BCMB/CHEM 8190
PROBLEM SET 6

1) A NOESY experiment is conducted on a small protein using a short mixing time (50ms). Crosspeaks are observed and integrated for a glycine residue. Using the distance between the two alpha protons in this amino acid (0.175nm) as a distance standard, and the following crosspeak intensity data, estimate the dihedral angle phi (use other standard bond and angle geometries as necessary).

Ha1 - Ha2 28.0

Ha1 - HN 1.6

Ha2 - HN 0.5

2) Couplings between 5' and 5'' protons and the phosphate phosphorus in a 5' nucleotide are observed to be 6.0 and 8.0 Hz, respectively. Using the formula J(PH) = 21(cos(theta)**2 -2.25, and assuming idealized rotomer geometries about the C5 - O5 bond, calculate the rotamer populations for this molecule.

3) An adenine in a bulge of a nucleic acid helix is said to be flipped out in solution instead of being stacked between adenine rings of adjacent base pairs. Using the remote group model for benzene to approximate the effect of the adenine rings, what would you expect for the chemical shift of the H2 proton of the flipped out adenine compared to other adenine H2s?

4) What would you expect for the alpha carbon chemical shift of an alanine when it was in an alpha helix of a protein as compared to a beta sheet?

5) A dilute protein solution at 330K gave rise to 13Calpha resonances with spin lattice relaxation times of 30ms when examined at a spectrometer frequency of 15MHz. A full NOE was also observed. Estimate the size of the protein. Note:  You will need the Stokes formula relating the molecular correlation time to solvent viscosity, temperature and radius of an equivatent sphere.  (page 17 of Cavanagh).  tc = (4pha**3)/(3kT).