Measurement of (carbon) kinetic isotope effect by Rayleigh fractionation using membrane inlet mass spectrometry for CO₂-consuming reactions

Methods for determining carbon isotope discrimination, Δ, or kinetic isotope effects, α, for CO₂-consuming enzymes have traditionally been cumbersome and time-consuming, requiring careful isolation of substrates and products and conversion of these to CO₂ for measurement of isotope ratio by mass spectrometry (MS). An equation originally derived by Rayleigh in 1896 has been used more recently to good effect as it only requires measurement of substrate concentrations and isotope ratios. For carboxylation reactions such as those catalysed by d-ribulose-1,5-bisphosphate carboxylase / oxygenase (RuBisCO, EC 4.1.1.39) and PEP carboxylase (PEPC, EC 4.1.1.31), this has still required sampling of reactions at various states of completion and conversion of all inorganic carbon to CO₂, as well as determining the amount of substrate consumed. We introduce a new method of membrane inlet MS which can be used to continuously monitor individual CO ₂ isotope concentrations, rather than isotope ratio. This enables the use of a simplified, new formula for calculating kinetic isotope effects, based on the assumptions underlying the original Rayleigh fractionation equation and given by: 1 + Δ = α = d(ln[¹²C])/d(ln[¹³C]). The combination of inlet membrane MS and this formula yields measurements of discrimination in less than 1 h. We validate our method against previously measured values of discrimination for PEP carboxylase and RuBisCO from several species.