Advances in constraint-based models: methods for improved predictive power based on resource allocation constraints

The concept of metabolic models with resource allocation constraints has been around for over a decade and has clear advantages even when implementation is relatively rudimentary. Nonetheless, the number of organisms for which such a model is reconstructed is low. Various approaches exist, from coarse-grained consideration of enzyme usage to finegrained description of protein translation. These approaches are reviewed here, with a particular focus on user-friendly solutions that can introduce resource allocation constraints to metabolic models of any organism. The availability of kcat data is a major hurdle, where recent advances might help to fill in the numerous gaps that exist for this data, especially for nonmodel organisms

Stoichiometric representation of geneproteinreaction associations leverages constraint-based analysis from reaction to gene-level phenotype prediction

Genome-scale metabolic reconstructions are currently available for hundreds of organisms. Constraint-based modeling enables the analysis of the phenotypic landscape of these organisms, predicting the response to genetic and environmental perturbations. However, since constraint-based models can only describe the metabolic phenotype at the reaction level, understanding the mechanistic link between genotype and phenotype is still hampered by the complexity of gene-protein-reaction associations. We implement a model transformation that enables constraint-based methods to be applied at the gene level by explicitly accounting for the individual fluxes of enzymes (and subunits) encoded by each gene. We show how this can be applied to different kinds of constraint-based analysis: flux distribution prediction, gene essentiality analysis, random flux sampling, elementary mode analysis, transcriptomics data integration, and rational strain design. In each case we demonstrate how this approach can lead to improved phenotype predictions and a deeper understanding of the genotype-to-phenotype link. In particular, we show that a large fraction of reaction-based designs obtained by current strain design methods are not actually feasible, and show how our approach allows using the same methods to obtain feasible gene-based designs. We also show, by extensive comparison with experimental 13C-flux data, how simple reformulations of different simulation methods with gene-wise objective functions result in improved prediction accuracy. The model transformation proposed in this work enables existing constraint-based methods to be used at the gene level without modification. This automatically leverages phenotype analysis from reaction to gene level, improving the biological insight that can be obtained from genome-scale models.DM was supported by the Portuguese Foundationfor Science and Technologythrough a post-doc fellowship (ref: SFRH/BPD/111519/ 2015). This study was supported by the PortugueseFoundationfor Science and Technology (FCT) under the scope of the strategic fundingof UID/BIO/04469/2013 unitand COMPETE2020 (POCI-01-0145-FEDER-006684) and BioTecNorte operation (NORTE-01-0145FEDER-000004) fundedby EuropeanRegional Development Fund under the scope of Norte2020Programa Operacional Regional do Norte. This project has received fundingfrom the European Union’s Horizon 2020 research and innovation programme under grant agreementNo 686070. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Seeing the wood for the trees: a forest of methods for optimization and omic-network integration in metabolic modelling.

Metabolic modelling has entered a mature phase with dozens of methods and software implementations available to the practitioner and the theoretician. It is not easy for a modeller to be able to see the wood (or the forest) for the trees. Driven by this analogy, we here present a 'forest' of principal methods used for constraint-based modelling in systems biology. This provides a tree-based view of methods available to prospective modellers, also available in interactive version at http://modellingmetabolism.net, where it will be kept updated with new methods after the publication of the present manuscript. Our updated classification of existing methods and tools highlights the most promising in the different branches, with the aim to develop a vision of how existing methods could hybridize and become more complex. We then provide the first hands-on tutorial for multi-objective optimization of metabolic models in R. We finally discuss the implementation of multi-view machine learning approaches in poly-omic integration. Throughout this work, we demonstrate the optimization of trade-offs between multiple metabolic objectives, with a focus on omic data integration through machine learning. We anticipate that the combination of a survey, a perspective on multi-view machine learning and a step-by-step R tutorial should be of interest for both the beginner and the advanced user.This work was partially funded by a Teesside University doctoral scholarship, EPSRC, and the EU grant MIMOMICS

Predicting internal cell fluxes at sub-optimal growth

Background: Flux Balance Analysis (FBA) is a widely used tool to model metabolic behavior and cellular function. Applications of FBA span a breadth of research from synthetic engineering of biofuels to understanding evolutionary adaptations. FBA predicts metabolic reaction fluxes that optimize a given objective. This objective is generally defined for unicellular organisms by a theoretical reaction which simulates biomass production. FBA has been extremely successful at predicting in E. coli growth rates under different media and gene essentiality, amongst other things. In order to improve predictions, additional constraints are coupled with optimization of the biomass function. Studies have suggested, however, that unicellular organisms - like multicellular organisms - do not grow at optimal rates. To further improve FBA predictions, particularly of internal cell fluxes, new techniques to explore the sub-optimal solution space need to be developed. Results: We present an innovative FBA method called corsoFBA based on the optimization of protein cost at sub-optimal objective levels. Our method shows good agreement with experimental data of E. coli grown at different dilution rates. Maintaining the objective function close to its maximum value predicts metabolic states that closely resemble low dilution rates; while higher dilution rates can be mirrored by lowering the biomass production value. By using a modified version of Extreme Pathways, we are also able to quantify the energy production and overall protein cost for all possible pathways in the central carbon metabolism. Conclusion: Metabolic flux distributions at the optimal objective can be substantially different from the near-optimal distributions. Importantly, the behavior of E. coli central carbon metabolism can be better predicted by exploring the sub-optimal FBA solution space. The corsoFBA method presented here is able to predict the behavior of PEP Carboxylase, the glyoxylate shunt and the Entner-Doudoroff pathway at different glucose levels, a behavior not predicted by the minimization of metabolic steps and FBA alone. This technique can be used to better predict internal cell fluxes under different conditions, and corsoFBA will be of great help for the study of cells from multicellular organisms using Flux Balance Analysis