CIRM
- Centre International de Rencontres Mathématiques
Luminy - Marseille - France
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Most biological processes are controlled by regulatory networks, which involve various kinds of molecular interactions. Decades of genetic and molecular analysis, more recently complemented by high-throughput functional genomic experiments, have progressively uncovered many of the numerous interactions controlling several crucial biological processes (e.g. cell cycle and various developmental pathways). The complexity of the networks delineated often defies intuitive reasoning, consequently calling for the development of proper mathematical and computational tools.
The present meeting aims at gathering researchers in mathematics, physics, computer science and biology to address theoretical and methodological questions related to the modelling and the analysis of biological networks.
During the meeting, the mathematical models considered deal with the regulatory networks involved in the control of cell cycle, cell differentiation and pattern formation in animals. Modelled systems will encompass early embryonic development of the fly D. melanogaster, as well as the control of lymphocytes differentiation and proliferation in mammal. In both model systems, it is now possible to delineate various interactions coupling cell proliferation, growth and differentiation. Consequently, it becomes possible to integrate and simulate these different processes and their coupling in the form of dynamical models.
In such networks, various classes of interactions are involved: genetic and metabolic regulations, signal transduction cascades... Each of these classes has its own semantics, time scale, etc. The participants will thus confront the problem of the integration of these different types of interactions in the context of a unified and coherent mathematical framework.
Various theoretical approaches can be applied. In the course of the meeting, we will particularly focus on the articulation of qualitative versus quantitative approaches, encompassing discrete (logical) as well as continuous (differential or stochastic) formalisms, including various flavours of Petri nets, model checking and constraints programming approaches. Refering to these different formal frameworks, we will focus on the delineation of relevant dynamical properties, such as the existence of specific types of attractors.
The participants will endeavour to connect properties of the regulatory graph with specific dynamical properties. In this respect, it has been recently proven (in the differential framework) that a necessary condition for multistationarity is the existence of a functional positive circuit in the regulatory graph. We will lean on such results to define further formal relationships between specific regulatory structures and dynamical properties. These relationships can also been investigated starting from dynamical information obtained with high throughput methodologies such as DNA arrays, with the aim to infer regulatory interactions between genes from their expression profiles.