Chemistry Reference
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Fig. 9.4
Equilibrium concentrations for (free) BiP and reaction products BiP-ERjX (X = 1,2,3,5,7)
as a function of the initial concentration of BiP as calculated numerically with the reaction equa-
tions, shown below, and using the experimentally determined rate constants k
a
and k
d
and initial
concentrations [ERjX] in rough microsomes from canine pancreas (Table
9.2
). The time evolution
of the concentrations is then given by a coupled set of ordinary differential equations:
d
dt
7
{
}
[
]
=
∑
[
]
−
[
] [
]
BiP
k
()
X
BiP ERjXkBiP
−
()
X
·
ERjX
,
d
a
X
=
1
and
d
dt
[
]
=
[
]
−
[
] [
]
ER
jX k iP ERjXkBiP
()
X
−
()
X
·
ERjX
,
d
a
d
dt
[
]
=−
[
]
+
[
] [
]
BiP ERjXk
−
(
X
)
X
BiP ERjXkBiP
−
(
)
·
ERjX
,
d
a
where [BiP], [ERjX], and [BiP-ERjX] denote the concentrations of BiP, ERjX (X = 1,2,…,7), and
[BiP-ERjX], respectively. Due to the lack of data we set [ERj6] and [BiP-ERj6] constant to zero.
Using the measured values for the initial concentrations [ERjX](t = 0) and the rate constants k
a
and
k
d
from Table
9.1
we solved the above differential equations numerically for various initial con-
centrations [BiP](t = 0) and zero initial concentrations of the reaction products [BiP-ERjX](t = 0).
In Fig.
9.1
we show the results of the stationary (equilibrium) concentrations of BiP and the reac-
tion products, [BiP]
eq
and [BiP-ERjX]
eq
, respectively, as a function of the initial BiP concentration
[BiP](t = 0)—which is equal to the total BiP concentration [BiP]
total
, since [BiP-ERjX](t = 0) is zero
for X = 1,…7
In Fig.
9.4
, we have modelled the equlibrium concentrations of free BiP and
complexes of BiP with its co-chaperones for canine pancreatic microsomes, based
on the determined concentrations of the various proteins and the rate constants for
their interacttion with BiP (Table
9.2
). The complexes are formed transiently in or-
der to stimulate the ATPase activity of BiP, thus creating the form of BiP with high
substrate affinity. Typically, the ER lumenal concentrations of BiP are in the mil-
limolar range and similar to the total concentration of ERjs (Weitzmann et al.
2007
).
The model illustrates that under normal conditions there is enough BiP available for
interaction with all ERjs and that under conditions of UPR induction, where BiP and
ERj3 through ERj6 are over-produced, BiP becomes limiting for ERj2, thus, selec-
tively preventing import of additional precursor polypeptides. This can be deduced
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