A Mapped Clock Oscillator Model for Transmembrane Electrical Rhythmic Activity in Excitable Cells

Excitable cells such as smooth muscle, nerve, cardiac, and pancreatic β cells exhibit rhythmic transmembrane depolarizations which have been modelled by nonlinear oscillators. This study deals with a general nonlinear oscillator with three different input portals. The oscillator consists of two coupled components: a clock which generates two interacting variables, and a transformer which maps the clock variables onto an observable output variable representing the transmembrane depolarizations. The clock determines the frequency, and the transformer determines the waveshape of the output. A computer model of the electrical rhythmic activity in gastric tissue was used as an example to illustrate the properties of the proposed oscillator model. A functional gastric oscillator may consist of a group of smooth muscles, or a group of interstitial cells of Cajal coupled to smooth muscles. Long, short and periodic pulses were applied to each input portal to examine their effects on the oscillator output with regards to amplitude and frequency characteristics, refractory properties, and entrainment properties, respectively.