Determining enzyme kinetics for systems biology with nuclear magnetic resonance spectroscopy

Enzyme kinetics for systems biology should ideally yield information about the enzyme's activity under in vivo conditions, including such reaction features as substrate cooperativity, reversibility and allostery, and be applicable to enzymatic reactions with multiple substrates. A large body of enzyme-kinetic data in the literature is based on the uni-substrate Michaelis-Menten equation, which makes unnatural assumptions about enzymatic reactions (e.g., irreversibility), and its application in systems biology models is therefore limited. To overcome this limitation, we have utilised NMR time-course data in a combined theoretical and experimental approach to parameterize the generic reversible Hill equation, which is capable of describing enzymatic reactions in terms of all the properties mentioned above and has fewer parameters than detailed mechanistic kinetic equations; these parameters are moreover defined operationally. Traditionally, enzyme kinetic data have been obtained from initial-rate studies, often using assays coupled to NAD(P)H-producing or NAD(P)H-consuming reactions. However, these assays are very labour-intensive, especially for detailed characterisation of multi-substrate reactions. We here present a cost-effective and relatively rapid method for obtaining enzyme-kinetic parameters from metabolite time-course data generated using NMR spectroscopy. The method requires fewer runs than traditional initial-rate studies and yields more information per experiment, as whole time-courses are analyzed and used for parameter fitting. Additionally, this approach allows real-time simultaneous quantification of all metabolites present in the assay system (including products and allosteric modifiers), which demonstrates the superiority of NMR over traditional spectrophotometric coupled enzyme assays. The methodology presented is applied to the elucidation of kinetic parameters for two coupled glycolytic enzymes from Escherichia coli (phosphoglucose isomerase and phosphofructokinase). 31P-NMR time-course data were collected by incubating cell extracts with substrates, products and modifiers at different initial concentrations. NMR kinetic data were subsequently processed using a custom software module written in the Python programming language, and globally fitted to appropriately modified Hill equations.