Flux Design: In silico design of cell factories based on correlation of pathway fluxes to desired properties
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The identification of genetic target genes is a key step for rational engineering of production strains towards bio-based chemicals, fuels or therapeutics. This is often a difficult task, because superior production performance typically requires a combination of multiple targets, whereby the complex metabolic networks complicate straightforward identification. Recent attempts towards target prediction mainly focus on the prediction of gene deletion targets and therefore can cover only a part of genetic modifications proven valuable in metabolic engineering. Efficient in silico methods for simultaneous genome-scale identification of targets to be amplified or deleted are still lacking.
Here we propose the identification of targets via flux correlation to a chosen objective flux as approach towards improved biotechnological production strains with optimally designed fluxes. The approach, we name Flux Design, computes elementary modes and, by search through the modes, identifies targets to be amplified (positive correlation) or down-regulated (negative correlation). Supported by statistical evaluation, a target potential is attributed to the identified reactions in a quantitative manner. Based on systems-wide models of the industrial microorganisms Corynebacterium glutamicum and Aspergillus niger, up to more than 20,000 modes were obtained for each case, differing strongly in production performance and intracellular fluxes. For lysine production in C. glutamicum the identified targets nicely matched with reported successful metabolic engineering strategies. In addition, simulations revealed insights, e.g. into the flexibility of energy metabolism. For enzyme production in A.niger flux correlation analysis suggested a number of targets, including non-obvious ones. Hereby, the relevance of most targets depended on the metabolic state of the cell and also on the carbon source.
Objective flux correlation analysis provided a detailed insight into the metabolic networks of industrially relevant prokaryotic and eukaryotic microorganisms. It was shown that capacity, pathway usage, and relevant genetic targets for optimal production partly depend on the network structure and the metabolic state of the cell which should be considered in future metabolic engineering strategies. The presented strategy can be generally used to identify priority sorted amplification and deletion targets for metabolic engineering purposes under various conditions and thus displays a useful strategy to be incorporated into efficient strain and bioprocess optimization.
KeywordsMetabolic Network Flux Balance Analysis Glyoxylate Shunt Relative Flux Amplification Target
cell dry weight
elementary flux mode
flavin adenine dinucleotide (oxidized)
flavin adenine dinucleotide (reduced)
fructose mannose metabolism
metabolic flux analysis
nicotinamide adenine dinucleotide (oxidized)
nicotinamide adenine dinucleotide (reduced)
nicotinamide adenine dinucleotide phosphate (oxidized)
nicotinamide adenine dinucleotide phosphate (reduced)
pentose phosphate pathway
The identification of genetic target genes is a key step in rational engineering of production strains towards bio-based chemicals, fuels or therapeutics. To fully account for the high complexity of metabolic networks and select promising genes out of many possible candidates, systems-wide approaches have recently emerged from the rapidly increasing amount of genome-scale models . As example, OptKnock  OptGene , minimization of metabolic adjustment (MOMA)  as well as strain design based on optimum theoretical yield  display efficient in silico algorithms that allow the prediction of promising gene deletion targets towards overproduction of chemicals. They do, however, not provide a prediction of genes to be amplified for superior performance. This rather important information on potential amplification targets can be extracted on basis of experimental 13C metabolic flux data including comparative 13C flux studies of mutants with different properties  or a bi-level optimization framework (OptReg) which predicts gene amplification, attenuation or deletion targets on the basis of experimental flux data and regulation strength parameters . The value of such approaches, exploiting 13C flux data, has been successfully demonstrated e. g. for lysine producing C. glutamicum [8, 9]. They, however, require the availability of experimental data as basis of identifying amplification targets which is linked to increased experimental effort and might not give access to all potentially interesting gene candidates. Also metabolic control analysis, allowing the prediction of rate-limiting steps, gives access to amplification targets, but relies on experimentally data, e.g. in vivo kinetic data of the enzymes involved . Thus, efficient in silico methods for simultaneous genome-scale identification of targets to be amplified or deleted, which do not rely on available experimental data or a priori assumptions, are still lacking.
