A graphical method for reducing and relating models in systems biology

Abstract

Motivation: In Systems Biology, an increasing collection of models of various biological processes is currently developed and made available in publicly accessible repositories, such as biomodels.net for instance, through common exchange formats such as SBML. To date, however, there is no general method to relate different models to each other by abstraction or reduction relationships, and this task is left to the modeler for re-using and coupling models. In mathematical biology, model reduction techniques have been studied for a long time, mainly in the case where a model exhibits different time scales, or different spatial phases, which can be analyzed separately. These techniques are however far too restrictive to be applied on a large scale in systems biology, and do not take into account abstractions other than time or phase decompositions. Our purpose here is to propose a general computational method for relating models together, by considering primarily the structure of the interactions and abstracting from their dynamics in a first step.Results: We present a graph-theoretic formalism with node merge and delete operations, in which model reductions can be studied as graph matching problems. From this setting, we derive an algorithm for deciding whether there exists a reduction from one model to another, and evaluate it on the computation of the reduction relations between all SBML models of the biomodels.net repository. In particular, in the case of the numerous models of MAPK signalling, and of the circadian clock, biologically meaningful mappings between models of each class are automatically inferred from the structure of the interactions. We conclude on the generality of our graphical method, on its limits with respect to the representation of the structure of the interactions in SBML, and on some perspectives for dealing with the dynamics.Availability: The algorithms described in this article are implemented in the open-source software modeling platform BIOCHAM available at http://contraintes.inria.fr/biocham The models used in the experiments are available from http://www.biomodels.net/Contact: francois.fages@inria.fr

Computational Models to Decipher Cell-Signaling Pathways

“…76,77 However, the reduction is often performed manually because it should not be only based on graph properties. 76,77 However, the reduction is often performed manually because it should not be only based on graph properties.…”

Egac

“…Notions of CRN comparison that do not consider quantitative dynamics ( [13,18,19]) do not allow answering questions regarding important dynamical properties: for instance, whether two distinct CRNs can achieve the same switch-like behavior under appropriate conditions [6]. A kinetics-aware CRN comparison is presented in [24], but this is specialized for DNA implementation.…”

Inferring reaction systems from ordinary differential equations

“…This approach has rapidly developed in Systems Biology for reasoning on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks à la Thomas [3,4,5], reachability and temporal logic properties in reaction networks [6,7,8,9,10], structural invariants in the Petri net representation of the reactions [11,12,13,14,15,16], or model reductions using graph theory concepts [17,18]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be correctly written as a set of formal reactions, with well-identified reactants, products and modifiers (and in certain cases their stoichiometry) for each reaction.…”