Biology Reference
In-Depth Information
To distinguish the 'normal'
PPP
path (1) from the new reaction path (2) we have to introduce new
token-colors, G
and H
say, for (2). With exception of
l
2', the processing of G
and H
is identical to
that of G and H. Therefore in the
PPP
-branch, the token color instances (identifiers) are replaced by the
variables
x
(for G or G
)
and
y
(for H or H
)
, and - a technicality - appropriate guards are attributed
to the reactions
r
1to
r
4. Finally, because the molecules moved onto F6P by the glycolysis resp. the
'normal'
PPP
are C resp. H, the reaction
l
2' may be enabled only for H
-molecules. Hence, the arc
pointing to
l
2' gets the label H
and the reaction
l
3 gets the guard [
x<>H
].
This leads to
P
∗
in Fig. 4 which is appropriate both for computing T-invariants and for simulation
because all unreasonable processes and cyclic loops have been excluded.
Looking for T-invariants which describe the feasible processes in the net we stay, for a moment, with
rev
. Clearly, for each reversible reaction
t
and the reverse reaction
t
, the vector [(
t
, 1), (
t
, 1)] is a
T-invariant. But, these T-invariants lack a sensible biochemical. For this reason all reverse reactions
except
l
2' have been omitted at the end of section “Models of the glycolysis and pentose phosphate
pathway”. On the other hand, we observe that
l
2' gives rise to a process that is different from both the
GP
and the
PPP
, namely the gluconeogenesis. The tokens of that extra process got the identifiers G
and
H
, leading to the net model
P
∗
.
As with the S-vectors, also the T-vectors shall be established stepwise, i.e., not automatically but
systematically. Apart from being able to see, from the
effects
computed at each step, the weight factor(s)
of the transition(s) to be added successively to the T-vector, there is still another advantage of this
approach. If we proceed along the causal chain of transitions, i. e., at each step selecting a subsequent
transition which is enabled, we can compile knowledge about the amount of molecules which are needed
in course of
the run from Gluc to Lac and which have to be restored later during the run or after its end.
This information is not provided by the effect of the complete T-vector. It only shows the
overall
effect
of the vector.
When looking for the possible processes in the
GP
/
PPP
system
P
∗
we soon find out that there are (at
least) three sorts of processes (modes) that can be run independently from each other. Therefore, we can
attribute to each of them a characteristic parameter by which the weighted vector elements are multiplied
additionally, namely
-
gly
for the glycolysis pathway,
-
hex
for the pentose (or hexose mono-) phosphate pathway, and
-
rev
for the pathway including the reverse reaction
l
2'.
During the stepwise construction of the T-vector(s) we gather, on the one hand, information about those
molecules that are needed at the beginning or in the course of a run to reach its end at Lac.
P
These
molecules and their amounts are:
The final result of the construction is the complete parameterized T-vector.
5
τ
=[(
l
1, [(1,
gly
'(x
C)), (1,
hex
'(x
G)),
G
))]),
(2,
hex
'(x
H)), (1,
rev
'(x
(
l
2, [ (1,
gly
'( )) ]),
5
Adopting the conventions of the package SY in a simplified version, T-vectors are written as lists of pairs (transition name,
list of weighted substitutions). A weighted substitution consists of an integer weight, followed by an integer parameter, a
multiplication sign “
'
” and a substitution in parentheses ( ). A substitution, represented by “ ”, indicates which variable(s) of
the arc labels have to be substituted by which color(s). If the arc labels are constant colors the don't-care symbol (
) is used.
The effect of a T-vector
τ
is presented as a list of constructs s: lico(CS), where lico(CS) denotes a linear combination of tokens
that has to be added to (or subtracted from) place s to make
τ
a T-invariant.
