Flux balance analysis: a geometric perspective

Predicting microbial interactions with approaches based on flux balance analysis: an evaluation

BACKGROUND

Given 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.

RESULTS

Here, 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.

CONCLUSIONS

Prediction of growth rates with FBA using semi-curated GEMs is currently not sufficiently accurate to predict interaction strengths reliably.

Applications of genome-scale metabolic models to investigate microbial metabolic adaptations in response to genetic or environmental perturbations

Environmental perturbations are encountered by microorganisms regularly and will require metabolic adaptations to ensure an organism can survive in the newly presenting conditions. In order to study the mechanisms of metabolic adaptation in such conditions, various experimental and computational approaches have been used. Genome-scale metabolic models (GEMs) are one of the most powerful approaches to study metabolism, providing a platform to study the systems level adaptations of an organism to different environments which could otherwise be infeasible experimentally. In this review, we are describing the application of GEMs in understanding how microbes reprogram their metabolic system as a result of environmental variation. In particular, we provide the details of metabolic model reconstruction approaches, various algorithms and tools for model simulation, consequences of genetic perturbations, integration of '-omics' datasets for creating context-specific models and their application in studying metabolic adaptation due to the change in environmental conditions.

Characterizing cancer metabolism from bulk and single-cell RNA-seq data using METAFlux

Cells often alter metabolic strategies under nutrient-deprived conditions to support their survival and growth. Characterizing metabolic reprogramming in the tumor microenvironment (TME) is of emerging importance in cancer research and patient care. However, recent technologies only measure a subset of metabolites and cannot provide in situ measurements. Computational methods such as flux balance analysis (FBA) have been developed to estimate metabolic flux from bulk RNA-seq data and can potentially be extended to single-cell RNA-seq (scRNA-seq) data. However, it is unclear how reliable current methods are, particularly in TME characterization. Here, we present a computational framework METAFlux (METAbolic Flux balance analysis) to infer metabolic fluxes from bulk or single-cell transcriptomic data. Large-scale experiments using cell-lines, the cancer genome atlas (TCGA), and scRNA-seq data obtained from diverse cancer and immunotherapeutic contexts, including CAR-NK cell therapy, have validated METAFlux's capability to characterize metabolic heterogeneity and metabolic interaction amongst cell types.

Genome-scale metabolic network models: from first-generation to next-generation

Over the last two decades, thousands of genome-scale metabolic network models (GSMMs) have been constructed. These GSMMs have been widely applied in various fields, ranging from network interaction analysis, to cell phenotype prediction. However, due to the lack of constraints, the prediction accuracy of first-generation GSMMs was limited. To overcome these limitations, the next-generation GSMMs were developed by integrating omics data, adding constrain condition, integrating different biological models, and constructing whole-cell models. Here, we review recent advances of GSMMs from the first generation to the next generation. Then, we discuss the major application of GSMMs in industrial biotechnology, such as predicting phenotypes and guiding metabolic engineering. In addition, human health applications, including understanding biological mechanisms, discovering biomarkers and drug targets, are also summarized. Finally, we address the challenges and propose new trend of GSMMs. KEY POINTS: •This mini-review updates the literature on almost all published GSMMs since 1999. •Detailed insights into the development of the first- and next-generation GSMMs. •The application of GSMMs is summarized, and the prospects of integrating machine learning are emphasized.

Constraint-Based Reconstruction and Analyses of Metabolic Models: Open-Source Python Tools and Applications to Cancer

The influence of metabolism on signaling, epigenetic markers, and transcription is highly complex yet important for understanding cancer physiology. Despite the development of high-resolution multi-omics technologies, it is difficult to infer metabolic activity from these indirect measurements. Fortunately, genome-scale metabolic models and constraint-based modeling provide a systems biology framework to investigate the metabolic states and define the genotype-phenotype associations by integrations of multi-omics data. Constraint-Based Reconstruction and Analysis (COBRA) methods are used to build and simulate metabolic networks using mathematical representations of biochemical reactions, gene-protein reaction associations, and physiological and biochemical constraints. These methods have led to advancements in metabolic reconstruction, network analysis, perturbation studies as well as prediction of metabolic state. Most computational tools for performing these analyses are written for MATLAB, a proprietary software. In order to increase accessibility and handle more complex datasets and models, community efforts have started to develop similar open-source tools in Python. To date there is a comprehensive set of tools in Python to perform various flux analyses and visualizations; however, there are still missing algorithms in some key areas. This review summarizes the availability of Python software for several components of COBRA methods and their applications in cancer metabolism. These tools are evolving rapidly and should offer a readily accessible, versatile way to model the intricacies of cancer metabolism for identifying cancer-specific metabolic features that constitute potential drug targets.

Modeling energy depletion in rat livers using Nash equilibrium metabolic pathway analysis

The current gold standard of Static Cold Storage (SCS), which is static cold storage on ice (about + 4 °C) in a specialized media such as the University of Wisconsin solution (UW), limits storage to few hours for vascular and metabolically active tissues such as the liver and the heart. The liver is arguably the pinnacle of metabolism in human body and therefore metabolic pathway analysis immediately becomes very relevant. In this article, a Nash Equilibrium (NE) approach, which is a first principles approach, is used to model and simulate the static cold storage and warm ischemia of a proposed model of liver cells. Simulations of energy depletion in the liver in static cold storage measured by ATP content and energy charge are presented along with comparisons to experimental data. In addition, conversion of Nash Equilibrium iterations to time are described along with an uncertainty analysis for the parameters in the model. Results in this work show that the Nash Equilibrium approach provides a good match to experimental data for energy depletion and that the uncertainty in model parameters is very small with percent variances less than 0.1%.

