Biomedical Engineering Reference
In-Depth Information
Figure 10.12
Equilibrium concentrations as obtained after 5 s of kinetic simulations
as a function of total metal concentration. This simulation time is 50
times as long as is needed to reach equilibrium. [Cd]
free
is blue; [P] is
black; [Q] is red; [R] is green; [S] is purple. Simulation conditions: total
protein 4 mM; k
PQ
5 k
RS
5 k
int
5 3 6 10
5
M
21
s
21
; k
QP
5 k
SR
5 0.01
s
21
; k
PR
5k
QS
5 k
ext
510
7
M
21
s
21
; k
RP
5 k
SQ
5 10
3
s
21
, k
RQ
5 10
3
s
21
, k
QR
5 0.333 s
21
(corresponding to the equilibrium association
constants K
PQ
5 3 6 10
7
M
21
and K
PR
5 10
4
M
21
).
change the thermodynamics (all is balanced in Carnot cycles), or the NMR
linewidths (see below), it forms a realistic pathway for the binding Cd
2+
to the
internal site (discussed below).
The detailed-balanced equilibrium kinetic site-site exchange parameters
were inserted into five-site chemical exchange Bloch-McConnell equations
extended from eqn (10.29) with transition probabilities as defined in
Figure 10.13. The parameters chosen correspond to slow exchange for all
sites. The obtained FIDs were Fourier transformed yielding the spectra shown
in Figure 10.14. Figure 10.14 zooms in on the 'bound' signal (site b in species
Q)
Cd
2+
-to-tripeptide
as
a
function
of
the
ratio.
The
simulated
spectra
correspond
very
closely
to
the
experimental
NMR
data
for
site
(GrandL26AL30C)
3
.
The progressive broadening, consistent with the experimental data, is caused
by increasing lifetime broadening of site b in species Q, because it is converted
to site d in species S, with an increasing rate depending on the concentration of
free Cd
2+
:
p
BZ
~k
QP
zk
QR
zk
ext
Cd
½
eq
