Local Control of Postinhibitory Rebound Spiking in CA1 Pyramidal Neuron Dendrites

Results

Our basic hypothesis is that I_h provides a mechanism for latent postinhibitory rebound spiking in CA1 pyramidal neurons that is usually silenced by K_A, but can be unmasked by K_A reduction. To quantitatively define and substantiate this hypothesis, we first used an existing computational model of CA1 pyramidal cells, previously validated against a number of standard conditions (Migliore et al., 2005), without altering any biophysical parameter. In particular, we hyperpolarized the soma with a square current injection in simulated current-clamp conditions, and recorded the resulting voltage. Although we always observed a postinhibitory rebound depolarization (Fig. 1a), under control conditions, no amount or duration of the hyperpolarization led to somatic spiking within a broad range of conditions (up to 500 ms and −4 nA, corresponding to a peak somatic hyperpolarization of −125 mV). In contrast, after removing K_A from the model, the hyperpolarizing somatic step was systematically followed by a rebound spike over the entire range of tested parameters for both duration and intensity of the current injection. However, further turning off I_h in the model completely abolished rebound spiking (Fig. 1a, left).

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Figure 1.

Postinhibitory rebound spiking in CA1 pyramidal neurons: hypothesis and experimental validation. a, Simulated (left) and experimental (right) response to somatic hyperpolarization in control conditions, after blocking K_A, and after blocking both K_A and I_h. b, Dual recordings of dendritic and somatic membrane potential obtained during a dendritic current injection (−1 nA, 200 ms at ∼250 μm from the soma). The drawing on the left shows the experimental configuration. c, Voltage traces of the dendritic membrane potential recorded in response to a train (20 IPSCs at 100 Hz) injected in the apical trunk at 300 μm from the soma in control conditions, in the presence of Ba²⁺ (150 μm), and in the presence of Ba²⁺ and ZD 7288 (20 μm). The current trace below represents the injected train of IPSCs. d, Somatic voltage traces recorded in response to a 200 ms, −400 pA current injection to show the differences in sag and rebound from a neuron that shows rebound spiking (black trace) and one that does not (gray trace). e, Cumulative probability to have a rebound spike as a function of the time constant of the sag; symbols on the two sides of the curve show the average values (±SEM) for the two groups of cells, those that show rebound firing (black) and those that do not (gray); the inset shows the number of neurons initiating a rebound spike as a function of the amplitude of somatic current injection.

The hypothesis demonstrated in these initial simulations was then tested experimentally. We first performed a series of experiments to analyze the conditions for the generation of a rebound spike in CA1 pyramidal neurons. To this purpose, we injected variable hyperpolarizing current steps through somatic patch-clamp electrodes (Fig. 1a, right). Neurons responded with a sag during the hyperpolarization and a depolarizing rebound at the end of the current injection, consistent with the slow activation and deactivation of I_h (Pape, 1996). A rebound spike could never be elicited in control conditions, regardless of the duration (100–500 ms) and the amplitude (100–920 pA) of the hyperpolarizing current injected in the soma (n = 56). However, when I_A was partially blocked by bath perfusion of Ba²⁺ (150 μm) (Gasparini et al., 2007), a rebound spike could be elicited in most neurons (15 of 20 for a 200 ms, 300–600 pA hyperpolarizing step, with an average of −457 ± 23 pA, n = 15).

Because the densities of K_A and I_h in the apical dendrites of CA1 pyramidal neurons increase with the distance from the soma (Hoffman et al., 1997; Magee, 1998), this mechanism could be particularly significant at more distal dendritic locations, with important consequences for gated transmission of the dendritic spike to the soma (Jarsky et al., 2005) and local plasticity phenomena (Golding et al., 2002; Magee and Johnston, 2005). Thus, we performed a series of experiments in which either a hyperpolarizing step or a train of 20 IPSC-shaped currents at 100 Hz was injected in the distal apical dendrite (>240 μm from the soma, for an average distance of 267 ± 11 μm, n = 8) to simulate a barrage of synaptic inhibition (Fig. 1b,c). Under control conditions, none of the eight neurons tested showed a rebound spike for 200 ms hyperpolarizing steps up to −2000 pA and IPSCs up to 4200 pA. In the presence of Ba²⁺ (150 μm) to partially block K_A (Gasparini et al., 2007), seven of the eight neurons showed a rebound spike (Fig. 1b).

