Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks

Methods

Results

To examine the functional properties of inhibitory synaptic transmission in hippocampal interneuron networks, we focused on the parvalbumin-positive BC, a major type of interneuron that participates in nested theta-gamma oscillations (6, 7). To obtain recordings from pairs of synaptically connected BCs in slices, we made use of transgenic mice that expressed EGFP under the control of the parvalbumin promoter (Fig. 1; ref. 26). In hippocampal slices from these mice, several EGFP-labeled somata were observed in or close to the principal neuron layers under epifluorescence illumination (Fig. 1A). Double labeling confirmed that >80% of EGFP-positive cells were immunoreactive for the Ca²⁺-binding protein parvalbumin (Fig. 1B). Intracellular biocytin filling (Fig. 1C and D) revealed that their axons mainly arborized in the principal cell layers (11 of 11 EGFP-positive neurons; Fig. 1D). In whole-cell recordings, these cells generated high-frequency trains of action potentials during long depolarizing current pulses (mean action potential frequency 287 ± 18 Hz, range 110–420 Hz; 22 cells). In conclusion, these results demonstrate selective labeling of parvalbumin-positive fast-spiking BCs in hippocampal slices, ensuring reliable identification under experimental conditions.

Recordings from pairs of EGFP-positive cells in DG, CA3, and CA1 revealed that BCs were coupled by both chemical and electrical synapses (Fig. 2). The key properties of chemical synaptic transmission were as follows (Fig. 2 A and B). First, unitary IPSCs showed very fast kinetics. The amplitude-weighted decay time constant obtained from a biexponential fit of the decay phase of average unitary IPSCs was 1.2–2.5 ms, with significant differences among regions (CA3 < CA1 < DG; P < 0.05; Fig. 2A Left; see Table 1). This fast IPSC decay time constant was a specific property of BC–BC synapses, because IPSCs generated at BC–principal neuron synapses in the same regions exhibited a slower decay (P < 0.05; Fig. 2A Right). Second, the IPSC peak amplitude was very large, particularly in CA3 and CA1 (93–208 pA; see Table 1). Third, IPSCs were blocked by bicuculline methiodide, a competitive antagonist of GABA_ARs (Fig. 2A Bottom; ref. 30). Finally, unitary IPSCs showed PPD during a pair of presynaptic action potentials (Fig. 2B Left; refs. 16, 31, and 32). PPD appeared to be independent of the type of target cell, because the extent of PPD was similar at BC–BC synapses and BC–principal neuron synapses in all three regions (P > 0.05; Fig. 2B Right). In contrast, slight differences in PPD were observed for BC–BC synapses among hippocampal subfields (CA3 > CA1 > DG; P < 0.05).

In a subset of BC–BC pairs, presynaptic spikes evoked fast electrical PSCs (33–35), which were characterized by minimal latency, invariant peak amplitude (Fig. 2C), and bidirectionality (not illustrated). Furthermore, application of long current pulses to one cell resulted in correlated voltage changes in the other cell, which unequivocally demonstrates the electrical nature of the coupling (Fig. 2D). The mean coupling ratio for long current pulses, determined from pre- and postsynaptic voltages, was 0.11 ± 0.01 (three BC–BC pairs in DG). Electrical coupling was never observed between BCs and principal cells.

Our results show that the presence of fast and strong inhibitory synapses in networks of parvalbumin-positive perisomatic inhibitory interneurons is a general principle of synaptic organization of the hippocampus. The observed properties of BC–BC synapses challenged several assumptions of existing models of interneuron gamma oscillations (e.g., refs. 11–14). We therefore developed an interneuron network model based on realistic assumptions about synaptic properties and network structure, using the experimentally determined parameters from the CA1 region, and examined its oscillatory properties in the presence of a tonic excitatory drive (see Methods). With the realistic time course of the inhibitory synaptic conductance [τ₁ = 1.2 ms (90%), τ₂ = 8.0 ms (10%)] and a heterogeneity of the tonic excitatory drive (I_σ/I_μ) of 0.1, coherent oscillations emerged in the network model when chemical and electrical synapses were activated (Fig. 3). Synchronized activity was evident in the raster plots (Fig. 3 A and B Upper) and the corresponding spike frequency histograms (Fig. 3 A and B Lower). Synchronized activity was also apparent in the total inhibitory conductance in a given interneuron (Fig. 3 C and D Upper) and the inhibitory output simulated in a principal cell (Fig. 3 C and D Lower). Thus the model showed coherent activity over a wide range of tonic excitatory drive (Fig. 3 A and B).

