Reduction and Simplification of Reaction Networks

The theoretical background of the above formulated principle of extremum resistance may be deduced from the following considerations. Let us examine first a one RR mechanism 

Obviously, all of the elementary reactions in this RR are coimected in series and each elementary reaction sj in the sequence occurs Oj times. Thus, we can define a 

The reasoning behind this definition is the following. Firstly, we observe that because the stoichiometric numbers are squared the resistance of a RR is necessarily positive. Secondly, Eq. (26) should be consistent with the QSS conditions. Indeed, once we have defined the resistance of the RR and the affinity of the OR, we can employ the analog of Ohm s law to define an overall rate of the reaction 

In this case the remaining elementary reactions may be considered at quasiequilibrium and may be lumped into a single, intermediate, quasi-equilibrated reaction [8]. This is similar to the case of the two-step mechanism of Boudart [28]. 

Similarly, the overall resistance in a set of parallel branches of elementary reactions may be estimated for the linear case in analogy to Ohm s Law according to 

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