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.     

Metabolic stasis in an ancient symbiosis: genome-scale metabolic networks from two <Emphasis Type="Italic">Blattabacterium cuenoti</Emphasis> strains,primary endosymbionts of cockroaches

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

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.     

A Probabilistic Model to Predict Clinical Phenotypic Traits from Genome Sequencing

Genetic screening is becoming possible on an unprecedented scale. However, its utility remains controversial. Although most variant genotypes cannot be easily interpreted, many individuals nevertheless attempt to interpret their genetic information. Initiatives such as the Personal Genome Project (PGP) and Illumina''s Understand Your Genome are sequencing thousands of adults, collecting phenotypic information and developing computational pipelines to identify the most important variant genotypes harbored by each individual. These pipelines consider database and allele frequency annotations and bioinformatics classifications. We propose that the next step will be to integrate these different sources of information to estimate the probability that a given individual has specific phenotypes of clinical interest. To this end, we have designed a Bayesian probabilistic model to predict the probability of dichotomous phenotypes. When applied to a cohort from PGP, predictions of Gilbert syndrome, Graves'' disease, non-Hodgkin lymphoma, and various blood groups were accurate, as individuals manifesting the phenotype in question exhibited the highest, or among the highest, predicted probabilities. Thirty-eight PGP phenotypes (26%) were predicted with area-under-the-ROC curve (AUC)>0.7, and 23 (15.8%) of these were statistically significant, based on permutation tests. Moreover, in a Critical Assessment of Genome Interpretation (CAGI) blinded prediction experiment, the models were used to match 77 PGP genomes to phenotypic profiles, generating the most accurate prediction of 16 submissions, according to an independent assessor. Although the models are currently insufficiently accurate for diagnostic utility, we expect their performance to improve with growth of publicly available genomics data and model refinement by domain experts.     

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol⁻¹, and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.     

Metabolic stasis in an ancient symbiosis: genome-scale metabolic networks from two Blattabacterium cuenoti strains,primary endosymbionts of cockroaches

Background

Cockroaches are terrestrial insects that strikingly eliminate waste nitrogen as ammonia instead of uric acid. Blattabacterium cuenoti (Mercier 1906) strains Bge and Pam are the obligate primary endosymbionts of the cockroaches Blattella germanica and Periplaneta americana, respectively. The genomes of both bacterial endosymbionts have recently been sequenced, making possible a genome-scale constraint-based reconstruction of their metabolic networks. The mathematical expression of a metabolic network and the subsequent quantitative studies of phenotypic features by Flux Balance Analysis (FBA) represent an efficient functional approach to these uncultivable bacteria.

Results

We report the metabolic models of Blattabacterium strains Bge (iCG238) and Pam (iCG230), comprising 296 and 289 biochemical reactions, associated with 238 and 230 genes, and 364 and 358 metabolites, respectively. Both models reflect both the striking similarities and the singularities of these microorganisms. FBA was used to analyze the properties, potential and limits of the models, assuming some environmental constraints such as aerobic conditions and the net production of ammonia from these bacterial systems, as has been experimentally observed. In addition, in silico simulations with the iCG238 model have enabled a set of carbon and nitrogen sources to be defined, which would also support a viable phenotype in terms of biomass production in the strain Pam, which lacks the first three steps of the tricarboxylic acid cycle. FBA reveals a metabolic condition that renders these enzymatic steps dispensable, thus offering a possible evolutionary explanation for their elimination. We also confirm, by computational simulations, the fragility of the metabolic networks and their host dependence.

Conclusions

The minimized Blattabacterium metabolic networks are surprisingly similar in strains Bge and Pam, after 140 million years of evolution of these endosymbionts in separate cockroach lineages. FBA performed on the reconstructed networks from the two bacteria helps to refine the functional analysis of the genomes enabling us to postulate how slightly different host metabolic contexts drove their parallel evolution.

     

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.     

Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis

Flux balance analysis (FBA) is an increasingly useful approach for modeling the behavior of metabolic systems. However, standard FBA modeling of genetic knockouts cannot predict drug combination synergies observed between serial metabolic targets, even though such synergies give rise to some of the most widely used antibiotic treatments. Here we extend FBA modeling to simulate responses to chemical inhibitors at varying concentrations, by diverting enzymatic flux to a waste reaction. This flux diversion yields very similar qualitative predictions to prior methods for single target activity. However, we find very different predictions for combinations, where flux diversion, which mimics the kinetics of competitive metabolic inhibitors, can explain serial target synergies between metabolic enzyme inhibitors that we confirmed in Escherichia coli cultures. FBA flux diversion opens the possibility for more accurate genome-scale predictions of drug synergies, which can be used to suggest treatments for infections and other diseases.     

基于基因组数据分析的细菌耐药基因识别与表型预测

利用基因组数据和生物信息学分析方法,快速鉴定耐药基因并预测耐药表型,为细菌耐药状况监测提供了有力辅助手段。目前,已有的数十个耐药数据库及其相关分析工具这些资源为细菌耐药基因的识别以及耐药表型的预测提供了数据信息和技术手段。随着细菌基因组数据的持续增加以及耐药表型数据的不断积累,大数据和机器学习能够更好地建立耐药表型与基因组信息之间的相关性,因此,构建高效的耐药表型预测模型成为研究热点。本文围绕细菌耐药基因的识别和耐药表型的预测,针对耐药相关数据库、耐药特征识别理论与方法、耐药数据的机器学习与表型预测等方面展开讨论,以期为细菌耐药的相关研究提供手段和思路。     

Stoichiometric network constraints on xylose metabolism by recombinant Saccharomyces cerevisiae

Metabolic pathway engineering is constrained by the thermodynamic and stoichiometric feasibility of enzymatic activities of introduced genes. Engineering of xylose metabolism in Saccharomyces cerevisiae has focused on introducing genes for the initial xylose assimilation steps from Pichia stipitis, a xylose-fermenting yeast, into S. cerevisiae, a yeast traditionally used in ethanol production from hexose. However, recombinant S. cerevisiae created in several laboratories have used xylose oxidatively rather than in the fermentative manner that this yeast metabolizes glucose. To understand the differences between glucose and engineered xylose metabolic networks, we performed a flux balance analysis (FBA) and calculated extreme pathways using a stoichiometric model that describes the biochemistry of yeast cell growth. FBA predicted that the ethanol yield from xylose exhibits a maximum under oxygen-limited conditions, and a fermentation experiment confirmed this finding. Fermentation results were largely consistent with in silico phenotypes based on calculated extreme pathways, which displayed several phases of metabolic phenotype with respect to oxygen availability from anaerobic to aerobic conditions. However, in contrast to the model prediction, xylitol production continued even after the optimum aeration level for ethanol production was attained. These results suggest that oxygen (or some other electron accepting system) is required to resolve the redox imbalance caused by cofactor difference between xylose reductase and xylitol dehydrogenase, and that other factors limit glycolytic flux when xylose is the sole carbon source.     

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.     

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.     

Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass “reaction”, which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed “without cancellations”. In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.     

A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments

While flux balance analysis (FBA) provides a framework for predicting steady-state leaf metabolic network fluxes, it does not readily capture the response to environmental variables without being coupled to other modelling formulations. To address this, we coupled an FBA model of 903 reactions of soybean (Glycine max) leaf metabolism with e-photosynthesis, a dynamic model that captures the kinetics of 126 reactions of photosynthesis and associated chloroplast carbon metabolism. Successful coupling was achieved in an iterative formulation in which fluxes from e-photosynthesis were used to constrain the FBA model and then, in turn, fluxes computed from the FBA model used to update parameters in e-photosynthesis. This process was repeated until common fluxes in the two models converged. Coupling did not hamper the ability of the kinetic module to accurately predict the carbon assimilation rate, photosystem II electron flux, and starch accumulation of field-grown soybean at two CO₂ concentrations. The coupled model also allowed accurate predictions of additional parameters such as nocturnal respiration, as well as analysis of the effect of light intensity and elevated CO₂ on leaf metabolism. Predictions included an unexpected decrease in the rate of export of sucrose from the leaf at high light, due to altered starch–sucrose partitioning, and altered daytime flux modes in the tricarboxylic acid cycle at elevated CO₂. Mitochondrial fluxes were notably different between growing and mature leaves, with greater anaplerotic, tricarboxylic acid cycle and mitochondrial ATP synthase fluxes predicted in the former, primarily to provide carbon skeletons and energy for protein synthesis.