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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Neurosci. Author manuscript; available in PMC 2012 September 14.
Published in final edited form as:
PMCID: PMC3316126

Spike Resonance Properties in Hippocampal O-LM cells are Dependent on Refractory Dynamics


During a wide variety of behaviors, hippocampal field potentials show significant power in the theta (4–12 Hz) frequency range and individual neurons commonly phase-lock with the 4–12 Hz field potential. The underlying cellular and network mechanisms that generate the theta rhythm, however, are poorly understood. Oriens-lacunosum moleculare (O-LM) interneurons have been implicated as crucial contributors to generating theta in local hippocampal circuits because of their unique axonal projections, slow synaptic kinetics and the fact that spikes are phase locked to theta field potentials in vivo. We performed experiments in brain slice preparations from Long-Evans rats to investigate the ability of O-LM cells to generate phase-locked spike output in response to artificial synaptic inputs. We find that O-LM cells do not respond with any preference in spike output at theta frequencies when injected with broadband artificial synaptic inputs. However, when presented with frequency-modulated inputs, O-LM spike output shows the ability to phase-lock well to theta-modulated inputs, despite their strong low-pass profiles of subthreshold membrane impedance. This result was dependent on spike refractory dynamics and could be controlled by real-time manipulation of the post-spike afterhyperpolarization. Finally, we show that the ability of O-LM cells to phase-lock well to theta-rich inputs is independent of the h-current, a membrane mechanism often implicated in the generation of theta frequency activity.

Keywords: Oriens-Lacunosum Moleculare, interneuron, hippocampus, theta, h-current, dynamic clamp, after-hyperpolarization, resonance, refractory


The mechanisms by which the 4–12 Hz theta rhythm is generated in hippocampus remain unclear. The traditional in vivo model is that hippocampal theta is imposed by rhythmic input from the medial septum and diagonal band of Broca (Bland and Oddie, 2001). However, detailed in vivo recordings from septum and hippocampus (King et al., 1998; Nerad and McNaughton, 2006) suggest that hippocampal theta is not simply paced by the septum. Furthermore, under the appropriate pharmacological conditions, hippocampal brain slices can generate in vivo-like theta activity autonomously (Gillies et al., 2002). The hypothesis of intrinsically generated theta is strengthened by more recent recordings from isolated hippocampus (Goutagny et al., 2009), data suggesting that individual layers of hippocampus contain independent theta generators (Montgomery et al., 2009; Shirvalkar and Bahar, 2009) and that some hippocampal interneurons display subthreshold oscillations (Morin et al., 2010).

Much of the work on intrinsically-generated hippocampal theta has focused on the contributions of interneurons (Cobb et al., 1995; Klausberger et al., 2003; Rotstein et al., 2005; Goldin et al., 2007). In particular, oriens-lacunosum moleculare (O-LM) cells of the hippocampus have been suggested to contribute to the local theta rhythm by providing theta-frequency inhibition to principal cells (Pike et al., 2000; Gloveli et al., 2005a) or by providing slower inhibition onto basket cells and principal cell distal dendrites (Gillies et al., 2002; Rotstein et al., 2005). A common assumption has been that O-LM cells are intrinsic theta oscillators (Pike et al., 2000; Gillies et al., 2002; Rotstein et al., 2005; Gloveli et al., 2005a) and thus, that intrinsic membrane conductances, especially the h-current (Maccaferri and McBain, 1996), contribute to theta-frequency subthreshold oscillations and spike discharge. While it has been shown that O-LM cell spikes phase lock to the theta rhythm in vivo (Klausberger et al., 2003) and can generate spike rates within the theta range in vitro (Gillies et al., 2002; Gloveli et al., 2005b; Goldin et al., 2007), the ability for O-LM cells to resonate or generate pace-making activity at theta has not been shown. Lastly, it is not well understood how spiking and subthreshold membrane dynamics interact and influence spike output in O-LM cells.

In the present study, we investigated the ability of O-LM cells to generate oscillatory spike activity in response to either unmodulated or sinusoidally-modulated artificial synaptic activity. We were particularly interested in the biophysical mechanisms leading to patterned spike output in response to modulation of synaptic activity at theta frequencies. We find that O-LM cell spiking does not produce autonomous or pace-making activity at theta frequencies in response to unmodulated inputs. Instead, we find that O-LM cells support a modest amplification of inputs modulated at theta frequencies due to specific refractory dynamics associated with the spike after-hyperpolarization. These dynamics amplify spike output at 8 Hz to a greater extent than would be expected from subthreshold membrane voltage responses. Our data suggest that intrinsic biophysical properties of O-LM cells can potentially transmit network theta activity but do not themselves generate theta oscillations.



All protocols were approved by the University of Utah Institutional Animal Care and Use Committee (IACUC). Brain slices were prepared using established techniques (Netoff et al., 2005). Briefly, young (postnatal days 18–28) Long-Evans rats of either sex were anesthetized using isoflurane and decapitated. The brain was removed rapidly and placed in a beaker of ice-cold, oxygenated artificial cerebrospinal fluid (ACSF) containing (in mM): NaCl 125, KCl 2.5, NaH2PO4 1.25, CaCl2 2, MgCl 1, NaHCO3 25, D-glucose 25. The pH was maintained at 7.4 by saturation with 95% O2-5% CO2. The brain was dissected down to a block of tissue containing the region of interest. A vibrating microtome was used to cut slices, 350–400μm thick, in the horizontal plane. Slices were incubated at 32 °C for at least 30 min and 30 min at room temperature before use.

All recordings were performed in the CA1 region of the hippocampus and carried out at 35 °C. O-LM cells were identified under differential interference contrast (DIC) optics based on the location of the cell body in stratum oriens and the presence of horizontally-extending dendrites. Subsequent unequivocal identification of O-LM cells was based on post-hoc morphological analysis but cells were preliminarily identified based on AHP shape and membrane voltage ‘sag’ in response to a strong hyperpolarzing current step.

Cell were patched with 4–6 MΩ glass pipettes filled with internal solution that contained (in mM): 120 K-Gluconate, 20 KCl, 10 HEPES, 0.2 EGTA, 2 MgCl2, 4 Na2-ATP, 0.3 Tris-GTP, 7 diTris-Phosphocreatine and 0.6% biocytin by weight. Pipettes were connected to the headstage of an amplifier (MultiClamp 700B) set in “bridge” mode to obtain current clamp recordings. Bridge balance correction was used for all recordings and a criterion based on resting membrane voltage (< −50 mV) and spike height (overshooting 0 mV) was used to identify healthy O-LM cells.

