and I.E. approved final version of manuscript.

APPENDIX: STOCHASTIC STELLATE CELL MODEL

We based our model on a previously published stochastic stellate cell model (Dudman and Nolan 2009). To make the data easily comparable with previously published results, we kept the basic cell geometry and dynamics of individual current as in the original model. We extended the model to include I_M and then readjusted the maximum values for individual currents to produce the closest fit to our experimental data.

In brief, we considered a single-compartment model with membrane surface area 7.85 × 10⁻⁵ cm² and specific capacitance 1.67 μF/cm². All channels have been modeled as stochastic components with the following channel densities (μS/cm²): the transient sodium current (I_NaT), 24,000; the persistent sodium current (I_NaP), 180; the delayed rectifier potassium current (Kdr), 11,000; the AHP current, 425 (deactivation rate was set to 0.5 to match experimental data); fast inactivating potassium current (A-type, Ka), 100; slowly inactivating potassium current (A-type, Kd), 500; leak current (Kl), 155; muscarinic current (I_M), 1,500; and the HCN-mediated current (I_H), 480 (fast) and 40 (slow).

Implementation of I_M.

The KCNQ2/3-mediated I_M (with single-channel conductances 7–11 pS) plays an important part in regulating cellular excitability near the threshold and is under the control of a number of signaling cascades (for a review see Hernandez et al. 2008). Hence, the overall kinetics of the channel are complex and depend on G protein signaling (Falkenburger et al. 2010; Suh et al. 2004). At a given constant level of external modulation, channel activity can be approximated by a simplified five-state kinetic schema proposed (Selyanko and Brown 1999):

$${\text{C}}_{\text{L}}\rightleftharpoons {\text{O}}_{\text{S}}\rightleftharpoons {\text{C}}_{\text{M}}\rightleftharpoons {\text{O}}_{\text{L}}\rightleftharpoons {\text{C}}_{\text{S}}$$ (A1)

where C_L, C_M, and C_S are closed states with long, medium, and short dwelling times, respectively, and O_L and O_S are long and short open states, respectively (Selyanko and Brown 1999; Selyanko et al. 2001; Tatulian et al. 2001) with transition coefficients between the states K_ij.

In normal physiological conditions the current is activated at near-threshold potentials (above −50 mV) and increases on depolarization (Selyanko et al. 2001). The voltage-dependent transition rates (τ, ms⁻¹) were derived from fitting single-channel average closed and open times at three different levels of membrane potentials [−50, −30, and 0 mV; based on the measurements reported (Selyanko and Brown 1999; Tatulian and Brown 2003)] as follows:

$$\begin{array}{c}{\tau }_{{\text{C}}_{\text{S}}}=\frac{1}{K_{{\text{C}}_{\text{S}}{\text{O}}_{\text{L}}}}\\ {\tau }_{{\text{C}}_{\text{M}}}=\frac{1}{K_{{\text{C}}_{\text{M}}{\text{O}}_{\text{L}}}+K_{\text{C}{}_{\text{M}}{\text{O}}_{\text{S}}}}\\ {\tau }_{{\text{C}}_{\text{L}}}=\frac{1}{K_{{\text{C}}_{\text{L}}{\text{O}}_{\text{S}}}}\\ {\tau }_{{\text{O}}_{\text{S}}}=\frac{1}{K_{{\text{O}}_{\text{S}}{\text{C}}_{\text{L}}}+K_{\text{O}{}_{\text{S}}{\text{C}}_{\text{M}}}}\\ {\tau }_{{\text{O}}_{\text{L}}}=\frac{1}{K_{{\text{O}}_{\text{L}}{\text{C}}_{\text{S}}}+K_{\text{O}{}_{\text{L}}{\text{C}}_{\text{M}}}}\end{array}$$ (A2)

and approximated in the near-threshold range as follows:

$$\begin{array}{l}{K}_{{\text{C}}_{\text{L}}{\text{O}}_{\text{S}}}=\alpha \hfill \\ K_{{\text{C}}_{\text{M}}{\text{O}}_{\text{L}}}=2\alpha \hfill \\ \alpha =0.0003+\frac{0.0071}{1+\exp \left(\frac{-20.3-V_{\text{m}}}{7.2}\right)}\hfill \\ K_{{\text{C}}_{\text{S}}{\text{O}}_{\text{L}}}={\alpha }_1\hfill \\ {\alpha }_1=0.13+\frac{1.29}{1+\exp \left(\frac{-20.3-V_{\text{m}}}{2.1}\right)}\hfill \\ K_{{\text{C}}_{\text{M}}{\text{O}}_{\text{S}}}={\alpha }_2\hfill \\ {\alpha }_2=\frac{0.025}{1+\exp \left(\frac{-28.7-V_{\text{m}}}{10.3}\right)}\hfill \\ K_{{\text{O}}_{\text{S}}{\text{O}}_{\text{L}}}=K_{{\text{O}}_{\text{S}}{\text{C}}_{\text{M}}}={\beta }_1\hfill \\ {\beta }_1=0.04+0.00023{\left(V_{\text{m}}+28.3\right)}^2\hfill \\ K_{{\text{O}}_{\text{L}}{\text{C}}_{\text{S}}}=K_{{\text{O}}_{\text{L}}{\text{C}}_{\text{M}}}={\beta }_2\hfill \\ {\beta }_2=0.008+0.000035{\left(V_{\text{m}}+27.2\right)}^2\hfill \end{array}$$ (A3)

The steady-state probabilities of the channel to be in a given state were then found using Hill's method (Hill 1999) as a ratio of the direction diagram of a given state and the sum of all directional diagrams. The effect of the channel blocker XE991 was modeled by removing I_M from the model while preserving all the other parameters. The effect of the channel enhancer retigabine was modeled on the basis of single-channel data (Tatulian and Brown 2003). Retigabine shifted activation of the current by 12 mV to the left toward more hyperpolarized potentials without affecting the overall number of channels or single-channel conductance and thus increased maximum open probability up to 46% at 0 mV. To reproduce this effect, the gating variables were modified as follows:

$$\begin{array}{l}{\alpha }_{\text{R}}=0.0003+\frac{0.0182}{1+\exp \left(\frac{-32.3-V_{\text{m}}}{6.9}\right)}\hfill \\ {\alpha }_{\text{R}1}=0.15+\frac{0.456}{1+\exp \left(\frac{-32.3-V_{\text{m}}}{4.1}\right)}\hfill \\ {\alpha }_{\text{R}2}=\frac{0.053}{1+\exp \left(\frac{-41.3-V_{\text{m}}}{10.3}\right)}\hfill \\ {\beta }_{\text{R}1}=0.04+0.00006{\left(V_{\text{m}}+32.3\right)}^2\hfill \\ {\beta }_{\text{R}2}=0.06+0.00012{\left(V_{\text{m}}+32.3\right)}^2\hfill \end{array}$$ (A4)