An improved method for statistical analysis of metabolic flux analysis using isotopomer mapping matrices with analytical expressions

Analytical expressions were derived for calculating the sensitivities of isotopomer distribution vectors, the weighted output matrix with respect to the fluxes, and the covariance matrix for the metabolic flux analysis based on isotopomers mapping matrices (IMM). These expressions allow us to implement efficient statistical analysis, avoiding the time-consuming Monte Carlo techniques for estimating the confidence interval of the fluxes. The analytical expressions are also useful in implementing a faster design of experiment, which requires repetitive computation of the covariance matrix that is not straightforward to make in practice with the numerical techniques based on the conventional IMM. The proposed method was applied for analyzing the central carbon metabolism of the mixotrophically cultivated Synechocystis sp. PCC6803, and the confidence intervals of all its fluxes were computed based on the isotopomer distribution measured using NMR and GC-MS. It was found that the best feasible mixture for labeling experiment is 70% unlabeled, 10% U-13C] and 20% 1,2-13C2] labeled glucose to obtain the most reliable metabolic fluxes.