Section: Behavioral/systems Neuroscience Section Editor: Paradoxical Eeects of External Modulation of Inhibitory Interneurons

The neocortex, hippocampus, and several other brain regions contain populations of excitatory principal cells with recurrent connections and strong interactions with local inhibitory interneurons. To improve our understanding of the interactions between these cell types, we modeled the dynamical behavior of this type of network, including external inputs. A surprising nding was that increasing the direct external inhibitory input to the inhibitory interneurons, without directly a ecting any other part of the network, can in some circumstances cause the interneurons to increase their ring rates. The main prerequisite for this paradoxical response to external input is that the recurrent connections among the excitatory cells be strong enough to make the excitatory network unstable when feedback inhibition is removed. Because this requirement is met in the neocortex and several regions of the hippocampus, these observations have important implications for understanding the responses of interneurons to a variety of pharmacological and electrical manipulations. The analysis can be extended to a scenario with periodically varying external input, where it predicts a systematic relationship between the phase shift and depth of modulation for each interneuron. This prediction was tested by recording from interneurons in the CA1 region of the rat hippocampus in vivo, and the results broadly con rmed the model. These ndings have further implications for the function of inhibitory and neuromodulatory circuits, which can be tested experimentally. Several regions of the mammalian brain, including the neocortex and hippocampus, consist largely of intermixed excitatory and inhibitory subpopulations (see (Jones, 1986; Amaral and Witter, 1995)). The excitatory cells are generally more numerous and project extensively to each other as well as to the inhibitory cells. The inhibitory cells, which are primarily GABAergic, project strongly to the excitatory cells; recent evidence indicates that they also project to each other (Sik et al., 1995). In the hippocampus and neocortex, complete blockade of inhibition with GABA antagonists leads to runaway activity in the excitatory cells, culminating in an epileptic seizure (Traub and Miles, 1991; Grinvald et al., 1988). Thus interneurons govern the activity of principal cells in somewhat the same sense that shepherds govern the activity of sheep. Because this type of neural organization appears so commonly in the brain, it is important to have a good understanding of its dynamical properties. The analysis presented here was originally motivated by an observation while simulating an integrate-andre model of the hippocampal theta rhythm (Tsodyks et al., 1996) a strong, regular oscillation that dominates the hippocampal electroencephalogram (EEG) of some mammals during behavioral states of active movement, rapid eye-movement sleep, or light dissociative anesthesia (Vanderwolf, 1969). Theta oscillations are controlled by inputs from the medial septal area, and vanish from the hippocampus if the medial septum is lesioned or inactivated. A substantial fraction|probably more than half|of the projection from medial septum to hippocampus arises from GABAergic cells, and terminates almost exclusively on interneurons (Freund and Antal, 1988). It is therefore generally believed that the theta-rhythmic activity of hippocampal cells is entrained by rhythmic inhibition of inhibitory interneurons. The model consisted of two pools of neurons, one excitatory and the other inhibitory; and the hippocampal theta rhythm was modeled as an external, rhythmically varying, inhibitory 1 input to the inhibitory neurons. When the model was simulated, we noticed, to our surprise, that the excitatory and inhibitory pools both oscillated in synchrony with the external input and thus in synchrony with each other (Fig. 1). This seemed quite paradoxical: if the only external input was to the inhibitory cells, a decrease in their activity would be expected to provoke an increase in the activity of the excitatory cells, so that the two would oscillate 180 out of phase. In an e ort to understand this phenomenon, we constructed a simpli ed averagering-rate model of the network whose dynamics could be examined analytically. A straightforward phase plane analysis shows that a \paradoxical" response of inhibitory neurons to external modulation is a very general feature of this type of network, and can be expected to be observable in real brains. The model is abstract, but its essential features are quite robust, and the main conclusions of the present analysis have been veri ed using more realistic integrate-andre models. We therefore used simultaneous recordings from interneurons and pyramidal cells of rat hippocampus to test some of the predictions of the model which relate the phase shift and depth of modulation of interneurons. Methods Experimental Procedure The experimental data considered in this paper were recorded using methods that have previously been described in detail (Skaggs et al., 1996). Brie y, hippocampal unit activity was recorded using tetrodes, which consisted of four 12m wires twisted together. The tetrodes were placed in or near the CA1 cell body layer of the dorsal hippocampus. Di erent cells recorded from a single tetrode were distinguished on the basis of their spike amplitudes on the four tetrode channels. A cell was classi ed as an interneuron if (1) it had a narrow spike waveform, less than 300 sec from peak to valley, (2) it did not re in complex-spike bursts, and (3) it had a mean rate greater than 5 Hz averaged across the whole session. The hippocampal EEG was recorded from a separate electrode positioned near the ssure separating the CA1 region from the dentate gyrus, because this is the best location for recording large, robust theta waves. Theta phases were calculated by digitally ltering the EEG signal with a bandpass of 6{10 Hz and then using the peaks of the resulting waves as reference points. The phase of an interneuron and its depth of modulation were obtained by plotting a histogram of the interneuron's ring rate for di erent theta phases of EEG, and comparing this with a similar histogram for the whole population of pyramidal neurons recorded simultaneously during the same session. An example of such a histogram for one of the interneurons is shown in Fig. 2. The depth of modulation of the ring rate obtained from this plot was then normalized by the maximal ring rate. The Model Consider a recurrent network model consisting of two populations: Ne excitatory neurons and Ni inhibitory neurons. In a coarse-grained description, detailed speci cation of activity in each individual neuron can be replaced by the average activity of the corresponding population (the fraction of neurons active within a certain time window around t). This 2 0 100 200 300 400 500 600 700 800 90