Understanding the Adaptive Growth Strategy of Lactobacillus plantarum by In Silico Optimisation

In the study of metabolic networks, optimization techniques are often used to predict flux distributions, and hence, metabolic phenotype. Flux balance analysis in particular has been successful in predicting metabolic phenotypes. However, an inherent limitation of a stoichiometric approach such as flux balance analysis is that it can predict only flux distributions that result in maximal yields. Hence, previous attempts to use FBA to predict metabolic fluxes in Lactobacillus plantarum failed, as this lactic acid bacterium produces lactate, even under glucose-limited chemostat conditions, where FBA predicted mixed acid fermentation as an alternative pathway leading to a higher yield. In this study we tested, however, whether long-term adaptation on an unusual and poor carbon source (for this bacterium) would select for mutants with optimal biomass yields. We have therefore adapted Lactobacillus plantarum to grow well on glycerol as its main growth substrate. After prolonged serial dilutions, the growth yield and corresponding fluxes were compared to in silico predictions. Surprisingly, the organism still produced mainly lactate, which was corroborated by FBA to indeed be optimal. To understand these results, constraint-based elementary flux mode analysis was developed that predicted 3 out of 2669 possible flux modes to be optimal under the experimental conditions. These optimal pathways corresponded very closely to the experimentally observed fluxes and explained lactate formation as the result of competition for oxygen by the other flux modes. Hence, these results provide thorough understanding of adaptive evolution, allowing in silico predictions of the resulting flux states, provided that the selective growth conditions favor yield optimization as the winning strategy.     

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

MotivationGenome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.ResultsHere, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.AvailabilityMMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.     

ΔFBA—Predicting metabolic flux alterations using genome-scale metabolic models and differential transcriptomic data

Genome-scale metabolic models (GEMs) provide a powerful framework for simulating the entire set of biochemical reactions in a cell using a constraint-based modeling strategy called flux balance analysis (FBA). FBA relies on an assumed metabolic objective for generating metabolic fluxes using GEMs. But, the most appropriate metabolic objective is not always obvious for a given condition and is likely context-specific, which often complicate the estimation of metabolic flux alterations between conditions. Here, we propose a new method, called ΔFBA (deltaFBA), that integrates differential gene expression data to evaluate directly metabolic flux differences between two conditions. Notably, ΔFBA does not require specifying the cellular objective. Rather, ΔFBA seeks to maximize the consistency and minimize inconsistency between the predicted flux differences and differential gene expression. We showcased the performance of ΔFBA through several case studies involving the prediction of metabolic alterations caused by genetic and environmental perturbations in Escherichia coli and caused by Type-2 diabetes in human muscle. Importantly, in comparison to existing methods, ΔFBA gives a more accurate prediction of flux differences.     

Improving the accuracy of flux balance analysis through the implementation of carbon availability constraints for intracellular reactions

Constraint-based modeling methods, such as Flux Balance Analysis (FBA), have been extensively used to decipher complex, information rich -omics datasets to elicit system-wide behavioral patterns of cellular metabolism. FBA has been successfully used to gain insight in a wide range of applications, such as range of substrate utilization, product yields and to design metabolic engineering strategies to improve bioprocess performance. A well-known challenge associated with large genome-scale metabolic networks is that they result in underdetermined problem formulations. Consequently, rather than unique solutions, FBA and related methods examine ranges of reaction flux values that are consistent with the studied physiological conditions. The wider the reported flux ranges, the higher the uncertainty in the determination of basic reaction properties, limiting interpretability of and confidence in the results. Herein, we propose a new, computationally efficient approach that refines flux range predictions by constraining reaction fluxes on the basis of the elemental balance of carbon. We compared carbon constraint FBA (ccFBA) against experimentally-measured intracellular fluxes using the latest CHO GEM (iCHO1766) and were able to substantially improve the accuracy of predicted flux values compared with FBA. ccFBA can be used as a stand-alone method but is also compatible with and complimentary to other constraint-based approaches.     

