Biomedical Engineering Reference
In-Depth Information
Table 10.3
Transition probabilities in the three-site exchange scheme for the
IP6-Hb system, based on the results in Table 10.2.
p 1f /s 21
p 1b /s 21
p 2f /s 21
p 2b /s 21
p 3f /s 21
p 3b /s 21
Ratio
2.0 6 10 7
2.0 6 10 7
7.5 6 10 9
1.0 6 10 4
7.5 6 10 5
0.25
1.0
2.0 6 10 7
2.0 6 10 7
5.0 6 10 9
1.0 6 10 4
5.0 6 10 5
0.50
1.0
2.0 6 10 7
2.0 6 10 7
2.5 6 10 9
1.0 6 10 4
2.5 6 10 5
0.75
1.0
2.0 6 10 7
2.0 6 10 7
1.4 6 10 7
1.0 6 10 4
1.4 6 10 3
1.00
1.0
1.8 6 10 7
2.0 6 10 7
7.5 6 10 4
8.8 6 10 3
1.25
7.5
1.0
1.6 6 10 7
2.0 6 10 7
3.6 6 10 4
7.8 6 10 3
1.50
3.6
1.0
1.4 6 10 7
2.0 6 10 7
2.3 6 10 4
6.9 6 10 3
1.75
2.3
1.0
1.2 6 10 7
2.0 6 10 7
1.6 6 10 4
6.2 6 10 3
2.00
1.6
1.0
8.3 6 10 6
2.0 6 10 7
7.1 6 10 3
4.1 6 10 3
7.1 6 10 21
3.00
1.0
4.7 6 10 6
2.0 6 10 7
3.1 6 10 3
2.4 6 10 3
3.1 6 10 21
5.00
1.0
2.2 6 10 6
2.0 6 10 7
1.2 6 10 3
1.1 6 10 3
1.2 6 10 21
10.0
1.0
In Table 10.2 we list the resulting equilibrium conditions for several
calculations. In Table 10.3 we show the corresponding transition probabilities
at the different equilibrium conditions. Table 10.3 shows that the transition
probabilities p 1f , p 1b , p 2f and p 2b are all larger than the chemical shift difference
of 20 Hz. p 3f and p 3b are small, but this is inconsequential, since the state IC
can be reached quickly through site S.
The situation is fast-intermediate exchange, with a single line per phosphate
group and resonance position
$ ~f I v I zf IS v IS zf IC v IC
ð 10 : 28 Þ
When choosing v IS to lie halfway between v I and v IC , we calculate from the
entries in Table 10.2 the results in Figure 10.7. The figure shows a fast-exchange
titration trajectory that closely resembles a simple two-site exchange for a high-
affinity system, in agreement with the experimental data in Figure 10.6.
In order to probe the effects of these exchange kinetics on the NMR
spectrum, we carried out a numerical integration of the Bloch-McConnell
equations:
2
3
M I
M IS
M IC
4
5
d
dt
~
ð 10 : 29 Þ
2
4
3
5
2
3
M I
M IS
M IC
iv I {R 2 {p If {p 3f
p 1b
p 3b
4
5
iv IS {R I 2 {p 2f {p 1b
p 1f
p 2b
iv IC {R I 2 {p 2b {p 3b
p 3f
p 2f
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