Modelling spatio-temporal interactions between second messengers Ca 2 + and cAMP in a pancreatic β -cell

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca ${}^{2+}$ ), and linkages between Ca ${}^{2+}$ and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca ${}^{2+}$ levels in pancreatic $\beta$ -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca ${}^{2+}$ in $\beta$ -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca ${}^{2+}$ and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the $\beta$ -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca ${}^{2+}$ and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the $\beta$ -cell. The model gives the individual effect of each parameter on the regulation of Ca ${}^{2+}$ and cAMP profiles in a $\beta$ -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.