System-level insights into yeast metabolism by thermodynamic analysis of elementary flux modes

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.     

Thermodynamics-based metabolic flux analysis

A new form of metabolic flux analysis (MFA) called thermodynamics-based metabolic flux analysis (TMFA) is introduced with the capability of generating thermodynamically feasible flux and metabolite activity profiles on a genome scale. TMFA involves the use of a set of linear thermodynamic constraints in addition to the mass balance constraints typically used in MFA. TMFA produces flux distributions that do not contain any thermodynamically infeasible reactions or pathways, and it provides information about the free energy change of reactions and the range of metabolite activities in addition to reaction fluxes. TMFA is applied to study the thermodynamically feasible ranges for the fluxes and the Gibbs free energy change, Delta(r)G', of the reactions and the activities of the metabolites in the genome-scale metabolic model of Escherichia coli developed by Palsson and co-workers. In the TMFA of the genome scale model, the metabolite activities and reaction Delta(r)G' are able to achieve a wide range of values at optimal growth. The reaction dihydroorotase is identified as a possible thermodynamic bottleneck in E. coli metabolism with a Delta(r)G' constrained close to zero while numerous reactions are identified throughout metabolism for which Delta(r)G' is always highly negative regardless of metabolite concentrations. As it has been proposed previously, these reactions with exclusively negative Delta(r)G' might be candidates for cell regulation, and we find that a significant number of these reactions appear to be the first steps in the linear portion of numerous biosynthesis pathways. The thermodynamically feasible ranges for the concentration ratios ATP/ADP, NAD(P)/NAD(P)H, and H(extracellular)(+)/H(intracellular)(+) are also determined and found to encompass the values observed experimentally in every case. Further, we find that the NAD/NADH and NADP/NADPH ratios maintained in the cell are close to the minimum feasible ratio and maximum feasible ratio, respectively.     

A reliable simulator for dynamic flux balance analysis

Dynamic flux balance analysis (DFBA) provides a platform for detailed design, control and optimization of biochemical process technologies. It is a promising modeling framework that combines genome‐scale metabolic network analysis with dynamic simulation of the extracellular environment. Dynamic flux balance analysis assumes that the intracellular species concentrations are in equilibrium with the extracellular environment. The resulting underdetermined stoichiometric model is solved under the assumption of a biochemical objective such as growth rate maximization. The model of the metabolism is coupled with the dynamic mass balance equations of the extracellular environment via expressions for the rates of substrate uptake and product excretion, which imposes additional constraints on the linear program (LP) defined by growth rate maximization of the metabolism. The linear program is embedded into the dynamic model of the bioreactor, and together with the additional constraints this provides an accurate model of the substrate consumption, product secretion, and biomass production during operation. A DFBA model consists of a system of ordinary differential equations for which the evaluation of the right‐hand side requires not only function evaluations, but also the solution of one or more linear programs. The numerical tool presented here accurately and efficiently simulates large‐scale dynamic flux balance models. The main advantages that this approach has over existing implementation are that the integration scheme has a variable step size, that the linear program only has to be solved when qualitative changes in the optimal flux distribution of the metabolic network occur, and that it can reliably simulate behavior near the boundary of the domain where the model is defined. This is illustrated through large‐scale examples taken from the literature. Biotechnol. Bioeng. 2013; 110: 792–802. © 2012 Wiley Periodicals, Inc.     

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     

Optimizing metabolic pathways by screening for feasible synthetic reactions

Background

Reconstruction of genome-scale metabolic networks has resulted in models capable of reproducing experimentally observed biomass yield/growth rates and predicting the effect of alterations in metabolism for biotechnological applications. The existing studies rely on modifying the metabolic network of an investigated organism by removing or inserting reactions taken either from evolutionary similar organisms or from databases of biochemical reactions (e.g., KEGG). A potential disadvantage of these knowledge-driven approaches is that the result is biased towards known reactions, as such approaches do not account for the possibility of including novel enzymes, together with the reactions they catalyze.

Results

Here, we explore the alternative of increasing biomass yield in three model organisms, namely Bacillus subtilis, Escherichia coli, and Hordeum vulgare, by applying small, chemically feasible network modifications. We use the predicted and experimentally confirmed growth rates of the wild-type networks as reference values and determine the effect of inserting mass-balanced, thermodynamically feasible reactions on predictions of growth rate by using flux balance analysis.

Conclusions

While many replacements of existing reactions naturally lead to a decrease or complete loss of biomass production ability, in all three investigated organisms we find feasible modifications which facilitate a significant increase in this biological function. We focus on modifications with feasible chemical properties and a significant increase in biomass yield. The results demonstrate that small modifications are sufficient to substantially alter biomass yield in the three organisms. The method can be used to predict the effect of targeted modifications on the yield of any set of metabolites (e.g., ethanol), thus providing a computational framework for synthetic metabolic engineering.     

