Male Sprague Dawley rats, from 18 to 30 days-old, were anesthetized and decapitated. The brain was rapidly removed and transferred to an ice-cold dissection solution containing (in mM): 206 sucrose, 2.8 KCl, 1 MgCl₂, 2 MgSO₄, 1 CaCl₂, 26 NaHCO₃, 1.125 NaH₂PO₄, 10 glucose, and 0.4 ascorbic acid (equilibrated with 95% O₂ and 5% CO₂), pH 7.3. Septotemporal slices (400 μm) containing dorsal hippocampus, were obtained with a vibratome (Vibratome Sectioning System 102, Pelco, USA). Slices were placed in a holding chamber with standard artificial cerebro-spinal fluid (ACSF) and were left to recover during at least 1 h at 30°C before using them for recordings.

Whole cell patch-clamp recordings were conducted under visual guidance with an upright microscope (Nikon Eclipse E600FN, Nikon Corp. Instruments Co., Japan) equipped with oblique infrared and DIC optics. Electrodes (2.5–3.0 and 3.5–4.0 MΩ for voltage and current-clamp experiments, respectively) were fabricated from borosilicate glass capillary tubing (0.8–1.10 × 100 mm; Kimble Glass Inc., USA) using a horizontal puller (Flaming/Brown P-97, Sutter Instrument Co., USA). Current-clamp and voltage-clamp recordings were made with an EPC-10 patch-clamp amplifier (Heka, Heidelberg, Germany); signals were filtered at 10 kHz and acquired 25 kHz using the Heka Patchmaster software. In voltage-clamp experiments series resistance was compensated by 60–70%. Only cells with a stable resting membrane potential negative to −60 mV were used for recordings. Spike threshold was measured either during stimulation with a current ramp (8 pA/ms; from −80 mV until firing) or during the application of a pseudo-sinusoidal current of linearly increasing frequency and constant amplitude (ZAP stimulus). Threshold was defined as the membrane potential for which the time derivative exceeded 5 mV/ms.

All experiments were performed in presence of 10 μM CNQX and 100 μM PTX to block AMPA-R and GABA_A-R mediated currents. In some experiments 100 μM APV was also added.

CA1 pyramidal neurons were identified morphologically by their soma located in the stratum pyramidale that extend to stratum radiatum with a prominent apical dendrite. Once in whole-cell configuration was confirmed a resting membrane potential below −70 mV (−81.5 ± 0.8 mV, n = 32) and input resistance at −80 mV near 60 MΩ (55.9 ± 2.3 MΩ, n = 32).

Artificial cerebro-spinal solution (ACSF) contained (in mM): 124 NaCl, 2.8 KCl, 1.25 NaH₂PO₄, 26 NaHCO₃, 10 Glucose, 2 MgCl₂, 2 CaCl₂, and 0.4 ascorbic acid (equilibrated with 95% O₂ and 5% CO₂), pH 7.3 and 285–295 mOsm.

Low Na⁺ ACSF (in mM): 38 NaCl, 80 NMDG, 80 HCl, 2.8 KCl, 1.25 NaH₂PO₄, 26 NaHCO₃, 10 Glucose, 2 MgCl₂, 2 CaCl₂, and 0.4 ascorbic acid (equilibrated with 95% O₂ and 5% CO₂), pH 7.3 and 285–295 mOsm.

Internal pipette solution was based in previous works reporting stability of resting membrane potential, action potential threshold, and after-potential depolarization (Xu et al., 2005; Kaczorowski et al., 2011), in mM: 123 K-Gluconate, 10 KCl, 4 Glucose, 1 EGTA, 10 HEPES, 2 Na₂ATP, 0.2 Na₃GTP, 10 phosphocreatine, 1 MgCl₂, 0.1 CaCl₂, and 0.1% biocytin, pH 7.35, and 285–290 mOsm.

We measured the LJP between pipette solution and both ACSF (~13 mV) and low Na⁺ ACSF (~17.5 mV), according to the procedure described by Neher (1992), and recorded values were corrected offline during analyses.

