1200 Hz) where theR 2 obsis dependent onνCPMG(Fig.3). The
intensity of the peaks can be taken and converted to plots ofR 2 obsvs
νCPMGby the following expression:
R 2 obs¼ln
IvCPMG
I 0
=TCPMG ð 11 Þ
whereIνCPMGis the intensity of the peak andI 0 is the intensity of
the peak in a reference spectrum whereνCPMG¼0. These R 2 obs
profiles can be fit to an appropriate exchange model in order to
obtain structural (chemical shiftΔω¼ωA+ωB), kinetic (exchange
ratekex), and population (pAandpB) parameters [5, 7, 12]. For a
two-state binding model, CPMG data can be fitted to [12]:
Rcalc 2 ¼ln
MBð 4 nδÞ
MBð 0 Þ
ð 12 Þ
whereMðÞ¼ 4 nδ expðÞAδexpA~δ
expA~δ
expðÞAδ
nMðÞ 0 ,TCPMG
¼4nδwith 2nthe number of 180pulses within theTCPMGperiod,M
(t) is the magnetization vector given by (MB(t), and MA(t))Tfor
two-site binding between statesAandB,andAandA ̃by:
A¼ R
A
2 k
0
onþiΔω koff
k^0 on koffR 2 B
ð 13 Þ
A~ ¼ R
A
2 k
0
oniΔω koff
k^0 on koffR 2 B
ð 14 Þ
wherek^0 on is defined in eq. (10),Δω(s^1 ) is the chemical shift
difference of the free (A) and bound (B) states, andR 2 AandR 2 Bare
the transverse relaxation rates of the free and bound states.
Fig. 3Schematic of CPMG relaxation dispersion NMR spectroscopy—(a) Peaks of a 2D spectra intensify with
increasingνCPMGand are used to create aR 2 relaxation profile. (b)R 2 relaxation profile is obtained by plotting
the observed relaxation rate (R 2 obs) against theνCPMGfrequency. These plots can then be fit to appropriate
models in order to obtain exchange rates (kex,kon,koff), populations of states (pAandpB), and chemical shifts
(Δω¼ωA-ωB)
92 Paul R. Gooley et al.