Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of  The artificial and industrial uses of microorganisms for material production have a long history of more than a thousand years. Recently, genetic operations have been widely applied to improve production. Two generally considered approaches introduce enzymes that have higher activities from other organisms or species and introduce enzymes to realize metabolic pathways that do not naturally occur in the microorganisms. The former method is popular because its operation is simpler and improvements are more predictable than with the latter method. Conventional gene modifications using ultraviolet or other radiation types are easy to achieve and have been widely applied in many industries. Nevertheless, the efficiency of such improvements is quite low because gene modifications occur accidentally and uncontrollably, and progress is made serendipitously. Therefore, gene introduction is currently used along with conventional methods.Target genes for modification are chosen based on information including the reaction rates of the respective reaction steps within the metabolic pathway and include the production materials and substrates of microorganisms, as well as changes in the reaction rates through changes in the concentrations of the metabolites that consist of the pathway. Bottleneck reaction steps and feedback loop inhibitions are suggested based on this information. The genes of enzymes used in such reactions are candidates for modification.2 Several formulae are established for the types of enzymic reactions, such as inhibition schemes. The most popular is the Michaelis-Menten law4 for a simple one-to-one enzymic reaction without any inhibition or catalysis using an enzyme. The reaction rate is modeled based on the following reaction scheme:The rates of enzymic reactions are generally defined as the limit of changes in the compounds over time.in which 6Therein, a pair of square brackets denotes the concentration of the compound, 7 the values of the kinetic parameters have not been sufficiently published or accumulated. An enzyme generally has different parameter values for the various conditions and species of organisms. Moreover, the parameter values generally differ between in vitro and in vivo (in living cells) conditions.9 For most industrial applications, a dynamical analysis of the pathways must be conducted without reaction scheme information or kinetic parameter values.Generally, finding the parameter values is difficult and expensive because it requires enzyme isolation and measurements of the reaction rates in test tubes (in vitro measurements). Although the amount of enzyme information in the literature and public databases is growing,6 is one such canonical ODE model. For a reaction scheme with 2 reactions, the following is used:The ODE systems in canonical forms are applicable because they are independent of the molecular mechanism of the reaction scheme. The S-systemwhere where 6 which can be presented as follows:The S-system above is a simplified form of the general mass action law,Therein, the 10 because several sets of different parameter values are generally found for the given observed time series data. Restrictions and limitations are effective for difficulties such as fixing some The parameter values of Numerical optimizations require a sufficient number of observed samples. Smaller needs are better because observations entail a certain amount of costs. A mathematical model with fewer parameters requires fewer samples. We propose a canonical ODE model for small samples through the simplification of the second term of By the mass action law, the decomposition rate of a compound depends solely on its concentration in many biological processes, such as Michaelis-Menten–type reactions shown in our model includes a nonlinear decomposition term because we suspect that a linear term might be too simple for the metabolite in a complex biological network system containing many unknown reactions. Our assumption is reasonable when regulation of the degradation processes by these unknown reactions is not significant.The resulting time series of the model based on a numerical integration varies greatly through a change in the initial value. Finding the best initial value is difficult because the observed initial value frequently has errors, particularly for small sample data sets. Therefore, we compare the model and data in differential spaces. The differential of the observed data can be calculated through a numerical differentiation, and the parameter values can be evaluated by comparing the differential values with the values of Escherichia coli. For a pathway that includes branches and feedback loops, we estimated the actually activated reaction steps and activities of the feedback inhibitions suggesting strategies for an improvement in production.We evaluated the proposed method according to its application to the phenyl lactate (PL) production pathway from glucose using First, we build a pathway map based on information from the literature and different databases. We then choose some metabolites in the map as observation targets. A pathway map is reconstructed using only the target metabolites. The observations are measurements of the target metabolite concentration at sampling time points with equal intervals. A simplified S-system model is defined based on the reconstructed pathway map by fixing some 10 or differential evolution11 to minimize the difference between differentials of the observed data through a numerical differentiation and those from 1215  pathways. Phenyl lactate is produced from phenyl pyruvate (PP), PP is from phenylalanine (PA), and PA is from prephenic acid. In addition, prephenic acid is from chorismic acid in the SA pathway. Choosing phosphoenolpyruvate (PEP), erythrose 4-phosphate (E4P), SA, PA, PP, and PL as the observation targets, we then reconstruct the pathway for these 6 metabolites . The patChanges in concentration of metabolites in the reconstructed pathway are modeled mathematically using the following ODE models:Actually, production of PEP and E4P is not controlled by any other metabolites, and these compounds are independent variables in the ODE system above. Their respective dynamics are not modeled. Parameter 11 to find the parameter values that minimize the differences between the differential of the concentration values calculated using the ODE system, as shown below:Time differential values of the metabolite concentration are calculable using the ODE system by determining all parameter values. We introduce the differential evolution algorithmt of the observed data. Here, Therein, The ODE system with the determined parameter values is shown below :The ODE system suggests that the reaction chain to SA from PEP is more active than that from E4P. In addition, PP production is inhibited by feedback loops from both PA and PL.13 These negative parameters may suggest unknown regulatory pathways whose effects look substrate inhibitions.There are 3 negative value parameters. Reaction steps that are represented by these parameters consist of only productive enzymic reactions in the literature.The changes in metabolite concentration over time can be modeled using the Michaelis-Menten law, as shown below:For each metabolite, there are 8 parameters for SA, 10 for PP, 6 for PA, and 4 for PL because a model of the reaction step (single enzymic reaction) has 2 parameters. Changes of concentrations in time of SA and PP cannot be modeled using the 6 sampling data in this study. There are a total of 16 parameters for the reconstructed pathway because some parameters are common (1 of the outgoing reactions of SA is an incoming reaction of PP). Some numerical optimization methods can search for the 16 parameters simultaneously. However, such a simultaneous nonlinear numerical optimization is not easy, and the difficulty increases significantly with an increase in the number of parameters .The form of the S-system model is reduction or simplification of general mass action (GMA) law model shown as follows:For each metabolite, there are 7 S-system parameters for SA, 8 for PP, 5 for PA, and 4 for PL, or 18 in total because some of the parameters are the same. The number of parametes are reduced for SA, PP, and PA compared with Michaelis-Menten models; however, concentrations of SA and PP cannot be modeled even when using the GMA. In our proposed model, the corresponding numbers are 5, 6, 5, and 4, or 20 in all, which is not a small number; however, it is not a problem that the total number of parameters is larger than in the S-system because no parameters are common to any 2 metabolites, and the parameters of each metabolite are optimized independently of the other metabolites. Our model has fewer parameters for each metabolite, which indicates that our model is more robust against errors than the S-system and Michaelis-Menten models.The less number of model parameters means that the model needs a less number of data. Michaelis-Menten model consists of 2 parameters for each reaction, thus Although the model and data do not match perfectly because the data generally include errors in the probabilistic distributions, the optimization precision of the parameters (model fitness to the data) shown in The parameter values of the Two negative feedback loops exist: PP production is inhibited by PL, and PA production is inhibited by PP. Although it can be readily imagined that the inhibition of the feedback reactions increases the production of PL, the main inhibitory effect on PP production is from the SA. Disrupting one or more genes of the reactions to PP from SA might improve the PL production.Phenylalanine decreases gradually , but shoIn conclusion, the results show that the reliability of the estimated parameter values might not be the best or even very high because the reconstructed pathway and the ODE system are simplified. These values suggest that the target genes can be modified for an industrial improvement in production using microorganisms. This case study presents several suggestions that may be useful when constrained to only a few samples or low observation costs.


Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.The online version of this article (doi:10.1186/s12859-016-1240-1) contains supplementary material, which is available to authorized users. Constraint-based reconstruction and analysis (COBRA) methods enable systems level computation of cellular functions using genome-scale biochemical reaction networks, including metabolism . Metabolv is the vector of fluxes, vL and vU are lower and upper flux bounds, S is the stoichiometric matrix, and c is the vector of objective coefficients . We refer to , bisection converges to specified accuracy ε in log2((b−a)/ε) iterations. We implemented bisection as Algorithm bisectME using the simplex method in quad precision  as in . Dattorrn) as in  proves tad MINOS ).μk, k=0,1,2,… }. (The objective function for each subproblem is an augmented Lagrangian.) If MINOS converges, it will be to a global optimum μ∗. Furthermore, the subproblems converge quadratically when μk is close enough to μ∗ .μ0 and the MINOS scaling option on the computation time and final solution. Empirical tests showed that μ0=0.0 should be avoided, as should μ0>μ∗   for imprtart Eq.  reliablyμ-dependent)  Fig. . For morCompared to the combined solveME, bisectME (with golden section search) took an average of 75 and 103 s for 3 and 6 decimal points respectively, while binary search (not GSS) required an average of 93 and 124 s for 3- and 6-digit precision in growth rate. All runs were performed in quad-precision using Quad MINOS.In summary, the combined solveME was up to 10 and 34 % faster than golden section search, or 27 and 45 % faster than binary search, for 3- and 6-digit accuracy in growth rate. Another advantage of the combined solveME over bisection methods was that the growth rate was always returned to about 15 digits because of the tolerances set for Quad MINOS; therefore solution time was not a function of final solution precision. To reach the same precision, bisection would require about 50 iterations, or over 400 s. Furthermore, double-precision solvers would have difficulty achieving even 6 or 7 digits.−9 but are not certain to achieve them. Using quad-precision, we achieved feasibility and optimality tolerances below 10−15, and often less than 10−20.In particular, commercial double-precision solvers such as CPLEX and Gurobi handle feasibility and optimality tolerances as small as 10In addition to growth rate maximization, we developed quad-precision flux variability analysis (FVA)  for ME mEmpirical tests demonstrated the importance of quad-precision when FVA is applied to ME models. Specifically, without quad-precision, errors such as maximum flux being less than the minimum flux were observed Table . AnotherWhen varyME was performed at growth rates below the maximum, non-zero flux variability was observed Fig. . Again, E. coli and T. maritima ME models, respectively  using tly Table . This reME models have imminent utility for systems metabolic engineering. In particular, biochemical overproduction strain design often involves gene knockouts and modulating the expression of production pathways. These genetic manipulations impact host fitness in part by forcing reallocation of the host proteome away from growth and stress response functions. ME models now allow genome-wide accounting of proteome reallocation for engineered strains.sdhCDAB) knockout, together with overexpression of fumarate reductase (frdABCD), isocitrate lyase (aceA), or both.To demonstrate, we analyzed the overproduction of succinate using growth-coupled designs that had been found using a metabolic reconstruction , 19. In sdhCDAB, we set zero upper bounds for the translation reactions of the four sdhCDAB subunit genes. Overexpression of frdABCD and aceA was performed in three steps. First, we determined the maximum growth rate with sdhCDAB deleted. We then used varyME to determine the feasible flux ranges for the complex formation fluxes of the overexpressed enzymes with growth rate fixed to a small fraction  of the maximum. We then set the lower bound of complex formation fluxes to linearly spaced fractions of the maximum expression flux, from 0.05 to 0.95. Since we were investigating two production pathways, we sampled a grid of 11 by 11 samples for a total of 121 combinations of pathway expression levels. For each expression combination, we solved Eq.  increased with product yield, as expected. Interestingly, the remaining (Other) proteome increased in mass fraction up to four-fold, from 1.6 to 6.7 %, as product yield increased. Therefore, production pathway overexpression entailed a significant proteomic cost.The ME model revealed trends in proteome re-allocation with increasing product yield. Specifically, we traced the relative mass fraction of five proteome sectors, by summing the product of translation rate (mmol/gDW/h) with the protein molecular weight (g/mol) over all proteins in each sector. The core proteome and glucose-niche proteome sector definitions were based on . The cor4frdABCD vs. aceA translation rates varied strongly, such that only one pathway was expressed at varying expression levels. However, higher succinate yields were achieved when both pathways were expressed simultaneously at a relatively constant ratio  , and Pearson correlation of 0.87 (p=0.025)   ratio  led to t87 p=0.02 Fig. 5)p=0.017),p<10−15) and Spearman rank correlation of 0.68 (p<10−15). When considering only the core proteome [p<10−15) and Spearman rank correlation of 0.63 (p<10−15)  , 6 have With advances in ME solution methods enabling rapid prototyping, we anticipate the acceleration of ME model development for additional organisms, such as phototrophs . DevelopE. coli. Unlike metabolic reconstructions that predict maximal product yield when the most metabolically efficient production pathway is used, the ME model predicted that simultaneous expression of multiple pathways led to the highest yields when proteome reallocation requirements were considered. These predictions were consistent with literature, where simultaneous expression of two succinate-producing pathways led to increased yield [To demonstrate possible application of our solution methodology in an engineering context, we analyzed growth-coupled succinate overproduction by ed yield . As showed yield –30 to MEWe developed an efficient methodology for solving nonlinear, multiscale models of metabolism and macromolecule expression (ME models). In particular, we showed that the growth rate maximization problem for ME models is a quasiconcave maximization problem in general and quasilinear for special cases as demonstrated here. In both cases, the global optimum is found efficiently using the projected Lagrangian method. Using the quad-precision LP/NLP solver Quad MINOS, we obtained up to 45 % speedup over conventional bisection. Currently, a phylogeny of in silico methods has emerged around metabolic reconstructions . Our newSerial computations were performed on 2.70 GHz Intel(R) Core(TM) i7-4800MQ processors with 8 GB of RAM and the Arch Linux operating system. Parallel computations were performed using resources of the National Energy Research Scientific Computing Center (NERSC).μAv+Bv=Bv−μCv=0 (where C=−A). Here, we show that these constraints are quasilinear. First, recall that a quasilinear function is both quasiconvex and quasiconcave [μ-sublevel sets are all convex while a quasiconcave function has convex μ-superlevel sets. Accordingly, a quasilinear function has all convex μ-level sets. The μ-level set of constraint i∈DIL is For our reduced ME model, the dilution and growth rate-dependent protein-per-RNA constraints are gathered into the general form, iconcave . A quasiμ is fixed in the level set). Therefore, every μ-level set is convex; hence the dilution constraints are quasilinear.which is a 0-level set of the sum of linear functions, i.e., a convex function  problem whose global optimum is again found readily .−15. To determine orders of magnitude of ME fluxes  and for oxygen uptake. Unlike metabolic models that require physiologically determined uptake rate bounds, ME models predict a limit to maximum uptake. This maximum uptake occurs at the max growth rate where additional RNA and protein machinery cannot be produced to meet growth demands .−20) encoding an essential gene. On glucose minimal medium, this flux was 9.35×10−14 mmol/gDW/h. Note that the smallest translation flux was 9.13×10−13 mmol/gDW/h. The maximum flux was 45.4 mmol/gDW/h, for H2O exchange. Thus, on glucose minimal medium, fluxes spanned nearly 15 (14.7) orders of magnitude.To estimate the orders of magnitude spanned by ME fluxes, we first found the smallest transcription flux for genes determined to be essential experimentally and by the ME simulation. Because multiple transcription units (TUs) can encode a gene, and multiple genes can be encoded by a TU, we found the smallest transcription flux greater than the solver feasibility tolerance , the reduced ME model of E. coli has a similar number of reactions but considerably fewer constraints. The reduced ME model has a number of simplifications compared to the full ME models of E. coli: iOL1650 [The reduced ME model of parately  and was


Clostridium thermocellum is a gram-positive thermophile that can directly convert lignocellulosic material into biofuels. The metabolism of C. thermocellum contains many branches and redundancies which limit biofuel production, and typical genetic techniques are time-consuming. Further, the genome sequence of a genetically tractable strain C. thermocellum DSM 1313 has been recently sequenced and annotated. Therefore, developing a comprehensive, predictive, genome-scale metabolic model of DSM 1313 is desired for elucidating its complex phenotypes and facilitating model-guided metabolic engineering.iAT601 for DSM 1313 using the KEGG database as a scaffold and an extensive literature review and bioinformatic analysis for model refinement. Next, we used several sets of experimental data to train the model, e.g., estimation of the ATP requirement for growth-associated maintenance (13.5 mmol ATP/g DCW/h) and cellulosome synthesis (57 mmol ATP/g cellulosome/h). Using our tuned model, we investigated the effect of cellodextrin lengths on cell yields, and could predict in silico experimentally observed differences in cell yield based on which cellodextrin species is assimilated. We further employed our tuned model to analyze the experimentally observed differences in fermentation profiles  between cellobiose- and cellulose-grown cultures and infer regulatory mechanisms to explain the phenotypic differences. Finally, we used the model to design over 250 genetic modification strategies with the potential to optimize ethanol production, 6155 for hydrogen production, and 28 for isobutanol production.We constructed a genome-scale metabolic model iAT601 is capable of accurately predicting complex cellular phenotypes under a variety of conditions and serves as a high-quality platform for model-guided strain design and metabolic engineering to produce industrial biofuels and chemicals of interest.Our developed genome-scale model The online version of this article (doi:10.1186/s13068-016-0607-x) contains supplementary material, which is available to authorized users. For a sustainable energy economy, the necessity of producing fuels and chemicals from renewable feedstocks is well acknowledged, and the use of bio-based resources is a promising route for significantly lowering the carbon footprint of liquid transportation fuels . To prodClostridium thermocellum, which exhibits a high growth rate on cellulose ..−1)  of C. thermocellum provides key precursors for cell synthesis, and consists of alternative means of generating energy and shuttling electrons, especially when coupled to the complex redox metabolism [In particular, the cascade of carbon from PEP to pyruvate to acetyl-CoA in tabolism . ExaminiC. thermocellum. Four key, interrelated motifs can help to shed light on this mechanism: Motif 1—energy modulation via acetate production, Motif 2—redox metabolism, Motif 3—regulation of PEP to pyruvate conversion, and Motif 4—PFL-dependent redox relief valve.Taken altogether, we can use the simulation results presented along with literature reports to propose a mechanism which explains the metabolic differences between cellobiose and cellulose cultures of C. thermocellum. Acetate production during growth on cellobiose likely drops because less PTA-ACK activity would be necessary to generate the required ATP for cellulosome synthesis. Indeed, it has been estimated previously that the amount of ATP required for cellulosome synthesis and the amount of ATP produced by PTA-ACK are roughly equivalent [C. thermocellum, and it has been proposed that electron perturbations are more influential than PTA-ACK perturbations on ethanol production [Energy modulation via acetate production is one of the critical motifs regulating bioenergetics of uivalent . While nuivalent  and tranuivalent  Fig. 8)C. thermouivalent  which suoduction .Fig. 8PrC. thermocellum is very robust and a critical motif in controlling cellular bioenergetics. To account for high E:A ratios for growth on cellobiose, the cell must have an ample supply of NADH. This is facilitated by an increase in RNF and decrease in BIF activities on cellobiose as observed in the simulations  responsible for ethanol production are also seen to be highly expressed under multiple conditions, although ethanol production varies , 64. TheC. thermocellum in its native environment, i.e., degrading complex biomass in a co-culture in soil [C. thermocellum prefers to make acetate and hydrogen if these products can be consumed by its cohabitant [The simulation results and literature summaries presented above offer some interesting suggestions. To properly understand why cellobiose cultures produce so much more ethanol, it is useful to think of  in soil , 70, whehabitant . Isolatehabitant . This reWithout the ATP burden of cellulosome synthesis, less flux through PTA-ACK is needed, and this triggers a dramatic restructuring of carbon and electron fluxes to maintain the rates of glycolysis examined here. As a result, there is an increase in RNF flux, which leads to more PPDK flux. Both these reactions can enhance the supply of NADH and lead to the observed overflow of ethanol production on cellobiose. As RNF reaches its maximum capacity, PFL flux increases to balance the need for acetyl-CoA and the redox state of the cell.C. thermocellum. However, we believe these questions can be addressed as more OMICs and fermentation datasets become available and are integrated.Generally, these results indicate that for growth on cellulose, a high glycolytic flux and sufficient conversion of reduced ferredoxin to NADH  will be critical for high ethanol production. A significant level of control is necessary to accomplish this goal, although it is still unclear at this point how exactly the proposed motifs are controlled with respect to each other, or what additional regulatory elements might be active with, or instead of, the proposed mechanism above. There are still many questions regarding the bioenergetic control mechanisms which balance carbon and electron fluxes in C. thermocellum, with its dynamic cellulosome component, displays a significant increase in function and predictive capability to the previous model. We built and extensively refined this model using the KEGG database and our previously reported core model [Our genome-scale model for re model . From thre model . As an aC. thermocellum metabolism which arose after compiling multiple sets of training data. Namely, what is the mechanism behind the increase in ethanol production when growing on cellobiose versus cellulose? Using our GEM, we sampled 100,000 flux distributions for simulations on cellobiose and cellulose which were constrained to experimental data. By examining the difference between the carbon sources at different growth rates, we show how ethanol production in C. thermocellum is part of the overflow metabolism when growing on cellobiose.We then used the model to address a few fundamental questions about iAT601, C. thermocellum can be designed as a manufacturing CBP platform to produce a large space of potential biofuels and chemicals beyond ethanol, isobutanol, and hydrogen using the modular cell design concept [We envision that with the tuned GEM  concept . AltogetgetKEGGModelForOrganism of the RAVEN toolbox [ctx) with the complete set of coding sequences from the genome assembly (GenBank: CP002416.1) so that each reaction is linked to a specific protein encoded by the genome [A workflow of the model construction process is given in Fig.  toolbox . This fue genome . This drClostridial GEMs [hmmscan [hmmscan and 1e−50 for RBH.Transport reactions were linked to genes by compiling a list of putative transporters and then curating reactions via manual inspection. The list was compiled by three methods. The first method used InterProScan 5 , 75 to fial GEMs , 76, 77 [hmmscan  to deter[hmmscan  to extraC. thermocellum cofactor specificity in glycolysis is atypical [Further, as it is known that atypical , we inveatypical . For enzatypical . This soi.The central metabolic network recently reported  was manuii.We adapted the dry cell weight composition presented for strain ATCC 27405  to refleiii.d-fructose 6-phosphate → d-fructose 6-phosphate) within the network to efficiently close gaps between discrepancies.We added in several artificial reactions to convert identical yet alternately described metabolites .The refined model is included in the Supplementary Materials and has been deposited in the DOE KBase  and elementary mode analysis (EMA)-based techniques were employed to analyze the GEM i can be calculated byj in which the metabolite participates.FBA is a commonly used computational tool using stoichiometric and thermodynamic constraints to optimize a cellular objective, such as maximum cell growth . In our EMA seeks to find all solutions to Eqs. p (mmol/g DCW/h) is the specific rate (or flux) of metabolite P, μ (h−1) is the specific growth rate, YP/X is the yield of metabolite P per unit DCW X, and CP (mmol/L) and CX (g DCW/L) are concentrations of P and X, respectively.Experimental data were obtained from multiple sources see “”, and asD is the dilution rate (h−1).For chemostat cultures, the fluxes were calculated as follows:C. thermocellum. The previous GEM of C. thermocellum, iSR432 [The cellulosome is the cellulose-degrading protein complex covalently bound to the surface of certain cellulolytic bacteria, such as , iSR432 , 27, rou, iSR432 , and the, iSR432 , 95, 96.The fractional composition for dry cell weight was 0.5285 g protein + 0.026 g DNA + 0.0655 g RNA + 0.076 g lipid + 0.2242 g cell wall + 0.00494 g solute pool + 0.0304 g total_LTA → g dry cell weight (DCW). A second reaction was implemented to combine the DCW term and the cellulosome term, and this whole cell term was adjusted depending on carbon source, specifically: 1 g DCW + 0.02 g cellulosome term → biomass for cellobiose cultures and 1 g DCW + 0.2 g cellulosome term → biomass for cellulose cultures [A was created by counting the amino acids required to synthesize cellulosomal proteins. The entry Ai,j corresponds to the number of amino acid i encoded by the sequence of protein j. Second, the abundances of each protein were condensed into a condition-specific vector c normalized to CipA as presented by Raman et al. [A·c. Finally, the condition-specific amino acid count is converted to mmol/g cellulosome similar to the calculation of protein or DNA terms  to cellohexaose (G6). Glucose and cellobiose transport were included in the automatic reconstruction. It has been shown that ligomers . Furtherligomers  and, conligomers . Upon enligomers  and so rligomers .rN)G was set at 3.27 mmol ATP/g DCW/h  and no gTo tune the ATP cost of cellulosome synthesis, the coefficient for ATP in the cellulosome synthesis reaction was varied from 40 to 100 mmol ATP/g cellulosome/h while optimizing for maximal growth and maintaining experimental constraints, similar to above. Tuning these additional ATP requirements allowed finding the best fit to experimentally observed growth rate. All subsequent simulations used these parameters.Investigation of the difference in ethanol production between culture conditions was performed by constraining ethanol and acetate production as a function of cell growth. To implement these constraints, we used a series of flux ratios. First, to constrain the sum of ethanol and acetate yields, we calculated the following flux ratio:−1) as well as 100 values for the glucose uptake rate between 5.5 and 7.5 mmol glucose equivalent/g DCW/h, the range seen across multiple datasets. For each growth rate and glucose uptake rate, the sum of ethanol and acetate yields and E:A ratios was calculated. All other fermentation products were unconstrained. The uniform sampling was performed using optGpSampler [Given the variability in reported E:A ratios, we chose to sample the phenotypic space of cellobiose and cellulose cultures given the constraints above to minimize bias between flux distributions. To perform the sampling, we first randomly generated 100 normally distributed values of μ between 0 and 0.3 (hpSampler  with a s


