Modeling and simulation of spatial-temporal calcium distribution in T lymphocyte cell by using a reaction-diffusion equation
Authors: Naik Parvaiz Ahmad , Zu Jian 
Published: February 2020

T lymphocytes are white blood cells that play a central role in cell-mediated immunity. Ca[Formula: see text] has its major signaling function when it is elevated in the cytosolic compartment. The free cytosolic Ca[Formula: see text] 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[Formula: see text] dynamic model which includes, the Ca[Formula: see text] releasing channels ER leak and voltage-gated Ca[Formula: see text] 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[Formula: see text] 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[Formula: see text] regulation in T lymphocytes. ER leak and voltage-gated Ca[Formula: see text] channel provides the necessary Ca[Formula: see text] to the cell when required for its proper functioning, while on the other side buffers and Na[Formula: see text]/Ca[Formula: see text] exchanger makes balance in the Ca[Formula: see text] 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[Formula: see text] concentration with parameters like VGCC, Na[Formula: see text]/Ca[Formula: see text] exchanger, ER leak and buffers. The significance of the study reveals that there is a significant variation in Ca[Formula: see text] profiles due to the effect of VGCC, Na[Formula: see text]/Ca[Formula: see text] exchanger, ER leak, and buffers. The results give us better insights of coordinated effect of VGCC, Na[Formula: see text]/Ca[Formula: see text] exchanger, ER leak, and buffers on Ca[Formula: see text] 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[Formula: see text] 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[Formula: see text] dynamics.