In all recordings, series resistances were less than 15 MΩ. O-LM cells have relatively high membrane resistance (>250 MΩ) and injected currents were small (less than 100 pA) mitigating any potential problems associated with series resistance and the implementation of dynamic clamp. Input resistance, resting potential, and capacitance compensation settings were continually monitored. Recordings were not corrected for the junction potential. All recordings were done in the presence of 10 μm DNQX (Sigma-Aldrich) and 50 μm picrotoxin (Sigma-Aldrich) in order to block endogenous synaptic activity. Synaptic block did not cause a significant change in the resting membrane resistance (control: 262 ± 155 MΩ, synaptic block: 246 ± 80 MΩ, p = 0.70, Kruskal-Wallis test).

Dynamic Clamp and Recordings

For dynamic clamp experiments, the current-clamp amplifier was driven by an analog signal from an x86 personal computer running Real-Time Application Interface Linux and an updated version of the Real-Time Linux Dynamic Clamp called Real-Time Experimental Interface (Dorval et al., 2001; Bettencourt et al., 2008). The dynamic clamp system update rate and data acquisition rate were both 5 kHz. A custom protocol was developed to generate two separate Poisson processes representing excitation and inhibition. Individual excitatory and inhibitory synaptic conductance waveforms were modeled as a difference-of-exponentials function with a rise time of 0.5 ms and decay time of 6.8 ms, which is within the range of normal values for GABAergic synapses (Netoff et al., 2005) and accounts for the fact that OLM cells receive predominantly slower, kainate based excitation (Goldin et al., 2007). Reversal values for the excitatory and inhibitory synaptic conducntaces were 0 and −80 mV, respectively. Conductance injection is different from traditional current injection in that it is a voltage-dependent process. Thus, rather than injecting a fixed current waveform, the injected current is subject to modification depending on the voltage of the target cell in the same manner that a biological synapse depends on post-synaptic voltage.

Synaptic input frequency modulation was modeled as a modulation of the Poisson rate of the inhibitory process. Frequency modulation was 20% in all cases. This was implemented by sinusoidally-modulating the rate of generation of events by the Poisson process from 0.8 to 1.2 times the baseline rate. In order to represent the ensemble of activity from numerous slow firing individual synapses onto O-LM cells, the rates of excitation and inhibition were set to 500 and 1000 Hz, respectively(Pare et al., 1998; Destexhe and Pare, 1999). These frequency values also produced an approximate net balance in the excitatory and inhibitory currents such that the turning on of the Poisson stimulus kept cells near the threshold voltage for spiking at low rates. The amplitude of single events was adjusted on a per cell basis to achieve approximately 3 mV standard deviations in the fluctuation of the membrane voltage. When required, small amounts of DC current were used to achieve an approximate firing rate of 2.5 Hz in all cells. A protocol to control spike rate automatically was adapted from existing code found at

Artificial h-current (Ih) was added with a separate dynamic clamp model utilizing a first order differential equation described by the following equations:





Parameters were as follows: τpeak =150ms, V1/2 = −75mV, k = −8, and Eih = −20mV

We manipulated the spike after-hyperpolarizations (AHPs) by injecting a spike-triggered current that was modeled as a difference-of-exponentials function. After spikes had been detected, a 1 ms delay was observed until the start of the AHP, at which point a difference-of-exponentials waveform was injected and tuned to qualitatively alter the AHP in the desired manner. These waveforms had peak injected currents ranging between 20 pA and 40 pA. The rise times of the AHP manipulating waveform was set to 10 ms and the decay time to 50 ms.


All recordings of O-LM cells were done with intracellular pipette solution containing 0.6% biocytin (Invitrogen) by weight. Cells were allowed to passively fill with biocytin for at least one hour before they were fixed in 4% paraformaldehyde. To visualize neurons, slices were washed 3 times for 15 minutes in 0.1 M phosphate buffered saline (PBS) and then incubated for 2 – 4 hours in a solution containing 1 mg/mL streptavidin-Alexa 488 or 532 (Invitrogen) and 0.75 mL/100mL triton X-100 (Sigma-Aldrich) in PBS. After another 3 washes for 15 minutes each in PBS slices were mounted on microscope slides in Mowiol. Slides were imaged on a custom built 2-photon microscope. Image stacks were processed with ImageJ (NIH) and processes were traced with the Neuromantic ( tracing software. O-LM cells were characterized on the basis of horizontally-oriented dendrites relative to str. pyramidale with cell bodies in str. oriens. Furthermore, we required that identified O-LM cells have axons passing through str. pyramidale and radiatum and branching in str. lacunosum moleculare. Only cells with this characteristic morphology were included in the study.


Analysis was done in MATLAB (The MathWorks) with custom scripts. Spike times from traces of identified O-LM cells were extracted from voltage traces and spike trains were converted to binary trains. A power spectral density was computed from binary spike trains to determine power in the spike train at each frequency between 0 and 100 Hz using the spectrum.welch function in MATLAB. FFT length was chosen such that resulting power spectra had integer frequencies falling exactly on bin centers. To quantify the relative amount of spike power at the modulation frequency, we took the ratio of the peak power at the modulation frequency divided by the mean steady-state power (power at 0 Hz). We refer to this quantity as the power ratio.

Subthreshold impedance (Z(f)) was assessed using the membrane voltage response to a white noise current stimulus. Impedance was defined as the ratio of the absolute magnitudes of the FFT of voltage traces and current input:


The amount of resonance was quantified using a “Q-value”, which was defined as the maximum impedance value divided by the average impedance value between 1.5 and 2 Hz. For measures of spike train power spectra and vector strength we used 300 s traces (~750 spikes) of spike train data in response to artificial synaptic stimuli. For assessment of impedance, we used 30 s traces of membrane voltage response to a white noise stimulus.

Vector strength was computed using tools from the Circular Statistics Toolbox in MATLAB (Berens, 2009). Vector strength is the summed normalized vector length of circular data and provides a measure of phase locking of a series of spiking events relative to an ongoing oscillation.

