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

Abstract

We have developed a mathematical model of arterial vasomotion in which irregular rhythmic activity is generated by the nonlinear interaction of intracellular and membrane oscillators that depend on cyclic release of Ca2+ from internal stores and cyclic influx of extracellular Ca2+, respectively. Four key control variables were selected on the basis of the pharmacological characteristics of histamine-induced vasomotion in rabbit ear arteries: Ca2+ concentration in the cytosol, Ca2+ concentration in ryanodine-sensitive stores, cell membrane potential, and the open state probability of Ca2+-activated K+ channels. Although not represented by independent dynamic variables, the model also incorporates Na+/Ca2+ exchange, the Na+-K+-ATPase, Cl- fluxes, and Ca2+ efflux via the extrusion ATPase. Simulations reproduce a wide spectrum of experimental observations, including 1) the effects of interventions that modulate the functionality of Ca2+ stores and membrane ion channels, 2) paradoxes such as the apparently unpredictable dual action of Ca2+ antagonists and low extracellular Na+ concentration, which can abolish vasomotion or promote the appearance of large-amplitude oscillations, and 3) period-doubling, quasiperiodic, and intermittent routes to chaos. Nonlinearity is essential to explain these diverse patterns of experimental vascular response.