Mathematical modelling of weakly nonlinear pulses in a retinal neuron

In the nervous system, most processing of information and its transmission over short distances occurs in dendrites and short axons whose membranes are weakly nonlinear. We discuss the behaviour of a particular cell, the photoreceptor cell of the honey-bee drone, for which the normal physiological input is well defined. In this cell, weakly nonlinear membrane properties (resulting from the presence of voltage-gated sodium channels) amplify and speed up small voltage pulses in a way that should be more useful to the animal than would be conversion into strongly nonlinear action potentials. Three different computational methods are compared for solving the partial differential equations that model this system.