These analyses include concertedly linked experimental and computational stages: (i) assuming the metabolic model and optimizing the experimental design; (ii) feeding the investigated organism using a chosen 13C-labeled substrate (tracer); (iii) measuring the extracellular effluxes and detecting the 13C-patterns of intracellular metabolites; and (iv) computing flux parameters that minimize the differences between observed and simulated measurements, followed by evaluating flux statistics. In its early stages, 13C-MFA was performed on the basis of data obtained in a single labeling experiment (SLE) followed by exploiting the developed high-performance computational software. Recently, the advantages of parallel labeling experiments (PLEs), where several LEs are conducted under the conditions differing only by the tracer(s) choice, were demonstrated, particularly with regard to improving flux precision due to the synergy of complementary information. The availability of an open-source software adjusted for PLE-based 13C-MFA is an important factor for PLE implementation.Steady-state in silico simulation confirmed that flux precision is improved when 13C-MFA is implemented by fitting PLE data to the common model compared with SLE-based analysis. Efficient flux resolution could be achieved in the PLE-mediated analysis when the choice of tracer was based on an experimental design computed to minimize the flux variances from different parts of the metabolic network. The analysis provided by OpenFLUX2 mainly includes (i) the optimization of the experimental design, (ii) the computation of the flux parameters from LEs data, (iii) goodness-of-fit testing of the model’s adequacy, (iv) drawing conclusions concerning the identifiability of fluxes and construction of a contribution matrix reflecting the relative contribution of the measurement variances to the flux variances, and (v) precise determination of flux confidence intervals using a fine-tunable and convergence-controlled Monte Carlo-based method.The open-source software OpenFLUX, initially developed for the analysis of SLEs, was extended for the computation of PLE data. Using the OpenFLUX2, open-source OpenFLUX2 provides a friendly software environment that facilitates beginners and existing OpenFLUX users to implement LEs for steady-state 13C-MFA including experimental design, quantitative evaluation of flux parameters and statistics.The developed The online version of this article (doi:10.1186/s12934-014-0152-x) contains supplementary material, which is available to authorized users. The corresponding calculations were provided for 5 independent SLE with earlier simulated MIDs and the measured effluxes with the η -function. The summarized values of the η -function for all fluxes, (Ση(0.95)([1 − 13C]SLE))k, which were calculated for each flux from k = 1, 2, …, 5 SLEs, varied in a rather narrow range (between 37.9 and 38.5). Considering the total number of fluxes  for the assumed metabolic model and the detected measurement-dependent sensitivity of the η -function, if the difference between the Ση(0.95) values is no greater than 1, then the LEs can be considered to be provided with an essentially equivalent flux precision. Certainly, the value of Ση(0.95) could be considered only as a general, conditional measure of flux resolutions in the investigated network: some metabolic branches could be resolved better, and other branches – worse in different experiments with, perhaps, equal values of summing normalized flux precision functions. So, only the value of the ηγ(ui) -function could be considered as the absolute measure of the ui-flux resolution efficiency that could be compared with other LEs performed with the same metabolic model.Concerning the tracer-specific values of entclass1pt{minima13C-MFA included the set of estimated fluxes, the goodness-of-fit of the model’s adequacy, and the confidence intervals of fluxes, in accord with the recently recommended publishing guidelines -glucose as a tracer (see Table (Exp_3.1)). The “contribution matrix” , u(θtrue), as an important component of the flux statistics ij elements of this matrix indicate the relative importance of the variance of the j-th measurement to the local variance of the i-th flux. As can be observed in Additional file F P5P + CO2; PYR + CO2 →F OAA; OAA →F PYR + CO2; and CO2_EX →R CO2, respectively. The new set of “experimental data” was generated in the following fashion: the measured effluxes and all MIDs, except for “SER” MIDs, were considered as in the previously analyzed example. The “SER” MIDs were modified as in the case of “poor” resolution of the SER-390 (m + 0) MID, which exhibited an unknown by-product that increased the value of the corresponding SER peak to +4.5%. Due to the necessity of normalizing all SER-isotopomers, the applied modification resulted in a proportional decrease in the other SER MID portions; therefore, the SER-390 MIDs were modified from (m + 0)/(m + 1)/(m + 2)/(m + 3) = 0.443/0.357/0.140/0.042 (in the previously described example) to a ratio of 0.463/0.344/0.135/0.040.In this report, an example is presented in which the mistaken flux parameters could be assumed when the statistical analysis of the obtained solution was partially provided but to an insufficient extent. Let us analyze the first from five earlier described with 99% -13C-glucθ) objective function with the empty null space of the Jf(θ) matrix evaluated at the new point of convergence, χ2 -statistically acceptable interval (see Table (Exp_4.1)). Simultaneously, the parameters obtained for several fluxes did not coincide with the true flux values even in the range of their confidence intervals. Among them there were fluxes θ8 and θ31 ij elements in the Additional file It is obvious that measured MIDs and effluxes’ parameters are completely separate categories of experimental data that could not be trivially compared. It is well established  that lab13C-labeled isotopomer of glucose, [U-13C]-glucose, is often used as a tracer in 13C-MFA. In the present study, new sets of “experimental data” were generated for the same metabolic model when different relative amounts of [U-13C]-glucose  mixed with non-labeled ([U-12C]) glucose were used as the sole carbon source  and Additional file 13C-MFA resulted in values between 35.4 and 40.4 for the Ση(0.95)([U − 13/12C]SLE) function , e.g., θ22: PYR + CO2 →F OAA; v23: OAA →F PYR + CO2; θ31: CO2_EX →R CO2. The PLE-based 13C-MFA of experiments using [U-13/12C]-glucose as the carbon source actually improved the resolution of all fluxes estimated in the corresponding SLEs, Ση(0.95)([U − 13/12C]PLE) = 42.4. Moreover, the tracer-specific behavior described in relation to SLEs was reproduced in the PLE. The colored scheme presented in Figure η -function for all fluxes obtained in different experiments, illustrating this fact and demonstrating that optimization of the experimental design is necessary to increase the precision of the targeted fluxes -glucose as the tracer) using the value of the To achieve the best flux resolution in an LE employing a mixture 78 %/[U − 13C]22 % glucose isotopomers in the SLE  when some modifications differed in the metabolic model of the l-lysine-producing C. glutamicum strain applied in the present study, and plans were made to obtain another set of measurements , [U − 13C] and [U − 12C] glucose isotopomers (“randomly mixed”) as the tracers. As shown in the presented results ([1 − 13C]78 %[U − 13C]22 %SLE) = 38.4, with “partially optimized” conditions – Ση(0.95) = 38.4 was detected here, and among described earlier . Simultaneously, the free fluxes, θi, that were used as the targets for the partial optimization generally showed the best resolutions ,  function ). On the other hand, the real difference between summarized values of the η -function for all fluxes determined for these PLEs was very small  in the individual LEs of the PLE, was recently developed to evaluate metabolic fluxes for the metabolic model of wild-type Escherichia coli with a high precision [13C]-glucose, and separate [3-13C]-glucose in the medium provided the most precise fluxes for the E. coli model among all possible paired combinations of singly labeled glucose added as the sole tracer.It has been repeatedly shown ,59,72 threcision . Additio13C-glucose isotopomers, which were separately added to the medium as tracers for SLEs and PLEs, was investigated. The solutions of the corresponding constrained NLLSPs are summarized in Additional file D-factor (see (S − 1.5.14)) for the six singly labeled tracers, the volume of the confidence ellipsoid for free fluxes had to be increased in the following order for the applied tracers:It was of interest to evaluate the advantages of this approach in the case of another metabolic model used in the present study. Initially, the possible exploitation of all six singly labeled 13C]-glucose as a singly labeled glucose tracer. Simultaneously, a different order of the tracers could be formed by increasing the summarized values of the normalized flux precision functions, Ση(0.95)([i − 13C]SLE) ≡ Ση(i), i = 1, 2, …, 6:13C]-glucose was the best tracer according to this Ση -based criterion; namely, [4-13C]-glucose was the best tracer for determining 13 fluxes, and the corresponding values of the η -function for this tracer for 28 other fluxes were among the maximal values in the range of no more than 0.02, which is a typical value for measurement-specific errors. Notably, the applicability of [4-13C]-glucose as the tracer for the efficient resolution of primary branch points and reversibilities was previously demonstrated for a similar C. glutamicum metabolic model -glucose and [1-13C]-glucose provided the most precise fluxes. In contrast, the use of [2-13C]-glucose and [5-13C]-glucose as the tracers in two independent LEs provided the least precise fluxes:The flux resolution obtained in each of the six independent LEs could clearly be improved via PLE-based flux analysis if two or more LEs were combined in the PLE. The corresponding calculations for the possible pair combinations are provided  that previously resulted in the best flux resolution according to the Ση -based criterion . The obtained results are presented in Additional file θ4, θ14, θ22, see Additional file θ8, θ10, θ26, see Additional file 13C] labeled glucose. The second PLE consisted of six LEs, where, in addition to the three LEs from the previous PLE, three LEs used the optimized mixed paired combinations of glucose isotopomers. The corresponding PLEs were simulated, and 13C-MFA was performed, resulting in solutions of NLLSPs with highly resolved fluxes PLE = 44.6 Additional file , Figure To test this possibility, partial optimization was conducted by searching the minimal linear approximation of free flux variances in the triangle composed of all possible mixed tracers, which consisted of the three singly labeled glucose isotopomers  > 0; i.e., the length of the 95% confidence interval did not exceed the value of the corresponding flux corrected by the scaling factor.Notably, an exceptionally high flux resolution was obtained in both PLEs including 6 LEs. For all fluxes, 13C-MFA. These extensions included (i) fitting the obtained experimental data, not only in SLEs but also in PLEs, to the assumed metabolic model; (ii) computing the flux parameters and providing the goodness-of-fit of the model’s adequacy, followed by an estimation of the model’s viability and its probable improvement; (iii) fine-tunable and convergence-controlled Monte Carlo-based approach to obtain distribution of optimized flux estimations followed by precise computing of flux confidence intervals; and (iv) conducting general and/or partial experimental design through searching for the minimal value to characterize the average confidence interval length for all free fluxes and/or the minimal linear approximation of the targeted free flux variances, respectively. The considered examples demonstrated the specific features of these steps and their concerted essentiality for obtaining statistically verified results of the described 13C-MFA provided with the help of OpenFLUX2.The main aim of the present study was to extend the possibilities of the previously developed open-access OpenFLUX software for comprehensive ηγ, allowed for the quantitative