DETERMINISTIC CHAOS IN MATHEMATICAL-MODEL OF PACEMAKER ACTIVITY IN BURSTING NEURONS OF SNAIL, HELIX-POMATIA

Chaotic regimes in a mathematical model of pacemaker activity in the b ursting neurons of a snail, Helix pomatia, have been investigated. The model includes a slow-wave generating mechanism, a spike-generating m echanism, an inward Ca current, intracellular Ca ions, [Ca2+](in), the ir fast buffering and uptake by intracellular Ca stores, and a [Ca2+]( in)-inhibited Ca current. Chemosensitive voltage-activated conductance , g(B), responsible for termination of the spike burst, and chemosens itive sodium conductance, g(Na), responsible for the depolarizing pha se of the slow-wave, were used as control parameters. These conductanc es in intact snail bursting neuron are regulated by neuropeptides. Tim e courses of the membrane potential and [Ca2+](in) were employed to an alyse different regimes in the model. Histograms of interspike interva ls, autocorrelograms, spectral characteristics, one-dimensional return maps, phase plane trajectories, positive Lyapunov exponent and especi ally cascades of period-doubling bifurcations demonstrate that approac hes to chaos were generated. The bifurcation diagram as a function of g(B) and the ([Ca2+](in)-V) phase diagram of initial conditions revea l fractal features. It has been observed that a short-lasting depolari zing current or elevation of [Ca2+](in) may evoke transformation of ch aotic activity into a regular bursting one. These kinds of transitions do not require any changes in the parameters of the model. The result s demonstrate that chaotic regimes of neuronal activity modulated by n europeptides may play a relevant role in information processing and st orage at the level of a single neuron. (C) 1996 Academic Press Limited