Genome-scale metabolic network reconstructions provide a basis for the investigation of the metabolic properties of an organism. There are reconstructions available for multiple organisms, from prokaryotes to higher organisms and methods for the analysis of a reconstruction. One example is the use of flux balance analysis to improve the yields of a target chemical, which has been applied successfully. However, comparison of results between existing reconstructions and models presents a challenge because of the heterogeneity of the available reconstructions, for example, of standards for presenting gene-protein-reaction associations, nomenclature of metabolites and reactions or selection of protonation states. The lack of comparability for gene identifiers or model-specific reactions without annotated evidence often leads to the creation of a new model from scratch, as data cannot be properly matched otherwise. In this contribution, we propose to improve the predictive power of metabolic models by switching from gene-protein-reaction associations to transcript-isoform-reaction associations, thus taking advantage of the improvement of precision in gene expression measurements. To achieve this precision, we discuss available databases that can be used to retrieve this type of information and point at issues that can arise from their neglect. Further, we stress issues that arise from non-standardized building pipelines, like inconsistencies in protonation states. In addition, problems arising from the use of non-specific cofactors, e.g. artificial futile cycles, are discussed, and finally efforts of the metabolic modelling community to unify model reconstructions are highlighted. Escherichia coli http://ww(MIRIAM) , PDB , only one variant, or often both variants associated with both genes in these instances, which makes it challenging to assign the correct reaction to the respective isoform. In addition, several enzymes are able to catalyze various reactions, and the catalyzed reactions depend on the availability of a specific cofactor. This leads to the incorporation of all potentially catalyzed reactions that vary only by their cofactor requirements [Another issue commonly observed when reconstructing metabolic networks is the difficulty of selecting the right cofactors for reactions, specifically the right redox pairs. The assignment of cofactors to reactions is complicated by the fact that the cofactor requirement is organism specific and cell specific, explaining at least partially that the cofactors requirements vary between databases . Furthertor used . The reacofactor . Unfortuirements , which iirements . Howeverirements  and are There have been attempts to create collections of metabolic networks, e.g. Model SEED  or BiGG Model SEED is aimed at providing a platform for model reconstruction based on automated genome annotation using RAST . While tet al. [In contrast to this approach, MetRxn and MetaNetX aim at identifying common reactions by combining multiple pieces of information. Bernard et al.  give a get al. . Both MeS. cerevisiae. Several models of yeast had been published [The first example of a successful community effort for organism-specific reconstruction is the creation of the consensus model of ublished  until, iublished . This eaublished , which iet al. [et al. [Key PointsThe increasing amount of metabolic reconstructions necessitates a more unified way of representation to make models comparable.Available unification sources could provide a basis for this process.Associations to genetic information in metabolic reconstructions need a clearer and more structured association.Transcript-specific association rules would improve the specificity of network activities.Cofactor specificity needs to be addressed more carefully during reconstruction.Another example of community effort to merge models is the HMR Recon 2 . The firet al. , and the [et al. . These c [et al.  and furt [et al.  in an ef


Machine learning uses experimental data to optimize clustering or classification of samples or features, or to develop, augment or verify models that can be used to predict behavior or properties of systems. It is expected that machine learning will help provide actionable knowledge from a variety of big data including metabolomics data, as well as results of metabolism models. A variety of machine learning methods has been applied in bioinformatics and metabolism analyses including self-organizing maps, support vector machines, the kernel machine, Bayesian networks or fuzzy logic. To a lesser extent, machine learning has also been utilized to take advantage of the increasing availability of genomics and metabolomics data for the optimization of metabolic network models and their analysis. In this context, machine learning has aided the development of metabolic networks, the calculation of parameters for stoichiometric and kinetic models, as well as the analysis of major features in the model for the optimal application of bioreactors. Examples of this very interesting, albeit highly complex, application of machine learning for metabolism modeling will be the primary focus of this review presenting several different types of applications for model optimization, parameter determination or system analysis using models, as well as the utilization of several different types of machine learning technologies. Metabolism is the basic process in every biological system providing energy, building blocks for cell’s development and adaptation, as well as regulators of a variety of biological processes. It is becoming generally understood and accepted that metabolomics delivers the closest insight into physiological processes, providing valuable data for disease diagnostics, toxicological studies and treatment follow-up or optimization in a variety of applications from clinical to environmental or agricultural sciences. Recent analysis has shown that in the domain of precision medicine metabolomics provides highly complementary information to next generation sequencing, allowing a very good method for distinguishing between genes that are actually causing disease or are benign mutations, therefore helping in disease risk assessment and customization of drug therapy . In addiMachine learning has been defined in many ways, from “a field of study that gives computers the ability to learn without being explicitly programmed”  to the mBox 1Unsupervised learning algorithms identify patterns from data without any user input providing for example data-driven sample separation or feature grouping based only on the data;Supervised learning algorithms use previously labeled data (training set) to learn how to classify new, testing data. This approach determines major features or combinations of features that can provide the highest sample label accuracy in the training set and uses this information for future input labelling.Classification is a process of mapping input data to a discrete output, e.g., sample label. The quality of classification results is determined using accuracy, i.e., sensitivity and specificity;Regression is a process of mapping input data to a continuous output variable, e.g., quantity or the size. The quality of regression prediction is determined using root mean squared error.Analyses of points or bins from the metabolomics measurements such as NMR spectra or MS spectrograms (examples of use of PCA and PLS methods are too many to reference). A recent example of an application of deep learning, as well as SVM, RF and several other machine learning algorithms was presented by Alakwaa et al. ;Assignment of peaks in spectrograms or spectra for metabolite identification ,21;Quantification of metabolite concentrations from high throughput data ,23;Selection of a sets of the most informative attributes (“feature selection”) for given sample groups ,24;The combination of features or points using certain rules  aimed at reducing the number of features for analysis or selection of major variances .Machine learning methods have been used for analyses in all steps of the metabolomics process  includinExamples include unsupervised and supervised  type anaSeveral different applications of machine learning in modeling of cell metabolism will be presented in an attempt to show the variety of possibilities that can result from combining metabolism modelling, omics data and machine learning rather than trying to show all examples of machine learning utilization in metabolism modelling and metabolomics.in silico models provide an avenue for a controlled analysis of targets, biomarkers or cell growth under different conditions. In this way, modeling can help unravel complex diseases while at the same time allowing the determination of possible treatment targets or in silico testing of drug or toxin effects. Integrated analysis of the heterogeneous, high-throughput omics data is necessary in order to determine true factors leading to observed or possible physiological states, to obtain the most sensitive and specific markers or fully understand the effects of treatments, pathogens or toxins. Mathematical and computational models provide platforms for the integration of disperse knowledge and for testing and prediction of behaviours under different environments or following different manipulations. In other words, Any biological process, including metabolic processes, can be represented as a pathway with interconnected nodes, and thus, mathematical models such as graph theory, ordinary differential equations, Petri nets, etc., have an obvious role in the simulation of biological systems. For a structural view, a metabolic network can be perceived as a bipartite graph that consists of two sets of nodes representing metabolites and biochemical processes. Graph visualization of the metabolic network provides a way to gather and combine information from the literature, expert knowledge, public databases, as well as omics results, but does not allow simulation of the processes in the network. In a simulation, the dynamics of chemical processes in the metabolic network can be described at various levels of detail. Models can, on one side, include comprehensive kinetic representation of each included pathway thus allowing accurate prediction of the dynamic behavior of a subset of pathways or, at the other extreme, the genome scale models of the whole network can be subjected to stoichiometric analysis with constrained parameter ranges and the assumption of the steady state while allowing modeling of a complete cell network showing the steady state behavior of cells or even organisms . BetweenDetailed kinetic models have been built from ex vivo enzymatic measurements and Michaelis–Menten or related kinetic laws with the possibility for optimization of a few factors using experimental data and optimization methods. An increasing availability of genomics data and a variety of highly innovative bioinformatics techniques led to an ever-increasing number of biological networks constructed and presented . Genome-Machine learning algorithms have been used to build or optimize kinetic and genome-scale models from example data in order to make