characterization of the efficiency of the flux resolution at a confidence level of γ, with values of η close to “1” or “0” being obtained for efficiently or poorly resolved fluxes, respectively, depending on β as the scaling parameter, in particular. Moreover, the sum of η for all of the evaluated fluxes in the model, Ση, could be a rather convenient parameter for conditional comparison of the flux precision achieved in different experiments, i.e., depending on the tracer(s) used.Introducing the normalized flux precision function, χ2 -statistically acceptable value of the Ξ objective function but also confirmation of the expectation concerning the The goodness-of-fit test of the assumed metabolic model’s adequacy is an essential and extremely important part of the statistically verified solution of the NLLSP. This test involved not only obtaining the 13C-labeled glucose isotopomers or combinations of mixed labeled tracer(s), chosen according to the partial optimization of the targeted fluxes, usually resulted in better flux precision compared with the resolution of fluxes computed from SLE data, which were provided according to a sophisticated general experimental design strategy. Only one simplified metabolic model, consisting of an l-lysine-producing C. glutamicum strain, was used for the simulation of experimental data and for comprehensive 13C-MFA in the present study; however, the obtained general conclusions coincided well with the data reported by other groups working with other models  using as e.g., ,58)..13C-labe13C-MFA of SLE and PLE data will help to broaden investigations aimed at quantitatively estimating the cellular metabolic state with high precision.We hope that the developed OpenFLUX2 open-access software adjusted for comprehensive OpenFLUX2 is being released as open-source software. Regarding the citation of the OpenFLUX2 application, it is highly recommended that the present paper be cited, adding that this software is an extended version of the OpenFLUX open-source software described in .C. glutamicum metabolic model used as an example included catabolic reactions of the central metabolism, such as the Embden-Meyerhof-Parnas (EMP) and pentose phosphate (PP) pathways, the tricarboxylic acid (TCA) cycle, anaplerotic carboxylation, and the decarboxylation reaction of oxaloacetate and malate. Moreover, the pathways for the biosynthesis and transport of l-lysine and different extracellular co-products  were included. For glycine synthesis, two possible pathways, starting from serine and threonine [2-associated carbon transfer, the reactions, accompanied by CO2 production or consumption, were expressed in an explicit manner, including an anabolic reaction and a reaction involving CO2 exchange with environment. Additionally, the linear consequence of the irreversible reactions was represented as a single reaction. The forward and reverse components of a bi-directional reaction were considered as two non-negative fluxes. The biosynthetic pathways for the following amino acids were expressed explicitly: (i) the amino acids whose mass isotopomer distribution (MID) was assumed to be measured and (ii) the amino acids whose synthesis was accomplished by CO2 release. In Figure C. glutamicum [The hreonine ,76, werehreonine . Pools outamicum  as the sutamicum .S, dim(S) = (36 × 51), with 36 balanced metabolites, 51 unknown fluxes, and r = rank(S) = 36, was finally generated. As a result, 15 fluxes should be assigned as free. Seven fluxes were experimentally determined effluxes, which included biomass biosynthesis (1 flux), the effluxes of secreted products (5 fluxes), and the glucose uptake rate (1 flux). Unless otherwise stated, these fluxes were considered free fluxes constrained according to Eq. (S − 1.2.2) with the experimentally determined parameters S − 1.3.7), which was subjected to a least-squares minimization procedure. Five free fluxes were automatically assigned due to their accordance to the reverse reactions: (i) in the non-oxidative branch of the PP pathway (3 fluxes), (ii) catalyzed by glucose-6-phosphate isomerase (1 flux), and (iii) for the carbon dioxide intracellular exchange (1 flux). The three remaining free fluxes were previously automatically assigned using OpenFLUX software [The resulting metabolic model contained 54 reactions and 36 balanced metabolites. The reactions, which only map the labeled distribution of the metabolite onto the corresponding amino acid , did not participate in the stoichiometric balance. Thus, the stoichiometric matrix software . There w2 (13C isotope abundance of 1.07%). In total, 17 sets of matrix equations of EMU balances were used to calculate the 107 unknown EMUs from 15 known EMUs of input substrates. The application of the EMU approach reduced the number of unknown variables from 9,138 unknown scalar variables in the full isotopomer model to 360 scalar MID variables, corresponding to 107 unknown EMUs.An isotopomer model was automatically built based on the EMU approach that simulated the MIDs of target compounds from the known MIDs of input substrates. The input substrates were specifically labeled glucose and naturally labeled COn carbon backbone atoms was represented by a mass distribution column vector (MDV), whose elements corresponded to the fractional abundances , with m0 is the molecular weight of an unlabeled compound. As the published MIDs were uncorrected in accordance with the natural mass isotopomer abundance, all the simulated EMU variables were modified for mass interference from non-carbon backbone isotopes in dependence on the chemical structure of the derivatized substance according to the method developed in [n + 1) simulated mass isotopomers  were normalized to unit followed by truncation of the isotopomers number to the dimension of the m0, m1, m2) were presented for derivatized mass isotopomers fragments of Ala-260, Val-288, Thr-404, Asp-418, Glu-432, Ser-390, Phe-336, Tyr-466, Tre -361 isotopomers, and MIDs m0, m1) of Gly-246. At the same time, an extremely small MID variance of 0.15% for mass isotopomer fractional abundances was indicated in [SF-1.3.). These MID variances were assumed to be significantly underestimated. Indeed, the minimal published GC-MS measurement errors are usually approximately 0.2-0.4 mol% [13C-MFA has been applied [Initially, the calculation of “true” flux values for the assumed metabolic model was performed using experimental data on effluxes and MIDs, together with their variances, available from the literature ,68. The loped in . Then fomentclass2pt{minim0.4 mol% , and val applied ,58,79. Tin silico LEs, the OpenFLUX(2) forward simulation option was used, which calculated the MIDs of selected EMU variables from the assumed metabolic and isotopomer networks as well as the known label states of input substrates (13C-tracer(s)) and the assumed values of the fluxes. Unless otherwise stated, the true flux values, utrue(θtrue), were used for direct “experimental” data simulation in the present study. An isotopic purity of 99% was assumed for all of the specifically labeled carbons in the input substrates, and natural enrichment (1.07%) was assumed for other carbons. Again, the simulated MIDs of a substance with n carbon backbone atoms were represented by MDV with (n + 1) elements, n + 1)  .Flux estimation, identifiability, and goodness-of-fit analyses were performed using OpenFLUX2 software. To determine the global minimum of the constrained NLLSP, as a rule, 100 independent iterative trials, starting from randomly selected points from a feasible constrained domain in the free flux variation space, ℜSF-1.7. for details).Monte Carlo-based approach included previously in OpenFLUX, but significantly modified in the OpenFLUX2 software for convenience of the computation process tuning and control of convergence, was used for estimation of the flux confidence intervals. Usually the most reliable results could be obtained if the variant when “multi runs per trials” approach was chosen for estimation of the optimized flux parameter distributions followed by determination of flux confidence interval borders according to “discarding” strategy after confirmation of the borders convergence  requires Java and MATLAB, including the Optimization and Statistics Toolboxes. The current version of the OpenFLUX2 software was tested using Java 6  and MATLAB 7.12.0  software, together with the Optimization Toolbox (version 6.0) and the Statistics Toolbox (version 7.5), on the Microsoft Windows 7 Professional  platform on a PC equipped with a 3.2 GHz CPU and 4 Gb of RAM. Using these computation facilities, the calculation of 51 fluxes for the applied metabolic model (see OpenFLUX2 (odel see  requiresodel see  takes ap


Shewanella oneidensis MR-1 is one of the model microorganisms used for extracellular electron transfer. In this study, to elucidate the capability and the relevant metabolic processes of S. oneidensis MR-1 involved in an electron transferring environment, we employed genome-scale modelling to model the necessary metabolic states and flux adjustments for electricity generation in the cytochrome c-based direct electron transfer (DET) mode, the NADH-linked mediated electron transfer (MET) mode and a presumable mixed mode comprising DET and flavin secretion. These are difficult to develop experimentally.The results showed that the microbe had the potential to achieve current outputs of up to 2.610 A/gDW in the DET mode, 2.189 A/gDW in the MET mode and 2.197 A/gDW in the mixed mode. Compared with the DET mode, which relied on cytochrome c oxidase (EC: 1.1.1.2) to mediate the electron transfer, the MET mode was mainly dependent on two routes, catalysed by isocitrate dehydrogenase (NAD) (EC: 1.1.1.4) and NAD transhydrogenase, for the computed high current density value. In the mixed mode, whereas the cytochrome c-based DET accounted for most of the computed maximum current output value, the two flavins combined, riboflavin and FMN, played a much less important role in the probed current value.Shewanella oneidensis MR-1 has the potential to sustain a high extracellular electron transfer rate similarly to Geobacter sulfurreducens, but relies on different intracellular mechanisms. Various levels of electron transfer rates are achieved by different combinations of metabolic pathways. Flavins can significantly degenerate the maximum electricity generation capability of the cell and the biomass formation, and thus should be avoided in order to achieve a high coulombic efficiency.The online version of this article (doi:10.1186/s13068-014-0118-6) contains supplementary material, which is available to authorized users. Shewanella oneidensis MR-1 is a facultative aerobic, Gram-negative bacterium capable of using various reducing exogenous extracellular acceptors such as Fe (III) to preserve energy for growth [S. oneidensis MR-1 has been used in microbial fuel cells (MFCs) for wastewater treatment and bioelectricity generation [, S. oneidensis can potentially produce electricity through three modes: 1) the direct electron transfer (DET) mode based on c-type cytochromes on the outer membrane of the cell and cell appendages called conductive pili , 2) self-secretion of flavins to convey electrons toward the electrode and 3) the mediated electron transfer (MET) mode, which relies on exogenous mediators .Geobacter: the first claims that the cytochromes mediate the electron transfer via the pilus with metallic-like conductivity, and the second suggests that the electrons are hopping between heme groups in cytochromes aligned with the pilus to reach remote electron acceptors [Geobacter sulfurreducens [S. oneidensis [G. sulfurreducens and S. oneidensis have been studied extensively and proposed as classic models in MFC research [Geobacter, Shewanella can use oxygen and thus can have wider applications.The DET route depends on the c-type cytochrome (MtrC and OmcA) in the cytoplasmic membrane interacting with the electrode and supplying electrons to the electric circuit . The DETcceptors . These preducens –12, and eidensis . Both dieidensis . The metresearch ,15. UnliS. oneidensis can still reduce a remote electron acceptor by producing flavins into the surrounding medium to serve as extracellular electron shuttles [Without a direct contact with external electron acceptors via pili, shuttles ,17. The shuttles ,19. The shuttles . The flashuttles ,21. This+ cycle could be considered as a way to probe the maximum metabolic potential for ideal electricity generation.For the MET mode, the reduced form of nicotinamide adenine dinucleotide (NADH) has been suggested as the optimal intracellular electron-shuttling compound to be targeted in electricity generation , becauseShewanella cells in a microbial biofilm [In conventional MFC research, a few pathways  can  biofilm –28, whicShewanella with a certain level of oxygen was able to achieve higher maximum current outputs [S. oneidensis MR-1 under aerobic conditions, in order to identify its maximum potential for electricity generation and the pertaining metabolic mechanisms. To achieve this goal, we followed a five-step procedure. 