Among the available genome-scale modelling approaches, elementary flux mode analysis constitutes an important tool for the efficient study of cellular systems, since it allows the in silico prediction of desirable cell phenotypes that result either from the variation of process parameters or from the perturbation of genotypes . In comparison to alternative methods, such as linear programming, elementary flux mode analysis enables the investigation of all possible physiological states in the cell and can identify all existing metabolic flux vectors without any a priori knowledge or assumption on measured fluxes . Elementary flux mode analysis has been applied to predict promising gene deletion strategies as shown for rational design of L-methionine production in bacteria , the identification of genetically independent pathways in recombinant yeast  or the construction of a minimal E. coli cell for high yield ethanol production was enabled by prediction of gene deletion targets using elementary flux mode analysis . Here we present an in silico approach for quantitative target prediction towards superior cell factories. To this end we extend elementary flux mode analysis to a network-wide search for flux changes among all possible modes which are specifically correlated to a chosen target flux, i.e. the production capacity of the cell. Recent modelling studies showed that such a coupling of fluxes is an important behaviour of biological systems e.g. with respect to co-regulation of genes . However, a direct application towards target identification and superior production strains has not been considered. The potential of our approach is demonstrated for industrially relevant cell factories of different complexity. The soil bacterium C. glutamicum is one of the dominating bacteria in biotechnology and applied to produce more than 2.000.000 tons of amino acids per year . Its valuable product lysine, almost exclusively derived through fermentation by this microorganism, is used in animal nutrition. Due to its high relevance, C. glutamicum has been extensively investigated including the construction of a genome-scale model  and different success stories towards optimization lysine production by metabolic engineering which display an excellent basis as relevant test case for the simulations shown here . The filamentous fungus A. niger is widely exploited for the production higher-value enzyme products . The recently published genome-wide network model of A. niger illustrates its complex metabolism located in different intracellular compartments . Here we focus on the industrial enzymes fructofuranosidase, used to obtain valuable oligosaccharides , glucoamylase, applied in starch conversion , and epoxide hydrolyase, a highly useful biocatalyst for kinetic resolution of racemic epoxides .
Computation of elementary flux modes
In the present work, elementary flux mode calculation was performed using the double description method (null space approach) introduced by Wagner  and extended with the recursive enumeration strategy with bit pattern trees by Terzer and Stelling . An implementation of the algorithm in Java, with integration into MatLab (Mathworks Inc., Natick, MA) is available at http://csb.inf.ethz.ch and was applied in this work. On basis of the determined elementary modes, a detailed investigation of metabolic network properties was carried out. This included the estimation of theoretical (maximum) yield, relative fluxes through intracellular metabolic pathways, and target prediction for strain engineering. Calculations were partially automated and implemented into MatLab (Mathworks Inc., Natick, MA) and evaluated in Excel™ (Microsoft Office 2007, version 12.0).
Calculation of relative flux normalized to substrate uptake
Calculation of theoretical (maximum) yield
Since every real flux distribution in a biological system is a linear combination of elementary modes, the mode with the highest product or biomass yield, respectively, gives direct access to the maximum capacity of the underlying network, i.e. the maximum theoretical yields YP/C, max, and YX/C, max.
Target potential based on flux correlation
Positive values of αi, obj account for amplification targets, whereas negative values denote deletion or attenuation targets.
The major characteristics of the models used in the present work were as follows. A detailed description of the biochemical reactions in the different networks is given in the supplement files.
Small example network of TCA cycle and supporting pathways
The principle of the developed approach is elucidated using a simple metabolic network from E. coli, which was previously used for the discussion of the concept of elementary flux mode analysis . It includes the TCA cycle, the glyoxylate shunt and connected reaction of amino acid bio-synthesis. In this example, 2-phosphoglycerate, ammonium, carbon dioxide, and the cofactors, such as ATP and NAD, are considered as external metabolites. Arbitrarily, succinyl-CoA was defined as desired product and its formation as objective reaction. The stoichiometric equations of the metabolic model are listed in the supplement [Additional file 1].