The hyperpolarizing current amplitude required to elicit a rebound spike in the presence of Ba²⁺ was on average −1057 ± 115 pA in the case of the 200 ms current step (n = 7) and −1990 ± 230 pA in the case of the IPSC train (n = 4) (Fig. 1c). The perfusion of ZD 7288 to block I_h abolished the rebound spikes in all neurons tested. In a subset of experiments, a second electrode was used to measure the somatic output of the CA1 neuron (Fig. 1b). These recordings showed that in these conditions, with the dendritic electrode injecting current in the main apical dendrite, the rebound spike was still initiated in the soma (always in the presence, but not in the absence, of Ba²⁺) and subsequently backpropagated in the apical dendrite, as visible from the superimposition of the somatic and dendritic voltage traces (n = 3) (Fig. 1b, inset). As shown before, the perfusion of ZD 7288 to block I_h prevented the rebound spike (Fig. 1b,c).

The neurons that displayed rebound spiking in the presence of Ba²⁺ (150 μm) during somatic hyperpolarizing current injections were characterized by a sag with slower time constants than those that did not fire (63.3 ± 4.0 ms vs 34.8 ± 4.9 ms, measured for a −400 pA hyperpolarizing step of 200 ms, n = 15 and 5, respectively, p < 0.005, Kolmogorov–Smirnov test) (Fig. 1d). This trend can be appreciated in Figure 1e, where the cumulative probability of firing is expressed as a function of time constant of the sag. This different behavior could be due to a different relative distribution of HCN1 and HCN2 subunits in the dendrites of the CA1 neurons examined (Brewster et al., 2007), since the two subunits are characterized by distinct activation kinetics (Santoro et al., 2000; Ulens and Tytgat, 2001). Interestingly, a gradient in the properties of I_h along the hippocampal axis has been recently suggested, with more functional HCN1 subunits in the dorsal hippocampus and more functional HCN2 subunits in the ventral hippocampus (Diaz and Johnston, 2009). Slower activating HCN2 subunits also display slower deactivation kinetics (van Welie et al., 2005); this feature could be reflected in a larger and/or longer rebound. We found that the area under the curve delimited by the rebound was larger for the group of neurons that showed rebound spiking (0.32 ± 0.01 mV · ms vs 0.13 ± 0.03 mV · ms, n = 15 and 5, respectively, p < 0.001, Kolmogorov–Smirnov test) (Fig. 1d). The smaller rebound depolarization generated by the neurons characterized by faster I_h kinetics could thus be responsible for the lack of rebound firing in a smaller population of neurons. Noticeably, the neurons that displayed rebound spikes in the presence of Ba²⁺ and those that did not failed to reveal statistically significant differences in the resting membrane potential V_m (−65.27 ± 0.52 mV vs −65.74 ± 1.38 mV), the peak hyperpolarization (−24.87 ± 0.84 mV vs −22.18 ± 1.07 mV), the steady-state hyperpolarization (−20.60 ± 0.77 mV vs −18.85 ± 0.58 mV), and the peak rebound potential measured from V_m (3.29 ± 0.24 mV vs 2.00 ± 0.65 mV; in all four cases p > 0.1, Kolmogorov–Smirnov test; parameters measured for a 200 ms, −400 pA hyperpolarizing current step). The fundamental role of I_h in initiating the spike was demonstrated by the fact that rebound spiking was completely abolished by the perfusion (20 μm) of the I_h blocker ZD 7288 in all neurons tested. Together, these data confirm the hypothesis that I_h is responsible for the depolarizing phase that leads to rebound spikes in CA1 neurons, but that in control conditions this depolarization is dampened by the activation of K_A.

We therefore tried to reproduce these experimental data using the model. The experimental curves in control conditions were fitted according to the morphology of two different neurons (Fig. 2a). The best-fitting model parameters (Table 1) and I_h distributions (Fig. 2b) were used in all subsequent simulations. Figure 2c shows the superimposition of the experimental and model voltage traces after fitting.

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Figure 2.

Postinhibitory rebound spiking in CA1 pyramidal neurons: computational model. a, Drawings of the two model neurons used in all simulations (scale bar: 100 μm). b, Dendritic distribution for K_A (closed circles, same distribution for both neurons) and I_h (triangles). c, Simultaneous fitting of both somatic and dendritic experimental recordings in control conditions, performed independently for the two model neurons. Actual dendritic locations for current injection were at 219 and 224 μm from the soma for neurons pc2b and ri06, respectively. d, Model traces for neuron pc2b, using the same experimental protocol described in Figure 1b.