Dynamic flux balance analysis of diauxic growth in Escherichia coli

Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.     

Flux analysis and metabolomics for systematic metabolic engineering of microorganisms

Rational engineering of metabolism is important for bio-production using microorganisms. Metabolic design based on in silico simulations and experimental validation of the metabolic state in the engineered strain helps in accomplishing systematic metabolic engineering. Flux balance analysis (FBA) is a method for the prediction of metabolic phenotype, and many applications have been developed using FBA to design metabolic networks. Elementary mode analysis (EMA) and ensemble modeling techniques are also useful tools for in silico strain design. The metabolome and flux distribution of the metabolic pathways enable us to evaluate the metabolic state and provide useful clues to improve target productivity. Here, we reviewed several computational applications for metabolic engineering by using genome-scale metabolic models of microorganisms. We also discussed the recent progress made in the field of metabolomics and ¹³C-metabolic flux analysis techniques, and reviewed these applications pertaining to bio-production development. Because these in silico or experimental approaches have their respective advantages and disadvantages, the combined usage of these methods is complementary and effective for metabolic engineering.     

Error propagation in constraint-based modeling of Chinese hamster ovary cells

Chinese hamster ovary (CHO) cells are the most popular mammalian cell factories for the production of glycosylated biopharmaceuticals. To further increase titer and productivity and ensure product quality, rational system-level engineering strategies based on constraint-based metabolic modeling, such as flux balance analysis (FBA), have gained strong interest. However, the quality of FBA predictions depends on the accuracy of the experimental input data, especially on the exchange rates of extracellular metabolites. Yet, it is not standard practice to devote sufficient attention to the accurate determination of these rates. In this work, we investigated to what degree the sampling frequency during a batch culture and the measurement errors of metabolite concentrations influence the accuracy of the calculated exchange rates and further, how this error then propagates into FBA predictions of growth rates. We determined that accurate measurements of essential amino acids with low uptake rates are crucial for the accuracy of FBA predictions, followed by a sufficient number of analyzed time points. We observed that the measured difference in growth rates of two cell lines can only be reliably predicted when both high measurement accuracy and sampling frequency are ensured.     

The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.     

Predictive Potential of Flux Balance Analysis of Saccharomyces cerevisiae Using as Optimization Function Combinations of Cell Compartmental Objectives

Background

The main objective of flux balance analysis (FBA) is to obtain quantitative predictions of metabolic fluxes of an organism, and it is necessary to use an appropriate objective function to guarantee a good estimation of those fluxes.

Methodology

In this study, the predictive performance of FBA was evaluated, using objective functions arising from the linear combination of different cellular objectives. This approach is most suitable for eukaryotic cells, owing to their multiplicity of cellular compartments. For this reason, Saccharomyces cerevisiae was used as model organism, and its metabolic network was represented using the genome-scale metabolic model iMM904. As the objective was to evaluate the predictive performance from the FBA using the kind of objective function previously described, substrate uptake and oxygen consumption were the only input data used for the FBA. Experimental information about microbial growth and exchange of metabolites with the environment was used to assess the quality of the predictions.

Conclusions

The quality of the predictions obtained with the FBA depends greatly on the knowledge of the oxygen uptake rate. For the most of studied classifications, the best predictions were obtained with “maximization of growth”, and with some combinations that include this objective. However, in the case of exponential growth with unknown oxygen exchange flux, the objective function “maximization of growth, plus minimization of NADH production in cytosol, plus minimization of NAD(P)H consumption in mitochondrion” gave much more accurate estimations of fluxes than the obtained with any other objective function explored in this study.     

