Validity of natural isotope abundance correction for metabolic flux analysis

A pervasive issue in stable isotope tracing and metabolic flux analysis is the presence of naturally occurring isotopes such as 13C. For mass isotopomer distributions (MIDs) measured by mass spectrometry, it is common practice to correct for natural isotopes within metabolites of interest using a particular linear transform based on binomial distributions. However, the origin and mathematical derivation of this transform is rather obscure, and it may be difficult for nonexperts to understand precisely how to interpret the resulting corrected MIDs. Moreover, corrected MIDs are often used to fit metabolic network models and infer metabolic fluxes, which implicitly assumes that corrected MIDs will yield the same flux solution as the actual observed MIDs. Yet, there seems to be no published proof of this important property. Here, we provide a detailed derivation of the MID-correcting linear transform, reflecting its historical development, and describe some interesting properties. We also provide a proof that for metabolic flux analysis on noise-free MID data at steady state, observed and corrected MIDs indeed yield the same flux solution. On the other hand, for noisy MID data, the flux solution will generally differ between the two representations.