Modeling of oscillations in endocrine networks with feedback

In most cases, excessive hormone production is prevented by negative feedback—a loop that starts with a stimulus inducing the release of a particular substance, like a hormone, to maintain a certain level before triggering a signal that results in a decrease in further release of the hormone.

The endocrine system, a complex network of glands, orchestrates physiological balance within the body through the production and secretion of hormones. These hormones are chemical messengers in intercellular communication, acting as conduits between the secretory cells and distant target sites. They traverse the circulatory system by being released into the extracellular fluid, and their impact is specific to cells possessing receptors for a particular hormone.
The endocrine system collaborates...

Regulation of hormone secretion is a finely tuned orchestration driven by various types of stimuli, encompassing neural, humoral, and hormonal signals. Environmental cues instigate neural stimuli, where action potentials traverse nerve fibers to reach their designated targets. An illustrative scenario is the body's response to stress, wherein the sympathetic nervous system releases epinephrine from the adrenal glands, inducing the well-known 'fight or flight' reaction.
Humoral stimuli,...

Endocrine cells produce hormones to communicate with remote target cells found in other organs. The hormone reaches these distant areas using the circulatory system. This exposes the whole organism to the hormone but only those cells expressing hormone receptors or target cells are affected. Thus, endocrine signaling induces slow responses from its target cells but these effects also last longer.

Calcium is an essential signaling molecule required for various cellular functions. Calcium pumps and ion channels on cell and organellar membranes, such as those on the endoplasmic reticulum (ER), regulate calcium concentrations inside the cell. They remain closed, keeping the cytosolic calcium levels low at a resting state.
Various transmembrane receptors, such as G protein-coupled receptors (GPCRs), elicit a response to extracellular signals by increasing cytosolic calcium. Activated GPCRs...

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...