^{13}C-Based Metabolic Flux Analysis

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The ^{13}C-based metabolic flux analysis (^{13}C-MFA) provides valuable information regarding cell physiology. Bioinformatics tools have been developed to estimate metabolic flux distributions from the results of tracer isotopic labeling experiments using a ^{13}C-labeled carbon source. Metabolic flux is determined by nonlinear fitting of a metabolic model to the isotopic labeling enrichment of intracellular metabolites measured by mass spectrometry. Whereas ^{13}C-MFA is conventionally performed under isotopically constant conditions, isotopically nonstationary ^{13}C metabolic flux analysis (INST-^{13}C-MFA) has recently been developed for flux analysis of cells with photosynthetic activity and cells at a quasi-steady metabolic state (e.g., primary cells or microorganisms under stationary phase). Here, the development of a novel open source software for INST-^{13}C-MFA on the Windows platform is reported. OpenMebius (Open source software for Metabolic flux analysis) provides the function of autogenerating metabolic models for simulating isotopic labeling enrichment from a user-defined configuration worksheet. Analysis using simulated data demonstrated the applicability of OpenMebius for INST-^{13}C-MFA. Confidence intervals determined by INST-^{13}C-MFA were less than those determined by conventional methods, indicating the potential of INST-^{13}C-MFA for precise metabolic flux analysis. OpenMebius is the open source software for the general application of INST-^{13}C-MFA.

The^{13}C-based metabolic flux analysis (^{13}C-MFA) provides valuable information regarding cell physiology in fields ranging from the metabolic engineering of microorganisms to the analysis of human metabolic diseases [^{13}C-MFA is desired for further methodology improvement and wider applications for

In ^{13}C-MFA, after feeding of a ^{13}C-labeled carbon source into a cell culture, amino acids or intermediates are extracted and subjected to mass spectrometric analysis. For the simplest example, [1-^{13}C] glucose is converted to pyruvate (PYR) and then alanine (Ala) via two glycolytic pathways including the Embden-Meyerhof-Parnas (EMP) pathway and the pentose phosphate (PP) pathway (Figure ^{13}C-labeled molecule and one nonlabeled molecule of Ala are generated from one molecule of [1-^{13}C] glucose by the EMP pathway, no ^{13}C-labeled Ala is produced via the PP pathway, because the ^{13}C atom is metabolically discarded as CO_{2}. Thus, the metabolic flux ratio between the EMP and PP pathways could be estimated from the relative abundances of ^{13}C-labeled and nonlabeled Ala using mass spectrometry.

Principle of ^{13}C-based metabolic flux analysis. (a) Principle of ^{13}C-based metabolic flux analysis (^{13}C-MFA). Isotopic enrichment of alanine depends on metabolic flux via the Embden-Meyerhof-Parnas (EMP) pathway or the pentose phosphate (PP) pathway. (b) The configuration of the model is described in “Metabolic_network.xlsx.” The metabolic reactions and the carbon transfer are described in the “Rxns” and “Carbon_transitions” columns, respectively. Detailed rules are provided in the tutorial on the project home page. ((c) and (d)) Metabolic steady state and isotopically stationary. The isotopic labeling experiment is performed under metabolic steady state. After feeding ^{13}C-labeled glucose, isotopic labeling enrichment changes in a time-dependent manner and then reaches a stationary condition. Whereas cells are sampled under isotopically stationary conditions in conventional ^{13}C-MFA, time courses of isotopic labeling enrichment during an isotopically transient state are used for INST-^{13}C-MFA.

In ^{13}C-MFA of complex networks of carbon central metabolism, metabolic fluxes are computationally estimated by a nonlinear optimization method since the relationship between metabolic fluxes and isotopic labeling enrichment is usually nonlinear. For that purpose, a metabolic model

The optimized value ^{13}C-MFA such as 13CFLUX [

In the case of conventional ^{13}C-MFA, isotopic labeling data must be obtained from cell culture under metabolic steady state and isotopically stationary conditions (Figures ^{13}C-labeled substrate.

