1.1.2 Conservation Analysis
A conservation relationship occurs when a linear combination of a subset of species within a reaction network model remains constant at all times. For example, consider the following classical example of substrate \(S\) conversion to product \(P\) catalysed by an enzyme\(E\).
\(S\ +\ E\ \ \par \begin{matrix}k_{1}\\ \rightleftarrows\\ k_{-1}\\ \end{matrix}\ \ E:S\ \par \begin{matrix}k_{1}\\ \rightleftarrows\\ k_{-1}\\ \end{matrix}\ \ \ P\ +\ E,\) (1)
where \(E:S\) is a complex formed between the enzyme and substrate. Here, the moles of (\(E\ +\ E:S)\) is constant and is equal to the initial concentration of the enzyme \((E_{0})\). The model can therefore be simplified be removing the constant term. For large models, conservation analysis typically achieves a modest 10–15% reduction in the number of state variables [33]. However, conservation relations in such large models are not obvious and algorithmic approaches are needed to find those relations [27,34,35].