This is a short set of questions on the thermodynamics and statistical mechanics relevant to protein conformations and folding. This assignment is due in my mailbox (in mailroom, 2nd floor of NPB) before 5:00 pm, February 1, 2002

1. Two energy levels of a molecule are separated by 10^-22 Joules. The higher level consists of twice as many microstates as the lower level.
• What is the relative population of the two levels at a temperature of 0 degrees Celsius?
• At what temperature are the two energy levels equally populated?
2. The Ramachandran plot showed that each amino acid residue in the backbone of a polypeptide chain has about 3 possible configurations (ignoring the orientation of the amino acid side chain). About how many configurations do you estimate are available to an unfolded protein of 100 residues?
3. A protein of 100 residues might have a molecular weight near 12,000. Imagine that you have 1 mg of protein unfolded in solution. What fraction of the total number of unfolded configurations are actually represented in your sample at any given instant?
4. We said in class that the entropy of a macroscopic state is given by S = k log(&Omega), where &Omega is the number of microscopic states (configurations) that are associated with the macroscopic state, and k is Boltzmann's constant. What is the entropy of this hypothetical unfolded molecule, in units of Joules/mol/Kelvin ?
5. Assume that there is only one configuration associated with the folded state of the protein. What is the total entropy change dS = S(folded) - S(unfolded) for folding of this molecule?
6. The free energy change of folding is dG = dH - TdS. If the folded state becomes thermodynamically stable at a temperature T* = 333 K (= 60 C), then what is the enthalpy change dH of folding?
7. What is the source of this enthalpy change? How does the enthalpy change per amino acid residue compare with your expectations for the scale of energy of interaction for amino acid side chains?