Computer simulations of high-pass filtering in zebrafish larval muscle fibres

Larval somatic muscle of the zebrafish, Danio rerio, like that of some other organisms, responds to a sustained depolarization with one, and only one, action potential. Here, we report computer simulations, using the NEURON simulation programme, of sodium and potassium currents of somatic muscle of larval Danio rerio to investigate their possible contribution to once-only firing. Our computer model incorporated simulated sodium and potassium ion channels based on steady-state and kinetic parameters derived from a recent electrophysiological study. The model responded to sustained depolarizations with a single action potential at all levels of depolarization above threshold. By varying several parameters of the sodium and potassium currents systematically, the minimum changes necessary to produce repetitive firing were found to be a positive shift in the half-inactivation and a negative shift in the half-activation potentials for the sodium current, accompanied by a slowing of the rate of inactivation to half of the experimentally observed values. This suggests that once-only spiking can be attributed to the steady-state values of activation and inactivation of the sodium current, along with a slower rate of inactivation. Mapping of the resultant firing properties against steady-state and kinetic ion channel parameters revealed a high safety factor for once-only firing and showed that the time constant of inactivation of the sodium current was the key determinant of once-only or repetitive firing. The rapidly inactivating potassium current does not influence once-only firing or the maximum rate of firing in response to periodic excitation in these simulations. Although a contribution of other currents to produce once-only firing has not been excluded, this model suggests that the properties of the sodium current are sufficient to account for once-only firing.