**A ****mathematical model of the cytosolic-free calcium response in endothelial cells to fluid shear stress**
*(calcium influx / agonist / mechanotransduction)*

**Theodore F. Wiesner, Bradford C. Berk, and Robert M. Nerem**

*Bioengineering Center, Georgia Institute of Technology, Atlanta, GA 30332-0405; and Division of Cardiovascular Research, University of Washington, Seattle, WA 98195. **Communicated by Yuan-Cheng Fung, University of California at San Diego, La Jolla, CA, December 16, 1996 (received for review April 18, 1996)*

Important among the responses of endothelial cells to flow stimuli are cytosolic-free calcium transients. These transients are mediated by several factors, including blood-borne agonists, extracellular calcium, and fluid-imposed shear forces. A mathematical model has been developed describing the recognition and transduction of shear stress to the second messenger cytosolic calcium. Shear stress modulates the calcium response via at least two modalities. First, mass transfer of agonist to the cell surface is enhanced by perfusion and is thus related to shear stress. Second, the permeability of the cell membrane to extracellular calcium increases upon exposure to shear stress. A mass balance for agonist in the perfusate is coupled to a previously published calcium dynamics model. Computations indicate a flow region where the transient moves from transport limited to kinetically limited. Parametric studies indicate distinct contributions to the time course by each step in the process. These steps include the time to develop the concentration boundary layer of agonist, receptor activation, and the mobilization of calcium from intracellular stores. Exogenous calcium is presumed to enter the cell via shear stress-gated ion channels. The model predicts a sigmoidal dependence of calcium influx upon shear stress. The peak value of the transient is determined largely by the agonist pathway, whereas the plateau level is governed by calcium influx. The model predicts the modulation of the calcium transient in the physiologically relevant range of flow and the associated shear stress. This implies that hemodynamics is important in regulating endothelial biology.

*Proc. Natl. Acad. Sci. USA. Vol. 94, pp. 3726-3731, April 1997.*