Ion Transport Through a Membrane
In this chapter, we study simple models related to ion transport through a membrane. We draw a close analogy to electronic circuit theory and describe the ion transport similar to a simple RC-network. We study the Goldman–Hodgkin–Katz model for a steady state with more than one ionic species present. The membrane potential is calculated as a function of the ion concentrations inside and outside the membrane. We discuss the famous Hodgkin–Huxley model for the quantitative description of the squid giant axon dynamics, which received the Nobel prize. Finally, we study models for ion channel cooperativity with a two-state model in analogy to ligand binding. We derive the master equations for ligand-gated channels within the MWC and KNF models and calculate the ratio of active channels as a function of ligand concentration to show the cooperative effect.