Metabolic network of C. glutamicum
The metabolic reaction model of C. glutamicum considered the actual knowledge from the genome scale model recently created . It included all relevant pathways of central carbon, nitrogen and sulphur metabolism as well as the entire subset of anabolism and the corresponding reactions linked to formation and secretion of extracellular products. For elementary flux mode analysis, 7 external compounds were considered including the substrates glucose, ammonium, sulphate and oxygen and the products lysine, biomass and carbon dioxide. Additionally, ATP, required for maintenance, was considered as an external metabolite. The stoichiometric equation for biomass synthesis included all relevant precursor metabolites. The relative amount and composition of the macromolecules DNA, carbohydrates, lipids, protein and RNA was taken from thorough analysis of cellular composition . For ATP production from NADH and menaquinol in the respiratory chain, a P/O ratio of 2 was assumed . The stoichiometric equations of the metabolic model are listed in the supplement [Additional file 2].
Metabolic network of Aspergillus niger
The metabolic reaction model of the central metabolism of A. niger contained was constructed on basis of the genome scale model recently published . The model included all relevant pathways of central carbon, nitrogen and sulphur metabolism as well as the entire subset of anabolism and the corresponding reactions linked to formation of extracellular products. Hereby, the cellular compartment mitochondrion, glyoxysome and cytosol were considered together with the respective transport reactions. For elementary flux mode analysis, external compounds were substrates (sources of carbon, nitrogen, sulphur, oxygen) and products (enzyme, biomass, carbon dioxide, gluconate, oxalate, citrate). Additionally, ATP for maintenance was included in the model and considered as an external metabolite. For ATP production the P/O ratio for mitochondrial NADH was assumed as 2.64 and that for succinate and cytosolic NADH as 1.64 . The stoichiometric equation for biomass synthesis included all relevant precursor metabolites from the central carbon metabolism. The relative amount and composition of the macromolecules DNA, glucan, glycogen, lipid and RNA was taken from . The amino acid composition of the cell protein was calculated from the average protein content of A.niger using the program IdentiCS . Glycosylation of cellular protein was considered, taking Galf2Man8(GlcNAc) as average composition of the glycosylation residues in filamentous fungi  and an average number of 33 sugar residues  into account. This resulted in the stoichiometric fraction of Galf6Man24(GlcNAc)3 per protein. For the calculation of the exact demand it was assumed that on average 64% of all proteins are glycosylated . The cellular demand for synthesis of the enzymes fructofuranosidase, glucoamylase and epoxide hydrolase was calculated as follows. Fructofuranosidase is highly glycosylated , whereby half of the enzyme consists of glycosylation chains (NetNGlyc, http://www.cbs.dtu.dk/). Hereby, the glycosylation pattern Galf18Man308(GlcNAc)8.5, as previously determined for this enzyme, was considered . The amino acid composition of fructofuranosidase was derived from the corresponding open reading frame-ID An08 g11070 . Similarly, the amino acid composition (An03 g06550) and the glycosylation pattern  was taken into account for glucoamylase. Epoxide hydrolase is non-glycosylated so that only the protein itself had to be considered (An16 g02170). The stoichiometric equations of the metabolic model are listed in the supplement [Additional file 3].
Target identification based on flux correlation - small example network
Lysine production in C. glutamicum
Maximum production performance using glucose as carbon source
Prediction of amplification and deletion targets
The obtained alternative optima and the various interesting suboptimal solutions now provided a rich source for target search. The elementary modes were now screened for statistically significant correlation of fluxes as indicator of targets to be amplified or deleted. Most targets were identified for the subset of non-growth modes which do not exhibit biomass formation. Here, flux correlation analysis clearly identified a number of reactions as potential targets (Figure 4B). Targets to be amplified are attributed to all reactions of the pentose phosphate pathway, as well as ammonium uptake and assimilation, different enzyme of the lysine biosynthesis and the lysine secretion. Interestingly, also the entry enzyme into the glycolysis, glucose 6-phosphate isomerase is classified as amplification target. This can be understood from its role in re-cycling carbon back into the pentose phosphate cycle enabled by its reversible nature (Figure 4A). Deletion or attenuation targets are located in the glycolysis, the TCA cycle and also the oxidative respiratory system. When ranked by priority, i.e. the value of the target potential coefficient α, the most striking targets predicted are located at the glucose 6-phosphate node, which reveal this node as key to successful engineering of C. glutamicum for improved lysine production. The simultaneous consideration of the potential targets reveals a systems-wide redirection of flux towards a superior producer as indicated by the desired flux distribution at optimal performance (Figure 4A).