In recent years, a novel method has been developed to determine metabolic flux using a time course of isotopic labeling data obtained from an isotopically transient state (Figure ^{13}C-MFA), an expanded metabolic model ^{13}C-MFA [^{13}C-MFA to analyze the fast turnover of isotopic labeling enrichment in carbon central metabolism [^{13}C-MFA would be essential for the analysis of photoautotrophic organisms using CO_{2} as a carbon source. Metabolic flux cannot be determined by conventional ^{13}C-MFA using ^{13}CO_{2} as a carbon source, because all metabolites are uniformly labeled after reaching an isotopically stationary phase [^{13}C-MFA, a software package with a graphical user interface has recently been reported (INCA [^{13}C-MFA are also useful for facilitating the further development of INST-^{13}C-MFA [

Here, a novel open source software package for INST-^{13}C-MFA, OpenMebius (Open source software for Metabolic flux analysis), is reported. OpenMebius has been developed to perform INST-^{13}C-MFA and conventional ^{13}C-MFA using a user-defined metabolic model. A metabolic model

OpenMebius is implemented in MATLAB (MathWorks, Natick, MA, USA) for the Windows platform. The software consists of two parts: automated model construction and metabolic flux estimation by nonlinear optimization. Functions for processing raw mass spectrum data and the determination of confidence intervals are also included. OpenMebius is designed for conventional ^{13}C-MFA and INST-^{13}C-MFA using mass spectrometry data. Isotopic labeling enrichment of metabolites is described by a mass distribution vector (MDV) [^{13}C. To obtain the

In conventional ^{13}C-MFA, a metabolic model

Since the metabolic flux is determined in cells at metabolic steady state,

In the case of INST-^{13}C-MFA, the metabolic model

The procedure for estimating metabolic flux is shown in Figure

Procedure for metabolic flux estimation. Step 1: initial estimates of metabolic fluxes are given at random following the constraints of the mass balance, biomass synthetic rate, and substrate consumption and production rate. Step 2: metabolic fluxes are determined by minimizing the difference between simulated and measured isotopic labeling enrichment using the

Confidence intervals of estimated fluxes are determined by OpenMebius using the grid search method [

OpenMebius is a toolbox for conventional ^{13}C-MFA and INST-^{13}C-MFA using mass spectrometry data implemented in MATLAB on the Windows platform. Figure ^{13}C-MFA on a simplified TCA cycle model mentioned below. A metabolic model is generated by the “ConstEMUnetwork” function from user-defined metabolic network information described in text or Excel worksheet files. After loading related data, a metabolic flux distribution is estimated by the “marquardt_inst” function using a nonlinear optimization (

Representative Matlab code and structure of the metabolic model directory for isotopically nonstationary-^{13}C-metabolic flux analysis using OpenMebius. (a) A metabolic model “model” is generated from information described in “TCA cycle model” directory by “Modelconfig” and “ConstEMUnetwork” functions. After loading time course mass spectrometry data in “Artificial data” directory, isotopic labeling data of carbon sources and an initial metabolic flux distribution are prepared. A metabolic flux distribution (“Flux”) is estimated by the “marquardt_inst” function using nonlinear optimization (Levenberg-Marquardt method). (b) Directory structure of the TCA cycle model. Configuration for simulating isotopic labeling, carbon source, and mass balance are described in MSReac.csv, Substrate.csv, and Mass_balance.csv, respectively. The simulated data directory includes a series of experimental data. Fluxes for biomass syntheses and product excretion, isotopic labeling information of substrate, metabolic concentrations of intracellular metabolite, and sampling times are described in efflux.csv, Substrate.csv, Initial_pool.csv, and Time_course.csv, respectively. Components.csv defines chemical elements in a mass fragment. A series of Abandance_list.csv are time course of isotopic labeling enrichment data. The “TCA cycle model” and online manual are available on web page (

The performance of OpenMebius for conventional ^{13}C-MFA was tested with the simplified metabolic network used in the previous study [^{13}C and 50% U-^{13}C) and glutamate (100% 1-^{13}C). Considering the simulated data as the measured MDV, the metabolic flux distribution was determined by the conventional ^{13}C-MFA function of OpenMebius. The estimated flux distribution was essentially identical to that of simulated distribution, which was consistent with the results of 13CFLUX [

Configuration of TCA cycle model.

FluxID | Rxns | Net flux | Carbon transitions |
---|---|---|---|

R1 | Subs_PYR_EX → PYR | 0 | abc → abc |

R2 | PYR → ACCOA + Ind_CO2 | 0 | abc → bc + a |

R3 | ACCOA + OAA → IsoCit | 0 | ab + cdef → fedbac |

R4 | IsoCit → AKG + Ind_CO2 | 0 | abcdef → abcde + f |

R5 | AKG → Sym_SUC + Ind_CO2 | 0 | abcde → abcd + e |

R6 | Sym_SUC → OAA | 1 | abcd → abcd |

R7 | PYR + Ind_CO2 → OAA | 2 | abc + d → abcd |

R8 | AKG → |
0 | |

R9 | OAA → |
0 | |

R10 | OAA → |
0 | |

R11 | PYR → |
0 | |

R12 | PYR → |
0 | |

R13 | PYR → |
0 | |

R14 | Subs_GLU_EX → AKG | 0 | abcde → abcde |

R15 | OAA → Sym_SUC | 1 | abcd → abcd |

R16 | OAA → PYR + Ind_CO2 | 2 | abcd → abc + d |

^{13}C-MFA of simplified TCA model. Fluxes were calculated using OpenMebius, OpenFLUX, and 13CFLUX. Dotted lines indicate reactions whose metabolic fluxes are predetermined. Solid line arrows: intracellular metabolic reactions. Dotted line arrows: substrate consumption and biomass synthesis. Suffix: _B, biomass drain; _EX, exo-metabolites. Metabolites: PYR, pyruvate; ACCOA, acetyl-CoA; IsoCit, isocitrate;

