Question

Protein molecules in the cytosol of a cell have different half-lives t _½. The half-life is the time needed for 50% of the molecules to be lost or altered. Half-lives are determined by several factors, one of which is the “marking” of the protein by ubiquitin, which signals that the protein is intended for digestion by proteases. Ubiquitin binds differently to proteins due to differences in their amino ends. The following table gives the half-lives t _½ for some proteins with different amino ends:  

Amino Acid End of Protein	t ½
MET	> 20 hrs
SER	> 20 hrs
THR	> 20 hrs
ALA	> 20 hrs
VAL	> 20 hrs
LEU	< 3 min
PHE	< 3 min
ASP	< 3 min
LYS	< 3 min
ARG	< 2 min

Half-life is related to the rate K of protein loss by the following equation:

t _½ = 0.693 / K

where 0.693 is the natural logarithm of 2, and K is measured in reciprocal time units.

a. What is the rate of protein loss per minute when MET is the amino terminal?   (Assume t _½ = 24 hr).

K = 0.693 / 24 x 60 = 0.00048 / minute

b. Compare this with the rate when ARG is the amino terminal end. (Assume t _½ = 2 min).

K = 0.693 / 2 = 0.35 / minute

c. What percentage of the protein with a MET amino end exists in the cell after 5 half-lives?

100 / 2^5 = 3.125%

d. What percentage of the protein with an ARG amino end exists in the cell after 5 half-lives?

100 / 2^5 = 3.125%

e. How much faster (as a percentage) is the rate of ARG-amino-end protein degradation as compared to MET-amino-end degradation?

0.35 / 0.00048 = 729.2

729.2 x 100 = 72,920%

f. Plot the loss of a population of protein molecules that have a MET amino end. Use time t on the horizontal axis and size of the population on the vertical axis, starting with 100% of the population at the starting time t = 0.

g. On the same graph, plot the loss of a protein with ARG as the amino terminus.

h. Hemoglobin exists in the cytoplasm of a red blood cell (RBC). Red blood cells last about 120 days in the bloodstream. In your initial experiments you find that the amino terminus of one protein chain in RBCs is either a valine or a leucine (so a difference of only one methyl group). Which is more likely to be the correct amino acid terminus of this protein? (Assume t _½ = 24 hr for valine and 2 min for leucine).

I need help with the graph for parts (f) and (g), I don't understand how to do the plotting.

Thank you in advance!

Answer 1

Answer:

Q-1):

• We are given with the equation t 1⁄2 = 0.693 / K
• Where 0.693 is the natural logarithm of 2, and K is measured in reciprocal time units.
• t 1⁄2 = 24 hr (1440min) is the half-life for MET amino terminal protein.

so rate of protein loss per minute (K) when MET is the amino terminal = 0.693 / 1440 = 0.00048

Q-2):

• And t 1⁄2 = 2 min when ARG is the amino terminal end,
• so K = 0.693 / 2 = 0.346, which is nearly 1000 times more than the MET-amino terminal protein.

Q-3):

• For this kind of situation we have the general formula Nn = No (1/2)ⁿ, where Nt = amount of element at time Tn, N0 is the initial amount present and n is the number of half-lives.
• so protein with a MET amino terminal after 5 half-lives, if we started with 100% amount of protein.
• N₅ = 100 (1/2)⁵
• N₅ = 100/32 = 3.125 %, means 3.125 % of protein is left after 5 half-lives.

Q-4):

• Similarly, if we started with 100 % protein with Arg amino terminal. after 5 half-lives
• N₅ = 100 (1/2)⁵
• N₅ = 100/32 = 3.125 %, means 3.125 % of protein is left after 5 half-lives.

Note: there is no difference in amount of two different molecules undergone same number of half-lives

Q-5):

• As we have already calculated the rate of loss of protein in case MET amino terminal and in other case when Arm amino terminal as 0.00048 rate for the MET amino terminal and for ARG amino terminal as 0.346.
• So to compare both these rate, we need to take their ratio; protein loss rate in case of ARG/protein loss rate of MET. = 0.346/0.00048 = 720.83, which means rate of loss of protein with my ARG is 720 times faster than the MET amino terminal protein side.

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