Reduced Single Neuron Models

A principle that has proven fruitful in modeling neural systems is to consider the simplest model capable of predicting the experimental phenomenon under consideration. This approach allows one to capture the essential points of a particular phenomenon without obscuring the picture with unnecessary details. This is precisely the approach taken by Hodgkin and Huxley to model action potential propagation along the squid giant axon in terms of sodium and potassium conductances. We have also seen how a simplification of the Hodgkin–Huxley model to a two-variable reduced FitzHugh model allows to characterize the firing properties of the Hodgkin–Huxley system in terms of phase plane analysis (Exercise 4.6). A set of simplified models are often used as a first pass to study issues related to synaptic integration or the impact of subthreshold membrane conductances on the processing of sensory inputs by neurons. In this chapter, we first present the most elementary model usually employed to simulate neurons, called the leaky integrate and fire model. Next, we introduce a class of neurons that have the ability to fire short bursts of spikes and briefly discuss their role in information processing in the nervous system. Finally, we analyze two simplified models of bursting neurons that highlight different mechanisms of burst generation within a single neuron.