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Fig. 5. Petrinet representation of the biocatalytic reaction using self-modified arcs.
the inhibitor. F and H are elements of the arrow weight description. Therefore, the Petrinet represents
self-modified arrows. The reaction t produces the product RP using three units of S 1 and four units
of S 2 . These values are multiplied with a factor, that represents the actual concentration of activators,
inhibitors, and the actual configuration. For every place capacity values are defined. These values signal
concentration intervals, which describe the correct flux of the metabolism.
Biocatalytic reaction
For the simulation of the flux of biochemical reactions our model has to be able to represent the
concentrations of the simulated metabolites. Using our formalization of self-modified Petrinets these
features are available. The identifier of any place, which represents the enzyme, can be used as a parameter
inside any definition of an arrow weight. Therefore, our model is able to simulate biocatalytic reactions
using the theory of Petrinets. The transitions are biochemical reactions, which will not consume the
enzyme, and the places are metabolites of these reactions. The formal description of a simple biocatalytic
reaction can be given:
P = {
Substance, Enzyme, Product
}
}
F = { ( Substance, Reaction ), ( Enzyme, Reaction ), ( Reaction, Enzyme ), ( Reaction, Product ) }
Regarding this process, Reaction is the catalysed transition of one unit of the Substance into two units
of the Product . The arrow weight can be defined:
V( Substance, Reaction )=1
V( Enzyme, Reaction )= Enzyme
V( Reaction, Reaction )= Enzyme
V( Reaction, Product )=2
The flexible simulation will use functions as:
V( Substance, Reaction )=1* Enzyme
V( Reaction, Product )=2* Enzyme
T = {
Reaction
Gene regulation
With regard to gene regulation processes, we have to distinguish positive and negative control. Both
regulation processes can be either inducible or repressible. Regarding the positive control, we know that
the activator will initiate the transcription process. Regarding the inducible positive control, an effector
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