To validate the likelihood-based gap filling approach, we applied it to models where essential pathways were removed, finding that likelihood-based gap filling identified more biologically relevant solutions than parsimony-based gap filling approaches. We also demonstrate that models gap filled using likelihood-based gap filling provide greater coverage and genomic consistency with metabolic gene functions compared to parsimony-based approaches. Interestingly, despite these findings, we found that likelihoods did not significantly affect consistency of gap filled models with Biolog and knockout lethality data. This indicates that the phenotype data alone cannot necessarily be used to discriminate between alternative solutions for gap filling and therefore, that the use of other information is necessary to obtain a more accurate network. All described workflows are implemented as part of the DOE Systems Biology Knowledgebase (KBase) and are publicly available via API or command-line web interface.Genome-scale metabolic models provide a powerful means to harness information from genomes to deepen biological insights. With exponentially increasing sequencing capacity, there is an enormous need for automated reconstruction techniques that can provide more accurate models in a short time frame. Current methods for automated metabolic network reconstruction rely on gene and reaction annotations to build draft metabolic networks and algorithms to fill gaps in these networks. However, automated reconstruction is hampered by database inconsistencies, incorrect annotations, and gap filling largely without considering genomic information. Here we develop an approach for applying genomic information to predict alternative functions for genes and estimate their likelihoods from sequence homology. We show that computed likelihood values were significantly higher for annotations found in manually curated metabolic networks than those that were not. We then apply these alternative functional predictions to estimate reaction likelihoods, which are used in a new gap filling approach called  Genome-scale metabolic modeling is a powerful approach that allows one to computationally simulate a variety of metabolic phenotypes. However, manually constructing accurate metabolic networks is extremely time intensive and it is thus desirable to have automated computational methods for providing high-quality metabolic networks. Incomplete knowledge of biological chemistries leads to missing, ambiguous, or inaccurate gene annotations, and thus gives rise to incomplete metabolic networks. Computational algorithms for filling these gaps in a metabolic model rely on network topology based approaches that can result in solutions that are inconsistent with existing genomic data. We developed an algorithm that directly incorporates genomic evidence into the decision-making process for gap filling reactions. This algorithm both maximizes the consistency of gap filled reactions with available genomic data and identifies candidate genes for gap filled reactions. The algorithm has been integrated into KBase's metabolic modeling service, an automated metabolic network reconstruction framework that includes the ModelSEED automated metabolic reconstruction tools. Genome-scale metabolic models (GEMs) integrate available information about metabolism to provide a basis for holistic modeling and prediction of metabolic phenotypes Since the advent of genome-scale metabolic modeling, protocols Existing algorithms for filling gaps, or dead-end reactions, in metabolic networks broadly fall into approaches based on network topology While existing methods capably activate the necessary reactions to allow growth simulations, they often do so by fitting to phenotype data. Such fitting may result in the inclusion of spurious pathways which cause failures when testing the models against independent datasets http://kbase.us) and a web service API.The goal of our work is to improve the quality of automatically generated metabolic reconstructions and models by explicitly incorporating alternative potential gene annotations and their estimated likelihoods into the gap filling process. We have developed a likelihood-based gap filling workflow that (1) assigns likelihood scores based on sequence homology to multiple annotations per gene and, from these, likelihoods for reactions in a network and (2) identifies maximum-likelihood pathways for gap filling using a mixed-integer linear programming (MILP) formulation. We have also developed a workflow to iteratively identify pathways that activates gene-associated orphaned reactions in a network and assesses the likelihood of these pathways. Critically, the likelihood-based approach makes the gap filling solution genome-specific and provides users with putative gene-protein-reaction relationships and confidence metrics for each result. We show that our likelihood-based approach improves the quantity and quality of new gene annotations compared to the existing gap filling algorithm. The resulting models have comparable accuracy when simulating high-throughput growth phenotype data, when compared with previous parsimony-based gap filling algorithms. The workflow tools are fully integrated within the Department of Energy's System Biology Knowledgebase (KBase), and are publicly available via both a web-based command line interface . These four workflows use two gap filling algorithms (parsimony-based versus likelihood-based gap filling) as applied to two separate gap filling strategies (targeted versus iterative gap filling). The goal of both algorithms is to alter the reaction network by adding new reactions or altering existing reactions. Here, we use the terms parsimony-based and likelihood-based to describe the two gap filling schemes according to their core mode of reaction addition. Both schemes can prioritize changes in reversibility or add special consideration to edge cases such as the addition of transporter reactions. However, in parsimony-based gap filling, the overall goal of parsimony-based gap fill is to make the least number of modifications in order to fill a gap. In general, this means that the shortest reaction path is incorporated into a network. In contrast, likelihood-based gap filling weights genomic evidence and takes into account how likely a reaction is to be included in the network. Likelihood-based gap filling favors reaction paths supported by evidence over paths without any supporting evidence from the genome.In order to assess the efficacy of the likelihood-based gap filling approach, we implemented four gap filling workflows .In the second strategy, which we call irst see . One couEscherichia coli K12 Bacillus subtilis str. 168 E. coli model than the most recent, was used because the ModelSEED database does not yet link annotations to periplasmic reactions and the gap filling implementation does not yet properly support compartmentalized models). We found that highly likely gene-reaction links were significantly enriched in the models compared to less-likely gene-reaction links . Larger penalties for these types of changes make it less favorable for the algorithm to pick them over other changes to the network when fixing network gaps. Since the removed set of reactions did not include transporters or reversibility changes, higher penalties for transporters or reversibility changes led to greater accuracy in the returned reactions. The penalty for transporters that maximized the accuracy of the returned pathways was higher for parsimony-based gap filling  than for likelihood-based gap filling (25 or greater). The penalties for thermodynamically unfavorable reversibility changes that maximized accuracy were also higher for parsimony-based than likelihood-based gap fill . Therefore, likelihood-based gap filling reduced the need to have very large penalties for these categories of network changes in order to obtain accurate solutions.Dataset S2). The failures in parsimony-based gap filling were a result of picking shorter pathways to fill certain gaps for which longer pathways are the correct choice. For example, the synthesis of isopentyl diphosphate (IPDP), a primary precursor for lipid synthesis, can occur by one of two routes, the mevalonate pathway and the non-mevalonate pathway B. subtilis uses the non-mevalonate pathway for IPDP synthesis Although both methods had the same number of tuning parameters available, likelihood-based gap filling successfully outperformed the parsimony-based method by replacing a maximum of 31 of the 32 gold-standard reactions. Parsimony-based gap filling only replaced only a maximum of 24 reactions, regardless of the chosen penalties . However, the use of likelihoods did not significantly affect the phenotype predictions. For Biolog data, iterative gap filling increased the aggregate sensitivity by 11% compared to targeted gap fill, but decreased aggregate specificity  by 10%–13%. The aggregate accuracy decreased by about 1% for iterative compared to targeted gap filling.One commonly-used method to verify the integrity of genome-scale metabolic models is to compare their predictions with high-throughput phenotyping data, such as knockout lethality screens Since gap filling only adds a small number of genes to the model compared to the number in the draft model (about a 6% increase for iterative gap filling), the sensitivity and specificity of knockout lethality predictions were very similar for all four workflows. The aggregate sensitivity was 84–86% for all four workflows while aggregate specificity was 64–68%. We also examined the lethality predictions specifically for genes added in gap filling Figure 6An important feature of the likelihood-based gap filling algorithm is that it can differentiate between genomes by assigning organism-specific likelihoods for each reaction in a network. As a direct result, the gap filling solutions resulting from this algorithm are also organism-specific. This direct link back to evidence in the genome directly enables the identification of pathways that are not parsimonious, but that are most consistent with genomic data. We have shown that the likelihood-based approach increases both the quality and the quantity of hypothesized gene associations from gap filling, especially when using the iterative approach to maximize the number of activated reactions subject to evidence constraints. Of course, when building a high-quality network model, gap filled pathways should be evaluated by experts to evaluate the evidence cited in the algorithm, to search for existing experimental evidence in favor of or refuting the suggested solutions, or to design new experiments to test the existence of the hypothesized functions in the modeled organism The likelihood-based gap filling methods described in this manuscript use genomic evidence-based metrics for the confidence that can be placed in annotations and reactions. The pathways that result from maximizing confidence have a greater genomic coverage and stronger evidence for inclusion of genes compared with the