Small-Signal Neural Models and Their Applications

This paper introduces the use of the concept of small-signal analysis, commonly used in circuit design, for understanding neural models. We show that neural models, varying in complexity from Hodgkin-Huxley to integrate and fire have similar small-signal models when their corresponding differential equations are close to the same bifurcation with respect to input current. Three applications of small-signal neural models are shown. First, some of the properties of cortical neurons described by Izhikevich are explained intuitively through small-signal analysis. Second, we use small-signal models for deriving parameters for a simple neural model (such as resonate and fire) from a more complicated but biophysically relevant one like Morris-Lecar. We show similarity in the subthreshold behavior of the simple and complicated model when they are close to a Hopf bifurcation and a saddle-node bifurcation. Hence, this is useful to correctly tune simple neural models for large-scale cortical simulations. Finaly, the biasing regime of a silicon ion channel is derived by comparing its small-signal model with a Hodgkin-Huxley-type model.