A closed form solution of convective mass transfer model for intracellularcalcium response of endothelial cells

Endothelial cells, lining the entire vascular system, respond to change in concentration of specific agonist like adenosine triphosphate (ATP) by incr easing cytosolic Ca2+ concentration, producing prostacyclin, endothelium de rived relaxing factor and ectoenzymes. Three different ecto-enzymes metabol ize ATP in three steps (ATP --> ADP --> AMP --> adenosine). Normally experi ments with endothelium are carried out in a rectangular flow chamber provid ed with a cell surface at one of its walls and feed stream containing ATP. The ATP concentration near the cell surface depends upon two factors, rate of its degradation and the rate at which it reaches from upstream. Closed f orm solutions for the concentration profile of ATP in such a flow chamber i ndicates that concentration near the cell surface is lower than the bulk co ncentration depending on the activity of ecto-enzymes and it increases with increase in tangential now rate (shear stress). This indicates that shear induced response of endothelial cell (at least for low shear rate) may be d ue to change in ATP concentration near the cell surface which is sensed by purinoreceptors instead of a mechanoreceptor. Several workers have tried to investigate this problem analytically. Unfortunately, solutions obtained b y these workers have limited success. In the present work, exact solution o f the problem has been obtained in terms of a confluent hypergeometric func tion. Solution of the transformed equation gives accurate results even in t he entrance region of the flow chamber which eliminates the need of solutio ns based on approximate methods like perturbation or finite difference tech niques.