Exploiting biological processes to recycle renewable carbon into high value platform chemicals provides a sustainable and greener alternative to current reliance on petrochemicals. In this regard Cupriavidus necator H16 represents a particularly promising microbial chassis due to its ability to grow on a wide range of low-cost feedstocks, including the waste gas carbon dioxide, whilst also naturally producing large quantities of polyhydroxybutyrate (PHB) during nutrient-limited conditions. Understanding the complex metabolic behaviour of this bacterium is a prerequisite for the design of successful engineering strategies for optimising product yields. We present a genome-scale metabolic model (GSM) of C. necator H16 (denoted iCN1361), which is directly constructed from the BioCyc database to improve the readability and reusability of the model. After the initial automated construction, we have performed extensive curation and both theoretical and experimental validation. By carrying out a genome-wide essentiality screening using a Transposon-directed Insertion site Sequencing (TraDIS) approach, we showed that the model could predict gene knockout phenotypes with a high level of accuracy. Importantly, we indicate how experimental and computational predictions can be used to improve model structure and, thus, model accuracy as well as to evaluate potential false positives identified in the experiments. Finally, by integrating transcriptomics data with iCN1361 we create a condition-specific model, which, importantly, better reflects PHB production in C. necator H16. Observed changes in the omics data and in-silico-estimated alterations in fluxes were then used to predict the regulatory control of key cellular processes. The results presented demonstrate that iCN1361 is a valuable tool for unravelling the system-level metabolic behaviour of C. necator H16 and can provide useful insights for designing metabolic engineering strategies.

Abstract Motivation: In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis. Results: Elementary modes analysis (EMA) of a set of enzymes corresponding to the Krebs cycle, glycolysis and gluconeogenesis supports the scientific evidence showing that there is no pathway capable of converting acetyl-CoA to glucose at steady state. This conversion is possible after the addition of isocitrate lyase and malate synthase (forming the glyoxylate shunt) to the system. Dealing with the same example, we compare EMA with two tools based on graph theory available online, PathFinding and Pathway Hunter Tool. These automated network generating tools do not succeed in predicting the conversions known from experiment. They sometimes generate unbalanced paths and reveal problems identifying side metabolites that are not responsible for the carbon net flux. This shows that, for metabolic pathway analysis, it is important to consider the topology (including bimolecular reactions) and stoichiometry of metabolic systems, as is done in EMA. Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

Contact:[email protected]; [email protected] The main points of criticism by Faust et al. (2009) concerning the work in de Figueiredo et al., (2009a) are the following: the cases presented are biased; different tools should be supplied with the same input networks; the number of study cases should be representative; and tools should be evaluated by neutral assessors. We think that the models in de Figueiredo et al. (2009a) illustrate concrete biological problems that are very well documented. In particular, the conversion of fatty acids into sugars was not so trivial to be answered and is historically relevant (cf. Weinman et al., 1957). Today, many biochemistry textbooks dedicate at least one paragraph explaining why there is no net conversion of acetyl-CoA to glucose via the tricarboxylic acid cycle in vertebrates (cf. Nelson and Cox, 2000; Stryer, 1995; Voet and Voet, 2004). Thus, new tools for metabolic pathway prediction have to be able to answer these problems correctly. Analysing the same network used in (de Figueiredo et al., 2009a) by Path Finding (Croes et al., 2006), paths converting acetyl-CoA into glucose are computed, even though this is impossible for humans in the network studied. Thus, the critique of Faust et al. (2009) does not bring anything new to what was discussed in de Figueiredo et al. (2009a). It is often said that the size of the input network limits the computation of elementary flux modes (EFMs; Faust et al., 2009; Papin et al., 2003, 2004). Indeed, the enumeration of all EFMs in genome-scale models with the existing methods is difficult (Klamt et al., 2007; Schwarz et al., 2005; Terzer and Stelling, 2008; von Kamp and Schuster, 2006). However, there are approaches to compute at least a subset of EFMs in such models (Acuña et al., 2009; de Figueiredo et al., 2009b; Kaleta et al., 2009), for example, the shortest EFMs (de Figueiredo et al., 2009b). Regarding the number of test cases presented in (de Figueiredo et al., 2009a), we are sure they are representative of the issue that is discussed in that article. More cases exist, for example, the conversion of hypoxanthine into ATP in human erythrocytes, for which EFM analysis can be performed at the cell level (Schuster and Kenanov, 2005). Of course, a comparison between tools is preferably made by neutral assessors. However, it is usual in bioinformatics that authors who have established a new tool compare their method with others (Klamt et al., 2007; Urbanczik and Wagner, 2005; Wagner and Urbanczik, 2005). In addition, one co-author (C.K.) has written an article where EFMs are compared with chemical organizations (Kaleta et al., 2006). In the letter by Faust et al. (2009), it is argued that an incorrect definition of internal metabolites in EFM analysis, can generate wrong pathway predictions. The study of any biochemical system requires the definition of the system's boundary (see, e.g. Schilling and Palsson, 1998). Thus, the definition of internal and external metabolites in EFM analysis is nothing more than the definition of the boundary conditions found in many other modelling methods. Faust et al. (2009) say that the steady-state constraint is not always an appropriate assumption. Although, in some cases, this assumption is not justified, in many other cases, it is. Accordingly, it is used in many approaches such as Metabolic Control and Flux Balance Analyses. Faust et al. (2009) cite the work of Teusink et al. (2000) to support their statement. However, that work shows that the experimental system does reach a steady state. Additionally, we do not think that the study summarized in Table 1 of Faust et al. (2009) is exhaustive enough with respect to EFMs (cf. Trinh et al., 2009, for a review). Nevertheless, the communication from Faust et al. (2009) raises an important point concerning the comparison of tools for metabolic pathway prediction. It is suggested to follow a CASP-like protocol to evaluate the methods for metabolic pathway prediction and that this task should be performed by an independent committee. The validation process of some of the new tools for metabolic pathway prediction has been performed using the pathway information present in metabolic pathway databases (Blum and Kohlbacher, 2008; Croes et al., 2006). A CASP-like protocol, to be developed, has to take into account the fact that these databases contain errors (Likić, 2006; Poolman et al., 2006). On the other hand, only very well-documented pathways are stored in these databases. Many pathways are missing due to the lack of information or simply due to the fact that this classification is performed manually. Furthermore, these databases do not contain all the functional modes of a pathway within a metabolic network, e.g. all the five functional modes of the pentose phosphate pathway in conjunction with glycolysis (Schuster et al., 2000; Stryer, 1995). Moreover, EFM analysis has been successful in predicting relevant, hitherto unknown pathways, for example, the catabolic PEP-glyoxylate cycle in Escherichia coli (Schuster et al., 1999), which was later found in experiment (Fischer and Sauer, 2003) and that, to our knowledge, is not present in KEGG nor in MetaCyc (Caspi et al., 2008; Kanehisa et al., 2008). In conclusion, it is a challenge to represent the combinatorial multitude of biochemical pathways in metabolic databases (Sauer, 2006). Funding: PhD grant SFRH/BD/32961/2006 (to L.F.F.); by the following Portuguese entities: Fundaçãao Calouste Gulbenkian, Fundação para a Ciência e a Tecnologia (FCT) and Siemens SA Portugal (to L.F.F.); Biotechnology and Biosciences Research Council (BB/·E00203X/1 to D.A.F.); German Ministry for Research and Education (BMBF) within the Forsys Partner initiative (to C.K.). Conflict of Interest: none declared.

