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 occurrence of isotopes within metabolites of interest using a linear transform based on binomial distributions. The resulting 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. Although this assumption can be empirically verified in special cases by simulation studies, there seems to be no published proof of this important property for the general case. In this paper, we prove that this property holds for the case of noise-free MID data obtained at steady state. On the other hand, for noisy MID data, the flux solution will generally differ between the two representations. These results provide a theoretical foundation for the common practice of MID correction in metabolic flux analysis.