dataesr/scientific-paragraphs-categorization huggingface dataset:
First, this study simulates different degrees of manual curation using the model Escherichia coli  [1]. For this purpose, 3,600 metabolic networks were generated from randomly degraded E. coli metabolic networks. In this benchmark, when the reference database used for completion was the real-case study Metacyc, Meneco outperformed the GapFill, the fastGapFill and the MIRAGE algorithms in terms of performance or accuracy. On a larger benchmark of 10,800 metabolic networks, our analysis suggests that Meneco is functionally relevant by identifying all essential reactions for more than 95% of the degraded networks. We advocate that the identification of such essential reactions is a key step towards the understanding of the metabolic capabilities of the species of interest, because they are related to key enzymes which, when removed, most likely prevent the viability of the species.
Our second case study presents the first metabolic network for E. mutabilis, based on transcript sequences assembled from previously published transcriptomic and metabolomic data  [18]   [19]. In order to complete this draft with Meneco, we selected a set of targets from the list of metabolites that E. mutabilis can accumulate or secrete in minimum mineral medium  [19]. Except for cobalamine, a cofactor that is not produced by this organism but is required for methionine synthesis, E. mutabilis can grow on a strictly mineral medium and is able to synthesize all the basic components of its biomass from mineral compounds only. Gaps in the draft network were filled iteratively with Meneco, using for each iteration a different subset of the 72 targets to solve the problem of cycles and circular dependencies.
Handling a real-scale reference completion database with gap-filling algorithms The gap-filling problem. Starting point for any metabolic gap-filling problem  [23]  is a draft GEM consisting of reactions and metabolites. A set of target metabolites (targets) that were experimentally shown to be produced by the organism of interest, possibly described as a linear combination of fluxes (e. g. , a biomass function), is used. A set of nutrients (seeds) describes the growth medium. Finally, a pool of metabolic reactions (reference database) is assumed to be available to fill the network. We assume that the draft GEM contains at least one blocked reaction with respect to the production of the targeted compounds from the seeds. In other word, there exists at least one targeted compound which does not admit a nonzero steady state flux.
A gap-filling method reports at least one reaction from the reference database that needs to be added such that at least one formerly blocked reaction can carry flux. Obviously, the solution to a gap-filling problem may not be unique. The sizes of both of the search space and the solution space for the gap-filling problem grow exponentially with the size of the reference database from which the reactions are taken. Any gap-filling method thus needs to find a suitable trade-off between the number of solutions reported by the method, that should not be too large to enable a manual curation, and their biological significance, in order to capture the main properties of the GEM being reconstructed. Gap-filling methods may report one, a few, or many sets of reactions to complete the draft GEM. When several solutions are produced by a gap-filling algorithm, there are no a priori criteria to select one rather than the other.
Then, a cautious strategy is to compute the set of all reactions contained in at least one solution reported by the algorithm and to manually curate them. Stoichiometry-based heuristics to approximate gap-filling solutions. Three main approaches can be distinguished according to the number of solutions they report and the characteristics of these solutions (see their main features in S1 Appendix). The associated tools were run on a toy example depicted in  Fig 1,  to produce the biomass constituents T 1 , T 2 , T 3. GapFill uses a parsimonious bottom-up strategies  [8, 10] , which enriches the draft metabolic network until the targeted properties are satisfied. More precisely, GapFill detects a minimal number of reactions from the reference database to enable the synthesis of the targeted compounds according to stoichiometry-based producibility constraints.
Importantly, GapFill allows the accumulation of internal compounds in the model. Applied to our toy Seeds (e. g. growth medium) and targets are S and T circles, respectively. The labels on the arrows depict the stoichiometry of the reactions. Green dotted arrows represent reactions that can be added to the network (reference database). The purple arrows represent reactions proposed by different gap-filling tools. GapFill (A) reported two reactions as a minimal completion and two different combinations to produce biomass from T 1 , T 2 and T 3 , {R 3 , R 7 } and {R 7 , R 8 }. fastGapFill (B) reports one unique set of seven reactions to unblock all reactions of the example: {R 1 , R 2 , R 3 , R 4 , R 6 , R 7 , R 9 }. It also add an import/export reaction for the reactant of the reaction producing T 3.
Then GapFill uses either the reaction R 8 or the reaction R 3 to produce T 2 since it considers T 3 as already producible despite a possible accumulation of the reactant of R 3. One limitation of this approach is that it reports a bounded (parameterized) number of solutions to the problem, although there is no a priori estimation of the number of iterations needed to solve the problem. fastGapFill  [9]  is an extension of the GapFill approach combined with the Fastcore algorithm, which eliminates the focus on the biomass production by identifying a single set of reactions which unblocks all reactions within the draft metabolic network. The price to pay is to allow import and export fluxes, especially to resolve issues related to the activation of isolated reactions in the GEM. When applied to our toy example, fastGapFill reported seven reactions from the reference database and one import/export reaction of the reactant of the reaction producing T 3 that was not present in the database to be added to the model.
A subset-minimal reaction set might include of a higher number of reactions but it is minimal in the sense that it loses its capability to restore biomass functionality as soon as any one reaction is removed from the set. As the number of such sets of reactions increases dramatically with the size of the reference database, MIRAGE samples the space of solutions by randomly iterating the search algorithm. In our toy example, the algorithm was iterated 100 times without applying a priori scores to reactions of the database. Four different sets of reactions were obtained {R 3 , R 7 }, {R 3 , R 6 , R 7 }, {R 3 , R 4 , R 7 } and {R 3 , R 7 , R 9 }. The reaction R 3 is mandatory to produce T 3 and it also produces T 2. Therefore, no other reaction producing T 2 is necessary, so that R 1 , R 2 , R 5 and R 8 were never used.
Given the cycle, the reaction R 7 would be the minimal completion to produce T 1 from a stoichiometric point of view, but the subsetminimality criterion also enables the MIRAGE algorithm to find the reactions R 4 , R 6 and R 7. Together, we noticed that the criteria used to complete the network highly impact on the reconstruction procedures which all report different solutions. In particular, the reaction R 5 is identified by none of the stoichiometry-based methods. Meneco: Using a topological over-approximation to enable an exhaustive enumeration of parsimonious solutions. Stoichiometry-based tools fail to address the fact that speciesspecificity of cofactors in the reactions is often not precisely described in databases neither is stoichiometry of reactions. This may lead to predictions errors for degraded metabolic networks while producing biomass.
doi:10. 1371/journal. pcbi. 1005276. g002 objective function was only formed by the reaction producing metabolite d, the only way to enable it from a stoichiometric point of view would be to have n = 1. Using a topologic based approach, d would be always producible from S. Based on this topological producibility criterion, Meneco uses the ASP paradigm  [29]  to efficiently model the logic of bio-synthetic producibility and to solve the gap-filling problem as a combinatorial optimization problem. For each network that does not satisfy this criterion, Meneco attempts to complete the network by importing minimal sets of reactions from a metabolic reference database such that the resulting network provides the required functionality with respect to topological metabolite producibility. The ASP technology is not only able to enumerate all minimal network completions, but also to compute the union and intersection of all minimal network completions without enumerating them, leading to strong gains in efficiency while still being exhaustive.
Together, we obtained a benchmark of 3,600 (40 Ã 90) GEMs. None was capable of producing the corresponding biomass. In order to complete these degraded metabolic networks, we selected the MetaCyc reference database (version 18. 5)  [17] , motivated by both its wide content (eukaryotic and prokaryotic reactions) and its accessibility (freely downloadable). This benchmark represents the usecase where the networks that must be gap-filled depict organisms that cannot be naturally associated to a precise phylogenetic taxa (see for example the case of E. siliculosus), requiring to explore all possible metabolic reactions to fill the network. The identifiers of iJR904 were manually mapped to identifiers of the MetaCyc database and both files were merged to create a complete reference database which contains all the reactions removed from the original GEM.
