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. 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 (). Axons are traced in black and arborize in str. oriens, and more extensively in str. lacunosum-moleculare (). 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 (). The example cell shown in has recurrent axonal collaterals that can be seen branching in str. pyramidale to project back to str. oriens (black star).
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 (). 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 (, 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 ( 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 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 () did not generate any peak in spike train power or ISI distribution at theta frequencies (, black traces). In all O-LM cells tested, we observed the same outcome (n = 8).
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 (). 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 (, 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 we provide an example of our analysis from a single cell for input modulation rates of 2 and 8 Hz.
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 (). With 2 Hz modulation, bimodality was evident in the histogram (, 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 (). Likewise, the spike phase histograms also indicated a large modulation of spike phase in response to modulated input (, 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, ). Average power spectra indicated that peak power at 8 Hz modulation was larger than 2, 20 and 30 Hz (). 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 (, 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 (, 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.
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 () and calculated the vector strength (, see Methods) associated with the spike phase distribution. Power ratios () and vector strengths () 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 (, top panel) showed the same biomodality seen in the representative example (, 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 (, 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 (). 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 (), 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 (, first two bars). Average power spectra from these recordings mirrored this conclusion and neither spectrum had a peak in the theta range (, top).
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 (, 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 (, p = 0.83) or amplitude (, 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, ). 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, ). 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
; 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 (, 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.
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 (, 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 (, 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 (, p = 0.94) or amplitude (, 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 (), 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 (, inset) to inject either a depolarizing (AHP attenuating) or hyperpolarizing (AHP enhancing) current. In , we provide an example of the average control spike overlaid onto a spike with an attenuated and enhanced AHP (). 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 ().
Spike triggered current alters shape of the AHP
For comparison, we provide the spike power ratios for each modulation frequency under control conditions (). We measured the change in the spike output modulation using the power ratio when the AHP modifying current was used to attenuate () or amplify () 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 (, 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 (, p = 0.01, n = 9; 2 Hz power ratio was increased by 0.11, 8 Hz power ratio was increased by 0.15).
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 (, 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 (, arrow). As a result, the bimodality seen in the interspike interval distribution with 2 Hz modulation under control conditions () becomes more dramatic when the AHP is attenuated (, 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 (, 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, ). We then compared the responses of the model when the AHP was attenuated as in our in vitro experiments (). 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 (). Conversely, when the AHP was enhanced, the spiking resonance profile of the model was unchanged relative to control (). Like in the real neuron, attenuation of the AHP leads to an increase in the high frequency ISI values for 2 and 8 Hz (, 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.
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% () and then decreased them by the same percentage (). 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 (), modulation became less effective at modulating the spike output.
Next, we substituted an NMDA conductance for half of the AMPA conductance () as well as another set of tests in which we substituted a GABAB conductance for half of the GABAA conductance (). 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.