When datasets were found to be non-normally distributed based on the Lilliefors test, we used non-parametric statistical tests to compute significance values. For datasets of equal size we used the Kruskal-Wallis test (the non-parametric version of a one-way ANOVA). When data sets were of unequal size we used the Wilcoxon rank-sum test (the non-parametric version of a two-sample t-test). When multiple comparisons were performed, the threshold for significance was adjusted according to α =1 − (1 − α0)n where α0 is the default significance level of 0.05 and n is the number of comparisons. Plots were prepared for publication in Inkscape (


A simple computational model was constructed with equations described in (Izhikevich, 2004). The equations were:


with the reset condition:


and parameters a = 0.03, b = 0.25, c = −60, d = 4. The computational model was implemented using the dynamic clamp software and the exact same protocols used in experimental recordings were used to drive activity in the model. Specifically, artificial synaptic fluctuations were generated identically to the experimental setup with the maximal conductance parameters for individual excitatory and inhibitory events adjusted to achieve the same 10 mV peak to peak voltage fluctuations as in the experimental data. Spike rate was controlled as in experiments and kept at 2.5 Hz. AHP attenuating/enhancing currents were generated identically to the experimental data by using a difference-of-exponentials waveform with rise and fall kinetics of τrise = 10 ms and τfall = 50 ms. Measures of spike analysis and power ratio in the model were carried out in the same way as for experimental data.

The NMDA conductance was implemented with the same equations as the other synaptic inputs but with kinetics of τrise = 5 ms and τfall = 150 ms and with voltage-dependent Mg2+ block modeled as described elsewhere (Fernandez and White, 2008) using a published set of parameters (Harsch and Robinson, 2000) and the equation:


with Vhalf = −10 and k = 12. GABAB was model with the same equation as GABAA using kinetics of τrise = 170 ms and τfall = 3400 ms (Pfrieger et al., 1994).


Anatomical and electrophysiological identification of O-LM cells

O-LM cells possess a distinct anatomy among hippocampal interneurons (Freund and Buzsáki, 1996) that suggests a unique functional role and provides a convenient feature by which they can be unambiguously identified. O-LM cells are named after their somatic location and axonal projection pattern. The cell body and dendrites are found in the stratum oriens, often close to the alveus, while the axon projects to the stratum lacunosum-moleculare (Lorente De Nó, 1934). Given this unique structure, visual identification of O-LM cells is straightforward when the dendritic, and particularly axonal, morphologies are visualized. Due to the diversity of interneurons in the hippocampus (Freund and Buzsáki, 1996), we anatomically identified all cells to ensure recordings were from the appropriate cell type. Figure 1A and B show two representative O-LM cells. Hippocampal lamina are labeled and delimited by dotted black lines. Projections in gray denote dendrites and are restricted to str. oriens (Figure 1). Axons are traced in black and arborize in str. oriens, and more extensively in str. lacunosum-moleculare (Figure 1). In general, cells show minimal axonal branching in str. radiatum; the axon nearly completely traverses the pyramidal cell layer and str. radiatum, a distance of several hundred microns, before extensively branching in str. lacunosum-moleculare (Figure 1A,B). The example cell shown in Figure 1A has recurrent axonal collaterals that can be seen branching in str. pyramidale to project back to str. oriens (black star).

Figure 1
Reconstructed O-LM cells show characteristic anatomical and electrophysiological features

We used current step injections and subthreshold impedance analysis to identify O-LM cells electrophysiologically. The profile of O-LM cells in response to hyperpolarizing current steps showed a characteristic ‘sag’ in membrane voltage (Figure 1C). Significant hyperpolarization, however, was required to elicit a visible sag in the voltage response. This indicated a relatively hyperpolarized voltage for activation of the h-current, the mechanism responsible for producing a sag in membrane voltage. Next, we measured the impedance profile by injecting white current noise into O-LM cells at near-threshold potentials. In agreement with more recent findings measuring impedance and the h-current activation voltage in O-LM cells (Zemankovics et al., 2010), we found no resonance peak in our impedance measurement (Figure 1D, n = 8).

To quantify the responsiveness of O-LM cells to theta frequencies in the subthreshold voltage range, we measured the relative impedance between a slow frequency response (2 Hz) and a theta range response (8 Hz). The ratio of impedance at these two frequencies (Figure 1D inset, theta ratio) indicated that O-LM cells strongly attenuated the theta response compared with slower frequencies (mean ratio value of 0.71 ± 0.01). The impedance values at 2 Hz (320 ± 13 MΩ) and 8 Hz (220 ± 8 MΩ) were significantly different (n = 8, p < 0.04). Thus, rather than amplify theta inputs, subthreshold properties in O-LM cells near threshold have no resonance at theta and greatly reduce the size of membrane voltage fluctuations with frequency components greater than 5 Hz. The absence of a peak at theta and the relative low frequency cutoff of the O-LM cell response are likely due to an absence of h-current activation near threshold.

O-LM cells do not show theta spiking in response to artificial synaptic input

Results in Figure 1 and those from other groups using similar analyses have shown little subthreshold resonance at theta in O-LM cells. Instead, ideas attributing a pace-making role in theta generation have stemmed from studies measuring spike rate. The reported tendency of O-LM cells to fire at spike rates within theta frequencies in vitro (Maccaferri and McBain, 1996) has been used to conclude that O-LM cells are endogenous theta oscillators that pace network activity (Pike et al., 2000; Gloveli et al., 2005b; Goldin et al., 2007). A distinct role for O-LM cells in generating hippocampal theta field potentials has emerged from network modeling studies incorporating the aforementioned ability for O-LM cells to fire at a steady rate of ~10 Hz in slices (Gloveli et al., 2005b; Rotstein et al., 2005; Tort et al., 2007). The implication from previous work is that O-LM cells, as endogenous oscillators, should discharge preferentially at theta frequencies when presented with broadband artificial synaptic input as in other theta-rhythmic cells (Fernandez and White, 2008). We used a dynamic clamp system (Dorval et al., 2001; Bettencourt et al., 2008; to provide conductance-based synaptic inputs into O-LM cells. Importantly, the artificial synaptic input resulted in significant membrane voltage fluctuations that simulated conditions prevalent in vivo and which drove spikes via brief excursions in membrane voltage similar to in vivo conditions (Crochet and Petersen, 2006; Destexhe and Contreras, 2006). Finally, using this form of stimulation allowed a time varying modulation of the synaptic input rate.

To be consistent with in vivo recordings from O-LM cells (Klausberger et al., 2003), we held average spike rate at 2.5 Hz. The low firing rate has several important implications. First, any theta-frequency peak observed in the cell spike train power spectrum is due to an intrinsic oscillatory dynamic that is able to cluster spikes at theta. Thus, rather than simply firing at a mean rate of theta all the time, which many cells are capable of, the cell actively generates interspike intervals at theta. Second, imposing a low average firing rate allowed moderate variance in the input to achieve the desired values of spike time variability observed in numerous in vivo recordings (Smith and Smith, 1965; Calvin and Stevens, 1968; Noda and Adey, 1970; Softky and Koch, 1993; Holt et al., 1996; Shadlen and Newsome, 1998; Harvey et al., 2009). The low average spike rate still allows for potential epochs of theta to occur in response to the synaptic stimulus but does not bias the cell to fire only in the theta range at a constant spike frequency and with low spike time variability.

To quantify a potential oscillatory output in response to broadband and unmodulated synaptic input, we used the power spectrum of the spike train. Quantification of oscillatory properties using the spike train is important since only the spike train information, and not the membrane voltage, is likely to propagate to post synaptic cells. Thus, the spike train power spectrum represents the actual output quantity that needs to be oscillatory if the cell is to behave as a pacemaker in a network.

The amplitude of individual events in the input train was adjusted such that the standard deviation of the membrane fluctuations in the near-threshold range was near 3 mV, consistent with subthreshold voltage variability values reported in vivo (Pare et al., 1998; Fellous et al., 2003; Destexhe et al., 2003). The rate of synaptic inputs onto O-LM cells was chosen to maintain membrane voltage near threshold and produce the desired size in voltage fluctuations to drive spiking. O-LM cell spike trains recorded in response to artificial synaptic stimulation (Figure 2A) did not generate any peak in spike train power or ISI distribution at theta frequencies (Figure 2C,D, black traces). In all O-LM cells tested, we observed the same outcome (n = 8).

Figure 2
O-LM cells do not discharge with any frequency preference when driven with either conductance or current noise

We considered the possibility that the conductance component associated with the artificial synaptic activity was attenuating potential oscillatory dynamics, as has been reported for medial entorhinal cortical stellate cells (Fernandez and White, 2008). To test for this possibility, we repeated our recordings with current-based artificial synaptic stimulation (Figure 2B). Hence, similar levels of voltage fluctuations were used to generate spikes without adding a mean conductance to the O-LM cell membrane. Under these conditions, O-LM cells continued to show no signs of oscillatory output in the spike train power spectra or the ISI distributions (Figure 2C,D, gray traces). Both spike train power spectra and ISI distribution data remained unchanged compared with conductance-based synaptic activity.

The above results indicate that given broadband synaptic drive, O-LM cells generate no pacemaking or oscillatory output in the spike train. Thus, unlike strongly oscillatory cells (Fernandez and White, 2008), spike trains showed no preference for generating periods of interspike intervals at theta frequencies. These results suggest that O-LM cells have no intrinsic biophysical properties that endow them with a theta pace-making role in hippocampus.

O-LM cells follow 8-Hz-modulated synaptic input well

Although O-LM cells did not respond rhythmically when driven with broadband artificial synaptic stimuli, we reasoned that the cells might modulate spike output rate preferentially in response to a stimulus modulated at theta frequencies. Thus, O-LM cells, while not endogenous theta oscillators, could amplify, or at least effectively transmit, existing theta activity by responding well to synaptic input that is modulated at theta. A preference for modulating spike output rate in response to theta modulated inputs would constitute a form of spike resonance analogous to the well-established subthreshold membrane resonance measured in several cell types (Alonso and Llinas, 1989; Hu et al., 2002). Theta spiking resonance in O-LM cells would be meaningful because it would suggest that O-LM cells could be involved in stabilizing extant theta activity.

To measure spiking resonance in O-LM cells we modulated the baseline Poisson rate of the inhibitory synaptic input train. Hence, the process determining the timing of inhibitory synaptic stimulus became an inhomogeneous Poisson process whereby the baseline rate of 1000 Hz, representing total summed inhibitory activity, was modulated at a set frequency. We used four physiologically meaningful frequencies for the modulation of the inhibitory process: 2, 8, 20 and 30 Hz. We modulated the Poisson rate of the inhibitory input train at 20%, a reasonable level given the strong phase modulation observed in O-LM and other hippocampal cells in vivo during ongoing theta rhythm in the field potential (Klausberger et al., 2003). As a consequence, the inhibitory Poisson rate was modulated from a trough of 800 Hz to a peak of 1200 Hz at the desired frequency (2, 8, 20 and 30 Hz). In all recordings, we continued to keep the cell’s average firing rate near 2.5 Hz.

We used multiple measures to quantify the resulting spike rate modulation. These measures included interspike interval (ISI) histograms, spike phase histograms in relation to the phase of the modulating input; and spike power spectra. In Figure 3A, B we provide an example of our analysis from a single cell for input modulation rates of 2 and 8 Hz.

Figure 3
O-LM cell spikes phase lock to frequency modulated artificial synaptic conductance inputs

When ISI histograms were plotted from these examples, clear peaks emerged showing that the cell preferred certain interspike intervals over others in its output (Figure 3C, E). With 2 Hz modulation, bimodality was evident in the histogram (Figure 3C, black arrow). The sharp distribution at smaller ISI values is a result of high frequency spike discharge near the peak of the slow 2 Hz modulation. At 8 Hz input modulation multiple peaks emerge that are integer multiples of the 125-ms period associated with the 8-Hz modulator.

For the power spectra, a clear peak at the modulation frequency was present (Figure 3D, F). Likewise, the spike phase histograms also indicated a large modulation of spike phase in response to modulated input (Figure 3C, E, inset). To assess any potential preference in modulation frequency, we compared the average spike power spectra and spike phase histograms of the O-LM spike trains in response to a physiological range of modulation frequencies of the synaptic inhibitory Poisson rate (2, 8, 20 and 30 Hz, Figure 4). Average power spectra indicated that peak power at 8 Hz modulation was larger than 2, 20 and 30 Hz (Figure 4A). The relative amount of power at the modulation frequency was quantified by taking the peak power and dividing by the power at 0 Hz, which is directly proportional to the number of spikes in each trial. This measure was used as an estimate of the proportion of spike train power at the modulation frequency. We termed this quantity the power ratio. We compared this value for each of the modulation frequencies tested. Although the effect was modest, we found that modulation of synaptic input rates at 8 Hz generated the highest power ratio. The average power ratio for 2 Hz modulation was significantly lower than that at 8 Hz modulation (Figure 4B, p = 0.02, n = 8). Additionally, 20 and 30 Hz modulation produced less power at their respective modulation frequencies when compared with either 8 Hz (Figure 4B, 8 Hz vs. 20 Hz p = 0.001 and 8 Hz vs. 30 Hz p = 0.0008). The lack of spike output modulation at 20 and 30 Hz in spike power spectra can be accounted for by the significant filtering that results from the membrane time constant at high frequencies.