Voltage responses to an intracellularly injected pseudo-sinusoidal current of linearly decreasing or increasing frequency and constant amplitude (10 pA) (ZAP stimulus; frequency interval: 0–15 or 20 Hz, 10 s duration) were recorded in current clamp conditions. In experiments with blockers of voltage-dependent channels the amplitude of ZAP stimuli was adjusted to maintain a peak to peak voltage response comparable to the control condition (5–10 mV) and to favor the evaluation of perithreshold resonance in the absence of spikes. In all experiment the protocol was repeated 8–10 times in every neuron, for each condition. The output equipotential subthreshold waves were averaged to proceed with the impedance analysis.

The impedance frequency profile (Z(f)) was obtained from the output (voltage) and input (current) waves Fast Fourier Transforms (FFT) ratio (Z(f) = FFT[V(t)]/FFT[I(t)]). The impedance is a complex quantity (Z(f) = Z, Real + Z, Imaginary), where the real part (Z, Real) is the resistance and the imaginary part (Z, Imaginary), the reactance. For each given frequency, the complex impedance can be plotted as a vector with magnitude (|Z(f)|) and phase. We only focused on the effects on impedance magnitude obtained with the following expression. (1)|Z(f)|=(Z, Real)2+(Z, Imaginary)2 Throughout the text the term impedance will be used to refer to the magnitude of the impedance vector, unless otherwise stated. Frequencies below 0.5 Hz were not plotted in the impedance profiles graphs, to avoid low frequency distortions. Off-line analyses and graphs were performed with Igor Pro 6.2 software (WaveMetrics Inc., USA).

Resonance is defined as the band-pass filter property of the impedance profile (Hutcheon and Yarom, 2000). The Q factor or value is a measure of resonance strength and is quantified as the ratio between the maximal impedance (i.e., the impedance at the resonance frequency, |Z(f_res)|) and the impedance at the lowest frequency (|Z(0.5)|) (Hutcheon et al., 1996). Here we used Q = 1 in the subthreshold depolarized voltage response as a criterion to define non-resonant behavior. To quantify resonance from recordings containing action potentials we defined an apparent Q value (Q′-value) using as point of reference the impedance at 1 Hz (Figures 2, 6) and 2 Hz (Figure 7) instead of 0.5 Hz, to discard suprathreshold contribution of spike firing to impedance profile.

Firing probability under ZAP stimulation was computed for each oscillatory period as the number of sweeps in which neurons fired a spike divided by the total number of sweeps (typically 8). The frequency of stimulation associated to each depolarized excursion was the frequency at the peak of each current oscillation (starting near 1.2 up to 20 Hz). For instance, if a neuron fired a spike at a given frequency in 4 out of 8 sweeps, its firing probability at that frequency is 0.5.

Despite technical limitations of whole-cell voltage clamp technique on neurons with complex morphology, numerous studies have shown that single-electrode voltage-clamp measurement of whole cell currents is suitable for recording in brain slices, including kinetics and voltage sensitivity of I_NaP and I_M (Halliwell and Adams, 1982; French et al., 1990; Hu et al., 2009). However, it is necessary to be aware of the lack of space-clamp control and its effects on regions distal to the soma. Three reasons support an acceptable quality of our measurements. First, both I_NaP and I_M are conductances located mainly at the soma where space-clamp control is possible. Second, the current injection needed for depolarizing to perithreshold potential is low (below 800 pA), reducing the error of our measurements. In addition, the reduction of Na⁺ driving force together with a slow ramp protocol allows inactivation of I_NaT and a low amplitude and well-clamped I_NaP recording. And third, most of our conclusions are taken from a relative comparison of I_NaP and I_M, with both currents sequentially recorded in the same cell, with the same pipette under the same conditions, thus decreasing possible bias due to different experimental configurations.

Furthermore, our voltage clamp data agree with values recorded in dissociated neurons (French et al., 1990), with voltage dependent behavior of neurons recorded in current clamp (Figures 2, 3) and also our voltage clamp data is able to reproduce voltage dependent behavior of neurons when are used to feed the computational models (Figure 5).

To characterize voltage dependence of G_NaP and G_M we fitted the following sigmoid curve: (2)Gi(V)=GMax11+eV-V0.5s

G_Max is the maximal conductance, V_0.5 is the voltage for half activation and s is the slope of voltage sensitivity. Despite experimental curves for G_M did not reach saturation, fitting values allowed a good mathematical characterization of conductance curve at the voltage range of interest.

