Introduction

The last decade witnessed a strong development and an institutional recognition of a long time marginal approach of research in Life Science now known as System Biology .30>35 This domain, also called Integrative Biology or Holistic Biology, aims at the understanding of biological structures and behaviors on a larger scale than the range of individual molecules and interactions of classical molecular biology. Different from the mainstream reductionist approach pursued during the last 50 years, System Biology de velops a constructivist approach of molecular cell biology in line with the ideas on synergetics and complexity that emerged in the 70s' and 80s'. Its fundamental goal is to understand how the observed physiological properties of the living cell arise from the combined, integrated, activity of the elementary components.

Systems-level approaches in biology have a long history,34'51'63 but until recently limited available data and painstaking experimental resources limited their range of application. The advent during the last decade of high-throughput technologies in molecular biology drastically changed this situation. Whole genomes are now deciphered, proteins increasingly characterized as well as the interactions between them and genes. The quantity of data produced each day gives the impression that constructivist systemic approaches are now possible in biology thus opening the way to new subjects unreachable before and to significant advances in biomedical research. For instance, the integration of numerous and diverse facts in the field of scientific analysis is expected to help understanding multifactorial diseases that depend on combinations of several causes and/or environmental conditions impossible to grasp in isolation.29 As genetic and molecular data becomes increasingly available, the grand challenge will be to assemble all the pieces into a working model of a living, responding, reproducing cell; a model that gives a reliable account of how the physiological properties of a cell derive from its underlying molecular machinery.

One of the principal characteristics in the recent Systems Biology literature is the spread of the interaction network paradigm. Molecular biologists have been widely successful in identifying the molecular components of the chains of chemical reactions and regulatory systems within living cells. These components have traditionally been painstakingly pieced together into schematic "wiring" diagrams that represent a synthesis of the knowledge of the studied system. Biochemistry, for instance, commonly represents on large charts the set of all the biochemical metabolic reactions known in cells (the Boehringer poster20 being a popular example). This procedure is now extended and systematized by Systems Biology for the representation of information stored in genomic databases. Compared to the generic Boehringer chart, it is now possible for example to generate graphs that are specifically tuned to the metabolism of given organisms of interest.66 Some of the key questions in genomics ask which genes are expressed in given cells at certain times and conditions. How does gene expression differ from cell to cell in multicellular organisms? Which proteins are affected when one gene is mutated or silenced? By displaying chains of dependencies, macro-molecular interaction networks are expected to play a major role in answering such questions. This picture is complemented by the generalization of genome scale surveys of gene activity with techniques such as DNA microarrays53 that simultaneously measure the expression levels of all the genes of an organism. Although subject to numerous experimental artifacts, this can be interpreted as the measurement of a state "vector" of the genetic activity that is occurring on the gene interaction. Figure 9.1 illustrates how gene interaction networks and biological sampling are expected to interact and contribute to elucidate biological functions.

From a theoretical standpoint, the questions on the behavior of macro-molecular network dynamics and the required methodology of investigation do not fundamentally differ from other fields of applications of dynamic systems such as population genetics, ecological and trophic networks.33 The goal is basically to build dynamic models reproducing the temporal evolution of proteins or other bio-molecules, and to analyze the dynamic regimes and sensitivity against parameter changes. Even in the case of biochemical networks these questions are not new, and have already been addressed, for example, in theoretical studies of enzyme kinetics,24'44 or in models of biological pattern formation.

Different kinds of investigations are possible on the networks deduced from genomic data depending on the scale considered. First we present some studies centered on the network structure - the topology - that aim to discover fundamental principles in the organization of groups of interacting genes. We shall then briefly review the principal modeling approaches of genetic networks. The type of modeling to be used depends on the biological question and the knowledge available. These approaches have opened the way to several theoretical attempts to rationalize the link between structure and dynamics of the networks. We finally conclude by discussing some of the difficulties of modeling systemic approaches to produce results useful for biologists.

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