The effects of ER (endoplasmic reticulum) Ca2+ on cytosolic Ca2+ oscillations in pancreatic acinar cells were investigated using mathematical models of the Ca2+ oscillations. We first examined the mathematical model of SERCA (sarcoplasmic/endoplasmic reticulum Ca2+-ATPase) to reproduce the highly co-operative inhibitory effect of Ca2+ in the ER lumen on ER Ca2+ uptake in the acinar cells. The model predicts that luminal Ca2+ would most probably inhibit the conversion of the conformation state with luminal Ca2+-binding sites (E2) into the conformation state with cytoplasmic Ca2+-binding sites (E1). The SERCA model derived from this prediction showed dose–response relationships to cytosolic and luminal Ca2+ concentrations that were consistent with the experimental data from the acinar cells. According to a mathematical model of cytosolic Ca2+ oscillations based on the modified SERCA model, a small decrease in the concentration of endoplasmic reticulum Ca2+ (approx. 20% of the total) was sufficient to abolish the oscillations. When a single type of IP3R (IP3 receptor) was included in the model, store depletion decreased the spike frequency. However, the frequency became less sensitive to store depletion when we added another type of IP3R with higher sensitivity to the concentration of free Ca2+ in the cytosol. Bifurcation analysis of the mathematical model showed that the loss of Ca2+ from the ER lumen decreased the sensitivity of cytosolic Ca2+ oscillations to IP3 [Ins(1,4,5)P3]. The addition of a high-affinity IP3R did not alter this property, but significantly decreased the sensitivity of the spike frequency to IP3. Our mathematical model demonstrates how luminal Ca2+, through its effect on Ca2+ uptake, can control cytosolic Ca2+ oscillations.

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