selleck compound Conductivity of a steel-wire mesh is studied during the procedure of cutting wires (bonds) in the mesh. The goal is to find an average number of bonds which should be removed …In each iteration of the experiment, a steel wire (a ��bond��) is cut (Watson and Leath actually studied ��site�� percolation; i.e., in each iteration they cut the four wires coming to a junction). The electric conductance of the lattice gradually decreases by cutting the wires. The idea is to cut steel wires randomly until no electrical current can pass through the mesh.Let P be the ratio of unblocked bonds to the total number of bonds. On average, when bonds are cut, at a critical value, say PC, conductivity of the lattice vanishes to zero [35]. Therefore, PC is a random variable which can be estimated by repeating the experiment several times.

The method used in present study is based on solving a sequence of linear programming (LP) problems. In our algorithm, we used F2C2 [34] to study reactions deletions and their consequences on the activity of metabolic fluxes. The algorithm starts by correcting reversibility of reactions in a metabolic network and deleting all dead-end reactions. Then, in each iteration, one column of the stoichiometric matrix of the metabolic network (or equivalently, a reaction in metabolic network) is randomly deleted (Figure 1(b)). The procedure continues until all reactions become blocked based on the F2C2 program. Finally, the critical ratio is computed as follows:PC=Number??of??deleted??reactionsNumber??of??unblocked??reactions??in??the??original??network.

(2)The experiment is repeated 100 times for each network, and average PC values were computed for each of the metabolic network models.We also compared our results with a classical measure of metabolic network robustness [38] based on flux balance analysis (FBA) [39]. This approach is based on in silico deletion of reactions. In each iteration, a reaction is deleted from the network and the sensitivity of the growth rate to the reaction deletion is modeled. We used the core reductive algorithm [8, 9, 40] for this purpose. In each iteration, we find a (randomly selected) minimal reaction set which can be used to produce biomass from a minimal growth medium in steady-state conditions. In a highly robust network, a considerable number of reactions can be deleted without influencing growth, while in a sensitive network deletion of a few reactions can result in no biomass production.

Therefore, the average ratio of ��unnecessary�� reactions to the total number of reactions can be used as a measure of network robustness. For each metabolic network, the experiment was repeated 1000 times to have a good estimation of this ratio.2.4. Batimastat Statistical AnalysisThe R package (http://www.r-project.org/) was used for statistical analyses. In order to compare the PC distributions in two organisms, one-sided two-sample t-test was used.