Rapid intensification of an established CHO cell fed-batch process

Currently, the mammalian biomanufacturing industry explores process intensification (PI) to meet upcoming demands of biotherapeutics while keeping production flexible but, more importantly, as economic as possible. However, intensified processes often require more development time compared with conventional fed‐batches (FBs) preventing their implementation. Hence, rapid and efficient, yet straightforward strategies for PI are needed. In this study we demonstrate such a strategy for the intensification of an N‐stage FB by implementing N‐1 perfusion cell culture and high inoculum cell densities resulting in a robust intensified FB (iFB). Furthermore, we show successful combination of such an iFB with the addition of productivity enhancers, which has not been reported so far. The conventional CHO cell FB process was step‐wise improved and intensified rapidly in multi‐parallel small‐scale bioreactors using N‐1 perfusion. The iFBs were performed in 15 and 250 ml bioreactors and allowed to evaluate the impact on key process indicators (KPI): the space–time yield (STY) was successfully doubled from 0.28 to 0.55 g/L d, while product quality was maintained. This gain was generated by initially increasing the inoculation density, thus shrinking process time, and second supplementation with butyric acid (BA), which reduced cell growth and enhanced cell‐specific productivity from ~25 to 37 pg/(cell d). Potential impacts of PI on cell metabolism were evaluated using flux balance analysis. Initial metabolic differences between the standard and intensified process were observed but disappeared quickly. This shows that PI can be achieved rapidly for new as well as existing processes without introducing sustained changes in cellular and metabolic behavior.

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.

Metabolic flux configuration determination using information entropy

Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli’s glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.

A Distance-Based Framework for the Characterization of Metabolic Heterogeneity in Large Sets of Genome-Scale Metabolic Models

Gene expression and protein abundance data of cells or tissues belonging to healthy and diseased individuals can be integrated and mapped onto genome-scale metabolic networks to produce patient-derived models. As the number of available and newly developed genome-scale metabolic models increases, new methods are needed to objectively analyze large sets of models and to identify the determinants of metabolic heterogeneity. We developed a distance-based workflow that combines consensus machine learning and metabolic modeling techniques and used it to apply pattern recognition algorithms to collections of genome-scale metabolic models, both microbial and human. Model composition, network topology and flux distribution provide complementary aspects of metabolic heterogeneity in patient-specific genome-scale models of skeletal muscle. Using consensus clustering analysis we identified the metabolic processes involved in the individual responses to endurance training in older adults.

Metabolic control analysis of L-tryptophan production with Escherichia coli based on data from short-term perturbation experiments

E. coli strain NT1259 /pF112aroFBL_kan was able to produce 14.3 g L^-1 L-tryptophan within 68 h in a fed-batch process from glycerol on a 15 L scale. To gain detailed insight into metabolism of this E. coli strain in the fed-batch process, a sample of L-tryptophan producing cells was withdrawn after 47 h, was separated rapidly and then resuspended in four parallel stirred-tank bioreactors with fresh media. Four different carbon sources (glucose, glycerol, succinate, pyruvate) were supplied individually with varying feeding rates within 19 min and the metabolic reactions of the cells in the four parallel reactors were analyzed by quantification of extracellular and intracellular substrate, product and metabolite concentrations. Data analysis allowed the estimation of intracellular carbon fluxes and of thermodynamic limitations concerning intracellular concentrations and reaction energies. Carbon fluxes and intracellular metabolite concentrations enabled the estimation of elasticities and flux control coefficients by applying metabolic control analysis making use of a metabolic model considering 48 enzymatic reactions and 56 metabolites. As the flux control coefficients describe connections between enzyme activities and metabolic fluxes, they reveal genetic targets for strain improvement. Metabolic control analysis of the recombinant E. coli cells withdrawn from the fed-batch production process clearly indicated that (i) the supply of two precursors for L-tryptophan biosynthesis, L-serine and phosphoribosyl-pyrophosphate, as well as (ii) the formation of aromatic byproducts and (iii) the enzymatic steps of igps and trps2 within the L-tryptophan biosynthesis pathway have major impact on fed-batch production of L-tryptophan from glycerol and should be the targets for further strain improvements.

Human Systems Biology and Metabolic Modelling: A Review-From Disease Metabolism to Precision Medicine

In cell and molecular biology, metabolism is the only system that can be fully simulated at genome scale. Metabolic systems biology offers powerful abstraction tools to simulate all known metabolic reactions in a cell, therefore providing a snapshot that is close to its observable phenotype. In this review, we cover the 15 years of human metabolic modelling. We show that, although the past five years have not experienced large improvements in the size of the gene and metabolite sets in human metabolic models, their accuracy is rapidly increasing. We also describe how condition-, tissue-, and patient-specific metabolic models shed light on cell-specific changes occurring in the metabolic network, therefore predicting biomarkers of disease metabolism. We finally discuss current challenges and future promising directions for this research field, including machine/deep learning and precision medicine. In the omics era, profiling patients and biological processes from a multiomic point of view is becoming more common and less expensive. Starting from multiomic data collected from patients and N-of-1 trials where individual patients constitute different case studies, methods for model-building and data integration are being used to generate patient-specific models. Coupled with state-of-the-art machine learning methods, this will allow characterizing each patient's disease phenotype and delivering precision medicine solutions, therefore leading to preventative medicine, reduced treatment, and in silico clinical trials.

