BCMB 8190

PROBLEM SET 7

1)   Estimate the rates of chemical exchange for the following    
     examples:                                            

     a) The NMR spectrum of N,N-dimethylnitrosamine shows         
        distinct cis and trans methyl lines with width at 
        half height = 1 Hz and a separation of 100 Hz.  The
        inherent resolution due to homogeneity is 0.5 Hz.

     b) The same molecule in the same spectrometer shows a 
        single line of width 5 Hz.

2) In an SAR by NMR experiment two ligands, A and B, are found to perturb resonances in an HSQC experiment that belong to sites that are within 6 A of one another. Ligand A has a dissociation constant of 2 X 10**-4 and ligand B has a dissociation constant of 5 X 10**-6. If we successfully link these in such a way that their individual binding geometries are not perturbed, and entropy effects are minimal, what would you expect to find for the dissociation constant of the linked ligand? 

3) We have a ligand of molecular weight 2000 that binds with fast exchange to a protein of molecular weight 300,000. At 600 MHz the ligand is giving negative NOEs by itself in solution. We would like to see transferred NOEs that are contaminated by no more than 20 % by NOEs from the unbound state. What is the highest ligand to protein ratio that we could safely use?

4) Suppose we observe a reduction in spin lattice relaxation times for H8 protons on G7, A8, and A9 of a nucleic acid double helix on substituting Mn(2+) for Mg(2+) as follows:  G7 from 2.0 to 1.5, A8 from 2.0 to 0.5, and A9 from 2.0 to 1.5.  Assuming the protons are 5 A apart and on a straight line, how far is the binding site from each proton?