Kinetic Models of Synaptic Transmission

The remarkably successful quantitative description of the action potential introduced by Hodgkin and Huxley (1952) is still widely used over 40 years since its introduction. The classical Hodgkin-Huxley description was not only accurate, it was also readily extensible to many other voltage-dependent currents. More recent single channel recording techniques (Sakmann and Neher, 1995) have been used to prove that voltage-dependent currents arise from populations of individual ion channels undergoing rapid transitions between conducting and non-conducting states. The macroscopic behavior of the currents can be accurately captured using kinetic models that describe the transitions between conformational states of these ion channels. This class of models, of which the Hodgkin-Huxley model is an instance, are commonly known as Markov models. Kinetic models not only provide good descriptions of voltage-dependent ionic currents but are general enough to describe almost all processes essential to neurophysiology. We will focus in this chapter on synaptically-gated currents of all kinds, including neuromodulators, which are readily modeled by Markov kinetics. Moreover, many important biochemical reactions, including second-messenger systems, synaptic release, and enzymatic cascades can also be described by kinetic schemes. As a consequence, kinetic models provide means to build coherent neural models in which subcellular, cellular, and network properties are described within the same formalism (see Destexhe et al., 1994c). Kinetic models are inherently exible in their level of detail, ranging from the most detailed and biophysically realistic gating models to highly simpli ed representations. Some detailed models determined from voltage-clamp studies have more than a dozen states (e.g.,