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 inputoutput
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).

