Biology Reference
In-Depth Information
3.9.1 Modeling Strategy
The modeling strategy consisted in deriving equations that enabled the calculation
of expected radiolabel incorporation from a precursor P into a compound B, when
“B” is formed exclusively from an immediate precursor “A”, via pathway I
(Fig.
3.1
).
It was conjectured that a comparison of expected radiolabel incorporations into
“B”, that are derived by calculation, with experimentally determined incorporations,
should reveal, whether compound B is formed exclusively from compound A or not.
For example, if compound B is formed exclusively from compound A, then within
the range of experimental error, the theoretical (i.e. calculated) and experimental
radiolabel incorporations into “B” should be identical or reasonably similar (Pathway
IinFig.
3.1
). On the other hand, if compound B is not formed from compound
A (pathway III, in Fig.
3.1
) or is found to be partially formed from “A” via pathway II
(Fig.
3.1
), then the calculated and experimental radiolabel incorporations into “B”"
should be different. In that latter case, another equation is derived that enables the
evaluation of the partial contribution of compound A to the formation of compound B
via pathway II (Fig.
3.1
). The derivations of these equations are described below.
B. Relationships Between the Specific Radioactivity of Compound A and Label
Incorporation into Compound B, if Compound B is formed Exclusively from
Compound A During Any Time Interval t
1
-t
2
Let a radiolabelled precursor P and radiolabeled products A and B be related by the
precursor-product relationship depicted in Fig.
3.1a
. Furthermore, let:
Y
A1
,Y
A2
,Y
A3
...
represent the specific radioactivity of compound A at the end of
time intervals
t
0
-t
1
,t
1
-t
2
, and
t
2
-t
3
respectively.
Q
B1
,Q
B2
,Q
B3
...
represent the amount of radiolabel incorporated into compound
B by the end of time intervals
t
0
t
1
;
t
1
t
2
;
and
t
2
t
3
(3.84)
Δ
Β
3
represent the amount of compound B synthesized by the end of
time intervals
t
0
-t
1
,
t
1
-t
2
, and
t
2
-t
3
.
If the formation and accumulation of radio labeled compound B from radio
labeled compound A during any time interval
t
1
to
t
2
,
is a linear function of time,
then the accumulation of compound B can be described by the function
Δ
Β
1
,
Δ
Β
2
,
B
¼
at
b
;
(3.85)
where “
a
” is the rate constant and “
b
” the intercept on the ordinate axis. The rate of
change of
B
with respect to time is then given by
d
B
=
d
t
¼
a
(3.86)
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