Differential algebra and system modeling in cellular biology

François Boulier (1, 2) , François Lemaire (2, 1)

1 LIFL - Laboratoire d'Informatique Fondamentale de Lille
2 CALFOR - Calcul Formel

Among all the modeling approaches dedicated to cellular biology, differential algebra is particularly related to the well-established one based on nonlinear differential equations. In this paper, it is shown that differential algebra makes both simple and algorithmic one of the model reduction methods, the quasi-steady state approximation theory, in the particular setting of generalized chemical reactions systems. This recent breakthrough may suggest some evolution of modeling techniques based on nonlinear differential equations, by incorporating the reduction hypotheses in the models. Potential improvements of parameters fitting methods are discussed too.

Mots clés: differential algebra; system modeling; cellular biology; computer algebra

Domaines: Calcul formel [cs.SC]; Bio-Informatique, Biologie Systémique [q-bio.QM]; Bio-informatique [q-bio.QM]; Systèmes dynamiques [math.DS]

François Boulier, François Lemaire. Differential algebra and system modeling in cellular biology. AB 2008, 2008, Hagenberg, Austria. pp.22-39. ⟨hal-00274689⟩