We describe four different mechanisms that lead to oscillations in a network of two reciprocally inhibitory cells. In two cases (intrinsic release and intrinsic escape) the frequency of the network oscillation is insensitive to the threshold voltage of the synaptic potentials. In the other two cases (synaptic release and synaptic escape) the network frequency is strongly determined by the threshold voltage of the synaptic connections. The distinction between the different mechanisms blurs as the function describing synaptic activation becomes less steep and as the model neurons are removed from the relaxation regime. These mechanisms provide insight into the parameters that control network frequency in motor systems that depend on reciprocal inhibition.

The M-current (I M ), comprised of Kv7 channels, is a voltage-activated K ϩ conductance that plays a key role in the control of cell excitability. In hippocampal principal cells, I M controls action potential (AP) accommodation and contributes to the medium-duration afterhyperpolarization, but the role of I M in control of interneuron excitability remains unclear. Here, we investigated I M in hippocampal stratum oriens (SO) interneurons, both from wild-type and transgenic mice in which green fluorescent protein (GFP) was expressed in somatostatin-containing interneurons. Somatodendritic expression of Kv7.2 or Kv7.3 subunits was colocalized in a subset of GFPϩ SO interneurons, corresponding to oriens-lacunosum moleculare (O-LM) cells. Under voltage clamp (VC) conditions at Ϫ30 mV, the Kv7 channel antagonists linopirdine/XE-991 abolished the I M amplitude present during relaxation from Ϫ30 to Ϫ50 mV and reduced the holding current (I hold ). In addition, 0.5 mM tetraethylammonium reduced I M , suggesting that I M was composed of Kv7.2-containing channels. In contrast, the Kv7 channel opener retigabine increased I M amplitude and I hold . When strongly depolarized in VC, the linopirdine-sensitive outward current activated rapidly and comprised up to 20% of the total current. In current-clamp recordings from GFPϩ SO cells, linopirdine induced depolarization and increased AP frequency, whereas retigabine induced hyperpolarization and arrested firing. In multicompartment O-LM interneuron models that incorporated I M , somatodendritic placement of Kv7 channels best reproduced experimentally measured I M . The models suggest that Kv3-and Kv7-mediated channels both rapidly activate during single APs; however, Kv3 channels control rapid repolarization of the AP, whereas Kv7 channels primarily control the interspike interval.

1. The dynamic clamp was used to create reciprocally inhibitory two-cell circuits from pairs of pharmacologically isolated gastric mill neurons of the stomatogastric ganglion of the crab, Cancer borealis. 2. We used this system to study how systematic alterations in intrinsic and synaptic parameters affected the network behavior. This has previously only been possible in purely computational systems. 3. In the absence of additional hyperpolarization-activated inward current (IH), stable half-center oscillatory behavior was not observed. In the presence of additional IH, a variety of circuit dynamics, including stable half-center oscillatory activity, was produced. 4. Stable half-center behavior requires that the synaptic threshold lie within the voltage envelope of the slow wave oscillation. 5. Changes in the synaptic threshold produce dramatic changes in half-center period. As predicted by previous theoretical work, when the synaptic threshold is depolarized, the period first increases and then decreases in a characteristic inverted U-shaped relationship. Analysis of the currents responsible for the transition between the active and inhibited neurons shows that the mechanism of oscillation changes as the synaptic threshold is varied. 6. Increasing the time constant and the conductance of the inhibitory synaptic current increased the period of the half-center oscillator. 7. Increasing the conductance of IH or changing the voltage dependence of IH can either increase or decrease network period, depending on the initial mode of network oscillation. A depolarization of the activation curve causes the network to respond in a similar fashion as increasing the conductance of IH. 8. Many neuromodulatory substances are known to alter synaptic strength and the conductance and voltage dependence of IH, parameters we studied with the dynamic clamp. To understand the response of the network to modulation of a single parameter, it is necessary to understand the nature of the altered conductance and how it interacts with the other conductances in the system.

Rodent hippocampal slices of < or = 0.5 mm thickness have been widely used as a convenient in vitro model since the 1970s. However, spontaneous population rhythmic activities do not consistently occur in this preparation due to limited network connectivity. To overcome this limitation, we develop a novel slice preparation of 1 mm thickness from adult mouse hippocampus by separating dentate gyrus from CA3/CA1 areas but preserving dentate-CA3-CA1 connectivity. While superfused in vitro at 32 or 37 degrees C, the thick slice exhibits robust spontaneous network rhythms of 1-4 Hz that originate from the CA3 area. Via assessing tissue O2, K+, pH, synaptic, and single-cell activities of superfused thick slices, we verify that these spontaneous rhythms are not a consequence of hypoxia and nonspecific experimental artifacts. We suggest that the thick slice contains a unitary circuitry sufficient to generate intrinsic hippocampal network rhythms and this preparation is suitable for exploring the fundamental properties and plasticity of a functionally defined hippocampal "lamella" in vitro.

The coupling of high frequency oscillations (HFOs; >100 Hz) and theta oscillations (3–12 Hz) in the CA1 region of rats increases during REM sleep, indicating that it may play a role in memory processing. However, it is unclear whether the CA1 region itself is capable of providing major contributions to the generation of HFOs, or if they are strictly driven through input projections. Parvalbumin-positive (PV+) interneurons may play an essential role in these oscillations due to their extensive connections with neighboring pyramidal cells, and their characteristic fast-spiking. Thus, we created mathematical network models to investigate the conditions under which networks of CA1 fast-spiking PV+ interneurons are capable of producing high frequency population rhythms. We used whole-cell patch clamp recordings of fast-spiking, PV+ cells in the CA1 region of an intact hippocampal preparation in vitro to derive cellular properties, from which we constrained an Izhikevich-type model. Novel, biologically constrained network models were constructed with these individual cell models, and we investigated networks across a range of experimentally determined excitatory inputs and inhibitory synaptic strengths. For each network, we determined network frequency and coherence. Network simulations produce coherent firing at high frequencies (>90 Hz) for parameter ranges in which PV-PV inhibitory synaptic conductances are necessarily small and external excitatory inputs are relatively large. Interestingly, our networks produce sharp transitions between random and coherent firing, and this sharpness is lost when connectivity is increased beyond biological estimates. Our work suggests that CA1 networks may be designed with mechanisms for quickly gating in and out of high frequency coherent population rhythms, which may be essential in the generation of nested theta/high frequency rhythms.