Biomedical Engineering Reference
In-Depth Information
exchange with the minor species.
1
For motions on the 0.3-10.0 ms timescale,
the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence
108,109
is used to
separate the contribution of relaxation caused by chemical exchange, R
ex
, from
relaxation from other causes, R
2
, to the effective transverse relaxation rate,
R
2,eff
, according to eqn (6.9):
R
2,ef f
~R
2
zR
ex
ð
6
:
9
Þ
The CPMG sequence consists of a series of spin-echo refocusing pulses in
the form t-180u-t where t is a refocusing delay period.
5
R
2,eff
can be
determined by comparing the peak intensity, I, at a given CPMG frequency
[u
CPMG
5 1/(4t)] compared to the peak intensity, I
0
, in a reference spectrum,
eqn (6.10):
1
R
2,ef f
~
1
I
0
I (u
CPMG
)
T
ln
ð
6
:
10
Þ
where T is the total time of all CPMG intervals. This delay is kept constant
except for the reference spectrum where T 5 0. The intensities can be
determined by using peak height or peak volume. The contribution of R
ex
is
obtained by altering the number of refocusing pulses at a given delay. A
greater number of refocusing pulses will enhance refocusing efficiency and
limit line broadening due to R
ex
for residues affected by exchange.
110
The RD profile, a plot of R
2,eff
versus u
CPMG
, is a sensitive measure of protein
dynamics. Site-specific kinetic and structural information can be obtained by
applying a least-square fit of the RD profile against approximate expressions of
two-state exchange, such as the Carver-Richards equations
111
or numerical
fitting to the Bloch-McConnell equations for multi-state systems. For example,
in the case of fast exchange, the RD profile can be fit using eqn (6.11):
P
A
P
B
Dv
2
k
ex
4u
CPMG
k
ex
k
ex
4u
CPMG
R
2,ef f
~R
2
z
1{
tanh
ð
6
:
11
Þ
This provides information on k
ex,
Dv and the populations of exchanging
states, P
A
or P
B
.
112
For chemical exchange on the 20-100 ms timescale, rotating frame relaxation
dispersion (RFRD) is preferred.
113
RFRD reduces the contribution of R
ex
to
R
1r
relaxation by spin-locking the magnetisation in the rotating frame using a
radio frequency (rf) field.
114
The offset between the nuclear precession
frequency and the radio frequency of the pulse (V 5 v
0
2 v
rf
) is small
relative to the precession rate from the radio frequency pulse (v
1
). The
contribution of R
ex
is then determined by eqn (6.12):
R
1r
~R
1
cos
2
hz(R
2
zR
ex
)sin
2
h
ð
6
:
12
Þ