data-driven predictions or conclusions ,57,58. FRegardless of the application, the development of predictive models using a machine learning approach is accomplished in several steps: (a) selection of learning attributes; (b) construction of training and test sets; (c) selection of learning algorithms; (d) design of the machine learning approach; (e) evaluation of the predictive performance of models. All of these steps have to be considered and optimized in machine learning development or the application of metabolism models, either kinetic, genome scale or mixed. In the following, we will present examples of machine learning application in kinetic, genome-scale and mixed model development and their applications.Machine learning methods can enhance the development and application of metabolism models with applications broadly divided into model parameter determination, metabolic network analysis and model application. A schematic, highly simplified example of the model parameter determination is outlined in Parameters used in metabolic models, kinetics or flux ranges can be determined using either the in vitro enzymatic assay in the bottom-up approach or can be indirectly inferred from metabolomics time series data in the top-down method. The bottom-up approach for the development of kinetic models requires experimental measurements of the kinetics of each enzyme providing information that is then integrated in the model. This approach is highly experimentally demanding, and although information has been made available for many enzymes leading to a number of kinetic models of some major pathways, the bottom-up approach is unlikely to provide information for all enzymes, particularly when considering possible kinetic changes under different conditions present in vivo . Optimization of kinetic parameters can be done from metabolomics time series data. The majority of methods use optimization algorithms that try to find the best model parameters from available experimental data. Examples of the utilized optimization methods are: genetic algorithms, evolutionary programming, simulated annealing, Newton–Raphson and Levenberg–Marquardt methods (reviewed in ). HoweveSaa and Nielsen ,60 have Decision trees have been used to search for discriminating patterns in the model parameter space in structural kinetic modeling ,61,62, bMycobacterium tuberculosis, and this type of analysis was used to determine targets for inhibitors, as well as suggesting several possible modulators of the production of mycolic acid by this bacterium [Both kinetic and structural kinetic models provide very detailed simulation avenues for the subset of pathways. Metabolic network models, on the other hand, try to describe all reactions that are available to an organism with every node in the network representing an intermediate in a chain of chemical, metabolic reactions. These large networks can be modeled in the constraint-based approach where models have an associated solutions space in which all feasible phenotypic states exist under imposed constraints. Typically in these models, metabolite flow is constrained by network topology, the steady state assumption and by upper and lower bounds for each individual reaction flux. The challenge then in this type of modelling is to determine and impose major constraints in order to define and investigate the solution space in a way that determines physiologically-relevant fluxes or phenotypes ,66,67,68acterium   satisfies the given property. In the presented case, the requirement was that f <0 without knowing the exact functional form of f. With an adequate training dataset, machine learning, in this case, the decision tree learning algorithm, was able to determine allowed ranges for kinetic parameters of metabolic reactions that were consistent with observed physiology. The ORACLE approach combined with machine learning iSCHRUNK analysis of allowed ranges for kinetic parameter provides a very interesting approach for the creation of genome-scale kinetic models that will be increasingly feasible and increasingly accurate as more data become available.Genome-scale stoichiometric models lack information about enzyme kinetics and cannot accurately account for the response of metabolism to changes in enzyme expression or enzyme inhibition. Development of large, genome-scale kinetic models is therefore of great interest; however, it is still hampered by uncertainty in metabolite concentration levels and thermodynamic displacement, as well as uncertainty in the kinetic properties of enzymes ,74. TowaEscherichia coli to create reaction-gene combinations and label the essentiality of each combination based on experimental data. The authors also combined the data from Flux Coupling Analysis (FCA) in order to account for the inherent limitations of metabolic network flux distribution analysis on environmental dependences. FCA was included as one of 64 features describing each reaction-gene combination. SVM-RFE was trained using experimentally-determined gene essentiality information and 64 features determined for each reaction-gene combination providing information about major features and essential genes.Metabolic pathways have to be sufficiently robust to be able to tolerate fluctuations in protein expression levels, as well as changes in environmental conditions. Analysis of metabolic models can thus help in identifying genes that might be essential for cell growth, survival or production. Machine learning models can be trained to predict and classify genes of an organism as essential or non-essential based on a training set of known, labelled essential or non-essential genes. A number of different machine learning methods has been used to try and determine gene essentiality from metabolic network information, including: SVM, ensemble-based learning, probabilistic Bayesian methods, logistic regression and decision tree-based methods (reviewed in ). PlaimaA method, SELDOM (enSemble of Dynamic lOgic-based Models), was recently presented by Henriques et al. , attemptMetabolomics or genomics data can be used to discover unknown metabolic pathways and their regulation, as well as to determine preferred metabolic routes in a particular system with a known metabolic network. In this application, the goal is the construction of correlation and causation networks between metabolites. The correlation network determines the probable relation between metabolites and enzymes using usually statistical analysis of measurements from different biological conditions. The correlation network provides static information about the most likely network. The causation network is usually obtained from time series metabolomics data and provides cause-effect information about the metabolites in the network. Some examples of methods used for causation network determination are dynamic Bayesian models, Granger causality approaches, as well as the BST-loglem approach, which combines mathematical and statistical methods .Machine learning has been used to predict inhibitory effects of substances on the metabolic network. In the examples presented by Tamaddoni-Nezhad et al. ,80, backE. coli metabolism; the second layer represents the abundance of resulting essential proteins; third layer represents the phenotypes of E. coli; the fourth and fifth layers were reconstructed protein and gene layers, respectively. Layers in the presented work were not fully connected. Instead, the authors used biological knowledge to define rational connections, thereby reducing the risk of over-parametrization. Connections between the first, second, as well as fourth and fifth layers were built from gene-protein associations from the genome-scale metabolic model of E. coli; connections between the second and third and the third and fourth layers was determined from COBRA analysis of the genome-scale model of E. coli used to identify proteins that were essential for given phenotypes. A schematic presentation of the deep network created is shown in In order to try and take advantage of the large amount of sequencing data and detailed genome scale models for more accurate phenotype prediction, Guo et al.  have devMachine learning methods have also been utilized for pathway prediction, showing good performance when compared with standard methods presented in the hard-coded pathway prediction tool PathoLogic, while at the same time allowing easier extensibility, tenability and explanation of the results . MachineExperimental analyses measure values, i.e., concentrations, of variables in a model, e.g., metabolite concentrations or gene or protein expressions. In order to define the model, it is necessary to obtain information about the parameters that control the changes in these variables. Solving the system identification problem, i.e., determining parameters from variables, is often very strongly underdetermined with many parameters that need to be resolved from few variables in addition to many possible combinations of parameters, leading to the obtained values for variables. Mechanistic models use expert knowledge to derive information and develop models from targeted experiments. However, the large amount of data makes the application of data-driven, machine learning methods a highly attractive option. In addition, metabolic models can provide a large amount of data, and deriving actionable information from these model results can also greatly benefit from machine learning approaches. Thus, recent developments in machine learning and metabolism modeling compounded by the huge increase in computer power accessible for this task have made it possible to link data-driven and mechanistic models. Machine learning algorithms are able to learn optimal solutions for the analysis of new data from previously determined information. Without a doubt, with the availability of more advanced algorithms and the mounting availability of data, machine learning will be increasingly relevant for the analysis of metabolism. One of the major applications of metabolism models is in metabolic engineering where models can test genetic and regulatory changes towards increased productivity and reduced cost of production. Metabolic network models have an important role in helping determine targets, the side effect and toxicities of either drugs or toxins, through their direct effects or side-effects, as well as test possible toxic effects of chemicals in the environment. Machine learning can be implemented to integrate metabolic networks with available data. A recent example presented by  shows anMetabolism modeling can also be utilized for integrated analysis of different types of omics data, and some examples of the use have been shown in several recent reviews ,88,89, oIn 2006, Kell  said: “B