An Improved Genome-Scale Metabolic Model of Arthrospira platensis C1 (iAK888) and Its Application in Glycogen Overproduction

Glycogen-enriched biomass of Arthrospiraplatensis has increasingly gained attention as a source for bioethanol production. To study the metabolic capabilities of glycogen production in A. platensis C1, a genome-scale metabolic model (GEM) could be a useful tool for predicting cellular behavior and suggesting strategies for glycogen overproduction. New experimentally validated GEM of A. platensis C1 namely iAK888, which has improved metabolic coverage and functionality was employed in this research. The iAK888 is a fully functional compartmentalized GEM consisting of 888 genes, 1,096 reactions, and 994 metabolites. This model was demonstrated to reasonably predict growth and glycogen fluxes under different growth conditions. In addition, iAK888 was further employed to predict the effect of deficiencies of NO₃⁻, PO₄³⁻, or SO₄²⁻ on the growth and glycogen production in A. platensis C1. The simulation results showed that these nutrient limitations led to a decrease in growth flux and an increase in glycogen flux. The experiment of A. platensis C1 confirmed the enhancement of glycogen fluxes after the cells being transferred from normal Zarrouk’s medium to either NO₃⁻, PO₄³⁻, or SO₄²⁻-free Zarrouk’s media. Therefore, iAK888 could be served as a predictive model for glycogen overproduction and a valuable multidisciplinary tool for further studies of this important academic and industrial organism.

A Review of Dynamic Modeling Approaches and Their Application in Computational Strain Optimization for Metabolic Engineering

Mathematical modeling is a key process to describe the behavior of biological networks. One of the most difficult challenges is to build models that allow quantitative predictions of the cells' states along time. Recently, this issue started to be tackled through novel in silico approaches, such as the reconstruction of dynamic models, the use of phenotype prediction methods, and pathway design via efficient strain optimization algorithms. The use of dynamic models, which include detailed kinetic information of the biological systems, potentially increases the scope of the applications and the accuracy of the phenotype predictions. New efforts in metabolic engineering aim at bridging the gap between this approach and other different paradigms of mathematical modeling, as constraint-based approaches. These strategies take advantage of the best features of each method, and deal with the most remarkable limitation—the lack of available experimental information—which affects the accuracy and feasibility of solutions. Parameter estimation helps to solve this problem, but adding more computational cost to the overall process. Moreover, the existing approaches include limitations such as their scalability, flexibility, convergence time of the simulations, among others. The aim is to establish a trade-off between the size of the model and the level of accuracy of the solutions. In this work, we review the state of the art of dynamic modeling and related methods used for metabolic engineering applications, including approaches based on hybrid modeling. We describe approaches developed to undertake issues regarding the mathematical formulation and the underlying optimization algorithms, and that address the phenotype prediction by including available kinetic rate laws of metabolic processes. Then, we discuss how these have been used and combined as the basis to build computational strain optimization methods for metabolic engineering purposes, how they lead to bi-level schemes that can be used in the industry, including a consideration of their limitations.

In silico engineering of Pseudomonas metabolism reveals new biomarkers for increased biosurfactant production

BACKGROUND

Rhamnolipids, biosurfactants with a wide range of biomedical applications, are amphiphilic molecules produced on the surfaces of or excreted extracellularly by bacteria including Pseudomonas aeruginosa. However, Pseudomonas putida is a non-pathogenic model organism with greater metabolic versatility and potential for industrial applications.

METHODS

We investigate in silico the metabolic capabilities of P. putida for rhamnolipids biosynthesis using statistical, metabolic and synthetic engineering approaches after introducing key genes (RhlA and RhlB) from P. aeruginosa into a genome-scale model of P. putida. This pipeline combines machine learning methods with multi-omic modelling, and drives the engineered P. putida model toward an optimal production and export of rhamnolipids out of the membrane.

RESULTS

We identify a substantial increase in synthesis of rhamnolipids by the engineered model compared to the control model. We apply statistical and machine learning techniques on the metabolic reaction rates to identify distinct features on the structure of the variables and individual components driving the variation of growth and rhamnolipids production. We finally provide a computational framework for integrating multi-omics data and identifying latent pathways and genes for the production of rhamnolipids in P. putida.

CONCLUSIONS

We anticipate that our results will provide a versatile methodology for integrating multi-omics data for topological and functional analysis of P. putida toward maximization of biosurfactant production.

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures-Systems biology-based interpretation using genome-scale metabolic flux balance model and multivariate data analysis

Genome-scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745-753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome-scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163-1173, 2016.

E-Flux2 and SPOT: Validated Methods for Inferring Intracellular Metabolic Flux Distributions from Transcriptomic Data

Background

Several methods have been developed to predict system-wide and condition-specific intracellular metabolic fluxes by integrating transcriptomic data with genome-scale metabolic models. While powerful in many settings, existing methods have several shortcomings, and it is unclear which method has the best accuracy in general because of limited validation against experimentally measured intracellular fluxes.

Results

We present a general optimization strategy for inferring intracellular metabolic flux distributions from transcriptomic data coupled with genome-scale metabolic reconstructions. It consists of two different template models called DC (determined carbon source model) and AC (all possible carbon sources model) and two different new methods called E-Flux2 (E-Flux method combined with minimization of l² norm) and SPOT (Simplified Pearson cOrrelation with Transcriptomic data), which can be chosen and combined depending on the availability of knowledge on carbon source or objective function. This enables us to simulate a broad range of experimental conditions. We examined E. coli and S. cerevisiae as representative prokaryotic and eukaryotic microorganisms respectively. The predictive accuracy of our algorithm was validated by calculating the uncentered Pearson correlation between predicted fluxes and measured fluxes. To this end, we compiled 20 experimental conditions (11 in E. coli and 9 in S. cerevisiae), of transcriptome measurements coupled with corresponding central carbon metabolism intracellular flux measurements determined by ¹³C metabolic flux analysis (¹³C-MFA), which is the largest dataset assembled to date for the purpose of validating inference methods for predicting intracellular fluxes. In both organisms, our method achieves an average correlation coefficient ranging from 0.59 to 0.87, outperforming a representative sample of competing methods. Easy-to-use implementations of E-Flux2 and SPOT are available as part of the open-source package MOST (http://most.ccib.rutgers.edu/).

