Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis

Metabolic flux analysis using carbon labeling experiments (CLEs) is an important tool in metabolic engineering where the intracellular fluxes have to be computed from the measured extracellular fluxes and the partially measured distribution of 13C labeling within the intracellular metabolite pools. The relation between unknown fluxes and measurements is described by an isotopomer labeling system (ILS) (see Part I [Math. Biosci. 169 (2001) 173]). Part II deals with the structural flux identifiability of measured ILSs in the steady state. The central question is whether the measured data contains sufficient information to determine the unknown intracellular fluxes. This question has to be decided a priori, i.e. before the CLE is carried out. In structural identifiability analysis the measurements are assumed to be noise-free. A general theory of structural flux identifiability for measured ILSs is presented and several algorithms are developed to solve the identifiability problem. In the particular case of maximal measurement information, a symbolical algorithm is presented that decides the identifiability question by means of linear methods. Several upper bounds of the number of identifiable fluxes are derived, and the influence of the chosen inputs is evaluated. By introducing integer arithmetic this algorithm can even be applied to large networks. For the general case of arbitrary measurement information, identifiability is decided by a local criterion. A new algorithm based on integer arithmetic enables an a priori local identifiability analysis to be performed for networks of arbitrary size. All algorithms have been implemented and flux identifiability is investigated for the network of the central metabolic pathways of a microorganism. Moreover, several small examples are worked out to illustrate the influence of input metabolite labeling and the paradox of information loss due to network simplification.     

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 101-117, 1997.     

A transient isotopic labeling methodology for 13C metabolic flux analysis of photoautotrophic microorganisms

Metabolic flux analysis is increasingly recognized as an integral component of systems biology. However, techniques for experimental measurement of system-wide metabolic fluxes in purely photoautotrophic systems (growing on CO(2) as the sole carbon source) have not yet been developed due to the unique problems posed by such systems. In this paper, we demonstrate that an approach that balances positional isotopic distributions transiently is the only route to obtaining system-wide metabolic flux maps for purely autotrophic metabolism. The outlined transient (13)C-MFA methodology enables measurement of fluxes at a metabolic steady-state, while following changes in (13)C-labeling patterns of metabolic intermediates as a function of time, in response to a step-change in (13)C-label input. We use mathematical modeling of the transient isotopic labeling patterns of central intermediates to assess various experimental requirements for photoautotrophic MFA. This includes the need for intracellular metabolite concentration measurements and isotopic labeling measurements as a function of time. We also discuss photobioreactor design and operation in order to measure fluxes under precise environmental conditions. The transient MFA technique can be used to measure and compare fluxes under different conditions of light intensity, nitrogen sources or compare strains with various mutations or gene deletions and additions.     

Metabolic flux analysis and visualization

One of the ultimate goals of systems biology research is to obtain a comprehensive understanding of the control mechanisms of complex cellular metabolisms. Metabolic Flux Analysis (MFA) is a important method for the quantitative estimation of intracellular metabolic flows through metabolic pathways and the elucidation of cellular physiology. The primary challenge in the use of MFA is that many biological networks are underdetermined systems; it is therefore difficult to narrow down the solution space from the stoichiometric constraints alone. In this tutorial, we present an overview of Flux Balance Analysis (FBA) and (13)C-Metabolic Flux Analysis ((13)C-MFA), both of which are frequently used to solve such underdetermined systems, and we demonstrate FBA and (13)C-MFA using the genome-scale model and the central carbon metabolism model, respectively. Furthermore, because such comprehensive study of intracellular fluxes is inherently complex, we subsequently introduce various pathway mapping and visualization tools to facilitate understanding of these data in the context of the pathways. Specific visualization of MFA results using the BioCyc Omics Viewer and Pathway Projector are shown as illustrative examples.     