The simulations reproduced the main experimental findings upon dendritic current injection (Fig. 2d). In particular, rebound spiking was (1) initiated only when K_A was partially blocked (i.e., reduced to 80% or less of control), (2) eliminated by the block of I_h, and (3) initiated in the soma (Fig. 2d). In the model, however, we did not observe the increased hyperpolarization (with respect to control) that was experimentally recorded during Ba²⁺ application (compare experimental traces in Fig. 1b and model traces in Fig. 2d). This was probably caused by an increase in input resistance due to the block by Ba²⁺ of additional K⁺ conductances not included in the model, such as K_M, inward rectifier K⁺ currents, and KCNK currents (Chatelain et al., 2005; Taverna et al., 2005; Gasparini et al., 2007). The block of Ba²⁺-sensitive K⁺ currents expressed in CA1 neurons and the consequent changes in input resistance could limit the proposed interpretation that the block of K_A is the main factor for the initiation of rebound spiking in our experimental conditions. However, the generation of a rebound spike in the model, even in the absence of the larger hyperpolarization observed in the experiments, demonstrates that, at least in principle, this phenomenon may be solely due to the interplay of I_h and K_A, rather than resulting from an input resistance increase as caused by Ba²⁺ application. Furthermore, to explore the possibility that an increase in input resistance due to unspecific effects of Ba²⁺ could contribute to rebound spiking, we performed a series of simulations that reproduced changes in input resistance equivalent to those observed in the presence of Ba²⁺. Rebound spikes were never initiated under these conditions (Fig. 3a).

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Figure 3.

Dissecting the mechanism underlying rebound spiking in CA1 pyramidal cells. a, Dendritic membrane potential from neuron pc2b, during a dendritic current injection (−1 nA, 200 ms) under control conditions (black trace), with a 50% higher input resistance (pink), with reduced K_A (10% of control, orange), and with I_h with a halved activation/deactivation time constant and reduced K_A (10% of control, green trace). b, Left, Somatic voltage traces recorded in response to a 200 ms, 500 pA hyperpolarizing current injection, under control conditions (black), in the presence of 2 mm 4-AP (red), and in the presence of 4-AP and 20 μm ZD 7288 (blue); right, somatic voltage traces from simulations with the model including K_M, with (bottom, green) or without (top, red) K_D. c, Plot of normalized K_A activation in the subthreshold range of membrane potential.

Starting from this model (cell pc2b), we also explored the effects of a faster time constant for I_h. Under control conditions, a somatic current injection resulted in the typical I_h-dependent sag, and produced a rebound spike after partial block of K_A (Fig. 3a, 10% of K_A from control trace). When the sag time constant was reduced using a faster I_h time constant, a reduction in K_A did not produce rebound spiking (Fig. 3a, I_h time constant reduced by half, 10% K_A trace). This finding suggests that rebound spiking is facilitated by slower I_h kinetics, confirming the experimental observation that cells showing a faster sag do not generate rebound spikes after Ba²⁺ application (Fig. 1d,e).

To further address the possibility that rebound spiking in the presence of Ba²⁺ could be due to the block of conductances other than K_A, we performed a series of experiments with 4-aminopyridine (4-AP, 2 mm). While Ba²⁺ and 4-AP block various K⁺ channels, the spectra of the channels blocked do not overlap except for A-type K⁺ channels (Storm, 1990). The approach of using two different nonspecific blockers for K_A such as 4-AP and Ba²⁺ was made necessary by the fact that selective blockers such as heteropodatoxin-2 (HpTx-2) failed to block K_A in our experimental conditions. In particular, we found that HpTx-2 did not affect the Ca²⁺ transients associated with backpropagating spikes at distal dendritic locations in CA1 pyramidal neurons (data not shown), where the decrease in amplitude along the dendrites is mediated by an increase in the density of K_A (Hoffman et al., 1997). We attribute this finding to the possible incomplete penetration of HpTx-2 in brain slices, as corroborated by the similar results of other researchers in CA1 pyramidal and ventral tegmental area neurons (personal communications from Drs. Dax Hoffman, Jeffrey Magee, Zayd Khaliq, and Bruce Bean).

