In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation analysis, etc. However, without requiring any in-formation on the reaction kinetics and parameter values, various qualitative analyses can be performed using the structure of the reactions, provided the reactants, products and mod-ifiers of each reaction are precisely defined […]
Tue, Sep 1, 2015
In this paper we study the problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex deletion and merge operations that transforms a first reaction graph into a second graph […]
Wed, Jan 1, 2014
In this work, we compare CLP and SAT solvers on the NP-complete problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex, species or reaction, deletion and merge operations which transforms a first reaction graph into a second graph […]
Sun, Sep 1, 2013
Mon, Oct 1, 2012
Sun, Jul 1, 2012
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 […]
Wed, Sep 1, 2010