A quantitative description of the contraction of blood vessels following the release of noradrenaline from sympathetic varicosities

A model is presented that highlights the principal factors determining the form and extent of contraction in arteries upon stimulation of their sympathetic nerve supply. This model incorporates a previous quantitative model of the process of noradrenaline (NAd) diffusion into the vascular media and reuptake into sympathetic varicosities during nerve stimulation (J. Theor. Biol. 226 (2004) 359). It is also dependent on a model of how the subsequent activation of metabotropic receptors initiates a G-protein cascade, resulting in the production of inositol trisphosphate (IP3) and an increase in intracellular calcium concentration, [Ca2+]i, in the smooth muscle cells (J. Theor. Biol. 223 (2003) 93). In the present work we couple this rise in [Ca2+]i to the increase in phosphorylated myosin bound to actin in the cells and hence determine the force development in arteries due to nerve stimulation. The model accounts for force development as a function of [Ca2+]i and for the rate of change of force as a function of the rate of change of [Ca2+]i in single smooth muscle cells. It also accounts for the characteristic time course of the force developed by the media of the rat-tail artery upon nerve stimulation. This consists of a rapid rise to a transient peak followed by a sustained plateau of contraction during the stimulation period, after which the contraction slowly decays back to baseline at a rate dependent on the strength of the stimulation. The model indicates that the transient peak is primarily due to the partial block of the IP3 receptor by the rise in [Ca2+]i and that the main determinant of the equilibrium condition indicated by the plateau phase is the rate of pumping of calcium into the sarcoplasmic reticulum. The relatively slow decline of contraction at the end of nerve stimulation is primarily a consequence of the slow rates of removal of NAd from the media by diffusion and reuptake into the sympathetic varicosities. The model thus provides a quantitative account of vascular smooth muscle contraction upon sympathetic nerve stimulation.