In the hydrophobic core of a folded protein there are two al

In the hydrophobic core of a folded protein, there are two alanine and four phenylalanine residues that are buried, and do not interact with water. Assume: In solution, waters can take on six energetically equivalent states Two water molecules are ordered around each alanine in the unfolded state Six water molecules are ordered around each phenylalanine in the unfolded state In the unfolded state, waters are ordered around alanine or phenylalanine residues and take on only two energetically equal states What is the difference in the entropy of the water due to the burying of these residues as the protein folds?

Solution

There are total water molecules ---> 2 * number of Ala + 6 * number of Phenyl alanine

                                                  --->   2* 2 + 6*4 -->   4 + 24 --> 28

                                                 --->   28 waters

S folded ----> Rln7²⁸ ----> 8.31 * 28 * ln7 = 452J•K –1 •mol –1

S unfolded = Rln2²⁸ ----> 8.31 * 28 * ln2 = 161J•K –1 •mol –1

S = S folded - S unfolded = 452 – 161 ---> 291J/K