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Fig. 1. Proposed quorum sensing system in Aliivibrio salmonicida *.
way. Furthermore, concurrent systems can be automatically determined for Petri nets, although some
of the systems are difficult and expensive to determine [Petri and Reisig, 2008]. For the modeling and
simulation of cell-to-cell communication processes we make use of Petri nets. The various modeling
possibilities and analytic power offer a well-developed basis for the description of chemical processes
and, in addition, a mathematical theory for process analysis.
A Petri net PN = ( P , T , F , W , m 0 ) consists of a finite set of transitions ( T ) and a finite set of places
( P ), which are connected by directed arcs ( F ).
F
( P
×
T ) ( T
×
P ) is a finite set of arcs. The
triple ( P , T , F ) is called net and W
N ). Regarding the graphical
representation, places are drawn as circles, transitions are drawn as rectangles and arcs are drawn as
directed arrows. Places may contain tokens, which are drawn as black dots. In the beginning, the start
configuration, which is called m 0 , will assign tokens to places. The definition of the basic Petri net is
given in [Reisig, 1982]. The first application of Petri nets for modeling simple biochemical reactions
was published by Reddy et al.
is called weight function ( W :
F
[Reddy et al. , 1993]. The idea presented in that paper was that Petri nets
*A colored version of the figure/chart is available at In Silico Biol. 10 , 0003 < http://www.bioinfo.de/isb/2010/10/0003/ > , 1
Feb uary 2010.
r
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