While rational design approaches were the original driving force in metabolic engineering, directed evolution and high throughput screens of mutant libraries have since become increasingly commonplace [3,4,8,11,12,102,103,104,105,106,107,108,109]. One of the main difficulties involved in these two “inverse metabolic engineering” approaches is the identification of the mutations responsible for the improved phenotype [110]. These frequently non-intuitive changes can often best be pinpointed with a direct, systems-scale readout of the metabolic state [107].

Common techniques employed in such approaches include HCA, PCA, and PLS-DA. These methods generate clusters or loadings that identify key metabolite differences, which in turn suggest what genetic changes may have been selected for. For example, Hong et al. used PCA and clustering analysis of metabolomics data, supplemented with transcriptional data, to investigate strains of S. cerevisiae that had been selected via directed evolution for improved galactose uptake [107]. They identified up-regulation of PGM2 as a common method for indirectly improving flux through the Leloir pathway for galactose utilization via relieved feed-forward inhibition of galactose-1-phospate and activation of reserve carbohydrate metabolism. The enrichment analysis methods used for the transcriptional data are discussed in further detail in the next section.

A study by Yoshida et al. examined metabolic differences between S. cerevisiae and Saccharomyces pastorianus in regards to SO₂ and H₂S production [111]. They generated metabolomic and transcriptomic datasets under typical beer fermentation conditions, and identified lowered transcription levels and increased levels of upstream metabolites for two reactions in S. cerevisiae that they subsequently hypothesized to be rate-limiting fluxes for desired production of H₂S and SO₂. They verified their prediction by exposing S. pastorianus to known inhibitors for the corresponding enzymes, which recapitulated this effect. They used this knowledge to engineer and test S. cerevisiae strains that relieved these bottlenecks, and then developed a mutant with similar properties via a directed evolution process for commercial use.

Similarly, Wisselink et al. investigated a xylose-utilizing strain of S. cerevisiae developed by introduction of L-arabinose pathway genes to an existing xylose-utilizing strain, followed by directed evolution to improve L-arabinose utilization [112]. They used fold-change and enrichment analysis of transcripts, coupled with thermodynamic analysis of reactions using metabolite mass action ratios and reaction driving forces, to identify an acquired response of the GAL regulon to arabinose levels as contributing to these improvements. They confirmed this discovery with subsequent knockouts of GAL2.

Other examples of using metabolomics for after-the-fact assessment of engineered strains include studying the effects of repeated exposure to vacuum fermentation conditions on S. cerevisiae [113], comparing evolved strains with knockouts proposed by the OptKnock algorithm [47], and identifying the differences between several yeast species during aerobic fermentation on glucose [62].

While the goal of metabolic engineering is to introduce a change on the metabolic level, many of these changes are necessarily implemented by introducing genetic modifications to affect transcriptional levels. As such, analysis of biological layers beyond the metabolome, such as the transcriptome and proteome, can provide further, and sometimes crucial, insight into the wide-reaching effects of an alteration.

A number of techniques widely used in metabolomics (such as PCA and HCA) are also well-established for many of these other “omics” datasets, though there are a number of other techniques that until recently were more specific to transcriptional or proteomic analyses. One of the most prominent examples of this is enrichment analysis, originally developed for transcriptomics datasets. Enrichment analysis uses information about the frequency of occurrence or the ranking of sets of gene names or functions in a given list of genes to examine the biological relevance of observed changes [114]. For example, the number of genes from a given pathway occurring in a list of interest (say, high-importance variables in PCA or a cluster from HCA) is assessed to see if that number of genes would be expected to be found in an arbitrary list of genes purely at random; this comparison is made using a hypergeometric distribution. If a list is statistically significantly “enriched” for a set of genes, one then may hypothesize that the list of genes plays an important role in the underlying biological process. This technique has recently been extended to metabolomics datasets [78,115]. A combination of enrichment, multivariate, and univariate analyses comprise the bulk of the strategies currently used in metabolic engineering to analyze “omics” datasets in parallel.

In metabolic engineering, use of metabolomics is comparatively much less common than using other global analysis approaches, perhaps attributable to the maturity of fields like transcriptomics and proteomics compared to metabolomics. Proteomics, transcriptomics and genomics have frequently been combined with small-scale metabolite measurements for metabolic engineering purposes. Examples of this include functional genomics with targeted metabolite measurements for isoprenoid production in E. coli [116], as well as the combination of the proteome, transcriptome and targeted metabolite measurements for E. coli carbon storage regulation [63], penicillin production in P. chrysogenum [101], glucose repression in S. cerevisiae [52], and relief from glucose deprivation in S. cerevisiae [100].