Conclusion

Our method represents a significant advance over existing methods for inferring intracellular metabolic flux from transcriptomic data. It not only achieves higher accuracy, but it also combines into a single method a number of other desirable characteristics including applicability to a wide range of experimental conditions, production of a unique solution, fast running time, and the availability of a user-friendly implementation.

Rapid Prediction of Bacterial Heterotrophic Fluxomics Using Machine Learning and Constraint Programming

13C metabolic flux analysis (13C-MFA) has been widely used to measure in vivo enzyme reaction rates (i.e., metabolic flux) in microorganisms. Mining the relationship between environmental and genetic factors and metabolic fluxes hidden in existing fluxomic data will lead to predictive models that can significantly accelerate flux quantification. In this paper, we present a web-based platform MFlux (http://mflux.org) that predicts the bacterial central metabolism via machine learning, leveraging data from approximately 100 13C-MFA papers on heterotrophic bacterial metabolisms. Three machine learning methods, namely Support Vector Machine (SVM), k-Nearest Neighbors (k-NN), and Decision Tree, were employed to study the sophisticated relationship between influential factors and metabolic fluxes. We performed a grid search of the best parameter set for each algorithm and verified their performance through 10-fold cross validations. SVM yields the highest accuracy among all three algorithms. Further, we employed quadratic programming to adjust flux profiles to satisfy stoichiometric constraints. Multiple case studies have shown that MFlux can reasonably predict fluxomes as a function of bacterial species, substrate types, growth rate, oxygen conditions, and cultivation methods. Due to the interest of studying model organism under particular carbon sources, bias of fluxome in the dataset may limit the applicability of machine learning models. This problem can be resolved after more papers on 13C-MFA are published for non-model species.

Flux Balance Analysis of Plant Metabolism: The Effect of Biomass Composition and Model Structure on Model Predictions

The biomass composition represented in constraint-based metabolic models is a key component for predicting cellular metabolism using flux balance analysis (FBA). Despite major advances in analytical technologies, it is often challenging to obtain a detailed composition of all major biomass components experimentally. Studies examining the influence of the biomass composition on the predictions of metabolic models have so far mostly been done on models of microorganisms. Little is known about the impact of varying biomass composition on flux prediction in FBA models of plants, whose metabolism is very versatile and complex because of the presence of multiple subcellular compartments. Also, the published metabolic models of plants differ in size and complexity. In this study, we examined the sensitivity of the predicted fluxes of plant metabolic models to biomass composition and model structure. These questions were addressed by evaluating the sensitivity of predictions of growth rates and central carbon metabolic fluxes to varying biomass compositions in three different genome-/large-scale metabolic models of Arabidopsis thaliana. Our results showed that fluxes through the central carbon metabolism were robust to changes in biomass composition. Nevertheless, comparisons between the predictions from three models using identical modeling constraints and objective function showed that model predictions were sensitive to the structure of the models, highlighting large discrepancies between the published models.

A Method of Accounting for Enzyme Costs in Flux Balance Analysis Reveals Alternative Pathways and Metabolite Stores in an Illuminated Arabidopsis Leaf

Flux balance analysis of plant metabolism is an established method for predicting metabolic flux phenotypes and for exploring the way in which the plant metabolic network delivers specific outcomes in different cell types, tissues, and temporal phases. A recurring theme is the need to explore the flexibility of the network in meeting its objectives and, in particular, to establish the extent to which alternative pathways can contribute to achieving specific outcomes. Unfortunately, predictions from conventional flux balance analysis minimize the simultaneous operation of alternative pathways, but by introducing flux-weighting factors to allow for the variable intrinsic cost of supporting each flux, it is possible to activate different pathways in individual simulations and, thus, to explore alternative pathways by averaging thousands of simulations. This new method has been applied to a diel genome-scale model of Arabidopsis (Arabidopsis thaliana) leaf metabolism to explore the flexibility of the network in meeting the metabolic requirements of the leaf in the light. This identified alternative flux modes in the Calvin-Benson cycle revealed the potential for alternative transitory carbon stores in leaves and led to predictions about the light-dependent contribution of alternative electron flow pathways and futile cycles in energy rebalancing. Notable features of the analysis include the light-dependent tradeoff between the use of carbohydrates and four-carbon organic acids as transitory storage forms and the way in which multiple pathways for the consumption of ATP and NADPH can contribute to the balancing of the requirements of photosynthetic metabolism with the energy available from photon capture.

Design Principles as a Guide for Constraint Based and Dynamic Modeling: Towards an Integrative Workflow

During the last 10 years, systems biology has matured from a fuzzy concept combining omics, mathematical modeling and computers into a scientific field on its own right. In spite of its incredible potential, the multilevel complexity of its objects of study makes it very difficult to establish a reliable connection between data and models. The great number of degrees of freedom often results in situations, where many different models can explain/fit all available datasets. This has resulted in a shift of paradigm from the initially dominant, maybe naive, idea of inferring the system out of a number of datasets to the application of different techniques that reduce the degrees of freedom before any data set is analyzed. There is a wide variety of techniques available, each of them can contribute a piece of the puzzle and include different kinds of experimental information. But the challenge that remains is their meaningful integration. Here we show some theoretical results that enable some of the main modeling approaches to be applied sequentially in a complementary manner, and how this workflow can benefit from evolutionary reasoning to keep the complexity of the problem in check. As a proof of concept, we show how the synergies between these modeling techniques can provide insight into some well studied problems: Ammonia assimilation in bacteria and an unbranched linear pathway with end-product inhibition.

