Bifurcation and negative self-feedback mechanisms for enhanced spike-timing precision of inhibitory interneurons

A high spike-timing precision characterized by a small variation in interspike intervals of neurons is important for information processing in various brain functions. An experimental study on fast-spiking interneurons has shown that inhibitory autapses functioning as negative self-feedback can enhance spike-timing precision. In the present paper, bifurcation and negative self-feedback mechanisms for the enhanced spike-timing precision to stochastic modulations are obtained in two theoretical models, presenting theoretical explanations to the experimental finding. For stochastic spikes near both the saddle-node bifurcation on an invariant cycle (SNIC) and the subcritical Hopf (SubH) bifurcation with classes 1 and 2 excitabilities, respectively, enhanced spike-timing precision appears in large ranges of the conductance and the decaying rate of inhibitory autapses, closely matching the experimental observation. The inhibitory autaptic current reduces the membrane potential after a spike to a level lower than that in the absence of inhibitory autapses and the threshold to evoke the next spike, making it more difficult for stochastic modulations to affect spike timings, and thereby enhancing spike-timing precision. In addition, firing frequency near the SubH bifurcation is more robust than that near the SNIC bifurcation, resulting in a higher spike-timing precision for the SubH bifurcation. The bifurcation and negative self-feedback mechanisms for the enhanced spike-timing precision present potential measures to modulate the neuronal dynamics or the autaptic parameters to adjust the spike-timing precision.