Meneco and fastGapFill efficiently complete GEMs using reference database of realistic size. The effect of the parsimonious criterion of Meneco, coupled with the fact that stoichoimetry information is not taken into account, can be seen in the benchmark in S1 Appendix. In this benchmark we completed 10,800 degraded E. coli networks with the Meta-Cyc database. The completion was performed using either the fastGapFill, MIRAGE or Meneco tools. Even if this comparison is not entirely representative due to the different backgrounds and aims of the methods, it is worth noting that Meneco in general selected smaller sets of reactions to complete the networks compared to the other methods. Indeed, on average, Meneco returned answers 8 times smaller than fastGapFill and 125 times smaller than MIRAGE.
Between 10% and 40% of reactions were removed from E. coli iJR904 reference network in order to block the FBA-based production of 40 different biomass functions. For each degraded GEM, both the Meneco and fastGapFill tools were used to restore the producibility of the biomass by picking reactions from the MetaCyc database. For 10% of the degraded GEMs in the benchmark, the MIRAGE tool was also tested. database) for gap-filling and that the algorithm needs all the recommended data (phylogenetic and/or transcriptomic scores) to perform correctly and gain robustness.
Functionality analysis: Meneco recovers essential reactions of a metabolic network Our results suggest that the topological parsimony criterion used in Meneco provides a good trade-off in terms of scalability with respect to the size of the reference database used for completion: the output of Meneco remains reasonable in terms of size (for an a posteriori manual curation), with a reasonable loss of impact on the restoration of biomass production compared to parsimonious approaches. To further evaluate the quality of the output of Meneco, we completed the 3,600 degraded GEMs of our benchmark derived from the iJ904 E. coli metabolic network by 7,200 (2 Ã 3,600) additional degraded GEMs of the iAF1260  [32]  and iJO1366  [33]  E. coli networks. The Meneco tool was applied to complete each of the 10,800 degraded GEMs by using the networks prior to degradation as a reference database.
The main motivation for changing the reference database was to be able to analyze how the classification of reactions into essential, alternative and blocked with respect to biomass production evolved with the completion process. Impact of the gap-filled network and the reference database. The results of the completion procedure detailed in Sections 2 and 5 in S1 Appendix show that the quality of the network used to generate the benchmark has a low impact on the size of the Meneco output, even if the size of the solution set increased linearly with the degradation rate of the network. Nevertheless, the quality of the reference E. coli network has a strong impact on the quality of the results as shown in Identification of essential and alternative reactions with Meneco. The reactions of the 40 degraded iJR904 were classified according to their functionality with respect to the production of their associated 90 random biomass functions.
For this purpose, we considered, as a fixed set of seeds, molecules found in the seawater medium and commonly used to grow these organisms  [21]. In parallel, we designed a large set of targets by identifying all reactions in MetaCyc 19. 0 for which at least one of the associated genes was supported by the presence of one or more expressed sequence tag (EST) within the dataset of 90,637 ESTs published in the original Ectocarpus genome paper  [34]. For each of these expressed reactions, we considered that both reactants and products should be available in the network and defined them as targets. Using Meneco we then identified which of these targets were producible in two situations. Firstly, we used as a draft network the algal network itself, more precisely a version of EctoGEM 1. 0  [21]  for which no functional gap-filling had been carried out.
mutabilis to be built based on metabolomic and de novo transcriptomic data As a second case study, we focused on the reconstruction of a metabolic network for E. mutabilis, a photosynthetic protist and primary producer in acidic aquatic environments. Despite important roles of E. mutabilis in those ecosystems and despite the fact that it has often been considered as an indicator species for acid mine drainages, this organism has been poorly described so far. Due to their complexity and size, no genome sequences are available so far within the genus Euglena. Therefore, we used assembled transcript sequences as described in  [18]  and annotated them by similarity search against enzyme reference sequences from MetaCyc. We used a stringent similarity threshold for function assignation to reduce as much as possible the rate of false positive reactions included in the initial network that was subsequently completed by Meneco.
