O. Millet et al., The static magnetic field dependence of chemical exchange linebroadening defines the NMR chemical shift time scale, J AM CHEM S, 122(12), 2000, pp. 2867-2877
The static magnetic field dependence of chemical exchange linebroadening in
NMR spectroscopy is investigated theoretically and experimentally. Two-sit
e exchange (A reversible arrow B) is considered with site A more highly pop
ulated than site B (p(a) > p(b)), a shift difference between sites equal to
aw, and an exchange rate constant given by k(ex). The exchange contributio
n to the transverse relaxation rate constant for the more highly populated
site is denoted R-ex. The dependence of R-ex,, on the static magnetic field
strength is characterized by a scaling parameter alpha = d In R-ex/d In De
lta omega in which 0 less than or equal to alpha less than or equal to 2 fo
r p(a) > 0.7. The value of alpha depends on the NMR chemical shift time sca
le for the exchange process: for slow exchange (k(ex)/Delta omega < 1), 0 l
ess than or equal to alpha < 1; for intermediate exchange (k(ex)/Delta omeg
a > 1), alpha = 1 and for fast exchange (k(ex)/Delta omega > 1), 1 < alpha
less than or equal to 2. Consequently, the static magnetic field dependence
of R-ex defines the chemical shift time scale for an exchange process even
if the populations are so highly skewed (p(a) much greater than p(b)) that
the minor resonance is not observable in the slow exchange limit. The theo
retical results are verified by measuring '5N transverse relaxation rate co
nstants at static magnetic fields of 11.7 and 14.1 T and temperatures of 30
0 and 313 K fur the protein basic pancreatic trypsin inhibitor. At each com
bination of static magnetic field and temperature, the rate constants were
measured using Carr-Purcel-Meiboom-Gill and Hahn echo techniques with spin-
echo delays ranging from 1.0 to 63.5 ms. '5N resonances for residues in the
region of the Cys14-Cys38 disulfide bond are broadened due to chemical exc
hange. Values of a obtained from the relaxation rate constants range from 0
.26 +/- 0.17 for Arg39 at 300 K to 1.96 +/- 0.25 for Cys38 at 313 K. For Cy
s38 and Arg39, the two residues most strongly affected by chemical exchange
, values of k(ex) were determined to be 380 +/- 70 s(-1) and 530 +/- 90 s(-
1) at 300 K and 1300 +/- 290 s(-1) and 1370 +/- 160 s(-1) at 313 K by globa
l analysis of the relaxation rate constants. The scaling parameters ex indi
cate that chemical exchange for most residues in basic pancreatic trypsin i
nhibitor does not satisfy k(ex) /Delta omega much greater than 1. Consequen
tly, the assumption of fast-limit quadratic scaling of exchange broadening
in proteins and other macromolecules may be incorrect, even if a single bro
adened resonance is observed for a nuclear spin. The theoretical results fo
r the static magnetic field dependence of chemical exchange broadening in N
MR spectroscopy are applicable to other nuclei and to other techniques for
measuring chemical exchange Linebroadening.