ATP hydrolysis kinetics and thermodynamics as determinants of calcium oscillation in pancreatic β cells

Cellular ATP plays an important role in the calcium oscillation signal transduction pathway of pancreatic $\ensuremath{\beta}$ cells. It triggers oscillation by binding the ATP-sensitive ${\text{K}}^{+}$ channels $({\text{K}}_{\mathrm{ATP}})$, and maintains the oscillation by providing ATP hydrolysis free energy for the normal function of ion pumps on the plasma membrane. To reveal how cellular ATP level and ATP hydrolysis free energy affect calcium oscillation, we first constructed a simplified kinetic model of ${\text{K}}_{\mathrm{ATP}}$ and calcium pumps, then analyzed their thermodynamic characteristics. Bifurcation of calcium oscillation is determined by both cellular ATP concentration and ATP hydrolysis free energy such that an insufficient ATP energy supply would result in dysfunctional calcium oscillation. Second, to investigate the glucose sensing in $\ensuremath{\beta}$ cells, we developed a glycolysis-calcium model that considers the dynamics of ATP and free energy levels. The model simulated three calcium patterns in wild type cells and impaired calcium response of ${\text{K}}_{\mathrm{ATP}}$ mutant cells, allowing the use of the ATP-free energy phase plane to explore the underlying mechanism. Our results reveal the thermodynamics of calcium oscillation and provide a framework for understanding the thermodynamics of other ion transport systems.