Flux measurements have also been commonly combined with other “omics” datasets, such as with the transcriptome and proteome in an analysis of lysine-producing Corynebacterium glutamicum during different stages of batch culture [46]. Other examples include the use of transcript data and ¹³C MFA to understand metabolic behavior in A. niger [7], transcriptional changes [117] and ¹³C MFA-derived fluxes [18] of C. acetobutylicum in response to stresses in bioreactors, and analysis of both systems-level MFA calculations [30] and Elementary Flux Modes [118] in tandem with transcriptomics data to assess metabolic control in S. cerevisiae.

The above examples at most used small-scale metabolite measurements, but a handful of studies have combined analysis of full metabolomics datasets with other “omics” datasets. Previously described analysis of adaptations from directed evolution generally fit this category: transcriptional measurements using microarrays [47,107,111,112] and genomic analysis [83] have each been combined with metabolomics to pinpoint the source of the observed phenotype.

In other applications, Piddock et al. assessed high gravity beer brewing conditions to determine the effect of the protease enzyme Flavourzyme on the free amino nitrogen content of the wort, and the resulting metabolomic and transcriptomic differences in a strain of brewer’s yeast [55]. A collaborative study by Canelas et al. investigated the growth characteristics of two strains of S. cerevisiae under two standard growth conditions. [66]. Datasets included intra- and extra-cellular metabolomes, the transcriptome, and the proteome, with an emphasis on reliable and quantitative measurements. They identified the specific growth rate and biomass yield differences between the strains that they attributed to differences in protein metabolism using analysis of variance (which determines statistical significance from comparisons of within-class and between-class variances) and gene enrichment analysis. Work by Dikicioglu et al. examined the combined metabolomic and transcriptomic response of S. cerevisiae to transient perturbations in glucose and ammonium concentrations [58]. Their work used HCA, t-tests, and analysis of fold-changes to study the short-term reorganization of the metabolome and transcriptome in response to temporary relief of nutrient-deprived conditions.

The emergence of genome-scale investigations has led to a deluge of information about all molecular layers in the cell. This in turn has provided a broader context in which metabolic engineering strategies can be evaluated. However, we note that many of the techniques discussed so far have focused on systematic assessment of the results of metabolic engineering strategies, rather than on systematic methods of designing strains to begin with. While some of these studies have used the insight gained from their evaluations to in turn design new strains, more systematic approaches to strain design are being developed – some of which are now capable of exploiting metabolomics datasets.

Flux Balance Analysis (FBA) is, in short, a modeling technique that uses metabolic network stoichiometry, a set of feasible flux ranges, and a cellular objective function to calculate an optimal flux distribution for a metabolic network [124,125]. To achieve this, FBA invokes a pseudo-steady state assumption. (Based on the fact that metabolic reactions occur more quickly than upstream cellular processes like signal transduction, transcription, and translation, this may often be a reasonable simplification.) As a result, the non-linear set of differential equations describing the stoichiometric metabolite mass balance is reduced to a set of linear equations in terms of unknown reaction fluxes. Since the number of reactions exceeds the number of metabolites in biologically relevant metabolic networks, the system is underdetermined. Bounds on the solution space and an objective function are required to fully specify a unique solution. Selection of a linear objective function, such as maximization of a flux corresponding to biomass generation, specifies a linear programming (LP) problem (which can be efficiently solved numerically). By construction, FBA does not use information on metabolite concentrations themselves in its calculations.

A few examples of basic FBA for metabolic engineering include estimation of flux distributions from MFA measurements [31,126], prediction of knockout performances to assess proposed strain designs [5], use of artificial (virtual) metabolites to better capture flux ratios from ¹³C MFA [127], systematic evaluation of different objective functions in E. coli [128], and evaluation of Elementary Flux Modes from flux measurements [129] and transcription datasets [118]. A study of E. coli metabolism comparing growth in aerobic and anaerobic culture by Chen et al. highlights the complementary nature of FBA and MFA [130]. They note that FBA often performs well when predicting extracellular fluxes, but intracellular flux distributions are more difficult; it is important to compare fluxes derived from FBA calculations against actual fluxes as derived from measurements and MFA. Tools such as the COnstraints Based Reconstruction and Analysis (COBRA) toolbox for MATLAB [131], CellNetAnalyzer [132], the Systems Biology Research Tool (SBRT) [133], and OptFlux [134] are available for simplified implementation of constraint-based modeling methods (and are listed in Table 1).

