Biomedical Engineering Reference
In-Depth Information
applied effective fields to allow full modulation of the observed R
2
values and
subsequent extraction of the relevant exchange parameters.
In such cases conformational exchange can also be quantified by monitoring
rotating frame spin relaxation in the presence of an off-resonance spin-locking rf
field.
41
Instead of measuring R
2
, this approach records another parameter, R
1r
,
which is a trigonometric combination of R
2
and the longitudinal relaxation rate,
R
1
. The applied spin-locking field 'locks' the magnetisation in a tilted frame in
which both R
1
and R
2
processes contribute to the spin-relaxation process. In the
slow to intermediate exchange regime this relationship is:
42
R
1r
~R
1
cos
2
hzR
2
sin
2
hz
sin
2
hp
A
p
B
Dv
2
k
ex
v
2
Ae
v
Be
v
e
zk
ex
ð
7
:
8
Þ
where v
2
Ae
=
Be
~v
2
A
=
B
zv
1
are the squares of the effective fields for sites A/B and
v
e
~v
avg
zv
1
. The terms, v
A
, v
B
and v
avg
are the frequency offsets of the A, B,
and population weighted averaged NMR resonances, from the rf carrier,
respectively and v
1
is the rf field strength with tilt angle, h 5 arctan(v
1
/v
avg
). In
the limit of fast exchange, the denominator in eqn (7.8) can be reasonably
approximated by v
e
zk
ex
. R
1
and R
2
are determined in separate experiments as
described elsewhere.
43,44
Alternatively R
1
can be eliminated as a fit parameter
through a constant-time relaxation variant of the R
1r
experiment.
41
In this case
an effective relaxation rate is measured
Dv
2
p
A
p
B
k
ex
(1zv
e
=
k
ex
)
R
ef f
=
sin
2
h~R
2
{R
1
z
ð
7
:
9
Þ
The constant-time approach obviates the need to independently measure R
1
,
though a decrease in S/N may render it undesirable for some systems. The R
1r
technique is capable of quantifying chemical exchange processes with k
ex
up to
y100 000 s
21
,
45
which is much faster than those accessible to the CPMG
approach. Though the ability to span the ms-ms timescale makes the R
1r
experiment more versatile, it is somewhat more involved to implement. As
intimated above, if a variable relaxation delay is used, a separate experiment must
be performed to quantify R
1
. Furthermore, care must be taken to calibrate the
strength of the spin-lock field so that accurate exchange parameters may be
obtained.
46
For these reasons the CPMG experiment may be preferable for
processes with exchange rate constants less than 3000 s
21
as shown in Figure 7.1.
7.3 The Benefits of TROSY
7.3.1
1
H-
15
N TROSY
Another consideration germane to the topic of this chapter is the
implementation of TROSY principles in the study of larger molecular weight
