Calcium (${\mathrm{Ca}}^{2+}$) oscillations in hepatocytes control many critical cellular functions, including glucose metabolism and bile secretion. The mechanisms underlying repetitive ${\mathrm{Ca}}^{2+}$ oscillations and how these mechanisms regulate these oscillations is not fully understood. Recent experimental evidence has shown that both ${\mathrm{Ca}}^{2+}$ regulation of the inositol 1,4,5-trisphosphate (${\mathrm{IP}}_3$) receptor and ${\mathrm{IP}}_3$ metabolism generate ${\mathrm{Ca}}^{2+}$ oscillations and co-exist in hepatocytes. To investigate the effects of these feedback mechanisms on the ${\mathrm{Ca}}^{2+}$ response, we construct a mathematical model of the ${\mathrm{Ca}}^{2+}$ signalling network in hepatocytes. The model accounts for the biphasic regulation of ${\mathrm{Ca}}^{2+}$ on the ${\mathrm{IP}}_3$ receptor (${\mathrm{IP}}_{3}R$) and the positive feedback from ${\mathrm{Ca}}^{2+}$ on ${\mathrm{IP}}_3$ metabolism, via activation of phospholipase C (PLC) by agonist and ${\mathrm{Ca}}^{2+}$. Model simulations show that ${\mathrm{Ca}}^{2+}$ oscillations exist for both constant $\left[{\mathrm{IP}}_3\right]$ and for $\left[{\mathrm{IP}}_3\right]$ changing dynamically. We show, both experimentally and in the model, that as agonist concentration increases, ${\mathrm{Ca}}^{2+}$ oscillations transition between simple narrow-spike oscillations and complex broad-spike oscillations. The model predicts that narrow-spike oscillations persist when ${\mathrm{Ca}}^{2+}$ transport across the plasma membrane is blocked. This prediction has been experimentally validated. In contrast, broad-spike oscillations are terminated when plasma membrane transport is blocked. We conclude that multiple feedback mechanisms participate in regulating ${\mathrm{Ca}}^{2+}$ oscillations in hepatocytes.

钙（${\mathrm{钙}}^{2+}$肝细胞的振荡控制着许多关键的细胞功能，包括葡萄糖代谢和胆汁分泌。重复机制${\mathrm{钙}}^{2+}$振荡以及这些机制如何调节这些振荡尚未完全了解。最近的实验证据表明${\mathrm{钙}}^{2+}$ 肌醇1,4,5-三磷酸（${\mathrm{知识产权}}_3$）受体和 ${\mathrm{知识产权}}_3$ 代谢产生 ${\mathrm{钙}}^{2+}$振荡并在肝细胞中共存。调查这些反馈机制对${\mathrm{钙}}^{2+}$ 响应，我们建立了一个数学模型 ${\mathrm{钙}}^{2+}$肝细胞中的信号网络。该模型说明了${\mathrm{钙}}^{2+}$ 在 ${\mathrm{知识产权}}_3$ 受体（${\mathrm{知识产权}}_3\mathrm{[R}$）以及来自的积极反馈 ${\mathrm{钙}}^{2+}$ 上 ${\mathrm{知识产权}}_3$ 通过激动剂激活磷脂酶C（PLC）进行新陈代谢 ${\mathrm{钙}}^{2+}$。模型仿真表明${\mathrm{钙}}^{2+}$ 两个常数都存在振荡 $\left[{\mathrm{知识产权}}_3\right]$ 和为 $\left[{\mathrm{知识产权}}_3\right]$动态变化。我们在实验和模型中均显示，随着激动剂浓度的增加，${\mathrm{钙}}^{2+}$振荡在简单的窄尖峰振荡和复杂的宽尖峰振荡之间转变。该模型预测，当${\mathrm{钙}}^{2+}$跨质膜的运输被阻止。该预测已通过实验验证。相反，当质膜运输受阻时，宽峰振荡终止。我们得出结论，多种反馈机制参与了调节${\mathrm{钙}}^{2+}$ 肝细胞振荡。