Quantifying noise-induced stability of a cortical fast-spiking cell model with Kv3-channel-like current

Population oscillations in neural activity in the gamma (>30 Hz) and higher frequency ranges are found over wide areas of the mammalian cortex. Recently, in the somatosensory cortex, the details of neural connections formed by several types of GABAergic interneurons have become apparent, and they are believed to play a significant role in generating these oscillations through synaptic and gap-junctional interactions. However, little is known about the mechanism of how such oscillations are maintained stably by particular interneurons and by their local networks, in a noisy environment with abundant synaptic inputs. To obtain more insight into this, we studied a fast-spiking (FS)-cell model including Kv3-channel-like current, which is a distinctive feature of these cells, from the viewpoint of nonlinear dynamical systems. To examine the specific role of the Kv3-channel in determining oscillation properties, we analyzed basic properties of the FS-cell model, such as the bifurcation structure and phase resetting curves (PRCs). Furthermore, to quantitatively characterize the oscillation stability under noisy fluctuations mimicking small fast synaptic inputs, we applied a recently developed method from random dynamical system theory to estimate Lyapunov exponents, both for the original four-dimensional dynamics and for a reduced one-dimensional phase-equation on the circle. The results indicated that the presence of the Kv3-channel-like current helps to regulate the stability of noisy neural oscillations and a transient-period length to stochastic attractors.