Persistent Interruption in Parvalbumin Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

Abstract

Persistent activity in principal cells is a putative mechanism for maintaining memory traces during working memory. We recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon which could serve as a substrate for persistent activity in principal cells through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modelling and mathematical analysis showed that the slowly inactivating potassium current Kv1 contributes to type 2 excitability, enables the multiple firing regimes observed experimentally in PV-INs, and provides a mechanism for robust persistent interruption of firing. Using a fast/slow separation of times scales approach with the Kv1 inactivation variable as a bifurcation parameter shows that the initial inhibitory stimulus stops repetitive firing by moving the membrane potential trajectory onto a co-existing stable fixed point corresponding to a non-spiking quiescent state. As Kv1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation then spirals out into repetitive firing. In a model describing entorhinal cortical PV-INs without Kv1, interruption of firing could be achieved by taking advantage of the bistability inherent in type 2 excitability based on a subcritical Hopf bifurcation, but the interruption was not robust to noise. Persistent interruption of firing is therefore broadly applicable to PV-INs in different brain regions but is only made robust to noise in the presence of a slow variable. Significance StatementPersistent activity in neuronal networks is thought to provide a substrate for multiple forms of memory. The architecture of neuronal networks across many brain regions involves a small number of inhibitory neurons that control many principal neurons. We propose that persistent silencing of fast-spiking parvalbumin-expressing inhibitory interneurons (PVINs) can result in persistent activity of principal neurons. We use a mathematical approach and computer simulations to investigate the mechanisms governing persistent interruption of firing in hippocampal and cortical PV-INs. We show how a slowly changing state of a particular ion channel controls the long-lasting silence imposed by persistent interruption. Overall, our results provide a conceptual framework that positions the persistent interruption of PV-INs firing as a potential mechanism for persistent activity in principal cells.