## Section: Scientific Foundations

### Systems biology: network modeling and analysis

Recent advances in functional genomics and in the study of complex diseases, such as cancer, immunodeficiencies, responses to infections, mitochondrial diseases, metabolic syndrome or aging, have shown the necessity of a new way of thinking in biology, which considers pathology and physiology as resulting from interactions between many processes at various scales. Systems biology emerged from this need. This scientific field addresses the study of genes (expression, evolution), protein interactions, biochemical reaction networks, cell populations and tissues in organisms considered as dynamical systems. It aims at studying the biological properties that result from the interaction of many components, investigating processes at different scales and achieving their integration.

Understanding will not arise from simulation alone (virtual cell or organism) but rather from the identification of relevant components for a given behavior and the reconstruction of the mechanisms involved. It concerns standard mathematical and physical tools, some borrowed from out-of-equilibrium thermodynamics and dynamical systems. New tools are also required. As coin by S. Brenner, complementary to bottom-up or top-down approaches, a middle-out strategy starting from the cell is likely to be efficient in the analysis of biological systems. Ultimately, injecting the systemic vision in the understanding of human physiopathology could lead to novel differential diagnosis and improve medical care [94] .

Cellular interactions' modeling is an old domain in biology, initiated by people interested in the dynamics of enzymes systems [88] . Models for transcriptional networks appeared as soon as gene interactions were discovered. The simplest static model consists in an oriented labeled graph, with labels + for activation or - for inhibition. Such graph representations are used to store known interactions in general databases. They are also the framework of Bayesian representations, used to infer gene networks from micro-array data, with the support of literature information [109] .

The **dynamical framework in systems biology** includes simulations and prediction of
behaviors. Models can be either qualitative or quantitative, as
reviewed in [74] , [69] , [93] . A first approach makes use of
continuous models: the concentrations of products are modeled by
continuous functions of time, governed by differential equations.
This framework allows one to state biological properties of networks,
eventually by using simulation software
[78] , [111] , [110] . The properties of
continuous models can be studied with convex analysis, linear and
non-linear control techniques
[85] , [98] , [61] . Stochastic
models transform reaction rates into probabilities and
concentrations into numbers of molecules, allowing to
understand how noise influences a system [89] . Finally,
in discrete models each component is assumed to have a small
number of qualitative states, and the regulatory interactions are
described by discrete functions [91] , [103] .
Piecewise linear differential models [75] , [80] try to build a bridge between continuous and discrete models.

These methods addresses fine dynamical properties such as the existence of attractors (limit cycles or steady states) and the behavior of these with respect to changes in the parameters [107] , [69] . However, they need accurate data on chemical reactions kinetics or qualitative information. These data are scarcely available. Furthermore, these methods are also computationally demanding and their practical use is restricted in practice to a small number of variables.

**Model identification** addresses a different objective, that is, to
build or update a model consistently with respect to a set of data.
When large amounts of data are available, Bayesian networks [79] or
kernels [113] have to be used.
Another efficient approach formalizes a priori knowledge as partially
specified models. Fitting models to data is obtained by means of various
techniques [62] , depending on the class of models, that can be discrete [100] ,
continuous [93]
or hybrid [67] . Qualitative reasoning, hybrid system, constraint programming
or model-checking allow either to identify
a subset of active processes explaining experimental time-series data or
to correct the models and infer some parameters from
data [63] , [68] .
Identification methods are limited to a few dozen components. Model
correction or parameter regression can cope with up to hundreds of
products [68] , [62] provided that the biomolecular mechanisms
and supplied kinetic data are accurate enough.

**Reasoning on models**
Model-based identification can hardly cope with
errors and variability that commonly
affect measured expression levels in DNA microarrays. Moreover, time
series data are absent in many situations, meaning that they inform
more on steady state shifts under perturbations than on the dynamics of the system.

Testing and refining models become central issues in such a situation cumulating incomplete knowledge and partial observations. Our own work addresses these questions using formal methods of constraint resolutions. Our purpose is to study large-scale incomplete networks with efficient qualitative equation solvers. Diagnosis of incoherent parts of the networks use specific consistency rules depending on interactions types. Then, specific dynamical modeling procedures can be applied on these subgraphs to exhibit new biological insights.

**Dynamical modeling, signalling and cancer**
Signalling mechanisms are essential in biological systems and represents a major research topic. At the cellular level, signalling networks allow detection and response to changes of the microenvironment and control various biological processes such as mobility, adhesion, differentiation, proliferation and apoptosis. The conservation during evolution of many signalling pathways and their implication in numerous pathologies such as cancer underlines the importance of these pathways for the life of the cell.

Research on molecular targets for cancer therapy relies to an increasing extent on understanding complex dynamical mechanisms, non-linear in time and space. Systems biology becomes a key appraoch in the understanding of such dynamical behaviours of cells from interaction between their components.