Mechanisms of Firing Patterns in Fast-Spiking Cortical Interneurons

Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na+, delayed-rectifier K+, and slowly inactivating d-type K+ conductances. The model is analyzed using nonlinear dynamical system theory. For small Na+ window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na+ window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na+ window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.: About 25% of the neurons in the mammalian neocortex are inhibitory, namely reduce the activity of neurons they contact. These inhibitory neurons exhibit diversity of morphological, chemical, and biophysical properties, and their classification has recently been the focus of much debate. Even neurons belonging to a single class of “fast-spiking” (FS) display a large variety of firing patterns in response to standard square current pulses. Previous works proposed that this class is in fact a discrete set of neuronal subtypes with biophysical properties differing in a discontinuous way. In this work, we propose an alternative theory, according to which the biophysical properties of FS neurons are continuously distributed, but distinct firing patterns emerge due to highly nonlinear dynamics of these neurons. We ascertain this theory by exploring with mathematical techniques a biophysically based model of FS neurons. We demonstrate that variable firing responses of cortical FS neurons can be accounted for if one assumes heterogeneity in the strength of some of the ionic conductances underlying neuronal activity. Our theory predicts the existence of two main firing patterns of FS neurons. This prediction is verified by direct recordings in cortical slices.