Enzyme production in Aspergillus niger
Maximum production performance using glucose as carbon source
Elementary flux mode analysis of fructofuranosidase (FFase) production by A. niger on different carbon and nitrogen sources.
Maximum carbon yield
Number of Elementary Modes
Carbon Source/Nitrogen Source
Modes linked to FFase production
(% of total EFM)
Modes linked to biomass and FFase production
(% of total EFM)
Optimal pathways for glucose based production
Impact of alternative carbon and nitrogen source
Elementary flux mode analysis was further carried out for the industrially relevant carbon sources xylose, glycerol and oleic acid (Table 1). The reduced substrate glycerol revealed an optimal production of 0.83 c-mol/c-mol and was the best carbon source (Figure 6B). Oleic acid (0.72 c-mol/mol) and xylose (0.73 c-mol/c-mol) were slightly less efficient Figures 6C, D). Glycerol was metabolized by simultaneous usage of the NADH-dependent glycerol-dehydrogenase and the FAD-dependent glycerol 3-phosphate dehydrogenase (Figure 7B). Due to this reducing equivalents were released into the cytosol and mitochondrion, respectively. This caused an increased flux through the NADH-ubiquinone oxidoreductase, counterbalancing the NADH excess in the cytosol. Probably linked to the different entry point of glycerol into metabolism, the supply of NADPH differed for this carbon source with respect to the reactions involved. Here, the oxidative PPP played only a minor role, whereas the mannitol cycle and the malic enzyme were recruited. For oleic acid the flux distribution differed drastically (Figure 7C). For optimal production, degradation involved two parallel routes, that in the mitochondrion as well as that in the glyoxysome resulting in a large relative flux through the glyoxylate shunt and reactions of the TCA cycle with the corresponding mitochondrial shuttle systems (Figure 7C). Additionally, the high supply of NADH by the degradation of the reduced fatty acids was obviously utilized by the mannitol cycle to form NADPH. The oxidative PPP was not involved in NADPH supply. Production on xylose demanded for increased NADPH supply, as indicated by average flux through the oxidative PPP (48 mol/mol hexose unit), the mannitol cycle (60 mol/mol hexose unit) and the malic enzyme (60 mol/mol hexose unit) (Figure 7D). This at least partly attributed to the NADPH demand linked to the xylose uptake system . As for glucose, by-product formation was not observed for the alternative carbon sources under maximal production. The degree of reduction also played a role for the nitrogen source. The optimum yield decreased by about 18% for all carbon sources when nitrate was used instead of ammonia.
Prediction of amplification and deletion targets
Other target enzymes studied, including glucoamylase or epoxide hydrolase which differ in amino acid composition and glycosylation degree yielded rather similar targets for all metabolic scenarios studied.
Elementary mode analysis provides a rigorous basis to systematically characterize cellular phenotypes, metabolic flexibility and robustness which facilitates the understanding of cell physiology [39, 40]. In the present work, this pathway analysis tool was applied and extended to predict systems-wide amplification and deletion targets in metabolic engineering towards improved bio-production in systems with optimally designed fluxes (FluxDesign). First evidence that the reactions derived here open realistic chances for improvement can be obtained from recent studies. An excellent test case is the very well studied C. glutamicum. From the targets predicted, various reactions have been successfully implemented towards superior production of lysine. This includes amplification of glucose 6-phosphate dehydrogenase , 6-phosphogluconate dehydrogenase , reactions within the lysine pathway  as well as product secretion , all shown to enhance lysine production Additionally, deletion of glucose 6-phosphate isomerase  or pyruvate dehydrogenase , have been successfully implemented into C. glutamicum for improved performance. Moreover, not yet validated targets such as the amplification of ammonium metabolism or reactions of the non-oxidative PPP or deletion/attenuation of TCA cycle reactions are predicted. For enzyme production in A. niger, much less metabolic engineering progress of central carbon metabolism is reported. The few studies available, however, illustrate that targets predicted here have proven valuable. As example, the amplification of the synthesis of glycosylation residues increased protein over-production [46, 47]. Similarly, the amplification of the protein assembly route itself, has been shown to result in enhancement of production in A. niger . Beyond, these experimental studies on more obvious targets, flux balance analysis and also stoichiometric flux analysis indicate the importance of sufficient NADPH supply for protein production in A. niger [49, 21] and A. oryzae [21, 50] whereby the PPP plays an important role which was also found in the present study.