Confirming our previous findings (Fig. 1), 200 ms hyperpolarizing steps in control conditions generated a sag during hyperpolarization and a depolarizing rebound (Fig. 3b), but a rebound firing was never initiated. The perfusion of 4-AP (2 mm) generated rebound spiking in 12 of the 14 neurons tested (for a −454 ± 16 pA average hyperpolarizing step, n = 12). The main role of I_h in the initiation of rebound spiking was again confirmed by the fact that the spikes were abolished by perfusion of ZD 7288 (Fig. 3b). The input resistance was unaffected in 6 of 12 neurons in the presence of 4-AP, while a small increase in the steady-state hyperpolarization was observed in the other 6 neurons (ranging from 1 to 4.5 mV for a −400 to −500 pA hyperpolarizing step). These data, together with the simulations in Figure 3a, argue against an influence in changes of the input resistance on the initiation of rebound spiking. However, the rebound spiking generated by 4-AP was more complex than that initiated by Ba²⁺, since most neurons (9 of 12) showed a complex pattern of two or more spikes (Fig. 3b). We attributed this finding to the fact that 4-AP blocked the dendrotoxin-sensitive K_D in addition to K_A (Storm, 1988). Blockage of K_D could unmask the effect of the K_M conductance, thus causing complex firing (Metz et al., 2007). To explore this possibility, we conducted a series of simulations to show the differential effect of blocking K_A and K_D (Fig. 3b) on rebound spiking. For this particular set of simulation, K_D and K_M were added to the model neuron, as explained in Materials and Methods. Blockage of all of K_D and half of K_A, simulating the effect of 2 mm 4-AP, elicited complex rebound spiking upon release from hyperpolarization (Fig. 3b, top right), very similar to that observed in our experimental conditions (Fig. 3b, left). However, selectively reducing K_A by 50%, leaving K_D unaffected, resulted in the initiation of a single rebound spike (Fig. 3b, bottom right), similarly to our initial model and to the experimental data with Ba²⁺. Together, the experimental data and simulations show that a decrease in K_A plays a major role in the initiation of rebound spiking in CA1 pyramidal neurons.

Both model and experiments indicate that K_A activation at subthreshold potentials normally balances activation of I_h, preventing rebound firing. Thus, if K_A is active subthreshold and blocked by 4-AP, it might appear surprising, in light of the clear effect of this blocker on the rebound firing, that 4-AP does not affect the input resistance in simulations and experiments alike. The reason can be found in the steep voltage dependence of K_A activation around the resting potential (Fig. 3c). At the peak rebound depolarization (approximately −54 mV), enough channels are open to compensate for I_h current, unless these channels are blocked. In contrast, at or below resting potential, and in particular at the hyperpolarized voltages reported above (approximately −85 mV), essentially all K_A channels are closed, therefore their blockage would not affect the input resistance at this level.

Next, we used this model (as described in Fig. 2) to explore the possibility of synaptically based activation of postinhibitory rebound spiking (Fig. 4). In particular, we examined the response to GABAergic signals on the distal apical tuft, the target of several CA1 interneurons (Klausberger and Somogyi, 2008), including oriens/lacunosum-moleculare, perforant-path-associated, neurogliaform, and radiatum-retrohippocampal projection cells. Simulations indicated that even a partial reduction of K_A (e.g., with 40% of the control conductance maintained) confined to the region of synaptic activation (e.g., single branches) may be sufficient to enable a dendritic rebound spike following release from inhibition. This local spike may or may not propagate to the soma depending on the dendrite morphology and the amount of K_A reduction (Fig. 4a).

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Figure 4.

Local modulation of K_A can result in a dendritic rebound spike that may or not propagate to the soma. a, Typical results obtained stimulating two different stretches of dendritic membrane (blue, 280 μm²; red, 368 μm²) in the same neuron (pc2b), with the same number of synapses (n = 25, schematically indicated on the red branch). In both cases, somatic and dendritic membrane potentials (traces on the right) are plotted after different reduction (15% or 40% of control) of local K_A channels. b, Conditions to initiate a dendritic rebound spike in the blue branch with different combinations of the peak synaptic conductance, I_h somatic density, and synaptic train duration after reducing the local K_A to 40% of control. Equal colors represent combinations with the same peak synaptic conductance. c, Conditions required to initiate a dendritic rebound spike in the blue or in the red branch with different combinations of the stimulation frequency, I_h time constant, and decay time constant of the inhibitory synapses. Equal colors represent combinations with the same stimulation frequency; in both branches, synapses were activated 20 times, with the local K_A reduced to 15% of control.

