Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...

Graded potentials are localized fluctuations in the cell membrane's electrical charge, commonly found in the dendrites of neurons. The magnitude of these potential changes depends on the strength of the initiating stimulus. In a membrane at its resting potential, a graded potential signifies a voltage shift either above -70 mV or below -70 mV.
Graded potentials fall into two categories: depolarizing and hyperpolarizing. Depolarizing graded potentials typically occur when sodium (Na+) or...

Heterotrimeric G proteins are guanine nucleotide-binding proteins. As the name suggests, heterotrimeric G proteins are composed of three subunits: alpha, beta, and gamma. They remain GDP-bound or GTP-bound inside the cells and switch between inactive/active states. The Gα subunit possesses the nucleotide-binding pocket that binds guanine nucleotides and switches between GDP or GTP-bound states. In contrast, the Gꞵ and Gγ subunits are always bound together with high...

Some GPCRs transmit signals through adenylyl cyclase (AC), a transmembrane enzyme. AC helps synthesize second messenger cyclic adenosine monophosphate (cAMP). AC catalyzes cyclization reaction and converts ATP to cAMP by releasing a pyrophosphate. The pyrophosphate is further hydrolyzed to phosphate by the enzyme pyrophosphatase, which drives cAMP synthesis to completion. However, cAMP is rapidly degraded to 5′ AMP by the enzymes phosphodiesterase (PDE), preventing overstimulation of...

Contact-dependent signaling, as the name suggests, requires that communicating cells be in direct contact with each other. This is achieved either through receptor-ligand interactions or by specialized cytoplasmic channels that allow the flow of small molecules between cells. In animal cells, channels called gap junctions facilitate contact-dependent signaling in certain tissues, whereas, plasmodesmata perform a similar function in plants.
Gap Junctions
In animal cells, gap junctions are formed...