Biomedical Engineering Reference
In-Depth Information
Eqns (10.12) and (10.13) can be readily inserted into a spreadsheet such as
Microsoft Excel, providing a tool valid for illustrating all exchange regimes.
The exchange equations lead to three limiting cases for the sites on speciesL
or PL:
For slow exchange, p
L?PL
zp
PL?L
vv v
PL
{v
j j
, there are two Lorentzian
lines with positions, intensity and widths given for L by
f
v
L
g
ex
~v
L
f
I
L
g
ex
~f
L
I
f
R
2
=
p
g
ex
~R
2
=
pzp
L?PL
=
p
ð
10
:
14
Þ
with analogous equations for PL.
For fast exchange, p
L?PL
zp
PL?L
ww v
L
{v
PL
j
j
, there is one Lorentzian
line with position, intensity and width given by
f
v
L
g
ex
~f
L
v
L
zf
PL
v
PL
f
I
g
ex
~I
ð
10
:
15
Þ
"
#,
(v
L
{v
PL
)
2
p
L?PL
zp
PL?L
f
R
2
=
p
g
ex
~ f
L
R
2
zf
PL
R
P
2
zf
L
f
PL
p
For intermediate exchange, p
L?PL
zp
PL?L
& v
L
{v
PL
j
j
, there is one line
with
position
f
L
v
L
zf
PL
v
PL
,
with
a
complicated
lineshape
given
by
eqn
(10.12), and a width that can be as broad as v
L
{v
PL
j
j=
p. Only a plot of eqn
(10.12) will yield insight in this situation.
For intermediate slow exchange, p
L?PL
zp
PL?L
v v
L
{v
P
j j
there are two
excessively broadened lines, which are slightly shifted towards each other. Also
here, only a plot of the equations will yield insight in this situation.
Multi-site exchange situations are straightforward extensions of the coupled
differential equations, with the kinetic constants chosen to suit the particular
model of interest, e.g.,
2
4
3
5
M
A
M
B
M
C
d
dt
~
ð
10
:
16
Þ
2
4
3
5
2
4
3
5
M
A
M
B
M
C
iv
A
{R
2
{p
AB
{p
AC
p
BA
p
CA
iv
B
{R
2
{p
BA
{p
BC
p
AB
p
CB
iv
C
{R
2
{p
CA
{p
CB
p
AC
p
BC
