BioMed Research International

Volume 2014, Article ID 627014, 10 pages

http://dx.doi.org/10.1155/2014/627014

## OpenMebius: An Open Source Software for Isotopically Nonstationary ^{13}C-Based Metabolic Flux Analysis

^{1}Department of Bioinformatic Engineering, Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita, Osaka 565-0871, Japan^{2}Quantitative Biology Center, RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan

Received 12 February 2014; Revised 17 April 2014; Accepted 8 May 2014; Published 11 June 2014

Academic Editor: Martin Robert

Copyright © 2014 Shuichi Kajihata et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The *in vivo* measurement of metabolic flux by ^{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.

#### 1. Introduction

The* in vivo* measurement of metabolic flux by ^{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 [1–3]. Since metabolic fluxes are estimated by a computational analysis of the isotopic labeling data produced by a series of wet experiments [4–7], the development of an open software platform for ^{13}C-MFA is desired for further methodology improvement and wider applications for* in vivo* metabolic flux measurement.

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 1(a)). Whereas one ^{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.

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 is constructed based on the metabolic pathway network and the carbon transition network, which represents the transitions of carbon atoms between substrates and products in a metabolic reaction (Figure 1(b)). is a function to calculate isotopic labeling enrichment or the mass distribution vector (MDV) of metabolites from the given metabolic fluxes and isotopic labeling patterns of carbon sources. Consider
Here, is a simulated mass spectrum of metabolite . and are the vectors of metabolic flux and isotopic labeling pattern of carbon source, respectively. A vector of metabolic flux is fitted to the observed mass spectrum () by a nonlinear optimization method:

The optimized value is the estimated metabolic flux distribution in the cells to minimize the covariance-weighted sum of squared difference. is the covariance matrix with a measurement standard deviation located on the diagonal. is the stoichiometric matrix. There are several software packages to perform conventional ^{13}C-MFA such as 13CFLUX [8], 13CFLUX2 [9], C13 [10], Metran [11], FIA [12], influx_s [13], and OpenFLUX [14].

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 1(c) and 1(d)). Here, metabolic steady state indicates the constant flux distribution and pool size of intracellular metabolites that has to be maintained during the isotopic labeling experiment (Figure 1(c)). An isotopically stationary condition means constant isotopic labeling enrichment of metabolites. A long culture period has often been required to achieve isotopically stationary conditions after feeding a ^{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 1(d)) [15–17]. For the isotopically nonstationary MFA (INST-^{13}C-MFA), an expanded metabolic model is used to simulate isotopic labeling dynamics, taking into consideration the metabolite pool size in the cell:
where is the time of the th sampling point. is the vector of the pool sizes of all metabolites in the metabolic system. The formulation indicates that the intracellular pool sizes of intermediates in central metabolism must be precisely determined for INST-^{13}C-MFA [18, 19]. Time course analysis by rapid sampling techniques has also been performed in INST-^{13}C-MFA to analyze the fast turnover of isotopic labeling enrichment in carbon central metabolism [20, 21]. Despite these technical challenges, INST-^{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 [22]. The methodology is also promising for the precise metabolic flux analysis of cells at a quasi-steady metabolic state (e.g., primary cells or microorganisms in stationary phase). In order to analyze a time course dataset produced by INST-^{13}C-MFA, a software package with a graphical user interface has recently been reported (INCA [23]). In addition to these sophisticated tools, open source software packages such as OpenFLUX [14] for conventional ^{13}C-MFA are also useful for facilitating the further development of INST-^{13}C-MFA [24].

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 can be automatically generated from a metabolic pathway and a carbon transition network described in text or Microsoft Excel worksheet files. The metabolic flux distribution can be estimated by nonlinear fitting of the metabolic model to the isotopic labeling enrichment data.

#### 2. Materials and Methods

##### 2.1. Model Construction

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) [25]:
where is the vector of isotopic labeling enrichment of metabolite . indicates the relative abundance of a metabolite in which carbons are labeled with ^{13}C. To obtain the of the carbon skeleton, mass spectrum data are corrected for the presence of naturally occurring isotopes using the correction matrix [26].

