Constraint-based metabolic modeling methods such as Flux Balance Analysis (FBA) are routinely used to predict the effects of genetic changes and to design strains with desired metabolic properties. The major bottleneck in modeling genome-scale metabolic systems is the establishment and manual curation of reliable stoichiometric models. Initial reconstructions are typically refined through comparisons to experimental growth data from gene knockouts or nutrient environments. Existing methods iteratively correct one erroneous model prediction at a time, resulting in accumulating network changes that are often not globally optimal. We present GlobalFit, a bi-level optimization method that finds a globally optimal network, by identifying the minimal set of network changes needed to correctly predict all experimentally observed growth and non-growth cases simultaneously. When applied to the genome-scale metabolic model of Mycoplasma genitalium, GlobalFit decreases unexplained gene knockout phenotypes by 79%, increasing accuracy from 87. 3% (according to the current state-of-the-art) to 97. 3%. While currently available computers do not allow a global optimization of the much larger metabolic network of E. coli, the main strengths of GlobalFit are already played out when considering only one growth and one non-growth case simultaneously. Application of a corresponding strategy halves the number of unexplained cases for the already highly curated E. coli model, increasing accuracy from 90. 8% to 95. 4%.
Metabolism is the best understood large cellular system. Genome-scale metabolic models that largely rely on constraints for mass balance (i. e. , all internal metabolites that are produced must also be consumed) are routinely applied to predict a wide range of metabolic phenomena [1]. The most widely-used of these constraint-based methods, Flux Balance Analysis (FBA), has been successfully applied to predict a range of biological phenomena such as gene knockout effects [1] and the evolutionary adaptation of microbial strains [2–4], and has been employed to predict drug targets [5] and to design microbial strains for bioengineering [6]. Network models are reconstructed by supplementing genomic annotation with information from biochemical characterizations and the organism-specific literature [7]. The resulting draft reconstructions often contain gaps: the modeled organism or its gene knockout strain can grow in vivo, while the model is unable to produce biomass in silico in the same metabolic environment (false-negative predictions, FNp). Gap filling methods have been introduced to resolve individual FNp through a minimal number of network changes, making irreversible reactions reversible or adding reactions from a database [8–11]. A second type of inconsistencies is the erroneous prediction of growth where the experiment shows no growth (false-positive predictions, FPp). Such cases can be rectified by deleting reactions, making reversible reactions unidirectional, or adding metabolites to the biomass (all reactions necessary for the production of a given metabolite become essential once this metabolite is added to the biomass). GrowMatch [12], the current state-of-the-art in automatic network refinement, uses bi-level optimization to identify reactions that must be deleted or modified for each FPp. GrowMatch also allows to add to the biomass products and/or substrates of reactions that are experimentally essential but are blocked in the model [12]. All currently available methods for network refinement based on growth data are greedy algorithms, solving one inconsistency between model and experiment at a time [8–15]. While each individual set of network changes is minimal, the union of these sets can become larger than a minimal set of changes that solves all inconsistencies simultaneously. Reactions considered essential or model changes introduced early may make the reconciliation of FNp or FPp considered later impossible (for an example, see our application to Mycoplasma genitalium below). Furthermore, experimental errors that happen to be consistent with the initial model can severely bias the results. Moreover, previous methods only alter the biomass equation independently of other network modifications [12,16] and may miss solutions that combine biomass and network changes.