Some modulation of these effects could be caused by fast, transient, low-threshold calcium channels (Ca_T). Thus, we performed additional simulations with Ca_T channels included in the model. From a series of 100 simulations, randomly redistributing 25 synapses over the entire tuft and using a K_A reduced to 40% of control, we calculated the minimum average peak inhibitory conductance resulting in a rebound spike in the tuft with or without Ca_T. The average values were very close (control: 2.0 ± 0.08 nS; with Ca_T: 1.94 ± 0.07 nS) and their difference statistically not significant (Mann–Whitney rank sum test, p > 0.5). One additional mechanism that can modulate the rebound process is the reversal potential of GABA_A currents, that can vary from values close to the cell resting potential (Gulledge and Stuart, 2003) to approximately −80 mV (Hevers and Lüddens, 1998). With the same protocol used to test the effect of Ca_T channels, we computed the minimum average reversal potential at which no rebound spike could be obtained. With the K_A reduced in the tuft to 15% of control, and 4 nS for the individual peak synaptic conductance, the simulations indicated a threshold value of −71.00 ± 1.12 mV (−71.06 ± 1.07 mV, with Ca_T), meaning that a rebound will be obtained for any E_Cl more hyperpolarized than this value.

Different inhibitory cells evoke synaptic patterns with diverse characteristics of firing frequency and durations. Thus we tested the conditions to initiate a dendritic rebound spike after partial reduction of the local K_A with different combinations of synaptic train duration and peak synaptic conductance. Moreover, to assess the sensitivity of the results to I_h density, we also varied this parameter from the initial best-fitting value. As expected, shorter train duration, i.e., fewer presynaptic action potentials, required larger synaptic conductance (Fig. 4b), possibly corresponding to the synchronous coactivation of a larger number of inputs. Nevertheless, rebound spiking was robust over a twofold change of I_h density (somatic values: 20–40 μS/cm²). Similarly, we explored the effect of a broader range of the time constant of the IPSCs (5–20 ms) and of the inhibitory firing frequency (50–200 Hz), varying at the same time the I_h kinetics within the experimental observations. These simulations (Fig. 4c) determined that rebound spiking is a robust phenomenon.

Finally, we characterized the distinct conditions for local and propagating spikes in terms of spatial extent and amount of K_A inactivation (Fig. 5). In particular, we activated inhibitory synapses on all combinations of three or five adjacent branches in the two morphological reconstructions. In each combination, we varied the amount of K_A reduction (in terms of residual peak conductance relative to control) and the proportion of the tuft in which K_A was reduced, starting from the synaptically activated branch and progressively involving greater surrounding dendritic areas. For each given pair of values for the spatial extent and amount of K_A inactivation, we expressed the fractions of all three-branch and five-branch combinations in which postinhibitory rebound led to a local dendritic spike that did not propagate or to a spike that propagated to the soma as corresponding “spike probabilities.” Both the spatial extent and amount of K_A reduction independently increased the local spike probability, as did the amount of dendritic inhibition (from three to five branches). Among these factors, the amount of K_A reduction was most influential. More extreme conditions also enabled the local spike to propagate to the soma. However, even relatively “mild” conditions (e.g., 50% of inactivation in 50% of the tuft) yielded local spikes in a large proportion of the branch combinations. Note that these simulation results relate specifically to synaptic activity in the terminal tuft of the apical tree, whose dendritic branches are located in stratum lacunosum-moleculare (at >400 μm from the soma). In these conditions, the rebound spike initiation always occurs in the vicinity of the inhibitory synaptic input, and may or may not propagate to the soma. This phenomenon is distinct from that observed upon rebound from hyperpolarization of the main apical trunk located in stratum radiatum (between 240 and 350 μm from the soma). In that case, the action potential is first generated in the soma rather than in the dendrites both in the experiments (Fig. 1b) and simulations (Fig. 2d).

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Figure 5.

Average dendritic or somatic spike probability as a function of local K_A channel density (% of control) and amount of the tuft on which K_A is reduced. Synaptic stimulation was localized in contiguous branches of different sizes. The average spike probability was calculated by testing all combinations of three (top panels) and five (bottom panels) branches in neuron pc2b.