Guidelines for metabolic flux analysis in metabolic engineering: methods, tools, and applications

Highlights

• Metabolic flux provides quantitative insights into carbon, energy, and electron flow.
• Flux Balance Analysis (FBA) evaluates the ability of metabolic network models.
• 13C Metabolic flux analysis (13C MFA) is used to estimate flux with high precision.
• The new method of 13C-MFA can measure flux in complex, non-standard biological systems.
• The predictive kinetic model of metabolism was constructed from a large-scale 13C-MFA dataset.

The field of metabolic engineering mainly focuses on improving the bioproduction of value-added chemicals, fuels, and drugs by designing, constructing, and optimizing metabolic pathways, redirecting intracellular flux, and improving cell characteristics related to industrial biotechnology implementation. The metabolic network model and metabolic flux are the core concepts of metabolic engineering.

Carbohydrate Metabolism Assay Kits

Metabolism Assay Kits

Flux balance analysis (FBA)

The concept of metabolic network model is mathematically represented by the stoichiometric matrix S (Orth et al., 2010). The S matrix lists the stoichiometric coefficients of all known metabolic reactions and transport processes occurring within cells. Assuming that intracellular metabolites are in a pseudo steady state, i.e. assuming that the levels of intracellular metabolites are relatively constant over time, these stoichiometry impose limitations on the flow of metabolites in the network model (indirectly affecting the flow of carbon, electrons, and energy). Specifically, the steady-state assumption requires that for each intracellular metabolite, the sum of all fluxes that produce that metabolite must be equal to the sum of all fluxes that consume that metabolite. These flux balance constraints are mathematically represented by the following equation:

S x v=0 (1) S x v=0 (1)

Figure 1 There are three main methods for analyzing metabolic network models and quantifying intracellular metabolic flux: flux balance analysis (FBA), metabolic flux analysis (MFA), and 13C metabolic flux analysis (13C-MFA). These three methods all use stoichiometric matrices to limit the flow of metabolites in the network model (S × v=0). In FBA, metabolic flux is predicted by maximizing growth rate. In MFA, flux is determined by fitting the measured nutrient absorption rate and product secretion rate with a network model. In 13C-MFA, flux is estimated based on isotopic labeling patterns measured in 13C tracer experiments.

One of the earliest and most successful applications of FBA was to calculate the maximum theoretical yield of metabolites for a given network model and substrate by solving the following linear programming problem:

Maximize vproduct (2)

S × v=0

-Vsubstrate=1

In short, under the limitations of chemometrics, fixing the substrate absorption at 1 mole and maximizing the desired product yield can easily determine the maximum product yield (product mole/substrate mole). The same method can also be used to calculate the maximum biomass yield. In this case, it is important to also include a one-time biomass formation reaction based on measuring biomass composition (Long and Antoniewicz, 2014a), as well as an additional reaction for energy dissipation in the network model (ATP → ADP+Pi) (Varma and Palsson, 1994). The latter reaction captures the additional energy required to perform various cellular maintenance processes, such as repairing damaged macromolecules. By limiting the ATP maintenance flux to an appropriate level, FBA can predict biomass growth under different carbon sources and environmental conditions (such as aerobic and anaerobic growth; or using ammonium as a nitrogen source and nitrate as a nitrogen source), and the results are in good agreement with experimental measurements (Varma and Palsson, 1994; Mahadevon and Schilling, 2003).

Another useful application of FBA is to predict the maximum growth rate of cells. This is based on the assumption that the maximum growth rate will be limited by the maximum nutrient uptake rate (Varma and Palsson, 1994). Solve the following linear programming problem:

Maximize vbiomass (3)

S × v=0

-Vglucose=GURmax

-Voxygen=OURmax

LB ≤ v ≤ UB

The inequality constraints on nutrient uptake rate, such as maximum glucose uptake rate (GURmax) and maximum oxygen uptake rate (OURmax), are based on arguments related to maximum cell membrane occupancy rate (Liu et al., 2014; Zhuang et al., 2011), that is, the portion of the cell membrane that can be occupied by transporters and electron transport chain proteins. Based on thermodynamic considerations (such as the assumption of reaction reversibility) and known kinetic limitations (such as maximum enzyme flux capacity), other constraints can also be incorporated, such as lower and upper limits of flux. One of the first applications of this method is to predict the maximum growth rate of Escherichia coli. The maximum growth rate of Escherichia coli predicted by FBA is approximately 1.0 h-1 (aerobic growth on glucose) (Zhuang et al., 2011), which is consistent with the growth rate of adaptive evolutionary Escherichia coli strains observed in experiments (Long et al., 2017b). The optimal flux solution also predicts that Escherichia coli will secrete acetate as a metabolic byproduct at high growth rates, which is consistent with experimental observations (Varma and Palsson, 1994; Mahadevon and Schilling, 2003).