Efficient Modeling of MS/MS Data for Metabolic Flux Analysis

Metabolic flux analysis (MFA) is a widely used method for quantifying intracellular metabolic fluxes. It works by feeding cells with isotopic labeled nutrients, measuring metabolite isotopic labeling, and computationally interpreting the measured labeling data to estimate flux. Tandem mass-spectrometry (MS/MS) has been shown to be useful for MFA, providing positional isotopic labeling data. Specifically, MS/MS enables the measurement of a metabolite tandem mass-isotopomer distribution, representing the abundance in which certain parent and product fragments of a metabolite have different number of labeled atoms. However, a major limitation in using MFA with MS/MS data is the lack of a computationally efficient method for simulating such isotopic labeling data. Here, we describe the tandemer approach for efficiently computing metabolite tandem mass-isotopomer distributions in a metabolic network, given an estimation of metabolic fluxes. This approach can be used by MFA to find optimal metabolic fluxes, whose induced metabolite labeling patterns match tandem mass-isotopomer distributions measured by MS/MS. The tandemer approach is applied to simulate MS/MS data in a small-scale metabolic network model of mammalian methionine metabolism and in a large-scale metabolic network model of E. coli. It is shown to significantly improve the running time by between two to three orders of magnitude compared to the state-of-the-art, cumomers approach. We expect the tandemer approach to promote broader usage of MS/MS technology in metabolic flux analysis. Implementation is freely available at www.cs.technion.ac.il/~tomersh/methods.html     

Tandem mass spectrometry: a novel approach for metabolic flux analysis

The goal of metabolic flux analysis (MFA) is the accurate estimation of intracellular fluxes in metabolic networks. Here, we introduce a new method for MFA based on tandem mass spectrometry (MS) and stable-isotope tracer experiments. We demonstrate that tandem MS provides more labeling information than can be obtained from traditional full scan MS analysis and allows estimation of fluxes with better precision. We present a modeling framework that takes full advantage of the additional labeling information obtained from tandem MS for MFA. We show that tandem MS data can be computed for any network model, any compound and any tandem MS fragmentation using linear mapping of isotopomers. The inherent advantages of tandem MS were illustrated in two network models using simulated and literature data. Application of tandem MS increased the observability of the models and improved the precision of estimated fluxes by 2- to 5-fold compared to traditional MS analysis.     

Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions

(13)C metabolic flux analysis (MFA) has become an important and powerful tool for the quantitative analysis of metabolic networks in the framework of metabolic engineering. Isotopically instationary (13)C MFA under metabolic stationary conditions is a promising refinement of classical stationary MFA. It accounts for the experimental requirements of non-steady-state cultures as well as for the shortening of the experimental duration. This contribution extends all computational methods developed for classical stationary (13)C MFA to the instationary situation by using high-performance computing methods. The developed tools allow for the simulation of instationary carbon labeling experiments (CLEs), sensitivity calculation with respect to unknown parameters, fitting of the model to the measured data, statistical identifiability analysis and an optimal experimental design facility. To explore the potential of the new approach all these tools are applied to the central metabolism of Escherichia coli. The achieved results are compared to the outcome of the stationary counterpart, especially focusing on statistical properties. This demonstrates the specific strengths of the instationary method. A new ranking method is proposed making both an a priori and an a posteriori design of the sampling times available. It will be shown that although still not all fluxes are identifiable, the quality of flux estimates can be strongly improved in the instationary case. Moreover, statements about the size of some immeasurable pool sizes can be made.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

Eukaryotic metabolism: measuring compartment fluxes

Metabolic compartmentation represents a major characteristic of eukaryotic cells. The analysis of compartmented metabolic networks is complicated by separation and parallelization of pathways, intracellular transport, and the need for regulatory systems to mediate communication between interdependent compartments. Metabolic flux analysis (MFA) has the potential to reveal compartmented metabolic events, although it is a challenging task requiring demanding experimental techniques and sophisticated modeling. At present no ready-made solution can be provided to cope with the complexity of compartmented metabolic networks, but new powerful tools are emerging. This review gives an overview of different strategies to approach this issue, focusing on different MFA methods and highlighting the additional information that should be included to improve the outcome of an experiment and associate estimation procedures.     

