Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm.

Metabolic network modeling, especially Flux Balance Analysis (FBA), plays a critical role in systems biology by providing insights into cellular behaviors. Although FBA is the main tool for predicting flux distributions, it can face challenges capturing flux variations under different conditions. Selecting an appropriate objective function is therefore important for accurately representing system performance. To address this, we introduce a novel framework (e.g., TIObjFind) that imposes Metabolic Pathway Analysis (MPA) with Flux Balance Analysis (FBA) to analyze adaptive shifts in cellular responses throughout different stages of a biological system. This framework determines Coefficients of Importance (CoIs) that quantify each reaction's contribution to an objective function, aligning optimization results with experimental flux data. By examining Coefficients of Importance, TIObjFind enhances the interpretability of complex metabolic networks and provides insights into adaptive cellular responses.

Metabolic engineering principles have long been applied to explore the metabolic networks of complex microbial cell factories under a variety of environmental constraints for effective deployment of the microorganisms in the optimal production of biochemicals like biofuels, polymers, amino acids, recombinant proteins. One of the methodologies used for analyzing microbial metabolic networks is the Flux Balance Analysis (FBA), which employs applications of optimization techniques for forecasting biomass growth and metabolic flux distribution of industrially important products under specified environmental conditions. The in silico flux simulations are instrumental for designing the production-specific microbial cell factories. However, FBA has some inherent limitations. The present review emphasizes how the incorporation of additional kinetic, thermodynamic, expression and regulatory constraints and integration of omics data into the classical FBA platform improve the prediction accuracy of FBA. A programmed comparison of the simulated data with the experimental observations is presented for supporting the claim. The review further accounts for the successful implementation of classical FBA in biotechnological applications and identifies areas in which classical FBA fails to make correct predictions. The analysis of the predictive capabilities of the different FBA strategies presented here is expected to help researchers in finding new avenues in engineering highly efficient microbial metabolic pathways and identify the key metabolic bottlenecks during the process. Based on the appropriate metabolic network design, fermentation engineers will be able to effectively design the bioreactors and optimize large-scale biochemical production through suitable pathway modifications.

The modeling of rates of biochemical reactions-fluxes-in metabolic networks is widely used for both basic biological research and biotechnological applications. A number of different modeling methods have been developed to estimate and predict fluxes, including kinetic and constraint-based (Metabolic Flux Analysis and flux balance analysis) approaches. Although different resources exist for teaching these methods individually, to-date no resources have been developed to teach these approaches in an integrative way that equips learners with an understanding of each modeling paradigm, how they relate to one another, and the information that can be gleaned from each. We have developed a series of modeling simulations in Python to teach kinetic modeling, metabolic control analysis, 13C-metabolic flux analysis, and flux balance analysis. These simulations are presented in a series of interactive notebooks with guided lesson plans and associated lecture notes. Learners assimilate key principles using models of simple metabolic networks by running simulations, generating and using data, and making and validating predictions about the effects of modifying model parameters. We used these simulations as the hands-on computer laboratory component of a four-day metabolic modeling workshop and participant survey results showed improvements in learners' self-assessed competence and confidence in understanding and applying metabolic modeling techniques after having attended the workshop. The resources provided can be incorporated in their entirety or individually into courses and workshops on bioengineering and metabolic modeling at the undergraduate, graduate, or postgraduate level.

Flux balance analysis (FBA) of a genome-scale metabolic model allows calculation of intracellular fluxes by optimizing an objective function, such as maximization of cell growth, under given constraints, and has found numerous applications in the field of systems biology and biotechnology. Due to the underdetermined nature of the system, however, it has limitations such as inaccurate prediction of fluxes and existence of multiple solutions for an optimal objective value. Here, we report a strategy for accurate prediction of metabolic fluxes by FBA combined with systematic and condition-independent constraints that restrict the achievable flux ranges of grouped reactions by genomic context and flux-converging pattern analyses. Analyses of three types of genomic contexts, conserved genomic neighborhood, gene fusion events, and co-occurrence of genes across multiple organisms, were performed to suggest a group of fluxes that are likely on or off simultaneously. The flux ranges of these grouped reactions were constrained by flux-converging pattern analysis. FBA of the Escherichia coli genome-scale metabolic model was carried out under several different genotypic (pykF, zwf, ppc, and sucA mutants) and environmental (altered carbon source) conditions by applying these constraints, which resulted in flux values that were in good agreement with the experimentally measured (13)C-based fluxes. Thus, this strategy will be useful for accurately predicting the intracellular fluxes of large metabolic networks when their experimental determination is difficult.