Shortcomings in FBA analysis

1) The intracellular flux predicted by FBA is not always consistent with the flux measured using more advanced methods such as 13 C-MFA.

2) FBA performs poorly in predicting the metabolic flux and growth phenotype of engineering strains, making it difficult to predict the growth rate and metabolic flux of gene knockout strains.

Toolkit: Many algorithms and related constraint based modeling methods of FBA have been integrated into the Matlab based toolkit COBRA Toolkit, which is available for free and widely used in metabolic engineering research (Heirendt et al., 2019)

Metabolic flux analysis (MFA)

Metabolic flux analysis (MFA) is a related constraint based analysis method that can be used to quantify flux (Antoniewicz, 2015a). In metabolic flux analysis, metabolic flux is estimated based on experimentally measured rates (such as substrate absorption rate, oxygen absorption rate, growth rate, and product secretion rate) and is constrained by chemometrics (Figure 1). The difference between MFA and FBA is that there is no assumption about the optimal performance of cells. Therefore, MFA can be used to quantify the flux of cells grown under industrial related growth conditions, such as in nutrient limitations or in the presence of growth inhibitory compounds, which goes beyond the scope of most current FBA based technologies. In MFA, calculate the metabolic flux through the network model by solving the following least squares regression problem:

Minimize SSR= Σ (r-rm) 2/ σ R2 (4)

S × v=0

R × v=r

In short, flux is estimated by minimizing the sum of squared residuals (SSR) between the measured rate (r m) and the model predicted rate (r), subject to stoichiometric constraints, where residuals measure the error squared（ σ R 2) Weighted (Antoniewicz, 2015a). One important application of MFA is to determine the production of key cell cofactors such as ATP, NADH, and NADPH under different growth conditions. This can provide valuable insights into the flow of energy and electrons.

The main limitation of MFA is that a simplified metabolic network model must be used for this analysis. This is because external rate measurements often cannot provide sufficient constraints to estimate the flux of all known intracellular pathways. The maximum estimated independent flux is limited by the number of independent extracellular rate measurements.

In practical application of MFA, multiple paths must be removed from the network model to ensure sufficient constraints to estimate the remaining selected path flux in the model. For example, for Escherichia coli that grow aerobic on glucose, the following reactions and pathways in core metabolism are usually excluded: Entner Doudoroff pathway, glyoxylate shunt, malic acid enzyme, phosphoenolpyruvate carboxyl kinase, phosphoenolpyruvate synthase, fructose-1,6-diphosphate enzyme, and hydrogenase reaction.

Note: Except for the hydrogenase reaction, which has high activity in Escherichia coli and is responsible for producing approximately 40% of the NADPH required for cell growth

13C metabolic flux analysis (13C MFA)

13 C-MFA has always been the gold standard for accurately and accurately quantifying live cell flux in metabolic engineering. In 13 C-MFA, one or more tracer experiments are conducted, in which 13C labeled substrates (such as [1,2-13C] glucose) are fed into growing cells until the 13C labeled carbon is completely incorporated into intracellular metabolites and macromolecules (such as proteins, RNA, and glycogen). Then, analytical techniques such as mass spectrometry (MS) (Antoniewicz et al., 2007a; McConnell and Antoniewicz, 2016), tandem mass spectrometry (MS/MS) (Antoniewicz, 2013a; Choi et al., 2012), and nuclear magnetic resonance (NMR) (Szyperski et al., 1999) were used to quantify the labeling patterns of various cellular metabolites.