We present GlobalFit, a novel bi-level optimization method capable of comparing flux-balance analysis (FBA) [17] model predictions to measured growth across all tested environments and gene knockouts (or subsets thereof) simultaneously. Allowed model changes are (i) removals or (ii) reversibility changes of existing reactions; (iii) additions of reactions to the model from a database of potential reactions; (iv) removals of metabolites from the biomass; and (v) additions of metabolites to the biomass. GlobalFit does not change gene-protein-reaction associations (GPRs), and thus isoenzymes should be identified and included in the model as a preprocessing step. The algorithm is first formulated as a bi-level linear problem, where each condition is represented by separate metabolites and fluxes (see the detailed method description in Methods). To ensure in silico growth for conditions with experimentally demonstrated growth, the biomass production for these conditions must be greater than a predefined threshold. For non-growth phenotypes, the inner optimization problem maximizes the biomass production to check whether it stays below a non-growth threshold. The outer optimization problem jointly minimizes the number of model changes and the number of experiments that are incorrectly predicted by the final model. The penalties for individual network changes can be set independently. This allows, for example, to prefer reversibility changes over reaction additions, to preferentially remove reactions not associated with a gene, or to preferentially include additional reactions from metabolic network reconstructions of close relatives (see some suggestions for setting these penalties in the S1 Table). The bi-level problem can be re-formulated as a single-level optimization problem [18]; a corresponding implementation of GlobalFit, integrated with the sybil toolbox for constraint-based analyses [19], is freely available from CRAN (http: //cran. r-project. org/web/packages/GlobalFit/). While GlobalFit is designed to find globally optimal network modifications by considering all experimental data simultaneously, the corresponding MILP problem rapidly becomes prohibitively large when considering high-throughput gene knockout data. For example, simultaneously considering all possible 1366 E. coli knockouts [20] with 4000 allowed network modifications would result in a matrix with 13 million columns by 37 million rows, a problem size not addressable with current computing infrastructures. However, when searching for model changes that rectify a FPp, trivial but unhelpful solutions such as the deletion of essential reactions are already avoided by simultaneously requiring growth in one or more specified true positive cases. When searching for model changes that rectify a FNp, overly generous changes (such as the removal of metabolites from the biomass) are avoided by simultaneously requiring non-growth in one or more specified true negative cases. Thus, while a globally optimal solution is only guaranteed when simultaneously considering all experimental growth data, a good approximation may be found by solving subsets of inconsistencies. We explore this “subset strategy” below in our application to the E. coli genome-scale model. We suggest contrasting each individual FPp with a wild-type growth case (or, if growth was assayed on different media, with a small set of wild-type growth cases). FNp may first be solved alone. However, if a suggested solution for a FNp or a FPp converts other previously correct predictions to false predictions (TPp to FNp or TNp to FPp), the originally considered case should be solved again, this time contrasting it with the complete set of these conflicting cases. This last step must be repeated until no more additional false predictions occur (or until no solution is found). The runtime of MILP solvers depends crucially on the number of binary variables. Importantly, this number depends only on the number of allowed changes (plus a single binary variable for the inclusion/exclusion of each growth/non-growth case). Thus, a MILP strategy that considers n possible model changes for a single growth/non-growth case solves a problem with n binary variables. In comparison, the number of binary variables in a GlobalFit run that considers n possible model changes and contrasts m growth and non-growth cases is n+m. The number of binary variables can be further reduced by a set of preprocessing steps (Methods). When reconciling a metabolic network with experimental data, the most parsimonious network modifications are not always those that best describe the true metabolic system. GlobalFit can also provide a specified number of alternative optimal or sub-optimal solutions (using the integer cut method). Thus, users can choose the solution (s) that best agree with available evidence, or design additional experiments that distinguish between competing network modifications. In cases where all suggested alternatives appear excessive or unrealistic, users may also consider modifying individual GPR rules. The runtime for n alternative solutions is approximately n times the runtime for a single optimum. In the test cases reported below, we only examined a small range of alternative solutions and did not consider manual modifications. We first applied GlobalFit to the genome-scale metabolic network of Mycoplasma genitalium [21], using the same gene knockout essentiality data [22] as the initial reconstruction with GrowMatch (reported by [21] to have a global accuracy of 87. 