A mathematical model of a bullfrog cardiac pacemaker cell

Previous models of cardiac cellular electrophysiology have been based largely on voltage-clamp measurements obtained from multicellular preparations and often combined data from different regions of the heart and a variety of species. We have developed a model of cardiac pacemaking based on a comprehensive set of voltage-clamp measurements obtained from single cells isolated from one specific tissue type, the bullfrog sinus venosus (SV). Consequently, sarcolemmal current densities and kinetics are not influenced by secondary phenomena associated with multicellular preparations, allowing us to realistically simulate processes thought to be important in pacemaking, including the Na(+)-K+ pump and Na(+)-Ca2+ exchanger. The membrane is surrounded extracellularly by a diffusion-limited space and intracellularly by a limited myoplasmic volume containing Ca2(+)-binding proteins (calmodulin, troponin). The model makes several predictions regarding mechanisms involved in pacing. 1) Primary pacemaking cannot be attributed to any single current but arises from both the lack of a background K+ current and a complex interaction between Ca2+, delayed-rectifier K+, and background leak currents. 2) Ca2+ current displays complex behavior and is important during repolarization. 3) Because of Ca2+ buffering by myoplasmic proteins, the Na(+)-Ca2+ exchanger current is small and has little influence on action potential repolarization but may modulate the maximum diastolic potential. 4) The Na(+)-K+ pump current does not play an active role in repolarization but is of sufficient size to modulate the rate of diastolic depolarization. 5) K+ accumulation and Ca2+ depletion may occur in the extracellular spaces but play no role in either the diastolic depolarization or repolarization of a single action potential. This model illustrates the importance of basing simulations on quantitative measurements of ionic currents in myocytes and of including both electrogenic transporter mechanisms and Ca2+ buffering by myoplasmic Ca2(+)-binding proteins.