The 13C labeling pattern is highly dependent on relative pathway flux, meaning that different flux distributions will produce different labeling patterns. Therefore, flux can be inferred from the measured isotope labeling patterns (Figure 2). In fact, to estimate metabolic flux from isotope labeled data and external rate measurements, the following least squares regression problems need to be addressed

The 13C labeling pattern is highly dependent on relative pathway flux, meaning that different flux distributions will produce different labeling patterns. Therefore, flux can be inferred from the measured isotope labeling patterns (Figure 2). In fact, to estimate metabolic flux from isotope labeled data and external rate measurements, the following least squares regression problem needs to be solved (Antoniewicz et al., 2006):

Minimize SSR= Σ (x-xm) 2/ σ X2+ Σ (r-rm) 2/ σ R2 (5)

S × v=0

R × v=r

Fisotonomer (v)=0

Flux is estimated by iteratively minimizing the sum of squared residuals (SSR) between measured and simulated isotope labeling patterns (x) and external rate measurements (r). At each iteration, it is necessary to simulate a set of isotopic labels for flux by solving a subproblem composed of a large number of coupled nonlinear equations. Over the past two decades, various mathematical methods have been developed to solve these nonlinear isotope labeling equilibrium problems (Zupke and Stephanopoulos, 1995; Schmidt et al., 1997; Wiechert et al., 1999; Antoniewicz et al., 2007b). At present, the most effective algorithms are based on the Basic Metabolic Unit (EMU) framework developed by Antoniewicz et al. in 2007 (2007b).

Figure 2 The 13C metabolic flux analysis (13C-MFA) technique for quantifying flux is based on fitting experimental data composed of external rate and isotope labeling patterns with metabolic network models. There are many software tools that can perform 13C-MFA calculations, including Metran, INCA, etc. Statistical analysis of flux fitting can determine the goodness of fit and be used to quantify the 95% confidence interval for estimating flux.

Compared to MFA, the main advantage of 13C-MFA is that isotopic labeling measurements provide a significant amount of redundant limitations for flux estimation. For example, a typical tracer experiment would generate 50 to 100 isotope labeled measurements to estimate approximately 10-20 independent metabolic fluxes. Therefore, in 13C-MFA, the number of measured data significantly exceeds the number of estimated flux parameters. Ultimately, this redundancy translates into higher flux accuracy and enhances confidence in estimating flux accuracy (Antoniewicz, 2015b). A recent paper compiled a comprehensive step-by-step approach and troubleshooting guidelines for high-resolution 13C-MFA research (Long and Antoniewicz, 2019a). Generally speaking, the five basic steps of 13C-MFA are:

1) Experimental design

2) Tracer experience

3) Isotopic labeling measurement

4) Flux estimation

5) Statistical analysis

The first step of 13C-MFA is to determine the optimal 13C tracer and labeling measurement method for specific organisms, growth conditions, and carbon substrates. In the early stages of the development of 13C-MFA, commonly used 13C-MFA glucose tracers include various mixtures of [1-13C] glucose, [U-13C] glucose, and unlabeled glucose. Their cost is relatively low (about $100 per gram). Recent studies have shown that although dual labeled glucose tracers such as [1,2-13C] glucose and [1,6-13C] glucose are relatively expensive (currently around $600/g), they can greatly improve flux accuracy (Crown et al., 2016). At present, it is recommended to use these glucose tracers as default tracers for high-resolution 13C-MFA (Long and Antoniewicz, 2019a). At present, gas chromatography-mass spectrometry (GC-MS) is the cheapest and most widely used analytical technique in conventional 13C-MFA research. In most cases, the information provided by gas chromatography-mass spectrometry measurements is sufficient to accurately estimate fluxes in microbial and mammalian systems.

The second step of 13C-MFA is to conduct one or more tracer experiments. The main consideration here is to ensure the maintenance of metabolic homeostasis, which means that the metabolic flux remains constant during the tracer experiment and reaches isotopic homeostasis. In most cases, this goal can be achieved by extending the constant temperature cultivation time (usually more than 5 residence times) or conducting batch cultivation experiments (maintaining a constant cell growth rate (such as exponential growth stage). The determination of how many tracer experiments should be conducted depends on the required flux resolution (Crown et al., 2015a; Antoniewicz, 2015b). Generally speaking, the more tracer experiments are conducted simultaneously, the more labeled measurements are made, and the higher the accuracy of flux estimation (Crown et al., 2015a). For conventional 13C-MFA applications, using the best tracer for two parallel labeling experiments is usually sufficient to accurately quantify flux, with an uncertainty of less than 5% (Long and Antoniewicz, 2019a).

