Chapter 3, Problem 9P

It is observed that as temperature is increased, most protein molecules go from their defined, folded state into a random-coil, denatured state that exposes more hydrophobic surface area than is exposed in the folded state.
a. Given what you have learned so about $\Delta$ H and $\Delta$ S, explain why this reasonable. (Hint Consider Problems 7.)
b. Sometimes, however, proteins as temperature is decreased. How might this be explained? (Hint: Consider Problem 8)

7. Assume that some protein molecule, in its folded native state, has one favored conformation. But when it is denatured, it becomes a “random coil,” with many possible conformations.
a. If we only consider the entropy for the protein, what must be the sign of $\Delta$ S for the charge native $\to$ denatured? (Note: As suggested in the next problem, this does not include solvent effects, which also make contributions to $\Delta$ S.)
b. How will the contribution of $\Delta$ S for native $\to$ denatured affect the favorability of the process? What apparent requirement does this impose on $\Delta$ H if proteins are to be stable structures?

8. When a hydrophobic substance like a hydrocarbon is dissolved in water, a clathrate cage of ordered water molecules is formed about it (see Figure 2.14). If we consider only the effects on water, what do you expect the sign of $\Delta$ S to be for this process? Explain your answer.