When a protein is damaged, it can be tagged with the molecule, ubiquitin. This signals to the cell that the protein is no longer functioning properly and needs to be degraded.

HMGCoA reductase is the rate-limiting enzyme in cholesterol synthesis. The reductase is present on the endoplasmic reticulum membrane. When levels of its product, cholesterol, are high, the enzyme gets ubiquitinated and degraded in smaller peptides and amino acids. It first binds to insulin-induced gene 1 protein before ubiquitination.

Trypsin will cleave the primary sequence after the lysine residue (on its carboxyl side). Thus, Lys will be the new carboxyl terminal and Glu will be the new amino terminal. Remember that a protein's primary sequence is written from N to C.

Trypsin will cleave lysine and arginine at the carbonyl side. Chymotrypsin will cleave phenylalanine, tyrosine, and tryptophan at the carbonyl side. Pepsin will cleave leucine, phenylalanine, tryptophan, and tyrosine at the amino side. Pepsinogen is the inactive form of pepsin, which gets activated via cleavage by hydrochloric acid in the stomach.

Chymotryspin cleaves Phe, Trp, and Tyr at the carbonyl side. This means that there will be a cleavage after any of these three amino acids appears. This results in Gly-Ala-Pro-Tyr, His-Cys-Gly-Phe, Gly-Gly-Asn.

In this question, we're provided with a description of turnover rate. We're then asked to identify the relative turnover rates for protein, mRNA, and DNA.

To answer this question, it's important to have a general understanding of the role each of these molecules has in the cell. DNA resides in the nucleus and functions to provide the blueprint for producing mRNA. This mRNA, in turn, is processed and exported to the cytoplasm, where it interacts with ribosomes to be translated into protein. Finally, these proteins can have a wide variety of functions, including structural proteins, enzymes, antibodies, etc.

Based on the function of each of these molecules, we can reason our way to see what their relative turnover rates are expected to be.

Since DNA essentially provides the blueprint for the production of all proteins from a cell, its role is extremely important. While it's true that genes can be turned on and off, there's always going to be activity going on in the form of transcription within the nucleus; genes are being converted into mRNA all the time. Because it serves such an important role, and is even needed for cells that divide, we would expect DNA to have a practically non-existent turnover rate.

Next, let's take a look at mRNA. Though DNA is the blueprint that directs the production of protein, mRNA acts as the intermediate between the two. The advantage of this is that it allows for more levels of control. In addition to regulating transcription of genes through various means, post-transcriptional control is also possible. This level of control involves modifying the mRNA transcript to make it more resistant to degradation, or sometimes even degrading it to turn off gene expression. Overall, mRNA doesn't have a very long half-life within the cells. Because it serves as the intermediate between protein and DNA, once the protein has been translated, the mRNA is not really needed anymore. Thus, mRNA tends to have a high turnover rate, being produced whenever the cell needs it (gene expression turned on) and degraded whenever it isn't needed (gene expression turned off).

Lastly, let's look at protein. As was said previously, proteins have a vast array of functions. Whereas DNA and mRNA are responsible for producing protein, it is the protein that serves as the actual effectors; they're the ones that take action to get things done, either inside or outside the cell. In addition to being produced from DNA and mRNA, proteins can also be degraded via a process called ubiquitination. But, overall, since proteins are the actual effectors in the whole process, their turnover is lower than mRNA but higher than DNA.

Overall, the turnover rate is greatest for mRNA, followed by protein, with DNA having the lowest.

This problem requires knowledge of the endopeptidase properties. Trypsin cleaves after the amino acids lysine and arginine, and chymotrypsin cleaves after the amino acids phenylalanine, tyrosine, and tryptophan. 

Using this information, the slashes below indicate where each enzyme cleaved the polypeptide.

(AM) (SAK)/ (YMPLWGIR)/ trypsin

(MPLW)/ (GIRAM) (SAKY)/ chymotrypsin

Because the (AM) and (GIRAM) fragments have no slash after M in both the first and second treatment, one can conclude that this piece is at the end of the polypeptide. The other two pieces are sequenced by realizing that S starts the (SAK) and (SAKY) fragments and is never found in the middle of a fragment. 

There are 4 main steps in the unfolded protein response: (1) Translation of proteins is stopped, (2) Chaperones are recruited to the location of misfolded proteins, (3) Misfolded proteins are "tagged" with ubiquitin chains for degradation by the 26S proteasome, (4) if the above steps fail, the cell undergoes programmed cell death. Thus, all of the answers choices are affiliated with the unfolded protein response.