2D dynamic analysis of the disturbances in the calcium neuronal model and its implications in neurodegenerative...

Ca²⁺ signaling is an essential function of neurons to control synaptic activity, memory formation, fertilization, proliferation, etc. Protein and voltage-dependent calcium channels (VDCCs) maintain an adequate level of calcium concentration ([Ca²⁺]). An alteration in [Ca²⁺] leads to the death of the neurons that start the primary symptoms of the disease. The present study deals with cell memory-based mathematical modeling of Ca²⁺ that is characterized by the presence of protein and VDCC. We developed a two-dimensional Ca²⁺ neuronal model to study the spatiotemporal behavior of the Ca²⁺ profile. All principal parameters like buffer concentration, diffusion coefficient, VDCC fluxes, etc. are incorporated in this model. Apposite initial and boundary conditions are applied to the physiology of the problem. We obtained an approximate Ca²⁺ profile by the fractional integral transform method. The application of obtained results is performed to provide its implications to estimate the [Ca²⁺] in neurodegenerative disease. It is observed that the protein and VDCC provide a significant impact in the presence of cell memory. The memory of cells shrinks the Ca²⁺ flow from elevation and provides better results to estimated Ca²⁺ flow in the disease state.