A mathematical model for ATP-mediated calcium dynamics in vascular endothelial cells induced by fluid shear stress

Abstract

In consideration of the mechanism for shear-stress-induced Ca 2+ influx via ATP(adenosine triphosphate)-gated ion channel P2X4 in vascular endothelial cells, a modified model is proposed to describe the shear-stress-induced Ca 2+ influx. It is affected both by the Ca 2+ gradient across the cell membrane and extracellular ATP concentration on the cell surface. Meanwhile, a new static ATP release model is constructed by using published experimental data. Combining the modified intracellular calcium dynamics model with the new ATP release model, we establish a nonlinear Ca 2+ dynamic system in vascular endothelial cells. The ATP-mediated calcium response in vascular endothelial cells subjected to shear stresses is analyzed by solving the governing equations of the integrated dynamic system. Numerical results show that the shear-stress-induced calcium response predicted by the proposed model is more consistent with the experimental observations than that predicted by existing models.

Fluid flow induced calcium response in osteoblasts: Mathematical modeling

“…In pretreatment group the cells were cultured in corresponding ATP environment for 10 min and then stimulated with shear stress of 3.5 Pa; un-pretreated curve was obtained by exposing the cell directly under shear stress (3.5 Pa) plus certain extra environment ATP condition without being incubated in extra ATP environment. experience fluid (blood) flow in vessel (Wong and Klassen, 1995;Wiesner et al, 1997;David, 2003;Qin et al, 2008;Hu et al, 2008). We applied the same idea on osteoblast to catch the features of bone cell response (in terms of calcium concentration) to fluid flow stimulation.…”

“…Theoretical models were also developed to analyze the ATP/ADP concentration on cell surface under SS stimulation (David, 2003), and the dynamic process of ATP release in vascular endothelial cells . The potential role of ATP release in [Ca 2 þ ] i response was simulated by a nonlinear dynamic model (Hu et al, 2008). The simulation results from these models shed new light on our understanding of calcium signaling.…”

Dynamic modeling for flow-activated chloride-selective membrane current in vascular endothelial cells

“…Mathematical models (Hu et al 2008;Schuster et al 2003;Silva et al 2007;Wiesner et al 1997;Wong and Klassen 1995) have also been proposed accordingly to describe the membrane electrophysiology and intracellular ion dynamics in VECs induced by fluid shear stress. However, most modeling work has focused on Ca 2+ transportation only (Hu et al 2008;Schuster et al 2003;Silva et al 2007;Wiesner et al 1997;Wong and Klassen 1995), and very little attention has been paid to the Cl − , an important anion and second messenger in shear stress signal transduction in VECs.…”

“…Mathematical models (Hu et al 2008;Schuster et al 2003;Silva et al 2007;Wiesner et al 1997;Wong and Klassen 1995) have also been proposed accordingly to describe the membrane electrophysiology and intracellular ion dynamics in VECs induced by fluid shear stress. However, most modeling work has focused on Ca 2+ transportation only (Hu et al 2008;Schuster et al 2003;Silva et al 2007;Wiesner et al 1997;Wong and Klassen 1995), and very little attention has been paid to the Cl − , an important anion and second messenger in shear stress signal transduction in VECs. It has been demonstrated that the activation of the Cl − current by flow may be involved in the regulation of many endothelial functions such as the depolarization of the membrane potential after flow-induced K + channelmediated hyperpolarization, the modulation of intracellular Ca 2+ and PH, and the volume changes that may occur as the cells prepare for the extensive cytoskeleton and morphological changes that occur in response to sustained flow (Barakat et al 1999).…”

“…Their experimental evidences facilitate us to construct a mathematical model to quantitatively analyze the Cl − selective membrane current and intracellular Cl − dynamics in VECs exposed to different flow patterns. In their experiments, the extracellular Cl − concentrations were set to be constants, which were also conventional in almost all the previous experimental investigations (Ando et al 1988;Barakat et al 1999;Gautam et al 2006b;Hoger et al 2002;Lieu et al 2004;Park et al 2007;Wang et al 2009) and modeling work (Hu et al 2008;Schuster et al 2003;Silva et al 2007;Wiesner et al 1997;Wong and Klassen 1995) on membrane electrophysiology or ion dynamics in VECs. However, in circulatory system in vivo, an intermittent release of substances in the blood is carried out by several organs and glands (Johnson 2003).…”