An asymmetrical kinetic model for veratridine interactions with sodium channels in molluscan neurons

Veratridine alkaloid induces bi-stability or saw-tooth-shaped long potential waves in molluscan neurons. Voltage clamp experiments reveal the production of a slow sodium current whose changes are described by an asymmetric kinetic diagram relating the states of the sodium channels. Methods of the qualitative theory of differential equations were used to determine the condition necessary for such a model to have either an oscillatory solution or a bi-stable behavior. The kinetic diagram was modified to account for the frequency dependence of the slow sodium current production upon repeated short depolarizations. The modified kinetic diagram suggests that open and inactivated sodium channels are turned into channels with slow kinetic parameters; the transition from open channels would be fast, irreversible and restricted to part of the open channels, whereas that from inactivated channels would be slow and fully reversible upon repolarization.