To understand why the interneuron network model based on realistic assumptions was a robust gamma frequency oscillator, we varied individual network parameters and examined the effects on coherence and frequency (Fig. 4; see legend for explanation of the color code for frequency). We first ran simulations in which both tonic drive (I_μ) and unitary postsynaptic peak conductance (g_GABA) were varied systematically (Fig. 4A). With a heterogeneity I_σ/I_μ of 0.1, our model produced coherent oscillations in a large part of the parameter space corresponding to a broad range of frequencies (24–74 Hz for half-maximal κ). The maximum of coherence was close to the experimentally determined g_GABA [≈0.04 mS⋅cm⁻², estimated from a peak current of 208 pA (see Table 1), and a somatodendritic surface area of approximately 12,000 μm² (16)], suggesting that synaptic strength in the network is optimized for maximizing synchronization.

We then varied the synaptic decay time constant, the structural properties of the network, and the gap junction coupling conductance (Fig. 4 B–D). The synaptic decay time constant influenced both coherence and frequency of the oscillations (Fig. 4B). If the synaptic decay time constant was set to the value of the fast component, high coherence was mainly reached with high excitatory drive and large g_GABA, which corresponded to the upper gamma frequency band (37–79 Hz for half-maximal κ; Fig. 4B Left). Conversely, if the decay time constant was set to the value of the slow component, high coherence was mainly reached with low drive and small g_GABA, which corresponded to the lower gamma frequency band (18–55 Hz for half-maximal κ; Fig. 4B Right). The “realistic” network (Fig. 4A) appeared to inherit properties of both networks (Fig. 4B), resulting in flexible frequency control.

In contrast, structural properties of the network primarily affected the frequency, and to a smaller extent the coherence of the oscillations (Fig. 4C). Decreased spacing between neurons in the network (i.e., decreased conduction delay) increased the frequency (Fig. 4C Left), whereas increased spacing reduced it (Fig. 4C Right). Unexpectedly, both decreased and increased spacing reduced the average coherence value, indicating that an intermediate spacing (i.e., intermediate conduction delay) maximizes synchronization in the gamma frequency range (Fig. 4A). Finally, changes in gap junction conductance affected coherence selectively, with only minimal effects on frequency (Fig. 4D). An increase in gap junction conductance increased coherence (Fig. 4D Left), whereas a block of gap junctions reduced it (Fig. 4D Right). Thus the robustness of coherence appears to emerge from the combined effects of synaptic properties, network structure, and gap junction coupling.

In several types of oscillatory activity in vivo (e.g., during nested theta-gamma activity) the excitatory drive is nonstationary, unlike in the simulations shown (Fig. 4 A–D). To examine how the temporal–spatial structure of the excitatory drive affected coherence and frequency, we used a step-like excitatory drive applied to either all cells or to a subpopulation of neurons (Fig. 4E). If a drive with synchronized onset was applied to all cells, the network oscillated with higher coherence, but at approximately the same frequency (22–78 Hz for half-maximal κ; Fig. 4E Left) in comparison to the network subjected to an asynchronous excitatory drive (Fig. 4A). In contrast, if the synchronized drive was applied to a cluster of 20 adjacent interneurons, coherent oscillations were generated at markedly higher frequencies (30–110 Hz for half-maximal κ; Fig. 4E Right). In conclusion, the temporal–spatial structure of the stimulus critically shapes the oscillatory properties of the interneuron network. Our interneuron network model, if stimulated synchronously and focally, may explain “fast” (>90 Hz) gamma oscillations in the hippocampal CA1 region in vivo (36).

Discussion

Using transgenic mice that express EGFP under the control of the parvalbumin promoter, we found that unitary IPSCs at hippocampal BC–BC synapses showed rapid time course and large amplitude. Electrical coupling occurred in a subset of pairs. Both the fast kinetics of unitary IPSCs and the presence of gap junction coupling were target cell-specific, but region-independent properties. Thus, interneurons selectively express an extensive repertoire of fast signaling mechanisms (27, 37–42).

