Biomedical Engineering Reference
In-Depth Information
R
2
, and broadens the NMR signal. This increase in R
2
is dependent on k
ex
, Dv,
and the equilibrium populations of the spin in state A (p
A
) and state B (p
B
).
Relaxation dispersion experiments can quantify these exchange parameters
by modulating the observed R
2
value through alteration of the delay (t
cp
)
surrounding spin echo refocusing pulses in a Carr-Purcell-Meiboom-Gill
(CPMG) experiment
32
or by varying the strength of an applied spin-locking rf
field (v
eff
), in an R
1r
experiment.
35,36
For the CPMG experiment, the
relationship between the measured single quantum (SQ) transverse relaxation
rate R
2
(1/t
cp
) and the physical properties of the exchange phenomenon, is
generally expressed by the Carver-Richards equation,
37
ð
7
:
2
Þ
~
1
2
R
2A
zR
2B
zk
ex
{
1
t
cp
cosh
{1
R
2
1
=
t
cp
D
z
cosh(g
z
){D
{
cos(g
{
)
2
4
3
5
2
+1z
Yz2Dv
2
D
+
~
1
ð
7
:
3
Þ
1
=
2
Y
2
zj
2
h
i
1
=
2
g
+
~
t
cp
p
+Yz(Y
2
zf
2
)
1
=
2
2
ð
7
:
4
Þ
2
{Dv
2
z4p
A
p
B
k
ex
Y~ R
2A
{R
2B
{p
A
k
ex
zp
B
k
ex
ð
7
:
5
Þ
f~2Dv R
2A
{R
2B
{p
A
k
ex
zp
B
k
ex
ð
7
:
6
Þ
which is valid for conformational exchange processes in the slow-to-
intermediate regime. For a robust determination of the exchange parameters,
relaxation dispersion data at multiple static magnetic fields are necessary.
38-40
In the fast limit, eqns (7.2)-(7.6) reduce to a simplified expression,
32
R
2
(1
=
t
cp
)~R
2
zw
ex
=
k
ex
1{2tanh(k
ex
t
cp
=
2)
=
(k
ex
t
cp
)
ð
7
:
7
Þ
In eqn (7.7), w
ex
5 p
A
p
B
Dv
2
in which case, without additional information,
the populations and chemical shift differences cannot be determined as in eqn
(7.2). The magnitude of the change in R
2
with 1/t
cp
, w
ex
/k
ex
is often referred to
as R
ex
(Figure 7.1). It can be more easily seen in eqn (7.7) than in the Carver-
Richards expression that as the pulse repetition rate increases (t
cp
decreases)
the observed R
2
decreases, resulting in a profile as shown in Figure 7.1. One
needs to pulse faster than the exchange process to suppress its effects on the
nuclear transverse relaxation rate. This limits the timescale of exchange
processes that can be studied by the CPMG technique. Rapid pulsing is limited
