Qualitative Modelling of genetic networks
using high level Petri nets
J.-P. Comet, H. Klaudel and S. Liauzu
LaMI UMR CNRS 8042, Université d'Evry Val d'Essonne
Boulevard F. Mitterrand
91025 Evry Cedex
Regulatory networks are found at the core of all biological functions
from bio-chemical pathways to gene regulation and cell communication
processes. Because of the complexity of the interweaving retroactions,
the overall behavior is difficult to grasp and the development of formal
methods is needed in order to confront the supposed properties of the
biological system to the model. We revisit here the tremendous work
of R. Thomas in term of high-level Petri nets.
It has been already shown that the boolean approach of R. Thomas can
be expressed with the formalism of standart Petri net. Here we show
that the previous approach but also the multi-valuated approach of
R. Thomas can be expressed with high level Petri nets. This formalism
allows us to unify the modelling of both approaches, to take advantage
of all results and tools in the field of high level Petri nets like
the model checking tool Maria and to prevent the explosion of the
number of places. Two modellings are passed in review.
The dynamical behavior of the system is based on the definition of a
certain number of biological parameters which often are unknown. The
analysis of functionality of circuits of the regulatory graph can
reduce the total number of sets of parameter values, which have to be
taken into account. The classical approach is then to generate all
Petri nets corresponding to all remaining sets of parameter values and
to confront each model to the available knowledge or hypothesis. By
introducing another place corresponding to the possible values of
parameters, it remains possible to incorporate all behaviors defined
by all possible parameter values, in the same high-level Petri net.
- In the first one each gene is represented by a specific place,
and the tokens in the places code for the abstract expression
of each gene. The unique transition allows the system to evolve:
each place is an input and an output of the unique transition.
The firing of the transition has to determine which kind of marking
is possible as a next state for the current situation.
- The second modelling is more compact since the unique place
abstracts the cell in which each token represents a specific gene
and its expression level. The firing of the unique transition
"reads" the current marking and generates a next one.