A) Receptor phosphorylation keeps the calcium signal bounded. Our calcium model (without receptor phosphorylation) exhibited a continuously increasing calcium response upon continuous stimulation with 10 mM of ligand (light gray); however, upon addition of receptor phosphorylation, the model showed a bounded response (black) under the same stimulation. B) Periodic stimulation conditions are described by three parameters: ligand concentration (C), stimulation duration (D), and rest period between stimulation events (TR). C) The calcium signals in our original model, which does not feature receptor phosphorylation, do not exhibit calcium amplitude attenuation, in contradiction with our experimental data in Table 1. Light gray trace: C = 500 nM, D = 6 s, TR = 128 s; dark gray dotted trace: C = 100 nM, D = 6 s, TR = 64 s; black trace: C = 100 nM, D = 6 s, TR = 128 s. Calcium levels for the three traces were normalized to their maximum values; the blue trace was also normalized by time to enable easy visual comparison of peak values between the three conditions. Figure 4C depicts responses predicted by the model that features receptor phosphorylation and matches experimental observations.