ABSTRACT
Electrical activity in the heart is generated at the molecular level by specialized membrane-spanning proteins that control the movement of ions either by passive electrodiffusion through transmembrane pores (i.e., channels) or translocation across the membrane by carrier proteins (pumps, exchangers, and transporters). As a first approximation, ion channels can be thought of as mediating the dynamic portions of the action potential, such as the upstroke and repolarization, and also providing the entry of trigger calcium to initiate excitation-contraction coupling. In contrast, pumps, exchangers, and transporters can be thought of as steadily working in the background to establish and maintain ionic gradients. Obviously, this is only an approximation: pumps, exchangers, and transporters can and do contribute to the overall behavior of the action potential, particularly in pathophysiological conditions, but they have slower effects than the rapidly opening and closing channels. Nonetheless, channels dominate depolarization and repolarization, and the process of repolarization is largely understood as the dynamic interaction of membrane ion channels. Consequently, in many situations the action potential can be approximated well using a model containing only channels. This chapter describes some of our current understanding of voltage-gated ion channel biophysics and the mathematical modeling of these processes. We hope it will serve as an introduction to engineers and scientists from other disciplines who are relatively new to the field, and who need a brief and simple explanation of the rationale behind many of the mathematical formulations routinely used in current cellular models.