Visual exploration of isotope labeling networks in 3D

Isotope labeling networks (ILNs) are graphs explaining the flow of isotope labeled molecules in a metabolic network. Moreover, they are the structural backbone of metabolic flux analysis (MFA) by isotopic tracers which has been established as a standard experimental tool in fluxomics. To configure an isotope labeling experiment (ILE) for MFA, the structure of the corresponding ILN must be understood to a certain extent even by a practitioner. Graph algorithms help to analyze the network structure but produce rather abstract results. Here, the major obstruction is the high dimension of these networks and the large number of network components which, consequently, are hard to figure out manually. At the interface between theory and experiment, the three-dimensional interactive visualization tool CumoVis has been developed for exploring the network structure in a step by step manner. Navigation and orientation within ILNs are supported by exploiting the natural 3D structure of an underlying metabolite network with stacked labeled particles on top of each metabolite node. Network exploration is facilitated by rotating, zooming, forward and backward path tracing and, most important, network component reduction. All features of CumoVis are explained with an educational example and a realistic network describing carbon flow in the citric acid cycle.     

Metabolic flux analysis in Escherichia coli by integrating isotopic dynamic and isotopic stationary 13C labeling data

The novel concept of isotopic dynamic 13C metabolic flux analysis (ID-13C MFA) enables integrated analysis of isotopomer data from isotopic transient and/or isotopic stationary phase of a 13C labeling experiment, short-time experiments, and an extended range of applications of 13C MFA. In the presented work, an experimental and computational framework consisting of short-time 13C labeling, an integrated rapid sampling procedure, a LC-MS analytical method, numerical integration of the system of isotopomer differential equations, and estimation of metabolic fluxes was developed and applied to determine intracellular fluxes in glycolysis, pentose phosphate pathway (PPP), and citric acid cycle (TCA) in Escherichia coli grown in aerobic, glucose-limited chemostat culture at a dilution rate of D = 0.10 h(-1). Intracellular steady state concentrations were quantified for 12 metabolic intermediates. A total of 90 LC-MS mass isotopomers were quantified at sampling times t = 0, 91, 226, 346, 589 s and at isotopic stationary conditions. Isotopic stationarity was reached within 10 min in glycolytic and PPP metabolites. Consistent flux solutions were obtained by ID-13C MFA using isotopic dynamic and isotopic stationary 13C labeling data and by isotopic stationary 13C MFA (IS-13C MFA) using solely isotopic stationary data. It is demonstrated that integration of dynamic 13C labeling data increases the sensitivity of flux estimation, particularly at the glucose-6-phosphate branch point. The identified split ratio between glycolysis and PPP was 55%:44%. These results were confirmed by IS-13C MFA additionally using labeling data in proteinogenic amino acids (GC-MS) obtained after 5 h from sampled biomass.     

Insights into metabolic efficiency from flux analysis

The efficiency of carbon and energy flows throughout metabolism defines the potential for growth and reproductive success of plants. Understanding the basis for metabolic efficiency requires relevant definitions of efficiency as well as measurements of biochemical functions through metabolism. Here insights into the basis of efficiency provided by (13)C-based metabolic flux analysis (MFA) as well as the uses and limitations of efficiency in predictive flux balance analysis (FBA) are highlighted. (13)C-MFA studies have revealed unusual features of central metabolism in developing green seeds for the efficient use of light to conserve carbon and identified metabolic inefficiencies in plant metabolism due to dissipation of ATP by substrate cycling. Constraints-based FBA has used efficiency to guide the prediction of the growth and actual internal flux distribution of plant systems. Comparisons in a few cases have been made between flux maps measured by (13)C-based MFA and those predicted by FBA assuming one or more maximal efficiency parameters. These studies suggest that developing plant seeds and photoautotrophic microorganisms may indeed have patterns of metabolic flux that maximize efficiency. MFA and FBA are synergistic toolsets for uncovering and explaining the metabolic basis of efficiencies and inefficiencies in plant systems.     