1) Seven assumptions were made based on previous experimental findings for the modelling  We then demonstrated theoretical trade-offs among the amperage yields, the biomass production (growth) rates, the flavin secretion rates and the cytochrome c regeneration rate. 4) The fundamental metabolic mechanisms behind the current outputs in the three modes were elucidated by flux variability analysis with target flux minimization (FATMIN). 5) Finally, a sensitivity analysis was conducted to investigate the effect of varying lactate uptake rate on the growth rate and the amperage output in the three modes, and the computed current outputs were compared and discussed.Previous findings showed that an MFC using a pure culture of  outputs –31. Ther see the  section.-1 , whereas in the MET mode, the electron flux always increased with the decrease in the growth rate. The slope of the DET and MET outputs versus biomass growth curve as shown in Figure Figure -1 did not improve the DET rate, forming a steady plateau at the DET output of 81.68 mmol gDW-1 h-1. Likewise, the MET production curve can also be divided into two stages: Stage 1, an increase in the MET rate was accompanied with a decrease in the biomass production rate, but the conversion efficiency of the metabolic resource into the MET flux decreased with the decline in the MET output; Stage 2, at the left-side tail of the net NADH production curve, the rise in the MET rate was linearly proportional to the drop in biomass production rate, indicating a constant efficiency. On the other hand, as a result of increasing DET or MET outputs, the relationships between the varying biomass production rate and the NADH consumption for maintenance  curve, Stage 1 of the MET production curve describes the compromise between the two goals, maximizations of biomass growth and NADH production. The higher growth rates correspond to more active metabolic pathways available to cope with the NADH drain, and thus the metabolism tends to choose those pathways with higher efficiency in converting the metabolic resource originally for the biomass production to the current output. As the current output augments, which means that the conversion efficiency becomes less important than the flux capability, the metabolism has to abandon the pathways with high conversion efficiency but lower maximum capability and reallocate the metabolic resources to those with higher flux capability.The Stage 2 behaviour sets in at extremely low growth rate values (less than about 10% of the maximum growth rates) in each of the two modes. In this stage, the reactions with lower catalytic efficiency in NADH regeneration were inactivated to leave the metabolic resources to a limited set of reactions with higher efficiency, in order to produce the extremely high current output. From an optimization point of view, the Stage 2 behaviour corresponds to the fact that the solution space was greatly reduced by the high MET rate and the remainder solutions are rigid in the selection of reactions. As a result, the decrease in the biomass production rate was linearly proportional to the increase in the MET flux.The right part of Stage 1 of the NADH production behaviour coincides with Type 1 of the NADH consumption behaviour, which means that the increase in the MET is accompanied by a drop in the NADH consumption for cellular maintenance. This indicates that, at those production rates of biomass and NADH (corresponding to Type 1), the increase in the flux of NADH_mfc  originates from a combination of two mechanisms: increasing the NADH production and decreasing the NADH needed for biomass production and maintenance.+, a building block for NADH production. Thus, Type 2 consumption of NADH is a metabolic mechanism enabling Shewanella to achieve higher current outputs. In addition, the increased consumption of cytosolic NADH can be considered as a metabolic strategy to reallocate the metabolic resources to those reactions that can regenerate NADH more efficiently.The left parts of the Stage 1 and Stage 2 productions are correlated with Type 2 consumption, at lower biomass production rates. Type 2 behaviour may be contrary to intuitive expectations, since a reduction in biomass growth and an increase in NADH demand would be anticipated to reduce the NADH consumption rate. However, the increased consumption of NADH is also a way to increase the availability of NADShewanella did not increase the “ceiling” regeneration rate of the reduced cytochrome c when current was generated in the DET mode. A flux value of 81.68 mmol/gDW/h for the reduced cytochrome c production was necessary for the optimal growth rate of 0.2864 h-1, and a metabolic perturbation of a drain flux of cytochrome c entailed a compromise on the growth rate. This suggests that the capability of the Shewanella cell for regeneration of the reduced cytochrome c is inherently fixed. For the MET mode, compared with the base state optimized for growth, the metabolism of Shewanella had a potential to increase the NADH regeneration rates by about 130% (2.297-fold) under the highly NADH-perturbed metabolic states.Overall, compared with the base state optimized for growth, the metabolism of B value, to quantitatively compare the suitabilities of different combinations of multi-objectives, so as to identify the metabolic state that can most efficiently coordinate pathways for achieving the objectives. The higher the calculated B value achieved, the more efficiently the metabolic state can produce the metabolite of interest. A detailed explanation for the calculation of a B value can be found in the Methods section. Figure Although the discussion above indicates that the reducing equivalent production competes with the biomass growth for metabolic resources, not all the gains in reducing equivalent production are derived from the decrease in the growth rate, and some of them can result from reconfiguration of metabolism. We used a fractional benefit measure, the B values increased from 50% at wild-type growth rates (right-hand side of the figure), to reach an apex of near 81% at a growth rate of 0.192 h-1, and then dropped to about 51% when the growth rate approached zero. The initial increase in the B values indicates that there is a rise in the metabolic output of the combined objectives - a small redox disturbance causes an adverse effect on the growth, but a further increase in the degree of the redox perturbation can improve the metabolic output of the combined two goals. The highest B value, about 81%, suggests that the corresponding metabolic state with a growth rate of 0.192 h-1 possesses the best output of the multi-objective. The subsequently declining B values indicate that the further, forced, increase in the DET is detrimental to biomass production. Similar to the B value curve of the DET mode, the B values calculated for the MET mode generally increased from a base value (50%) for the wild-type growth rates to reach an apex (57%), the best metabolic state for the dual objectives, and then decreased to the base value (50%), since the further improvement in reducing equivalent generation rate was at a high cost of biomass production rate. However, since the maximum B value could not exceed 57%, it is indicated that MET could not liberate the maximum metabolic capability of the cell for growth-coupled current production.The B value achieved for the DET mode (81%) was much higher than that for the MET mode (about 57%). This indicates that the metabolism of S. oneidensis MR-1 is much more suitable for the cytochrome c-based DET mode than the NADH-linked MET mode. In other words, the metabolism favoured the DET mode more than the MET mode for higher growth rates.Notably, the highest Shewanella strain needs to reduce the biomass production rate to a very low level and increase the reduced cytochrome c production rate to about 30 mmol/gDW/h. It was found that the highest B value of about 54.6% was achievable when the growth rate was lowered to 0.003 h-1 and the cytochrome c production rate stayed at about 29.36 mmol/gDW/h. A further increase in cytochrome c can compromise the capability of the cell to secrete flavins.Turning now to flavin-based current production, Figure The three-dimensional graph Figure  shows th-1), an increase in the flavin production rate did not always necessitate a decrease in cytochrome c production rate. When the flavin production rate was below about 0.45 mmol/gDW/h and the cytochrome c production rate was above about 78 mmol/gDW, the decrease in biomass growth did not further improve the production rates of cytochrome c.The vertical plane of the graph indicates that, at lower biomass production rates  cytochrome c and growth rate, 2) flavins and growth rate and 3) flavins and cytochrome c are further discussed and analysed in the following three sub-sections. The steepnesses of the curves are used in these discussions as indicators of the relative production efficiency. This is based on the interpretation that, for example, a steep downward curve means that a small increase in the quantity on the horizontal axis implies a large decrease of the complementary quantity on the vertical axis. As these are trade-offs consuming the same amount of metabolic resource, this implies that the vertical quantity is produced more efficiently than the horizontal one.-1 and Phase three, a efficiency plateau which means any further decrease in the biomass growth does not improve the cytochrome c production rate. Note that as the production rate of the flavins increased (indicated by the green dashed line with an arrowhead), the curve for the cytochrome c production versus biomass growth only comprised the Phase one and two relationships, and the Phase three relationship diminished, which indicates that the flavin synthesis rate increased, with a rise in the average slope for the curves of cytochrome c versus growth rates.Figure The zig-zag part of the curves corresponds to flux distribution solutions switching from one metabolic state to another. These adjacent metabolic states in the zig-zag areas are randomly obtained from independent calculations, indicating that a very tiny change in the numerical value of one parameter can produce a similar but distinct metabolic state. This is thought to correspond to the biological phenomenon that cells even maintained in the same environmental condition can express individual behaviours.