BackgroundThe increase in glycerol obtained as a byproduct of biodiesel has encouraged the production of new industrial products, such as 1,3-propanediol (PDO), using biotechnological transformation via bacteria like Clostridium butyricum. However, despite the increasing role of Clostridium butyricum as a bio-production platform, its metabolism remains poorly modeled.ResultsWe reconstructed iCbu641, the first genome-scale metabolic (GSM) model of a PDO producer Clostridium strain, which included 641 genes, 365 enzymes, 891 reactions, and 701 metabolites. We found an enzyme expression prediction of nearly 84% after comparison of proteomic data with flux distribution estimation using flux balance analysis (FBA). The remaining 16% corresponded to enzymes directionally coupled to growth, according to flux coupling findings (FCF). The fermentation data validation also revealed different phenotype states that depended on culture media conditions; for example, Clostridium maximizes its biomass yield per enzyme usage under glycerol limitation. By contrast, under glycerol excess conditions, Clostridium grows sub-optimally, maximizing biomass yield while minimizing both enzyme usage and ATP production. We further evaluated perturbations in the GSM model through enzyme deletions and variations in biomass composition. The GSM predictions showed no significant increase in PDO production, suggesting a robustness to perturbations in the GSM model. We used the experimental results to predict that co-fermentation was a better alternative than iCbu641 perturbations for improving PDO yields.ConclusionsThe agreement between the predicted and experimental values allows the use of the GSM model constructed for the PDO-producing Clostridium strain to propose new scenarios for PDO production, such as dynamic simulations, thereby reducing the time and costs associated with experimentation.

BackgroundConstraint-based approaches facilitate the prediction of cellular metabolic capabilities, based, in turn on predictions of the repertoire of enzymes encoded in the genome. Recently, genome annotations have been used to reconstruct genome scale metabolic reaction networks for numerous species, including Homo sapiens, which allow simulations that provide valuable insights into topics, including predictions of gene essentiality of pathogens, interpretation of genetic polymorphism in metabolic disease syndromes and suggestions for novel approaches to microbial metabolic engineering. These constraint-based simulations are being integrated with the functional genomics portals, an activity that requires efficient implementation of the constraint-based simulations in the web-based environment.ResultsHere, we present Acorn, an open source (GNU GPL) grid computing system for constraint-based simulations of genome scale metabolic reaction networks within an interactive web environment. The grid-based architecture allows efficient execution of computationally intensive, iterative protocols such as Flux Variability Analysis, which can be readily scaled up as the numbers of models (and users) increase. The web interface uses AJAX, which facilitates efficient model browsing and other search functions, and intuitive implementation of appropriate simulation conditions. Research groups can install Acorn locally and create user accounts. Users can also import models in the familiar SBML format and link reaction formulas to major functional genomics portals of choice. Selected models and simulation results can be shared between different users and made publically available. Users can construct pathway map layouts and import them into the server using a desktop editor integrated within the system. Pathway maps are then used to visualise numerical results within the web environment. To illustrate these features we have deployed Acorn and created a web server allowing constraint based simulations of the genome scale metabolic reaction networks of E. coli, S. cerevisiae and M. tuberculosis.ConclusionsAcorn is a free software package, which can be installed by research groups to create a web based environment for computer simulations of genome scale metabolic reaction networks. It facilitates shared access to models and creation of publicly available constraint based modelling resources.

An increasing number of genome-scale reconstructions of intracellular biochemical networks are being generated. Coupled with these stoichiometric models, several systems-based approaches for probing these reconstructions in silico have been developed. One such approach, called flux balance analysis (FBA), has been effective at predicting systemic phenotypes in the form of fluxes through a reaction network. FBA employs a linear programming (LP) strategy to generate a flux distribution that is optimized toward a particular 'objective,' subject to a set of underlying physicochemical and thermodynamic constraints. Although classical FBA assumes steady-state conditions, several extensions have been proposed in recent years to constrain the allowable flux distributions and enable characterization of dynamic profiles even with minimal kinetic information. Furthermore, FBA coupled with techniques for measuring fluxes in vivo has facilitated integration of computational and experimental approaches, and is allowing pursuit of rational hypothesis-driven research. Ultimately, as we will describe in this review, studying intracellular reaction fluxes allows us to understand network structure and function and has broad applications ranging from metabolic engineering to drug discovery.

BackgroundGiven a genome-scale metabolic model (GEM) of a microorganism and criteria for optimization, flux balance analysis (FBA) predicts the optimal growth rate and its corresponding flux distribution for a specific medium. FBA has been extended to microbial consortia and thus can be used to predict interactions by comparing in-silico growth rates for co- and monocultures. Although FBA-based methods for microbial interaction prediction are becoming popular, a systematic evaluation of their accuracy has not yet been performed.ResultsHere, we evaluate the accuracy of FBA-based predictions of human and mouse gut bacterial interactions using growth data from the literature. For this, we collected 26 GEMs from the semi-curated AGORA database as well as four previously published curated GEMs. We tested the accuracy of three tools (COMETS, Microbiome Modeling Toolbox and MICOM) by comparing growth rates predicted in mono- and co-culture to growth rates extracted from the literature and also investigated the impact of different tool settings and media. We found that except for curated GEMs, predicted growth rates and their ratios (i.e. interaction strengths) do not correlate with growth rates and interaction strengths obtained from in vitro data.ConclusionsPrediction of growth rates with FBA using semi-curated GEMs is currently not sufficiently accurate to predict interaction strengths reliably.