3%, corresponding to a Matthew’s correlation coefficient, a more balanced measure of classification quality [23], of MCC = 0. 56; Table 1). The growth medium used for the knockout experiments was chemically undefined [22]. When applying GlobalFit, we thus allowed the uptake of all nutrients for which transport reactions are included in the model. All other FBA parameters were set to the values used in [21]. The initial network obtained from [21] was not able to produce biomass; to rectify this problem, we had to convert three irreversible reactions (ZN2t4, INSK, LYSt3) to reversible reactions. With these modifications, the original model [21] has an accuracy of 85% and a Matthews’ correlation coefficient MCC = 0. 44. False predictions mainly occurred in the form of FPp, i. e. , by incorrectly establishing growth in silico where a lethal phenotype was observed in vivo (Table 1). To construct a database of potential additional reactions, we started from all reactions contained in metabolic networks provided by the BiGG database [24]. We removed globally blocked reactions, i. e. , those reactions of the database that were not able to carry any flux in a supernetwork containing all reactions. Reversible reactions were represented as two independent irreversible reactions, corresponding to forward and backward directions. The database is provided as S2 Database of the supplementary material. In our first analysis, we used a very restrictive, conservative set of potential network changes: (i) addition of reactions from other network reconstructions that are catalyzed by enzymes with significant sequence similarity to the M. genitalium genome (BLAST e-value <10−13); (ii) conversion of irreversible to reversible reactions for reactions that are at least classified as reversible with uncertainty in the E. coli model [25]; (iii) removal of reactions (separately for individual reaction directions for reversible reactions); (iv) removal of biomass components; and (v) addition of biomass components that occur in the biomass of other network reconstructions [16,20,24]. In this application, we assigned the same penalty (1. 0) for all changes. However, as the growth medium used in the knockout experiments was undefined, we assigned a lower penalty (0. 1) for the removal of exchange reactions. Thus, removal of a metabolite from the representation of the undefined medium (corresponding to the removal of an exchange reaction) was preferred to the removal of the corresponding transporter. To test the applicability of GlobalFit’s subset strategy to larger models, we next applied it to the most recent genome-scale metabolic reconstruction for E. coli, iJO1366 [20]. Again, we employed the same gene knockout essentiality data [30,31] as used in the initial reconstruction. For all FBA simulations, we used the same parameters as described in [20]. The maximal influx of all nutrients in the defined growth media was set to 10 mmol gDW-1h-1. The lower bound of the non-growth associated maintenance reaction (ATPM) was set to 3. 15 mmol gDW-1h-1. Gene essentiality was then calculated by FBA, considering any flux larger than 5% of the optimal biomass core reaction as growth. For the published iJO1366 model, we obtained the same accuracies as reported originally [20]: a combined global accuracy of 90. 8% calculated across knockout experiments on glucose and on glycerol media, corresponding to a Matthew’s correlation coefficient MCC = 0. 67 (Table 3). In the application of GlobalFit to the iJO1366 model, we only allowed conservative network modifications (as defined for the M. genitalium model). However, as the growth medium used in the E. coli experiments was chemically defined, we did not allow the removal of exchange reactions. We constructed a database of potential new reactions as for M. genitalium (S2 Database). The knockout data for E. coli includes growth data on two different media that contained either glucose or glycerol as carbon sources [30,31]. Accordingly, we solved all FPp against two wild-type growth cases, one on glucose and one on glycerol. While this increases the number of continuous variables compared to using only a single wild-type growth case, the number of binary variables is still the same as in algorithms that only consider a single non-growth case at a time [12] (note that we don’t allow the exclusion of any growth/non-growth case in this application). We tested if the order in which false growth/non-growth predictions are considered in GlobalFit’s subset strategy affects the final result; this was not the case. By applying the network modifications suggested by GlobalFit, we could strongly increase the quality of predictions for growth on both glycerol and glucose (Table 3); for the experiments on glucose and on glycerol combined, accuracy increased from 90. 8% to 95. 4%, while Matthew’s correlation coefficient increased from 0. 67 to 0. 84. The detailed model changes are outlined below.
