Biomedical Engineering Reference
In-Depth Information
using the starting conditions
½
P
t~0
~P
tot
½
L
t~0
~L
tot
½
PL
t~0
~0
ð
10
:
5
Þ
Ligand-binding events are biological switches for turning functional
processes on and off. For single-site binding, the switch is 'off' (,10%) when
[L] ,K
D
/10, and is 'on' (.90%) when [L] .K
D
6 10. In other words, the
switch operates in three log units of concentration. Nature has found ways to
make
the
switch
more
sensitive
(positive
co-operativity)
or
less
sensitive
(negative co-operativity).
10.1.2 Ligand Binding and NMR
Many reversible biological 'transient' processes, such as signal transduction,
involve interactions with affinities weaker than 1 mM. Often macromolecules
interact using more than one binding surface. These 'polyvalent' interactions
can be quite tight, while the individual binding interfaces can be weak with mM
to mM K
D
values. NMR is a good tool for monitoring ligand-binding events
with affinities weaker than 1 mM. As such it is complementary to the two other
popular methods that monitor ligand binding: isothermal calorimetry (ITC)
and surface plasmon resonance (SPR, with the trade name Biacore), which
both perform best for binding that is tighter than 1 mM.
The effect of chemical exchange on the NMR signals is described by the
Bloch-McConnell equations
3,4
which for two-site exchange for a resonance
associated with the ligand read:
dM
x
dt
~v
L
M
y
{R
2
M
x
{p
L?PL
M
x
zp
PL?L
M
PL
x
dM
y
dt
~{v
L
M
x
{R
2
M
y
{p
L?PL
M
y
zp
PL?L
M
PL
y
ð
10
:
6
Þ
dM
PL
x
dt
~v
PL
M
P
y
{R
PL
M
P
x
{p
PL?L
M
P
x
zp
L?PL
M
x
2
dM
PL
y
dt
~{v
PL
M
P
x
{R
PL
M
P
y
{p
PL?L
M
P
y
zp
L?PL
M
PL
2
y
In these equations, M
x
and M
y
are the components of the coherences along
the rotating frame axes x and y, respectively, independently defined for the free
and bound ligand. v
L
and v
PL
are the resonance frequencies of the two sites,
and the R
2
values are the transverse relaxation times (linewidths). The rates
p
i?j
are the probabilities (in sec
21
) that species i changes into species j.