Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution

The study of calcium dynamics is an important aspect as it regulates various processes viz metabolism, secretion etc. and also play the key role of second messenger. In the present work our main focus is over the variation of the cellular calcium with the various buffers after solving the advection-diffusion equation for the cellular calcium with inclusion of the calcium-binding buffers also. The presence of buffer lower the cellular calcium level and prevents its toxicity within cell. Buffers play key role in lowering the concentration level of cytosolic calcium, by binding with the intracellular free calcium ions. The model is incorporating association and dissociation rates, diffusion coefficients and buffer concentration. The fractional model for this is developed by using the Caputo-Fabrizio operator. The corresponding boundary and initial conditions are also framed accordingly. The integral transform technique is applied to obtain the analytical solution and simulation has been done to observe the effect of buffer on the distribution of calcium concentration.