Pathway knockout and redundancy in metabolic networks.

The robustness and stability of complex cellular networks is often attributed to the redundancy of components, including genes, enzymes and pathways. Estimation of redundancy is still an open question in systems biology. Current theoretical tools to measure redundancy have various strengths and shortcomings in providing a comprehensive description of metabolic networks. Specially, there is a lack of effective measures to cover different perturbation situations. Here we present a pathway knockout algorithm to improve quantitative measure of redundancy in metabolic networks grounded on the elementary flux mode (EFM) analysis. The proposed redundancy measure is based on the average ratio of remaining EFMs after knockout of one EFM in the unperturbed state. We demonstrated with four example systems that our algorithm overcomes limits of previous measures, and provides additional information about redundancy in the situation of targeted attacks. Additionally, we compare existing enzyme knockout and our pathway knockout algorithm by the mean-field analysis, which provides mathematical expression for the average ratio of remaining EFMs after both types of knockout. Our results prove that multiple-enzymes knockout does not always yield more information than single-enzyme knockout for evaluating redundancy. Indeed, pathway knockout considers additional effects of structural asymmetry. In the metabolic networks of amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes, we validate our mean-field solutions and prove the capacity of pathway knockout algorithm. Moreover, in the E. coli model the two sub-networks synthesizing amino acids that are essential and those that are non-essential for humans are studied separately. In contrast to previous studies, we find that redundancy of two sub-networks is similar with each other, and even sub-networks synthesizing essential amino acids can be more redundant.