Robust simplifications of multiscale biochemical networks
1 IRMAR (CNRS UMR 6025) and IRISA/INRIA, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France
2 Department of Mathematics, University of Leicester, LE1 7RH, UK
3 Institut Curie, Service Bioinformatique, Paris, 26 rue d'Ulm, Paris F-75248, France
4 INSERM, U900, Paris, F-75248, France
5 Ecole des Mines de Paris, ParisTech, Fontainebleau, F-77300, France
6 Institute of Computational Modeling SB RAS, Krasnoyarsk, Akademgorodok, 660036, Russia
7 Cytosquelette et Développement (CNRS UMR 7000), Faculté de Médecine Pitié-Salpêtrière, 105, boulevard de l'Hôpital, 75634 Paris cedex 13, France
8 Stress et Pathologies du Cytosquelette (EA300), Université Paris 7 Denis Diderot, 4, rue Marie-Andrée Lagroua Weill-Hallé 75013 Paris, France
BMC Systems Biology 2008, 2:86 doi:10.1186/1752-0509-2-86Published: 14 October 2008
Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.
We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in . Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway.
Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.