common procedure of post-processing parsimony-based solutions. Therefore, including likelihoods into the gap filling procedure directly improves on the state of the art in evaluating and selecting gap filling solutions.Despite the significantly increased level of evidence for gap filling solutions resulting from likelihood-based gap filling, we did not observe a significant difference from existing approaches in the accuracy of knockout lethality or growth (Biolog) predictions. This result suggests that using phenotype data to filter gap-filling solutions may not result in a more accurate metabolic network . Indeed, validation metrics such as consistency with knockout lethality predictions have a large number of ways in which they could be fit to become consistent with phenotype data, which can lead to decreases in observed accuracy when the model is tested on new data not available during its construction The proposed integration of likelihoods into gap filling can serve as a tool for hypothesis generation in biology. An initial pool of potential annotations with associated likelihoods can be generated using many different methods such as protein co-localization or co-occurrence in toto becomes increasingly important.Finally, the KBase framework in which all of our workflows are implemented helps address the need for a unified framework for systems biology. In addition to gap filling, KBase includes implementations of many other modeling and reconstruction tools such as tools for the automatic generation of compartmentalized community models Text S2) or the web service API (Text S3) to perform each of these workflows.We have developed four workflows in the DOE KnowledgeBase framework: parsimony-based gap filling, likelihood-based gap filling, iterative gap filling, and likelihood-based iterative gap filling Figure 1Text S1). Likelihood-based gap filling modifies the cost of adding reactions (but not the cost of reversibility changes) by incorporating an estimated likelihood of existence of a metabolic reaction in an organism. Reaction likelihoods are computed based on an estimate of the level of evidence for a gene annotation (e.g. annotation likelihoods) and a mapping from annotations to reactions (via protein complexes).Parsimony-based and likelihood-based gap filling attempt to activate single inactive reactions in a network by some combination of reversibility changes and addition of reactions from a universal reaction database. Parsimony-based gap filling assigns costs for adding reactions or changing their reversibility based on the source database for the reaction, the estimated standard Gibbs free energy of reaction, and whether it is a transport reaction .The following sections describe the parts of these workflows in detail.The first step of each workflow Figure 1Text S1.The annotations for genes in the genome are used to generate a draft model using the ModelSEED algorithm as previously described The computation of reaction likelihoods for likelihood-based gap filling is achieved by first estimating the likelihood of multiple annotations for each gene in the query organism based on sequence similarity, and then by using mappings from annotations to reactions found in the ModelSEED reaction database Annotation likelihoods are computed in reference to a database of genes with high-confidence annotations. For this purpose, we compiled a list of the protein sequences for all proteins whose function was either literature-supported or called as part of at least one SEED subsystem Escherichia coli K-12. If the representative organism for an OTU did not have a protein with that role in a subsystem or with a literature backing, a representative protein was chosen at random from another member of the OTU.To minimize the amount of redundancy in the list of target proteins, they were binned into organism taxonomic units (OTUs) with roughly 97% 16S rRNA similarity The computation of annotation likelihood scores was designed based on the principle that genes with more similar sequences are more likely to share the same function, but recognizing that these relationships are far from perfectly predictive −5 against all of the genes in the high-confidence gene annotation data set. A log-score for each  pair was computed as:ijE is the E-value for the BLASTP hit between the protein products of genes i and j and ijS is the log-score between them. The parameter k = 10−200 was used to prevent the log E-value from being undefined due to a reported E-value of zero. After calculating log-scores for all  pairs, a likelihood score that each gene i ∈ OG, where OG is the set of genes in the organism, is also a member of the set aA of genes with annotation a was computed as follows:aA represents the set of genes with annotation a, PC = 40 is a pseudocount used to dilute the likelihoods of annotations for annotations with weak homology to the query. The sum in the numerator is over all BLASTP hits from gene i to genes with a particular annotation a and the sum in the denominator is over all BLASTP hits from gene i. Squaring the scores prevents large numbers of weak hits from dominating the computed likelihood.Annotation likelihoods were calculated by first running BLASTP p(i ∈ aA) will be high only if the protein product of gene i possesses strongly significant sequence similarity to reference proteins with annotation a and does not possess similarly strong similarity to proteins with other annotations. Therefore, the metric takes into account two different sources of annotation ambiguity: divergence of sequence and disparity of annotations for similar proteins in the target database.The pseudocount was chosen to set the likelihood of a gene having moderately high homology (E = 1E-40) to a single protein in the database to 50% and is a typical parameter used in tools such as BLAST Annotation likelihoods are useful for evaluating individual annotations, but must be converted into likelihoods for metabolic reactions in order to use them in the context of evaluating a metabolic network. Reaction likelihoods represent the confidence in the inclusion of a particular reaction in a metabolic network. The conversion from annotation likelihoods into reaction likelihoods takes into account the facts that annotations can imply multiple functional roles, a protein with a particular functional role could be part of multiple protein complexes, and multiple complexes could catalyze the same reaction. We used the ModelSEED reaction database i ∈ OG also belongs to the set of genes rR with functional role r was computed as the sum of the likelihood that gene i had each annotation that maps to role r.a→r from annotations to roles is defined by the ModelSEED database. This definition ensures that if a protein could be multi or single-functional, the final reaction likelihoods reflect each of those possibilities.The first step in computation of reaction likelihoods is the conversion of gene annotations into functional roles, to account for the possibility that an annotation implies multiple protein functions. The likelihood that each gene at least one gene in OG had role r was computed as the maximum likelihood of the role across all genes in OG.r (within 80% of the maximum) were retained and linked with an OR relationship to form a Boolean Gene-Function relationship.In the second step, the likelihood that c in the cell was computed as the minimum likelihood of the roles associated with it.r→c from roles to complexes is provided by the ModelSEED reaction database. The sets of genes possessing each function in a complex were linked with an AND relationship to form a Boolean Gene-Protein relationship.In the third step, the ModelSEED reaction database was used to compute the likelihood of existence of protein complexes from the likelihood of existence of functional roles. A protein complex represents a set of protein functions that must all be present in order to build a multi-subunit enzyme . Since all of the subunits must be present to perform the function, the likelihood of the existence of a complex x in the cell was computed as the maximum likelihood of the possible complexes that could catalyze it.In the fourth step, reaction likelihoods were computed from protein complex likelihoods using complex-reaction links in the ModelSEED. Since multiple complexes can independently catalyze a reaction, the likelihood of the existence of a reaction In all workflows, targeted gap filling is performed first in order to activate the biomass equation and achieve growth on ‘complete’ media. Complete media consists of all compounds for which the organism has transport reactions in the draft reconstruction, and hence the solution to this gap filling problem represents reactions that would be necessary for growth on any more limited media for which the organism possesses transporters.Text S1.Targeted gap filling is performed using either the parsimony-based or the likelihood-based approach. The parsimony-based gap filling approach, used in the ModelSEED for auto-completing models p(x) are first converted into costs C(x) by inverting them:gapfillλx, are computed as follows:gapfillλx, is the objective coefficient in the gap filling formulation for reaction x and the P-values represent the same penalties as used in the existing parsimony-based approach (see Text S1). In our modified formulation, higher-likelihood reactions are given lower costs  and are therefore favored in the optimization provided their benefit outweighs costs of other reactions in a pathway. The numeric parameters (12 and 10) in the equation make changing the reversibility of a reaction with low estimated Gibbs energy equivalent to adding (on average) one to two intracellular reactions in a favorable direction, while changing a reaction with reaction with an estimated Gibbs energy of 10 kCal/mol is equivalent to adding three average intracellular reactions in a favorable direction.The likelihood-based gap filling approach uses the same MILP formulation as parsimony-based gap filling. However, likelihood-based gap filling uses reaction likelihoods to re-weigh the objective coefficients. To do this, the likelihoods of reactions Due to the difficult nature of mixed-integer programs, obtaining a solution can take a long time for certain problems. Therefore, we have implemented a system in which a time limit is initially imposed on solution time and automatically increased if solving fails. An error is ultimately thrown if the solver fails to find a solution within one day or if no solution exists.In iterative gap filling work flows, all reactions in the model that are associated with one or more genes are targeted to enable flux. Iterative gap filling is similar to the previously published gap find and gap fill algorithms The results of iterative gap filling depend on the order in which the targets are processed. In our studies, the order was selected based on the region of metabolism in which the reaction occurs. Central carbon reactions were gap filled first to ensure that core metabolism was functional. These were followed