REDUCTION OF A MODEL FOR AN ONCHIDIUM PACEMAKER NEURON

The eight-variable model for the giant neuron localized in the esophag eal ganglia of the marine pulmonate mollusk Onchidium verruculatum is reduced to four-and-three-dimensional systems by regrouping variables with similar time scales. These reduced models replicate the complex b ehavior including beating, periodic bursting and aperiodic bursting di splayed by the original full model when the parameter I-ext representi ng the intensity of the constant DC current stimulation is varied acro ss a wide range. The complex behavior of the full model arises from th e interaction of fast and slow dynamics, and depends on the time scale C-s of the slow dynamics. The four-variable reduced model is construc ted independently from the parameter C-s so that it reproduces the two -dimensional bifurcation structure of the full model for the two param eters I-ext and C-s. The three-variable reduced model is derived for a specific value of C-s. The parameters of this model are tuned so that its one-parameter bifurcation diagram for I-ext closely matches that of the full model. Correspondence between bifurcation structures ensur es that both reduced models reproduce the various discharge patterns o f the full model. Similarity between the full and reduced models is al so confirmed by comparing mean firing frequencies and membrane potenti al waveforms in various regimes. The reduction exposes the factors ess ential for reproducing the dynamics of the full model; indeed, it show s that the eight variables representing the membrane potential and sev en gating variables of six ionic currents in the full model account, i n fact, for three basic processes responsible for excitability, post-d ischarge refractoriness and slow membrane modulation.