Minimal Neuron Circuits: Bursters

This work introduces a novel methodology for designing biologically plausible bursting neuron circuits using a minimal number of components. We hypothesize that to design circuits capable of bursting, the neuron circuit design must mimic a neuron model that inherently exhibits bursting dynamics. Consequently, classical models such as the Hodgkin-Huxley, $I_{Na,p}+I_{K}$, and FitzHugh-Nagumo models are not suitable choices. Instead, we propose a methodology for designing neuron circuits that emulate the qualitative characteristics of the $I_{Na,p}+I_{K}+I_{K(M)}$ model, a well-established minimal bursting neuron model. Based on this methodology, we present two novel MOSFET-based circuits that exhibit bursting. Using the method of dissection of neural bursting, we demonstrate that the nullcline and bifurcation diagrams of the fast subsystem in our circuits are qualitatively equivalent to those of the $I_{Na,p}+I_{K}+I_{K(M)}$ model. Furthermore, we examine the effect of the type of bifurcation at burst initiation and termination on the bursting characteristics, showing that our circuits can exhibit diverse bursting behaviours. Importantly, the main contribution of this work lies not in the specific circuit implementation, but in the methodology proposed for constructing bursting neuron circuits.