Figure 4
O-LM cells phase lock better to 8 Hz modulation than to 2 Hz modulation

As an additional measure of the quality of phase locking, we constructed phase histograms for each data set (Figure 4C) and calculated the vector strength (Figure 4D, see Methods) associated with the spike phase distribution. Power ratios (Figure 4B) and vector strengths (Figure 4D) are qualitatively similar, but in the case of vector strengths, the difference between 2 and 8 Hz was not significant (p = 0.24; theta ratio = 1.07 ± 0.02). It is unclear why the power ratio reported a slightly larger difference in modulation between 2 and 8 Hz than did vector strength. Regardless, we conclude that O-LM neurons pass 8-Hz modulated stimuli well, and may exhibit modest resonance at 8 Hz in response to modulated inputs.

The average ISI histogram across all cells for 2 Hz modulation (Figure 4E, top panel) showed the same biomodality seen in the representative example (Figure 3C, black arrow). This result indicates that ISI values were reliably split between two clusters, with the peak at 0.5 s (2 Hz) being the smaller of the two. On the other hand, the average ISI histogram for 8 Hz input modulation (Figure 4E, second panel) has its largest peak at the modulation frequency (~125 ms). Peaks in the ISI histograms are not clearly discernable with 20 or 30 Hz input modulation.

Although O-LM cells produced marginal spike resonance to theta frequency inputs, the spike output was nonetheless much more strongly modulated at theta frequency compared with the subthreshold membrane impedance. To illustrate this point, we compared the subthreshold membrane impedance and the spike power ratio across all frequencies. In essence, we compared the input-output transfer function of the spiking behavior with that of the subthreshold membrane voltage response. The low-pass characteristic of the subthreshold response differed qualitatively from the spiking response. The subthreshold membrane voltage filters the 8 Hz response such that the theta ratio is 0.71 ± 0.01 (Figure 1D). In contrast to the subthreshold response, the spiking response of O-LM cells responded similarly to both 2 and 8 Hz inputs with a slight preference for 8 Hz inputs. Thus, the theta ratio calculated using either vector strength or power spectra was greater than one with values of 1.07 ± 0.02 (for vector strength) and 1.37 ± 0.05 (for power ratio).

Thus, by either measure, the spike train phase locks surprisingly well to 8 Hz modulatory input, despite significant filtering at this frequency in the subthreshold voltage response.

In summary, we have shown that O-LM cells phase lock well to 8-Hz stimuli, showing mild resonance as quantified by spectral analysis. Spike output was found to be filtered considerably less at 8 Hz than predicted by their subthreshold impedance. Taken together, these results indicate that theta-patterned inputs are unlikely to be substantially amplified by the intrinsic dynamics of O-LM cells, but that theta-band synaptic inputs are likely to be faithfully transmitted to their postsynaptic partners.

Ih block does affect responses to 8-Hz-modulated inputs in O-LM cells

While we observed no subthreshold resonance in O-LM cells (Figure 1D), we considered whether subthreshold membrane mechanisms, specifically the h-current, could influence the spike response properties. The h-current, mediated by HCN channels, is a hyperpolarization-activated cation current that is depolarizing in O-LM cells (Maccaferri and McBain, 1996). It has been linked to theta oscillations in the hippocampus because blocking it often reduces power in the field potential at theta in CA1 (Gillies et al., 2002) although complete genetic knockouts of the associated ion channel, HCN1, can cause enhancements in theta power (Nolan et al., 2004; Hussaini et al., 2011). Additonally, its slower kinetics correlate with the theta network oscillation time scale (Rotstein et al., 2005). We proceeded to test whether blocking the h-current could change the spike output statistics of fluctuation-driven spiking.

We first tested whether h-current block with 20 μM ZD7288 would change the baseline response of O-LM cells to the unmodulated synaptic stimulus. As in control conditions, when the h-current was blocked we still observed no measurable peak in the power spectrum in the theta range (Figure 5A, first two bars). Average power spectra from these recordings mirrored this conclusion and neither spectrum had a peak in the theta range (Figure 5B, C, top).

Figure 5
Blocking the h-current does not affect phase-locking to theta-modulated inputs in O-LM cells

We next tested whether h-current block could change the phase locking to 8 Hz modulated synaptic inputs. We found no significant difference between O-LM cells’ ability to respond to 8 Hz modulated inputs with or without h-current block. Thus, the power spectrum peaks at 8 Hz were not changed significantly when ZD7288 was applied (Figure 5A, last two bars, p = 0.18, n = 6, B, C, bottom). This again suggests that O-LM cells do not generate a significant peak in spike train power at theta in response to unmodulated synaptic stimuli and that this behavior is unchanged with bath application of ZD7288.

Previous studies have linked the ability of O-LM cells to spike at theta with the h-current because h-current block modifies the after-hyperpolarization (AHP), which in turn alters intrinsic excitability (Maccaferri and McBain, 1996). Hence, we compared the average AHP of O-LM cells between control and h-current blockade. We found no significant difference in either the absolute duration (Figure 5D, p = 0.83) or amplitude (Figure 5E, p = 0.65) of the AHP during fluctuation-driven spiking (n = 6 cells, averaged over ~750 spikes per cell).

Average resting membrane potential did not change with ZD7288 (mean membrane potential in control: −50.0 ± 3.8 mV, 20 μM ZD7288: −49.4 ± 3.6 mV, p = 0.75, n = 6, Kruskal-Wallis test, Figure 5F). Despite having little or no effect on spike train power spectrum, mean resting potential and AHP, 20 μM ZD7288 had a large effect on the membrane voltage sag resulting from strong hyperpolarization (p < 0.01, Figure 5G). Thus the application of ZD7288 was effective in blocking the h-current in O-LM cells despite a lack of effect on spike output.