The present approach did not reveal all relevant targets previously reported to redirect carbon flux. As example, the amplification of fructose bisphosphatase  or the deletion of phosphoenolpyruvate carboxykinase  both identified from 13C flux analysis as major targets for improved lysine production in C. glutamicum, was not predicted here. Still, the presented approach can be generally used to identify priority sorted amplification and deletion targets for metabolic engineering purposes under various conditions and thus displays a useful strategy to be combined with existing in silico tools  for strain engineering.
Due to the fact that elementary flux mode analysis enables the investigation of all possible physiological states in the cell, detailed insights into the underlying metabolism could be obtained. This includes the visualization of different flux states for optimum production which result from complementary pathways for the supply of NADPH (A. niger) or the regeneration of ATP (C. glutamicum). A closer inspection showed that this characteristic mainly originates from a small sub set of reactions, adding flexibility and robustness to the networks. The possibility to recruit different pathway modes for high production appears advantageous when approaching metabolic engineering strategies. Since it can be expected that certain genetic engineering strategies might not work for reasons of growth deficiency or undesired regulatory behaviour, the possibility to choose among different promising directions seems useful. Interestingly, the prediction of genetic targets depended on the metabolic state of the cell (Figure 7). Thus it turned out as relevant to focus the target search to a specific relevant scenario. Growing cells and non-growing cells pose different burdens on the metabolism, competing with product formation, so that different conclusions are derived. From practical perspective, both scenarios seem relevant, since for production were non-growing as well as growing cells can be applied [52, 53]. The metabolic state is therefore an important point to be considered.
The models used in the present work are a condensed representation of the genome-wide metabolism relevant for the present study. Guided by the focus of the study we have considered industrially relevant substrates and clear objective products, whereas unusual substrates or other possible products appeared irrelevant here. It seems, however, easily possible to extend our approach to larger networks if desired, with additional substrates or even mixtures or also more detailed resolution of anabolic routes at the network periphery which were lumped here. The latter would, however, require a more detailed experimental basis on cellular composition as currently available.
Combining elementary flux mode analysis with correlation of fluxes to desired network properties, potential amplification and deletion targets could be identified in industrially relevant production strains. Hereby, different scenarios considering the bioprocess environment or the metabolic state of the cell provided a detailed insight into the underlying pathway network. These findings appear very useful to guide strain engineers towards improved bio-production. This also might include a comparison among different potentially interesting hosts . Admittedly, not every target predicted by FluxDesign will necessary lead to improved production, since stoichiometric modelling as applied here cannot consider e.g. cellular regulation or enzyme properties limiting or even blocking the desired network response towards targeted genetic perturbation. Still, the presented approach can be easily used to identify priority sorted amplification and deletion targets for metabolic engineering purposes under various conditions and thus displays a useful strategy to be incorporated into strain and bioprocess optimization.
The authors gratefully thank the DFG (Deutsche Forschungsgemeinschaft) for financial support of subproject B11 within the framework of the Collaborative Research Center "SFB 578 - from Gene to Product". We acknowledge the support by Marco Terzer on the application and implementation of the bit pattern tree algorithm for elementary flux mode analysis. We further thank Jibin Sun and An Ping Zeng for providing information on the A. niger amino acid composition supplied by the software IdentiCS. This paper is dedicated to Dietmar Hempel on the occasion of his 65th birthday.
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