Linear noise approximation for stochastic oscillations of intracellular calcium

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...

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Smooth muscle contraction is a complex process vital for various bodily functions, from maintaining blood vessel tension to facilitating the movement of food through the digestive tract. Unlike striated muscles, smooth muscle contraction begins more slowly and lasts longer.
The onset of contraction is triggered by an increase in calcium ions within the sarcoplasm, similar to the process in striated muscle. However, smooth muscles have a relatively smaller reservoir of the sarcoplasmic...

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Calmodulin (CaM) is a calcium-binding protein in eukaryotes that controls various calcium-regulated cellular processes. It has four calcium-binding sites that bind calcium to form the calcium-calmodulin ( Ca2+-CaM) complex. GPCR stimulation increases the calcium levels in the cells that bind to CaM and induces a conformational change.
The Ca2+-CaM complex does not have enzymatic activity by itself. Instead, the complex binds downstream target proteins, including membrane proteins or enzymes,...

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...