-1; it then plummeted as the growth rate approached zero. The decrease in the cytochrome c production rate not only augmented the maximum capability of the cell for flavin secretion, but it also raised the efficiency of the flavin synthesis, as is evident from the elevated slopes of the curves (indicated by the green dashed line with an arrowhead).Figure Figure -1, corresponding to the bottom curve of the graph), there is generally a simple linear relationship between the flavin production and cytochrome c production. This indicates that, to maintain an optimal or high growth rate, all efficient metabolic pathways need to be exploited to convert metabolic resources into the biomass components, leaving no freedom for the metabolism to adjust the priority of producing flavins versus cytochrome c.At very high growth rates , based on the efficiency of conversion of riboflavin versus cytochrome c, the curves can be divided into three regions.High efficiency of producing flavins compared to cytochrome c. In the metabolic states of this region (bottom right of the curve), the synthesis of cytochrome c is relatively less metabolically costly than the synthesis of flavins, and FMN did not influence the maximum capability of the cell to produce reduced cytochrome c.Medium efficiency. In the metabolic states of this region (the part of the curve for which the cytochrome c production rate ranges from about 80 to 30 mmol/gDW/h), the further reduction in production rate of cytochrome c increased the flavin production with a decreased conversion efficiency (a steep slope) of metabolic resource into flavins. Compared to the previous high efficiency region, a downward curvature can be seen with decreasing slopes of the lines between the data points.Low efficiency. At the left-side tail of the curve (top left of the curve), a significant drop in the cytochrome c production rate is required for a rise in the secretion rate of the flavins, which is reflected by the gentle slope of the line.At lower growth rates  for cytochrome c production than for the flavins, the cytochrome c production is much more important in the metabolism. This can also be seen by the fact that the flavins change by a factor of about 5, that is, 1.44 (flavins)/0.286 (growth rate), to obtain a zero growth rate, whereas the cytochrome c changes by a much larger factor of around 286, that is, 81.68 (cytochrome c)/0.286, to reach a zero growth rate. The present modelling results indicate that a high and flexible production rate of cytochrome c is allowed by the stoichiometric constraints of the MR-1’s metabolism, which is in keeping with the experimental genome evidence of more cytochrome c-type proteins being found in the MR-1 than in other prokaryotes .Our results also show that the production of riboflavins and FMN can heavily suppress the growth rate and the availability of cytochrome c. This implies that regulation of expressions of particular enzymes can cause a significant change to the metabolic flux distribution, and the metabolism of MR-1 is not as naturally optimized for cytochrome c production as for synthesis of the flavins.The reactions (enzymes) that were responsible for the enhanced diversion of the reducing equivalent flux towards current production are summarized in Tables During MFC operation of the DET mode, the electrons are continuously extracted from the membrane by the anode, imposing a metabolic pressure on cellular activities. The surplus flux of the reduced cytochrome c for the DET mode was derived from the reaction CYOO2 EC: 1.1.1.2)  to regenerate reduced cytochrome c, S. oneidensis MR-1 did not use CYOR1m and chose CYOO2  to produce the high flux of the reduced cytochrome c.Unlike + at a high rate had to be activated to restore the redox balance for survival (growth). It is suggested that two mechanisms will be triggered to avoid NADH imbalance: 1) the growth rate decreases, and 2) a metabolic reconfiguration mechanism is employed by the cell to restore the balance.As a response to draining electrons away from NADH, a metabolic mechanism that regenerates NADH from NADS. oneidensis MR-1 was much less than the ten reactions for the MET mode of G. sulfurreducens [In total, there were 63 reactions associated with NADH production or consumption. Among them, only two reactions, ICDHxi (EC: 1.1.1.4) and THD5, were responsible for the identified maximum net NADH flux (48.53 mmol/gDW/h) Table . Each ofreducens .+ oxidoreductase. A high NADH flux (47.03 mmol/gDW/h) yielded from NADPH by THD5 was also observed for modelling an optimal anaerobic growth of S. oneidensis MR-1 in a previous study [Whereas ICDHxi is associated with the tricarboxylic acid (TCA) cycle, THD5 is catalysed by NADPH:NADus study . On the i min/vi max > 0.99) under high current output. The low flux values and rigid variability reflect the fact that NADH is involved in many reactions and that increasing NADH fluxes in a few reactions can limit the variability of metabolic fluxes through many other reactions.The excess fluxes (the flux portion higher than 48.53 mmol/gDW/h) were mainly consumed by GAPD (EC: 1.2.12), which can consume up to 8.745 mol/gDW/h of the NADH flux, accounting for 18.02% of the maximum net NADH flux. All other NADH-involved reactions usually have extremely low flux values  with no variability  were concurrently up-regulated to sustain the high reducing equivalent fluxes. As a result of maximization of the production rates of both the cytochrome c and flavins, two reactions in the metabolism, CYOO2 EC: 1.9.3.1) and SO3De (EC: 1.8.2.1), were mainly associated with the maximum cytochrome c output flux (75.12 mmol/gDW/h) (Table .1 and SOThe maximum net flux (0.5008 mmol/gDW/h) of the flavins was achieved by a combination of fluxes of three reactions, RBFK (EC: 2.7.1.26), RBFSb (EC: 2.5.1.9) and FMNRx (1.5.1.29). Half of the flux of RBFSb was responsible for the surplus riboflavin flux of 0.2504 mmol/gDW/h, and the other half was consumed to produce FMN. The riboflavin flux value was the same as the FMN flux value, indicating that the metabolic costs for synthesis of the two metabolites are the same. The three reactions underlying the flavin-linked current production had rigid flux ranges, implying that the synthesis of the flavins is limited by the diversion of metabolic resources toward biomass growth.To elucidate how the metabolism is reconfigured to cope with different levels of energy perturbation, we have examined the key solution reactions, of which the fluxes significantly contribute to a series of selected growth rates and current outputs. The results are shown in Tables As the redox perturbation increases from the lowest level (DET flux is zero) to the highest level (DET flux is maximized using a λ of 0.999926), the metabolism decreases the cytochrome c flux diverted to the two reactions, CYOR7 and SO3D3, and increases the cytochrome c production of the reaction CYOO2, to achieve a high net cytochrome c flux for the DET mode current production Table .A low redox perturbation of NADH_mfc drain (λ below 0.9934) did not have an impact on the choice of metabolic pathways involving NADH regeneration, when compared with the control metabolic state Table . As the Table The maximum flux of the flavin secretion was relatively low (about 1.441 mmol/gDW), and to achieve such a flavin secretion rate, the cell needs to heavily decrease the reduced cytochrome c production and the growth rates Table . Since tThe simulation results obtained by varying λ for the cytochrome c output while fixing a λ of 0.023399 for the flavin secretion show that, under the mixed mode, the metabolism had rigid solutions in choosing pathways to synthesize flavins, but had flexible solutions comprising a number of different combinations of the cytochrome c-producing and consuming reactions.Based on the conversion efficiency of lactate to biomass, the relationship between biomass production rates and the lactate uptake rates can be categorized into two stages Figure : 1) a hiIn the DET mode, it was found that, when the lactate uptake rate was below 8 mmol/gDW, the biomass production rates or the electron transfer rates were linearly proportional to the lactate uptake rate in the MET and the mixed modes  was higher than the mixed mode (slope = 7.5622) and the MET mode (slope = 4.8532)  can lead to a plateau of the flavin production, we artificially increased the literature value of lactate uptake rate, 10 mmol/gDW/h, to 15 mmol/gDW/h, and found that any lactate uptake rates higher than 11.05 mmol/gDW/h could not further increase the total redox flux production rate; the highest total redox flux production rate stayed at 82.22 mmol/gDW/h. A lactate uptake flux of 15 mmol/gDW/h may not be practical, but using such a high value in the simulation can predict the trend of the curve  for the flavin production rate versus lactate uptake rate if the innate burden on the lactate uptake capability were to be removed.The mixed mode (slope = 7.5622) achieved a higher efficiency of converting the substrate into electricity in MFCs compared to the MET mode (slope = 4.8532), but a lower efficiency than the DET mode. This suggests that the stoichiometry of the metabolism is naturally optimized for synthesis of the reducing equivalent in the following order: cytochrome c > flavins > NADH.Finally, the three operation modes are compared for their theoretically maximum current output  supplying an electron uptake flux of 144 mmol/gDW/h, which is higher than the lactate uptake rate of 10 mmol/gDW/h comprising an electron uptake flux of 120 mmol/gDW/h used in the simulation of S. oneidensis MR-1.neration . The comG. sulfurreducens, are generally in agreement with previous experimental opinions that Geobacter can generate higher current densities in MFCs than all other pure cultures [G. sulfurreducens PCA produced ten times higher current levels in lactate-fed microbial electrolysis cells than S. oneidensis MR-1 [S. oneidensis MR-1 to secrete flavins can preclude the need for direct contact with the electrode, establishing a long-distance electron transfer without involvement of exogenous mediators and can be exploited in the development of some particular applications.Our calculations showing that the MR-1 produced a slightly lower maximum current output than its counterpart, cultures .This consis MR-1 . DespiteShewanella containing MFCs [Compared with the sole DET mode, the present calculation did not show a further increase in the total current output for the assumed DET mode with flavin secretion, and any flavin synthesis rate higher than 0.2587 mmol/gDW/h can significantly reduce the overall capability of the cell for current generation. This is partially contradictory to a previous conclusion that the two electron-mediated mechanisms - the nanowires-mediated electron transport and secretion of flavins - together determine the efficiency of the current generation in ing MFCs .S. oneidensis [Shewanella [Shewanella, and focuses on elucidation of the overall capability of a single cell for extracellular electron transfer. This is different from previous MFC studies that used to report the current output for the whole cell culture in MFCs, which resulted from a combination of contributions from different electron transfer mechanisms of cellular phenotypes, namely, secreted flavins of cells distant from the electrode and cytochrome c of cells near the electrode. Therefore, the observed importance of flavin secretion for cell culture-based extracellular electron transfer should not decrease the priority to develop cytochrome c-based DET mode for high current outputs in future studies.Previously, the flavins (riboflavin and FMN) were found to contribute as high as 73% of the total current generated in an MFC using eidensis . Therefoewanella . By contG. sulfurreducens (2.771 A/gDW) achieved a slightly higher maximum current output than that of S. oneidensis MR-1 (2.610 A/gDW), but with a lower CE of 71.79%. The use of exogenous electron shuttles in the MET mode of an MFC may be toxic to the normal metabolism of the MR-1, but can improve the current output when the self-synthesized flavins are not sufficient to convey all the available electrons inside the metabolism towards the electrode. This was confirmed by the observation that the addition of exogenous soluble flavins into the media can improve the electron transfer rates of an MFC [The MET mode of f an MFC .2) or current generated per unit volume of the cell (A/m3). Since different MFC studies use different configurations involving different types of reactors, surface area and types of electrodes , it is difficult to directly compare current output in these units (A/m2 or A/m3) with the unit (A/gDW) in the metabolic flux model. The advantage of the flux unit (A/gDW) is that it allows the calculated current density values to be applied to any MFC configuration by taking into account the cells that are actually contributing to the current generation in that situation.Experimentally, it is very difficult to measure the number of cells that actually contribute to the observed electric current output. Consequently, the MFC experimental studies often report the current density as current generated per unit area of the anode surface area /cm2 [A recent study has reported a maximum current output of 11.09 ± 0.28 A/mght)/cm2 . With thS. oneidensis MR-1 