The Agility of a Neuron: Phase Shift Between Sinusoidal Current Input and Firing Rate Curve

The response of a neuron when receiving a periodic input current signal is a periodic spike firing rate signal. The frequency of an input sinusoidal current and the surrounding environment such as background noises are two important factors that affect the firing rate output signal of a neuron model. This study focuses on the phase shift between input and output signals, and here we present a new concept: the agility of a neuron, to describe how fast a neuron can respond to a periodic input signal. In this study, we derived three agility score functions for the balanced leaky integrate-and-fire model, the Hodgkin-Huxley model, and the Connor-Stevens neuron model. By applying the score of agility, we are capable of characterizing the surrounding environment; once the frequency of the periodic input signal is given, the actual angle of phase shift can then be determined and, therefore, different neuron models can be normalized and compared with each other.