Consider a planar region bounded by two curves that are both written as functions of the vertical variable, y. The left and right boundary curves are continuous between y = c and y = d, and these two horizontal lines define the vertical limits of the region. Because the boundaries depend on y rather than x, the area is most appropriately evaluated using horizontal slices.The area is obtained using the Riemann sum method. The region is divided into many thin horizontal strips, each having an...

Consider two continuous functions defined on a closed interval from a to b. The region between these curves is bounded vertically by their graphs and horizontally by the endpoints of the interval. The objective is to measure the area of this region.An initial estimate of the area can be obtained by dividing the interval into a large number of narrow vertical strips of equal width. Each strip is approximated by a rectangle whose height is given by the vertical difference between the two...

In eukaryotes, transcription and translation are compartmentalized; an mRNA is first synthesized in the nucleus and then selectively transported to the cytoplasm for protein synthesis. Before transport, a pre-mRNA undergoes several steps of post-transcriptional modifications including splicing, 5' capping, and the addition of a poly-adenine tail. Various proteins bind to the pre-mRNA during these modifications. The mRNA transport takes place with the help of multiple proteins playing...

Epigenetic mechanisms play an essential role in healthy development. Conversely, precisely regulated epigenetic mechanisms are disrupted in diseases like cancer.

Guanine nucleotide-binding proteins (G-proteins), also known as GTPases, are a superfamily of proteins that regulate many cellular processes, such as cell signaling, vesicular transport, and the regulation of cell shape and motility. Mutation or dysfunction of these proteins can lead to disease. There are around 40,000 known G-proteins that can broadly be classified into two groups ‒  small G-proteins consisting of a single domain and large multi-domain G-proteins.
Large G-proteins,...

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...