A theoretical model of the cellular calcium dynamics and vasomotion in muscular arteries

Muscular arteries possess the ability to control actively their lumen by altering the tone of the smooth muscle cells of the arterial wall, a property which is vital for a large number of the hemodynamical functions of the body. Arterial contraction is due to an increase in the smooth muscle cytosolic calcium concentration. Abnormalities in the contractile mechanisms of arteries contribute to a variety of cardiovascular diseases such as hypertension. The understanding of the mechanisms of vascular smooth muscle functions can therefore contribute to a better diagnosis and treatment of such diseases. Muscular arteries, arterioles and capillaries display also slow rhythmic diameter variations, called vasomotion, independent on other rhythms in the body (cardiac, respiratory, circadian). It is well established that vasomotion is due to the contractile activity of vascular smooth muscle cells, but its underlying mechanisms are not well understood. The aim of the present thesis is to develop a theoretical model to get a better understanding of vasomotion in muscular arteries and arterioles. Many experimental studies have shown that arterial smooth muscle cells respond with cytosolic calcium rises to stimulation by substances causing arterial contraction (vasoconstrictors). A low vasoconstrictor concentration gives rise to asynchronous "all or none" calcium rises (calcium flashes) in few cells. With a higher vasoconstrictor concentration, the number of smooth muscle cells responding in this way increases (recruitment). When all cells are recruited, synchronous calcium oscillations are observed that generate arterial contraction and vasomotion. We show that these phenomena of recruitment and synchronization naturally emerge from a theoretical model of a population of smooth muscle cells coupled through their gap junctions. The effects of electrical, calcium and inositol 1,4,5-trisphosphate couplings are studied. In our model, the asynchronous calcium flashes arise from stochastic opening of channels. The calcium oscillations result from a dynamic system instability and can be synchronized by gap junctional coupling. Our model is validated by published in vitro experiments obtained on rat mesenteric arterial segments. Several experimental studies report that cells presenting only a transient calcium increase when freshly dispersed may present calcium oscillations when they are coupled. Such observations suggest that the role of gap junctions is not only to coordinate calcium oscillations of adjacent cells. Gap junctions may also be important to generate oscillations. To address this point, we study in more detail the properties of electrically coupled smooth muscle cells. We show that the effect of electrical coupling may not only be to synchronize the calcium oscillations in smooth muscle cells, as intuitively expected. A bifurcation analysis in the case of two cells reveals that electrical coupling can cause the calcium oscillations to be synchronous or asynchronous. In a larger population of smooth muscle cells, electrical coupling may result in the formation of groups of cells presenting synchronous calcium oscillations. The elements of one group may be distant from each other. Moreover, our results highlight a general mechanism by which gap junctional electrical coupling can give rise to out of phase calcium oscillations in smooth muscle cells that are non oscillating when uncoupled. Even though it is now established that vasomotion is induced by synchronous calcium oscillations of smooth muscle cells, the role of the endothelium for vasomotion is still unclear and controversial. Some experimental studies claim that the endothelium is necessary for synchronization and vasomotion, whereas others report rhythmic diameter oscillations in absence of endothelium. Moreover, endothelium derived factors have been shown to abolish vasomotion by desynchronizing the calcium signals in smooth muscle cells. By modeling the calcium dynamics of a population of smooth muscle cells coupled to a population of endothelial cells, we analyze the effects of a smooth muscle vasoconstrictor stimulation on endothelial cells and the feedback effects of endothelium derived factors. Our results show that the endothelium essentially decreases the calcium level in smooth muscle cells and may move these cells from a steady state to an oscillatory domain, and vice versa. In the oscillatory domain, a population of coupled smooth muscle cells exhibits synchronous calcium oscillations. Outside this domain, the coupled smooth muscle cells present only irregular calcium flashes. Our findings provide explanations for the published contradictory experimental observations. Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed, blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Vasomotion has also been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the arterial wall is thickened. Our results are in agreement with experimental observations concerning a broad range of vessels. In vitro different techniques are used to study the calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric (i.e. the arterial diameter is kept constant) or an isobaric (i.e. the intraluminal pressure is kept constant) setup. However none of these setups correspond to the in vivo situation. In vivo, a blood vessel is neither isobaric nor isometric nor isotonic (i.e. the wall tension is kept constant), since it is continuously submitted to intraluminal pressure variations arising from heart beat. We determine theoretically whether results may be considerably different depending on the experimental setup (isometric, isobaric, or isotonic) used. We show that the vasoconstrictor sensitivity is higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. The threshold vasoconstrictor concentration necessary for vasomotion is therefore higher in isobaric than isometric setups. The model suggests that isometric conditions may generate the coexistence of multiple stable states. The contraction is less pronounced in isotonic than in isobaric conditions, in agreement with experimental findings.