Mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia

On the basis of experimental data we have developed a mathematical model of pacemaker activity in bursting neurons of snail Helix pomatia which includes a minimal model of membrane potential oscillation, spike-generating mechanism, voltage- and time-dependent inward calcium current, intracellular calcium ions, [Ca2+]in, their fast buffering and accumulation, 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 for membrane potential oscillation including (a) the effect of polarizing current on bursting activity, (b) an increase of input resistance during depolarizing phase, (c) induced hyperpolarization, etc. This model demonstrates adaptation of bursting activity to both the polarizing current and changes in the stationary sodium or potassium conductances. The model also reproduces the behavior of the transmembrane ionic current at membrane potentials clamped in different phases of slow-wave development; the calculated current-voltage relationships of the model neuronal membrane using a slow ramp potential clamp demonstrate hysteresis properties. Relationships between the model of bursting activity and the properties if intact bursting neurons are discussed.