In silico analysis of bioethanol overproduction by genetically modified microorganisms in coculture fermentation

Lignocellulosic biomass is an attractive sustainable carbon source for fermentative production of bioethanol. In this context, use of microbial consortia consisting of substrate-selective microbes is advantageous as it eliminates the negative impacts of glucose catabolite repression. In this study, a detailed in silico analysis of bioethanol production from glucose-xylose mixtures of various compositions by coculture fermentation of xylose-selective Escherichia coli strain ZSC113 and glucose-selective wild-type Saccharomyces cerevisiae is presented. Dynamic flux balance models based on available genome-scale metabolic networks of the microorganisms have been used to analyze bioethanol production and the maximization of ethanol productivity is addressed by computing optimal aerobic-anaerobic switching times. A set of genetic engineering strategies for ethanol overproduction by E. coli strain ZSC113 have been evaluated for their efficiency in the context of batch coculture process. Finally, simulations are carried out to determine the pairs of genetically modified E. coli strain ZSC113 and S. cerevisiae that significantly enhance ethanol productivity in batch coculture fermentation.

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology

Background

Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions.

Results

Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker’s yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation.

Conclusions

This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0144-4) contains supplementary material, which is available to authorized users.

Dynamic epistasis under varying environmental perturbations

Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current knowledge for epistatic dynamics under multiple conditions is limited by the technological difficulties in experimentally screening epistatic relations among genes. We explored this issue by applying flux balance analysis to simulate epistatic landscapes under various environmental perturbations. Specifically, we looked at gene-gene epistatic interactions, where the mutations were assumed to occur in different genes. We predicted that epistasis tends to become more positive from glucose-abundant to nutrient-limiting conditions, indicating that selection might be less effective in removing deleterious mutations in the latter. We also observed a stable core of epistatic interactions in all tested conditions, as well as many epistatic interactions unique to each condition. Interestingly, genes in the stable epistatic interaction network are directly linked to most other genes whereas genes with condition-specific epistasis form a scale-free network. Furthermore, genes with stable epistasis tend to have similar evolutionary rates, whereas this co-evolving relationship does not hold for genes with condition-specific epistasis. Our findings provide a novel genome-wide picture about epistatic dynamics under environmental perturbations.

Perturbation Experiments: Approaches for Metabolic Pathway Analysis in Bioreactors

In the last decades, targeted metabolic engineering of microbial cells has become one of the major tools in bioprocess design and optimization. For successful application, a detailed knowledge is necessary about the relevant metabolic pathways and their regulation inside the cells. Since in vitro experiments cannot display process conditions and behavior properly, process data about the cells' metabolic state have to be collected in vivo. For this purpose, special techniques and methods are necessary. Therefore, most techniques enabling in vivo characterization of metabolic pathways rely on perturbation experiments, which can be divided into dynamic and steady-state approaches. To avoid any process disturbance, approaches which enable perturbation of cell metabolism in parallel to the continuing production process are reasonable. Furthermore, the fast dynamics of microbial production processes amplifies the need of parallelized data generation. These points motivate the development of a parallelized approach for multiple metabolic perturbation experiments outside the operating production reactor. An appropriate approach for in vivo characterization of metabolic pathways is presented and applied exemplarily to a microbial L-phenylalanine production process on a 15 L-scale.

Promise and reality in the expanding field of network interaction analysis: metabolic networks

In the last few decades, metabolic networks revealed their capabilities as powerful tools to analyze the cellular metabolism. Many research fields (eg, metabolic engineering, diagnostic medicine, pharmacology, biochemistry, biology and physiology) improved the understanding of the cell combining experimental assays and metabolic network-based computations. This process led to the rise of the “systems biology” approach, where the theory meets experiments and where two complementary perspectives cooperate in the study of biological phenomena. Here, the reconstruction of metabolic networks is presented, along with established and new algorithms to improve the description of cellular metabolism. Then, advantages and limitations of modeling algorithms and network reconstruction are discussed.

Systematic construction of kinetic models from genome-scale metabolic networks

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.

Metabolic modeling for multi-objective optimization of ethanol production in a Synechocystis mutant

Cyanobacteria have potential to produce drop-in bio-fuels such as ethanol via photoautotrophic metabolism. Although model cyanobacterial strains have been engineered to produce such products, systematic metabolic engineering studies to identify optimal strains for the same have not been performed. In this work, we identify optimal ethanol producing mutants corresponding to appropriate gene deletions that result in a suitable redirection in the carbon flux. In particular, we systematically simulate exhaustive single and double gene deletions considering a genome scale metabolic model of a mutant strain of the unicellular cyanobacterium Synechocystis species strain PCC 6803. Various optimization based metabolic modeling techniques, such as flux balance analysis (FBA), method of minimization of metabolic adjustment (MOMA) and regulatory on/off minimization (ROOM) were used for this analysis. For single gene deletion MOMA simulations, the Pareto front with biomass and ethanol fluxes as the two objectives to be maximized was obtained and analyzed. Points on the Pareto front represent maximal utilization of resources constrained by substrate uptake thereby representing an optimal trade-off between the two fluxes. Pareto analysis was also performed for double gene deletion MOMA and single and double gene deletion ROOM simulations. Based on these analyses, two mutants, with combined gene deletions in ethanol and purine metabolism pathways, were identified as promising candidates for ethanol production. The relevant genes were adk, pta and ackA. An ethanol productivity of approximately 0.15 mmol/(gDW h) was predicted for these mutants which appears to be reasonable based on experimentally reported values in literature for other strains.

