C2005/F2401 ’06– Recitation Problems #3 -- Answers

1A. Hint: What's being held together here?

1A. Answer: Quaternary structure is defined as the association of two or more polypeptides in a protein.

1B. Hint: What R groups are involved?

1B. Answer: Hydrophobic forces and van der Waals bonds. The leucine side chains consist of hydrocarbon, are non-polar and thus hydrophobic. Once aggregated due to hydrophobic forces, they can form van der Waals bonds due to fluctuating induced dipoles where two leucine molecules approach each other closely.

1C Hint: Try to draw a picture of the structure.

1C. Answer: The alpha-helix is formed by hydrogen bonding interactions between the backbone atoms of a polypeptide; the side chains protrude from the surface of this cylinder in all directions. For a series of side chains of two alpha-helices to interact with each other, they must all protrude from the same side of the cylinder; leucines pointing away from other leucines cannot contribute to the interaction. Since the alpha-helix has 3.6 amino acids per turn, leucines that occur about every 3-4 amino acids will be positioned on the same face of the helix, so one answer is 36/3.6 = 10 leucines. A better answer for the minimum number of leucines would be half this number, or 5. A space between leucines on one helix would allow the leucines from the partner helix to interdigitate between them. If the glycines and alanines, with their small side chains, alternate between these protruding leucines, there would be room for the leucine from the other chain to fit in. Such an arrangement would maximize the hydrophobic interactions along the length of the leucine hydrocarbon side chains.

1-D-1.Hint: What is protonated or ionized at pH 1? At pH 7?

1-D-1. Answer: At pH 1, all basic side chains will be charged, but the glutamates and aspartates will not be charged (their carboxyls will be protonated). The alpha amino group at the N-terminus will also be charged at pH 1, so there must be 6 basic side chains present to give a total charge of +7. At pH 7, all ionizable side chains will be charged, and the N and C-terminus charges will cancel each other out. At pH 7, the negatively charged glutamate + aspartates must just equal the number of basic amino acids with positively charged side chains to produce a zero net charge, so glu + asp must also equal 6, the number of basic side chains.

1-D-2. Hint: What amino acids contain sulfur?

1-D-2. Answer: Sulfur >2; sulfate 0, sulfhydryls 2, disulfides 1 or 0 (depending on how you read the Q; see below). Sulfur could be present in methionine residues (in addition to the one cysteine/subunit): so max # is >2. There's no sulfate group in any of the amino acids, so max # is 0. Sulfhydryls are found only in the amino acid cysteine, and 2 could be present if the 2 cysteines (1 per subunit) are not hooked up in a disulfide. One inter-chain disulfide could be formed between the 2 cysteines. However the statement in the beginning of the question says that "these (leucine) interactions are the only ones responsible for holding the two polypeptides together." This statement precludes disulfides from playing a role in the 4^o structure. So the max. # of disulfides is 1 (if you forgot about the statement at the beginning) or 0, if you take it into account.

2. Hint: Is V vs S linear? 2. Answer: (> 1/2 the V_max but < the V_max). In words: As [S] increases, rate of increase of V increases more slowly than value of [S]. Value of V starts to plateau, so adding more S doesn’t increase V very much at large values of S. Doubling [S] won’t double V. Graphical solution: Show a line rising from 2X K_m to the V curve, and then left to the y-axis to intersect it between 1/2 V_max and V_max.

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