Biomedical Engineering Reference
In-Depth Information
receptor CAR1 has two distinct states [3]. In this model, schematically repre-
sented in Figure 3.3, cAMP can bind both to an activated form of the receptor
(R) and a desensitized form (D). Upon stimulation, cAMP can bind to both
R (which activates ACA resulting in cAMP production), and to D (which is
unable to activate ACA). Both bound and unbound R can be converted into
the bound and unbound D, respectively, with the conversion thought off as a
phosphorylation step. The produced cAMP is secreted into extracellular space
and its degraded by both internal and external phosphodiesterases.
Figure 3.3.
A schematic representation of the MG model. cAMP can bind to both
the desensitized form (D) and the active form of the receptor (R), which can activate
ACA (C). Activated ACA can generate cAMP, using ATP as a substrate, and the
resulting internal cAMP gets secreted to the extracellular space.
The MG model includes a nonlinearity via the requirement that two active
receptor complexes bind to ACA before it gets activated. This is one of the
weaknesses of the model, as will be mentioned later.
After casting all the reaction steps into ordinary differential equations, the
MG model consists of nine equations. Fortunately, this number can be reduced
significantly by realizing that some processes occur on a much smaller time
scale than others. Then, via singular perturbation methods, the MG model
can be reduced to only four equations. One of these is describing the ATP
concentration, and when examining the dynamical behavior of this concentra-
tion one realizes that it is safe to assume that it is constant. The MG model
thus reduces to the following three variable model
d
ρ
T
d
t
=
−
f
1
(
γ
)
ρ
T
+
f
2
(
γ
)(1
−
ρ
T
)
d
β
d
t
=
qφ
(
ρ
T
,γ,α
)
−
(
k
i
+
k
t
)
β
d
γ
d
t
=
k
t
β/h
−
k
e
γ
(3.1)
