AMPK Methods and Protocols

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.