Numerical study of one-dimensional buffered advection–diffusion of calcium and \({\text {IP}}_{3}\) in a hepatocyte cell

The intracellular calcium signaling plays a crucial role in maintaining chemical homeostatic in all human organelles. In the hepatocyte cell, interdependent calcium and \({\text {IP}}_{3}\) dynamics are affected by numerous physiological processes such as advection, diffusion, and buffering. The higher amount of calcium is hazardous to cell; therefore, various factors like influxes, effluxes of calcium from internal storage compartments play vital role for supplying or pumping calcium back into the compartment. \({\text {IP}}_{3}\) is needed for calcium release, while the increase in calcium decreases the \({\text {IP}}_{3}\) concentration. The one-dimensional nonlinear partial differential equation involving the entire phenomenon under consideration is solved by employing the finite volume method and simulated on MATLAB to study the results. The computational study has been made with and without advection of calcium, without and with buffer, by varying pump rate constant, etc. The results obtained are discussed in the latter part of the paper. The numerical results obtained here shows beautiful patterns of calcium and \({\text {IP}}_{3}\) interdependent coordination in a hepatocyte cell.