Bifurcation analysis in a delay model of IVGTT glucose-insulin interaction

The pancreatic islets comprising only 1%-2% of the volume are highly vascularized and innervated mini-organs. They contain five endocrine cell types, including β cells that secrete insulin, which is synthesized as a single polypeptide chain, preproinsulin, processed to proinsulin, and finally to insulin and C-peptide. This process is complex and regulated, involving the Golgi complex, the endoplasmic reticulum, and the secretory granules of the β cell.
Insulin and C-peptide are...

Carbohydrates consumed through foods are converted into glucose, a crucial energy source for the body. In the prandial state, high blood glucose levels stimulate the secretion of insulin from the pancreas. Insulin inhibits hepatic glucose production and stimulates glucose uptake and metabolism by muscle and adipose tissue. The excess glucose is converted into glycogen and stored in the liver and muscles.
During fasting, when blood glucose levels are low, the pancreas secretes glucagon. it...

Glucose transporters facilitate the transport of glucose across the cell membrane. In addition to glucose, some glucose transporters can also aid the movement of other hexoses such as fructose, mannose, and galactose.
Facilitated diffusion-glucose transporters (GLUTs) are encoded by the solute-linked carrier (SLC) family 2, subfamily A gene family, or SLC2A. The 14 GLUT protein members are distributed into three classes:

Insulin secretory vesicles release insulin to stimulate blood glucose uptake and regulate carbohydrate metabolism. When the blood glucose levels increase, glucose enters the pancreatic β-islet cells through glucose transporters. Once inside, glucose is metabolized through glycolysis, the citric acid cycle, and the electron transport chain, producing ATP. This increase in ATP concentration closes ATP-sensitive potassium channels, leading to depolarization of the membrane and the opening of...

Insulin action is mediated through a receptor tyrosine kinase, akin to the IGF-1 receptor. The number of receptors per cell varies significantly, from 40 on erythrocytes to 300,000 on adipocytes and hepatocytes. The insulin receptor consists of linked α/β subunit dimers, forming a heterotetramer glycoprotein with two extracellular α subunits and two β subunits spanning the membrane. The α subunits inhibit the inherent tyrosine kinase activity of the β subunits, but...

Insulin preparations are categorized by their duration of action into short-acting and long-acting types. Two strategies are used to modify insulin's absorption and pharmacokinetic profile: slowing the absorption post-subcutaneous injection, or altering human insulin's amino acid sequence or protein structure. These changes retain the insulin's ability to bind to the insulin receptor, but alter its behavior in solution or after injection.
Short-acting insulins are divided into...