The third step of 13C-MFA is to measure the isotopic labeling of the collected samples. As mentioned above, GC-MS is currently the most widely used analytical technique for quantitative isotope labeling. In most cases, these measurement results are sufficient to accurately quantify flux. To provide more information and improve flux resolution, multiple analytical techniques can be used and data can be merged (Tang et al., 2007c). Other analytical techniques include 1) NMR, 2) LC-MS (/MS), and 3) tandem mass spectrometry (such as GC-MS/MS). It is expected that tandem mass spectrometry measurements will be more widely used in the future, especially in applications that require improved flux resolution.

The fourth step of 13C-MFA is to solve the nonlinear regression problem (i.e. equation (5)), which will return a set of metabolic fluxes that best reproduce the measured isotope labeling patterns and external rates. In the past decade, many software tools have been developed to perform these 13C-MFA calculations, including Metran (Yoo et al., 2008), INCA (Young, 2014b), OpenFLUX2 (Shupletsov et al., 2014), 13CFLUX2 (Weitzel et al., 2013), OpenMebius (Kajihata et al., 2014), and WUFlux (He et al., 2016). All these software tools are based on the EMU framework (Antoniewicz et al., 2007b; Young et al., 2008).

The fifth step of 13C-MFA is to conduct statistical analysis on flux solutions. Firstly, it is necessary to evaluate the size of SSR values to ensure satisfactory fitting results (Antoniewicz et al., 2006). Assuming the model is correct and there is no significant measurement error in the data, then the minimum SSR is one with χ A random variable with a distribution of 2. The acceptable range of SSR values is between χ two α/ 2 (n-p) and χ 21- α/ Between 2 (n-p), where α It is a selected critical value, such as a 95% confidence interval of 0.05. If the minimum SSR value is too high, i.e. there is a significant difference between the measured data and the best model fit, the flux solution must be rejected and the flux analysis hypothesis must be re evaluated. The common reasons for obtaining high SSR values are: 1) incomplete metabolic models, such as not including important active reactions or pathways in cells; 2) The reversibility of reactions, i.e. forward and reverse fluxes, is not included in the metabolic network model; 3) There are serious measurement errors in one or more isotope labeling measurements, such as errors caused by improper calibration of analytical instruments, signal saturation, or co elution effects; 4) Measurement errors greater than expected, such as errors caused by low signal strength. After identifying and correcting the reasons for obtaining high SSR values, flux estimation (i.e. step four) must be repeated. Once a statistically acceptable fitting result is obtained, the next step is to calculate the confidence interval for the estimated flux. The accurate 95% confidence interval can be calculated by evaluating the sensitivity of minimizing SSR to flux changes or conducting Monte Carlo simulations (Antoniewicz et al., 2006).

Dynamic metabolic flux analysis

The flux analysis method for estimating dynamic metabolic flux is called the Dynamic MFA (DMFA) (Leighty and Antoniewicz, 2011; Antoniewicz, 2013c) or the Dynamic 13C-MFA (13C-DMFA) method (Antoniewicz, 2015a). Given that many industrial processes are dynamic, developing efficient algorithms and experimental programs for executing 13C-DMFA should be the top priority in the future. In some cases, such as if the change in flux is much slower than the change in isotopic labeling, it is possible to use 13C-MFA or isotopic non-stationary 13C-MFA (13C-NMFA) as the first approximation to quantify flux in transient systems (Ahn and Antoniewicz, 2011, 2013; He et al., 2014; Noack et al., 2011).

13C-MFA with G-values

For slow-moving organisms, even if the stable state of metabolism can be maintained for a long time, it is often unrealistic to wait long enough for biomass macromolecules (such as proteins and RNA) to reach isotopic stability. In this case, measuring isotopic labeling of intracellular metabolites may be easier than measuring macromolecules. Due to the much faster turnover rate of intracellular metabolites (~seconds) compared to the turnover rate of macromolecules (~hours), intracellular metabolites typically reach isotopic homeostasis in a relatively short period of time. Therefore, using these measurement results, the classic fixed 13C-MFA method can be used to quantify flux. However, even if intracellular metabolites cannot be easily measured with high precision, or these measurement results do not provide enough information to quantify flux with high precision, flux can still be estimated through isotopic measurements of macromolecules. In this case, the 13C-MFA model was extended to include so-called G-values (Antoniewicz et al., 2007c). A G value represents a portion of the biomass metabolites produced during the tracer experiment, while 1-G represents a portion of the biomass metabolites that existed before the start of the tracer experiment, and therefore will have natural isotope labeling:

