Pathways piecewise simple

If only a small minority of reaction steps are non-simple, much benefit can be had by breaking the pathway or network down into "piecewise simple" portions and then applying the methods described in the preceding sections to these [8], To this end the pathway or network is cut at the offending intermediates or steps, as will now be shown. 

Many reactions of practical interest have non-simple pathways or networks, i.e., the concentration of an intermediate rises above trace level or a (forward or reverse) step involves two or more molecules of intermediates as reactants. If the majority of the steps meet the simplicity conditions, a significant reduction in mathematical complexity can still be achieved by cutting the network into piecewise simple portions at the offending steps. In some other instances, the quasi-equilibrium or long-chain approximations can be invoked in order to obtain explicit rate equations although the network is non-simple. On the other hand, if a majority of steps in a network are non-simple, the tools described here are of little use. 

If a pathway or network should turn out to contain a step in which two or more molecules of the same or different intermediates react with one another, it can be cut at the offending species into piecewise simple portions as discussed in Section 6.5. However, it will rarely be possible to study these portions independently because, more often than not, the respective trace intermediates cannot be synthesized for use as starting materials. 

If a pathway or network turns out to be non-simple, a good strategy is to try to break it up into piecewise simple portions that can be studied independently. Whether and how this can be done depends on the reaction at hand. The job is easiest if the portions are irreversible, so that none of them feeds back into a preceding one, and if the non-trace intermediates can be synthesized. 

A non-simple pathway or network can be broken at the offending point or points into piecewise simple portions (see Section 6.5). 

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