Analyzing fuzzy boundary value problems: a study on the influence of mitochondria and ER fluxes on calcium ions in neuron cells

A Comprehensive Fuzzy Model for Understanding Neuronal Calcium Distribution in Presence of VGCC, Na+/Ca2+ Exchanger, Buffer, and ER Fluxes

Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer's disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer's disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological conditions of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer's disease.

Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

The hepatocyte cells regulate the wide range of liver function by moderating cellular activities such as lipid, protein metabolism, carbohydrate, and interact with other cells for proliferation and maintenance. In hepatocyte cells, the concentration of calcium uptake is quite extensive from various agonists such as activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum. The overproduction and degradation of calcium signals can cause homeostasis, liver inflammation, and liver diseases. The spatiotemporal behavior of calcium oscillation reveals the physiological role of these cellular entities in understanding the process of production and degradation. No computational attempt has been registered to date on the compound calcium regulation of these cellular entities including the memory of cells. Hence, the authors proposed a fractional order compartmental model that systematically simulates the exchange of calcium intake in cellular entities. The nonlinear equations of the rate of changes in the activeG α ${G_\alpha}$ subunit, active phospholipase C, free calcium in the cytosol, and endoplasmic reticulum are coupled to form a nonlinear fractional order initial value problem. The existence and uniqueness, stability analysis of the model is performed that validate the theoretical results and explore the dynamic behaviour of calcium oscillation in each compartment.