Modeling and simulation of spatial-temporal calcium distribution in T lymphocyte cell by using a reaction-diffusion equation.

T lymphocytes are white blood cells that play a central role in cell-mediated immunity. Ca has its major signaling function when it is elevated in the cytosolic compartment. The free cytosolic Ca dynamics plays a very important role in the activation, and fate decision process in the T lymphocytes. Here, we develop a quantitative spatio-temporal Ca dynamic model which includes, the Ca releasing channels ER leak and voltage-gated Ca channel, buffering and re-uptaking mechanism in the T lymphocytes. In this model, the cell is represented as a circular-shaped geometrical domain. This representation introduces modeling flexibility needed for detailed representation of the properties of Ca dynamics in the cell including important parameters. The proposed mathematical model is solved using a finite difference method and the finite element method. Appropriate initial and boundary conditions are incorporated in the model based on biophysical conditions of the problem. Computer simulations in MATLAB R2010a are employed to investigate mathematical models of reaction-diffusion equation. The estimation is based on reaction-diffusion equation associated with biophysical and biochemical reactions taking place in the cell. From our results, it is observed that, the coordinated combination of the incorporated parameters plays a significant role in Ca regulation in T lymphocytes. ER leak and voltage-gated Ca channel provides the necessary Ca to the cell when required for its proper functioning, while on the other side buffers and Na/Ca exchanger makes balance in the Ca concentration, so as to prevent the cell from death as higher concentration for longer time is harmful for the cell and can cause cell death. These results have been used to study the relationship of Ca concentration with parameters like VGCC, Na/Ca exchanger, ER leak and buffers. The significance of the study reveals that there is a significant variation in Ca profiles due to the effect of VGCC, Na/Ca exchanger, ER leak, and buffers. The results give us better insights of coordinated effect of VGCC, Na/Ca exchanger, ER leak, and buffers on Ca distribution in T lymphocytes. T lymphocytes are the primary host cells to receive the viral infections which transmits the signal then to other cell types. The proper quantity of Ca concentration makes T lymphocytes more active and healthier to fight the infection properly and can protect the immune system from various fatal viral infections. Thus, the application of the study lies in the field of immunology to protect a susceptible from various viral infectious diseases like HIV, HBV, HINI, etc. by strengthening the immune system. The outcomes of the study reveal that the applied finite element method is computationally very strong and effective to analyze differential equations that arise in Ca dynamics.