Georg Basler, Oliver Ebenhoeh, Joachim Selbig, Zoran Nikoloski

• Motivation: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem. Results: We first review the shortcomings of the existing generic sampling scheme-switch randomization-and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of theMotivation: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem. Results: We first review the shortcomings of the existing generic sampling scheme-switch randomization-and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of the proposed method on seven genome-scale metabolic networks, and empirically validate the theoretical findings. The proposed method allows a biologically meaningful estimation of significance for metabolic network properties.…