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

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Abstract
A mathematical model of the electrical activity of the slowly adapting lobster stretch receptor neuron 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. In addition to the classical action potential generating mechanisms (Hodgkin et 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 and repetitive firing with respect to stimulus dependence (sensitivity) and time dependence (adaptation) during prolonged electrical stimulation. In the living cell, firing adaptation consists of an initial pahse with a relatively high, and a later phase with a low rate of adaptation. From the model properties it can be concluded that the initial phase is mainly caused by the slow Na inactivation; the later phase is due to a slow Na+ influx dependent pump current activation.