Dynamical Systems in Neuroscience:

Chapter 2Electrophysiology of NeuronsIn this chapter we remind the reader of some fundamental concepts of neuronal electrophysiology,which are necessary to understand the rest of the book. We start with ionsand currents, and move quickly toward the dynamics of the Hodgkin-Huxley model.If the reader is already familiar with the Hodgkin-Huxley formalism, this chapter canbe skipped. Our exposition is brief, and it cannot substitute a good introductory neurosciencecourse or reading of such excellent textbooks as Theoretical Neuroscience byDayan and Abbott (2001), Foundations of Cellular Neurophysiology by Johnston andWu (1995), Biophysics of Computation by Koch (1999) or Ion Channels of ExcitableMembranes by Hille (2001).2.1 IonsElectrical activity in neurons is sustained and propagated via ionic currents throughneuron membranes. Most of these transmembrane currents involve four ionic species:sodium (Na + ), potassium (K + ), calcium (Ca 2+ ), and chloride (Cl − ). The first threehave a positive charge (cations) and the fourth has a negative charge (anion). Theconcentrations of these ions are different on the inside and outside of a cell, whichcreates electrochemical gradients — the major driving forces of neural activity. Theextracellular medium has high concentration of Na + and Cl − (salty like seawater) and arelatively high concentration of Ca 2+ . The intracellular medium has high concentrationof K + and negatively charged molecules (denoted by A − ), as we illustrate in Fig. 2.1.The cell membrane has large protein molecules forming channels through whichions (but not A − ) can flow according to their electrochemical gradients. The flow ofNa + and Ca 2+ ions is not significant, at least at rest, but the flow of K + and Cl − ionsis. This, however, does not eliminate the concentration asymmetry due to the followingtwo reasons.• Passive redistribution. The impermeable anions A − attract more K + into the cell(opposites attract) and repel more Cl − out of the cell, thereby creating concentrationgradients.• Active transport. Ions are pumped in and out of the cell via ionic pumps. Forexample, the Na + -K + pump depicted in Fig. 2.1 pumps out three Na + ions for25