has an unusually high growth rate-dependent ATP requirement (GAR) [Shewanella model contains a high stoichiometric value for the ATP, the free electron fluxes divertible for electricity generation are suppressed. Although the high GAR is required to account for the fact that energy-dissipating futile cycles can be activated in S. oneidensis MR-1 under aerobic conditions [2 concentrations or O2-rich conditions, which may lead to a lower GAR, leaving more free electrons for diversion towards the electrode.Based on the previous study, nt (GAR) . Such a nditions , in the Furthermore, because the current metabolic network cannot distinguish the difference in the metabolic cost and pathways underlying the production of the two flavin molecules, riboflavin and FMN, the priorities for these two flavin molecules are set to be the same in the modelling. However, the phenomenon that the two flavins are exchangeable based on the stoichiometric constraints of the model may be attributed to the incomplete set of constraints in the model . To further investigate the relationships between syntheses of riboflavin and FMN, integration of the thermodynamic constraints into the metabolic model is required, to quantitatively differentiate the metabolic costs of the syntheses of the two redox molecules. In addition, identification of the kinetic parameters through isotopic tracers such as 13C-metabolic flux analysis and measurement of enzymatic concentrations can also elucidate the exact relationships between riboflavin and FMN for a particular metabolic state of the cell.S. oneidensis MR-1 for MFC current production and examine the properties of alternative genotypes arising from the energy perturbation. The results show that S. oneidensis MR-1 has the potential to produce an electric current at up to 2.610 A/gDW in the DET mode, 2.189 A/gDW in the MET mode and 2.197 A/gDW in a presumed mixed mode based on cytochrome c and flavins.In this study, we integrated electron transfer mechanisms with a genome-scale metabolic mode to determine the capability of To maximize the current output, the DET mode relied on only one reaction, mediated by cytochrome c oxidase (EC: 1.9.3.1), and the NADH-linked MET mode was mainly contributed by two reactions, catalysed by isocitrate dehydrogenase (NAD) (EC: 1.1.1.41) and NAD transhydrogenase. The maximum secretion rate of flavins was quite low, namely, 1.414 mmol/gDW/h, and the flavin production can lead to significantly repressed growth and c-type cytochrome production rates. Therefore, although the flavin secretion can improve the long-distance electron transfer in the absence of exogenous mediators, it can significantly curtail the objective to maximize the overall availability of the electrons for the electrode.G. sulfurreducens and S. oneidensis MR-1 shows that the two microbes are likely to employ different mechanisms to sustain the high current outputs. This suggests that the differences in the fundamental metabolic mechanisms, in addition to the engineering aspects of the configuration, should be taken into account in the optimization of the performance of MFCs based on different organisms.Furthermore, the comparison of S. oneidensis MR-1 culture is used for electricity generation. ii) The MFC reactor is fed continuously, providing all the necessary nutrients to meet the requirements for optimal microbial growth. iii) Sufficient oxygen was present to ensure the aerobic metabolism of S. oneidensis MR-1. Oxygen intrusion into MFCs used to be considered detrimental since it can intercept the electrons from anodes, resulting in a lower coulombic efficiency. However, recent studies have suggested that addition of oxygen to the anodic chamber does not necessarily lower the performance of MFCs based on the pure culture S. oneidensis MR-1, and instead can prominently increase their maximum current outputs [The modelling conducted was based on seven assumed conditions: i) Only a pure  outputs –31. The  outputs . iv) In  outputs ) can be The interactions with an MFC anode were captured by adding additional transport reactions into the model. These reactions are subject to the mass balance law in the FBA modelling. The process of conveying electrons towards the electrode is schematically shown in Figure FB and the reducing equivalent diversion flux FN. There are two objective formulations; one (Equation The objective equation was formulated as described in previous studies . BrieflyEquation  is for mEquation  is for tFB and FN are measured respectively in units of mmol/gDW/h and g/gDW/h or (h−1). For the MET mode, gN is set as 0.66343 g/mmol, which is the molar mass of NADH, and for the DET mode, gN is set as 0.8869 g/mmol, which is the molar mass of cytochrome c. These g values ensure that the λ is a dimensionless fraction that can be directly interpreted as the relative contribution of the reducing equivalent fluxes to the combined objective.Here a and λb. The one (λa) inside the square brackets adjusts the priority between biomass and cytochrome c, and then the other (λb) adjusts the priorities between the flavins and the combination of the biomass and cytochrome c.Here mentclass2pt{minimB, is computed by adding up the fractions of the maximal values of the objectives that they can ever achieve in a particular metabolic state. Equation B values for a dual objective optimization , whereas Equation A fractional benefit analysis, as described previously ,52, was B value of 100% would be attained if a metabolic state reaches the “utopian” ideal of simultaneously producing the maximal growth rate and the maximal reducing equivalent production. On the other hand, based on Equation B value of 50%. B values above 50% signify that the gain in achieving the target objective  outweighs the losses in the others, and vice versa for values below 50%.Here B value of 50% (25% for biomass formation and 25% for cytochrome c production), whereas the two flavins (riboflavin and FMN) combined give a base B value of 50% . A value of 25% indicates that either a wild phenotype of maximal growth rate or a maixmum cytochrome c production rate is achieved. In the theoretically ideal situation, a maximum B value of 100% would be reached, implying that the flavin secretion is not metabolically competitive with the biomass and cytochrome c productions. In reality, the productions of the various metabolites often involve different combinations of pathways and thus compete with one another for the limited pools of cellular resources, resulting in B values lower than 100%. Similar to the dual objective formulation , and vice versa for values below 50%.Based on Equation Equation , a B valB measure was used in Figure This 18 electrons, and 1 mol = 6.02 × 1023 electrons . Therefore, one flux unit (mmol/g/h) can be converted into A/g as follows:Current (in amperes) was integrated over time and converted to electrons recovered by using the following conversions: 1 C = 1 A × 1 s, 1 C = 6.24 × 10Coulombic efficiency (CE) is commonly used to quantify the performance of MFCs and is defined as the ratio of electrons transferred to the anode to that in the starting substrate. We use the full oxidation of lactate with oxygen as the oxidant as the reference reaction to characterize the energy efficiency of the respiratory metabolism:3H6O3 + 3 H2O → 3 CO2 + 12 H+ + 12 e-.Lactate oxidation reaction: C2, such as in the aerobic conditions [Each molecule of lactate oxidation can donate up to a maximum of 12 electrons per molecule if all of the carbon is oxidized to COnditions ,53.\docuAn upper limit for the cell voltage is calculated in this work based on formal potentials of the biological and electrochemical redox processes, as given by:Here, S. oneidensis MR-1 was chosen as the analysis backbone for all the simulations [S. oneidensis uses lactate as the sole source of carbon and energy. When lactate is sufficient, the Shewanella strain produces pyruvate and acetate, and the carbon utilization is in the following order: lactate ➔ pyruvate ➔ acetate [Shewanella strain. The maximum oxygen consumption rate was constrained to -20.42 mmol/gDW/h [2, Fe2+ Fe3+ Na+, NH4+, PO43-, NO2-, NO3- and SO42- were allowed to freely enter and leave the network, since they are required for optimal growth of the cell, as described previously [The iSO783 metabolic construction of ulations . This meulations . S. onei acetate . In the  acetate . The max acetate . These vol/gDW/h . The oxyol/gDW/h . CO2, Feeviously . The comSetting a lower limit on growth rate is necessary to ensure that the cell maintains a viable metabolic state at which the redox molecules  can be derived from the metabolism. To obtain a realistic upper value for the current that can be extracted from a microbe, 5% of the maximum theoretical biomass production rate was chosen as the viability threshold for computational identification of the lowest growth rate.The flux balance analysis (FBA) and flux variability analysis with target flux minimization (FATMIN) were implemented in MATLAB , using the ORCA toolbox . The max


Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type  Cellular metabolism involves a myriad of regulatory processes and metabolic components functioning together through a complex set of interactions and reactions. Although “omics” technologies provide an increasingly large body of information on each individual component involved in metabolism, our knowledge of how these components as a system give rise to multiple phenotypes under different conditions is far from complete. A powerful approach to investigate metabolism and metabolic processes is to analyze the flow of material and energy through a metabolic network. In particular, the analysis of metabolite fluxes in a metabolic network serves as an essential tool in many biotechnology and biomedical applications, for example, to enhance the production of food and biofuels 13C) 13C-MFA traces isotope-labeled metabolites using mass spectrometry and determines individual reaction fluxes by fitting 13C data to a network model with the help of additional measurements on exchange fluxes, such as nutrient uptake and product excretion rates. Due to experimental difficulties in obtaining quantitative and precise measurements that cover a large-size network with diverse pathways and many metabolites, the use of 13C-MFA is typically limited to the determination of fluxes related to the central carbon metabolism A standard experimental technique to quantify the distribution of fluxes in a network is to perform a metabolic flux analysis (MFA), which is based on isotope labeling techniques  S. cerevisiae and Escherichia coli metabolism by a comparison with experimentally determined flux data and other model predictions discussed above. The analysis showed that, whereas other algorithms performed well for one condition/organism, our algorithm showed consistently good predictions of flux distribution for both organisms under different conditions. Thus, we believe that E-Fmin will provide a robust capability for analyzing complex metabolic systems.We evaluated the developed E-Fmin algorithm through case studies of E-Fmin employed a similar structure to that of GIMME, with the following optimization problem that minimizes a weighted sum of flux magnitudes, i.e., ir is the ith flux, its weight iw is a function of gene expression level, m×n) stoichiometric matrix, r is the vector of rL and rU are vectors of upper and lower limits of r, respectively, RMF stands for required metabolic functionalities, and Eq. 2 denotes stoichiometric balances of fluxes under steady-state conditions. Flux bounds in Eq. 3 are determined by accounting for their directionality as constrained by thermodynamics, i.e., upper and lower bounds are ±∞ if a reaction is reversible, and if one of the reactions is irreversible, the opposite reaction bound was set to zero. By the inequality constraint in Eq. 4, one or more reactions classified as RMF are forced to carry fluxes above iw as ith reaction and Eq. 4 with the constraint Br is the specific rate of biomass production and Eq. 5 allows the specific rate of biomass production to vary from a negligible value to its theoretical maximal value, and thus should be valid even under conditions of significantly suppressed growth. In this regard, we view Eq. 5 as a