Genome-scale metabolic reconstructions are currently available for hundreds of organisms. Constraint-based modeling enables the analysis of the phenotypic landscape of these organisms, predicting the response to genetic and environmental perturbations. However, since constraint-based models can only describe the metabolic phenotype at the reaction level, understanding the mechanistic link between genotype and phenotype is still hampered by the complexity of gene-protein-reaction associations. We implement a model transformation that enables constraint-based methods to be applied at the gene level by explicitly accounting for the individual fluxes of enzymes (and subunits) encoded by each gene. We show how this can be applied to different kinds of constraint-based analysis: flux distribution prediction, gene essentiality analysis, random flux sampling, elementary mode analysis, transcriptomics data integration, and rational strain design. In each case we demonstrate how this approach can lead to improved phenotype predictions and a deeper understanding of the genotype-to-phenotype link. In particular, we show that a large fraction of reaction-based designs obtained by current strain design methods are not actually feasible, and show how our approach allows using the same methods to obtain feasible gene-based designs. We also show, by extensive comparison with experimental 13C-flux data, how simple reformulations of different simulation methods with gene-wise objective functions result in improved prediction accuracy. The model transformation proposed in this work enables existing constraint-based methods to be used at the gene level without modification. This automatically leverages phenotype analysis from reaction to gene level, improving the biological insight that can be obtained from genome-scale models. Genome-scale models of metabolism enable the exploration of the phenotypic landscape of an organism. Unlike probabilistic approaches such as genome-wide association studies, these models describe the mechanistic link between genotype and phenotype, predicting the response to genetic and environmental perturbations. However, this connection is hampered by the complexity of gene-protein-reaction associations. In this work, we implement a model transformation method that untangles this complexity by allowing gene-wise phenotype predictions using genome-scale models. The transformed model explicitly accounts for the individual flux carried by the enzyme or subunit encoded by each gene. Previously published simulation methods are automatically leveraged by this transformation, enabling new features such as the formulation of objectives and constraints at the gene/protein level. We demonstrate the application of different kinds of analysis and simulation methods, showing in each case how the gene-wise formulation can result in higher prediction accuracy in comparison to experimental data and improve the biological insight that can be obtained from available models. At the rbations , 3. Studrbations , drug tarbations  and pathrbations , and therbations  and syntrbations .Understanding the complex relation between the genotype and phenotype of an organism is a fundamental part of systems biology research. Unlike statistical approaches such as genome-wide association studies (GWAS) , genome-ad-hoc fashion. This is the case in rational strain design, where optimization procedures are used to find optimal interventions to maximize the production of a given compound [a posteriori, without guarantee that the optimality of the predicted phenotype is preserved. Undesired side-effects may arise if any of the target reactions involve promiscuous enzymes.Since most constraint-based methods do not explicitly account for GPR associations, they can only provide analysis at the reaction level. For instance, simulating a steady-state flux distribution predicts the rates of all metabolic reactions for a given phenotypic state, but fails to elucidate the contribution of individual genes/enzymes to that phenotype. GPR associations, typically implemented as Boolean rules, can be used to interpret the results of constraint-based analysis in an compound , 10. Witcompound –13, suchIn this work, we present a model transformation that generates a stoichiometric representation of GPR associations that can be directly integrated into the stoichiometric matrix. We show that the results obtained with the transformed model are consistent with those obtained from reaction-level models, and highlight the advantages of performing different kinds of analysis at the gene level. We also propose new variants of existing methods that take advantage of this representation to formulate gene-wise objective functions and test their predictive ability using experimental datasets.enzyme usage reactions (u), are added to the model. For each gene, this variable accounts for the total amount of flux carried by the respective enzyme (or enzyme subunit). This model transformation can be represented by an extended stoichiometric matrix  stand out as outliers with regard to promiscuity due to their participation in nearly 250 transport reactions.The iAF1260 genome-scale model for se study . A statiThe proposed transformation was applied to the model after pre-processing to remove blocked reactions . The simplified model contains 914 genes, 1532 reactions, and 1032 metabolites . After transformation, the extended stoichiometric matrix contains 3853 (pseudo-)reactions and 1946 (pseudo-)metabolites. The increase in the size of the stoichiometric matrix is caused by introducing the genes as species in the model, decomposing reversible and isozyme-catalyzed reactions, and introducing the artificial “enzyme usage” reactions see . In the enzyme usage variables, which determine the amount of flux carried by each individual enzyme.Simulating steady-state flux distributions using flux balance analysis (FBA) is the most common application of constraint-based models. FBA requires the definition of an objective function based on evolutionary assumptions . The maxin vivo, if such a considerable deviation of flux would occur, it would have been frequently reported. Hence the pFBA prediction seems less plausible .FBA results are usually affected by solution degeneracy, as different flux distributions can have the same objective value. Parsimonious FBA (pFBA) is a two-step variant of FBA that determines the flux distribution that satisfies the optimal objective while also minimizing total absolute flux through all reactions. It is based on the assumption that the cell tries to achieve its goal with the most efficient allocation of resources . AlthougE. coli ME-model [We compared our simulation results with those obtained using the recent ME-model  under thMultiple alternative methods to standard FBA simulations have been proposed for prediction of phenotypic effects of gene deletions in the constraint-based framework –21. SuchE. coli mutants [In order to evaluate the simulation accuracy of the proposed methods we performed a systematic evaluation using a fluxomics dataset for 24 single gene  mutants  , which is only the case under particular circumstances . Also, ilpd gene  and only afterwards affect the rate of 2-oxoglutarate-dehydrogenase (AKGDH). Using reaction-based constraints to simulate the over/under-expression of any of these reactions would predict a linear effect between the regulation level and the respective flux, disregarding the potential redistribution of flux between promiscuous enzymes and isozymes. Considering the large fraction of promiscuous enzymes  see . For eacnditions . In thisThis analysis is more informative then traditional determination of essentiality (binary test) as it reveals the minimal  flux that can be carried by each enzyme. With this approach one can also determine “blocked” genes (i.e. genes encoding enzymes that cannot be used under any conditions), which can be used to guide the model reconstruction process. Furthermore, one can use the shadow price and reduced costs information to analyse the sensitivity of the results with respect to internal  and external  constraints. For instance, the non-zero shadow prices for an essential gene represent the set of precursor metabolites that cause the essentiality, whereas the reduced costs of exchange reactions represent the effect of changing the medium composition with regard to essentiality.Random sampling of the flux solution space is a suitable strategy to analyse all possible physiological states described by a model . Like FVE. coli [Lpd relative to other enzyme subunits  given its simultaneous participation in different enzyme complexes.One limitation of flux sampling is that it does not account for the flux load distribution between isozymes or the overall flux carried by promiscuous enzymes. With the extended representation, it is now possible to analyse flux sampling results at the gene/enzyme level. An illustrative example for a model of core metabolism of E. coli  is presesdh* and overexpression of frd*, ppc, and aceA) are commonly proposed interventions to increase succinate production. It is also possible to observe some extent of agreement between our sampling results and gene expression measurements of succinate producing mutants [aceE, aceF, icd, pykA and pykF.Flux sampling at the gene level can be used to guide rational strain design, since non-overlapping sampling distributions for a given gene between wild-type and the desired mutant indicate that the flux carried by the respective enzyme must necessarily change. We compared these results with those obtained by strain design methods that account for modulation of gene expression –28. Some mutants , most noomics data has fostered the development of constraint-based methods that make use of these data to improve predictions. In a recent work, we evaluated several methods for integration of transcriptomics (and proteomics) data into constraint-based simulations, and observed that none of the methods resulted in consistent improvement of flux predictions compared to simple FBA simulation under the assumption of optimal growth and parsimonious enzyme usage [The continuous improvement of high-throughput techniques to measure different kinds of me usage . This lime usage , 39.enzyme usage variable  . Elementenzyme usage reactions become part of the support vector of EFMs, being automatically computed by any EFM computation algorithm. This extended support vector contains a gene-wise representation of each EFM, denoting the genes that participate in the given pathway.Since EFM computation does not account for GPR associations, they do not entirely reflect the topology of a metabolic network, disregarding that a promiscuous enzyme is a common link between different pathways and that isozymes provide alternative routes within the same pathway. Our stoichiometric