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Figure 1. Effects of flow upon an endothelial cell monolayer in a square capillary tube. Cells are cultured to confluence on the bottom surface, whereas the upper and lateral surfaces are cell free. The tube is perfused with media in laminar flow containing known quantities of thrombin and calcium. Knowledge of the perfusion rate and tube geometry permits calculation of the shear stress and mass transfer of agonist to the monolayer.
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Figure 2. Dependence of calcium influx upon shear stress as calculated from the Goldman-Hodgkin-Katz equation. A sigmoidal dependence of influx upon shear stress is predicted. The parameter is the load fraction, 
, borne by nonmembranous structures. As increases, less strain energy is available to gate mechanosensitive ion channels.
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Figure 3. Response of calcium transient to agonist-free media (cs = 0, Caex = 1.5 mM. The calculation indicates a lack of the peak associated with agonist stimulation. Variation of flow rate indicates that the plateau level increases with increasing shear stress. These results are in qualitative agreement with experiment (25).
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Figure 4. Receptor dynamics and mass transport limitations introduce significant delay into calcium dynamics. Simulation of Eq. 1 only yields a very high and rapid transient. Dotted line, stimulus is a step increase in receptor activity. Solid line, simulation of Eqs. 1 and 6 coupled via the phosphoinositide pathway. Addition of receptor dynamics significantly attenuates and delays the transient. Broken line, stimulus as a step increase in cs. Simulation of Eqs. 1 and 6 coupled to thrombin balance in the perfusate further attenuates and delays the transient (cs = 1 unit per ml, c0 = 1 unit per ml, Caex = 0, 
= 0.1 N/m2).
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Figure 5. Response of calcium transient to agonist-bearing media. As the perfusion rate (and shear stress) increases, the response accelerates. The influence is significant at low shear stresses (2), where mass transfer is rate-limiting. Above 0.5 N/m2, perfusion rate has diminishing effects because receptor dynamics are rate-limiting (C0 = 1 unit per ml, Caex = 0).
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Figure 6. Synergistic effects of calcium influx and agonist stimulation upon the calcium transient. For 0.1 2, shear stress exerts a relatively small influence upon the calcium transient. This influence is exerted through modulation of mass transfer of agonist. Above 1 N/m2, the influence becomes larger through enhanced transplasmalemmal calcium influx. Also plotted is a comparison of an experimental calcium transient to the model prediction ( = 3 N/m2, c0 = 1 unit per ml thrombin, Caex = 1.5 mM). The time to peak and peak values are reasonably simulated. There is a discrepancy between the plateau regions. The elevated plateau in the simulation is due to a sustained increase in calcium influx.
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