In conventional ^{13}C-MFA, a metabolic model is an algebraic equation used to generate from the vector of metabolic flux () and the isotopic labeling pattern of a carbon source , as shown in (1).

Since the metabolic flux is determined in cells at metabolic steady state, follows the stoichiometric equation described by where is the stoichiometric matrix. In OpenMebius, is constructed from a metabolic network described in the “Rxns” column in a user-defined configuration worksheet (Figure 1(b)), taking into consideration the fluxes for biomass syntheses and product excretion. is calculated by the framework of elementary metabolite units (EMU) [27] using the carbon transition information described in the “carbon_transitions” column of the configuration worksheet (Figure 1(b)). In the framework, the carbon transition network is decomposed to cascade networks of EMUs depending on those carbon numbers. The cascade networks of the EMUs with th carbon follow the EMU balance equation [27]: Here, each row in matrix is MDV of corresponding EMU. The matrix includes EMUs of the carbon source or the smaller size EMUs. The element in row and column of matrices and the element of matrix are described, respectively, as follows:

In the case of INST-^{13}C-MFA, the metabolic model is expanded to describe a transition state of isotopic labeling (Figure 1(d)) by considering the dilution of isotopic labeling enrichment depending on the pool size of intermediates, as shown in (3), where is a vector of the pool size of each metabolite that is constant under metabolic steady state. is the time of the th sampling point. In this study, instead of a direct description of the metabolic model , time-dependent changes in the isotopic labeling enrichment of metabolite are described by the differential equation as follows:
where and represent the fluxes of the th inflow reaction and the th outflow reaction of metabolite , respectively. The model is automatically constructed by “ConstEMUnetwork.m.” Detailed rules to describe a user-defined metabolic pathway and carbon transition network are provided on the project home page (http://www-shimizu.ist.osaka-u.ac.jp/hp/en/software/OpenMebius.html).* Euler*’s method is implemented to solve the ordinary differential equation (8) without adaptive step size control. Stiff equations can be resolved by carefully selecting the step size. The are standardized for each step to prevent divergence. Moreover, no specific libraries were used to implement the algorithm for solving differential equations.

##### 2.2. Metabolic Flux Estimation

The procedure for estimating metabolic flux is shown in Figure 2. In Step 1, the initial flux distribution is given considering the rates of biomass synthesis, substrate consumption, and product excretion (Figure 2, Step 1). In Step 2, the metabolic flux vector is optimized to minimize the covariance-weighted sum of squared difference (SSD) using the* Levenberg-Marquardt* method [28] (Figure 2, Step 2):
Here, is the vector of experimental data at . is the total number of measured metabolites for data fitting. is the total number of sampling points ( in the case of isotopically stationary), and is the measurement covariance matrix with the measurement standard deviation located on the diagonal.

##### 2.3. Calculation of Confidence Interval

Confidence intervals of estimated fluxes are determined by OpenMebius using the grid search method [29, 30]. The metabolic flux of reaction is fixed to and the objective function is reoptimized. Here, is the optimized metabolic flux of reaction and is the perturbation level. The procedure is iterated with increased or decreased . The range of fixed metabolic flux whose SSD is less than the threshold level is the confidence interval. The threshold level is determined by where is the minimized SSD with one fixed flux, is the original minimized SSD, is the number of independent data points used in the fitting, is the degrees of freedom in the original flux fit, is the -distribution, and is the confidence level.

#### 3. Results and Discussion

##### 3.1. Implementation

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 3 shows a representative MATLAB code to perform INST-^{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 (*Levenberg-Marquardt* method). For a routine analysis, a batch execution of metabolic flux estimations is also supported. See Materials and Methods for detailed information.

##### 3.2. Test Case of Isotopically Stationary MFA: Simplified TCA Cycle Model

The performance of OpenMebius for conventional ^{13}C-MFA was tested with the simplified metabolic network used in the previous study [14] (Figure 4). The metabolic network consisted of the 16 reactions of the TCA cycle using pyruvate and glutamate as substrates described by Table 1. Among 16 metabolic fluxes, one influx (R1) and six effluxes (R8–R13) were predetermined. The metabolic model was successfully constructed from the metabolic pathway and carbon transition networks. Here, the vector of experimental mass spectra () of valine, lysine, aspartate, and succinate was artificially created using the metabolic model, the flux distribution described in the previous research [14], and the isotopic labeling of pyruvate (mixture of 50% 1-^{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 [8] and OpenFLUX [14] (Figure 4). The total computation time was 6 seconds for 10 cycles of optimization (Intel Core i7 2.80 GHz), which was the same as in OpenFLUX.

