3. Results and DiscussionPC was defined as the critical ratio of the fluxes to be removed such that a metabolic network becomes entirely blocked (Figure 1(b)). The higher the average PC is, the higher the number of nonessential selleck chemicals reactions is. Thus, we chose PC to estimate the robustness of the metabolic networks.Each set of deleted reactions is a cut set for the network [41] (but presumably not a minimal cut set). Therefore, the average PC is an estimate for the average cut set size. For each of the fourteen metabolic networks in our dataset, we computed average PC by repeating the reaction deletion procedure 100 times. The results of this analysis are summarized in Figure 2. From this figure, one can observe that there is comparable range of PC values for metabolic networks in group 1 and group 2.

However, for group 3, we face a range of PC values which does not overlap with the range of PC values for groups 1 and 2. This observation implies that the network robustness of group 3 is much less than that of groups 1 and 2.Figure 2Average PC for the fourteen metabolic network models. The histograms for group 1 (eukaryotes), group 2 (��free-living�� prokaryotes), and group 3 (highly-adapted prokaryotes) are shown in dark blue, green, and yellow, respectively. The error …To investigate the significance of differences between PC values of different groups, one-sided two-sample t-test was used. We tested whether the PC values of eukaryotes (group 1) are significantly greater than PC values of free-living prokaryotes (group 2) and whether the PC values of free-living prokaryotes (group 2) are significantly greater than PC values of prokaryotes with highly specific growth conditions.

The results are summarized in Figure 3. Obviously, the differences between group 2 and group 3 are much more significant than the differences between group 1 and group 2. This observation confirms that prokaryotes with highly specific growth conditions are significantly less robust than the free-living prokaryotes.Figure 3The upper box shows the P values of t-test for PC (group 1) > PC (group 2), while the lower box shows the P values of t-test for PC (group 2) > PC (group 3).We also tested whether the number of unblocked reactions (and not the network structure) determines the network robustness. We found that although the correlation between the number of reactions and PC is positive (R2 = 0.

26), it is not statistically significant (P value > 0.05 in Pearson’s product-moment correlation test). Therefore, there is only a weak, if any, relationship Entinostat between the number of reactions and network robustness. This finding emphasizes the importance of the network ��structure�� and ��wiring�� (as an intrinsic property in each metabolic network) in shaping the network mutational robustness.