Biomedical Engineering Reference
In-Depth Information
Figure 5.5
A five-state model.
the doubly occupied state opens very much more quickly and closes somewhat more
slowly than the singly occupied state. Take the agonist concentration as
x
A
=
100
nM
.
There is one more rate constant to fix, the dissociation rate
k
−
2
from the doubly
occupied open state. To obtain this we appeal to the principle of
microscopic re-
versibility
. This states that, in the absence of a source of energy, a system will move
to thermodynamic equilibrium in which each individual reaction will proceed, on
average, at the same rate in each direction. In particular, if there is a cycle in the re-
action, there can be no tendency to move round the cycle in one particular direction.
In the model under consideration the states 1
4 form a cycle and the assumption
of microscopic reversibility implies that the product of transition rates around the
cycle are the same in both directions, i.e.,
k
+
2
x
A
,
2
,
3
,
2
2
k
−
2
. Then,
=
α
2
2
k
−
2
1
k
+
2
x
A
1
with the constants previously defined,
k
−
2
=
k
+
2
(
α
/
β
)(
k
−
2
/
k
+
2
)(
β
/
α
)=
1
/
3.
2
2
1
1
With these values the transition rate matrix becomes
$
%
.
−
3050
50
0
3000
0
667 .
0
.
667
−
500
.
500
0
0
.
······
······
······
······ ······
Q
=
(5.4)
.
0
15000
−
19000
4000
0
.
15
0
0
−
2065 2000
.
0
0
0
0
−
10
The reason for partitioning of the above matrix will be explained later. As men-
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