representation of GPRs solves this problem by explicitly accounting for this complexity in the computation of EFMs. This concept is illustrated in E. coli . The deletion of this gene would cause the least impact in the network. We also compared the frequency of each reaction in the original model and the transformed model , that are guaranteed to couple product formation to growth . This meGiven that any gene encoding a subunit of an enzyme complex can be deleted to disable the respective function, the number of potential designs significantly increases when converting reaction to gene deletions . This maIn order to test the feasibility of each design, accounting for possible side-effects, we calculated the actual set of reactions effectively disabled by the gene deletions required to implement a given cMCS. We then evaluated each phenotype and observed that only a small fraction of the original set of solutions (∼7%) are valid with respect to the original production constraints . This drThe shortcomings of reaction-based design can be avoided by directly searching for gene-based designs. We applied MCSEnumerator to the transformed model and computed all minimal gene-based cut sets up to 8 deletions . It can E. coli and the same production goals as before, thousands of designs were found with as few as 3 gene manipulations  and methods for integration of transcriptomics data , where the objective function and model constraints are reformulated in a gene-based representation. Systematic evaluation of these methods by comparison with experimental flux data revealed that the new methods have higher average prediction accuracy than their original versions. This shows that not only it is possible to reformulate the evolutionary assumptions that support these methods in a more biologically meaningful way, but doing so can actually improve flux predictions.enzyme usage variables. This representation is more accurate than applying these constraints at reaction level. For instance, deleting a single isozyme has no effect in a reaction-based representation, whereas the gene-based representation accounts for the redistribution of flux among other isozymes of the affected reaction. We also demonstrated the non-trivial consequences of performing over/under-expression of promiscuous enzymes. Forcing an increased or decreased activity in a promiscuous enzyme results in an uneven redistribution of flux among the respective reactions in order to reach a new optimal phenotype. This effect would not be predictable by current methods.Predicting the effect of gene-level modifications with our extended model representation can be directly performed by constraining the respective The integration of GPR associations reveals a distinct topology of the metabolic network. It accounts for the fact that promiscuous enzymes provide a common link between different pathways, and that isozymes provide alternative routes within a pathway. We demonstrated how this affects the characterization of the network in terms of its elementary flux modes. The EFMs computed for the transformed model have an extended support vector that accounts for the genes that must be active to support the respective pathways. This enables different types of elementary mode analysis  to be performed at the gene level. One disadvantage of the extended representation is the combinatorial explosion of EFMs caused by the decomposition of isozyme-catalyzed reactions. Nonetheless, gene-wise EFM computation is still amenable to the application of EFM-based methods that do not require complete enumeration of the full EFM set –51.post hoc analysis of proposed designs. We used MCSEnumerator to determine all minimal reaction cut sets (up to size 7) for ethanol production in E. coli. We tested the feasibility of these cut sets when GPR associations are considered, and observed that only less than 10% of the solutions are actually feasible. Since many of these reaction-based solutions would also be determined by other strain design methods, this problem affects such methods as well. Another advantage of computing gene-based designs is to effectively minimize the number of genetic interventions, which is the desired scenario for in vivo construction of the mutant strain. We observed that determining minimal reaction deletions can result in a large number of gene deletions. On the other hand, gene-based design effectively minimizes the number of gene deletions regardless of the number of affected reactions. In terms of computation costs, one would expect the increased model size to be detrimental for efficiency. However, the complexity of MILP problems (used in MCSEnumerator and many other strain design methods) is related to the number of decision variables (deletion targets). Since the number of genes is lower than the number of reactions, we were able to compute gene-based cMCS up to size 8 with the same computational resources used to compute reaction-based cMCSs up to size 7.Rational strain design is likely the application where our proposed transformation will be most useful. The large number of strain design methods published so far (∼50) can be automatically used to search for gene-based manipulations without any modification to the underlying method by first applying our transformation to the model. This provides several significant advantages compared with reaction-based design. First, reaction-based design ignores the side-effects of enzyme promiscuity and requires careful It is important to note that other strategies to integrate GPR associations in constraint-based simulations have been proposed. All methods that integrate transcriptional regulatory networks and metabolic networks need to account for GPRs, as they provide the connection layer between the two types of network. In SR-FBA, genes are encoded as integer variables and the GPR associations are encoded as linear inequalities, transforming the model into an MILP formulation . This apE. coli [etc), GPR associations can only rely on the quality of gene annotations. With our approach, incorrect assignment of GPR associations will be reflected in the extended stoichiometric matrix and may generate misleading results. On the positive side, our proposed approach may also facilitate the development of new methods for curation of GPRs (e.g.: gene-wise gap-filling). Another potential disadvantage of performing gene-level analysis is the increased computational cost of working with an extended stoichiometric matrix. Although the effect is barely noticeable for single simulations (∼ 1.5-fold increase in simulation time) it may be undesirable for more computationally intensive types of analysis such as random flux sampling or flux variability analysis.Finally, it is important to note the potential pitfalls of using a gene-based analysis. In this work, we used a highly curated genome-scale model of E. coli . NowadayE. coli –58. Whilunderground metabolism of E. coli revealed an even larger number of metabolic reactions available in the cell as a result of enzymatic side activities, playing an important role in the fitness landscape of the organism [The integration of GPRs directly into the stoichiometric matrix enables bidirectional analysis between the gene and reaction levels. In one direction it is possible to observe the impact of gene perturbations on reaction fluxes. In the other direction one can perturb the environmental conditions and observe the required adaptations at the gene level. The complexity of GPR associations and their evolution has been recently analysed considering the role of environmental adaptation in driving enzyme specificity . A recenorganism .Our framework provides a mechanistic link between genotype and phenotype and should facilitate the development of new methods to integrate multi-omics datasets into genome-scale models, as well as methods to integrate metabolism with other biological processes. In this work, we explored the reformulation of previously published simulation methods with gene-wise constraints. It would be interesting to explore other suitable applications, such as the formulation of simulation methods that account for enzyme production costs , 62.A new generation of genome-scale models and simulation methods is on the rise . This inhttps://github.com/cdanielmachado/GPRTransform.All the source code, models, and generated data are publicly available in the following repository: E. coli [Unless otherwise stated, all simulations were performed using the iAF1260 genome-scale metabolic model for E. coli  and the E. coli  was usedE. coli .S be the original stoichiometric matrix, v the steady-state flux vector , and ub the respective vector of flux bounds, such that S ⋅ v = 0 and 0 ≤ v ≤ ub. The extended stoichiometric matrix S′, flux vector v′, and flux bounds ub′ are defined as:Sgpr is the stoichiometric representation of GPRs , Ik is the identity matrix for k genes, and u is the enzyme usage vector. This transformed model can be readily used by any kind of constraint-based method with the general form:f is a given objective function.The model transformation to explicitly include GPRs in the stoichiometric matrix .The methods to predict mutant phenotypes  method of the COBRA toolbox . The wilEFMs for the simplified glycolysis model were computed using CellNetAnalyzer version 2015.1 .enzyme usage reactions. Computations were performed with CPLEX 12.6.3 using a 6-core Intel i7 processor with 64 GB of RAM.MCSEnumerator  was testE. coli core model [cRegMCS  was testre model  was usedS1 Figenzyme usage variables, calculated for a minimum biomass production of 10% of the maximum theoretical yield on glucose minimal media.Gene essentiality determined by the flux variability analysis of the (TIFF)Click here for additional data file.S2 FigE. coli. For each gene, the curves represent the probability distribution of the flux carried by the respective enzyme. Two scenarios are considered: wild-type phenotype near optimal growth (blue curves) and succinate overproduction near optimal yield (green curves). Genes where the blue and green distributions do not overlap are targets for modulation of gene expression.Flux sampling results for the core metabolism of (TIFF)Click here for additional data file.S3 FigE. coli under anaerobic conditions : a) size of the solution pool for each cut size; b) total number of interventions of each type in the solution pool.Gene-based strain design using cRegMCS for growth-coupled ethanol production in (TIFF)Click here for additional data file.S4 FigComparison between the protein translation rates predicted by the ME-model and the respective enzyme usage predicted with gene-pFBA for a wild-type strain growing under aerobic conditions on glucose minimal medium with a glucose uptake rate of 10 mmol/gDW/h.(TIFF)Click here for additional data file.