MOTIVATION: In recent years, several methods have been proposed for determining metabolic pathways in an automated way based on network topology. The aim of this work is to analyse these methods by tackling a concrete example relevant in biochemistry. It concerns the question whether even-chain fatty acids, being the most important constituents of lipids, can be converted into sugars at steady state. It was proved five decades ago that this conversion using the Krebs cycle is impossible unless the enzymes of the glyoxylate shunt (or alternative bypasses) are present in the system. Using this example, we can compare the various methods in pathway analysis. RESULTS: Elementary modes analysis (EMA) of a set of enzymes corresponding to the Krebs cycle, glycolysis and gluconeogenesis supports the scientific evidence showing that there is no pathway capable of converting acetyl-CoA to glucose at steady state. This conversion is possible after the addition of isocitrate lyase and malate synthase (forming the glyoxylate shunt) to the system. Dealing with the same example, we compare EMA with two tools based on graph theory available online, PathFinding and Pathway Hunter Tool. These automated network generating tools do not succeed in predicting the conversions known from experiment. They sometimes generate unbalanced paths and reveal problems identifying side metabolites that are not responsible for the carbon net flux. This shows that, for metabolic pathway analysis, it is important to consider the topology (including bimolecular reactions) and stoichiometry of metabolic systems, as is done in EMA. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Metabolic modelling provides a mathematically rigorous basis for system-level analysis of biochemical networks. However, the growing sizes of metabolic models can lead to serious problems in their construction and validation. In this work, we describe a relatively poorly investigated type of modelling error, called stoichiometric inconsistencies. These errors are caused by incorrect definitions of reaction stoichiometries and result in conflicts between two fundamental physical constraints to be satisfied by any valid metabolic model: positivity of molecular masses of all metabolites and mass conservation in all interconversions. RESULTS: We introduce formal definitions of stoichiometric inconsistencies, inconsistent net stoichiometries, elementary leakage modes and other important fundamental properties of incorrectly defined biomolecular networks. Algorithms are described for the verification of stoichiometric consistency of a model, detection of unconserved metabolites and inconsistent minimal net stoichiometries. The usefulness of these algorithms for effective resolving of inconsistencies and for detection of input errors is demonstrated on a published genome-scale metabolic model of Saccharomyces cerevisiae and one of Streptococcus agalactiae constructed using the KEGG database. AVAILABILITY: http://mudshark.brookes.ac.uk/index.php/Albert_Gevorgyan.