BCMB/CHEM 8190
Answers, Problem Set 8
1)
Dissociation constant = 2X10^-4 X 5X10^-6 = 1X10^-9
2) The relative rate of build-up of NOEs will be 300,000/2000. A 20% contribution from the
free NOE would occur with a free to bound ratio of X/(X-1) where X*2)/((1-X)*300) = 0.2.
Assuming the ligand binding constant is relatively high, 20% would occur at a 30:1 ligand to
protein ratio.
3) Iron oxide nano particles exert their greatest effect on T2 – making it shorter. You would
use a T2 enhanced sequence. T2 filters usually result in loss of signal from regions having the
shortest T2 – these regions would appear dark.
4)
a) Assuming polarization of the electron is still in the linear limit of the Boltzmann factor
DNP enhancement is proportional to e / C. Using e = 650 x H, P(DNP) = 650 x 4 = 2600.
b) P  1/T. P(T) = 298/4 = 74.5
c) P(total, max) = 74.5 x 2600 = 193,000
5) Scaling in solids NMR is by a factor of (1-3cos2)/2. This factor is zero at 54.7, but 0.12 at
50. The line would be 0.12 x 200 = 24 ppms wide or 24 X 500 X 0.25 = 3000 Hz at 125 MHz
for 13C.