The example shows that (1) these two methods are complementary to each other; and (2) there is a need to take into account Gibbs energy errors. Better estimations of metabolic phenotypes will be obtained when further constraints are included in the analysis.Metabolite profiling technologies have improved to generate close to quantitative metabolomics data, which can be employed to quantitatively describe the metabolic phenotype of an organism. Here, we review the current technologies available for quantitative metabolomics, present their advantages and drawbacks, and the current challenges to generate fully quantitative metabolomics data. Metabolomics data can be integrated into metabolic networks using thermodynamic principles to constrain the directionality of reactions. Here we explain how to estimate Gibbs energy under physiological conditions, including examples of the estimations, and the different methods for thermodynamics-based network analysis. The fundamentals of the methods and how to perform the analyses are described. Finally, an example applying quantitative metabolomics to a yeast model by  In recent years, the field of microbial metabolomics has expanded dramatically. This has been mainly due to improvements in analytical platforms, such as mass spectrometry (MS) and nuclear magnetic resonance (NMR), and a more widespread accessibility to these technologies in the research community. While firstly developed for the analysis of plants , metabolUnlike plant tissue, microbial metabolomics faces two major problems. Firstly, the cells often need to be separated from a complex culture broth prior to analysis. This is a major challenge since absolute metabolite amounts inside the cells are often multiple orders of magnitude smaller than the respective amounts outside the cells. This means that the smallest carryover from the separation process may bias the measured intracellular concentrations. The second problem is the rapid growth of microbes and their optimization for fast turnover of substrates. This means that metabolism needs to be efficiently stopped (quenched) in a matter of seconds ,4. It haThe most common procedure for quenching involves rapid cooling to temperatures below −20 °C which, for many different bacteria, leads to leakage of the cytoplasm into the extracellular solution ,6. This Overcoming the hurdles of sampling mentioned above enables further advancement of metabolomics to a more quantitative approach. Given the original definition of metabolomics as a non-targeted analysis of all metabolites , the terMicrobial systems biotechnology is systems biology with an applied focus . Rather 13C fluxomics is performed, labelling enrichment data for metabolites is acquired using MS or NMR. This review will describe recent developments for the quantitative analysis of metabolites in microbial experiments and will then explain how a thermodynamic approach can be implemented and used to constrain the solution space for flux analysis. Finally, metabolic flux analysis principles, especially 13C fluxomics, will be introduced.While thermodynamics relies on accurate measurements of intra- and extracellular metabolite concentrations, fluxomics relies on the quantitative measurements of only a few substrates being taken up and products being secreted by the cells, as well as growth and biomass composition. When Several analytical platforms are available for the quantitative analysis of metabolites from microbial origins. Here, some of the most commonly used platforms will be presented.HPLC remains a workhorse technology for the quantification of metabolites, with a broad range of available columns and detectors enabling the targeted analysis of many compound classes. Its advantage over other platforms is the robustness of the methods and the availability of many detectors which are compatible with buffers or salt gradients which are unsuitable for mass spectrometry-based applications. However, sensitivity and selectivity can be an issue with HPLC. These depend on the chromatography applied, the detection method and the sample matrix. Derivatized amino acids, for example, can be detected at very low fluorescence levels (picomoles injected) with good selectivity. Another problem is that separate instrument runs are usually required for each compound class and, since identification relies on the retention times of external standards rather than mass fragmentation patterns or chemical shifts, this bears the risk of false positives. Some examples of commonly used methods are amino acid analysis , organicGC-MS in metabolomics is mainly applied as a non-targeted semi-quantitative profiling tool, but it is a powerful tool for the quantification of volatile compounds. Quantification of non-volatile, polar compounds (after derivatization) is more complicated, since the derivatization chemistry is very matrix-dependent and the concentration of different compounds influences the derivatization efficiency of others. Each compound usually has its own reaction kinetics with the derivatization reagent , making 13C fluxomics, however, GC-MS is currently the instrument of choice, delivering highly reproducible mass isotopomer distributions with the relative error of technical repeat injections often under 0.5%. This is possible because derivatization of the target compounds  or multiple (MRM) reaction monitoring mode on a triple quadrupole instrument. These modes select a target parent ion in quadrupole 1, fragment it in the collision cell (quadrupole 2), and then measure the abundance of the daughter ion selected in quadrupole 3. The idea is that the parent-daughter relationship is very specific, enabling the filtering of a small peak among a vast pool of compounds and achieving high sensitivity when quantifying in the presence of a very small background. For example, LC-ESI-MS/MS in combination with ion-pairing chromatography was used to quantify metabolites of the central carbon metabolism .The major problem with LC-ESI-MS/MS is ion suppression or enhancement during ionization . This meThe second problem with LC-ESI-MS/MS is its inherently low dynamic range. In order to get quantitative data for a microbial extract it is not uncommon to run each sample in a whole range of dilutions, especially when trying to analyze a broad range of metabolites that usually cover multiple orders of magnitude in concentration.Another problem, that affects all analytical platforms, can be the availability of metabolite standards. For many intracellular metabolites, calibration standards may be not available off the shelf and need to be custom synthesized, adding significantly to the analysis cost, while other metabolites might not be available at all.13C labelled internal standards to overcome the ion suppression/enhancement effects caused by the sample matrix k the concentration of reactant I at the power of its stoichiometric coefficient k. ΔrG determines the directionality of a reaction, i.e., the net flux of the reaction occurs in the direction where ΔrG is negative.The criterion of spontaneity is difficult to grasp because the entropy of the universe cannot be measured. For biological systems, where constant temperature and pressure apply, spontaneity is defined by the Gibbs free energy (ΔG ≤ 0). For a generic reaction (Equation (1)), the Gibbs free energy of the reaction  and the standard Gibbs energy of reaction (ΔrG0); which finally depends on the standard Gibbs energy of formation of the metabolites (ΔfG0) and the stoichiometric coefficients  (see Equation (3)). Thus, the directionality of reactions depends on the metabolites’ concentrations and their thermodynamic properties. The ‘'’ notation indicates physiological conditions are assumed rather than the standard biological conditions  , differing from the experimentally-observed value of −915.9 [kJ/mol] by 2%  instead of standard conditions (ΔrG0) ), and are likely to be genetically or allosterically regulated  glucose and 99% [U-13C] glucose was used as the labelled substrate together with naturally-distributed glutamate. Cell hydrolysis and labelling analysis are described elsewhere . 13C fluxomics independently confirmed that the net flux of this reaction was in the direction the metabolite data and the thermodynamics predicted (d-ribose-5-phosphate ketol-isomerase and triose-P-isomerase. In these cases the ΔrG was between −1.3 and −0.2 (kJ/mol) and 0.22–28.32 [kJ/mol], respectively (13C fluxomics. This highlights the fact that a ΔrG range close to equilibrium (ΔrG = 0) meaning that the reaction is likely to be reversible. In fact, the 13C fluxomics also showed a high reversibility for these reactions. There was no measurement of di-hydroxy acetone phosphate (DHAP) available, which may help to fix the directionality of the triose-P-isomerase reaction, underlining the importance of complete metabolite datasets.Subsequently, metabolite data of the  pathway , namely redicted . Two othectively . The pre13C fluxomics to describe the metabolic phenotype. Moreover, when opposing information on reactions directionality was found between the methods, the reactions are close to equilibrium and should be described as reversible. If it is not possible to estimate metabolic fluxes with 13C fluxomics due to the impossibility to reach metabolic pseudo-steady state or the feeding with labeling substrate is too expensive, thermodynamic-based network analysis is presented as a powerful tool to determine a reactions’ directionality, information that can be used with conventional MFA to determine a reduced solution space for the metabolism of the studied organism.In summary, this example shows how the different datasets are complementary to one another and can be used to gain deeper insights into metabolism and higher confidence in the results. Thermodynamics is useful to check the quality of the metabolomics data and 13C-labelled metabolites are required the availability of standards become an issue due to the high price of these labelled metabolites. An approach recently applied to overcome this issue is the use of labelled internal standards generated by culturing microbes with labelled carbon substrates. However, the generated labelled metabolites will depend on the used organism and the reproducibility is highly dependent on the standardization of the culture conditions. Therefore, there are still challenges that need to be overcome in order to increase metabolomics data quality.Despite a great increase in sensitivity, selectivity, and coverage of the platforms to measure metabolomics, it is still not possible to generate a full organism’s quantitative metabolomics data. Furthermore, when The introduction of the second law of thermodynamics into a metabolic network will determine directionality of initially-reversible reactions, constraining the solution space of metabolic networks using experimental data and thermodynamics principles. With the increase on coverage an accuracy of Gibbs energy determination is now possible to include thermodynamics constraints into metabolic flux determinations. The determination of compartment/organelle specific metabolite concentrations is in its infancy, presenting an extra challenge when working with compartmentalized models, such us yeast and humans. Despite NET analysis being able to estimate compartment-specific ranges of metabolites concentrations from average cell metabolites concentrations, the higher coverage of compartment specific metabolomic data will increase the power of network thermodynamics approaches.13C fluxomics and network thermodynamics analysis. It was shown that both approaches complement each other. However, some discrepancies were found which are mainly explained by the need of; (1) more accurate Gibbs energy or known errors of the Gibbs energy values; and (2) higher coverage of endo-metabolomics data. Moreover, other omics data, such as proteomics and transcriptomics, could be used in combination with the previous technologies to provide a deeper biological understanding of the organism metabolic phenotype and regulation.Here an example was presented on how quantitative metabolomics data: endo- and extra-metabolites’ concentrations and enrichment level of isotopically-labelled metabolites are used to determine an organism metabolic phenotype. Two different approaches were employed: