アブストラクト
| Date | October 23, 2006 |
| Speaker | Dr. Ovidiu Radulescu, Universite de Rennes 1 |
| Title | Complex biological systems : hierarchical models, robustness, and qualitative modeling. |
| Abstract | 1) Hierarchical models and robustness of complex biological systems
We present mathematical methods allowing to identify modules and hierarchies with several levels of complexity in biological systems. These methods are based either on the properties of the input-output characteristic of the modules or on global properties of the dynamics such as the distribution of timescales or the stratification of attractors with variable dimension. We also discuss the consequences of the hierarchical structure on the robustness of biological processes. Stratified attractors lead to Waddington's type canalization effects. Successive application of the many to one mapping relating parameters of different levels in an hierarchy of models (analogue to the renormalization operation from statistical mechanics) leads to concentration and robustness of those properties that are common to many levels of complexity. Examples such as the response of the transcription factor NFkB to signalling, and the segmentation patterns in the development of Drosophila are used as illustrations of the theoretical ideas. 2) New qualitative approaches in molecular biology We introduce a mathematical framework that allows to test the compatibility between differential data and knowledge on genetic and metabolic interactions. Within this framework, a behavioral model is represented by a labeled oriented interaction graph; its predictions can be compared to experimental data. The comparison is qualitative and relies on a a system of qualitative equations derived from the interaction graph. The system is solved by an efficient representation as a polynomial equation on a finite field. This approach can be used to identify incompatibilities between model and data, describe functioning of networks in terms of balances and competitions, perform experiment design. The qualitative approach formalizes the biologist's intuition in a simple mathematical way; it has the great advantage of being automatized and thus applicable to large networks (concerning scalability, networks of hundreds of nodes are solved within minutes). |