context-independent constraint that can be applied across a wide range of conditions. It should be noted that iw is represented as all reactions (except those fully expressed) in inverse proportion to their associated gene expression levels. For more details on the E-Fmin algorithm, see materialsandmethods. To develop a tool that enables quantitative flux predictions, we made modifications to GIMME. First, we replaced P1 to P4) for converting substrate into product and biomass. Path P1 leads to product formation through reactions r1 and r2, whereas paths P2, P3, and P4 lead to biomass formation through reactions , , and , respectively. This metabolic network is underdetermined, as it has nine unknown fluxes, r1 to r9, but only five available equations given by the stoichiometric matrix S in iw = 1 . E-Fmin then selects P2, the shortest among the biomass-producing pathways, as the solution. Note that P1, while shorter than P2, is not the solution of E-Fmin due to the constraint that forces biomass production to carry flux.In the absence of gene expression data, E-Fmin treats all weights as equal, i.e., cases 1 and 2). The weights are given as a function of expression level, 1 – ig, where ig is the normalized gene expression level for the ith reaction, ranging from 0 to 1. We set the weights of the reactions for which no gene expression levels are available to 1. In case 1, E-Fmin discards P2 as the associated genes are not highly expressed. For paths P3 and P4, which are similar in their gene expression levels, E-Fmin selects the former because of the smaller sum of flux magnitudes. Case 2 shows that even the longest pathway, P4, can be selected as the solution of E-Fmin if the associated relative gene expression levels are sufficiently high.Incorporation of gene transcript expression levels into E-Fmin allows us to use biological and condition-specific information to estimate the flux distribution in the system. case 1, it is probable that both P3 and P4 could carry nonzero throughput fluxes. To account for these situations, we would implement flux variability analysis (FVA) after the E-Fmin analysis to account for the range of flux variation through each reaction.E-Fmin, like other LP-based algorithms, yields only a single pathway among alternative solutions, despite the likelihood that multiple routes can simultaneously be activated at a certain ratio according to their associated gene expression levels. For example, in S. cerevisiae. We used experimental data collected by Lee et al., which included RNA-seq transcriptomic data and exchange flux measurements of S. cerevisiae aerobically growing in chemostat cultures. This study provides data under two different growth conditions, i.e., glucose uptake fluxes of 16.5 and 11.0 mmol/(gDW⋅h), which correspond to 75% and 85% of the maximal attainable biomass levels, respectively. We used a genome-scale metabolic network of S. cerevisiae, Yeast 5 We applied our algorithm to the aerobic growth of materialsandmethods for details on their implementation.2 are the predominant products, whereas the production of glycerol, acetate, trehalose, lactose, and biomass is insignificant. This trend is well captured by E-Fmin, E-Flux, and Lee et al., but not by GIMME, FBA, and iMAT. aterialsand Methods, we obtained a P value of 0.04 and rejected the null hypothesis that the ranking of average correlation coefficients in a priori. We provided the flux data and model predictions in The experimental data showed that ethanol and COE. coli in chemostat cultures. We obtained microarray gene expression profiles  and 13C-MFA-based flux data of E. coli K-12 strains from Ishii et al. E. coli to environmental and genetic perturbations and provided multiple high-throughput omics data for both wild-type and mutant strains. To study the effect of environmental perturbations, they cultured wild-type cells at varied dilution rates, while the effect of genetic perturbations was examined by disrupting 24 single genes contained in glycolysis and in the pentose phosphate pathway. As a result, they observed that gene disruptions lead to only subtle changes in mRNA levels, suggesting that E. coli is able to adequately compensate for the loss of a single gene or enzyme in the central metabolism by using excess or complementary capacity of other available enzymes. Conversely, they reported that wild-type E. coli cells appreciably change mRNA levels in response to the variation of the dilution rates but exhibit low-variations (robustness) in metabolite concentration levels. To test our algorithm across organisms, we additionally applied it to the aerobic growth of E. coli network model into the E-Fmin framework as detailed in materialsandmethods. Multiple genome scale metabolic reconstructions of E. coli have been built in the last decade E. coli K-12 strain, iAF1260 E. coli's genome For computational predictions, we incorporated the gene expression data of Ishii et al. and an E. coli strains obtained from E-Fmin and 13C-MFA at respective dilution rates. Predicted fluxes show good matches with 13C-MFA data in all cases. P values. Low P values indicate that the correlations obtained from E-Fmin are statistically significant. 2 production rate in all cases.−10 and rejected the null hypothesis that the ranking of average correlation coefficients in E. coli growing under these specific conditions. Interestingly, despite using the same objective function, the prediction of E-Flux was not comparable to that of FBA. It seems that the E-Flux predictions in this system are more affected by the imposed flux bounds than the choice of objective function. Algorithms based on the direct association with expression levels, such as in Lee et al., showed weak predictive powers, which may be ascribed in part to the use of gene expression data covering only the central carbon metabolism. Similarly to the classical FBA, the flux vector predicted by iMAT also contained outlier fluxes that reached their bounds. After removing them, iMAT showed an improved predictive capability. We provided the intracellular flux data and model predictions at the dilution rate of 0.1 1/h in −10 and rejected the null hypothesis that the ranking of average correlation coefficients in S. cerevisiae and E. coli despite the different metabolic characteristics of these organisms. For E. coli, the assumption of maximal production of biomass underlies the successful application of FBA in many studies of this organism E. coli at balanced growth conditions are close to the theoretical maximum predicted by FBA As demonstrated in the case studies considered above, E-Fmin has strong predictive capabilities for the metabolism of both E. coli, E-Fmin predicted biomass yield of 0.095 gDW/(mmol-glucose) for both wild-type and mutant E. coli strains, which is close to the FBA prediction of 0.096 gDW/(mmol-glucose), but without requiring biomass production to be maximized. In the case of yeast, E-Fmin predicted a biomass yield of 0.028 gDW/(mmol-glucose) for both uptake fluxes of 16.5 and 11.5 mmol/(gDW⋅h), which correspond to ∼25% of the theoretical maximum 0.104 gDW/(mmol-glucose). While Crabtree-negative yeast strains, such as Pichia stipitis, show high biomass yield close to the FBA prediction, the biomass yield of Crabtree-positive yeast S. cerevisiae is known to be much lower due to appreciable production of fermentation products, particularly ethanol S. cerevisiae growing in aerobic cultures has also been observed in other experiments. For instance, Papini et al. S. cerevisiae growing on glucose as 0.031 gDW/(mmol-glucose), which is close to our prediction. Conversely, the algorithm by Lee et al. predicted zero biomass yields for both E. coli and S. cerevisiae. The prediction of iMAT also led to zero biomass yields without additional constraint for biomass production to be larger than a certain level  of the theoretical maximal.The E-Fmin algorithm was designed to account for all of these features. For Eq. 5. The flux distribution obtained as the solution of E-Fmin becomes the same after normalization regardless of the value of ε. The normalized flux vector (obtained from E-Fmin) can be scaled to ‘actual’ values using experimentally measured fluxes, whenever available. Finally, the formulated LP problem leads to fast simulations. This is an important consideration when performing extensive FVA or analyzing systems for a large number of conditions.The main distinguishing features of the E-Fmin algorithm provide multiple advantages when analyzing cellular metabolism based on gene expression data. First, E-Fmin can use a generic network model to predict context-specific flux distribution. This is not the case for other methods, such as EXAMO, where the reconstruction of a condition-specific subnetwork is a prerequisite. Second, E-Fmin uses absolute gene expression data that can be collected directly from a single condition without defining or determining a standard reference conditions. This is advantageous over many of the currently available methods that are based on relative expression data In addition, due to the principle of flux minimization, fluxes predicted by E-Fmin contain no thermodynamically infeasible cyclic paths. The flux minimization also shrinks the space of alternative optimal solutions, leading to very narrow flux variation through individual reactions. We observed no appreciable changes in E-Fmin predictions from the implementation of FVA.In all simulation studies including E-Fmin, we assumed that the cellular composition was known. For cases in which cells grow in conditions that significantly differ from standard cultures, additional measurement of biomass composition is likely to improve model predictions.a priori knowledge of context-specific metabolic functionalities. This feature allows E-Fmin to be applicable across different conditions/organisms without modifying any components of the framework. We validated this capability through studies of S. cerevisiae and E. coli strains exhibiting distinct metabolic characteristics. In comparing the overall ability of the different methods to achieve a ranking above average, i.e., a meta-analysis of all rankings from the separate Saccharomyces cerevisiae data. Thus, compared with other methods, E-Fmin provided more consistently reliable predictions for both organisms. While these studies used gene expression measurements, E-Fmin could incorporate protein expression data as an alternative input to predict flux distribution.The work reported in this article addresses the issue of how one can effectively use gene expression data to study a phenotypic response of metabolism under various conditions by estimating flux distribution. Although a direct link between transcriptomic and fluxomic data is generally weak due to posttranscriptional modifications, the framework we developed was able to extract maximal information of metabolic fluxes by integrating mRNA data with a metabolic network model based on the principle of flux minimization. Importantly, E-Fmin does not require E. coli and low in S. cerevisiae, based on absolute gene expression data. Nevertheless, the inclusion of an expanded set of key reactions may be required to obtain physiologically reliable prediction for a specific condition. A systematic basis for the identification of additional condition-specific constraints is therefore a topic of great general interest. In our future work, we will expand the applications of the E-Fmin framework to examine a broader range of physiological conditions.As a basic constraint, E-Fmin forced nonzero flux through the biomass-producing reaction. This constraint was sufficient for E-Fmin to be able to correctly predict biomass production, high in E. coli and S. cerevisiae reconstructions iAF1260 We used genome-scale metabolic network models taken from the recent 13C-MFA data of E. coli from Ishii et al. S. cerevisiae from Lee et al. 2, glycerol, acetate, trehalose, and lactose. In both experiments, data were collected from glucose-limited chemostat cultures.We obtained preprocessed gene expression profiles and ig to denote the resulting normalized gene expression values for the ith reaction.The initial step in predicting fluxes using E-Fmin is to map gene expression data onto reactions based on gene-protein-reaction associations, which