Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+ oscillators.
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.
Parthimos
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Department of Diagnostic Radiology, Cardiovascular Sciences Research Group, University of Wales College of Medicine, Cardiff CF4 4XN, United Kingdom.
Edwards
D H
DH
Griffith
T M
TM
D000818:Animals; D001158:Arteries / Q000502:physiology*; D002118:Calcium / Q000502:physiology*; D015220:Calcium Channels / Q000502:physiology; D002462:Cell Membrane / Q000502:physiology; D006801:Humans; D017136:Ion Transport; D008954:Models, Biological; D008962:Models, Theoretical; D009119:Muscle Contraction / Q000502:physiology*; D011817:Rabbits; D012964:Sodium / Q000502:physiology; D015222:Sodium Channels / Q000502:physiology; D000254:Sodium-Potassium-Exchanging ATPase / Q000502:physiology
D015220:Calcium Channels; D015222:Sodium Channels; D012964:Sodium; D000254:Sodium-Potassium-Exchanging ATPase; D002118:Calcium