New tools for mass isotopomer data evaluation in (13)C flux analysis: mass isotope correction, data consistency checking, and precursor relationships

13C metabolic flux analysis (MFA) is based on carbon-labeling experiments where a specifically (13)C labeled substrate is fed. The labeled carbon atoms distribute over the metabolic network and the label enrichment of certain metabolic pools is measured by using different methods. Recently, MS methods have been dramatically improved-large and precise datasets are now available. MS data has to be preprocessed and corrected for natural stable mass isotopes. In this article we present (1). a new elegant method to correct MS measurement data for natural stable mass isotopes by infinite dimensional matrix calculus and (2). we statistically analyze and discuss a reconstruction of labeling pattern in metabolic precursors from biosynthesis molecules. Moreover, we establish a new method for consistency checking of MS spectra that can be applied for automatic error recognition in high-throughput flux analysis procedures. Preprocessing the measurement data changes their statistical properties which have to be considered in the subsequent parameter fitting process for (13)C MFA. We show that correcting for stable mass isotopes leads to rather small correlations. On the other hand, a direct reconstruction of a precursor labeling pattern from an aromatic amino acid measurement turns out to be critical. Reasonable results are only obtained if additional, independent information about the labeling of at least one precursor is available. A versatile MatLab tool for the rapid correction and consistency checking of MS spectra is presented. Practical examples for the described methods are also given.     

Selection of tracers for 13C-metabolic flux analysis using elementary metabolite units (EMU) basis vector methodology

Metabolic flux analysis (MFA) is a powerful technique for elucidating in vivo fluxes in microbial and mammalian systems. A key step in (13)C-MFA is the selection of an appropriate isotopic tracer to observe fluxes in a proposed network model. Despite the importance of MFA in metabolic engineering and beyond, current approaches for tracer experiment design are still largely based on trial-and-error. The lack of a rational methodology for selecting isotopic tracers prevents MFA from achieving its full potential. Here, we introduce a new technique for tracer experiment design based on the concept of elementary metabolite unit (EMU) basis vectors. We demonstrate that any metabolite in a network model can be expressed as a linear combination of so-called EMU basis vectors, where the corresponding coefficients indicate the fractional contribution of the EMU basis vector to the product metabolite. The strength of this approach is the decoupling of substrate labeling, i.e. the EMU basis vectors, from the dependence on free fluxes, i.e. the coefficients. In this work, we demonstrate that flux observability inherently depends on the number of independent EMU basis vectors and the sensitivities of coefficients with respect to free fluxes. Specifically, the number of independent EMU basis vectors places hard limits on how many free fluxes can be determined in a model. This constraint is used as a guide for selecting feasible substrate labeling. In three example models, we demonstrate that by maximizing the number of independent EMU basis vectors the observability of a system is improved. Inspection of sensitivities of coefficients with respect to free fluxes provides additional constraints for proper selection of tracers. The present contribution provides a fresh perspective on an important topic in metabolic engineering, and gives practical guidelines and design principles for a priori selection of isotopic tracers for (13)C-MFA studies.     

Optimization of 13C isotopic tracers for metabolic flux analysis in mammalian cells

Mammalian cells consume and metabolize various substrates from their surroundings for energy generation and biomass synthesis. Glucose and glutamine, in particular, are the primary carbon sources for proliferating cancer cells. While this combination of substrates generates static labeling patterns for use in (13)C metabolic flux analysis (MFA), the inability of single tracers to effectively label all pathways poses an obstacle for comprehensive flux determination within a given experiment. To address this issue we applied a genetic algorithm to optimize mixtures of (13)C-labeled glucose and glutamine for use in MFA. We identified tracer combinations that minimized confidence intervals in an experimentally determined flux network describing central carbon metabolism in tumor cells. Additional simulations were used to determine the robustness of the [1,2-(13)C(2)]glucose/[U-(13)C(5)]glutamine tracer combination with respect to perturbations in the network. Finally, we experimentally validated the improved performance of this tracer set relative to glucose tracers alone in a cancer cell line. This versatile method allows researchers to determine the optimal tracer combination to use for a specific metabolic network, and our findings applied to cancer cells significantly enhance the ability of MFA experiments to precisely quantify fluxes in higher organisms.     