Overall, these results show that the h-current has little effect on spike output properties of OLM cells under a regime where spikes are driven by membrane voltage fluctuations. The lack of effect on resting membrane potential, despite a large effect on membrane voltage sag response, likely occurs because the h-current is activated only in a strongly hyperpolarized region of membrane voltage. For this reason, the role of h-current is limited in the spiking regime.

Added “virtual” h-current with depolarized activation curves fails to produce theta power in the spike train

It is known that the h-current can be modulated to remain active in a more depolarized range in vivo (Pape, 1996; Biel et al., 2009; Emery et al., 2011). This can occur when beta-adrenergic receptors are activated resulting in elevated cAMP levels which then shift the activation voltage of the h-current to a more depolarized range. Furthermore, it is known that such receptors are present in somatostatin-positive interneurons such as O-LM cells (Cox et al., 2008). We thus considered the hypothesis that in our slice preparations, the h-current had an excessively hyperpolarized half-activation voltage and that with a more depolarized activation profile it could contribute significantly to generating theta modulated spike rates. To test this hypothesis, we used dynamic clamp to add additional artificial h-current (2 – 2.5 nS) to O-LM cells with a half-activation of -75 mV (Maccaferri and McBain, 1996). This level of conductance was sufficient to produce a resonance peak in the subthreshold impedance profile in the voltage range immediately hyperpolarized to spike threshold that was significantly different from control (Figure 6A,B, n = 5, Q-values significantly different with p = 0.0039). This result confirmed that the added artificial h-current was behaving as expected and that the modified O-LM cells had a resonant membrane.

Figure 6
Additional artificial h-current does not produce theta power in the spike power spectrum

We injected a broadband synaptic stimulus and asked whether a peak at theta would emerge given the subthreshold resonance induced by the artificial h-current. Under these conditions, we found no peak in the spike train power spectrum in response to the unmodulated synaptic stimulus (Figures 6C,D, n = 5, p = 0.87). We next tested whether an artificial h-current that induced subthreshold resonance could change the ability of O-LM cells to alter spiking in response to an 8 Hz modulated synaptic stimulus. We observed no significant change in the ratio of the modulation frequency power to the zero frequency power compared with control (Figure 6E, p = 0.25, n = 5). Finally, we tested a small number of cells for spiking resonance when the half-activation of the h-current was depolarized further. Stepping the half-activation voltage from −75 mV to −55 mV in increments of 5 mV maintained subthreshold resonance but did not produce spiking resonance in response to broadband input for any voltage in the cells tested (n = 2, data not shown).

Because past work has linked oscillatory spike output properties in O-LM cells to specific features of the AHP (Maccaferri and McBain, 1996), we tested the effects of the artificial h-current on the AHP voltage trajectory. We compared average AHPs of O-LM cells between control and with added artificial h-current. We found no difference in either the duration (Figure 6F, p = 0.94) or amplitude (Figure 6G, p = 0.76, n = 5) of the AHP. Together, these results show that a level of h-current capable of inducing substantial subthreshold resonance is by itself insufficient to either induce spiking resonance or enhance the spiking response to 8 Hz modulated fluctuations.

Sensitivity to 8-Hz modulation in O-LM cells is dependent on AHP characteristics

Given that measures of spike output modulation were much stronger in the spiking regime at 8 Hz input modulation than the subthreshold response would predict (Figure 4), we reasoned that specific spiking dynamics could be the critical factor in setting the spike response of O-LM cells. Previous work has established that features of the AHP are an important spike-dependent mechanisms for setting either an oscillatory/pace-making behavior (Fernandez and White, 2008) or a resonance behavior in the spike rate response (Higgs and Spain, 2009). For example, in stellate cells of the medial entorhinal cortex, reducing the AHP has a detrimental effect on those cells’ ability to cluster spikes at interspike intervals values within the theta range (Fernandez and White, 2008). In neocortical regular-spiking cells, which, like OLM cells, do not have subthreshold resonance, the AHP is responsible for producing spiking resonance at some input frequencies (Higgs and Spain, 2009).

To directly test whether the AHP was required for increased responsiveness in spike output modulation at 8 Hz in O-LM cells, we measured the change in resonance behavior when the AHP was reduced or enhanced. We avoided the use of pharmacological agents to modify the cell’s AHP because in addition to modifying the AHP (Klink and Alonso, 1993; Yue and Yaari, 2004; Yoshida and Alonso, 2007; Nolan et al., 2007) pharmacological block can produce undesired changes in spike shape, adaptation rate or other interrelated parts of the cell’s dynamics. As in previous studies (Fernandez and White, 2008; Higgs and Spain, 2009), we used dynamic clamp to provide a more specific manipulation of the AHP. We used a difference-of-exponentials waveform with a rise time constant of 10 ms and a decay time constant of 50 ms (Figure 7B, inset) to inject either a depolarizing (AHP attenuating) or hyperpolarizing (AHP enhancing) current. In Figure 7, we provide an example of the average control spike overlaid onto a spike with an attenuated and enhanced AHP (Figure 7A, B). When magnified, the voltage trajectory after the spike shows that the AHP has been changed substantially by the spike-triggered current and that, on average, spiking can either continue sooner or later depending on the sign of the AHP manipulation (Figure 7B).

Figure 7
Spike triggered current alters shape of the AHP

For comparison, we provide the spike power ratios for each modulation frequency under control conditions (Figure 8A). We measured the change in the spike output modulation using the power ratio when the AHP modifying current was used to attenuate (Figure 8B) or amplify (Figure 8C) the AHP. For measures of power ratios, the AHP attenuation eliminated the significant difference between the 2 Hz and 8 Hz peaks seen in control (Figure 8B, p = 0.53, n = 9; 2 Hz power ratio was increased by 0.29, 8 Hz power ratio was increased by 0.05). Conversely, amplifying the AHP maintained the peak in the power ratio at 8 Hz (Figure 8C, p = 0.01, n = 9; 2 Hz power ratio was increased by 0.11, 8 Hz power ratio was increased by 0.15).

Figure 8
AHP attenuation with dynamic clamp makes O-LM cells more strongly low-pass

To account for these results it is important to consider that the AHP reducing current represents a form of positive feedback that leads to higher gain and more high-frequency events (i.e. smaller ISI values). Although we kept average spike rate at 2.5 Hz, attenuation of the AHP increased the cells’ propensity to fire sequences of higher frequency spikes. Consistent with previous studies, high frequency events (burst-like events by some definitions) are better elicited by low frequency input modulation (Oswald et al., 2004; Higgs and Spain, 2009). Low frequency 2 Hz input, in contrast to 8, 20 and 30 Hz, provides sufficient time in a depolarized voltage to elicit numerous high-frequency ISI values at the peak of the modulation. At 8, 20, and 30 Hz, one spike per cycle can be generated at most; thus, an O-LM cell with a reduced AHP does not become better at representing those frequencies.

