# Tutor profile: Haafiz H.

## Questions

### Subject: MCAT

Which of these amino acid substitution mutations would be most likely to change protein function? A. G153A B. M1N C. D98E D. R6K

The correct answer is B, which involves substitution of an asparagine for a methionine. Unlike methionine which is a nonpolar amino acid, asparagine is polar, which makes this mutation likely to change the structure and function of the protein. The other mutations do not change the overall type of amino acid (i.e. nonpolar to nonpolar or acidic to acidic). Furthermore, the first amino acid of a protein being methionine is a hallmark of eukaryotic genes; changing this may cause problems with protein assembly and post-translational processing.

### Subject: Biology

Detective Dan is looking into a recent case of poisoning. He has narrowed down the possible poison to four candidates: Poison A, which attacks the mitochondria, Poison B, which destroys ribosomes when they attempt to translate RNA into protein, Poison C, which destroys the membrane of the Golgi Body, and Poison D, which prevents DNA from being replicated in cells. Detective Dan, in order to determine the identity of the poison, has decided to perform a biopsy of the victim's liver cells. In these cells, he is specifically looking for a certain cellular membrane transport protein Bleh. This protein is responsible for helping to transport vital nutrients into the cell. To Detective Dan's surprise, the surface of the cells are entirely lacking Bleh; instead, he finds large clumps of fully formed protein in the cellular cytoplasm. Based on this evidence, which of the poisons likely killed the victim and why?

The correct answer is poison C. The Golgi body is responsible for packaging proteins for transport to the cell membrane and outside of the cell. Because the victim's cells were full of properly formed protein which were meant to be moved to the surface, it seems that the cells' protein transport system was malfunctioning, suggesting trouble with the Golgi Body, or poison C.

### Subject: Calculus

Farmer Brown has been having trouble with coyotes recently. To combat this issue, Farmer Brown has decided to create a fenced in rectangular plot of land for his sheep. Farmer Brown is strapped for cash, and has only 5000 dollars to build his new sheep pen. Each yard of fencing costs $20 to install. Farmer brown wants to give his sheep at least 3000 square yards to graze. What length and width should he build the pen to minimize his costs?

This problem can be described with 3 equations: one describing the area of the pen, one describing the constraint, and one describing the costs of the pen. For the first equation, we know that the area of the pen is simply the length times the width, and that the total area is 3000 yards: $$l$$ x $$w$$ = $$3000$$ We also know that the length and width of the pen both cost $20 per yard of fencing. Using this information, we can construct the following equation: $$20(2l+2w)$$ = $$total$$ Now that we have obtained our equations, we can get down to solving the problem. The first order of business is to reduce the number of variables. Right now, we have two variables; if we can reduce this to one, we can solve this set of equations using derivatives and optimization. Rearranging the first equation, we see that $$l = 3000/w$$ Substituting this in for $$l$$ (from the constraint equation) into the cost equations, we obtain the following equation: $$20[2(3000/w) + 2w] = total$$ Simplifying, we obtain: $$120000/w + 40w = total$$ Now that we have a single equation describing cost, we can use the derivative to find the optimal value of w for Farmer Brown. First we take the derivative: $$-120000w^{-2} + 40 = total'$$ Now we solve to find the value of w which causes total' to equal 0: $$-120000w^{-2} + 40 = 0$$ $$-120000w^{-2} = -40$$ $$w^{-2} = 40/120000$$ $$w^2 = 12000/4$$ $$w^2 = 3000$$ $$w = \sqrt{3000} \approx 54.77 $$ Plugging back in to find $$l$$, we see that it is equivalent to $$w$$: $$lw = 3000$$ $$l\sqrt{3000} = 3000$$ $$l = \sqrt{3000}$$ Thus, we see that Farmer Brown should build a pen about 54.77 x 54.77 yards in size.

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