Modeling the mechanics of calcium regulation in T lymphocyte: A finite element method approach

Abstract

Changes in cellular Ca[Formula: see text] concentration control a variety of physiological activities including hormone and neurotransmitter release, muscular contraction, synaptic plasticity, ionic channel permeability, apoptosis, enzyme activity, gene transcription and reproduction process. Spatial–temporal Ca[Formula: see text] dynamics due to Ca[Formula: see text] release, buffering and re-uptaking plays a central role in studying the Ca[Formula: see text] regulation in T lymphocytes. In most cases, Ca[Formula: see text] has its major signaling function when it is elevated in the cytosolic compartment. In this paper, a two-dimensional mathematical model to study spatiotemporal variations of intracellular Ca[Formula: see text] concentration in T lymphocyte cell is proposed and investigated. The cell is assumed to be a circular shaped geometrical domain for the representation of properties of Ca[Formula: see text] dynamics within the cell including important parameters. Ca[Formula: see text] binding proteins for the dynamics of Ca[Formula: see text] are itself buffer and other physiological parameters located in Ca[Formula: see text] stores. The model incorporates the important biophysical processes like diffusion, reaction, voltage-gated Ca[Formula: see text] channel, leak from endoplasmic reticulum (ER), efflux from cytosol to ER via sarco–ER Ca[Formula: see text] adenosine triphosphate (SERCA) pumps, buffers and Na[Formula: see text] exchanger. 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 R2019b are employed to investigate mathematical models of reaction–diffusion equation. The effect of source, buffer, Na[Formula: see text]/Ca[Formula: see text] exchanger, etc. on spatial and temporal patterns of Ca[Formula: see text] in T lymphocyte has been studied with the help of numerical results. From the obtained 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, SERCA pump 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.