Biological pathways provide intuitive frameworks to co-analyze system-wide transcriptomics, proteomics, and metabolomics measurements. Using our open-source pathway analysis platform, PathVisio, we bridge pathway analysis to the wealth of quantitative approaches already in development for metabolic network modelling, such as flux balance analysis and dynamic<br>simulation. Our focus is on the integrated visualization of the modelled and experimental results, which will be critical for understanding how simulated models correlate with experimental measurements.

BackgroundOptimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation.MethodsIn this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock.ResultsOur new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

Genome Scale Metabolic Modeling methods represent one way to compute whole cell function starting from the genome sequence of an organism and contribute towards understanding and predicting the genotype-phenotype relationship. About 80 models spanning all the kingdoms of life from archaea to eukaryotes have been built till date and used to interrogate cell phenotype under varying conditions. These models have been used to not only understand the flux distribution in evolutionary conserved pathways like glycolysis and the Krebs cycle but also in applications ranging from value added product formation in Escherichia coli to predicting inborn errors of Homo sapiens metabolism. This chapter describes a protocol that delineates the process of genome scale metabolic modeling for analysing host-pathogen behavior and interaction using flux balance analysis (FBA). The steps discussed in the process include (1) reconstruction of a metabolic network from the genome sequence, (2) its representation in a precise mathematical framework, (3) its translation to a model, and (4) the analysis using linear algebra and optimization. The methods for biological interpretations of computed cell phenotypes in the context of individual host and pathogen models and their integration are also discussed.

Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.

BackgroundCockroaches are terrestrial insects that strikingly eliminate waste nitrogen as ammonia instead of uric acid. Blattabacterium cuenoti (Mercier 1906) strains Bge and Pam are the obligate primary endosymbionts of the cockroaches Blattella germanica and Periplaneta americana, respectively. The genomes of both bacterial endosymbionts have recently been sequenced, making possible a genome-scale constraint-based reconstruction of their metabolic networks. The mathematical expression of a metabolic network and the subsequent quantitative studies of phenotypic features by Flux Balance Analysis (FBA) represent an efficient functional approach to these uncultivable bacteria.ResultsWe report the metabolic models of Blattabacterium strains Bge (iCG238) and Pam (iCG230), comprising 296 and 289 biochemical reactions, associated with 238 and 230 genes, and 364 and 358 metabolites, respectively. Both models reflect both the striking similarities and the singularities of these microorganisms. FBA was used to analyze the properties, potential and limits of the models, assuming some environmental constraints such as aerobic conditions and the net production of ammonia from these bacterial systems, as has been experimentally observed. In addition, in silico simulations with the iCG238 model have enabled a set of carbon and nitrogen sources to be defined, which would also support a viable phenotype in terms of biomass production in the strain Pam, which lacks the first three steps of the tricarboxylic acid cycle. FBA reveals a metabolic condition that renders these enzymatic steps dispensable, thus offering a possible evolutionary explanation for their elimination. We also confirm, by computational simulations, the fragility of the metabolic networks and their host dependence.ConclusionsThe minimized Blattabacterium metabolic networks are surprisingly similar in strains Bge and Pam, after 140 million years of evolution of these endosymbionts in separate cockroach lineages. FBA performed on the reconstructed networks from the two bacteria helps to refine the functional analysis of the genomes enabling us to postulate how slightly different host metabolic contexts drove their parallel evolution.

Improvements in melanoma diagnosis, treatment and prognosis are urgently warranted, given that it causes 3 out of 4 skin cancer deaths. A large amount of genomic and molecular data indicate that alterations occur at multiple scales in different stages of melanoma. Metabolic rewiring is a characteristic feature of progressive cancers that facilitates sustenance of tumors, and caters to the changing energy requirements. Since such rewiring involves multiple variations in the metabolic network that are orchestrated, a systems perspective is necessary to understand the nature, significance, mechanisms and identification of the key steps. To address this, we integrate patient transcriptome data with a prior human reference metabolic model and construct stage-specific genome-scale metabolic models. Using flux balance analysis, we simulate the metabolic flows and compute the reaction fluxes specific to normal skin, primary melanoma and metastatic melanoma, from which the reactions with flux differences between conditions were identified. Reactions related to Warburg effect, as anticipated and in addition, ROS detoxification and tyrosine metabolism were largely altered in all stages of melanoma. Vitamin A and vitamin C sub-systems are identified to be involved in different stages, consistent with experimental studies from literature that indicate their support to cancer progression. Gene essentiality studies using the melanoma model identified 5 important genes NME2, CMPK1, HSD17B4, DTYMK and PRODH for the proliferation of melanoma cells, which can be explored as potential drug targets.

The concept of elementary vector is generalised to the case where the steady-state space of the metabolic network is not a flux cone but is a general polyhedron due to further inhomogeneous constraints on the flows through some of the reactions. On one hand, this allows to selectively enumerate elementary modes which satisfy certain optimality criteria and this can yield a large computational gain compared with full enumeration. On the other hand, in contrast to the single optimum found by executing a linear program, this enables a comprehensive description of the set of alternate optima often encountered in flux balance analysis. The concepts are illustrated on a metabolic network model of human cardiac mitochondria.