Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+ oscillators

We have developed a mathematical model of arterial vasomotion in which irre gular rhythmic activity is generated by the nonlinear interaction of intrac ellular and membrane oscillators that depend on cyclic release of Ca2+ from internal stores and cyclic influx of extracellular Ca2+, respectively. Fou r key control variables were selected on the basis of the pharmacological c haracteristics of histamine-induced vasomotion in rabbit ear arteries: Ca2 concentration in the cytosol, Ca2+ concentration in ryanodine-sensitive st ores, cell membrane potential, and the open state probability of Ca2+-activ ated K+ channels. Although not represented by independent dynamic variables , the model also incorporates Na+/Ca2+ exchange, the Na+-K+-ATPase, Cl- flu xes, and Ca2+ efflux via the extrusion ATPase. Simulations reproduce a wide spectrum of experimental observations, including I)the effects of interven tions that modulate the functionality of Ca2+ stores and membrane ion chann els, 2)paradoxes such as the apparently unpredictable dual action of Ca2+ a ntagonists and low extracellular Na+ concentration, which can abolish vasom otion or promote the appearance of large-amplitude oscillations, and 3) per iod-doubling, quasiperiodic, and intermittent routes to chaos. Nonlinearity is essential to explain these diverse patterns of experimental vascular re sponse.