In this work, we describe and implement a novel algorithm to automatically modify metabolic network models based on growth/non-growth data. The algorithm can utilize data from different growth environments and/or different gene knockouts. In contrast to previous approaches, the “global” mode of GlobalFit does not reconcile the network model with inconsistent experiments iteratively, but finds a globally minimal set of network changes that resolves all inconsistencies simultaneously (in so far as the inconsistencies are resolvable with the allowed model modifications). To make GlobalFit applicable to large metabolic network reconstructions, we also explored a subset strategy, where individual false predictions are solved simultaneously with small subsets of growth/non-growth cases. We demonstrate the utility of these approaches through applications to the previously published network models of M. genitalium [21] (optimizing model predictions for gene knockout data from Ref. [22]) and E. coli [20] (utilizing gene knockout data from Ref. [30,31]). Allowing only highly conservative network changes (e. g. , only adding reactions catalyzed by enzymes that are homologous to genes of the species studied), we were able to halve the number of false growth predictions in each case. Overall, GlobalFit improved the accuracy of growth/non-growth predictions for M. genitalium from 87. 3% to 93. 6% (MCC from 0. 56 to 0. 68) and for E. coli from 90. 8% to 95. 4% (MCC from 0. 67 to 0. 84). If we allow a much wider range of possible network modifications—which is routinely done in alternative approaches [12,21]–even higher accuracies can be achieved. Importantly, GlobalFit can enumerate alternative optimal or sub-optimal solutions, such that expert knowledge or additional experiments can help select the biologically most realistic modifications. For some inconsistencies, we found solutions that improved accuracy on one medium while decreasing accuracy on the other. For example, adding selenium to the biomass reaction of E. coli would resolve three FPp on glycerol, while converting four TPp to FNp on glucose. Thus, the accuracy achievable for one growth medium could be further improved by sacrificing the accuracy for the other medium, albeit at a likely loss of biological correctness. This observation emphasizes the utility of combining gene knockout data across different nutritional environments to avoid problems of overfitting. In other cases, several genes whose products act together in a protein complex had contradictory experimental results: in the same medium, some were found to be essential, while the rest was declared non-essential. Such contradictions may be caused either by experimental errors, by erroneous assignment of genes to reactions (incorrect GPRs), or by a residual function of the enzyme complex even with some of its components missing. GlobalFit may suggest a solution in this case, but this will simultaneously distort one or more true predictions. For example, the FPp for the E. coli gene b3560 (the α-subunit of glycine tRNA synthetase) could be resolved by adding the charged and uncharged glycine tRNA to the biomass reaction as substrate and product, respectively. This modification would at the same time transform the TPp of b3559 (the β-subunit) to a FNp, and would thus not improve accuracy. In the applications of GlobalFit, we adopted the in silico growth cutoffs used in the original model publications, i. e. , one third of the mean growth rate for M. genitalium [21] and 5% of the optimal biomass core reaction for E. coli [20]. A more general way to resolve FPp would be to treat the cutoff that distinguishes in silico growth from non-growth as an additional variable in the optimizations. For example, the knockout of E. coli ATPS4rpp reduced the biomass yield in glycerol below 10% of the wild-type yield. Such a substantial reduction in growth rate may explain why 6 out of 8 knockouts for the genes involved in the corresponding enzyme complex were labeled as essential in the experiment; however, following [20] in considering 5% biomass production as growth, we regarded these knockouts as FPp in this study. An adjustable growth threshold might have rectified these FPp cases without any model changes. It is not clear a priori which in silico cutoff corresponds best to a given set of experimental data. Thus identifying the cutoff value that minimizes the necessary model changes seems most appropriate. In this paper, we have explored the application of GlobalFit to the improvement of existing metabolic network reconstructions and showed that it can substantially reduce the number of false growth predictions even when restricted to conservative network changes. It is conceivable that GlobalFit can also be employed for other tasks related to metabolic model refinement. One possible such application is the initial reconstruction of a metabolic network model starting from a computer-generated template that is based on genome annotation (such as provided, e. g. , by the SEED algorithm [33]). GlobalFit might also be used to remove thermodynamically impossible energy-creating cycles, which sometimes plague initial network reconstructions. While we only score growth and non-growth, GlobalFit could also be applied using yield data by choosing appropriate thresholds. Finally, we envisage future usage of GlobaFit for strain optimization in metabolic engineering applications that combine gene knockouts [34] with gene additions.
