Constraint-Based Isotope Tracing (CBIT): Inferring Flux Constraints from Isotopic Tracing Data

Isotope tracing is the most direct experimental approach for quantifying intracellular metabolic flux. It works by feeding cells with isotopically labeled nutrients, measuring the isotopic labeling pattern of intracellular metabolites, and the application of computational Metabolic Flux Analysis (MFA) methods for inferring flux. The inference of metabolic flux from measurements of metabolite isotopic labeling (commonly performed via mass-spectrometry) is computationally hard, typically involving heuristic solving of non-convex optimization problems. Existing MFA methods, although found highly useful in numerous metabolic studies, have three notable limitations: (i) Not being scalable for large-scale networks; (ii) not necessarily converging to optimal solutions (and providing no information on whether the optimal solution has been obtained); (iii) having an overall poor running time performance, which is especially problematic when repeated runs of the algorithm are needed to obtain accurate confidence intervals.

Here, we present a new approach, Constraint-Based Isotope Tracing (CBIT), which enables to rigorously infer tight bounds on metabolic fluxes directly via measured isotopic labeling data. Unlike existing MFA methods, CBIT is a polynomial time algorithm (not involving non-convex optimizations). Given a metabolic network and reaction atom mappings, CBIT first constructs an isotopomer graph, whose vertices represent isotopomers (i.e. distinct labeling patterns of metabolites) and edges represent biochemical reactions. Then, it iteratively propagates lower and upper bound constraints on isotopomer abundances and fluxes throughout the isotopomer graph, utilizing the measured isotopic labeling data as input. Identified flux constraints obtained by CBIT are proved to be consistent with the true, biological flux distribution. CBIT performance, in terms of being able to infer tight bounds, depends on many factors, including the network structure and metabolites whose labeling is provided.

To evaluate the performance of CBIT, we first applied it to infer fluxes in central metabolism of the T-cell leukemia cell line CCRF-CEM. Towards this end, we applied LC-MS to measure the mass-isotopomer distribution of key metabolic intermediates in glycolysis and TCA cycle under metabolic and isotopic steady state. CBIT successfully identified unique fluxes through all 17 reactions in the employed metabolic network, with a mean flux range smaller than 0.1% (calculated as the difference between the identified upper and lower bounds; relative to glucose uptake). As a comparison, Flux Variability Analysis (FVA) predicted an average flux range of 17%, given the measured metabolite uptake and secretion rates. Both FVA and MFA failed to uniquely determine the forward and backward flux through several reversible reactions in the model. Furthermore, while the running time of CBIT was in the order a few seconds, repeatedly applying MFA to calculate accurate confidence intervals required a few hours. In an ongoing work, we are further evaluating the performance of CBIT in inferring fluxes in E. colivia a substantially larger metabolic network with hundreds of reactions, where standard MFA would be computationally intractable.

Overall, our preliminary results demonstrate that CBIT overcomes major limitations of current MFA methods, enabling rigorous quantitation of flux bounds, providing a several order of magnitude improvement in running time, and being scalable for large-scale networks.