The experimentally observed properties of BC–BC synapses were not consistent with assumptions of prevailing models of interneuron gamma oscillations (e.g., refs. 11–14). First, the decay time constant was markedly faster than assumed in existing models (typically 10 ms). Second, inhibitory coupling appeared to be stronger than previously thought. The estimated specific unitary postsynaptic conductance change is 0.04 mS⋅cm⁻² in the CA1 region, larger than suggested previously (e.g., 0.001–0.002 mS⋅cm⁻²; ref. 12). Third, electrical coupling was abundant, but was not considered in many earlier simulation studies (refs. 11–14; but see ref. 17).

We therefore developed an interneuron network model that incorporated both realistic synaptic properties (using the experimentally determined parameters from the CA1 region) and a spatial structure with conduction delays. In comparison to the model proposed by Wang and Buzsáki (12), our model showed higher maximal coherence, despite a higher heterogeneity in the tonic excitatory drive (I_σ/I_μ = 0.1 vs. 0.03). Furthermore, it generated highly coherent oscillations over a broad range of tonic excitatory drive, corresponding to a wide range of frequencies (20–110 Hz). Finally, it showed highly coherent oscillations at physiologically relevant values of the unitary postsynaptic conductance change (≈0.04 mS⋅cm⁻²). In conclusion, our model generates coherent oscillations very robustly, but allows for flexibility in the control of network frequency.

Why is the new model able to generate coherent oscillations more robustly than previous models? Our simulation results (Fig. 4) suggest that high coherence is an emerging property that arises from the combination of several factors. Specifically, it is the combination of fast inhibitory conductance, high synaptic strength, and the presence of conduction delays in a structured network that appears to be favorable for establishing and maintaining synchrony. This conclusion differs from the previous view that slow/weak synapses are optimal for synchronization in the absence of conduction delays (refs. 12–14; see refs. 43 and 44). Intuitively, however, a rapid inhibitory signal generated with a certain delay is a very effective synchronizing signal. In contrast, a slow inhibitory signal without delay is not as effective, because recovery from inhibition is temporarily less well defined. In addition, we find that gap junctions enhance coherent oscillatory activity. However, the effects (Fig. 4D) are smaller than reported previously (17). This difference may be interpreted as partial functional redundancy generated by the coexpression of two fast signaling mechanisms.

In contrast to our initial expectations, differences in the decay time course of the inhibitory postsynaptic conductance did not explain the different oscillatory properties of the hippocampal subfields. In the intact rat a high-frequency gamma oscillator (80 Hz) in the DG predominates, whereas after entorhinal lesion a lower frequency oscillator (40–60 Hz) in CA1 emerges (6). Similarly, in the in vitro slice preparation, the preferred oscillation frequency is higher in the DG than in CA1 under similar conditions [DG: 60–70 Hz (20, 21); CA1: 30–50 Hz (8, 11, 22–24)]. This trend is opposite to the observed differences in the kinetics of the postsynaptic conductance, which were slower in the DG than in CA1 (see Table 1). However, our results suggest several alternative mechanisms of frequency tuning (see ref. 11). Different preferred frequencies could be explained by the differences in g_GABA, as observed experimentally (see Table 1; CA1 > CA3 ≫ DG; Fig. 4A), a higher tonic excitatory drive in the DG, presumably generated by the perforant path input (6), and differences in network structure, such as spacing between synaptically connected interneurons (Fig. 4C). Finally, the oscillation frequency depends on the temporal and spatial structure of the stimulus. Intuitively, the higher frequency of the oscillations in a subnetwork of clustered cells (Fig. 4E) could be understood as the result of reduced average conduction delay and decreased total inhibition on individual neurons.

In conclusion, we have shown that an interneuron network model based on realistic assumptions generates highly coherent oscillations over a wide range of frequencies (20–110 Hz). The model may provide an adequate representation of certain forms of hippocampal gamma oscillations, such as pharmacologically isolated interneuron network gamma in vitro (8, 11) and nested theta-gamma oscillations in vivo (6, 7), in which the activity is markedly higher in interneurons than in principal cells. Whether our model can be applied to gamma oscillations in the neocortex, however, remains to be established.

We thank Drs. J. Bischofberger, M. Heckmann, and R. Traub for critically reading the manuscript. This work was supported by Deutsche Forschungsgemeinschaft Grants SFB 505/C5 (to P.J.) and SFB 505/C6 (to M.F. and P.J.), Human Frontiers Science Program Organization Grant RG0017/1998-B (to P.J.), and grants from the Alexander-von-Humboldt Foundation (to P.J. and M.F.), the Schilling Foundation (to H.M.), and Novartis (to H.M.).

Supplementary Material