are provided with the iAF1260 and Yeast 5 network models. This mapping is straightforward if a single gene product catalyzes a reaction, i.e., the association of a gene via mRNA and enzyme to a single reaction is unambiguous. In general, a reaction is associated with multiple gene products, and their relations are described using Boolean operators such as “AND” and “OR.” The AND operation represents the involvement of multiple gene products in catalyzing a reaction, whereas the OR operation signifies that only one of the gene products is involved in the reactions. We implemented these operations by taking the minimal and maximal value of the associated gene expression data iw in Eq. 1 as a linearly decreasing function of We designed Eq. 8 ensures that fluxes with lower (higher) gene expression levels are more (less) suppressed.Eqs. 1–3 and 5 into a linear form, as follows: Eqs. 2, 3, and 5. We used 0.01 for ε in Eq. 5.We recast the absolute-sum minimization problem presented in S. cerevisiae and E. coli metabolism, respectively.We solved the above problem using the CPLEX  LP solver. We ran all simulations on a desktop PC with an Intel  Pentium i3 CPU and 4-GM RAM. We provide the MATLAB scripts used for generating the results in Given a table of correlation coefficients of predicted intracellular flux distributions for various conditions and methods, we wanted to test whether the observed rankings could occur by chance. We first normalized the correlation coefficients to scores ranging from 0 to 1 by rank-ordering all of them from small to large and, for each observation, scoring its rank as a percentile. Then, we used the F-test in a one-way analysis of variance i in condition j, i in all conditions, i, The variability values were calculated asRP:i in table t. We exhaustively permuted the three, sorted lists, and computed the P value as the fraction of all permutations that had smaller or equal rank products.Finally, we used rank product analysis Figure S1Wild-type Escherichia coli data collected at different dilution rates : gene expression data , flux data , principal component analysis (PCA) using gene expression data , and flux data . Gene expression data were normalized to range from 0 to 1. Flux data were scaled so that the glucose uptake flux is 100 mmol/(gDW⋅h). For the PCA, both gene expression and flux data were normalized by their maximal value to range from 0 to 1. D denotes dilution rate [1/h].(TIFF)Click here for additional data file.Table S1Sum of squared error (SSE) of E-Fmin and other methods in predicting intracellular flux distributions in Saccharomyces cerevisiae at different glucose uptake rates, wild-type Escherichia coli at varied dilution rates, and mutated E. coli with single gene knockouts.(DOCX)Click here for additional data file.Table S2Comparison of exchange fluxes of Saccharomyces cerevisiae between experimental data and computational predictions.(DOCX)Click here for additional data file.Table S3Comparison of intracellular fluxes of wild-type Escherichia coli at a dilution rate (D) of 0.1 (1/h) between experimental data and computational predictions.(DOCX)Click here for additional data file.Data Set S1Matlab scripts. Provides numeric codes for running E-Fmin and other algorithms to predict flux distributions from given gene expression profiles. At the end of the simulation, the code calculates correlation coefficients (ρ) together with P values and coefficients of determination (R2) as performance measures for comparison.(ZIP)Click here for additional data file.Data Set S2Network model and data files used for simulations of Saccharomyces cerevisiae metabolism. Provides a zipped file containing a genome-scale metabolic network model of S. cerevisiae (Yeast 5) and two sets of gene expression and flux data for two different uptake fluxes of glucose.(ZIP)Click here for additional data file.Data Set S3Network model and data files used for simulations of Escherichia coli metabolism. Provides a zipped file containing a genome-scale metabolic network model of E. coli (iAF1260), five sets of gene expression and flux data for the wild-type strain, and 24 sets of the same for the mutant strains.(ZIP)Click here for additional data file.


E. coli to several different perturbations can always be derived from a sequence of greedy and myopic resilencings. This simple mechanism provides a detailed explanation for the experimental dynamics both at cellular (proliferation rate) and molecular level (13C-determined fluxes), also in case of appearance of multiple phenotypes. As additional support, we identified an example of a simple network motif that is capable of implementing this myopic greediness in the regulation of the metabolism.A way to decipher the complexity of the cellular metabolism is to study the effect of different external perturbations. Through an analysis over a sufficiently large set of gene knockouts and growing conditions, one aims to find a unifying principle that governs the metabolic regulation. For instance, it is known that the cessation of the microorganism proliferation after a gene deletion is only transient. However, we do not know the guiding principle that determines the partial or complete recovery of the growth rate, the corresponding redistribution of the metabolic fluxes and the possible different phenotypes. In spite of this large variety in the observed metabolic adjustments, we show that responses of  A considerable effort has recently been devoted to studying the effect of different genetic and environmental changes, both experimentally and from a theoretical point of view, e.g. by measuring genes expression, rationale that does not make use of any specific information from the available experiments, we formulated a simple hypothesis about a possible unifying principle; (II) we validated the proposed hypothesis by a stoichiometric reaction model: without any tuning of the parameter to fit the experimental data, we tested whether experimental results can be reproduced by this hypothesis, both as growth rate recovery and as fluxes redistribution; (III) once it has passed this validation, the criterion is used to predict and to derive an explanation for some interesting cases of metabolic responses; (IV) finally, we showed how a possible motif in the regulatory network can implement the proposed principle at the molecular level.In order to find such a basic interpretation, our analysis consists of four steps: (I) from a general biological rationale: as already mentioned, genetic and environmental perturbations cause a transient activation of the non-essential metabolic pathways that are progressively silenced as the microorganism adapts to the new conditionOur starting point is the following E. coli after a wide set of different perturbations  and because of the complete independence of the construction of the method from the specific experimental results it is asked to describe, we believe that the comparison between simulations and experimental data represents a stringent test on the validity of our hypothesis.where E. coli, namely glucose, α-ketoglutarate, lactate, malate and succinate as carbon source and acetate kinase (ack), fumarate reductase (frd), glucose-6-phosphate dehydrogenase (zwf), phosphoenolpyruvate carboxylase (ppc), phophoenolpyruvate carboxykinase (pck) and triose-phosphate isomerase (tpi) as deleted genes . These results suggested then a general validity of the greedy hypothesis regardless of the knockout and growing condition.We considered 17 different combinations of single carbon sources media with gene knockouts on It is worth noting that also in the case of high recovery, simulated growth rate does not reach exactly the maximal value suggested by classical FBA. Part of this small discrepancy might be due to the “calibration” of the nutrients availability see . Howeverm-th moment expressionTo further validate the greedy principle, we verified that the mathematical expression (1) used for greediness quantification was not stringent: as shown in was used instead of the Boltzmann 13C-determined fluxes at the intermediate steps and at the final steps of the adjustment in glucose for five different knockouts, namely zwf, ppc and tpi, plus phosphate transacetylase pta and phosphoglucose isomerase pgi1913C-labelling experimental data. Therefore, for each knockout and regardless to which intermediate state along the trajectory has been used for the validation , the observed flux re-routing can be well described by our hypothesis. A comparison with other FBA methods is reported in So far, we found that this greedy regulation of the metabolism appears to be a good principle for explaining the macroscopic evidence of the growth rate recovery. This led us to the question about the re-routing of the metabolic pathways. Can the redistribution of the reaction fluxes be explained by the greedy hypothesis? For this purpose we looked into the details of the dynamics by identifying which reactions have been resilenced/activated along the adjustment and comparing this result with the pgi knockout. It has been shown that this mutant is characterized by a reduction of the growth rate to approximately 0.3 h−1 and by a re-routing of the fluxes toward the pentose phosphate pathway21−1) has been identified. Measurements by 13C-labelling indicated that the difference between these two phenotypes is due to the use  of glyoxalate shunt and of acetate secretion. Surprisingly, these two possible growth rates were obtained also in our trajectories: 0.31 and 0.60 h−1 with about 70% and 20% probability, respectively. As indicated by 13C-measurements for both phenotypes , the final outcome is a phenotype with low proliferation rate. As seen before, Δ−1  ref. , which i−1) for about 10 days making these cells unable to compete for the common nutrients against the greedy cells that are transiently proliferating faster .The fact that the highly proliferating phenotype has not been observed can then be interpreted as a confirmation of the existence of the greedy strategy (i.e. the low probability for the resilencing of phosphoglucose isomerase): if the cells do not follow the greedy criterion, it would have been easier to find this high proliferation phenotype. Moreover, as seen in the trajectories in Concerning the resilencing time, pgi condition. Indeed, although a mutation that stops this reaction has been found in the adaptation of GLU-pgi−1, instead of 0.3 or 0.6 h−1  . Since M is used for the biomass production, this implies also that the growth rate recovery induced by resilencing reaction A is smaller that the growth rate recovery induced by the resilencing of reaction B  have been described through classical Hill equations with constants HA and HB, respectively. This led to the following set of equations:The sketch of the simple motif is reported in g(t) = h[M]. We considered the case when a previous step in the regulation dynamics has caused an increase of the availability u(t) of the precursor P. Given such a input, we analysed how the two feedbacks may affect the response of the systems to this change. HA and HB. This result shows that, in order to induce an higher increase of the growth rate, it is sufficient that evolution had shaped the inhibitory effects of M by increasing HA and/or decreasing HB such that HA > HB. We would like to point out that, as mentioned above, in such a simple network the induced short-term increase of the growth rate coincides with a global advantage: this is the reason why this system reaches high biomass production.The growth rate is then given by A through its effective kinetic parameter in A gives gA = h[M], this leads to:It is also interesting to estimate the probability of resilencing reaction HA such that hHA = gB, is identical to the second-moment formula (2) that we already proved to describe well the metabolic regulation (see m = 2). Indeed, simulations of the network motif (3) with HA = gB/h and HB = gA/h reproduces the resilencing of reaction B, coherently with our greedy criterion .The analogy with the energy minimization problem over a corrugated landscape is also straightforward. Considering the growth rate as the opposite of a Hamiltonian, a metabolic adjustment can be viewed as the dynamics of a particle that is moving toward the minimal energy .