by reactions involved in biosynthesis of essential metabolites , finally culminating in reactions involved in peripheral utilization and degradation pathways.After ordering reactions according to this priority, flux variability analysis Since iterative gap filling attempts to fill the maximum number of gaps in a model, solutions that fill different gaps in the model are often redundant or very poorly supported. To solve this problem, we have implemented a reaction sensitivity analysis that identifies for each gap filled reaction (including reversibility changes for existing reactions in a network): a) whether each gap filled reaction causes other reactions in the model to become inactive when it is removed and b) whether the gap filled reaction is predicted to be essential for growth. After performing reaction sensitivity analysis, any non-contributing reactions, which are non-essential gap filled reactions that do not activate any other reactions in the network, were removed from the model. For parsimony-based iterative gap filling, reaction sensitivity was performed on all reactions in the reverse order in which they were added, so that lower-priority gap filling solutions would be tested for removal first. For likelihood-based iterative gap filling, reaction sensitivity analysis was done in order from lowest to highest likelihood so that gap filled reactions that were unsupported by genetic evidence would be tested for removal first.In order to support simulations of Biolog data and achieve greater completeness of the metabolic network, the models gap filled on complete media are gap filled again to achieve non-zero biomass production on a minimal media. In this study Carbon-D-Glucose was used as the minimal media. This gap filling step can be performed using either the targeted or likelihood-based approach.To perform phenotype simulations, high-throughput data is imported into the KBase workspaces and saved as PhenotypeSet objects in the workspace. These objects contain links from phenotype sets to specific media and genes in a genome, and represent the results of Biolog or knockout lethality experiments in a consistent format.In this study, the ModelSEED algorithm Mycobacterium tuberculosis). Subsequently, the knockouts were simulated by evaluating the Boolean GPR rules for each reaction and setting the maximum rate of each reaction whose GPR evaluated to FALSE to 0. Flux balance analysis was then used to maximize the biomass equation. The knockout was considered lethal if the predicted biomass production rate was less than 10−9hr−1. For parsimony-based gap filling knockout simulations were performed both before and after integrating predicted gene protein reaction associations for gap filled reactions into the model.To simulate gene knockout lethality phenotypes, the models growing on Carbon-D-Glucose media were first further gap filled (if necessary) to achieve nonzero biomass production on the media in which knockout experiments had been performed . Detailed descriptions of all steps in the workflow are available in S3.All gap filling for this manuscript was performed outside of KBase using CPLEX under an academic license  Wilcoxon signed-rank tests were performed using the signrank function in MATLAB statistics toolbox version 7.1, using the ‘exact’ method and 2-tailed p-values.Dataset S1Gap filling data summary. Summary of gap filling data, including numbers and average likelihoods of added reactions and genes using the four workflows.(XLS)Click here for additional data file.Dataset S2Parameter sensitivity analysis using iBsu1103. Sensitivity of targeted gap filling results to changes in the unfavorable reversibility change and transporter penalties.(XLS)Click here for additional data file.Dataset S3Analysis of genes unique to particular workflows. Likelihoods and phenotype predictions for gene-reaction links specific to parsimony-based or to likelihood-based gap filling.(XLSX)Click here for additional data file.Figure S1Likelihood of reactions added in gap filling. Likelihoods of added reactions separated according to if they were only added in likelihood-based solutions, only added in parsimony-based solutions, or common to both solutions. Includes both iterative and targeted gap filling.(PNG)Click here for additional data file.Figure S2Number of reactions unique to likelihood-based gap fill workflows. Number of unique reactions to the likelihood-based workflow separated by organism.(PNG)Click here for additional data file.Software S1Workflow client API. Python code that may be readily installed and used to run the four complete workflows.(ZIP)Click here for additional data file.Text S1Supplemental methods. Descriptions of previously-published gap filling and model building methods implemented in the ModelSEED and elsewhere.(DOCX)Click here for additional data file.Text S2Use of the KBase web interface. Detailed documention of steps in the workflow and how to run each one using the KBase online command-line interface (http://iris.kbase.us).(DOC)Click here for additional data file.Text S3Use of the KBase client API. Documentation for use of the client API provided as (DOC)Click here for additional data file.Text S4Directions for use of the provided VM. How to set up and run your own services to run the code.(DOC)Click here for additional data file.


The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique  Developing better predictive models of metabolic network behavior is essential for exploiting microbial cell factories for biochemical production. Though microbial cell factories have been successfully engineered for the overproduction of a number of products including ethanol Biological networks have been described using kinetic models for decades in silico knockout strains that redirect flux from biomass to biochemical production A number of studies have been published that use the FBA framework to reveal non-obvious network characteristics. Optknock was developed for designing in silico strains, each representing an “expression state”, or a combination of gene expression levels -1-pyrroline-5-carboxylate (P5C) P. putida strains have been shown to produce 0.14 mol ethylene/mol glucose at a production rate of 2.86 mmol/gdcw/hr, which is the highest reported yield and production rate for ethylene in any microbial host E. coli, the maximum reported ethylene production rate is 0.008 mmol/gdcw/hr, which is less than 1% of the production rate in P. putidaEscherichia coli as the ethylene production host for the model, as E. coli represents a common bacterial production strain with a simple metabolic network, and low ethylene production in E. coli indicates the potential for optimization. Here, modifications to E. coli metabolism are combinatorially analyzed using Constrictor, with the goal of revealing gene repressions that can inform experimental efforts and improve bioethylene yields as well as yields of alternate products.Ethylene biosynthesis utilizing the ethylene forming enzyme (EFE) from E. coli, the E. coli core model iAF1260 was modified to build a focused metabolic network for heterologous ethylene production. The core model contains 95 reactions and 72 metabolite species, derived from the iAF1260 genome scale reconstruction (http://gcrg.ucsd.edu/Downloads/EcoliCore) Ps. syringae EFE reaction http://bigg.ucsd.edu/), KEGG (http://www.genome.jp/kegg/), and Ecocyc databases (http://ecocyc.org/) were used to locate the additional reactions and metabolites needed to complete the model E. coli iAF1260 and the iJO1366 models http://www.gurobi.com) to execute each FBA linear programming problem. All models were modified and solved using the COBRA toolbox http://www.colorado.edu/UCB/chatterjeelab/.To study ethylene production in -1, defined according to experimental observations for E. coli MG1655 in minimal media  and a maximum oxygen uptake of 15 mmol/gdcw/hr al media . ResultsConstrictor explores the system response for combinations of “inhibitory” rate adjustments . First, bv represents the baseline flux through each of r reactions and S is the stoichiometric matrix for the reaction network. For the majority of results presented, we maximize ethylene production in order to study maximum theoretical ethylene yield, while enforcing a minimum growth rate in order to simulate metabolically relevant flux distributions. To demonstrate that alternate objectives are supported, we also describe a study that maximizes growth (via biomass reactions). The LB and UB vectors contain the lower and upper bounds of the flux for each reaction, respectively, and limits are placed on ATP maintenance, glucose uptake, and oxygen uptake  to this linear programming problem is determined for the baseline strain without any genetic modifications. Though alternate optimal solutions exist with equivalent maximized ethylene production Minorf and Majorf are coefficients that are used to modulate the upper and lower bounds of the targeted metabolic reaction(s) at Minor and Major levels , all possible combinations of i = 1 through n. A representative solution (r levels . The resenerated . Each tamodLB and modUB) for each reaction respectively are obtained by replacing the original lower and upper bounds used in the baseline solution by the specific expression values  (1 possible combinations (“Major” and “Minor”). The modified lower and upper bounds of the flux  . Similarc = 2k×2h2, where k and h are the number of reversible and irreversible reactions respectively that are targeted by Constrictor  and lower bounds (-vmax) for Constrictor FBA optimizations. The biomass, glucose uptake, oxygen uptake, and ATP maintenance reactions are also excluded from Constrictor modifications. The resultant FBA linear programming problem is solved to obtain the globally optimal solution for ethylene production for each of the c expression states, where each column (j = 1 through c) is iteratively selected as the flux boundaries (Reactions that are inactive in the baseline solution (corresponding to zero flux through the reaction) are excluded from modifications, and allowed to vary between the original upper (vundaries .(4)cv, contains r rows and c columns. Each column in cv represents the solution obtained from a unique expression state.The final flux solution matrix, −1 through the biomass reaction. The Constrictor framework was used to iteratively target each reaction in the core ethylene network, with combinations of restrictions to 20% and 80% of the baseline flux. Individual modification of each of the 66 reversible reactions and 48 irreversible reactions in the core metabolic network would generate 360 expression states or FBA studies, as there are four possible expression states for each reversible reaction and two expression states for every irreversible reaction. However, Constrictor does not target the 42 reactions found to be inactive in the baseline solution, since the optimization of reaction network with modifications to inactive reactions results in solutions identical to the baseline case. Applying Constrictor to the remaining 72 active reactions gives rise to 222 expression states. While 12 of these expression states converge to the baseline solution and another 196 expression states decrease ethylene yield, 14 expression states positively impact the ethylene yield with respect to the baseline solution  is held to 80% of the baseline value. In mutant B, yield increases by 6% (0.37 mol ethylene/mol glucose) with respect to baseline when either glyceraldehyde-3-phosphate dehydrogenase (GAPD) or phosphoglycerate kinase (PGK) is restricted to 80% of baseline  is insufficient to compensate for the decrease in GAPD activity (by 4.2 mmol/gdcw/hr with respect to basline), so the ethanol production pathway shuts off and we observe increased flux through NADH dehydrogenase (NADH16). The decrease in ethanol production when the flux requirement for NAD+/NADH balance is reduced gives rise to improved ethylene yield in mutant A.The maximum yield of 0.38 mol ethylene/mol glucose, a 9% increase over the baseline yield is found for baseline . The difbaseline . We obseSimilarly, mutant B also has a lower ethanol yield than the baseline , again due to reduced NADH production by GAPD. In mutant B, as opposed to mutant A, we note that limiting GAPD or PGK causes a portion of the upstream flux to divert through the pentose phosphate pathway . By this mechanism, some carbon dioxide is released via phosphogluconate dehydrogenase (GND), which reduces the amount of carbon that passes through GAPD or PGK and allows the Constrictor constraint to be satisfied. Additionally, the pentose phosphate pathway produces NADPH, which is used by glutamate dehydrogenase (GLUDy) and N-acetylglutamylphosphate reductase (AGPR) to synthesize precursors of L-arginine. We note that flux decreases through the NAD(P) transhydrogenase (THD2), presumably because the NADPH produced by G6PDHyr and GND is sufficient to meet the NADPH requirement of the L-arginine biosynthesis pathway. Increases in ATP synthase (ATPS4r), cytochrome oxidase (CYTBD), and NADH16 flux for both mutants A and B show that additional cofactors also influence ethylene production in a non-intuitive manner, likely related to oxygen deficiency. Certain expression states are not able to be solved, pointing to bottlenecks in the network. For instance, neither a 20% or 80% reduction in phosphate uptake or ribose-5-phosphate isomerase (RPI) activity is tolerated, nor is an 80% reduction in nitrogen or glucose uptake .mutant C and D, Since decreasing glucose uptake improved yield in mutants A and B, we next examined the impact of fixing glucose uptake to 10.5 mmol/gdcw/hr during Constrictor analysis. Under this constraint none of the expression states lead to increased yield, though increased growth rates are noted when reactions in glycolysis are targeted  to slight reduction (f = 0.9). We maintained a minimum growth rate of 0.3 hrncreases . The higE. coli genome scale model. The baseline solution for each is obtained via the maximization of ethylene demand with constraints as described in mutant G) is obtained when glucose transport is restricted to 70% of the baseline value, while the second highest yield  is obtained when GAPD or PGK are held at 40% of their baseline flux. As in mutant B and mutant H, the highest yielding solutions mutants I and J associated with the iJO1366 model are obtained by targeting GAPD or PGK. In mutant I, these reactions are constricted to 30% of baseline to provide an 18% increase in yield, and in mutant J, held at 20% of baseline for a 5% yield increase. For each of these mutants, ethanol production decreases by 100% with respect to baseline, indicating that oxygen limitation plays a role in suppressing the baseline yield. The complete flux solutions for each mutant are available in Tables S5 and S6 in The analysis was repeated using two genome scale models: iAF1260 , from wh53 scenarios, many of which would be redundant. To reduce the combinatorial space when simultaneously modifying multiple reactions, we applied the Constrictor framework to restrict sets of metabolic reactions in various functional classes. The metabolic network is divided into fourteen functional classes, including glycolysis, the TCA cycle, pyruvate metabolism, anaplerotic reactions, oxidative phosphorylation, and ethylene production, among others , likely due to differences in metabolites involved in the biomass reaction. When Constrictor is applied to the core model, no solutions result in ethylene production; however, expression states that produce ethylene are found when Constrictor is applied to iAF1260 and iJO1366 genome scale models. In either of the genome scale models, restricting L-glutamate 5-semialdehyde dehydratase reaction (G5SADs) results in ethylene production. Ethylene production is higher when G5SADs is modified by the major restriction factor  in the core, iAF1260, and iJO1366 models, then applied Constrictor with 20% and 80% restrictions on individual reactions to search for modifications that increase ethylene yield. None of the baseline solutions produce ethylene when growth is the objective , which ide novo for desirable phenotypes. We applied Constrictor with fminor = 0.8, and fmajor = 0.2 to individual reactions in the core and genome scale model to locate modifications that increase production rate and yield of alternate metabolites. A summary of the targeted reactions in the core model that lead to increased production of ethanol, formate, acetate, or acetaldehyde is depicted in We also maximize growth to demonstrate an alternate application of Constrictor; rather than looking for modifications that improve yield of a specific product, it also possible to scan a network to search E. coli, and demonstrate the capability of Constrictor to generate unique in silico mutants that are predicted to produce high ethylene yields. By restricting single enzymatic reactions or combinations of reactions, thousands of possible network states are revealed. In both reduced and genome scale models of E. coli metabolism, alternate expression states predict improvements in ethylene yield. By limiting individual reactions, disproportionate shifts in the network are forced, which reveal alternate solutions that highlight network characteristics. Constricting many reactions simultaneously provides a means to scan a larger portion of the solution space, which can be used to infer reactions or metabolites that have large impact on ethylene yield. In this analysis of ethylene production, we conclude that glucose and oxygen cannot be balanced at their maximum allowable values to achieve the highest ethylene yield. Thus anaerobic limitations result in ethanol production in the baseline networks. Constrictor suggests that the imbalance in the network can be remedied by reducing flux through glycolysis. Depending on the model, the highest ethylene yields are obtained for different target reactions and different restriction factor values, which emphasizes the importance of using a high throughput experimental approach, such as MAGE Here, we present an FBA based optimization framework called Constrictor that predicts metabolic interventions by identifying unique “expression states” that give rise to overproduction of the biochemical target. We show that enforcing various levels of inhibition of flux constraints in metabolic network pathways can provide valuable engineering intervention strategies to achieve the overproduction target. We investigate heterologous ethylene production in efe sequences, testing different promoters to drive efe expression, and reducing homologous recombination between efe promoter and chromosome E. coli. In the ethylene-producing networks described here, we focused on modifying only flux through the metabolic reactions initially present in the network, and did not attempt to substitute enzymes with different cofactors or force alternate substrates as has been suggested via computational analysis to optimize ethylene production in other organisms E. coli metabolism for ethylene production.So far, improvements in ethylene production by selectively repressing metabolic activity have not yet been reported. Experimental attempts to engineer ethylene-producing microorganisms have included increasing media concentration, increasing gene copy number, inserting codon-optimized To achieve the overarching goal of creating robust platforms for predictive strain engineering, it is necessary to apply lessons learned from a multitude of FBA frameworks into experimental strain design strategies, including those that focus on improving computational efficiency in vivo modifications via a wealth of available strain engineering tools. Recently, characterization of promoter and upstream element sequences have enabled specific ranges of gene expression to be realized in silico predictions.Recent high-throughput recombineering techniques demonstrate that combinatorial exploration of the genomic space can reveal optimal mutants, while computational techniques prove to be well suited to analyze these combinations. Modifications suggested by Constrictor can be translated into Figure S1Map of the core metabolic network for ethylene production. The core metabolic network comprises of central metabolism, including glycolysis, the TCA cycle, and co-factor balancing equations (in grey box at top), as well as the arginine biosynthesis pathway. Ethylene production is carried out by the ethylene forming enzyme (EFE). Reaction abbreviations are in bold uppercase, and metabolite names are in lower case italics. Arrows indicate directionality of each reaction as allowed by the model. Refer to Table S2 in (TIFF)Click here for additional data file.Figure S2Experimental growth rate of E. coli K12 MG1655.E. coli (ATCC 700926) was grown at 37°C in M9 minimal media with 0.4% glucose. Optical density (OD562) was recorded every 20 minutes with a Tecan GENios plate reader (Tecan Group Ltd.) with Magellan software version 7.2. Normalized OD is presented (OD at time t divided by OD at t = 0). Error bars are standard deviation of n = 9 biological replicates. Growth rate (µ) was calculated with an exponential fit to the exponential growth portion of the curve (shadowed region in plot).(TIFF)Click here for additional data file.Figure S3Trade-off between growth rate and ethylene yield with and without Constrictor. The maximum theoretical ethylene yield was recorded for a range of minimum growth rates, with  and without Constrictor. In each of the three models (labeled in panels), a similar trend is noted, with Constrictor yields approaching baseline yields as growth rate is increased.(TIFF)Click here for additional data file.File S1Supplementary Tables.Table S1: Reactions and Parameters. Table S2: Reactions in the core model for ethylene production from EFE. Table S3: List of metabolites in the core model. Table S4: Selected solutions from Constrictor in ethylene core model. Table S5: Selected solutions from Constrictor in genome scale model iAF1260. Table S6: Selected solutions from Constrictor in genome scale model iJO1366.(XLSX)Click here for additional data file.


Cellular metabolism must ensure that supply of nutrient meets the biosynthetic and bioenergetic needs. Cells have therefore developed sophisticated signaling and regulatory pathways in order to cope with dynamic fluctuations of both resource and demand and to regulate accordingly diverse anabolic and catabolic processes. Intriguingly, these pathways are organized around a relatively small number of regulatory hubs, such as the highly conserved AMPK and TOR kinase families in eukaryotic cells. Here, the global metabolic adaptations upon dynamic environment are investigated using a prototypical model of regulated metabolism. In this model, the optimal enzyme profiles as well as the underlying regulatory architecture are identified by combining perturbation and evolutionary methods. The results reveal the existence of distinct classes of adaptive strategies, which differ in the management of storage reserve depending on the intensity of the stress and in the regulation of ATP-producing reaction depending on the nature of the stress. The regulatory architecture that optimally implements these adaptive features is characterized by a crosstalk between two specialized signaling pathways, which bears close similarities with the sensing and regulatory properties of AMPK and TOR pathways. The biological value of the basal consumption rate of ATP can be approximately derived from the respiratory rates JATP ∼ 50 mM.min−1 measured in yeast cells in the stationary phase  is a random number of uniform distribution: fw and p quantify the amplitude and the probability of the mutation. Specific boundary conditions may apply such as ai ∈  or periodic boundary condition for φi associated with n offspring, and then selects the n highest-fitness individuals in the pool of 2n parameter sets (parents plus offspring) to compose the parents of the next generation. The selection criterion is elitist and a parent can stay in the pool as long as its fitness allows it. Finally, the optimization process terminates after a maximal number of generations (Ngen = 4000) In this study, the values of optimization parameters are n = 10 and p = 1, while the mutation type (multiplicative or additive) and the mutation amplitude fw depend on the parameter that is optimized. The best parameter set can be further optimized via a stochastic hill climbing to check the finding of a maximum. Because the end result of an evolutionary computation is sensitive to the initialization procedure of the population, we have also used a continuation method  and statistical analysis of multiple evolutionary trials.For a fluctuation of egy (ES)  that is Model simulations and evolutionary computations are performed using Fortran programming language and numerical integration of differential equation is based on the extrapolation-based SEULEX Fortran routine.N0, energy demand K0 and enzyme-dependent rate coefficient N0, K0 and MA < 0), in which case metabolic death occurs. As mentioned in Methods section, an optimal stable metabolic steady state is associated with a set of enzyme parameters N0 and K0.A preliminary step in studying metabolic adaptation to transient stress is first to analyse the steady-state properties of the model. In stationary condition defined by constant levels of nutrient concentration N0 and increasing values K0 to Φ = 0 at a threshold value Nc0,(K0) and Kc0,(N0)   beyond w0,B to 0 , while tectively . In thisand flux . Furtherients N0 . Finallyed point , such thl values .In sum, the steady-state and bifurcation analysis of the model allowed to identify two properties that will be key for the further study of dynamic response to transient stress: (i) the existence of a dynamic instability (saddle-node bifurcation) that corresponds to metabolic collapse and death; (ii) the fact that steady-state adaptation can be different depending on whether the stress is primarily cause by lower nutrient in-flow or a higher metabolic demand.N(t) and K(t) of amplitudes aN,K given by After having characterized the main features of the optimal metabolic steady state, the following step is to search for optimal enzyme profiles in response to non-stationary environmental conditions such as oscillations of ei0,, the amplitudes ai and the phases φi can first be derived for small amplitude oscillations ai by using a perturbation method, and then obtained for any perturbation amplitude by using evolutionary methods  that is much smaller than the natural frequency ω0 of the metabolic system, while phase shifts would occur for ω ∼ ω0. However, above some critical perturbation amplitude ai,c > ai,c , the optimal solutions display qualitatively different properties characterized by a tight regulation of storage production and degradation . During the optimization procedure, all the enzymatic parameters converge to unique and precise values with relatively low variability. This reflects the identifiability or non-degeneracy of the model with respect to these enzymatic parameters. The means, amplitudes and phases of enzyme profiles are equally important in contributing to survival and to growth rate optimality as confirmed by the local analysis of the fitness landscape near a given optimum by measuring the variance and the correlation of enzymatic parameters  or K(t) below the threshold values of Nc0, or Kc0,, which would not be filtered out and would induce metabolic death in the absence of slow storage cycles. In turn, the lower-bound frequency indicates that a too long stress requires to be anticipated with high storage reserves that comes with an unbearable cost and death.These storage-based solutions occur for a given frequency range of oscillatory perturbations . The uppKS) increase. In that case, the value of the lower-bound frequency increases while the storage regime disapears at the expense of the death regime. In contrast, lower ATP consumption for maintenance (K0) or regulation (KE) or higher ATP production (kA) raises the stress amplitude threshold aN,c for which the storage strategy confers a benefit. Finally, increasing anabolic costs (kB) merely reduces the biomass production. Nevertheless, the optimality of storage-dependent and -independent modes of metabolic adaptation depending on perturbation frequency and amplitude is a robust feature of the model.The position of the boundaries that delimit the S-domain of storage-based solutions depends on model parameters . For insEi(t) = Ei0,  = E0,i . The domshown in , so as tEj tightly depends on the nature and the amplitude of the non-stationary conditions and emphasizes that a specific storage strategy appears for severe stress condition in terms of ampliitude and frequency, while the control of catabolism is slightly different depending on whether the stress corresponds to a lack of external nutrient or a strong energy requirement for homeostasis.In all, the results show that the optimal oscillatory profiles of enzymes Ej obtained for various non-stationary conditions provide guidance on the signaling and regulatory architecture, that is the manner how these enzymes would be optimally regulated by specific signaling cues. For instance, the optimal phases of enzyme oscillations with respect to signal oscillations , Yj is the signal input that can depend on any environmental or metabolic variables, and NY is the number of signaling pathways. The function fij is described by:λij > 1 and λij < 1 correspond respectively to the Yj-dependent activation and inactivation rate of Ei by Yj. θij is the regulatory threshold (the inflection point of the response curve for nH = 2), and nH is the Hill coefficient or slope factor that is set to 2, which is the minimal value that can be used to described the sigmoidal behavior of transcription kinetics. Such nonlinear behavior can arise through the affinity, cooperativity, or multimerization of transcription factors at their binding sites within target gene promoters.To address these issues, the metabolic network model given by μi, λij and θij that maximizes the flux. To begin with, we use constant value of the regulatory timescale τi = 1, which would correspond to a rapid mode of regulation , since, anyway, optimization leads to minimize τi in the absence of synthesis and degradation costs for enzymes. To compare the optimal solutions obtained in the cases of oscillatory versus regulated enzymes, a generic quantity for enzyme amplitude is defined as,x(t)). Optimization is first performed in the presence of a single stress conditions (N(t) or K(t) with ω = 0.01) and a single signaling pathway NY = 1 where Y1 is a function of N, K, MI or MA (Y(N) = N, Y(MI) = MI, Y(K) = 5 − K and Y(MA) = 0.1MA/(1 − MA) and have been chosen to display similar maximal and minimal values for Y given the stress intensities considered here.Evolutionary optimization technique is applied to determine the regulatory parameters N, MI or MA or high levels of K induces an inhibition of enzymes EB and activation of EA depending on whether it is an energy or a nutrient stress, respectively (Yj(t) which can be more or less sinusoidal or distorted. The result that the optimal growth rate Φ systematically augments by increasing the hill coefficient nH (result not shown) or by increasing the number of signaling pathways NY is consistent with the notion that signaling complexity improves metabolic fitness through refined control of enzyme time courses in the absence of costs associated with increases of NY or nH.Irrespective to the signaling cue, a stress associated with low levels of ectively . HoweverMA) to 40% (for MI) compared to the case where optimization is done for each stress condition separately. This result reflects the property that optimal regulation of the ATP-production enzyme EA depends on the stress type, giving rise to a compromise solution of intermediate regulation of EA. In contrast, optimization with two signaling pathways allows to recover the optimal fluxes obtained for each stress condition optimized separately with a single signaling pathway. This dual signaling and regulatory scheme shows a clear divisions of the sensing and regulatory task as the signaling sensitive to intermediate metabolites MI inhibits the ATP-production enzyme EA while the pathways sensitive to MA (ATP) activates EA  and stress timescale (ω = 0.01), the optimal regulatory schemes that have been obtained in various stress conditions are expected to weakly depend on τ as long as it is short enough compared to the period of stress oscillation T = 2π/ω. ES+/− and biomass production enzyme EB remains unchanged for a large range of τ as long as τ < T. For τ of a same or larger magnitude than T, the score of the optimal solution decreases reflecting the absence of temporal regulation of Ei due to a low-pass filtering effect of regulatory dynamics.Although evolutionary optimization of regulatory parameters have been performed for specific values of regulatory timescale  or aN = 0.7 (right) for which the evolved optimal solutions require storage metabolism or not.(A) Flowchart of the evolutionary algorithm. (B) Evolution of the growth rate score and the enzymatic parameters (mean enzyme level (PDF)Click here for additional data file.S2 FigLeft panel: The analysis is performed for the optimal solution associated with the stress condition of amplitude aN = 0.8 and frequency ω = 0.01 , amplitudes ai, phases φi with i = A, S+, S−, B. To determine the geometry of the fitness landscape around this optimum, we consider perturbation vector pi = popt, i + δpi with δpi = zi Δpi whereas Δpi corresponds to the maximal variations, which are set to 10% of the possible range of values for ai and φi and log(2)/2 for the means ei0,. Middle panel: Among 105 samples of random parameter perturbation sets θΦopt with θ = 0.9, from which we generate a data set Xθ whose columns correspond to those vectors Right panel: The last step is to perform a PCA on this fitness-dependent data set X, where principal components are the eigenvectors of the correlation matrix Xθ equal to the square roots of the diagonal elements of the covariance matrix φS− for phases and eB0, for means). (C) To uncouple the informations regarding the respective variances of parameter distributions shown in (B) and the correlation between different parameters, PCA is made as the eigencomposition of the correlation matrix. Up panel: The eigenvalue spectrum λQ of Q. Bottom panel: the contribution to each parameter (index is defined in (C)) to the two eigenvectors associated with the two highest eigenvalues λQ,1 and λQ,2. The large number of eigenvalues λQ of order of 1 precludes over-parameterization and guarantees parameter identifiability, while it also entails a complex fitness landscape with correlated parameters in many eigen-directions, especially for the two principal components. (D) Correlation matrix Q and four examples of correlation between the most correlated enzymatic parameters .(A) Schematic description of the analysis consisting in a principal component analysis (PCA) on a parameter set satisfying some fitness-based requirements. (PDF)Click here for additional data file.S3 FigaN = 0.8 and frequency ω = 0.01 . (B) Schematic representation of the influences of the non-optimized model parameters on the size and boundaries of the storage regime in the amplitude-frequency plane.(A) The analysis is performed for the optimal solution associated with the stress condition of amplitude (PDF)Click here for additional data file.S1 FileSet of equations and parameters of the biochemical network model as a System Biology Markup Language (SBML) file. The specific set of parameters corresponds to (XML)Click here for additional data file.


Genome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.Here, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of http://cs.ru.nl/~wmegchel/mmf.MMF is freely available as a MATLAB plugin at:  Successful metabolic modelling examples range from predicting the impact of cell perturbation experiments in micro-organisms  and in soethanol  to metaboethanol  and tumooethanol –8.S), containing m metabolites and n reactions. Entry Si,j denotes the stoichiometric coefficient of metabolite i in reaction j. The allowable flux range vj for reaction j is bounded by the mass-balance equations (considered at steady-state) and flux capacity constraintsS underdetermined [At the heart of these models lies the stoichiometric matrix  Computational methods that select flux distributions based on optimization of a biologically sound objective, such as biomass or ATP yield. Flux Balance Analysis (FBA) ,12 is ar2 are measured on a routinely basis. Unfortunately, measuring intracellular fluxes is currently limited by the available experimental techniques. A successful technique that measures intracellular fluxes is metabolic flux analysis (MFA) [ii) The most reliable method is direct measurement of the unknown intra- and extracellular fluxes. Extracellular or boundary reactions such as glucose and oxygen consumption, together with growth rates and byproduct secretion rates such as acetate, ethanol and COis (MFA) –23. MFA iii) Computational methods that use other omics sources such as gene- or protein expression –28. The It has been shown that microbes that normally grow in various environments favor a suboptimal growth in order to keep a metabolic state that allows for an easier switch towards other nutrient conditions ,33. HereE. coli and S. cerevisiae and show that measured reaction rates indeed correspond to a high MMF value within the solution space corresponding to suboptimal growth. This information can be used to discard fluxes that would severely affect the organisms’ metabolic flexibility and effectively reduces the flux range for each reaction considered. We compared our method with a uniform sampling approach and show that MMF provides a smaller prediction error rate when flux ranges are reduced at a similar cutoff. By applying pFBA after discarding all flux ranges that violate the MMF paradigm by more than 5%, better quantitative flux estimates are obtained. Finally, we demonstrate that our method selects reactions that contribute substantially to the uncertainty in the network. Measurement of the fluxes selected by our method provides a larger reduction and subsequently better prediction than can be expected from an approach that cannot estimate these most likely fluxes.We evaluated our method on the genome-scale models of n reactions:n reactions can be composed to cover all metabolic reactions in the network or only a specific subset of interest, such as the TCA cycle or the glycolysis pathway. The method proceeds in two phases. First, the feasible flux range i is binned into b bins. Denote with vi = δj that the lower- and upper flux bound for reaction i are constrained to the lower- and upper bound of bin j. TFR(v|vi = δj) then denotes the total flux range given the tightened bound on reaction i. TFR(v|vi = δj) is computed by adjusting the lower- and upper bound of reaction i and propagating this constraint through the other reactions in the network (e.g. using FVA). Finally, this expression is normalized, such that TFR(v|vi = δj) denotes the TFR fraction remaining after constraining reaction i.Our method uses the idea that micro-organisms, which can grow in various environments typically grow at a suboptimal rate on a certain substrate, to allow for an easier adaptation towards other nutrient sources ,33. Our 3 = [In the second phase, a unique flux distribution can be chosen with respect to the maximum metabolic flexibility paradigm. A first and straightforward approach is to discard all flux values that cause the TFR to drop below a certain cutoff. This can then be used to further constrain the flux bounds, such that the space of possible flux distributions shrinks. This approach is illustrated for the toy network in 3 = ,10) is 0A second option is to choose the flux distribution that maximizes the TFR under the mass-balance and flux capacity constraints directly. This can be useful in the case that a clear biological objective such as growth is not present, which is the case for instance in most mammalian cells. Because the TFR distribution was computed for each reaction separately, selecting for each reaction the flux value that maximizes the TFR yields a non-steady-state flux distribution imum TFR . The peai:Here, W is a diagonal matrix of weights and i has maximum entropy (uniform distribution), the weight i is minimal (0). The vector of weights Note that when the TFRMMF can be used to select or prioritize flux measurements. If measured flux data is available, it can be used to reduce the flux capacity constraints (the lower- and upper bounds). Furthermore, propagation (using FVA) of