Parallel labeling experiments with [U-(13)C]glucose validate E. coli metabolic network model for (13)C metabolic flux analysis

(13)C-metabolic flux analysis (MFA) is a widely used method for measuring intracellular metabolic fluxes in living cells. (13)C MFA relies on several key assumptions: (1) the assumed metabolic network model is complete, in that it accounts for all significant enzymatic and transport reactions; (2) (13)C-labeling measurements are accurate and precise; and (3) enzymes and transporters do not discriminate between (12)C- and (13)C-labeled metabolites. In this study, we tested these inherent assumptions of (13)C MFA for wild-type E. coli by parallel labeling experiments with [U-(13)C]glucose as tracer. Cells were grown in six parallel cultures in custom-constructed mini-bioreactors, starting from the same inoculum, on medium containing different mixtures of natural glucose and fully labeled [U-(13)C]glucose, ranging from 0% to 100% [U-(13)C]glucose. Macroscopic growth characteristics of E. coli showed no observable kinetic isotope effect. The cells grew equally well on natural glucose, 100% [U-(13)C]glucose, and mixtures thereof. (13)C MFA was then used to determine intracellular metabolic fluxes for several metabolic network models: an initial network model from literature; and extended network models that accounted for potential dilution effects of isotopic labeling. The initial network model did not give statistically acceptable fits and produced inconsistent flux results for the parallel labeling experiments. In contrast, an extended network model that accounted for dilution of intracellular CO(2) by exchange with extracellular CO(2) produced statistically acceptable fits, and the estimated metabolic fluxes were consistent for the parallel cultures. This study illustrates the importance of model validation for (13)C MFA. We show that an incomplete network model can produce statistically unacceptable fits, as determined by a chi-square test for goodness-of-fit, and return biased metabolic fluxes. The validated metabolic network model for E. coli from this study can be used in future investigations for unbiased metabolic flux measurements.     

A Peptide-Based Method for 13C Metabolic Flux Analysis in Microbial Communities

The study of intracellular metabolic fluxes and inter-species metabolite exchange for microbial communities is of crucial importance to understand and predict their behaviour. The most authoritative method of measuring intracellular fluxes, ¹³C Metabolic Flux Analysis (¹³C MFA), uses the labeling pattern obtained from metabolites (typically amino acids) during ¹³C labeling experiments to derive intracellular fluxes. However, these metabolite labeling patterns cannot easily be obtained for each of the members of the community. Here we propose a new type of ¹³C MFA that infers fluxes based on peptide labeling, instead of amino acid labeling. The advantage of this method resides in the fact that the peptide sequence can be used to identify the microbial species it originates from and, simultaneously, the peptide labeling can be used to infer intracellular metabolic fluxes. Peptide identity and labeling patterns can be obtained in a high-throughput manner from modern proteomics techniques. We show that, using this method, it is theoretically possible to recover intracellular metabolic fluxes in the same way as through the standard amino acid based ¹³C MFA, and quantify the amount of information lost as a consequence of using peptides instead of amino acids. We show that by using a relatively small number of peptides we can counter this information loss. We computationally tested this method with a well-characterized simple microbial community consisting of two species.     

