Nonlinear feedback model of neuronal populations in hippocampal CAl region.
1. A lumped-circuit model is proposed for the local interactions within the hippocampal CAl region. Each neuronal population is represented by a linear differential equation or a linear transfer function in the Laplace domain. Interactions between neuronal populations are represented by gain factors. Recurrent inhibition of pyramidal cells by the inhibitory interneurons is the important interaction represented by an asymmetric, bidirectionally saturating gain curve. The inputs to the model are orthodromic or antidromic inputs to the pyramidal cells and a tonic input from the brain stem. The outputs are the response ot pyramidal cells and interneurons. 2. The model is evaluated by data of intracellular and extracellular recordings from the hippocampus. Extracellular recordings consist of the average evoked potentials (AEPs), unitary poststimulus time histograms (PSTHs), and the spontaneous electroencephalogram (EEG). On account of the regular structure of the hippocampus, extracellular potentials are expected to correspond to the average intracellular potential among a local neuronal population. 3. Under deep anesthesia, all neuronal responses evoked by an electrical shock to the hippocampal afferents end in a prolonged inhibition of pyramidal cells. The model further predicts that the duration of inhibition increases with stimulus intensity, which is verified experimentally. 4. In the awake rat, especially during behaviors accompanied by a hippocampal theta rhythm (e.g., walking), the AEPs evoked by stimulation of afferent input to the CAl region were oscillatory with a frequency of 20-50 cycles/s. In the model an excitatory bias from the brain stem is assumed to linearize the local circuits, resulting in oscillatory responses similar to those obtained experimentally. 5. As observed by spectral analysis, the hippocampal EEG of the frequency 40-70 Hz varied in power and resonance during various behaviors of the rat. Except for the theta rhythm, analysis of the output(s) of the model given a Gaussian white-noise input showed similar power spectra as the EEG in vivo. The increase in power of the 40-70 Hz EEG in some behaviors, e.g., walking, is reproduced by assuming that during such behaviors a modulating bias from the brain stem linearizes the local CAl circuits. This latter circumstances underlies the generation of oscillatory AEPs and the high-frequency EEG. 6. When recurrent excitatory-inhibitory feedback is very large, the model produces a limit cycle of 50-65 cycles/s. The limit cycle is suggested to be the cause of a particular type of high-frequency (50-65 cycles/s) hippocampal afterdischarge that occurs after tetanization of the input pathways. The amplitude, frequency, and waveform of the model generated and experimental data are similar. 7. In conclusion, a nonlinear recurrent excitatory-inhibitory feedback model of the hippocampus explains and integrates various existing experimental data. The model further predicts results that can be experimentally tested.