Impulse firing in the slowly adapting stretch receptor neurone of lobster and its numerical simulation

A mathematical model of the electrical activity of the slowly adapting lobster stretch receptor neurone is presented. The model is based on constant field and state transition theory and employs measurements of the kinetics of membrane currents in sub- and near-threshold voltage regions (Gestrelius, Grammp & Sjölin 1981, Gestrelius & Grampp 1983, Gestrelius, Grampp & Sjölin 1983, Edman, Gestrelius & Grampp 1983). In addition to the classical action potential generating mechanisms (Hodgkin & Huxley 1952) the model also includes the processes of slow Na and K inactivation, ion flux dependent changes of the intracellular Na+ and K+ concentrations, and the activity of an electrogenic Na-K pump sensitive to intracellular Na+ accumulation. The model is able to correctly simulate recorded action potentials as well as repetitive firing both with respect to stimulus dependence (sensitivity) and time dependence (adaptation) during prolonged electrical stimulation. In the living cell firing adaptation is found to consist of an initial phase with a relatively high, and a later phase with a lower rate of adaptation. From the model properties it can be concluded that the initial phase is mainly caused by the slow Na inactivation, while the later phase is due to a slow Na+ influx dependent pump current activation.