13th International Conference on Membrane Computing - MTA Sztaki

<strong>13th</strong> <strong>International</strong> <strong>Conference</strong> on Membrane Computing, CMC13,
Budapest, Hungary, August 28 - 31, 2012. Proceedings, pages 125 - 141.
Mobile Membranes with Objects on Surface
as Colored Petri Nets
Bogdan Aman 1,2 and Gabriel Ciobanu 1,2
1 “A.I.Cuza” University of Iaşi
2 Romanian Academy, Institute of Computer Science
Blvd. Carol I no.8, 700505 Iaşi, Romania
bogdan.aman@gmail.com, gabriel@info.uaic.ro
Abstract. Mobile membranes with objects on surface represent a rulebased
formalism involving parallelism and mobility. We use this class of
mobile membranes to model the low-density lipoprotein degradation. A
translation of this formalism into colored Petri nets is provided in order
to analyze, using CPN Tools, some important properties of mobile membranes:
reachability, boundedness, liveness, fairness. In order to show
how this translation works, we translate the model of the low-density
lipoprotein degradation using mobile membranes into colored Petri nets.
1 Introduction
Formal models are used for many purposes, and each purpose influences the
degree of abstraction and detail. If we provide a greater detail, the number of
systems to which our model applies will decrease. A formal model should have
three properties, and each of these properties trades off against the other two [12]:
generality: the number of systems and situations to which the model correctly
applies, realism: the degree to which the model mimics the real world, power
and precision: collection of revealed properties, and the accuracy of the model
predictions.
In this paper we use two formalisms: mobile membranes (realism, being inspired
by cell biology) and colored Petri nets (power and precision provided
by complex software tools). A relation can be established between these two
formalisms by providing an encoding of mobile membranes into colored Petri
nets. By considering the endocytic pathway for low-density lipoprotein degradation,
we show how mobile membranes can be used to model such a biological
phenomenon, while colored Petri nets can be used to analyze and verify automatically
some behavioral properties of this pathway. The endocytic pathway for
low-density lipoprotein (LDL) degradation has been modeled before using other
formalisms (e.g., bioambients [15]). However, none of the previous descriptions
of the pathway is not translated into a formalism having software tools able to
check automatically some complex behavioral properties.
The first connections between membrane systems and Petri nets are presented
in [6] and [16]. In [10], a direct structural relationship between these two
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