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

Metabolic impact assessment for heterologous protein production in Streptomyces lividans based on genome-scale metabolic network modeling

The metabolic impact exerted on a microorganism due to heterologous protein production is still poorly understood in Streptomyces lividans. In this present paper, based on exometabolomic data, a proposed genome-scale metabolic network model is used to assess this metabolic impact in S. lividans. Constraint-based modeling results obtained in this work revealed that the metabolic impact due to heterologous protein production is widely distributed in the genome of S. lividans, causing both slow substrate assimilation and a shift in active pathways. Exchange fluxes that are critical for model performance have been identified for metabolites of mouse tumor necrosis factor, histidine, valine and lysine, as well as biomass. Our results unravel the interaction of heterologous protein production with intracellular metabolism of S. lividans, thus, a possible basis for further studies in relieving the metabolic burden via metabolic or bioprocess engineering.

Dynamic flux balance analysis of batch fermentation: effect of genetic manipulations on ethanol production

In silico optimization of bioethanol production from lignocellulosic biomasses is investigated by combining process systems engineering approach and systems biology approach. Lignocellulosic biomass is an attractive sustainable carbon source for fermentative production of bioethanol. For enhanced ethanol production, metabolic engineering of wild-type strains-that can metabolize both hexose and pentose sugars or microbial consortia consisting of substrate-selective microbes-may be advantageous. This study presents a detailed in silico analysis of bioethanol production from glucose-xylose mixtures of various compositions by batch mono-culture and co-culture fermentation of specialized microbes. Dynamic flux balance models based on available genome-scale reconstructions of the microorganisms have been used to analyze bioethanol production, and the maximization of ethanol productivity is addressed by computing optimal aerobic-anaerobic switching times. Effects of ten metabolic engineering strategies that have been suggested in the literature for ethanol overproduction, have been evaluated for their efficiency in enhancing the ethanol productivity in the context of batch mono-culture and co-culture processes.

An analysis of a 'community-driven' reconstruction of the human metabolic network

Following a strategy similar to that used in baker's yeast (Herrgård et al. Nat Biotechnol 26:1155-1160, 2008). A consensus yeast metabolic network obtained from a community approach to systems biology (Herrgård et al. 2008; Dobson et al. BMC Syst Biol 4:145, 2010). Further developments towards a genome-scale metabolic model of yeast (Dobson et al. 2010; Heavner et al. BMC Syst Biol 6:55, 2012). Yeast 5-an expanded reconstruction of the Saccharomyces cerevisiae metabolic network (Heavner et al. 2012) and in Salmonella typhimurium (Thiele et al. BMC Syst Biol 5:8, 2011). A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonellatyphimurium LT2 (Thiele et al. 2011), a recent paper (Thiele et al. Nat Biotechnol 31:419-425, 2013). A community-driven global reconstruction of human metabolism (Thiele et al. 2013) described a much improved 'community consensus' reconstruction of the human metabolic network, called Recon 2, and the authors (that include the present ones) have made it freely available via a database at http://humanmetabolism.org/ and in SBML format at Biomodels (http://identifiers.org/biomodels.db/MODEL1109130000). This short analysis summarises the main findings, and suggests some approaches that will be able to exploit the availability of this model to advantage.

Are we ready for genome-scale modeling in plants?

As it is becoming easier and faster to generate various types of high-throughput data, one would expect that by now we should have a comprehensive systems-level understanding of biology, biochemistry, and physiology at least in major prokaryotic and eukaryotic model systems. Despite the wealth of available data, we only get a glimpse of what is going on at the molecular level from the global perspective. The major reason is the high level of cellular complexity and our limited ability to identify all (or at least important) components and their interactions in virtually infinite number of internal and external conditions. Metabolism can be modeled mathematically by the use of genome-scale models (GEMs). GEMs are in silico metabolic flux models derived from available genome annotation. These models predict the combination of flux values of a defined metabolic network given the influence of internal and external signals. GEMs have been successfully implemented to model bacterial metabolism for over a decade. However, it was not until 2009 when the first GEM for Arabidopsis thaliana cell-suspension cultures was generated. Genome-scale modeling ("GEMing") in plants brings new challenges primarily due to the missing components and complexity of plant cells represented by the existence of: (i) photosynthesis; (ii) compartmentation; (iii) variety of cell and tissue types; and (iv) diverse metabolic responses to environmental and developmental cues as well as pathogens, insects, and competing weeds. This review presents a critical discussion of the advantages of existing plant GEMs, while identifies key targets for future improvements. Plant GEMs tend to be accurate in predicting qualitative changes in selected aspects of central carbon metabolism, while secondary metabolism is largely neglected mainly due to the missing (unknown) genes and metabolites. As such, these models are suitable for exploring metabolism in plants grown in favorable conditions, but not in field-grown plants that have to cope with environmental changes in complex ecosystems. AraGEM is the first GEM describing a photosynthetic and photorespiring plant cell (Arabidopsis thaliana). We demonstrate the use of AraGEM given the current (limited) knowledge of plant metabolism and reveal the unexpected robustness of AraGEM by a series of in silico simulations. The major focus of these simulations is on the assessment of the: (i) network connectivity; (ii) influence of CO₂ and photon uptake rates on cellular growth rates and production of individual biomass components; and (iii) stability of plant central carbon metabolism with internal pH changes.

