Guaranteed and randomized methods for stability analysis of uncertain metabolic networks

A persistent problem hampering our understanding of the dynamics of large-scale metabolic networks is the lack of experimentally determined kinetic parameters that are necessary to build computational models of biochemical processes. To overcome some of the limitations imposed by absent or incomplete kinetic data, structural kinetic modeling (SKM) was proposed recently as an intermediate approach between stoichiometric analysis and a full kinetic description. SKM extends stationary flux-balance analysis (FBA) by a local stability analysis utilizing an appropriate parametrization of the Jacobian matrix. To characterize the Jacobian, we utilize results from robust control theory to determine subintervals of the Jacobian’ entries that correspond to asymptotically stable metabolic states. Furthermore, we propose an efficient sampling scheme in combination with methods from computational geometry to sketch the stability region. A glycolytic pathway model comprising 12 uncertain parameters is used to assess the feasibility of the method. 1 Modeling metabolic networks Cellular metabolism, defined as the orchestrated biochemical interconversion of small molecules by dedicated proteins, is an important aspect of cellular physiology and of outstanding interest for many biotechnological and medical applications. In the past decades, great strides have been made to elucidate and compile the list of the biochemical reaction taking place in living cells and almost comprehensive stoHeinz Koeppl and Stefano Andreozzi Laboratory of Nonlinear Systems, School of Communication and Computer Sciences, Ecole Polytechnique Federale de Lausanne (EPFL), 1015 Lausanne, Switzerland e-mail: {heinz.koeppl, stefano.andreozzi}@epfl.ch Ralf Steuer Institute for Theoretical Biology, Humboldt University of Berlin, Invalidenstrasse 43, D-10115 Berlin, Germany and Manchester Interdisciplinary Biocentre, The University of Manchester, Manchester M1 7DN, UK. e-mail: [email protected]