Isotope-assisted metabolic flux analysis as an equality-constrained nonlinear program for improved scalability and robustness

Stable isotope-assisted metabolic flux analysis (MFA) is a powerful method to estimate carbon flow and partitioning in metabolic networks. At its core, MFA is a parameter estimation problem wherein the fluxes and metabolite pool sizes are model parameters that are estimated, via optimization, to account for measurements of steady-state or isotopically-nonstationary isotope labeling patterns. As MFA problems advance in scale, they require efficient computational methods for fast and robust convergence. The structure of the MFA problem enables it to be cast as an equality-constrained nonlinear program (NLP), where the equality constraints are constructed from the MFA model equations, and the objective function is defined as the sum of squared residuals (SSR) between the model predictions and a set of labeling measurements. This NLP can be solved by using an algebraic modeling language (AML) that offers state-of-the-art optimization solvers for robust parameter estimation and superior scalability to large networks. When implemented in this manner, the optimization is performed with no distinction between state variables and model parameters. During each iteration of such an optimization, the system state is updated instead of being calculated explicitly from scratch, and this occurs concurrently with improvement in the model parameter estimates. This optimization approach starkly contrasts with traditional “shooting” methods where the state variables and model parameters are kept distinct and the system state is computed afresh during each iteration of a stepwise optimization. Our NLP formulation uses the MFA modeling framework of Wiechert et al. [1], which is amenable to incorporation of the model equations into an NLP. The NLP constraints consist of balances on either elementary metabolite units (EMUs) or cumomers. In this formulation, both the steady-state and isotopically-nonstationary MFA (inst-MFA) problems may be solved as an NLP. For the inst-MFA case, the ordinary differential equation (ODE) system describing the labeling dynamics is transcribed into a system of algebraic constraints for the NLP using collocation. This large-scale NLP may be solved efficiently using an NLP solver implemented on an AML. In our implementation, we used the reduced gradient solver CONOPT, implemented in the General Algebraic Modeling System (GAMS). The NLP framework is particularly advantageous for inst-MFA, scaling well to large networks with many free parameters, and having more robust convergence properties compared to the shooting methods that compute the system state and sensitivities at each iteration. Additionally, this NLP approach supports the use of tandem-MS data for both steady-state and inst-MFA when the cumomer framework is used. We assembled a software, eiFlux, written in Python and GAMS that uses the NLP approach and supports both steady-state and inst-MFA. We demonstrate the effectiveness of the NLP formulation on several examples, including a genome-scale inst-MFA model, to highlight the scalability and robustness of this approach. In addition to typical inst-MFA applications, we expect that this framework and our associated software, eiFlux, will be particularly useful for applying inst-MFA to complex MFA models, such as those developed for eukaryotes (e.g. algae) and co-cultures with multiple cell types.     

A Method to Constrain Genome-Scale Models with 13C Labeling Data

Current limitations in quantitatively predicting biological behavior hinder our efforts to engineer biological systems to produce biofuels and other desired chemicals. Here, we present a new method for calculating metabolic fluxes, key targets in metabolic engineering, that incorporates data from ¹³C labeling experiments and genome-scale models. The data from ¹³C labeling experiments provide strong flux constraints that eliminate the need to assume an evolutionary optimization principle such as the growth rate optimization assumption used in Flux Balance Analysis (FBA). This effective constraining is achieved by making the simple but biologically relevant assumption that flux flows from core to peripheral metabolism and does not flow back. The new method is significantly more robust than FBA with respect to errors in genome-scale model reconstruction. Furthermore, it can provide a comprehensive picture of metabolite balancing and predictions for unmeasured extracellular fluxes as constrained by ¹³C labeling data. A comparison shows that the results of this new method are similar to those found through ¹³C Metabolic Flux Analysis (¹³C MFA) for central carbon metabolism but, additionally, it provides flux estimates for peripheral metabolism. The extra validation gained by matching 48 relative labeling measurements is used to identify where and why several existing COnstraint Based Reconstruction and Analysis (COBRA) flux prediction algorithms fail. We demonstrate how to use this knowledge to refine these methods and improve their predictive capabilities. This method provides a reliable base upon which to improve the design of biological systems.