To explore perithreshold behavior of neurons recorded under voltage-clamp we developed a point process conductance-based model following the Hodgkin-Huxley equations (Hodgkin and Huxley, 1952). The model included a passive leak current (I_Leak), a persistent (non-inactivating) Na⁺ current (I_NaP) (French et al., 1990) and the slow muscarine-regulated K⁺ current, I_M (Adams et al., 1982). The model did not include a firing mechanism (fast sodium and potassium conductances).

The equation describing the evolution of membrane voltage (V) in time is (3)CdVdt=IZAP - ILeak -IM -INaP  where C is the membrane capacitance estimated for each cell from the capacitive current elicited with a −5 mV step at −70 mV holding potential in voltage clamp configuration (Golowasch et al., 2009), and I_ZAP is the applied current. Intrinsic ionic currents in Equation 3 follow the next set of equations (4)ILeak=GLeak(V-ELeak) (5)INaP=GNaPw(V-ENa) (6)IM=GMr(V-EK) where G_Leak, G_M and G_NaP are the maximal conductances of the corresponding currents and E_Leak, E_K, and E_Na the reversal potentials of I_Leak, K⁺- and Na⁺-mediated currents, respectively, and r, w are the state variables (see below). E_Leak was set to −70 mV, E_K (−99 mV) and E_Na (47.1 mV) were calculated from the ionic conditions in our current clamp recordings. To simulate each recorded neuron, maximal conductance and steady-state values for I_NaP and I_M were obtained by fitting a sigmoid curve from experimental data (Figure 4) as explained above. This gave us a specific set of parameters for each neuron from −70 to −40 mV, allowing a precise characterization of voltage dependence at perithreshold region.

The dynamics of the state variables x_i = r and w is ruled by the following equation: (7)dxidt=xi∞(V)-xiτxi(V) where xi_∞ are the steady-state values of xi, and τ_xi are the corresponding time constants.

The time constant for I_NaP (τ_NaP) was set at 1 ms according to Vervaeke et al. (2006) and for I_M was modeled according to the voltage dependent equation (Adams et al., 1982): (8)τM=10003.3(e(V+35)/40+e-(V+35)/20 ) and was divided by the temperature-correcting factor 3^(T−22)/10 (Hodgkin and Huxley, 1952) to set simulations at 35°C.

Simulations were performed using Igor Pro 6.2 software on a Mac Book Pro (Apple Inc., USA) computer. An integration time step of 10 μs (100 kHz) was used for all simulations. The stimulation protocol used in all the cases comprised sequential ZAP current injections, each of 10 s duration and 5 pA amplitude, and ranging from 0 to 20 Hz. The ZAP injections were superposed to increasing holding current steps that moved the average potential between ~ −70 and −35 mV, as in the electrophysiological current-clamp experiments. The code for reproducing the computer simulations described in this paper is available upon request to authors.

For dynamic-clamp experiments, the current-clamp amplifier was driven by an analog signal from a desktop computer running Real-Time Linux Dynamic Clamp (Real-Time Experimental Interface, RTXI Dorval et al., 2001; Bettencourt et al., 2008) using an update frequency of 25 KHz.

Dynamic current used to decrease endogenous I_NaP or increase I_M, were introduced via dynamic clamp using Equations (5) and (6), where V is the online measured membrane potential. The dynamics of the state variables w and r were modeled according to Equation (7). The voltage dependence of the state variables at equilibrium was given by the equations: (9)w∞=11+e-(V+V0.5)/5 (10)r∞=11+e(V+35)/10 where V is the online recorded membrane potential and V_0.5 is the potential for half activation of I_NaP. Here we set V_0.5 as −52 mV according to our average voltage-clamp measurement (Figure 4).

The time constant for I_NaP, τ_NaP, was set at 1 ms according to Vervaeke et al. (2006) and for I_M was modeled according to Equation (8).

Here we show dynamic currents as the external current that was injected to neurons, following the standard convention were positive currents are depolarizing and negative currents are hyperpolarizing.

