AMPK Methods and Protocols

these experiments are conducted on isotope (^15 Nor^13 C)-enriched

molecules, and for that reason protein, rather than ligand, reso-

nances are most often monitored. Importantly, the resonances will

be those sensitive to the ligand and are most often in or near the

ligand binding site. Which experiment can be applied is dependent

on the rate of exchange of the ligand from the free to the bound

state under equilibrium conditions. It is expected that a resonance

that is sensitive to the presence of the ligand experiences chemical

exchange. At its essence chemical exchange is a rate measurement

between two states such as free protein (A) to ligand bound protein

(B) and can determine the appearance of an NMR spectrum. The

below equation describes this exchange:

A

kon½ŠX

⇌

koff

BX ð 7 Þ

wherekoff(s^1 ) is the first-order dissociation rate constant,kon

(M^1 s^1 ) is the second-order association rate constant, and [X]

is the concentration of unbound ligand in solution. Typically

exchange rate is categorized into three broad exchange regimes

which are determined by comparing exchange rate (kex¼kon+koff)

to the change in chemical shift (Δω¼ωAωB), both measures in

per second. In the slow exchange regime (kex<Δω), two distinct

peaks are observed for the two states (AandB) since there is little

interconversion between states (A⇌B) during the experiment.

The population of each state (pAandpB) can be obtained from the

intensity of each peak. In the intermediate (kexΔω) and fast

exchange regimes, a single population averaged peak is observed.

For fast exchange the rapid exchange between states (A⇌B)

results in a well-defined peak, whereas an exchange broadened

peak is observed in intermediate exchange due to the interference

from the interconversion between states [8, 9]. Two experiments

that are conducted at sub-stoichiometric concentrations of ligand

to protein can provide kinetic data of binding: ZZ-exchange spec-

troscopy is suited to slow exchange and can measure rates in the

millisecond to seconds, while CPMG relaxation dispersion is more

suited to intermediate to fast exchange and can measure rates in the

microsecond to millisecond timescale [7]. From these experiments

koffcan be determined and thenkonfromKdthat is measured by

ITC [5].

kon¼

koff

Kd

ð 8 Þ

In ZZ-exchange spectroscopy [10], for a typical experiment, a

sample is made such that approximately half the protein population

is in the free stateAand the other half is in the bound stateB.A

series of 2D spectra are recorded in which the magnetization is

90 Paul R. Gooley et al.