The modelling of complex biological systems does not benefit from the methods and tools that
exist for the development of technological products in software engineering. The main reason
for this is the impossibility of implementing a modular design: in biology, the introduction of
a new element in a previously validated model can drastically change its behaviour. Nevertheless, this thesis provides an incremental methodology, in order to design discrete models for
biology, which has some similarities to software spiral development model. The principal goal is to preserve the feasibility of proofs allowing to verify the non-regression at each enrichment.
Although the proposed method was developed within the framework of René Thomas’ formalism, it can be adapted to any other discrete modelling framework. It includes three distinct
phases: requirements analysis, model enrichment combined with validation by formal methods and finally a prediction phase. The substantial case study that anchors this work is a model
of metabolic regulation at different stages of progression in pancreatic ductal adenocarcinoma
(PDAC). In this work, we adopt an abstract modelling incremental approach, whose starting
point is an already consequent general model of eukaryotic metabolic regulation. Our method
allows us to enrich this initial model step by step to reach our aim, that is, a model covering the
evolution from the healthy cell to the aggressive cell through the non-aggressive cancer cell.
One has only little molecular a priori knowledge on the metabolic deregulation involved, and
the level of abstraction of this model is chosen to best guide biologists in their research and in
the choice of their working hypotheses.