The average ISI distributions of spike trains resulting from cells with alterations to the AHP in response to 2 and 8 Hz mirror the behavior observed with power ratio analysis (Figure 8D-I, n = 9). When the AHP is reduced, the cell generated an increase in the proportion of high frequency ISI values in response to 2 Hz modulation (Figure 8E, arrow). As a result, the bimodality seen in the interspike interval distribution with 2 Hz modulation under control conditions (Figure 8D) becomes more dramatic when the AHP is attenuated (Figure 8E, arrow). Conversely, increasing the size of the AHP swung the power ratio in the opposite direction by reducing the number of ISI values at high frequencies in response to 2 Hz modulation (Figure 8F, arrow). Thus, cells with an increase in the size of the AHP had far fewer high frequency ISI values in response to 2 Hz modulation. Thus, the modest spiking resonance observed in O-LM cell is a result of AHP characteristics that suppress responsiveness to 2 Hz input modulation relative to 8 Hz.

Responses to modulated stimuli are qualitatively reproduced in a simple model

To demonstrate that modest spiking resonance can be generated by refractory dynamics alone and does not require the subthreshold membrane dynamics of the h-current, we repeated the AHP attenuation experiment in a simple model that did not have an h-current. We used a quadratic integrate-and-fire neuron (Izhikevich, 2003) with a predetermined parameter set (cell type ‘M’ from (Izhikevich, 2004)) that was chosen because it has an AHP that is qualitatively similar to the AHP seen in O-LM cells. In general, however, this model was not meant to represent O-LM cells in a rigorous way but intended to be a simple representation of a cell in which the AHP contributes significantly to the timing of interspike intervals.

Using the same experimental setup from our previous results in biological O-LM cells, we were able to replicate our spike resonance findings in this simple model. We adapted the experimental protocols to first test the spiking response of the model in response to artificial synaptic fluctuations. For the model, the amplitude of individual excitatory and inhibitory events was adjusted to produce approximately a 3 mV standard deviation in the voltage fluctuations as in experiments; however, all other parameters of the experimental protocol remained the same. Like in the experimental recordings, spike rate was maintained at 2.5 Hz. We proceeded to measure the ability of the model to respond to artificial synaptic fluctuations modulated at different frequencies.

We found that the model displayed spiking resonance qualitatively similar to that seen in O-LM cells, with the largest peak spike power observed at 8 Hz when compared with all other frequencies tested (2, 20, 30 Hz, Figure 9A). We then compared the responses of the model when the AHP was attenuated as in our in vitro experiments (Figure 9B). Scaling parameters were adjusted to produce AHP attenuation results qualitatively comparable to the experimental data. We noticed that spiking resonance was abolished in this model as in our experimental data when the AHP was attenuated (Figure 9B). Conversely, when the AHP was enhanced, the spiking resonance profile of the model was unchanged relative to control (Figure 9C). Like in the real neuron, attenuation of the AHP leads to an increase in the high frequency ISI values for 2 and 8 Hz (Figure 9B, lower panels, arrows). These results suggest that the AHP-dependent mechanism, by which we have shown that O-LM cells produce a modest resonant response in their spiking behavior, is potentially applicable to a broad set of cell types.

Figure 9
Simple model replicates modest spiking resonance and abolition of resonance with AHP attenuation

To further test the generality of our results, we altered the stimulus given to the model in several ways. First, we altered the rate of the excitatory and inhibitory events to test whether our results were dependent upon specific choices for the rate parameter. We first increased the rate of both excitatory and inhibitory synaptic events by 25% (Figure 9D) and then decreased them by the same percentage (Figure 9E). In both cases, we continued to observe spiking resonance in the model suggesting that there is a wide range of rate values that yield results similar to what we observed in our experiments. When rate was decreased (Figure 9B), modulation became less effective at modulating the spike output.

Next, we substituted an NMDA conductance for half of the AMPA conductance (Figure 9F) as well as another set of tests in which we substituted a GABAB conductance for half of the GABAA conductance (Figure 9G). For both of these changes the qualitative result remained unchanged. Overall, these simulations suggest that a wide range of parameters can yield results similar to what we observed in our experiments, which suggests that an AHP-dependent mechanism of spiking resonance could apply to a wide range of cell and input types.


We have shown that O-LM interneurons of the hippocampus show no signs of pacemaker properties when driven with unmodulated synaptic stimuli. When synaptic input rates were modulated at certain frequencies, O-LM cells were able to follow theta frequencies effectively. The spike output rate of O-LM cells was much more strongly modulated at theta than would be expected from the subthreshold membrane voltage response. Thus, while subthreshold membrane properties attenuate 8 Hz inputs substantially, phase locking is similar for 8-Hz and 2-Hz modulation. Although our data do not support the idea that O-LM cells serve as pacemakers of the theta rhythm, they do suggest that these neurons could stabilize, transmit, or even amplify ongoing theta-modulated activity from pre-synaptic sources.

Comparison with previous studies

A major motivation for this work was to clear up confusion regarding the potential role of O-LM interneurons in the theta rhythm. On the one hand, O-LM cells can discharge at theta frequencies, both in vivo (Klausberger et al., 2003) and in some cases in the otherwise quiescent brain slices (Maccaferri and McBain, 1996). These findings have led authors of computational models of hippocampal theta to treat these cells as clock-like pacemakers (Rotstein et al., 2005; Gloveli et al., 2005a; Tort et al., 2007). This assumed role may be accurate if considered strictly from the standpoint of the neuronal targets of O-LM cells. However, the existing biophysical results from O-LM cells are compatible with our results here and also argue against a role as a theta pacemaker or resonator. For example, morphologically identified O-LM cells have Q-values (a measure of subthreshold resonance) of less than 1.05 (Zemankovics et al., 2010), substantially less than in several other cell types in the hippocampal formation. The h-current in O-LM cells, which has been implicated as the driver of the O-LM theta pacemaker, is not active for membrane potentials near threshold (Zemankovics et al., 2010).

