Position-specific kinetic isotope effects for nitrous oxide: A new expansion of the Rayleigh model

Abstract. Nitrous oxide (N₂O) is a potent greenhouse gas and the most significant anthropogenic ozone-depleting substance currently being emitted. A major source of anthropogenic N₂O emissions is the microbial conversion of fixed nitrogen species from fertilizers in agricultural soils. Thus, understanding the enzymatic mechanisms by which microbes produce N₂O has environmental significance. Measurement of the ¹⁵N/¹⁴N isotope ratios of N₂O produced by purified enzymes or axenic microbial cultures is a promising technique for studying N₂O biosynthesis. Typically, N₂O-producing enzymes combine nitrogen atoms from two identical substrate molecules (NO or NH₂OH). Position-specific isotope analysis of the central (N^α) and outer (N^β) nitrogen atoms in N₂O enables the determination of the individual kinetic isotope effects (KIEs) for N^α and N^β, providing mechanistic insight into the incorporation of each nitrogen atom. Previously, position-specific KIEs (and fractionation factors) were quantified using the Rayleigh distillation equation, i.e., via linear regression of δ¹⁵N^α or δ¹⁵N^β against [-flnf/(1-f)], where f is the fraction of substrate remaining in a closed system. This approach, however, is inaccurate for N^α and N^β because it does not account for fractionation at N^α affecting the isotopic composition of substrate available for incorporation into the β position (and vice versa). Therefore, we developed a new expansion of the Rayleigh model that includes specific terms for fractionation at the individual N₂O nitrogen atoms. By applying this Expanded Rayleigh model to a variety of simulated N₂O synthesis reactions with different combinations of normal/inverse/no KIEs at N^α and N^β, we demonstrate that our new model is both accurate and robust. We also applied this new model to two previously published datasets describing N₂O production from NH₂OH oxidation in a methanotroph culture (Methylosinus trichosporium) and N₂O production from NO by a purified Histoplasma capsulatum (fungal) P450 NOR, demonstrating that the Expanded Rayleigh model is a useful tool in calculating position-specific fractionation for N₂O synthesis.