the new bounds typically reduces the bounds of other reactions as well. The amount of reduction caused depends mainly on three factors. First, the reduction of the measured reaction depends on the experimental precision. More importantly, how this reduction affects the feasible ranges of other reactions in the network depends secondly on what the actual flux is that was measured and furthermore on how that reaction is connected to the rest of the network (the network topology). For instance, if a high excretion rate of ethanol was measured, then much of the carbon excreted cannot go to other pathways (under the steady-state assumption). On the other hand, when a low ethanol excretion flux is detected, then it is still unknown how for instance carbon is excreted in order to satisfy the steady-state constraint. In other words, the organism might excrete other products such as acetate, glycerol and lactate or dedicate much of this flux to growth. Thus, a high excretion rate would typically provide a much larger reduction of the feasible space than a low excretion rate.The TFR distribution is helpful, because it provides a reasonable estimate of the flux through a reaction . FurtherA recent review about computational methods that integrate quantitative “omics” (gene-expression) data, showed that pFBA in general provides better quantitative flux estimates than most computational methods that integrate this omics data . AlthougFeasible flux distributions form a high dimensional convex steady-state solution space. The hypervolume of this space indicates how “many”  alternative solutions exist. Unfortunately, exact computation of this volume is infeasible for genome-scale models ,41 and rIt is known that often, organisms do not grow at the theoretical optimal rate computed by FBA , but at By reducing the feasible ranges of the fluxes, better estimates can be made on how flux is actually distributed through the cell. A computational approach suitable for reducing the space of  feasible solutions is uniform random sampling –46. By rIn general, it is desirable to reduce the feasible space without excluding the real (i.e. the measured) fluxes. 2) in eqs A reduced solution space still does not provide a unique flux distribution. However, this can be obtained using either MMF to find the flux distribution that globally maximizes the TFR or by using pFBA on a model with refined bounds. 2 method works reasonably well for most models, except for S. cerevisiae growing under aerobic (high oxygen) conditions. The pFBA method, which assumes a maximization of the biomass yield is clearly a better approach here. Although MMF2 does not outperform MMF+pFBA or pFBA alone, it can be used to estimate fluxes for models where an optimization objective such a as growth is not applicable.MaxSpan reactions). Although the flux range of these MaxSpan reactions can be reduced considerably, they may or may not have a large constraining effect on other flux ranges in the network.We applied the MMF method to select among the measured fluxes, those that are expected to maximally reduce the TFR. Selecting fluxes that have a large impact on the TFR may help to reduce valuable experimental time and cost. We iteratively selected one reaction and constrained the model with the measured flux until seven fluxes were selected. Because adding an extra constraint always reduces the TFR, we compared our method with two simple approaches. A rather naïve approach is to select reactions randomly from those that have available measurement data. The second approach always selects those reactions that have the largest distance between their upper- and lower bound  alternative to minimizing the absolute sum of fluxes. Instead, a flux path is chosen that maximizes the “flexibility” or robustness of the network towards varying conditions, while maintaining a (sub)optimal growth rate. This robustness is believed to be an evolutionary design principle of the metabolic networks of many organisms and protects the cell against internal defects and varying environmental conditions ,48. The We would like to discuss our comparison with the uniform sampling approach. First, uniform sampling of metabolic networks is often done by the ACHR  method; Our method can also be used on networks that are made tissue- or environment specific with computational methods that integrate omics data with genome-scale networks, such as iMAT , GIM3E  or EXAMOMMF can also be used to identify the key intracellular reactions. Here, to test the performance of our method, we used flux data obtained with MFA, since data obtained with other techniques is scarce at the moment. Before MMF would be applicable as a measurement selection tool for MFA techniques, the main obstacle that has to be solved is taking into account the intrinsic coupling that exist between the tracers used and the pathways that are measured. That is, reactions measured with MFA cannot be chosen one at a time and the choice of isotopic label determines which reaction rates will be measured. A possible solution would be to extend the algorithm to a greedy heuristic that tries to select multiple consecutive measurements that best partition the flux space into smaller subspaces. This would be useful to compute a priori which labeling scheme provides most information about the network under study, especially since the error rates can also be computed in advance . Our metTaken together, we have presented a novel method, which predicts metabolic fluxes by adopting a maximum network flexibility paradigm. Our method can be used to further narrow the solution space in genome-scale metabolic networks and thereby improve existing methods such as pFBA. Our method can predict (intra)cellular fluxes in the absence of known cellular objectives and can be used to find important hubs in the metabolic network that contribute most to the large range of alternative distributions.S1 FileE. coli iAF1260  network . E. coli iAF1260  network . S. cerevisiae iMM904 high O2  network . S. cerevisiae iMM904 low O2  network .In this scenario, the glucose and oxygen consumption rates were set to their measured values, and the biomass flux was constrained to the observed growth rate. The TFR distribution depicts for each reaction the feasible rate that allows a TFR ≥ 0.95. Notice that most measured fluxes are indeed within the range that allows for this large “network flexibility”. The narrow sampling distributions allow for a larger reduction of the flux space, but unfortunately often do not capture the measured (13C) flux. Rectangular shapes indicate the predicted (pFBA and MMF variants) and measured flux (13C). (PDF)Click here for additional data file.S2 Fileprimary objective, which is probably incorrect . Scenario 2: the uptake rates of glucose and oxygen, as well as the measured growth rate are set in the model. MMF performs better than random sampling for at least 3 of the 4 models . Scenario 3: all exchange rates are constrained. Again MMF performs better on at least 3 of the 4 models .ACHR sampling compared to the MMF approach with TFR ≥ 0.99. Scenario 1: glucose and oxygen uptakes are constrained. MMF seems to perform better for the E. coli models compared to uniform sampling. For the yeast model with low oxygen, the reduction achieved by MMF is larger, but the error is also larger. Finally, uniform sampling performs better for the high oxygen yeast model. Notice that since the growth rate was not constrained, MMF in fact optimizes for “network flexibility” as its (PDF)Click here for additional data file.S3 File. Scenario 2: the growth rate is constrained in addition to the glucose and oxygen consumption rates. In this scenario MMF performs better, because a sub optimal solution space is considered . Scenario 3: all measured exchange fluxes are constrained. In this case, the MMF paradigm is also valid .Scenario 1: constrained glucose and oxygen consumption. MMF does not consider biomass pressure, but is designed to optimize the network flexibility under sub optimal growth rates. Therefore, it does not perform well in this scenario, where the growth rate is unknown (PDF)Click here for additional data file.S4 File. Scenario 2: the uptake rates of glucose and oxygen, as well as the measured growth rate are set in the model. Again MMF provides the best reduction of the flux ranges for all models . Scenario 3: all exchange rates are constrained. Also in this case, the best overall TFR reduction is achieved by MMF .The grey line denotes the mean flux range in the reference model. Scenario 1: fixed glucose and oxygen uptake rates. In this setting, MMF provides the best reduction of the flux ranges for all models (PDF)Click here for additional data file.S5 File. Scenario 2: the glucose and oxygen rates, as well as the biomass production rate are constrained. In most models, the strongly reduced prediction error correlates well with the reduced TFR, except for the E. coli iAF1260  model . Scenario 3: all exchange fluxes are constrained. Again, the error does not monotonically decrease with the number of constrained reactions, but does converge towards zero .The grey line denotes the mean error in the reference model. Scenario 1: constrained glucose and oxygen rates. A smaller TFR does not necessarily correlate with a reduced pFBA error (PDF)Click here for additional data file.


