Within a biological system, the DNA encodes the RNA, and the nucleotide sequence in the RNA further defines the amino acid sequence in the protein. This is referred to as “The Central Dogma of Molecular Biology” - a term coined by Francis Crick.  Central dogma is a firm principle in biology that defines the flow of genetic information within any life form. The two fundamental steps in central dogma are - transcription and translation.
Transcription is the synthesis of RNA...

It is vital to regulate the activity of enzymatic as well as non-enzymatic proteins inside the cell. This can be achieved either through creating a balance between their rate of synthesis and degradation or regulating the intrinsic activity of the protein. Both these regulation mechanisms play an essential role in the normal functioning of cells.
Protein degradation plays two important roles in the cells. It helps to protect cells from misfolded or damaged proteins before they lead to a...

The motion of a Ferris wheel rotating at a constant speed provides an intuitive model for understanding trigonometric functions and their derivatives. As a rider moves along the circular path, the vertical height above the ground changes smoothly and periodically over time. This vertical motion can be accurately represented by a sine function, reflecting the repeating pattern of ascent and descent inherent to circular motion.Height and Rate of ChangeIf the rider’s height is modeled by a...

Logarithmic and Exponential RelationshipA logarithmic function is the inverse of an exponential function. If y = logb x then, it can be rewritten as by = x. This relationship allows for implicit differentiation, making logarithmic functions useful in calculus. Logarithmic scales are widely used to represent data that span multiple orders of magnitude, such as earthquake magnitudes (Richter scale) and sound intensity (decibels).Differentiation of Logarithmic FunctionsTo differentiate y = logb x,...

Derivatives quantify the rate of change of a function and can be interpreted geometrically as the slope of a straight line or the slope of a tangent line to a curve at a given point. In the context of a roller coaster, the derivative of the function describing the track’s horizontal position provides a mathematical description of how steep the path is at any location along the ride.Constant and Linear PathsA horizontal segment of a roller coaster can be modeled by a constant function,...