Flux Imbalance Analysis and the Sensitivity of Cellular Growth to Changes in Metabolite Pools

Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some features of in vivo metabolite concentrations. Mathematically, the sensitivity of FBA to these flux imbalances is captured by a native feature of linear optimization, the dual problem, and its corresponding variables, known as shadow prices. First, using recently published data on chemostat growth of Saccharomyces cerevisae under different nutrient limitations, we show that shadow prices anticorrelate with experimentally measured degrees of growth limitation of intracellular metabolites. We next hypothesize that metabolites which are limiting for growth (and thus have very negative shadow price) cannot vary dramatically in an uncontrolled way, and must respond rapidly to perturbations. Using a collection of published datasets monitoring the time-dependent metabolomic response of Escherichia coli to carbon and nitrogen perturbations, we test this hypothesis and find that metabolites with negative shadow price indeed show lower temporal variation following a perturbation than metabolites with zero shadow price. Finally, we illustrate the broader applicability of flux imbalance analysis to other constraint-based methods. In particular, we explore the biological significance of shadow prices in a constraint-based method for integrating gene expression data with a stoichiometric model. In this case, shadow prices point to metabolites that should rise or drop in concentration in order to increase consistency between flux predictions and gene expression data. In general, these results suggest that the sensitivity of metabolic optima to violations of the steady state constraints carries biologically significant information on the processes that control intracellular metabolites in the cell.     

Escher-FBA: a web application for interactive flux balance analysis

Background

Flux balance analysis (FBA) is a widely-used method for analyzing metabolic networks. However, most existing tools that implement FBA require downloading software and writing code. Furthermore, FBA generates predictions for metabolic networks with thousands of components, so meaningful changes in FBA solutions can be difficult to identify. These challenges make it difficult for beginners to learn how FBA works.

Results

To meet this need, we present Escher-FBA, a web application for interactive FBA simulations within a pathway visualization. Escher-FBA allows users to set flux bounds, knock out reactions, change objective functions, upload metabolic models, and generate high-quality figures without downloading software or writing code. We provide detailed instructions on how to use Escher-FBA to replicate several FBA simulations that generate real scientific hypotheses.

Conclusions

We designed Escher-FBA to be as intuitive as possible so that users can quickly and easily understand the core concepts of FBA. The web application can be accessed at https://sbrg.github.io/escher-fba.

     

Molecular modeling,dynamics studies and virtual screening of Fructose 1, 6 biphosphate aldolase-II in community acquired- methicillin resistant Staphylococcus aureus (CA-MRSA)

Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) has recently emerged as a nosocomial pathogen to the community which commonly causes skin and soft-tissue infections (SSTIs). This strain (MW2) has now become resistant to the most of the beta-lactam antibiotics; therefore it is the urgent need to identify the novel drug targets. Recently fructose 1,6 biphosphate aldolase-II (FBA) has been identified as potential drug target in CA-MRSA. The FBA catalyses the retro-ketolic cleavage of fructose-1,6-bisphosphate (FBP) to yield dihydroxyacetone phosphate (DHAP) and glyceraldehyde-3-phosphate (G3P) in glycolytic pathway. In the present research work the 3D structure of FBA was predicted using the homology modeling method followed by validation. The molecular dynamics simulation (MDS) of the predicted model was carried out using the 2000 ps time scale and 1000000 steps. The MDS results suggest that the modeled structure is stable. The predicted model of FBA was used for virtual screening against the NCI diversity subset-II ligand databases which contain 1364 compounds. Based on the docking energy scores, it was found that top four ligands i.e. ZINC01690699, ZINC13154304, ZINC29590257 and ZINC29590259 were having lower energy scores which reveal higher binding affinity towards the active site of FBA. These ligands might act as potent inhibitors for the FBA so that the menace of antimicrobial resistance in CA-MRSA can be conquered. However, pharmacological studies are required to confirm the inhibitory activity of these ligands against the FBA in CA-MRSA.     

