Ao. Komendantov et Ni. Kononenko, DETERMINISTIC CHAOS IN MATHEMATICAL-MODEL OF PACEMAKER ACTIVITY IN BURSTING NEURONS OF SNAIL, HELIX-POMATIA, Journal of theoretical biology, 183(2), 1996, pp. 219-230
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