The modelling of a burst-generating neuron with a field-effect transistor analog

An electronic analog that models the burst generating neuronR₁₅ of theAplysia abdominal ganglion is described. The analog is based on the four branch Hodgkin-Huxley equivalent circuit for a patch of squid axon membrane, with a choice of parameter values appropriate to theAplysia cell membrane. To realize the slow subthreshold oscillations seen in cellR₁₅ upon exposure to the drug tetrodotoxin (TTX), it was necessary to include two additional conductance branches,g_Na andg_K, to the basic Hodgkin-Huxley circuit. Without these, the analog was capable of generating only action potentials and hence termed the suprathreshold analog. With all six branches operative, bursts very similar to those seen inR₁₅ were realized, and subsequent inhibition of the Hodgkin-Huxley sodium conductanceg_Na resulted in the desired subthreshold oscillations. The electronic circuitry and the performance of the suprathreshold and complete analog are described. An explanation is offered for the progressive widening of the action potentials within a burst seen inR₁₅. The analog also simulates the phenomenon of potassium ion accumulation outside the cell membrane during a burst, using a local feedback loop to reduce the potassium equilibrium potential in a manner roughly proportional to the logarithm of the time integral of the outward potassium current. Some consequences of this effect are also discussed.