A pervasive issue in stable isotope tracing and metabolic flux analysis is the presence of naturally occurring isotopes such as ${}^{13}$C. 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.

稳定同位素示踪和代谢通量分析中普遍存在的问题是存在天然同位素，例如 ${}^{13}$C.对于通过质谱法测量的质量同位素异构体分布（MID），通常的做法是使用基于二项分布的线性变换来校正目标代谢物中同位素的自然发生。生成的校正后的MID通常用于拟合代谢网络模型并推断代谢通量，这隐含地假设校正后的MID将产生与实际观察到的MID相同的通量解。尽管在特殊情况下可以通过模拟研究对这一假设进行实证验证，但是对于一般情况，似乎没有公开的证据证明这一重要特性。在本文中，我们证明了对于在稳态下获得的无噪声MID数据而言，该属性成立。另一方面，对于嘈杂的MID数据，通量解通常会在两种表示形式之间有所不同。