13th International Conference on Membrane Computing - MTA Sztaki

B. Aman, G. Ciobanu
The four transitions drawn as rectangles represent the events that can take
place in the system. The names of the transitions are written inside the rectangles;
these names have no formal meaning, but they are important for the
readability of the model. In Figure 3 the names of the transitions are step2,
step3, step4 and step5 indicating that each of these transitions simulates the
corresponding steps of the LDL degradation pathway described in Figure 1.
A transition with double-line border is a substitution transition; each of them
has a substitution tag positioned next to it. The substitution tag contains the
name of a submodule which is related to the substitution transition. Intuitively,
this means that the submodule presents a more detailed view of the behavior
represented by the substitution transition, and it is particularly useful when
modeling large systems. The input places of substitution transitions are called
input sockets, while the output places are called output sockets. The socket places
of a substitution transition constitute the interface of the substitution transition.
To obtain a complete hierarchical model, it must be specified how the interface
of each submodule is related to the interface of its substitution transition. This
is done by means of a port-socket relation which links the port places of the
submodule to the socket places of the substitution transition. Input ports are
related to input sockets, output ports to output sockets, and input/output ports
to input/output sockets.
Fig. 4. Step 4 Transition
For instance, behind the substitution transition step4 is another colored Petri
net presented in Figure 4. The substitution transitions appearing in this colored
Petri net are:
• the substitution transition phago1-step4 simulates the mobile membrane
rule 5 from the description of the LDL degradation pathway;
• the substitution transition exo1-step4 simulates the mobile membrane rule 6
from the description of the LDL degradation pathway;
• the substitution transition pino-step4 simulates the mobile membrane rule 7
from the description of the LDL degradation pathway;
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