Mathematical model of the rapidly activating delayed rectifier potassium current I(Kr) in rabbit sinoatrial node

A rapidly activating delayed rectifier potassium current (I(Kr)) is known to have an important role in determining the properties of spontaneous pacing in enzymatically isolated rabbit sinoatrial node (SAN) cells. The functional characteristics of I(Kr) are conferred by its dependence on time, voltage, and external potassium. The aim of this study was to develop a rigorous mathematical representation for I(Kr) based on experimental findings and to investigate the role of I(Kr) in the automaticity and intercellular communication of SAN cells.

A Markov model was developed using available experimental data for I(Kr) in rabbit SAN. The dependence of I(Kr) on external potassium, [K+]o, was incorporated using data from both in vitro preparations and results from heterologous expression experiments for this ether-a-go-go related gene product. Our simulation results show the following. (1) I(Kr) is the dominant repolarizing current in rabbit SAN cells. (2) Deactivation of I(Kr) contributes to the net current change during the early diastolic depolarization phase. (3) Inward rectification of I(Kr) results in a decrease in membrane resistance during repolarization relative to plateau. (4) The complex [K+]o dependence of I(Kr) confers [K+]o insensitivity on isolated cells, which may account for the sensitivity of pacing rate to elevated [K+]o at the tissue level.

Model results show that I(Kr) mediates diastolic depolarization by the kinetics of its decay and by lowering resistance during late repolarization. In elevated [K+]o, increased chord conductance is balanced by the changes in kinetics and voltage dependence of I(Kr) so that the pacing rate of single cells may be more [K+]o insensitive than expected. In addition, elevated [K+]o increases I(Kr) magnitude during repolarization but lowers resistance, so current flow through gap junctions is less able to hyperpolarize pacing cells.