Numerical Analysis of Compound Biochemical Calcium Oscillations Process in Hepatocyte Cells

Abstract

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 active 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 active 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.

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

“…𝜎 𝑐𝑎 = −𝐼 𝑐𝑎 𝑍 𝑐𝑎 𝐹𝑉 𝑛𝑒𝑢𝑟𝑜𝑛 (21) The principle that states the inward current must be negative is used to interpret the negative sign in (21).…”

“…A different mathematical model is developed to get further knowledge on calcium signaling in alpha cells, Cholangiocyte cells, Oocyte cells, Hepatocyte cells, etc. [18][19][20][21]. Initial and boundary value problems are used to solve mathematical models of calcium signaling.…”

Error Function Optimization to Compare Neural Activity and Train Blended Rhythmic Networks

“…There are two basic types of CPG models and their building blocks: biophysically realistic and phenomenological. Biophysical models incorporate known molecular mechanisms underlying the generation of electrical activity in neurons and synapses, while phenomenological models simplify the firing of an action potential (AP) as an instantaneous pulse and effective synaptic coupling [12][13][14][15][16][17].…”