A prerequisite step in FBA is the reconstruction of genome-scale metabolic networks for the organism of interest. Reviews by Fiest et al. [135] and by Thiele and Palsson [136] describe this process in detail, and new strategies for efficiently or even automatically performing parts of this process are being continuously developed (listed in Table 1) [137,138,139,140]. The reconstruction process involves the synthesis of a genome-scale model from established biochemical and genomic knowledge, stored in publically accessible databases. These databases span various organisms and layers of biological information (e.g., biochemical pathways, transcription factors, and nutrient transport mechanisms). Examples of relevant databases for this process (as well as several for metabolomics in general) are also listed in Table 1.

A few recent examples particularly relevant to metabolic engineering and metabolomics include models of A. niger [141], C. acetobutylicum [138], and Clostridium beijerinckii [142], updated reconstructions of E. coli [143,144], and addition of lipid metabolism to a model for S. cerevisiae [145]. Notably, a reconstruction of Mycoplasma genitalium [126] has recently been incorporated into a whole-cell computational model by Karr et al. [146], who have suggested development of a similar model for E. coli as a possible next step. Network reconstructions for several dozen species are publicly available, and programs such as MetRxn have been developed to aid comparison across model reconstructions [147]. Some examples of these are shown in Table 1.

The original FBA framework has been supplemented with dozens of refinements broadly referred to as constraint-based models. While these models retain the optimization problem framework based on stoichiometric constraints, the flux constraints or objective function are altered. We direct the reader to reviews on the topic of FBA by Lee, Gianchanani, and others for more complete discussion of these methods [148,149], though it is instructive to analyze a few representative classes relevant to metabolic engineering. Furthermore, we note that these approaches do not generally make use of metabolite measurements.

The most basic refinements are straightforward extensions of FBA, from adding a simplified representation of transcriptional regulatory constraints, to integrating uptake/effluxes and comparing against extracellular concentration profiles. Examples from this family include regulatory FBA (rFBA) [150,151,152], dynamic FBA (dFBA) [153,154], integrated FBA (iFBA) [154,155], and integrated-dynamic FBA (idFBA) [156]. While these refinements demonstrate improved accuracy over basic FBA, most dynamic examples only make use of targeted extracellular concentration profiles as a means of constraining their dynamic elements. Using metabolomics data to constrain FBA solutions could provide these strategies direct information about intracellular metabolite levels in place of relying purely on the calculated fluxes to infer intracellular behaviors. Similarly, regulatory versions of FBA have looked at transcriptional regulation, but not regulation at the metabolic level (e.g., allosteric regulation). Metabolomics can provide information necessary to capture these effects.

Another class of refinements to FBA comprises methods intended to better reduce the discrepancy between model predictions and experimental observations. Optimal metabolic network identification (OMNI) is used to identify discrepancies between measured and predicted fluxes, and then determine changes that need to be made to the model to better match the measurements [157]. As a proof of concept, it identified bottleneck reactions that, once removed from the model, accounted for reduced growth rates in evolved E. coli strains compared to the original model predictions. The GrowMatch algorithm uses growth and lethality data to correct a network reconstruction [158], and its application to a reconstruction of S. cerevisiae led to improved knockout lethality predictions. [159]. A number of these corrections were only identified by taking into account double gene deletion data, and improvements included growth-medium specific regulatory constraints. These (and other [160,161]) methods would also directly benefit from the additional information that metabolomics datasets can provide about the intracellular state of metabolism.

More directly relevant to metabolic engineering applications is a class of refinements focused on predicting the result of metabolic network alterations. An early and well-known example of this is Minimization of Metabolic Adjustment (MOMA), which formulates a quadratic programming (QP) problem to find the feasible flux distribution nearest to the original FBA solution in response to a gene knockout [162]. OptKnock uses a bi-level optimization framework to balance an FBA objective function with a desired overproduction target [163] (the work by Hua et al. compares the results of an evolved strain against an OptKnock prediction [47]). OptGene uses a genetic algorithm to generate metabolic engineering strategies [164], and was used by Asadollahi et al. to design a strain exhibiting improved sesquiterpene production in S. cerevisiae [165]. Another extension is OptForce, which uses flux measurement data to generate a minimal set of engineering interventions required to guarantee the desired overproduction target [166]. In addition to recapitulating already proven strategies for succinate production in E. coli, it also identified several other successful and nonintuitive strategies. Again, while none of these methods integrate metabolomics data into their calculations, they could potentially be improved significantly if they could harness such data.

