Characteristic reaction paths of biochemical reaction systems with time scale separation

A technique has been developed for characterizing the in vivo behavior of key enzymes from intermediate measurements. The technique is based on the identification of characteristic reaction paths, and it depends on the time scale separation characteristics of the systems. It is shown that useful information can be obtained from the phase plots of properly selected intermediate pairs or combinations which typically show process insensitive algebraic relations approached on time scales short compared to those of most practical interest. These characteristic reaction paths provide useful global measures of enzyme activity. The mathematical basis of reaction path analysis is investigated using linear transformation techniques. General theorems are developed predicting the existence of characteristic reaction paths as asymptotic limits whenever there is effective time scale separation. These limits are reached when fast reactions are relaxed, and available evidence suggests that these conditions will occur for the majority of reaction networks.