Statistical analysis was performed in GraphPad Prism 6.07 (GraphPad Software, Inc, USA). Group data is presented as the mean ± standard error together with the sample size of cells (n). For data with normal distribution (as Z_max, resting potential, R_in, G_max, G_(V), or I_(V)) we used different parametric tests. When data structure was a single variable measured at different membrane potentials and we needed to compare non-resonant vs. resonant cells (Figure 1) or non-resonant cells in control conditions vs. drug (Figures 3, 4), or the firing probability as function of stimulation frequency in the different experimental conditions (Figures 6, 7), we used two-way repeated measures ANOVA with Holm-Šídák's multiple comparison test. When comparing data at a single membrane potential between non-resonant and resonant cells we used Student's t-test (Figure 2). When comparing data at different conditions and a single membrane potential (Figures 6, 7) we used one-way ANOVA with matched samples and Tukey's multiple comparison tests.

When comparing Q or Q′ values we used a non-parametric Mann-Whitney rank test for unpaired data (Figures 1, 2), Wilcoxon rank test for paired data (Figure 3) and Friedman test with Dunn's multiple comparison test to evaluate the effect of PHT and dynamic clamp manipulations (Figures 6, 7). Most statistical tests were two-tailed with exception of those comparing non-resonant vs. resonant data in Figure 2. We used α = 0.05 as critic value.

Drugs were bath-applied at the following final concentrations: 10 μM 6-cyano-7-nitoquinoxaline-2,3-dione (CNQX; AMPA-type glutamate receptor antagonist), 100 μM d-2-amino-5- phosphonovaleric acid (APV; NMDA-type glutamate receptor antagonist), 100 μM picrotoxin (PTX; GABA_A receptor blocker), 1 μM tetrodotoxin (TTX; voltage-dependentNa⁺ channel blocker), 10 μM XE991 (KCNQ channel blocker), 60 μM phenytoin (PHT, I_NaP blocker). Drugs were obtained from Sigma, except for XE991 purchased from Tocris, and TTX that was obtained from Alomone Labs.

Our first approach for investigating the perithreshold behavior of pyramidal neurons was to measure their voltage response to ZAP stimulation under whole cell current clamp. We set the ZAP amplitude to produce a peak-to-peak voltage oscillation of ~5–8 mV, while neurons were maintained at different subthreshold potentials by the injection of a stable holding current; for simplicity, we will refer to this potential as “holding potential.” As expected, all CA1 pyramidal neurons displayed resonance at hyperpolarized potentials due to the presence of I_h (Hu et al., 2002; see below). However, these same neurons presented different behaviors at the perithreshold region, just below the spike threshold. We found that 21 out of 26 of recorded neurons (~80%) behaved as a pure low -pass filters, reaching an average perithreshold holding potential of −63.6 ± 2.8 mV. In contrast, the remaining ~20% of them showed a more depolarized perithreshold potential of −62.3 ± 0.6 mV (P = 0.014) and expressed a strong frequency preference at theta range (Figure 1A). After impedance analysis, we found that the larger group of neurons presented a Q = 1 and f_R of 0.5 Hz, characteristic of non-resonant neurons (Koch, 1984; Hutcheon et al., 1996). The other group displayed a strong resonant profile, with a Q of 1.24 ± 0.09 and a f_R at 3.5 ± 1.6 Hz (Figures 1A–C and raw data in Figure S1), proper of a I_M-dependent resonance (Hu et al., 2002). Those neurons presenting non-resonant behavior also displayed a higher Z_max, in agreement with a lack of activated I_M (Figures 1A–C, raw data in Figure S1). Thus, here we will refer to CA1 neurons as resonant or non-resonant according to their perithreshold behavior.

As mentioned, voltage responses at −85 mV after ZAP stimulus were similar in the two groups of cells, displaying strong I_h-dependent resonance without differences in Q value, f_R, or Z_max (Figures 1A–C, raw data in Figure S1). When stimulus was applied at −70 mV both groups of neurons showed reduced resonant behavior, together with similar resonant parameters (Q, f_R, and Z_max, Figures 1A–C, raw data in Figure S1).

To further study the transition from subthreshold to suprathreshold potential, we applied ZAP stimuli just overcoming action potential threshold and quantified the firing probability as a function of frequency (see Section Methods). We found that non-resonant neurons regularly started to fire during the first depolarizing incursion, occurring at 1.2 Hz (Figure 2A upper panel). Resonant neurons displayed higher firing probability at theta range (4–6 Hz), accompanied by a clear attenuation of firing at lower frequencies (Figure 2B). To compare impedance profiles at this suprathreshold region we calculated the Q′ value, using as a reference the impedance at 1 Hz (see Section Methods). While non-resonant neurons maintained a Q′ value near 1 (1.06 ± 0.02) with an average f_R at 1.7 ± 0.2 Hz, resonant neurons displayed a stronger Q′ value (1.35 ± 0.06) with an average f_R at 4.5 ± 0.2 Hz (Figures 2C,D). The peak impedance was higher for non-resonant (231.3 ± 22.4 MΩ) than in resonant (144 ± 22.4 MΩ) neurons, while the holding potential necessary to reach spike threshold with ZAP protocol was more hyperpolarized in non-resonant (−62.48 ± 0.7 mV) than in resonant (−60.0 ± 0.8 mV) neurons (Figures 2E,F).

Since a more depolarized action potential threshold would depolarize the perithreshold region, we measured the spike threshold using a depolarizing current ramp (see Section Methods). We obtained a slightly more depolarized value for resonant neurons, but without reaching statistical significance (−53.6 ± 0.7 mV vs. −52.2 ± 1.1 mV, P = 0.19).

The described difference in perithreshold behavior of pyramidal neurons suggests that the conductances involved in resonance in this voltage range, I_NaP and I_M, may have different levels of activation in the two populations.

To evaluate this possibility, we explored the ZAP-induced voltage response at depolarized potentials (up to −45 mV with 5 mV steps) in non-resonant neurons in presence of the selective Na⁺ channel blocker tetrodotoxin (TTX) to avoid spike generation. Interestingly, at voltages above −55 mV all studied neurons displayed strong resonant behavior, with Q values higher than 1.4 and f_R above 4 Hz (Figure 3), even though they were non-resonant near −60 mV. To corroborate that the observed resonant behavior was consequence of I_M activation we bath-applied the selective M-channel blocker XE991, which consistently eliminated resonance at depolarized potentials, but not at hyperpolarized potentials (Figure 3).

These experiments show that M-resonance consistently appears in all neurons at voltages more depolarized than −55 mV (see also Hu et al., 2002), which in most cases is above the spike threshold.

The difference in the holding voltage level at which resonant and non-resonant cells start firing (in a frequency-selective or unselective way, respectively; see Figure 2F) might reflect a different voltage window for interaction between I_NaP and I_M, with the consequent generation of resonant and non-resonant behaviors. To test this possibility, we investigated the degree of interaction between both currents in the same neuron.

We measured I_NaP under voltage clamp by eliciting whole cell currents with a slow voltage ramp (30 mV/s) (Magistretti and Alonso, 1999) to allow I_NaT inactivation, both in control condition and after the application of 1 μM TTX (Figure 4A). Then, I_NaP was obtained by digitally subtracting the recording in TTX from the control condition (Figure 4B). By this procedure, we obtained a persistent TTX-sensitive current that displayed non-linear voltage dependence, activated at command potentials above −70 mV and reached peak amplitude near −40 mV (Figure 4B). To achieve a better voltage clamp in the presence of Na⁺ currents, in these experiments we decreased the driving force by reducing extracellular Na⁺ concentration (see Section Methods). Therefore, to compare voltage-clamp results with the observations made in current clamp conditions we calculated the persistent Na⁺ conductance (G_NaP) by dividing the measured current by its driving force (V_m–E_Na). The voltage-dependent activation of G_NaP was characterized by fitting a sigmoidal curve to each trace (see Section Methods), obtaining a voltage for half activation (V_0.5) of −52.2 ± 1.0 mV, a slope constant of 4.9 ± 0.4 mV and a maximal conductance plateau of 5.3 ± 0.5 nS reached at voltages above −40 mV (n = 13; Figure 4C). These values are in agreement with previous investigations performed in dissociated CA1 neurons (French et al., 1990) and acute slices (Vervaeke et al., 2006), thus supporting the quality of our measurements. These results show that at perithreshold potential (near −58 mV) a substantial amount of G_NaP is active, thus strongly driving cells toward spike threshold.

Since I_M is absent at hyperpolarized potentials and activates with depolarization (Halliwell and Adams, 1982), we evoked whole-cell currents by 2 s depolarizing steps from a holding potential of −87.5 mV to voltages between −77.5 and −32.5 mV, with increments of 5 mV. To measure I_M in the same cells in which we previously measured I_NaP, we applied this voltage protocol in the presence of TTX as the control condition. The described voltage protocol elicited a sustained whole-cell outward current that contained a combination of several ionic currents (Figure 4D). To isolate I_M we bath-applied 10 μM of the selective blocker XE991 and repeated the protocol after 5–8 mins (Figure 4E), obtaining the XE991-sensitive current by digital subtraction (Figure 4F).

The isolated current showed a slow activation constant (60–200 ms) with no inactivation (Figure 4F), in agreement with the described I_M kinetics (Shah et al., 2002). The I-V curve shows that the isolated current is inactive at resting potential and begins to activate above −55 mV, increasing monotonically with voltage and reaching ~ 400 pA at −32.5 mV, the maximal voltage tested (Figure 4G). We computed the G-V curve dividing the I-V trace by the driving force for K⁺, obtaining a G_M curve that appears above -60 mV and reaches ~ 6 nS at −32.5 mV (Figure 4H).

Once we measured the voltage dependence of I_NaP and I_M under the same conditions and in the same cells, we were able to estimate their relative activation levels near perithreshold potential. Interestingly, the comparison of both curves shows that at all voltages between −62.5 and −42.5 mV, G_NaP is larger than G_M (Figure 4I). A closer inspection to activated conductances at perithreshold potentials (−62.5, −57.5, and −52.5 mV) shows that in all paired recordings the amount of G_NaP always exceeds G_M; with G_NaP ranging from 0.6 to 2.5 nS, whereas G_M only reaches a modest average activation of 0.6 nS at −52.5 mV (See paired values in Figure 4J).

Since at perithreshold potentials the driving force for Na⁺ is higher than for K⁺, is expected that the magnitude of the difference between I_NaP and I_M will be even higher than the difference of their respective conductances. With the driving force calculated from the ionic concentrations in our current clamp experiments (see Section Methods) we obtained that I_NaP is around −150 pA at spike threshold levels, while I_M is only 9 pA, maintaining this paired relative difference for each recorded neuron (See paired values in Figure 4K). These quantifications confirm the reduced contribution of I_M in the perithreshold region of non-resonant neurons.

To evaluate the expected perithreshold behavior of neurons recorded under voltage clamp we constructed a conductance-based computational model to be applied to each neuron according to their own measured I_NaP, I_M, and capacitance (see Section Methods). To gain detail and precision in the computer simulations we fed the model with the specific intrinsic parameters of each cell, instead of using the average values from a diverse population. As we were interested in evaluating perithreshold frequency preference we did not include in the model the conductances related to action potential generation.

We explored the voltage response to ZAP stimuli for membrane potentials maintained between −70 and −35 mV through injection of a holding current, thus simulating typical current-clamp experiments. Recreated neurons reproduced the variable behavior observed in current clamp experiments, as represented by cells #5 and #6 in Figure 5. Cell #5 displays non-resonant behavior between −70 and −60 mV. However, around the presumed perithreshold potential (near −58 mV), a voltage upstroke of about 10 mV is observed at the first and slowest oscillation of the ZAP, indicating a significant activation of I_NaP (note that a real spike is not seen because Hodgkin & Huxley conductances were omitted in the model; Figure 5A, red). Interestingly, at this point cell #5 holding potential became unstable, i.e., small increments in holding current generated a step-like transition from −58.6 to −43 mV, a potential at which the neuron stabilizes due to the compensatory effect of I_M activation, which also generates a strong resonant behavior.

In contrast, cell #6 displays a slight resonant behavior even at presumed perithreshold potentials. Further, current injection produces a gradual depolarization of holding potential accompanied by an increase in resonant behavior, instead of the discontinuous change observed in cell #5 (Figure 5A green). In this second example, the small amount of I_M activated at perithreshold potential allows the expression of resonance by decreasing voltage oscillations at lower frequencies and preventing the strong depolarization driven by I_NaP in the previous case. Further, co-activation of I_NaP and I_M by depolarization allows a balanced interplay between both currents that prevents voltage instabilities as in cell #5, producing a strong resonance with depolarization. The impedance profiles for both neurons also show the different behavior at each holding potential (Figure 5A bottom). Note that while responses are different at perithreshold potential, after depolarization to near −40 mV their impedance profiles are similar. Figure 5B shows the input resistance, peak frequency and resonance strength values against membrane potential for all recreated neurons. An important quality control of the simulations is the reproduction of the increase in input resistance caused by the amplifying effect of I_NaP, and the rise of Q value attained by I_M activation. While the general trend was to switch from non-resonant to resonant behavior upon increasing depolarization, resonance appears at different membrane potentials and in most cases following a membrane potential discontinuity as described above (note that this behavior is observed even when holding current increments are as small as 5 pA). As indicated by peak frequency and Q plots in Figure 5B, transition from non-resonant to resonant behavior is a heterogeneous process with a different voltage point for each neuron. Some neurons transit to depolarized potentials from values as hyperpolarized as −60 mV (cells #1, 3, 7, and 8, Figure 5B). Certainly, this transition is visible in our model due to the absence of spiking activity. In physiological conditions the transition to resonant behavior in most cases is occluded by the activation of the spiking machinery (as seen in Figures 1, 2). It should be noted that the experiments with TTX as those in Figure 3 are also not comparable with these simulations as this drug not only abolishes action potentials but also block I_NaP.

To predict the perithreshold behavior of recreated cells, we compared the membrane potential at which I_NaP activation drives the depolarizing voltage discontinuity (when present) with the membrane potential where resonance is expressed (Q > 1). If these two values are close to each other and more hyperpolarized than our measured spike threshold (near −52 mV, Figure 2) we considered that neuron as putative resonant (Figure 5C). According to this criterion, cells #2 and #6 are putative resonant neurons, while the other 6 neurons are presumed to be non-resonant, in agreement with the abundance of both perithreshold behaviors previously presented (Figure 1).

The computational exploration of voltage responses using experimentally measured combinations of I_NaP and I_M that constitutes a sample group in the physiological variability of these conductances, supports the idea that the expression of perithreshold resonance depends on their relative magnitudes.

Since we confirmed that all recorded pyramidal neurons have the intrinsic mechanism to display resonant behavior, we now explored if a partial block of I_NaP can produce resonance in non-resonant neurons. Therefore, we characterized perithreshold behavior and firing preference in control condition, after the addition of 60 μM of the I_NaP blocker and antiepileptic drug phenytoin (PHT; Chao and Alzheimer, 1995), and after washing out the drug. In control conditions neurons were non-resonant, with a high voltage response and firing probability at the slowest oscillations (Figure 6A). When the I_NaP blocker was added, was necessary to inject more DC current in order to depolarize neurons up to perithreshold potential, compensating the blocking of a depolarizing current (not shown). Moreover, the reduction of I_NaP also shifts to depolarized values the holding potential necessary to trigger spikes, consistent with a reduction in the intrinsic depolarizing force (note the more depolarized holding potential in Figures 6A,G). These changes are accompanied by modifications in the spiking behavior, displaying an attenuated response at low frequencies and a maximal firing probability in the theta range, thus becoming a resonant neuron (Figure 6A middle/green). When the drug was washed out the neuron recovered its original non-resonant dynamics (Figure 6A, n = 6). Figure 6B shows the average firing probability curves, indicating that cells moved from a robust low-pass filter behavior at control condition to a band-pass filter pattern when a fraction of I_NaP is blocked. The effect is almost completely reversed upon blocker removal. The suprathreshold impedance profile in control condition has a low-pass filter shape with a peak impedance of 233.5 ± 31 MΩ at 1 Hz. Note however that the curve displays a hump near 4 Hz that breaks the monotonic drop of impedance as frequency increases (Figure 6C, left). In presence of phenytoin the impedance at 1 Hz falls below 200 MΩ evidencing the band-pass filter pattern, with the impedance peak at the same frequency of the hump observed in control conditions (see overlapped curves in Figure 6C, middle). This change is partially reversed after washing out the drug, and the impedance at 1 Hz grew above 200 MΩ. Regarding resonant parameters, after partial block of I_NaP Q′ rises from 1.05 ± 0.03 to 1.7 ± 0.7, while f_R increases from 1.27 ± 0.10 Hz to 3.6 ± 0.5 Hz, consistent with a resonant behavior generated by I_M (Figures 6D,E). In agreement with the amplifying effect of I_NaP, phenytoin addition produced a 20% drop of peak impedance (Figure 6F).