GlobalFit compares flux-balance analysis (FBA) [17] model predictions to measured growth across all tested environments and gene knockouts simultaneously. Allowed model changes are (i) removals or (ii) reversibility changes of existing reactions; (iii) additions of reactions to the model from a database of potential reactions; (iv) removals of metabolites from the biomass; and (v) additions of metabolites to the biomass. We thus solve the following bi-level problem: min→δ (∑y∈M (δyRF+δyRB) ×wyR+∑x∈IδxI×wxI+∑z∈Dδzadd×wzadd+∑j∈ASδjAS×wjAS+∑k∈APδkAP×wkAP+∑l∈BSδlRS×wlRS+∑m∈APδmRP×wmRP+∑g∈GδgG×wgG+∑h∈NδhN×whN) (1) subject to: ∀g∈GS×vg=0 (2) ∀h∈GS×vh=0 (3) ∀y∈M, g∈G∪N vymin× (1−δyRB) ≤ vyg≤ vymax× (1−δyRF) (4) ∀x∈I, g∈G∪N−1000×δxI≤vxg (5) ∀z∈D, g∈G∪N 0≤ vzg≤1000×δzadd (6) ∀y∈M, g∈G∪N∑l∈BS (1−δlRS) ×clRS+∑j∈ASδjAS×cjAS→vBiog∑m∈BP (1−δmRP) ×cmRP+∑k∈APδkAP×ckAP (7) ∀g∈G (vBiog+1000× δBioiG≥ Tg) (8) ∀h∈N (v^Bioh−1000× δBioiN≤ Th) (9) with: Inner Problem: v^Bioh∶= maxv→hvBioh, (10) subject to: Eqs (3) – (7) and to the definitions following below. Line (7) defines the flux through the biomass reaction, vBiog, for condition g. The sets used in this system of equations are listed in Table 9, while the parameters are defined in Table 10. For binary variables, 1 corresponds to TRUE (i. e. , a model change is executed), while 0 corresponds to FALSE (no change compared to the initial network). What is the purpose of each of the lines in the above system of equations? The network must be in a steady state (i. e. , no concentration changes to internal metabolites) in all conditions g ∈ G Eq (2) and h ∈ N Eq (3) that are to be solved simultaneously. Lines (4) – (6) convert the binary variables for the removal or reversibility change of existing reactions, and for the addition of new reactions from the database, into constraints for the respective fluxes. In Eq (4), if δyRB=0 (i. e. , no change), then the lower limit for reaction y in all conditions g (vyg) remains at the predefined limit vymin; setting δyRB=1 instead sets the lower flux limit to 0, i. e. , removes the backwards reaction. Similarly, setting δyRF=0 keeps the upper flux limit for reaction y at the predefined limit vymax, while setting δyRF=1 sets the upper flux limit to 0, i. e. , removes the forward reaction. Line (5) sets the lower flux limit to -1000 for reaction y in all conditions g if δxI=1, i. e. , it makes an irreversible reaction (with flux vxg≥0) reversible in this case. Line (6) allows non-zero (positive) flux for reactions that are not part of the original (input) model if δzadd=1. Note that in the database of additional potential reactions, we consider bidirectional reactions as two separate reactions corresponding to forward and backward directions (both with fluxes ≥0). Metabolites can be removed from both sides of the biomass reaction (flux vBiog), and additional metabolites can be added Eq (7) with pre-specified stoichiometric coefficients c. To ensure in silico growth for conditions with experimentally demonstrated growth, the biomass flux for these conditions must be greater than a predefined threshold Tg in all conditions g ∈ G Eq (8). Conversely, to ensure in silico non-growth for conditions with experimentally demonstrated non-growth, the biomass flux for these condition must be less than a predefined threshold Th in all conditions h ∈ N Eq (9). The thresholds Tg and Th can be set separately for each phenotype, e. g. , to account for estimates of experimental errors. For non-growth phenotypes, a simple condition that forces the biomass production to be lower than a threshold is not sufficient, though, as a trivial solution with v→h=0 would satisfy this condition. To overcome this problem, the inner optimization problem maximizes the biomass production of non-growth cases Eq (9), and this maximum is compared against the non-growth threshold. Line (1) describes the outer optimization problem. GlobalFit aims to find a solution that is able to correctly predict all growth and non-growth cases with a minimal number of network changes (indicated by values 1 for the binary variables): δyRF, δyRB, δxI, δzadd, δjAS, δkAP, δlRS, δmRP, δgG, δhN The penalties for each type of network change, and even for each individual change, can be set independently. This allows, for example, to prefer reversibility changes over reaction additions, or to preferentially include new reactions with stronger genomic evidence, or reactions from metabolic network reconstructions of close relatives. Users should choose appropriate penalties based on the details of the network reconstruction and the proposed changes. As a starting point, we include a list of suggested penalty values in S1 Table). To guarantee a feasible solution, even if inconsistent growth cases are used, we implemented additional binary variables that allow the exclusion of individual growth (δgG Eq (8) ) and non-growth cases (δhN Eq (9) ) from the growth threshold conditions. In our application to the M. genitalium network, we penalize these condition exclusions with very high values wgG and whN; thus, any network modification that explains additional cases is preferred over the exclusion of conditions, regardless of the number of required changes. Instead, the penalties can be set to smaller values, so that the exclusion of potentially erroneous experiments is preferred over excessive network changes. Metabolic network reconciliation with large-scale experimental data usually incorporates a manual curation stage, where experts for the physiology and biochemistry of the organism under study review network changes suggested by automated methods. To support this process, GlobalFit can put out not just one best solution, but, e. g. , the five best solutions that can then be reviewed to identify the changes most compatible with existing knowledge. To speed up the calculations, network changes can also be limited to a maximal number. No efficient software tools for general bi-level optimization problems are available. Solving the inner problem for each possible combination of network changes would be computationally too slow. We adapt the “Reduction Ansatz” of Section 4. 3. 