In the initial MCS concept, the MCSs are based on EMs, whereas the generalized MCS concept [11] sees EMs and MCSs as dual representations of network functions, which can be converted into each other, i.e., MCSs are EMs in a dual metabolic network [29]. The generalized MCS concept offers a wider range of capacity to assess, manipulate and design biochemical networks. MCSs are no longer restricted to the removal of better reactions as shown in Figure 2 but can also contain network Inhibitors,research,lifescience,medical nodes such that more general deletion problems can be tackled. The MCSs

that involve the removal of other network parameters besides reactions are shown in the lower two tables (1b and 1c) of Table 1 below. From Table 1 we can compare the number of MCSs obtained from removing reactions only (initial MCS concept) or other parameters

(generalized Inhibitors,research,lifescience,medical concept). The least number of MCSs occurs when removing metabolites (1b), which implies that metabolites Inhibitors,research,lifescience,medical are more crucial for the production of P; this is evident when we look at the set of EMs which shows three metabolites as essential for PSynth compared to one essential reaction. This is because removing a metabolite results in eliminating all the reactions connected to it, thus eliminating the corresponding EMs, so MCSs from deleting metabolites would be more effective. MCSs could also be Inhibitors,research,lifescience,medical derived from a combination of reactions and metabolites, although these methods could quickly become computationally challenging [30,31]; computational complexity is discussed later. Constrained MCSs (cMCSs) provide further flexibility by providing

the capacity to specify, not only functionalities to be disabled, but also those that need to be preserved; the combination of these kinase inhibitor Pacritinib desirable and undesirable functionalities are represented by appropriate sets of target EMs and desired EMs. This allows for systematic Inhibitors,research,lifescience,medical enumeration of all equivalent AV-951 gene deletion combinations and subsequently assists in determining intervention problems and robust knockout strategies for coupled product and biomass synthesis. For example, consider our network example NetEx (Figure 1) which has six EMs; say the objective is to suppress the synthesis of P in order to maximise the production of X; the set of target modes would be T= EM2, EM3, EM4, EM5, EM6 with the eight MCSs as shown in the first set of MCSs in Table 1. The resulting intervention problems are shown in Table 2 below: Table 2 Intervention problems and resulting MCSs for the example network, NetEx. The above NetEx example is a very simple case and a more comprehensive example can be seen in [15] which describes cMCSs in detail. 3.