Simulated labeling=G æ (labeling under stable isotope state)+(1-G) Å (natural isotope labeling) (6)

In practice, each measured biomass metabolite will include a separate G value in the network model (Long and Antoniewicz, 2019a). In this extended 13C-MFA framework, G values are estimated together with metabolic flux. Another advantage of using the 13C-MFA method with G-values is that it can be used to determine the turnover rates of macromolecules such as proteins, RNA, and glycogen, as follows (Long et al., 2016b):

Large molecule turnover rate (h-1)=- ln (1-G)/ Δ T – μ (7)

In this formula, G is the estimated G value of 13C-MFA for specific biomass metabolites, such as amino acids in hydrolyzed biomass proteins or ribose in hydrolyzed RNA, Δ T is the length of the tracer experiment, μ It is the growth rate of cells.

Metabolic flux analysis of autotrophic metabolism

Quantifying the metabolic flux of autotrophic organisms (i.e. cells with CO2 as the sole carbon source) is challenging because in isotopic stable states, the labeling pattern only depends on CO2 labeling and not on flux. For example, if 100% 13CO2 is used as a tracer, all cellular metabolites will be labeled 100% with 13C in an isotopic stable state. Fortunately, in the instantaneous labeling state, where isotopic labeling is still incorporated into intracellular metabolites after the introduction of 13CO2, the measured labeling pattern depends on the flux. Therefore, flux information can be extracted by analyzing instantaneous labeled data.

Analysis of metabolic flux during non growth period

So far, most 13C-MFA studies have used growth active cells. However, there is an increasing interest in better understanding the metabolism of biological systems where metabolism may not be active in growth. For example, in the production stage of high cell density fed batch cultures, growth is typically significantly reduced due to product inhibition. To estimate flux during non growth stages, it is necessary to add tracers at the beginning of the metabolic stage to be studied. Due to limited cell growth, the amount of markers added to macromolecules is usually too low to perform 13C-MFA calculations. On the contrary, markers of intracellular metabolites can be measured. Due to the relatively high turnover rate of intracellular metabolites, labeled measurement results close to isotopic homeostasis can usually be obtained. In this case, 13C-MFA can be used for flux quantification (Ahn and Antoniewicz, 2013). Even if isotopic equilibrium cannot be achieved, it is still possible to estimate flux using 13C-NMFA (Ahn and Antoniewicz, 2011). When conducting these analyses, it is necessary to consider the potential dilution effect of unlabeled metabolites produced in the early stages of growth on isotopic labeling. For example, unlabeled acetic acid produced during the growth phase may be co utilized with glucose during the quiescent phase.

Summary and Outlook

1. At present, flux analysis technology based on 13C can provide the most reliable and accurate measurement of metabolic flux in vivo. Especially, 13C-MFA has been widely used to better understand model organisms such as Escherichia coli, brewing yeast, and Corynebacterium glutamicum, as well as an increasing number of non model organisms.
2. So far, most 13C-MFA studies have used chemically defined culture media and a single 13C labeled carbon source. However, many industrial fermentations involve complex culture media, including multiple carbon sources such as glucose and xylose, as well as undefined components such as yeast extracts or protein digests. In the future, it will be very important to extend 13C-MFA to systems that include rich medium formulations. This modeling strategy can also be used in the future for 13C flux analysis of microbial systems growing on complex media.
3. One of the main challenges and bottlenecks in metabolic engineering is the difficulty in predicting the phenotype of genetically engineered strains. In many cases, cell growth rate is negatively affected by genetic engineering, and metabolic flux can unexpectedly reconnect after pathway manipulation. To establish more predictive models in the future, it is necessary to fundamentally understand the driving forces that determine the flux redistribution of engineering cells.
4. Finally, adaptive laboratory evolution (ALE) research provides important supplementary information for metabolic regulation and metabolic bottlenecks. By performing multiple parallel ALE evolutions and identifying common mutations and trends in metabolic flux phenotypes, it is possible to distinguish between corresponding adaptations and less correlated mutations and flux mismatches.