INTERACTIVE DYNAMICS OF CA2+ AND ATP REGULATING ADP AND INSULIN SECRETION IN A β-CELL

Calcium ([Formula: see text]) signaling is reported as a critical factor in the insulin secretion mechanism of pancreatic [Formula: see text]-cells. Further, calcium signaling also has interactions with other similar signaling systems like adenosine triphosphate (ATP) to achieve the functions of [Formula: see text]-cells. Disturbances in any of these two interactive signaling systems can cause disorders in the secretion mechanism of insulin, leading to the onset of type-2 diabetes. Therefore, this paper presents a one-dimensional spatio-temporal mathematical model designed to explore the dynamic interactions between ATP and [Formula: see text] within a pancreatic [Formula: see text]-cell. The model under consideration comprises a set of nonlinear reaction–diffusion equations governing the behavior of [Formula: see text] and ATP. The formulation of the initial and boundary conditions takes into account the physical and physiological factors associated with the [Formula: see text]-cell. Further, the model also incorporates adenosine diphosphate (ADP) production due to the hydrolysis of ATP and [Formula: see text]-dependent insulin secretion of the [Formula: see text]-cell. The numerical results are acquired through the utilization of the finite element method. The time derivative terms are resolved through the utilization of the Crank–Nicolson method. The various glycemic states caused by variational impacts of system parameters are demonstrated.