A structural perspective on the dynamics of biochemical systems. (Une perspective structurelle sur la dynamique des systèmes biochimiques)

In recent years Systems Biology has become a rich field of study, trying to encompass all the information that has become available thanks to the new high-throughput techniques of biologists. Fifteen years ago, a fundamental breakthrough was the publication of Kurt Kohn’s map of the cell cycle control in mammals. Its similarity with electronic circuits was crucial in both making it impossible for humans to comprehend fully, and in prompting the use of formal methods. Since then however, the networks built by biologists and modellers have continued growing bigger, filled with more and more mechanistic details, especially recently acquired post-transcriptional information, but lacking most of precise kinetic data. Because analysis techniques providing dynamical insights mostly rely on complete kinetic information, what was challenging for the human ten years ago is now a challenge even for computers, In this manuscript we will try to give an account of our work of the last twelve years, centered around the question of model. We will define more precisely what this object is, formally, and try to handle the challenges raised by the ever growing amount of data, and corresponding size of models developed in Systems Biology. Our main focus will be the links between the structure and dynamics of those models, seen as means to use several formal methods, like Constraint Programming, to reason on their dynamics. Because of the size issue we will also discuss the question of model reduction, and the related relationships between models, formalisms and interpretations. The discrete nature of the structure underlying a model might seem opposed to the continuous dynamics often associated via differential equations to that model. Nevertheless, we hope to demonstrate that the gap between those two views is quite artificial, and that recent results offer very promising perspectives to bridge it.