As reviewed above, the majority of constraint-based modeling strategies make negligible use of systems-scale metabolite data in their calculations. The requirement that organisms adhere not only to stoichiometric mass conservation, but also to thermodynamic restrictions on energy and entropy, provides one means of introducing metabolite concentrations into the constraints. Several constraint-based model techniques make use of metabolite or metabolomics data in this fashion.

Network-embedded Thermodynamic (NET) Analysis combines pre-determined flux directions with quantitative metabolomics datasets and the metabolite Gibbs energy of formations to determine the feasible ranges of Gibbs free energy of reaction throughout the system [167]. This method can assess the internal consistency of a metabolomics dataset, predict thermodynamically feasible ranges for unmeasured metabolites, and identify putative sites of transcriptional regulation. anNET is a MATLAB implementation of the algorithm designed to facilitate straightforward application of NET analysis [168].

NET analysis of a metabolomics dataset for S. cerevisiae revealed a thermodynamic inconsistency in whole-cell NAD/NADH ratio, which led Canelas et al. to engineer a strain with a bacterial mannitol-1-phosphate 5-dehydrogenase to allow them to determine cytosolic levels from measurements of cytosolic pH, fructose-6-phosphate, and mannitol-1-phosphate [175]. They found that the ratio calculated from this method was consistent in NET analysis and displayed a sensitive response to redox perturbations. Other studies have also used NET analysis to verify the thermodynamic consistency of their measurements in a variety of metabolic engineering contexts [9,59,176].

Henry et al. developed Thermodynamic Metabolic Flux Analysis (TMFA), a constraint-based modeling approach similar to NET analysis [177]. While both methods calculate the feasible Gibbs energy of reaction ranges in the network, TMFA does not require user-supplied flux directions and by design excludes thermodynamically infeasible futile cycles from the resulting calculations. (It is worth noting, though, that the elimination of infeasible futile loops from the FBA solution space can be performed separately and without concentration data [178,179]). Henry et al. also discuss the use of group contribution methods to calculate Gibbs energy of formation and the effect of the associated estimation uncertainties on TMFA results [177]. Recent improvements to group contribution methods should improve this approach’s accuracy [180,181].

Garg et al. applied TMFA to ¹³C MFA calculations to produce thermodynamically consistent fluxes [182]. The E. coli network reconstruction published by Fiest et al. includes thermodynamic information, and the manuscript includes an assessment of thermodynamic consistency using TMFA [143]. Canelas et al. used TMFA as one criterion for identifying near-equilibrium reactions in an effort to use metabolomics datasets to determine in vivo thermodynamic (and kinetic) parameters [54].

While TMFA and NET analysis have been the prevailing approaches used to incorporate metabolite concentrations and thermodynamic constraints into constraint-based modeling approaches, several other methods have been developed. For example, Bordel et al. developed a constraint-based model based on Ziegler’s principle for the maximization of entropy production that uses non-equilibrium thermodynamics to identify flux bottlenecks; they identified reactions that impeded previous efforts to improve glycolytic flux via overexpression of glycolysis enzymes in S. cerevisiae [183]. Hoppe et al. designed a constraint-based model that combines thermodynamic constraints similar to TMFA and NET analysis with a penalty function for deviations from concentration measurements. The minimization of both the overall flux and the penalty function are used as the optimization criteria. In applying this new approach, they found that increased network size leads to increased sensitivity of the resulting flux distribution to metabolite concentrations and Gibbs free energy changes [184].

Kinetic models are built around explicit mathematical descriptions of enzyme-metabolite interactions. Natural choices for kinetic rate laws are mass-action kinetics and Michaelis-Menten kinetics, but a review by Heijnen highlights several approximate rate laws that require fewer parameters and are relevant to metabolic engineering applications [185]. Included are discussions of the S-system and power-law kinetic rate laws, long established by the early efforts at kinetic modeling that developed into Biochemical Systems Theory, and reviewed specifically in the context of metabolic networks recently by Voit [186,187,188,189].

In light of recent genome-scale reconstruction efforts, several investigators have sought to assess the properties of several of these approximate forms in the context of metabolic networks. Examples of this approach include study of the glycolytic pathway in S. cerevisiae using a local linearization method [190] and lin-log kinetics [191,192], as well as study of central carbon metabolism in E. coli to compare lin-log kinetics, convenience kinetics, power law kinetics, and Michaelis-Menten kinetics [193]. This last study found that mixed models of Michaelis-Menten and lin-log kinetics are well suited for large-scale networks where the true rate laws are often still unknown. While these studies are not examples of using kinetic models for metabolic engineering or with metabolomics per se, they demonstrate the principles underlying the effective implementation of kinetic modeling for those purposes.