Synechococcus elongatus PCC 7942. The model bridges metabolic data sets from cells grown at different CO2 conditions by integrating transcriptomic data and isozymes. Identification of the regulatory roles of isozymes allowed the calculation and explanation of the absolute metabolic concentration of 3-phosphoglycerate. To demonstrate that this method can characterize any isozyme, we determined the function of two glycolytic glyceraldehyde-3-phosphate dehydrogenases: one co-regulates high concentrations of the 3-phosphoglycerate, the other shifts the bifurcation point in hexose regulation, and both improve biomass production. Moreover, the regulatory roles of multiple phosphoglycolate phosphatases were defined for varying (non-steady) CO2 conditions, suggesting their protective role against toxic photorespiratory intermediates.Current standard methods for kinetic and genomic modeling cannot provide deep insight into metabolic regulation. Here, we developed and evaluated a multi-scale kinetic modeling approach applicable to any prokaryote. Specifically, we highlight the primary metabolism of the cyanobacterium  Bacteria. Recently, these prokaryotes have received increasing attention in applied research. Cyanobacterial production of bioenergy, such as hydrogen Cyanobacteria are a monophyletic group of oxygenic phototrophs in the phylum Synechocystis sp. PCC 6803 Most genome-scale models have used the model cyanobacterium Our preliminary study showed that a combination of genome-scale and kinetic models improves the model accuracy by implementing minor sink reactions for adjacent pathways Synechococcus elongatus PCC 7942 (hereafter referred to as Synechococcus 7942) and show its capabilities for explaining the metabolic and redox regulation of primary carbon metabolism. The model is constrained by metabolic and transcriptomic data, energy and redox levels , CO2 level, and growth rate. First, the model was evaluated regarding whether it robustly mimics the experimental data. We then focused on the following questions: 1) Can we reliably predict cellular metabolic concentrations; 2) What is the role of isozymes and their position in the network; and 3) How is photorespiration integrated into the primary carbon metabolism system?This work aimed to present a multi-scale kinetic model of primary carbon metabolism for the model cyanobacterium max parameters and transcriptomic weight factors, is available in the 2 are available in The presented multi-level kinetic model is based on Michaelis-Menten kinetics. The scheme of employed model is presented on Synechococcus 7942 cells grown at high CO2 (5% CO2) and low CO2 conditions (0.038% CO2) were taken from a previous study 2 acclimation, we included a metabolic dataset for cells shifted from high to low CO2 conditions for 3 h  was recalculated compared with our previous study timation . The con2 conditions.Presented multi-level kinetic model includes all enzymatic steps of the Calvin-Benson cycle, photorespiration, glycolysis, and simplified carbohydrate synthesis . The modEscherichia coli. In this experiment In general, the multi-scale kinetic model describes more than one layer of cellular function. To describe changing metabolic states under different environmental conditions within a model, information about changes in the amount of enzymes is necessary. Instead of proteomic data, which do not reflect all primary metabolism enzymes in a cyanobacterial cell Synechococcus 7942 cultivated at high and low CO2 conditions. The model focuses on the major routes of primary carbon metabolism in Synechococcus 7942, as well as other phototrophic organisms that perform oxygenic photosynthesis.Multi-scaling improves the accuracy of parameter fitting enormously because, compared with traditional kinetic modeling, it fits metabolic data for more than one steady state with the same kinetic parameters. In our case, we analyzed metabolic changes in cells of 2. The model validation on energy charge assumes the same ATP · (ADP+ATP)−1 ratio in high and low CO2, and was maintained in a narrow range 0.74–0.78 as proposed before +)−1 ratio in high and low CO2 corresponds with measured data  and reached level 0.33 for high CO2 and 0.43 for low CO2. The employed mean values for transcriptomic changes implies robustness of the whole system to parameter change and thus against the environmental changes. Finally, as shown in 2 conditions correspond with each other.The model has been validated for growth rate, metabolic, transcriptomics, redox and energy levels under two growing conditions: high and low CO2. Next step includes a switch from high to low CO2 and applying the mean values of measured transcript changes as weight factors for each Vmax estimated for high CO2. The third step simulates a transition to steady state in low CO2 and evaluates the match with experimental data from cells grown at low CO2. If no match is found after hundreds of parameter estimation runs, the model is re-evaluated and missing reaction(s) or regulatory steps, e.g., izoenzyme, are implemented. Finally, if the match is found, it is the first step for the model validation, followed by comparing calculated and measured energy and redox levels and growth rate ratio between high and low CO2 states.The employed systems biology workflow for identification of kinetic parameters has several steps. The first step is a search for various sets of kinetic parameters matching the metabolic data from cells grown at high CO2 greatly impact metabolic concentrations Different levels of CO2 and checked whether the following simulation in low CO2 matched the changes in metabolome as well. In the case of positive result, we stored the result and repeated it many times in order to get the highest biomass production. The final step was a search for any trend allowing to predict the absolute concentration of 3PGA. We note that the biomass production in the model means the accumulation of carbon atoms in sinks, i.e., pyruvate has 3 carbons so it contribute less than ribulose with 5 atoms; the nitrogen metabolism is not included in the model but it is not a limiting under our growth conditions We focused on a broad range of 3PGA concentrations around the measured levels . We calculated concentrations of other metabolites based on measured relative ratios 2 revealed a clear trend. Increasing cellular 3PGA concentrations have a positive impact on biomass production at both CO2 conditions and reveal a clear trend and a connection between 3PGA accumulation and biomass production, as shown on 2 conditions 2) or a negligible impact on growth rate (low CO2). Taken together, the model predicts the absolute concentration of 3PGA at the level providing the highest biomass production. This conclusion is supported by experimentally estimated concentrations of 3PGA, which are positioned on both calculated curves at the very beginning of the saturated region . GAP catalyzes the conversion between glyceraldehyde 3-phosphate (G3P) and glycerate 1, 3-bisphosphate . Comparegap1, gap2, and gap3) have been annotated. NAD-dependent GAP1 (synpcc7942_0245) was reported to primarily act as a glycolytic enzyme, whereas GAP2 operates within the Calvin-Benson cycle gap1 and gap3 encode isozymes responsible for glycolytic glucose conversion. Our model analysis of glycolytic GAPs showed that a simulated double knock-out of GAP1 and GAP3 significantly impacts biomass production, leading to a 24.3% decrease of biomass in ambient air but only a 4% decrease in the high CO2 condition. Interestingly, the simulated knock-out of either GAP1 or GAP3 had negligible (approximately 2%) impact on biomass production in ambient air. This finding corresponds well with the fact that GAP3 is missing in some cyanobacteria . Thus, we focused on the role of the Synechococcus 7942 GAP3.In most cyanobacteria, three genes encoding for GAP isozymes . We tested whether the lower flux of NADPH due to cyclic electron transport around photosystem I at low CO22 remains implemented in the model. Furthermore, the test scenario revealed that neglecting the possible NADH regulation of GAP1 and 3 does not allow for the aforementioned measured changes in the NADPH/NADP+ ratio. However, it is possible that the two glycolytic GAPs do not exclusively use NADH but could be NADPH-dependent in the non-compartmented cyanobacterial cell + ratios under both CO2 conditions , back into the Calvin-Benson cycle intermediate 3PGA. Despite the occurrence of an active CO2 steady states is not sensitive to the presence of putative PGPase  was analyzed. In contrast to PGM and GAP isozymes, which perform an important role in steady state metabolic regulation, the estimated level of photorespiration in cells grown at high or low COe PGPase . It was 2 have been considered. Thus, we analyzed additional transcriptomic 2). Assuming the activity of only one PGPase was able to match the level of 2PG but resulted in a gradual increase of photorespiration (2 conditions. Since it is has been shown that 1) the photorespiratory flux particularly increases during the transition phase of shifts from high to low CO2Thus far, only steady states at high and low COpiration , black. piration , gray. I2 conditions (ambient air) was 11.3% without active photorespiratory pathway. This lower productivity is partially due to losing organic carbon in the form of glycolate and partially by rebalancing metabolism, namely the phosphoserine pathway. However, the 11.3% calculated biomass decrease is valid only for ATP non-limited systems and can increase to 18% under ATP-(light)-limiting conditions in the natural environment. This growth reduction may partially explain why all cyanobacteria kept the photorespiratory pathway in addition to its role of detoxifying critical intermediates, such as 2PG.Finally, our analysis supported the notion that cyanobacteria, similar to other oxygenic phototrophs, perform better with lower or even no photorespiration. However, it is unclear why all cyanobacteria harbor the genomic capacity for photorespiration and do not release the low levels of photorespiratory glycolate from the cell. If we take our estimation of photorespiration Synechococcus 7942 cultivated at high and low CO2 conditions and two isozymes from central carbon metabolism, glyceraldehyde-3-phosphate dehydrogenase and 2PG phosphatase. The heterogeneity of their roles includes boosting the glycolytic flux, tuning the hexose regulation and protection against toxic substrate in changing environment. Finally, we also showed that complex model is able to predict the absolute concentration of metabolites, in our case shown for the first stable molecule of carbon synthesis, 3-phosphoglycerate.The main goal of this work is to show the diversity of iso-enzymatic regulatory roles in prokaryotes and to show how to decipher the functions of particular isozyme. The essential part for such analysis is combining metabolic and transcriptomic data within the multi-level kinetic model. In our study we have focused on Synechocystis sp. PCC 6803, and eventually for other prokaryotes. Starting with Synechococcus 7942 reduces a risk of errors for more “prominent” species, cross-validate the gene annotation between species, double amount of processed metabolic and transcriptomic data and enable to explain the difference between both species, and eventually among other cyanobacteria and bacteria.The presented multi-level kinetic model introduces a new methodology identifying the iso-enzymatic regulation which will be employed for main cyanobacterial model organism, Finally, it might be possible to partially validate the model-based prediction by knocking down certain isozyme and making a metabolic and transcriptomic screening for at least two different conditions. Moreover, the model predicts changes in the level of metabolites, which are currently not quantified by the GC-MS-based metabolome protocol. Efforts to quantify those metabolites by alternative methods would represent another strategy for future model validation.Table S12.Metabolic data for transition phase 3 h after shifts from high to low CO(XLS)Click here for additional data file.File S1max parameters and transcriptomic weight factors.A list of reactions, including V(DOC)Click here for additional data file.Model S12 condition.The model of primary carbon metabolism in cyanobacterium Synechococcus elongatus PCC 7942 for high CO(XML)Click here for additional data file.Model S22 condition.The model of primary carbon metabolism in cyanobacterium Synechococcus elongatus PCC 7942 for low CO(XML)Click here for additional data file.