13th International Conference on Membrane Computing - MTA Sztaki

B. Aman, G. Ciobanu
formalisms is established by defining a new class of Petri nets called Petri nets
with localities. This new class of Petri nets has been used to show how maximal
evolutions from membrane systems are faithfully reflected in the maximally concurrent
step sequence semantics of their corresponding Petri nets with localities.
In this paper, we present the syntax and semantics of mobile membranes with
objects on surface in Section 2, and in Section 3 we use this formalism to model
the LDL pathway. In order to be able to use a complex software called CPN
Tools, a translation of a system with a bounded number of mobile membranes
into colored Petri nets (described briefly in Section 4) is provided in Section 5.
The description of the LDL degradation obtained via the given translation is
presented in Section 6. The colored Petri nets software tools are used to analyze
automatically some behavioral properties. Conclusion and references end
the paper.
2 Mobile Membranes with Objects on Surface
To be able to model nondeterministic, spatial and dynamic biological processes,
we use a rule-based model of computation called mobile membranes [2]. The first
systems with mobile membranes were introduced in [11] as a particular class of
membrane computing [14], while mobile membranes were studied in detail in [3].
A specific feature of this formalism is given by the parallel application of rules;
this feature is inspired from biology, and it is not present in process calculi with
mobility that use interleaving semantics [1]. The parallel application of rules
depends on the available resources (i.e., elements of the left hand side of the
rules). The mobile membranes systems are defined by two features:
1. A spatial structure consisting of a hierarchy of membranes (which are either
disjoint or included) with multisets of objects on their surface; a membrane
without any other membrane inside is called elementary, while a nonelementary
membrane is called a composite membrane.
2. The biologically inspired rules describing the mobility of membranes inside
the structure: pinocytosis (engulfing zero external membranes), phagocytosis
(engulfing just one external membrane), and exocytosis (expelling the content
of a membrane outside the membrane where it is placed). Pinocytosis
and phagocytosis represent different types of endocytosis.
In terms of computation, we are working with membrane configurations. We
define the set M of membrane configurations (ranged by M, N, . . . ) by using
the free monoid O ∗ (ranged over by u, v, . . . ) generated by a finite alphabet O
of objects (ranged over by a, a, b, b, . . . ).
Definition 1. The set M(Π) of membrane configurations in a system Π of
mobile membranes with objects on their surfaces is defined inductively as follows:
• if w is a multiset over O, then [ ] w ∈ M(Π);
[ ] w is called an elementary membrane configuration;
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