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Am J Physiol Heart Circ Physiol 277: H1119-H1144, 1999;
0363-6135/99 $5.00
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Vol. 277, Issue 3, H1119-H1144, September 1999

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

D. Parthimos, D. H. Edwards, and T. M. Griffith

Department of Diagnostic Radiology, Cardiovascular Sciences Research Group, University of Wales College of Medicine, Cardiff CF4 4XN, United Kingdom

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.

nonlinear dynamics; vasomotion; calcium channels; potassium channels; sodium/calcium exchange; calcium-adenosinetriphosphatase; sodium-potassium-adenosinetriphosphatase; chloride channels


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