On the origin and dynamics of the vasomotion of small arteries.
A system of differential equations describing stationary vasomotion is formulated. It incorporates the ionic transports, cell-membrane potential, muscle contraction of the vessel smooth muscle cells, and the mechanics of a thick-walled cylinder. It is shown that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, brings about periodicity of those transports. This results on a time-periodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridges formation with the attending muscle stress. The vessel's transmural pressure determines a hoop stress. The resultant hoop, elastic, and muscle stresses determine the rate of change of the vessel's diameter: vasomotion. The model results agree with the experimental observations. The sensitivity of the vasomotion's dependence on parameter values and its significance to experimental protocols are examined. Further, it is hypothesized that the dependence of calcium-channel openings on voltage is shifted by changes on transmural pressure. Thus, Harder's experimental results are reproduced, among them the decreasing of vessel diameter with increasing pressure. Those behaviors are associated with a pattern of change of the singularities of the system of equations describing the model. This suggests a functional relationship on the interactions of Ca2+ and K+ fluxes responsible for the myogenic response; it may not result from a single molecular mechanism. The model is constructed so that additional experimental information can be readily incorporated.
Gonzalez-Fernandez
J M
JM
Mathematics Research Branch, NIDDK, National Institutes of Health, Bethesda, Maryland 20892.
Ermentrout
B
B
D000818:Animals; D001158:Arteries / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D008955:Models, Cardiovascular; D009119:Muscle Contraction; D009131:Muscle, Smooth, Vascular / Q000502:physiology*; D009218:Myosins / Q000378:metabolism
D009218:Myosins