4 in [18] to eliminate the inner problem in line (9). In this approach, the optimality conditions of the inner optimization problem are expressed as equality and inequality conditions using additional “dual” variables. For fixed δ→ and h, the inner problem is simply a linear program; thus, the assumptions in [18] are trivially satisfied. Because of the use of binary variables, algorithms to solve this type of optimization problem are termed mixed integer linear programming (MILP). MILP is NP hard [35]; while no known algorithms can guarantee to find a solution efficiently, algorithms that work well for many practical problems exist in software solvers. We used the solver of IBM ILOG CPLEX 12. 5; to avoid trickle flow, we implemented indicator constraints. Alternatively, our implementation of GlobalFit also allows using the GUROBI solver. Academic users can obtain both CPLEX and GUROBI free of charge. The search for a globally minimal set of network changes is a computationally very intensive task. To speed up this process, it is advisable to restrict the examined conditions to a maximal consistent (“feasible”) set, i. e. , a maximal set of conditions that can all be correctly predicted with the same modified metabolic network (regardless of the type and number of modifications). To identify such feasible condition sets, GlobalFit provides a simple mode, which only minimizes the number of erroneous predictions of growth regardless of the number of network changes. To speed up the calculation of a feasible condition set, it is possible to first solve individual wrong predictions against a “control” condition, thereby identifying conditions that cannot be reconciled with the network with the allowed modifications. We applied this strategy for the pre-processing of the M. genitalium data (see Results). Furthermore, the number of binary variables can be reduced by a set of additional preprocessing steps. First, binary variables for changes to the network not allowed (such as reversibility changes to reactions strictly considered irreversible) should be constrained to zero. Second, we can consider a “supermodel” that encompasses the input model with all allowed reactions converted to reversible reactions and all reactions from the database of potential additional reactions. We can then reduce the number of binary variables further by (i) excluding all reactions that are blocked in this supermodel, (ii) constraining to zero the binary variables for the removal of reactions that are essential in this supermodel. GlobalFit can optionally calculate a user-defined number n of alternative optimal or suboptimal solutions. The search for alternative solutions is executed using the integer cuts method. Thus, the complexity for each additional alternative solution is only increased through a single linear constraint. Consequently, the runtime for n alternative optimal or suboptimal solutions is approximately n times the runtime for a single optimum. We provide an implementation of GlobalFit, integrated with the sybil toolbox for constraint-based analyses [19], which runs in the R environment for statistical computing [36]. The source code and documentation is available free of charge from CRAN (http: //cran. r-project. org/web/packages/GlobalFit/). The optimized models for E. coli and M. genitalium are provided as SBML files that can be read, e. g. , by sybil [19] and the COBRA toolbox [37].
Mathematical models that aim to describe the complete metabolism of a cell help us understand cellular metabolic capabilities and evolution, and aid the biotechnological design of microbial strains with desired properties. Draft models are frequently improved through adjustments that increase the agreement of growth/non-growth predictions with observations from gene knockout experiments. Automated methods for this task typically correct one erroneous prediction after the other. We present GlobalFit, a novel method that can consider all experiments and all possible changes simultaneously to identify model modifications that are globally optimal (i. e. , that correct the largest possible number of wrong predictions while introducing sets of changes that are most compatible with existing knowledge). This becomes computationally very hard when considering large metabolic models; however, a reduced application of GlobalFit that only looks at small subsets of experiments simultaneously works very well in practice. Allowing only changes that are conservative (e. g. , introducing new reactions only if supported by significant genomic evidence), GlobalFit halves the number of wrong growth/non-growth predictions for the state-of-the-art metabolic models of E. coli and Mycoplasma genitalium, increasing prediction accuracy to 95. 4% and 93. 0%, respectively. By additionally allowing less conservative changes, we are able to improve accuracy further to 97. 3% for the M. genitalium model.
medicine and health sciences
chemical compounds
metabolic networks
gene knockout
carbohydrates
organic compounds
glucose
genomic databases
optimization
monomers (chemistry)
metabolites
mathematics
network analysis
genome analysis
molecular biology techniques
pharmacology
drug metabolism
research and analysis methods
polymer chemistry
computer and information sciences
biological databases
chemistry
artificial genetic recombination
molecular biology
pharmacokinetics
biochemistry
organic chemistry
database and informatics methods
glycerol
genetics
monosaccharides
biology and life sciences
physical sciences
genomics
metabolism
computational biology
Improved Metabolic Models for E. coli and Mycoplasma genitalium from GlobalFit, an Algorithm That Simultaneously Matches Growth and Non-Growth Data Sets