The partial block of I_NaP produced a raise in the potential at which transition to spiking occurs from −63.1 ± 1.5 to −59 ± 1.8 mV (Figure 6G), while the spike threshold measured with a voltage ramp was not modified. However, the spike threshold measured when spikes were fired during suprathreshold oscillations suffered a depolarizing shift from −54.1 ± 1.4 to −49.5 ± 2.3 mV (Figures 6H,I). The transformation of perithreshold behavior induced by phenytoin was partially reverted after drug washout.

These results confirm that non-resonant hippocampal neurons are able to change their firing frequency preference to a resonant behavior by a moderate reduction in I_NaP.

Our following goal was to evaluate the effect of changing the perithreshold balance of I_NaP and I_M in non-resonant neurons using dynamic clamp (Dorval et al., 2001). We produced a virtual knock-down of I_NaP by injecting a negative I_NaP (−I_NaP) to neutralize a fraction of total endogenous I_NaP (see Section Methods). This strategy is comparable to the previous pharmacological blockade of I_NaP but now with the possibility to determine the conductance change necessary to produce the switch in perithreshold behavior.

To investigate whether non-resonant neurons are able to resonate with their natural intrinsic levels of I_NaP in specific conditions, we used dynamic clamp to incorporate a virtual I_M (+I_M) based on the activation curve previously obtained by voltage-clamp experiments, but shifting the voltage sensitivity toward hyperpolarized potentials to increase the voltage window of interaction with I_NaP (see Section Methods).

We first characterized the frequency preference of a neuron in control condition, corroborating the lack of frequency preference in voltage response and firing probability (Figure 7A, left). Then we injected −I_NaP, beginning with a maximal conductance (G_NaPMax) of 2 nS. This amount was enough to observe resonance in three out of six neurons (Figures 7A–C). In the other three neurons, it was needed to increase the amount of −I_NaP to 4.5 nS in one case and to 9 nS in the other two cells to obtain a similar response. Despite the differences in the amount of injected −I_NaP (canceling an average of −147.6 ± 61.9 pA of endogenous I_NaP, not shown), it was possible to induce an equivalent resonant behavior in all 6 neurons, as expressed in the impedance profile (Figure 7C) and in the drop of firing probability at low frequencies (Figure 7D). Reduction of I_NaP modified Q′ from 1.0 to 1.18 ± 0.06, but without reaching statistical significance (P = 0.12, Figure 7F) and shifted f_R from 0.7 to 5.2 Hz (Figure 7G). In agreement with the amplifier role of I_NaP, its neutralization reduces peak impedance from 259 ± 44.1 to 88.8 ± 15.6 MΩ (Figures 7C,H).

The injection of −I_NaP depolarizes the holding potential just below threshold from −61.1 ± 1.2 to −56.3 ± 1.8 mV (Figure 7I) as in phenytoin experiments. Importantly, the modification of I_NaP did not alter drastically the action potential threshold measured during oscillatory stimulation (Figure 7J).

After evaluating the effect of −I_NaP injection we explored the consequences of injecting +I_M in the same cells. It was needed to shift the V_0.5 of the activation curve from −39 to −49 mV (n = 3), −54 mV (n = 1) or −59 mV (n = 2), to achieve a critical amount of virtual I_M allowing to change the perithreshold behavior from non-resonant to resonant (average +I_M current injected during voltage oscillations was −20.1 ± 7.3 pA, not shown). As expected, intrinsic I_NaP interacted with +I_M to induce a perithreshold resonant behavior able to translate frequency preference to spiking regime, with a reduction in firing probability at 1.2 Hz from 1.0 to 0.15 ± 0.07 (Figure 7E). +I_M injection only reduced impedance at frequencies below 4 Hz (Figure 7C) and presented a trend to reduce peak impedance (Figure 7I). The combination of endogenous high levels of I_NaP plus a critical amount of +I_M produces a strong resonant behavior, rising Q′ and shifting average f_R from 0.7 ± 0.2 to 3.1 ± 0.4 Hz (Figures 7F,G). As expected from the unaltered I_NaP, in the +I_M condition resonant behavior develops without altering the perithreshold holding membrane potential, nor the spike threshold (Figures 7I,J).

Taken together, these results show that the behavior of CA1 pyramidal neurons can be transformed from non-resonant to resonant by changing the relative contributions of I_NaP and I_M.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.