Assignment Task for Introduction to Biological Physics

1. The Cys side chain has a pKA of 9.2. What fraction of a population of cysteines are protonated at pH 8? pH 10?

2. The NADH cofactor has a midpoint potential of -320 mV vs NHE. What fraction of a population of these cofactors would be in the NAD+ form in a pH 0 solution with a potential of -300 mV vs NHE? -350 mV vs NHE?

3. How many mV corresponds to a 10-fold change in equilibrium populations?

4. In isolation, a DNA-binding protein binds to its regulatory sequence with a Kd of 1.0 μM. Another DNA-binding protein binds to another sequence on the same DNA a few bases away with a Kd of 0 μM when alone. The two proteins each have a domain which binds to the other, with an interaction energy of -2.7 kcal/mole:

   • Draw the thermodynamic box which represents all four states of this system.
   • What are the affinities for each protein in the presence of saturating amounts of the other?

5. The following are data for the equilibrium constant for the unfolding of a protein as a function of temperature:

   T (in K)	KEQ
   290	5x10^-5
   300	2x10^-4
   310	8x10^-4

   • What are the ΔH, ΔS, and Tm of unfolding of this protein?

6. A myoglobin similar to the example we did in class had the protonation of a histidine residue coupled to the oxidation of a heme. The histidine had a pKA of 6.0 when the heme is oxidized and when the heme is reduced. At pH 9.5, the reduction potential of the heme is +275 mV vs NHE.

   • Draw the thermodynamic box that describes this system.
   • Predict the reduction potential at pH 7.
   • The net charge at the iron center cycles between 0 and +1, as the nitrogens at the center of the porphyrin ring have a total net charge of -2. Assuming a dielectric constant of 6, predict the distance between the heme iron and the histidine side chain.

7. E. coli Mn(II) superoxide dismutase is a homodimer in which one manganese atom binds to each monomer. When one monomer’s metal is oxidized (in the +3 state) the other monomer’s iron reduction potential is 25 mV higher than when that first monomer’s iron atom is reduced. What is the effective dielectric between the two metal atoms?

8. The smallest independently folding protein domain we know of is called the trp cage. Download structure 1L2Y into PyMOL. Use the intermolecular forces that you learned in class to tabulate all of the energies involved in its folding – the hydrophobic effect, hydrogen bonds, polar interactions, configurational entropy, etc. – and predict the folding energy. Show your calculations. The more detail you use, the higher your score will be.

9. Download the protein structure 3NVY, the human xanthine oxidase enzyme bound to the inhibitory flavonoid drug quercetin, which is used in the treatment of gout.

   • What exactly is bound to this protein?
   • Using PyMOL, create an image of only the drug and every protein residue that it makes contact with.
   • Enumerate the different stabilizing forces that make the drug bind to the protein at that position, and estimate their energies.
   • Sum these energies and use them to estimate a Kd of binding. Is this value likely too high or too low? Why?
   • Looking at the bound drug, suggest a change in the molecule that might make it bind even better.

10. Read the Richardson Penultimate rotamer library paper. Look at the total population numbers, not broken down by secondary structure, for the amino acid.

• Draw the Newman projections for the lowest energy rotamers.
• Use the data in this table to predict the energy difference between the mt and pt rotamers.
• Using a cutoff of 3% (meaning that it is not a significant isomer if the population is less than 3%), what is the entropic cost in kcal/mol at 25ºC of making a lysine side chain go from an unfolded state to a folded state in which its rotamer is fixed?

11. The solution pKa of cysteine is 8.6. In a solution of water (ε = 80) at pH 10, how close can two cysteine side chains get before one of them protonates (i.e., the electrostatic repulsion energy is greater than the cost of protonation)?

12. Have a great summer!