Design constraints on a synthetic metabolism

A metabolism is a complex network of chemical reactions that converts sources of energy and chemical elements into biomass and other molecules. To design a metabolism from scratch and to implement it in a synthetic genome is almost within technological reach. Ideally, a synthetic metabolism should be able to synthesize a desired spectrum of molecules at a high rate, from multiple different nutrients, while using few chemical reactions, and producing little or no waste. Not all of these properties are achievable simultaneously. We here use a recently developed technique to create random metabolic networks with pre-specified properties to quantify trade-offs between these and other properties. We find that for every additional molecule to be synthesized a network needs on average three additional reactions. For every additional carbon source to be utilized, it needs on average two additional reactions. Networks able to synthesize 20 biomass molecules from each of 20 alternative sole carbon sources need to have at least 260 reactions. This number increases to 518 reactions for networks that can synthesize more than 60 molecules from each of 80 carbon sources. The maximally achievable rate of biosynthesis decreases by approximately 5 percent for every additional molecule to be synthesized. Biochemically related molecules can be synthesized at higher rates, because their synthesis produces less waste. Overall, the variables we study can explain 87 percent of variation in network size and 84 percent of the variation in synthesis rate. The constraints we identify prescribe broad boundary conditions that can help to guide synthetic metabolism design.

Improving metabolic flux predictions using absolute gene expression data

Background

Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.

Results

An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon maximisation of the rate of biomass production.

Conclusion

Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single cellular systems. Subsequent work will investigate the method’s ability to generate condition- and tissue-specific flux predictions in multicellular organisms.

Dynamic epistasis for different alleles of the same gene

Epistasis refers to the phenomenon in which phenotypic consequences caused by mutation of one gene depend on one or more mutations at another gene. Epistasis is critical for understanding many genetic and evolutionary processes, including pathway organization, evolution of sexual reproduction, mutational load, ploidy, genomic complexity, speciation, and the origin of life. Nevertheless, current understandings for the genome-wide distribution of epistasis are mostly inferred from interactions among one mutant type per gene, whereas how epistatic interaction partners change dynamically for different mutant alleles of the same gene is largely unknown. Here we address this issue by combining predictions from flux balance analysis and data from a recently published high-throughput experiment. Our results show that different alleles can epistatically interact with very different gene sets. Furthermore, between two random mutant alleles of the same gene, the chance for the allele with more severe mutational consequence to develop a higher percentage of negative epistasis than the other allele is 50~70% in eukaryotic organisms, but only 20~30% in bacteria and archaea. We developed a population genetics model that predicts that the observed distribution for the sign of epistasis can speed up the process of purging deleterious mutations in eukaryotic organisms. Our results indicate that epistasis among genes can be dynamically rewired at the genome level, and call on future efforts to revisit theories that can integrate epistatic dynamics among genes in biological systems.

Yeast 5 - an expanded reconstruction of the Saccharomyces cerevisiae metabolic network

Background

Efforts to improve the computational reconstruction of the Saccharomyces cerevisiae biochemical reaction network and to refine the stoichiometrically constrained metabolic models that can be derived from such a reconstruction have continued since the first stoichiometrically constrained yeast genome scale metabolic model was published in 2003. Continuing this ongoing process, we have constructed an update to the Yeast Consensus Reconstruction, Yeast 5. The Yeast Consensus Reconstruction is a product of efforts to forge a community-based reconstruction emphasizing standards compliance and biochemical accuracy via evidence-based selection of reactions. It draws upon models published by a variety of independent research groups as well as information obtained from biochemical databases and primary literature.

Results

Yeast 5 refines the biochemical reactions included in the reconstruction, particularly reactions involved in sphingolipid metabolism; updates gene-reaction annotations; and emphasizes the distinction between reconstruction and stoichiometrically constrained model. Although it was not a primary goal, this update also improves the accuracy of model prediction of viability and auxotrophy phenotypes and increases the number of epistatic interactions. This update maintains an emphasis on standards compliance, unambiguous metabolite naming, and computer-readable annotations available through a structured document format. Additionally, we have developed MATLAB scripts to evaluate the model’s predictive accuracy and to demonstrate basic model applications such as simulating aerobic and anaerobic growth. These scripts, which provide an independent tool for evaluating the performance of various stoichiometrically constrained yeast metabolic models using flux balance analysis, are included as Additional files 1, 2 and 3.

Conclusions

Yeast 5 expands and refines the computational reconstruction of yeast metabolism and improves the predictive accuracy of a stoichiometrically constrained yeast metabolic model. It differs from previous reconstructions and models by emphasizing the distinction between the yeast metabolic reconstruction and the stoichiometrically constrained model, and makes both available as Additional file 4 and Additional file 5 and at http://yeast.sf.net/ as separate systems biology markup language (SBML) files. Through this separation, we intend to make the modeling process more accessible, explicit, transparent, and reproducible.

Genome-scale metabolic flux analysis of Streptomyces lividans growing on a complex medium

