Although only a small percentage of cortical cells is inhibitory, this group contains most morphological and electrophysiological diversity. The functional relevance of this diversity has been shown to span (long range) feedback [1], disinhibition [1,2] and modulation of the input-output gain [3,4]. The latter was studied extensively for two interneuron types: somatostatin (SOM) and parvalbumin (PV) positive interneurons. While activation of PV cells had a divisive impact on gain, it was indicated that the mode of gain modulation of SOM cells, either divisive or subtractive, depended on the size of stimulation. This finding indicates that the function of inhibition is a dynamic product of local circuit interactions [5].

The pyramidal cell (PC)-PV-SOM circuit has received much attention recently, but a theoretical framework is underdeveloped. Unlike the PC-PV motif, a characterization of the electrophysiological features of the three cell type circuit is missing. The third cell type can add several interactions: feedback inhibition, recurrent inhibition, feed-forward inhibition and disinhibition. A characterization of these motifs aids the identification of the PC-PV-SOM circuit in recordings and can help develop effective stimulation protocols.

Here, we characterize the features of a circuit model of three types of Izhikevich models [6]: regular spiking (RS), fast-spiking (FS) and low-threshold spiking (LTS). By merging the circuit from a RS-FS, through RS-FS-LTS, to RS-LTS, while tracking characteristics such as oscillation frequency, firing rate and phase of firing we identify the cell types involved in the behaviors of the network. By subsequently breaking connections the relevant interactions are identified. This approach yields the characterization of a variety of physiologically relevant network states for the RS-FS-LTS motif.

[1] X. Jiang, et al. Nat. Neurosci. 16:210-8 (2013).
[2] C. K. Pfeffer, et al. Nat. Neurosci. 16:1068-76 (2013).
[3] S.-H. Lee, et al. Nature 488:379-383 (2012).
[4] N. R. Wilson, et al. Nature 488:343-348 (2012).
[5] S. El-Boustani and M. Sur Nat. Commun. 5:5689 (2014).
[6] E. M. Izhikevich IEEE Trans. Neural Netw. 14:1569-72 (2003).