Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically relies on currents that provide slow positive feedback to the membrane potential. Such currents have the ability of making the total conductance of the circuit negative in a time scale that is termed slow because intermediate between the fast time scale of the spike upstroke and the ultraslow time scale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale.