Consider the case where the synthesis of product P is of particular interest; then, the reaction PSynth is the EGFR inhibition objective reaction in the same context as a target reaction [17], whereby all flux vectors with a non-zero flux through reaction PSynth are of importance. The first step would be

to determine the qualitatively distinct possible ways of producing P; this is equivalent Inhibitors,research,lifescience,medical to calculating EMs as illustrated in Figure 2 below. Figure 2 Elementary modes (EMs) for NetEx. The EMs are represented by the solid blue arrows. Adapted from [11]. As shown in the above figure, there are six EMs for NetEx, five of which involve the PSynth reaction (highlighted networks). In order to eliminate the production of P, all the EMs Inhibitors,research,lifescience,medical that involve PSynth need to be blocked. By definition, an EM is blocked by removing any of its constituent reactions, therefore, any combination of reactions, one taken from each EM, forms a cut set that disables flux through the EMs. For our network example, Inhibitors,research,lifescience,medical NetEx, a MCS for the objective reaction, PSynth, is a set of reactions whose knockout blocks the five EMs involving PSynth, thus disabling flux through PSynth at steady state. 2.3. Other Definitions The notion of MCSs does exist in other theories

and research areas, particularly in relation to risk analysis. In developing the algorithm for MCSs, S. Klamt and E.D. Gilles [12] looked at previous Inhibitors,research,lifescience,medical similar definitions of MCSs that existed in other areas at the time. These included fault trees and graph theory which shall be discussed here; other similar concepts are looked at later in Section 5. 2.3.1. Fault Trees

Fault Trees are non-recursive Boolean networks studied in reliability and risk assessment of industrial systems [18,19], which have Inhibitors,research,lifescience,medical similar definitions of MCSs. The Fault Tree diagrams use logic block diagrams to display the state of a system (top event) in terms of the states of its components (basic events). The basic events are ‘entries’ at the lowest level which form the leaves of the tree; intermediate events are those produced by binary operations (e.g., AND, OR, XOR) of other events, and the top event, representing a usually undesired system failure, unless is at the top of the Fault Tree. An example of a Fault Tree can be seen in the left hand graph of Figure 3 below. The right hand side graph is a Reliability Block Diagram (RBD) version of the Fault Tree. RBDs inversely represent Fault Trees: in RBDs one is working in the “success space” and thus looks at system success combinations, while in a Fault Tree one is working in the “failure space” and looks at system failure combinations. Figure 3 Example of a Fault Tree with equivalent Reliability Block Diagram (RBD). MCSs [20] for complex RBDs and Fault Trees are used to estimate their reliability.