13th International Conference on Membrane Computing - MTA Sztaki

B. Aman, G. Ciobanu
to reiterate the entire process. Applying CPN Tools on this extended system, we
obtain the following output file:
Home Markings: All
Dead Markings: None;
Dead Transition Instances: None Live Transition Instances: All
Fairness Properties: All,
meaning that from any reachable configuration M i we can always reach any
configuration M j (home marking), the computation never stops (dead marking),
and so there are infinite occurrence sequences.
7 Conclusion
In this paper we continue the research line started in [4], and present a new
connection between the systems of mobile membranes and colored Petri nets.
The novelty of this formal translation, with respect to the one presented in [4],
is that the number of membranes in the system could change during evolution.
The systems of mobile membranes with objects on surface used in this translation
are bounded to a given number of membranes.
The structure of the parallel computations of the mobile membranes is faithfully
reflected by the parallel semantics of the corresponding colored Petri nets.
In mobile membranes, the parallel way of using the rules means that in each
step we apply a maximal set of rules, namely a set of rules such that no further
rule can be added to this set. Since we deal with mobility, each object and each
membrane can be used only once in the rules applied in a step.
We have considered the low-density lipoprotein degradation pathway, and
described this biological process by using the mobile membranes with objects
on membranes. The translation of mobile membranes into colored Petri nets
allows to obtain a description of the biological process into colored Petri net, and
then use a software called CPN Tools in analyzing several behavioral properties:
reachability, boundedness, liveness, fairness. By encoding biological systems in
this way, many interesting biological questions can get precise answers. Using
CPN Tools, several (potentially infinite) behaviors can be investigated, a fact
that is interesting from a biological point of view. Finally, we have provided a
new link between biology, membrane systems and Petri nets which is, hopefully,
useful for all these areas.
Acknowledgements
The work was supported by a grant of the Romanian National Authority for Scientific
Research CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0919.
The work of Bogdan Aman was also supported by POSDRU/89/1.5/S/49944.
References
1. B. Aman, G. Ciobanu. Mobility in Process Calculi and Natural Computing.
Springer, 2011.
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