MODELLING OF BIOCHEMICAL REACTION NETWORKS

Methods are developed for simplifying the dynamic description of non-linear biochemical reaction networks and characterizing the in vivo behavior of controlling enzymes from intermediate measurements. These methods are based on lumping and identification of characteristic reaction paths, and they depend for success on the time scale separation characteristic of these systems. They are applied with success to glycolysis in human red blood cells and baker's yeast, and their mathematical basis is provided via linearization techniques.;The experimental determination of characteristic reaction paths is illustrated for glycolysis in human red blood cells and baker's yeast (Saccharomyces cerevisiae), and it is shown how the results may be used to characterize kinetics under in vivo conditions. In the case of yeast, reaction path analysis is shown useful for determining the role of phosphofructokinase, an important control enzyme of glycolysis, in gas production during rising of bread dough.;The mathematical basis of reaction path analysis is investigated using linearization 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 vast majority of reaction networks.;The basic problem addressed is efficient model reduction in the analysis of the non-linear interacting enzymatic reactions comprising cellular metabolism. It is shown that a great deal of useful information can be obtained from phase plots of key intermediate pairs 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 and may also be used to reduce the number of differential equations needed for dynamic system description.