Test of the completed draft network with FBA. Once all the targets could be produced by the network using the Meneco criteria, we proceeded to verify whether it was functional in FBA. We created 10 import reactions (8 for mineral nutrients, one for light, and one for oxygen to enable respiration), a biomass reaction, and 54 output reactions for the 54 metabolites that were experimentally shown to be secreted by E. mutabilis. Forty dead-end metabolites, i. e. non-consumed products that may prevent the network from satisfying the stoichiometric constraints for the production of target metabolites (secreted metabolites and biomass) were identified manually and defined as boundaries (boundaryCondition="true"). Additionally, three reactions (FLAVONADPREDUCT-RXN, RXN0-882, RXN-9944) were added to the network in order to regenerate reduced flavodoxins, oxidized ferredoxins, and thioredoxin since the corresponding transcripts could be identified in the transcriptome.
Positioning of Meneco in the landscape of gap-filling methods Most gap-filling methods solve optimization problems over a search space whose size grows exponentially with the size of the reference database from which the reactions are taken. Two different strategies can then be used to explore the search space and compute solution sets to a gap-filling problem: either a parsimonious bottom-up strategy which enriches the draft metabolic network until the targeted properties are satisfied  [8, 10, 27] , or a top-down approach starting from all available information and removing reactions without added-value to the solution of the problem  [15, 23, 24]. Bottom-up methods often report few solutions and may miss alternative ones while top-down approaches capture more solutions but are computationally demanding, and sometimes require sampling of the solution space.
Conclusion As stated by Satish Kumar et al. in  [8] , "clearly, the role of a gap-filling method is to simply pinpoint a number of hypotheses which need to subsequently be tested". In this line of research, the Meneco tool constitutes a flexible framework to pinpoint hypotheses in the context of largescale datasets applied to newly investigated organisms. Meneco is a versatile tool to complete draft GEMs and to suggest relevant reactions with respect to the response of the system to environmental perturbations. Importantly, it does not aim at providing a complete functional network, but rather at pointing out essential reactions and some of the alternative ones, which are crucial to explain the system response. It can be then combined with refined stoichiometry-based analyses and gap-filling methods to produce functional networks.
In this sense, we promote Meneco as a tool to be used as an intermediary step within a workflow consisting of (i) producing a draft GEM  [5, 38] , (ii) parsimonious gapfilling based on metabolite profiles or RNA-seq datasets with Meneco, (iii) refinement of the model with stoichiometric-based approaches relying on additional data ([14]  [13] ), and (iv) manual curation process of metabolic networks described in  [1]. From a biological point of view, the examples show that Meneco cannot replace manual curation and network analysis, but it may provide a flexible tool to aid this process. Analyses are fast, easy to implement, and invaluable because they enable biologists to focus their attention on a few highly interesting compounds and reactions without making a priori assumptions.
Following  [25] [26] [27] , the (forward) scope of a set of metabolites S according to a reaction set R contains all metabolites which can be iteratively produced from the seed metabolites. It is the set of metabolites reachable from S through the reactions in R and can be defined by iterating the set relation M i+1 = M i [ prod({r 2 R|m 2 reac(M i ), 8m, (r, m) 2 E}), with M O = S until it reaches a fixed point. The scope can be computed in polynomial time. We assume that we are given (i) a draft network R draft ; (ii) a set M target & M of target metabolites that are produced by the organism of interest; (iii) a set M seed & M of seed nutrients found in the growth medium; and (iv) a database of metabolic reactions available to fill the network R database. The topological gap-filling problem is stated as follows.
