This is typically done by gene duplications [6] or by horizontal transfer of metabolic genes [7]. If alternative metabolic pathways are not present in a metabolic network, for example, due to reductive evolution [8, 9], then the metabolic network becomes extremely fragile [10]. It has been free overnight delivery shown that metabolic networks are exceptionally robust when compared to appropriate null models [11].In the present work, we introduce a novel approach to the analysis of metabolic network robustness. We study the resistance of metabolic networks to deletion of reactions by removing reactions until no flux can pass through the network. We show that eukaryotes and free-living prokaryotes show much higher mutational robustness compared to organisms which are highly adapted to their habitats.2. Materials and Methods2.

1. Genome-Scale Metabolic Network ModelsThe genome-scale metabolic network models of 14 species are used in this study, including 3 eukaryotes (group 1), 6 ��free-living�� prokaryotes (group 2), and 5 prokaryotes with highly specific growth conditions (group 3) [12�C20, 22, 24, 26, 28, 30]. Detailed information about the models is presented in Table 1.Table 1List of species used in the present work.2.2. Constraint-Based Analysis of Metabolic NetworksWe used constraint-based analysis of metabolic networks in our study (for a brief review, please see Chapter1 in [31]). In this modeling strategy, it is often assumed that steady-state conditions hold. Therefore, for a certain distribution of reaction fluxes, say v, the metabolic concentrations do not change during time.

In a metabolic network with m metabolites and n reactions, this assumption is equivalent to the following equation:S?v=0,(1)where S is an m �� n matrix representing stoichiometric coefficients of metabolites in the reactions, v is the vector of the n steady-state fluxes, and 0 is an m-dimensional zero vector. Blocked reactions [32] are those reactions which cannot carry any nonzero flux. In other words, for a blocked reaction i, we have vi = 0 subject to stoichiometric constraints (S ? v = 0) and reversibility constraints (vj �� 0 for all irreversible reaction like j). Finding blocked reactions is typically the first step of flux coupling analysis [32, 33]. In our study, we utilized F2C2 tool [34] for this purpose (see below).2.3. Measuring RobustnessOur algorithm is inspired by the concept of percolation.

For more information, the interested reader may refer to [35, 36]. Here, we briefly present the main idea of the percolation theory by an example.Figure 1(a) shows a schematic representation of the Watson-Leath experiment [37]. Suppose that we have a two-dimensional steel-wire mesh (lattice). Two copper electrodes with negligible resistance are soldered to the two GSK-3 opposite sites of this square lattice. The resistance of the steel mesh is measured externally.