Biomedical Engineering Reference
In-Depth Information
Figure 7.51
Functionalization of the surface of capture with ligands.
Modeling Displacement Reactions
If the technology of displacement reactions is now well known and biochips using
this type of reactions are currently used [ ], the modeling of such reactions is still
under development.
The model presented here is based on the analogy with the competition term in
the Lotka-Volterra equations [34]. First suppose that the analogs and the targets are
together in solution and consider the Langmuir equations for each antigen
A
*
and
A
(
A
*
refers to the target and
A
the analog).
d
G
1
=
k c
(
G - G - G -
)
k
G
1 1
0
1
2
-
1 1
d t
(7.94)
d
G
2
=
k c
(
G - G - G -
)
k
G
2 2
0
1
2
-
2 2
d t
The first equation in (7.94) considers that the analog
A
has the kinetics coefficient
k
1
and
k
-
1
and can bind to ligands in a concentration of (G
0
- G
1
- G
2
). The second
equation has the same meaning for the targets this time. In such an approach there is
no displacement because each type of molecule binds to the ligands independently.
In reality, because the analogs are immobilized first, and the targets arrive after
washing of the channel, the Langmuir system of equations should be
d
G
1
= -
k
G
-
1 1
d t
(7.95)
d
G
2
=
k c
(
G - G - G -
)
k
G
2 2
0
1
2
-
2 2
d t
Figure 7.52
Saturation of the functionalized sites with analogs tagged with a marker.