Recent advances in 13C-Metabolic flux analysis (13C-MFA) have increased its capability to accurately resolve fluxes using a genome-scale model with narrow confidence intervals without pre-judging the activity or inactivity of alternate metabolic pathways. However, the necessary precautions, computational challenges, and minimum data requirements for successful analysis remain poorly established. This review aims to establish the necessary guidelines for performing 13C-MFA at the genome-scale for a compartmentalized eukaryotic system such as yeast in terms of model and data requirements, while addressing key issues such as statistical analysis and network complexity. We describe the various approaches used to simplify the genome-scale model in the absence of sufficient experimental flux measurements, the availability and generation of reaction atom mapping information, and the experimental flux and metabolite labeling distribution measurements to ensure statistical validity of the obtained flux distribution. Organism-specific challenges such as the impact of compartmentalization of metabolism, variability of biomass composition, and the cell-cycle dependence of metabolism are discussed. Identification of errors arising from incorrect gene annotation and suggested alternate routes using MFA are also highlighted. Saccharomyces cerevisiae has been extensively utilized for the production of isoprenoids, polyphenols, and recombinant eukaryotic proteins. Central metabolism in yeast is typically quantified using isotope tracer techniques [S. cerevisiae have been used to identify essential genes and lethal gene pairs [E. coli [Metabolism in yeasts is primed for the maintenance of homeostasis while ensuring the ability to adapt to changing environmental conditions ,2. Uniquchniques , whereaschniques ,13,14. Achniques ,16, and chniques  using stchniques . GSM-aidchniques , succinachniques , vanillichniques , and seschniques . In addine pairs ,23, and ne pairs ,25,26. One pairs  employ sne pairs  and fermne pairs  and reve[E. coli , highlig[E. coli  and peri[E. coli .Saccharomyces cerevisiae is the most extensively studied species of yeast using 13C-MFA [ 13C-MFA . This te 13C-MFA  and oxyg 13C-MFA ,31, asse 13C-MFA , quantif 13C-MFA , explore 13C-MFA  and non- 13C-MFA ,38. In a 13C-MFA . 13C-MFA 13C-MFA ,41. The  13C-MFA . Increas 13C-MFA . More re 13C-MFA . Most of 13C-MFA . This is 13C-MFA ,45. Seve 13C-MFA ,47, thus 13C-MFA  is accomS. cerevisiae. Three major requirements in terms of accuracy of model annotation, reaction atom mapping and sufficiency of metabolite labeling data are established. The sources of flux resolution loss arising from compartmentalization of metabolism and alternate routes, and additional data necessary to completely resolve such flux are discussed. Finally, approaches to address the computational challenges arising from increased network complexity and variability of the biomass equation arising from accumulation of macromolecules are proposed.This review is aimed at outlining a workflow, key requirements, challenges, and considerations for successfully performing 13C-MFA at the genome-scale in S. cerevisiae, atom mapping data for every reaction within the GSM model, and intracellular metabolite labeling distribution data to resolve all fluxes within the GSM model. Despite various modifications to the consensus yeast model [S. cerevisiae containing 3494 reactions and 2223 metabolites [S. cerevisiae GSM model from 28% to 35%. In contrast, the E. coli GSM model (iAF1260) has a specificity of 79% [S. cerevisiae model arises from its poorly characterized sterol and soluble pool biosynthetic pathways, and differences in biomass composition of mutants and wild-type [E. coli model [2 and formate [The primary requirements for performing MFA at the genome-scale are the availability of a well curated GSM model for st model ,51,52,53st model . This moild-type  with an li model ,56 confi formate , which aS. cerevisiae is quantified in terms of growth rate, biomass and product (acetate and ethanol) yields on glucose. Respiratory quotient (CO2 evolved per mole oxygen consumed) is also routinely measured to constrain overall oxygen uptake. This restricts NADH re-oxidation and ATP synthesis via oxidative phosphorylation, thereby constraining network-wide redox metabolism. Incorporation of transcriptomic and proteomic data using frameworks such as binary ON/OFF type regulation [The reduction of this model can be accomplished by imposing fermentation data as mass balance constraints and eliminating all blocked reactions using FVA. A fermentation process involving gulation  or R-GPRgulation  may furtgulation . For exagulation ,61,62. HS. cerevisiae contains yeast-specific pathways such as the α-aminoadipate pathway for lysine biosynthesis for which atom mapping has been established [Atom mapping information for central metabolism remains conserved across all species and is largely readily available. Atom mapping for peripheral metabolism can be obtained from online databases such as MetaCyc , KEGG 6 and MetRablished . Charactablished  for whicablished . In partablished . Complexablished  or graphablished , which iablished  and MetRablished .2 [in vivo NMR spectroscopy can be utilized to obtain compartment-specific pool sizes and labeling distributions directly for some metabolites based on differences in the microenvironment of various compartments [Labeling distribution data for MFA is typically obtained using GC-MS , LC-MS , or NMR 2  have als2 ,76. Thisartments . This teartments ,79, but artments ,81 and tartments  and nuclartments  can be eartments  and evenartments  to betteartments  can be uartments  can be aS. cerevisiae occurs due to lack of probing techniques capable of obtaining compartment-specific labeling distribution of metabolites. Instead, existing procedures generate a pool-size-weighted average labeling distribution, which must be analyzed using corrections shown in 2 from aeration and pre-existing metabolite pools. Furthermore, catabolism of storage compounds also adds unlabeled carbons, which may alter the estimated flux distributions if not properly accounted for. The longer doubling time of yeast results in slower biomass labeling, which in turn delays the attainment of isotopic steady-state. From the experimental perspective, the above described factors contribute to resolution loss, thereby affecting MFA flux inference. However, recent efforts have confirmed that loss of resolution can also arise from structural identifiability issues existing within the metabolic network [S. cerevisiae, loss of resolution can result from the existence of the methylglyoxal pathway and the γ-aminobutyrate pathway as alternate routes to lower glycolysis and TCA cycle, respectively, resulting in loss of resolution between these two pathways. A previous study has already attributed local flux range expansion to the presence of such alternate pathways in E. coli. In addition to this, intracellular compartmentalization of metabolism introduces metabolic cycles such as the malate shuttle [S. cerevisiae.Inability to completely resolve all fluxes included within the GSM model for  network . In S. c shuttle , which a7 cells). It must be noted that the reliability of the flux estimation procedure depends strongly on the attainment of isotopic steady-state and therefore, at least six doublings [Another potential source of error is cell-cycle dependence of metabolic fluxes. It has already been demonstrated using synchronous cells that the glycolysis/PPP split ratio changes over a 24-h period , causingoublings  must be oublings , althougoublings .S. cerevisiae contain 3494 reactions and 2223 balanced metabolites [E. coli model in which case the number of active reactions was reduced to 697 from 2383 using a flux variability analysis based on growth conditions [S. cerevisiae and E. coli contain 32 [E. coli, this transformation reduces the number of free fluxes from 250 to 99, thereby ensuring statistical significance of the obtained flux distribution [MFA at the genome-scale is performed by first decomposing the genome-scale atom mapping model into subnetworks using an appropriate decomposition algorithm such as the EMU algorithm and then estimating fluxes so as to minimize the deviation of predicted metabolite labeling patterns from experimental data. The fluxes are estimated by solving a non-linear least squares problem, which is then subjected to a goodness-of-fit analysis followed by confidence interval determination ,86. The nditions . In contntain 32  and 75 [ntain 32  reactionntain 32  are repontain 32 . Presentntain 32  have beentain 32 ,92,94, ontain 32  and lackribution . The dirribution , howeverribution . Reductiribution .S. cerevisiae. While the biomass composition of a prokaryote such as E. coli remains relatively constant [S. cerevisiae [Growth-coupling as a means to speed up confidence interval estimation must be used with caution in an organism such as constant , much varevisiae ,101. In revisiae , thus, mrevisiae  using avrevisiae . While sSaccharomyces cerevisiae has a much lower prediction specificity compared to E. coli [In this review, we highlighted the various requirements, challenges, and considerations for achieving genome-scale flux resolution using 13C-MFA at isotopic and metabolic steady-state. While skeletal central metabolic models continue to be the norm, genome-scale MFA holds the potential to validate the various hypotheses proposed by previous analyses ,35,37,38 E. coli ,49, whic E. coli ,69. Spec E. coli ,31,104.  E. coli  for bett