##### 3.3. Test Case of Isotopically Nonstationary MFA: Simplified TCA Cycle Model

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 (8) combined with the pool size information . The current version of OpenMebius uses the pool size information as constant values, although should be estimated with an optimization procedure since the pool size data are less reliable than isotopic labeling measurements. That function will be supported in a future version of OpenMebius. The flux distribution and isotopic labeling patterns of substrate were identical to those of the previous section. The MDVs of oxaloacetate and succinate were sampled 17 times at 5-second intervals* in silico*, to which Gaussian noise (1%) was added to imitate actual measurements. Considering the simulated data as measured MDVs (), the metabolic flux distribution was estimated using OpenMebius. The step size was set to 0.01 seconds to compute the simulated MDVs. Although only two intracellular metabolites were used for data fitting, the fitted isotopic labeling dynamics and a flux distribution were consistent with the simulated data (Figure 5). The total computational time for one cycle of optimization was around 10 minutes (Intel Core i7 2.80 GHz).

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 6(a)). For INST-^{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 of oxaloacetate and succinate calculated using (1), 17 sets of simulated mass spectra () data were produced with the addition of Gaussian noise (1%). While an identical number of data points was used, the confidence intervals determined by INST-^{13}C-MFA were approximately 22% that of conventional ^{13}C-MFA (Figure 6(a)). The sharply curved parabolas were observed for INST-^{13}C-MFA, suggesting that the time course MDV data includes information for a more precise estimation of metabolic flux (Figure 6(b)). These results suggest that INST-^{13}C-MFA could be a reliable method to determine* in vivo* metabolic flux with narrow confidence intervals.

##### 3.4. Test Case of Isotopically Nonstationary MFA:* Escherichia coli* Model

INST-^{13}C-MFA was also performed using simulated data produced from the central metabolic model of* E. coli* with 54 reactions and 22 intermediates. A simulated experimental dataset was prepared based on the literature-reported metabolic flux distribution and metabolite pool size data [31]. Pool sizes of unmeasured metabolites (GAP, PYR, Xu5P, E4P, IsoCit, *α*KG, and glyoxylate) were arbitrarily set at 0.1 *μ*mol gDCW^{−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 7). The result indicates that OpenMebius could deal with INST-^{13}C-MFA using a realistic metabolic model of* E. coli*.

#### 4. Conclusions

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) [17] and cultivation with single carbon substrates (i.e., cyanobacteria) [15].

#### Abbreviations

MDV: | Mass distribution vector |

^{13}C-MFA: | ^{13}C-based metabolic flux analysis |

INST-^{13}C-MFA: | Isotopically nonstationary ^{13}C metabolic flux analysis |

KG: | -Ketoglutarate |

ACCOA: | Acetyl-CoA |

Cit: | Citrate |

DHAP: | Dihydroxyacetone phosphate |

E4P: | Erythrose-4-phosphate |

F6P: | Fructose-6-phosphate |

FBP: | Fructose-1,6-bisphosphate |

FUM: | Fumarate |

G6P: | Glucose-6-phosphate |

GAP: | Glyceraldehyde-3-phosphate |

GLX: | Glyoxylate |

IsoCit: | Isocitrate |

MAL: | Malate |

OAA: | Oxaloacetate |

PEP: | Phosphoenolpyruvate |

6PG: | 6-Phosphoglycerate |

3PG: | 3-Phosphoglycerate |

PYR: | Pyruvate |

R5P: | Ribose-5-phosphate |

Ru5P: | Ribulose-5-phosphate |

S7P: | Sedoheptulose-7-phosphate |

SUC: | Succinate |

SUC_FUM: | Sum of metabolite pool of succinate and fumarate |

Xu5P: | Xylulose-5-phosphate |

VAL: | Valine |

LYS: | Lysine. |

#### Conflict of Interests

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

#### Acknowledgments

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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