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Number of hours
Lectures : 18.0
ECTS : 1.75
In Systems Biology, and more generally in the study of complex systems, the notion of network is now prominent. This class pertains to the modeling of the dynamics of biological networks, in particular genetic regulatory networks and reaction networks. Several mathematical formalisms will be put to use, together with methods from Computer Sciences (such as model-checking for the verification of properties). Concrete modeling examples will be studied (e.g. the control of the cell cycle, the segmentation of an insect embryo) to illustrate the application of these techniques to Systems Biology.
The objectives are: to give some thoughts to the problems posed by the modeling of complex systems (eg the choice of an abstraction level); to get acquainted with different versions of hte concept of robustness used in the field; to learn to use different formalisms and to choose the most adequate in view of the knowledge and data available; to learn how to use biological data; to realize that any model has a limited domain of validity; and finally to learn about the challenges of the field, such as the design of combinatorial therapies. Contact Eric FANCHON
Reminder of dynamical systems and bifurcations. Study of a differential model of the control of the cell cycle. Model reduction based of the existence of several characteristic timescales. Formalisms of discrete networks, Boolean and multivalued. Study of a particular gene regulatory network. Inference of parameters. Application of model-checking and boolean satisfiability. Systems with many attractors. Notions of robustness. Relationship between structure and dynamics. Reminder on stochastic processes. Gillespie algorithm. Stochasticity in gene expression. Questions related to the evolution of networks.
Prérequis Basic knowledge of dynamical systems and bifurcations, and Basic knowledge of biology.