To simulate an isotopic labeling experiment during an isotopically nonstationary period, the pool size information of six intermediates was arbitrarily added to the above TCA metabolic network. A metabolic model for INST-^{13}C-MFA was successfully constructed by OpenMebius. To prepare simulated experimental data, time course data of isotopic labeling dynamics of oxaloacetate and succinate were created using the differential equation (

Dynamics of isotopic labeling enrichment. Time course of fitted (solid lines) and simulated (symbols) isotopic labelling enrichment is shown. OAA, oxaloacetate; SUC, succinate.

For a performance comparison between conventional ^{13}C-MFA and INST-^{13}C-MFA, the 95% confidence intervals of four representative reactions were determined by the grid search method (Figure ^{13}C-MFA, confidence intervals were estimated using the simulated data with the 17 time points prepared above. In the case of conventional ^{13}C-MFA, a novel simulated dataset was prepared by the following procedure. From the ^{13}C-MFA were approximately 22% that of conventional ^{13}C-MFA (Figure ^{13}C-MFA, suggesting that the time course MDV data includes information for a more precise estimation of metabolic flux (Figure ^{13}C-MFA could be a reliable method to determine

Comparison of confidence intervals between INST-^{13}C-MFA and conventional ^{13}C-MFA. (a) 95% confidence intervals of four representative fluxes were compared between conventional ^{13}C-MFA (red) and INST-^{13}C-MFA (blue). Black triangles indicate the actual values. (b) Shapes of reoptimized sum of squared difference (SSD) determined by the grid search. The red and blue lines show the results of conventional ^{13}C-MFA and INST-^{13}C-MFA, respectively. The horizontal lines represent the threshold value for the 95% confidence intervals.

INST-^{13}C-MFA was also performed using simulated data produced from the central metabolic model of^{−1}. Simulated MDVs were sampled 11 times at 1-second intervals using 100% [1-^{13}C] glucose as a carbon source. Considering the simulated dataset as experimental data, metabolic fluxes were estimated using the INST-^{13}C-MFA function of OpenMebius. The step size was set to 0.001 seconds to compute the simulated MDVs. Although the computation time took 7 h 42 min (Intel Xeon X5670 2.93 GHz), the estimated flux distribution was essentially identical to that of the simulated data (Figure ^{13}C-MFA using a realistic metabolic model of

Metabolic network of^{−1} s^{−1}). Abbreviations are shown in the Abbreviations section.

OpenMebius is the first open source software for metabolic flux analyses under both isotopically stationary and nonstationary conditions. The software supports the automatic construction of a metabolic model for INST-^{13}C-MFA from a user-defined metabolic network. Analysis using simulated data demonstrated not only the utility of OpenMebius for INST-^{13}C-MFA, but also its potential for use in metabolic flux analysis with reduced confidence intervals. OpenMebius provides an essential bioinformatics tool for INST-^{13}C-MFA to analyze metabolic flux in cells with slower metabolism (i.e., mammalian) [

Mass distribution vector

^{13}C-MFA:

^{13}C-based metabolic flux analysis

^{13}C-MFA:

Isotopically nonstationary ^{13}C metabolic flux analysis

Acetyl-CoA

Citrate

Dihydroxyacetone phosphate

Erythrose-4-phosphate

Fructose-6-phosphate

Fructose-1,6-bisphosphate

Fumarate

Glucose-6-phosphate

Glyceraldehyde-3-phosphate

Glyoxylate

Isocitrate

Malate

Oxaloacetate

Phosphoenolpyruvate

6-Phosphoglycerate

3-Phosphoglycerate

Pyruvate

Ribose-5-phosphate

Ribulose-5-phosphate

Sedoheptulose-7-phosphate

Succinate

Sum of metabolite pool of succinate and fumarate

Xylulose-5-phosphate

Valine

Lysine.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank Dr. Yoshihiro Toya, Dr. Katsunori Yoshikawa, Dr. Tomokazu Shirai, and all members of the Shimizu Lab for their help with the software development. This research was partially supported by JST, Strategic International Collaborative Research Program, SICORP for JP-US Metabolomics.

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