Measuring in vivo elasticities of Calvin cycle enzymes: network structure and patterns of modulations

To measure the kinetics of enzymes, the proteins are usually assayed in vitro after isolation from their parent organisms. We make an attempt to show how one might determine enzyme elasticities in an intact system by a multiple modulation approach. Certain target enzymes are modulated in their activities and the changes in metabolite concentrations and flux rates upon the modulations are used to calculate the enzyme elasticities. Central to this approach is that the modulations must be independent of each other, and an algorithm is developed for finding all independent modulations that allow determining the elasticities of a given enzyme. This approach is applied to a mass-action model of the Calvin cycle. The goal is to determine the elasticities of as many enzymes as possible by modulating the activities of as few of them as possible. It is shown that the elasticities of 20 (out of 22) Calvin cycle enzymes can be determined by modulating just five reactions. Moreover, visualization of independence of modulations may be used to decompose the Calvin cycle into several sections that are independent of each other regarding flow of matter and information.