Determination of the uncertainties in the theoretical mass isotopomer distribution of molecules

Abstract

A procedure for the determination of the uncertainties in the theoretical mass isotopomer distribution of molecules due to natural variations in the isotope composition of their constituting elements is described here for the first time. For this purpose, a Visual Basic macro for Microsoft Excel was written by adapting the direct stepwise calculation algorithm published by Kubinyi (Anal. Chim. Acta 1991, 247, 107-119, Fig. 1). In our procedure no pruning threshold factors were used to eliminate round up errors for large molecules. Then, the Kragten procedure of uncertainty propagation (Analyst 1994, 119, 2161-2165) was applied taking into account the correlation coefficients between the isotope abundances of the corresponding atoms. For bi-isotopic elements (C, H, N, Cl, Br) the correlation coefficients were given the value of -1. For tri- and tetra-isotopic elements the correlation coefficients were calculated using the mass dependent fractionation law used in stable isotope geochemistry and values of +1 or -1 were obtained depending on the isotope system considered. It was observed that for small organic molecules of natural isotope abundances, such as phenol or polybrominated diphenylethers, the method provided relatively small propagated uncertainties similar in magnitude to those measured experimentally. For (13)C-labelled molecules the calculated uncertainties were mainly due to the uncertainties in the isotope enrichment of (13)C and were much larger than the experimental uncertainties. For large molecules of natural isotope abundances, such as peptide C(68)H(107)N(17)O(25) (NIST 8327 RM), the uncertainties in their mass isotopomer distributions were much larger and their source could be assigned mainly to the uncertainty of the natural isotope composition of carbon. When the size of the molecule was even larger, such as bovine insulin (C(254)H(377)N(65)O(75)S(6)), Kragten procedure provided a good estimate for the uncertainty when the most probable isotope composition of carbon in mammals was used in the calculations.