Minimize SizeðR fill Þ s:t R fill & R database M target \ scope R fill [R draft ðM seed Þ is maximal ( This combinatorial problem, expressed as a logic encoding, is solved by the ASP solver clasp 3. 0. 5  [39]  with domain specific heuristics i. e. search space exploration strategies, preserving correctness and completeness of the search procedure. Clasp allows the computation of the brave and cautious consequences (union and intersection of all solutions) by means of a linear number of calls to a solver (internally computing one solution) rather than enumerating the entirety of all solutions. This is accomplished by consecutive refinements of an internal constraint by relying on the incremental solving techniques introduced in  [40]. Rather than computing a (possibly) exponentially increasing number of solutions, the idea is to compute a first solution, to record a constraint, eliminate it from further solutions, then to compute a second solution to strengthen the constraint in order to represent the intersection (or union) of the first two solutions, and to continue until no more solutions are obtained.
This process involves computing at most as many solutions as there are logic variables in the input program. Depending on the chosen reasoning mode, either the cautious (properties shared by all solutions) or the brave (properties satisfied by at least a solution) consequences are then given by the variable assignment captured by the final constraint. This process enable all cardinal minimal solutions to be found but does not allow finding suboptimal solutions. The ASP encoding, and the solver are encapsulated in a python package named Meneco  [27, 41]  which is freely available at http://bioasp. github. io/meneco. Experiments related to the E. coli benchmark were run on a node of 24 cores part of a computational cluster. Case studies were run on personal laptops: the computation time required to get the union of solutions was less than 30 seconds.
Stoichiometric gap-filling problem. A stoichiometric metabolic network can be viewed as an enrichment of a topological metabolic network with a stoichiometric matrix S. Under steady state conditions, metabolite balances yield ∑ j2R S ij v j = b j for all i 2 M where b i is a parameter standing for uptake or secretion. In this setting, the stoichiometric gap-filling problem consists in minimizing the number of added reactions from the database to restore fluxes through a metabolite i Ã which is not producible from the draft metabolic network. Minimize SizeðR fill Þ s:t : X j2R fill [R draft S ij v j 0 8 i 2 M seed X j2R fill [R draft S ij v j ¼ 0 8 i 6 ¼ iÃ X j2R fill [R draft S iÃj v j > 0 8 > > > > < > > > > : This problem is solved by the so-called GapFill tool, encoded in a GAMS (General Algebraic Modeling System) program  [8].
To solve this optimization problem, solutions to the stoichiometric gap-filling problems for each individual target were computed by running the GAMS encoding from  [8]  on the NEOS server  [42]. For each execution of the GAMS encoding, the program computed at most 30 sets of solutions to the gapfilling problem. The solution to the gap-filling problem was defined as the union of all reaction sets. Subset-minimal gap-filling. The MIRAGE algorithm was run to perform a subset-minimal gap-filling using the implementation provided in  [14]. Without any a priori information on the importance of the reactions in the draft networks, the biomass reaction was the only one added in the core reactions. The weights for all reactions of the databases were assigned to 1. To be able to run the software on a computer cluster, the code was compiled with the mcc function of MATLAB (R2014a).
Networks and datasets E. coli degraded metabolic networks. We analyzed the following GEMs of E. coli: iJR904  [44] , iAF1260  [32]  and iJO1366  [33]. The corresponding sbml files were downloaded from the associated publications or from the USCD repository USCD repository. To test the impact of the MetaCyc database on the gapfilling problem, cross-references between the SBML identifiers of metabolites (SBML species) in the networks and MetaCyc identifiers were created. To that end, we followed an iterative strategy based first on metabolite names and formulas, then on similar reactions. For the three E. coli models iJR904, iAF1260 and iJO1366, we generated 90 random biomass functions obtained by setting a defined percentage of non-zero coefficients of the true biomass to zero. The choice of replaced non-zero coefficients relied on Bernoulli-distributed random binary numbers.