Chapter 5: Modeling voltage-dependent channels

Many different types of voltage-dependent ion channels have been identified and are responsible for a rich repertoire of electrical behavior essential for neuronal function (Llinas, 1988). Modeling voltagedependent ion channels is crucial to assess their numerous roles in the genesis of the complex intrinsic properties of central neurons, as well as how such neurons integrate synaptic inputs with intrinsic excitability to generate spike output. The seminal work of Hodgkin, Huxley, Katz and others several decades ago still constitutes the basis of today’s models. The first accurate model of membrane excitability was introduced by Hodgkin and Huxley (1952), and was based on relatively simple biophysical mechanisms underlying the Na+ and K+ conductances that generate action potentials in the giant axon of the squid. This model reproduced well the behavior of the recorded currents, and its parameters are easy to determine from experimental data. This explains why Hodgkin-Huxley models are still widely used today, almost sixty years later. The postulate of the Hodgkin & Huxley model was that membrane currents result from the assembly of gating particles freely moving in the membrane. The molecular components responsible for ionic permeabilities have been later identified as being transmembrane protein complexes containing a pore