Genome-Scale Metabolic Network Validation of Shewanella oneidensis Using Transposon Insertion Frequency Analysis

Transposon mutagenesis, in combination with parallel sequencing, is becoming a powerful tool for en-masse mutant analysis. A probability generating function was used to explain observed miniHimar transposon insertion patterns, and gene essentiality calls were made by transposon insertion frequency analysis (TIFA). TIFA incorporated the observed genome and sequence motif bias of the miniHimar transposon. The gene essentiality calls were compared to: 1) previous genome-wide direct gene-essentiality assignments; and, 2) flux balance analysis (FBA) predictions from an existing genome-scale metabolic model of Shewanella oneidensis MR-1. A three-way comparison between FBA, TIFA, and the direct essentiality calls was made to validate the TIFA approach. The refinement in the interpretation of observed transposon insertions demonstrated that genes without insertions are not necessarily essential, and that genes that contain insertions are not always nonessential. The TIFA calls were in reasonable agreement with direct essentiality calls for S. oneidensis, but agreed more closely with E. coli essentiality calls for orthologs. The TIFA gene essentiality calls were in good agreement with the MR-1 FBA essentiality predictions, and the agreement between TIFA and FBA predictions was substantially better than between the FBA and the direct gene essentiality predictions.     

Predicting Growth Conditions from Internal Metabolic Fluxes in an In-Silico Model of E. coli

A widely studied problem in systems biology is to predict bacterial phenotype from growth conditions, using mechanistic models such as flux balance analysis (FBA). However, the inverse prediction of growth conditions from phenotype is rarely considered. Here we develop a computational framework to carry out this inverse prediction on a computational model of bacterial metabolism. We use FBA to calculate bacterial phenotypes from growth conditions in E. coli, and then we assess how accurately we can predict the original growth conditions from the phenotypes. Prediction is carried out via regularized multinomial regression. Our analysis provides several important physiological and statistical insights. First, we show that by analyzing metabolic end products we can consistently predict growth conditions. Second, prediction is reliable even in the presence of small amounts of impurities. Third, flux through a relatively small number of reactions per growth source (∼10) is sufficient for accurate prediction. Fourth, combining the predictions from two separate models, one trained only on carbon sources and one only on nitrogen sources, performs better than models trained to perform joint prediction. Finally, that separate predictions perform better than a more sophisticated joint prediction scheme suggests that carbon and nitrogen utilization pathways, despite jointly affecting cellular growth, may be fairly decoupled in terms of their dependence on specific assortments of molecular precursors.     

Segregated flux balance analysis constrained by population structure/function data: The case of PHA production by mixed microbial cultures

In this study we developed a segregated flux balance analysis (FBA) method to calculate metabolic flux distributions of the individual populations present in a mixed microbial culture (MMC). Population specific flux data constraints were derived from the raw data typically obtained by the fluorescence in situ hybridization (FISH) and microautoradiography (MAR)‐FISH techniques. This method was applied to study the metabolic heterogeneity of a MMC that produces polyhydroxyalkanoates (PHA) from fermented sugar cane molasses. Three populations were identified by FISH, namely Paracoccus sp., Thauera sp., and Azoarcus sp. The segregated FBA method predicts a flux distribution for each of the identified populations. The method is shown to predict with high accuracy the average PHA storage flux and the respective monomeric composition for 16 independent experiments. Moreover, flux predictions by segregated FBA were slightly better than those obtained by nonsegregated FBA, and also highly concordant with metabolic flux analysis (MFA) estimated fluxes. The segregated FBA method can be of high value to assess metabolic heterogeneity in MMC systems and to derive more efficient eco‐engineering strategies. For the case of PHA‐producing MMC considered in this work, it becomes apparent that the PHA average monomeric composition might be controlled not only by the volatile fatty acids (VFA) feeding profile but also by the population composition present in the MMC. Biotechnol. Bioeng. 2013; 110: 2267–2276. © 2013 Wiley Periodicals, Inc.     

Interpreting Expression Data with Metabolic Flux Models: Predicting Mycobacterium tuberculosis Mycolic Acid Production

Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.