Our data suggest that O-LM cells respond with theta-frequency spike trains because they can phase-lock effectively to theta-modulated inputs from other sources. Previously, it has been shown that excitatory synapses onto O-LM cells can follow 10 Hz stimulation without appreciable adaptation (Goldin et al., 2007), suggesting that phase-locked input from CA1 pyramidal cells may provide the sort of theta-rich input to which O-LM cells can lock. Also, “horizontal” interneurons in stratum oriens are sensitive to theta-frequency sinusoidal inputs (Pike et al., 2000), a finding compatible with our data as well. However, because Pike et al. did not reconstruct their cells, we do not know for sure which population(s) are represented in their data.

Our findings do differ from previous data in one regard: unlike Maccaferri and McBain (1996), we did not observe any spontaneous firing activity in O-LM cells. Although we are not entirely sure why O-LM cells in our conditions did not fire spontaneously, our use of slightly older animals and lower external K+ concentrations relative to previous work (Maccaferri and McBain, 1996) may be involved.

Existing biophysical models of O-LM cells include descriptions of h-currents from either thalamic relay neurons (Saraga et al., 2003) or entorhinal stellate cells (Rotstein et al., 2005; Gloveli et al., 2005a; Tort et al., 2007). Typically, these models exhibit strong theta resonance features or slow oscillatory bursting dynamics. In light of our data and those of (Zemankovics et al., 2010), these models should be modified to move the activation curve of the h-current to more hyperpolarized potentials, and to dampen the resonant properties of the modeled cells.

Stimulus parameters

Our stimuli included two properties that are shared by the vast majority of recordings in vivo (Destexhe et al., 2003). The first is the use of noisy membrane voltage fluctuations that produce spike time distributions with high CVs and low average spike rates. Second, the synaptic conductances significantly reduce the membrane resistance. Both these features have been observed in a wide range of different cell types. It seems likely that fluctuation-driven spiking and the concomitant increase in membrane conductance associated with synaptic inputs are general features of mammalian central neurons during active states (Rossant et al., 2011).

For our analysis of suprathreshold responses, we measured power spectral densities and spike phase of binary spike trains and not raw voltage traces as in previous work (Gillies et al., 2002; Gloveli et al., 2005b). This allows the separation of theta in the spike train from theta oscillations in the subthreshold voltage.

Role of h-current in theta activity

Our data indicate that the h-current has a limited role in spike output characteristics during fluctuation-driven spiking in O-LM cells. The role of h-current in O-LM cells is limited due to its hyperpolarized activation voltage. The h-current in O-LM cells is not active near spike threshold and thus cannot significantly influence spiking. These results are also consistent with voltage-clamp data in O-LM cells that indicate a hyperpolarized voltage for activation for h-current (Maccaferri and McBain, 1996; Zemankovics et al., 2010). Furthermore, we did not observe any influence of the h-current even when we used dynamic clamp to give O-LM cells a more depolarized h-current activation. Despite the fact OLM cells with the artificial h-current possessed robust subthreshold resonance, the h-current had no influence on the ability for O-LM cells to generate autonomous theta activity or amplify theta inputs in the spiking regime. The inability for h-current to influence spiking under these conditions is likely the result of the fluctuation-driven spiking regime, which does not provide the conditions in which h-current can pace spike activity with low interspike interval variability.

Although the role of the h-current is often emphasized in the literature, it is likely only one of many components that facilitate spike output resonance or pacing at theta. Even in entorhinal stellate cells, which have prominent h-currents and theta-frequency subthreshold oscillations, subthreshold oscillations can persist with h-currents clearly blocked (Haas et al., 2007). Also in stellate cells, factors that interact with the h-current, like the AHP, can form complex dynamics that support the transmission of subthreshold resonance into the spiking regime (Fernandez and White, 2008). We hypothesize that these other factors are missing in O-LM cells, with the consequence that adding virtual HCN channels to induce robust subthreshold resonance is insufficient alone to produce spike output resonance.

Role of AHP currents in O-LM spike activity

Our data show that the ability of O-LM cells to phase lock well to theta-modulated stimuli is regulated by the AHP voltage trajectory. These results are consistent with previous work that has shown that band-pass characteristics in spike coherence to inputs can be regulated by the AHP and spike refractory properties of the cell (Oswald et al., 2004; Higgs and Spain, 2009). Furthermore, it has been established in simple models of spike generation that increased refractoriness through threshold fatigue reduces overall power in spike trains at low frequencies (Chacron et al., 2004). Thus, the AHP in neurons likely plays an important role in establishing spike statistics in response to both broadband input as well as frequency modulated input.

Limitations of our approach

Our results suggest that O-LM cells do not act as theta resonators, and show only weak evidence of theta selectivity in response to sinusoidally modulated stimuli. It is still possible, however, that dendritic inputs coupled with nonlinearities in the dendrite may produce more complex and cell-specific patterns. Thus, the assessment of voltage and spike output resonance in our study is limited to inputs at the soma. It is possible that highly resonant compartments located in the dendrites could selectively amplify theta inputs and increase spike train power at this frequency. However, there is no evidence for this possibility, and our results with artificially added h-currents suggest that the spike-generating mechanism in O-LM cells is not responsive to such band-pass filtered inputs.

It is important to note that we do not exclude the possibility that O-LM cells are capable of discharging at 4–12 Hz with relatively low variability in their interspike intervals, thus helping to pace their postsynaptic targets. In fact, juxtacellular in vivo recordings of O-LM cells (Klausberger et al., 2003) support such a model. In this case, we believe that O-LM firing rates are constrained not by their intrinsic properties but rather by their synaptic inputs.

Theta activity in hippocampus

Recent whole hippocampal recordings in vitro provide the best evidence to date for the hypothesis that the CA1 region of the hippocampus can autonomously generate persistent theta activity (Goutagny et al., 2009). Those data suggest that theta can occur endogenously and need not be activated by pharmacological agents as in some slice recordings (Gillies et al., 2002). In the whole hippocampus preparation, theta was found to be dependent on AMPAergic excitation from pyramidal cells. It is also known that CA1 pyramidal cells also contain an h-current (Magee, 1998) and are theta resonant (Hu et al., 2002). Together, these data suggest that theta oscillations may be generated by the resonant properties of pyramidal cells and stabilized by feedback inhibition.


We are grateful to Nancy Kopell and Eve Marder for helpful discussions and critiques of the manuscript. Support was provided by NIH grants R01 MH085387, R01 MH085074, and R01 RR020115 (JAW).


The authors state no conflicting interests.

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