Constraint-based metabolic modeling comprises various excellent tools to assess experimentally observed phenotypic behavior of micro-organisms in terms of intracellular metabolic fluxes. In combination with genome-scale metabolic networks, micro-organisms can be investigated in much more detail and under more complex environmental conditions. Although complex media are ubiquitously applied in industrial fermentations and are often a prerequisite for high protein secretion yields, such multi-component conditions are seldom investigated using genome-scale flux analysis. In this paper, a systematic and integrative approach is presented to determine metabolic fluxes in Streptomyces lividans TK24 grown on a nutritious and complex medium. Genome-scale flux balance analysis and randomized sampling of the solution space are combined to extract maximum information from exometabolome profiles. It is shown that biomass maximization cannot predict the observed metabolite production pattern as such. Although this cellular objective commonly applies to batch fermentation data, both input and output constraints are required to reproduce the measured biomass production rate. Rich media hence not necessarily lead to maximum biomass growth. To eventually identify a unique intracellular flux vector, a hierarchical optimization of cellular objectives is adopted. Out of various tested secondary objectives, maximization of the ATP yield per flux unit returns the closest agreement with the maximum frequency in flux histograms. This unique flux estimation is hence considered as a reasonable approximation for the biological fluxes. Flux maps for different growth phases show no active oxidative part of the pentose phosphate pathway, but NADPH generation in the TCA cycle and NADPH transdehydrogenase activity are most important in fulfilling the NADPH balance. Amino acids contribute to biomass growth by augmenting the pool of available amino acids and by boosting the TCA cycle, particularly when using glutamate and aspartate. Depletion of glutamate and aspartate causes a distinct shift in fluxes of the central carbon and nitrogen metabolism. In the current work, hurdles encountered in flux analysis at a genome-scale level are addressed using hierarchical flux balance analysis and uniform sampling of the constrained solution space. This general framework can now be adopted in further studies of S. lividans, e.g., as a host for heterologous protein production.

Construction and completion of flux balance models from pathway databases

MOTIVATION

Flux balance analysis (FBA) is a well-known technique for genome-scale modeling of metabolic flux. Typically, an FBA formulation requires the accurate specification of four sets: biochemical reactions, biomass metabolites, nutrients and secreted metabolites. The development of FBA models can be time consuming and tedious because of the difficulty in assembling completely accurate descriptions of these sets, and in identifying errors in the composition of these sets. For example, the presence of a single non-producible metabolite in the biomass will make the entire model infeasible. Other difficulties in FBA modeling are that model distributions, and predicted fluxes, can be cryptic and difficult to understand.

RESULTS

We present a multiple gap-filling method to accelerate the development of FBA models using a new tool, called MetaFlux, based on mixed integer linear programming (MILP). The method suggests corrections to the sets of reactions, biomass metabolites, nutrients and secretions. The method generates FBA models directly from Pathway/Genome Databases. Thus, FBA models developed in this framework are easily queried and visualized using the Pathway Tools software. Predicted fluxes are more easily comprehended by visualizing them on diagrams of individual metabolic pathways or of metabolic maps. MetaFlux can also remove redundant high-flux loops, solve FBA models once they are generated and model the effects of gene knockouts. MetaFlux has been validated through construction of FBA models for Escherichia coli and Homo sapiens.

AVAILABILITY

Pathway Tools with MetaFlux is freely available to academic users, and for a fee to commercial users. Download from: biocyc.org/download.shtml.

CONTACT

mario.latendresse@sri.com

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0

Over the past decade, a growing community of researchers has emerged around the use of constraint-based reconstruction and analysis (COBRA) methods to simulate, analyze and predict a variety of metabolic phenotypes using genome-scale models. The COBRA Toolbox, a MATLAB package for implementing COBRA methods, was presented earlier. Here we present a substantial update of this in silico toolbox. Version 2.0 of the COBRA Toolbox expands the scope of computations by including in silico analysis methods developed since its original release. New functions include (i) network gap filling, (ii) (13)C analysis, (iii) metabolic engineering, (iv) omics-guided analysis and (v) visualization. As with the first version, the COBRA Toolbox reads and writes systems biology markup language-formatted models. In version 2.0, we improved performance, usability and the level of documentation. A suite of test scripts can now be used to learn the core functionality of the toolbox and validate results. This toolbox lowers the barrier of entry to use powerful COBRA methods.

Elimination of thermodynamically infeasible loops in steady-state metabolic models

The constraint-based reconstruction and analysis (COBRA) framework has been widely used to study steady-state flux solutions in genome-scale metabolic networks. One shortcoming of current COBRA methods is the possible violation of the loop law in the computed steady-state flux solutions. The loop law is analogous to Kirchhoff's second law for electric circuits, and states that at steady state there can be no net flux around a closed network cycle. Although the consequences of the loop law have been known for years, it has been computationally difficult to work with. Therefore, the resulting loop-law constraints have been overlooked. Here, we present a general mixed integer programming approach called loopless COBRA (ll-COBRA), which can be used to eliminate all steady-state flux solutions that are incompatible with the loop law. We apply this approach to improve flux predictions on three common COBRA methods: flux balance analysis, flux variability analysis, and Monte Carlo sampling of the flux space. Moreover, we demonstrate that the imposition of loop-law constraints with ll-COBRA improves the consistency of simulation results with experimental data. This method provides an additional constraint for many COBRA methods, enabling the acquisition of more realistic simulation results.

Why does yeast ferment? A flux balance analysis study

Advances in biological techniques have led to the availability of genome-scale metabolic reconstructions for yeast. The size and complexity of such networks impose limits on what types of analyses one can perform. Constraint-based modelling overcomes some of these restrictions by using physicochemical constraints to describe the potential behaviour of an organism. FBA (flux balance analysis) highlights flux patterns through a network that serves to achieve a particular objective and requires a minimal amount of data to make quantitative inferences about network behaviour. Even though FBA is a powerful tool for system predictions, its general formulation sometimes results in unrealistic flux patterns. A typical example is fermentation in yeast: ethanol is produced during aerobic growth in excess glucose, but this pattern is not present in a typical FBA solution. In the present paper, we examine the issue of yeast fermentation against respiration during growth. We have studied a number of hypotheses from the modelling perspective, and novel formulations of the FBA approach have been tested. By making the observation that more respiration requires the synthesis of more mitochondria, an energy cost related to mitochondrial synthesis is added to the FBA formulation. Results, although still approximate, are closer to experimental observations than earlier FBA analyses, at least on the issue of fermentation.