Biology Reference
In-Depth Information
Fig. 2. A self-modified Petrinet for the biocatalytic reaction of lactose.
MODELING OF BIOCHEMICAL NETWORKS
Self-modified Petrinets
The main feature of metabolic processes is that the concentration of metabolites will influence the
reaction activity of biochemical processes. Therefore, the actual concentration of any metabolite is
an important component of the model. This can be done by the extension of the place-transition net
including the self-modified component, which was at first defined by Valk [23]. The main feature of this
formalization is that each identifier of any place can be used as a parameter of any arrow weight formula.
Example 1:
The concentration of the enzyme is important for the biocatalytic process. Using self-
modification networks the biocatalytic reaction of lactose into glucose and galactose can be described
as follows: each unit lactose will produce one unit of galactose and one unit of glucose. The reaction
will only be activated if the enzyme ß-galactosidase is available. Therefore, the concentration of ß-
galactosidase will be used. The arrow weight from the place ß-galactosidase to the transition reaction
will be ß-galactosidase. This set will be used and produced.
Based on these ideas we give a formal definition of self-modified Petrinets and self-modified Petrinets
with capacity.
Definition: N
=
(P,T,F,V
s
,m
0
) is called
self-modified Petrinet
,iff
-
(P,T,F) is a net,
N
with P
N
:
=
P
∪
N,
-
m
0
start configuration.
Definition: N = (P, T, F, K
u
,K
o
,V
s
,m
0
) is called
self-modified Petrinet with capacity
,iff
-
-
V
s
:P
×
P
N
×
T
→
(P,T,F,V
s
,m
0
) is a self-modified net,
-
K
u
:P
→
N
is the minimal capacity of each place,
-
K
o
:P
→
N
is the maximal capacity of each place,
-
m
o
:P
→
N
a start mark with K
u
(p)
m
o
(p)
K
o
(p).
