Chapter 7, Problem 7.10PS

Hydropathy: The Plot Thickens. A hydropathy plot can be used to predict the structure of a membrane protein based on its amino acid sequence and the hydrophobicity values of the amino acids. Hydrophobicity is measured as the standard free energy change, ΔG°′, for the transfer of a given amino acid residue from a hydrophobic solvent into water, in kilojoules per mole (kJ/mol). The hydropathy index is calculated by averaging the hydrophobicity values for a series of short segments of the polypeptide, with each segment displaced one amino acid farther from the N-terminus. The hydropathy index of each successive segment is then plotted as a function of the location of that segment in the amino acid sequence, and the plot is examined for regions of high hydropathy index.

1.    (a)            Why do scientists try to predict the structure of a membrane protein by this indirect means when the technique of X-ray crystallography would reveal the structure directly?
2.    (b)            Given the way it is defined, would you expect the hydrophobicity index of a hydrophobic residue such as valine or isoleucine to be positive or negative? What about a hydrophilic residue such as aspartic acid or arginine?
3.     (c)            Listed below are four amino acids and four hydrophobicity values. Match the hydrophobicity values with the correct amino acids, and explain your reasoning.

   Amino acids: alanine, arginine, isoleucine, serine

Hydrophobicity (in kJ/mol): +3.1, +1.0, −1.1, −7.5

1.    (d)            Shown in Figure 7-29 is a hydropathy plot for a specific integral membrane protein. Draw a horizontal bar over each transmembrane segment as identified by the plot. How long is the average transmembrane segment? How well does that value compare with the number you calculated in Problem 7-6c? How many transmembrane segments do you think the protein has? Can you guess which protein this might be?

Figure 7-29 Hydropathy Plot for an Integral Membrane Protein. See Problem 7-10d.

QUANTITATIVE That’s About the Size of It. From chemistry, we know that each methylene (—CH₂—) group in a straight-chain hydrocarbon advances the chain length by about 0.13 nm. And from studies of protein structure, we know that one turn of an α helix includes 3.6 amino acid residues and extends the long axis of the helix by about 0.56 nm. Use this information to answer the following.

1.    (a)            How long is a single molecule of palmitate (16 carbon atoms) in its fully extended form? What about molecules of laurate (12 C) and arachidate (20 C)?
2.    (b)            How does the thickness of the hydrophobic interior of a typical membrane compare with the length of two palmitate molecules laid end to end? What about two molecules of laurate or arachidate?
3.     (c)            Approximately how many amino acids must a helical transmembrane segment of an integral membrane protein have if the segment is to span the lipid bilayer defined by two palmitate molecules laid end to end?