REDUCING THE COMPLEXITY OF COMPUTATIONAL MODELS OF NEURONS USING BIFURCATION DIAGRAMS

We reviewed the main features of a theoretical model of dopamineric neurons able to reproduce two features observed both in vivo and in vitro experiments: 1) slow oscillatory potentials (SOP) in the presence of tetrodoxin (TTX) and tetraethyl ammonium (TEA), and 2) the square wave that can be produced by the abolition of SOP by apamin. Using bifurcation analyses, we found that not all currents and activation/inactivation functions are equally important for a coherent mathematical description. In fact, only three currents are essential: 1) the L-type calcium current, which drives both types of oscillation, 2) the small conductance (SK) potassium current, which repolarizes SOP, and 3) a slowly activating potassium current, which repolarizes the square wave. Bifurcation diagrams revealed that the model is insensitive to the kinetic details of SK current activation and that both Botzmann and Michaelis-Menten activation functions offer good descriptions of calcium-activation mechanisms.