Independent of metabolomics, kinetic models have already been applied in several recent metabolic engineering contexts. Rasler et al. constructed a dynamical model of cellular redox state in S. cerevisiae to assess response to oxidative stress [194]. Literature kinetic values provided a qualitative fit to experimental data, and they achieved significantly improved quantitative matching by partially fitting parameter values (allowing them to vary by up to 4-fold from the literature values). Chassagnole et al. constructed a kinetic model of central carbon metabolism in E. coli in conjunction with MCA [120]. Their model captured most of the concentration trends, but even with parameter fitting, structural limitations of the model precluded complete agreement. A similar study by Oh et al. constructed a model of lactic acid fermentation in Lactococcus lactis, and the subsequent results were also used for MCA [20].

Ensemble approaches are also promising, and are in part a response to issues of parametric “sloppiness” which can preclude precise determination of kinetic parameters [123]. These entail constructing a set of models that are structurally identical, but each using a different parameter set. Each model fits the training data comparably well, and the behavior of the whole ensemble is used to make predictions. Tran et al. developed a model for central metabolism in E. coli as a proof of concept [195]. Starting with an ensemble spanning the entire thermodynamically feasible range of parameter combinations, they observed convergence to consistent fold-change behavior as training data were introduced. This effort led to an ensemble model constructed by Rizk et al. that predicted the effect of gene knockouts on the production of aromatic compounds in E. coli [196], and a model by Contador et al. to predict flux data in L-lysine-producing E. coli [197]. While these examples do not use metabolomics, we note that metabolomics datasets could in principle be easily adapted to this method and would be quite well-suited for further constraining the parameter ensembles.

None of the aforementioned ODE models explicitly look to integrate metabolomics data into their analyses, due in part to the only recent development of more quantitative metabolomics techniques. While scarce, there have been some efforts to use metabolomics data to improve or exploit ODE-based models of metabolism. For example, Klimacek et al. used published kinetic parameters with time-course metabolomics measurements to assess metabolic control in xylose-fermenting S. cerevisiae [9]. Similarly, a model of nitrogen assimilation in E. coli developed by Yuan et al. used kinetic parameters from the literature together with a genetic algorithm to fit undefined parameters to metabolomics data [60]. Proteomic and transcriptomic data were also used to adjust reaction rate predictions. While these examples both use metabolomics data, the modeling strategies focused only on capturing the dynamics of individual pathways and modules – not the whole metabolic network.

Two recent examples have attempted to apply metabolomics measurements to models of an entire metabolic network. Yizhak et al. developed a constraint-based modeling approach they referred to as integrative “omics”-metabolic analysis (IOMA), which solves a QP problem in a constraint-based model to fit a flux distribution to proteomic and metabolomics data [198]. Their approach introduces a reaction rate model based on Michaelis-Menten kinetics, and uses proteomic data in conjunction with metabolomics data to fit the kinetic parameters and satisfy the steady-state flux requirement in the unperturbed system. This results in a defined system of ODEs. When compared against FBA and MOMA to predict the effects of gene knockouts based on an erythrocyte kinetic model and published data for E. coli, IOMA demonstrated significantly improved recall, precision, and accuracy.

A mass action stoichiometric simulation (MASS) modeling strategy described by Jamshidi et al. follows a different scheme, by fitting thermodynamic equilibrium constants to a measured metabolomics dataset and a calculated flux distribution [199]. The kinetic rate law equations are then solved to obtain the forward reaction rate constants. As a proof of concept, they used this method to construct a human erythrocyte model, and compared it against a previously published model. They also included mechanisms to account for regulation of five enzymes using mass-action kinetics. They assessed metabolite and protein level trajectories in response to redox load simulations, and performed sensitivity analysis to determine the dominant time scales within the model. The MASS model demonstrated many of the key behaviors of the original erythrocyte model.

Notably, these last two methods both take advantage of constraint-based modeling strategies, but result in ODE-based kinetic models that can subsequently be used for strain design. This reflects the complementary nature of metabolite fluxes and concentrations, especially when faced with system-wide parametric uncertainty. However, to fully capture the wide-ranging dynamics that directly and indirectly contribute to the often subtle and nonintuitive behaviors exhibited in engineered strains, additional model detail is necessary. More advanced modeling strategies will need to find ways to integrate additional information, including proteomics and transcriptomics, to meet this need.