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

On the basis of experimental data we have developed a mathematical mod el of pacemaker activity in bursting neurons of snail Helix pomatia wh ich includes a minimal model of membrane potential oscillation, spike- generating mechanism, voltage- and time-dependent inward calcium curre nt, intracellular calcium ions, [Ca2+](in), their fast buffering and a ccumulation, stationary voltage-dependent [Ca2+](in)-inhibited calcium current. A resulting model of bursting pacemaker activity reproduces all experimental phenomena which were mimicked on the minimal model fo r membrane potential oscillation including (a) the effect of polarizin g current on bursting activity, (b) an increase of input resistance du ring the depolarizing phase, (c) induced hyperpolarization, etc. This model demonstrates adaptation of bursting activity to both the polariz ing current and changes in the stationary sodium or potasium conductan ces. The model also reproduces the behaviour of the transmembrane ioni c current at membrane potentials clamped in different phases of slow-w ave development; the calculated current-voltage relationships of the m odel neuronal membrane using a slow ramp potential clamp demonstrate h ysteresis properties. Relationships between the model of bursting acti vity and the properties of intact bursting neurons are discussed. (C) 1996 Academic Press Limited