A Generalized Framework for Targeted 13C Metabolic Flux Ratio Analysis

Flux balance analysis is widely used to investigate operation and regulation of metabolic networks. Recent advances in omics technologies gave rise to comprehensive genome-scale metabolic models describing various pathways and interspecies interaction points. In many cases, however, the system is largely underdetermined to obtain precise flux estimates based solely on stoichiometric balances, and independent experimental data becomes necessary to resolve alternative pathways. The most direct readout for flux propagation through the network is obtained in labeling experiments, where the substrates are ¹³C-labeled and intracellular metabolite labeling patterns are measured with mass spectrometry or nuclear magnetic resonanse.

There are two main strategies to infer flux information from ¹³C labeling data. Isotopomer balancing approach is used to find a general flux distribution which fits the measured labeling patterns, often resulting in multiple solutions. Flux ratio analysis estimates the local ratios with analytical formulas,  which have to be manually derived for each particular ratio, organism and condition. We propose to combine these two strategies to provide a fast and general approach to estimate flux ratios, applicable to any organism, substrates and available measurements.

We formulate the flux ratio estimation task as a regression problem, where the flux ratio is a function of measured intracellular labeling patterns, and use quantile regression algorithm [1] to build such predictor function. Machine learning algorithms require a rigorous training dataset with known flux ratio values and measured data, which is impossible to obtrain experimentally, thus we use isotopomer simulation procedure [2] to create an in silico dataset representing vast spectrum of flux distributions through the network with corresponding metabolite labeling patterns. We use an independently simulated test dataset to assess the theoretical flux ratio resolvability, and further apply the predictor to experimental data to provide flux ratio estimates with prediction quantiles. The in silico training and testing procedure is used for experimental design to find labeling strategies and set of measurements required to get better estimates for flux ratios of interest. As a proof of principle, we resolve several flux ratios in central carbon metabolism of Escherichia coli, and further apply the method to point out host-pathogen interactions in a poorly defined multisubstrate environment using amino acids measurements of Mycobacterium tuberculosis infecting human macrophage [3]. The developed flux ratio analysis framework is a powerful tool to estimate flux ratios given available network information and possibly scarce measurement data, which can be further used to provide additional constraints for global flux analysis methods.

[1] Meinshausen (2006). Quantile Regression Forests. Journal of Machine Learning Research, 7(2005), 983–999.

[2] Wiechert et al. (1999). Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnology and Bioengineering, 66(2), 69–85.

[3] Beste et al. (2013). (13)C-Flux Spectral Analysis of Host-Pathogen Metabolism Reveals a Mixed Diet for Intracellular Mycobacterium tuberculosis. Chemistry & Biology, 20(8), 1012–21.