Structural analysis of metabolic networks based on flux centrality

Metabolic reactions are fundamental to living organisms, and a large number of reactions simultaneously occur at a given time in living cells transforming diverse metabolites into each other. There has been an ongoing debate on how to classify metabolites with respect to their importance for metabolic performance, usually based on the analysis of topological properties of genome scale metabolic networks. However, none of these studies have accounted quantitatively for flux in metabolic networks, thus lacking an important component of a cell’s biochemistry.We therefore analyzed a genome scale metabolic network of Escherichia coli by comparing growth under 19 different growth conditions, using flux balance analysis and weighted network centrality investigation. With this novel concept of flux centrality we generated metabolite rankings for each particular growth condition. In contrast to the results of conventional analysis of genome scale metabolic networks, different metabolites were top-ranking dependent on the growth condition. At the same time, several metabolites were consistently among the high ranking ones. Those are associated with pathways that have been described by biochemists as the most central part of metabolism, such as glycolysis, tricarboxylic acid cycle and pentose phosphate pathway. The values for the average path length of the analyzed metabolite networks were between 10.5 and 12.6, supporting recent findings that the metabolic network of E. coli is not a small-world network.     

一种基于代谢网络分析最小化基因组的方法及其在大肠杆菌中的应用

最小生命体的合成是合成生物学研究的重要方向。最小化基因组的同时而又不对细胞生长产生影响是代谢工程研究的一个重要目标。文中提出了一种从基因组尺度代谢网络模型出发,通过零通量反应删除及对非必需基因组合删除计算获得基因组最小化代谢网络模型的方法,利用该方法简化了大肠杆菌经典代谢网络模型iAF1260,由起始的1 260个基因简化得到了312个基因,而最优生物质生成速率保持不变。基因组最小化代谢网络模型预测了在细胞正常生长的前提下包含最少基因的代谢途径,为大肠杆菌获得最小基因组的湿实验设计提供了重要参考。     

Genome-scale thermodynamic analysis of Escherichia coli metabolism

Genome-scale metabolic models are an invaluable tool for analyzing metabolic systems as they provide a more complete picture of the processes of metabolism. We have constructed a genome-scale metabolic model of Escherichia coli based on the iJR904 model developed by the Palsson Laboratory at the University of California at San Diego. Group contribution methods were utilized to estimate the standard Gibbs free energy change of every reaction in the constructed model. Reactions in the model were classified based on the activity of the reactions during optimal growth on glucose in aerobic media. The most thermodynamically unfavorable reactions involved in the production of biomass in E. coli were identified as ATP phosphoribosyltransferase, ATP synthase, methylene-tetra-hydrofolate dehydrogenase, and tryptophanase. The effect of a knockout of these reactions on the production of biomass and the production of individual biomass precursors was analyzed. Changes in the distribution of fluxes in the cell after knockout of these unfavorable reactions were also studied. The methodologies and results discussed can be used to facilitate the refinement of the feasible ranges for cellular parameters such as species concentrations and reaction rate constants.     

Quantification of metabolism in Saccharomyces cerevisiae under hyperosmotic conditions using elementary mode analysis

Yeast metabolism under hyperosmotic stress conditions was quantified using elementary mode analysis to obtain insights into the metabolic status of the cell. The fluxes of elementary modes were determined as solutions to a linear program that used the stoichiometry of the elementary modes as constraints. The analysis demonstrated that distinctly different sets of elementary modes operate under normal and hyperosmotic conditions. During the adaptation phase, elementary modes that only produce glycerol are active, while elementary modes that yield biomass, ethanol, and glycerol become active after the adaptive phase. The flux distribution in the metabolic network, calculated using the fluxes in the elementary modes, was employed to obtain the flux ratio at key nodes. At the glucose 6-phosphate (G6P) node, 25% of the carbon influx was diverted towards the pentose phosphate pathway under normal growth conditions, while only 0.3% of the carbon flux was diverted towards the pentose phosphate pathway during growth at 1?M NaCl, indicating that cell growth is arrested under hyperosmotic conditions. Further, objective functions were used in the linear program to obtain optimal solution spaces corresponding to the different accumulation rates. The analysis demonstrated that while biomass formation was optimal under normal growth conditions, glycerol synthesis was closer to optimal during adaptation to osmotic shock.     

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.     

Metabolic flux analysis for optimizing the specific growth rate of recombinant <Emphasis Type="Italic">Aspergillus niger</Emphasis>

A comprehensive metabolic network comprising three intracellular compartments (cytoplasm, mitochondrion and peroxisome) was developed for Aspergillus niger. The metabolic flux network includes carbohydrate and amino acid metabolism in both anabolic and catabolic reactions. Linear programming was used for the optimization of the specific growth rates in combination with 37 measured input and output fluxes of the key metabolites to evaluate corresponding intracellular flux distributions throughout the batch fermentations. Logarithmic sensitivity analysis revealed that the addition of proline, alanine and glutamate benefited growth in defined media. The experimental observations and flux analysis showed that tyrosine was a potential candidate for biomass production improvement. Model predictions was verified by conducting batch and fed-batch fermentations and it was found that the addition of the four amino acids according to the predetermined schedule resulted in a 44 and 41% improvements in biomass and recombinant protein productions, respectively.     

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.     

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.     

Prediction of microbial growth rate versus biomass yield by a metabolic network with kinetic parameters

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.     

Metabolic modeling of endosymbiont genome reduction on a temporal scale

A fundamental challenge in Systems Biology is whether a cell‐scale metabolic model can predict patterns of genome evolution by realistically accounting for associated biochemical constraints. Here, we study the order in which genes are lost in an in silico evolutionary process, leading from the metabolic network of Eschericia coli to that of the endosymbiont Buchnera aphidicola. We examine how this order correlates with the order by which the genes were actually lost, as estimated from a phylogenetic reconstruction. By optimizing this correlation across the space of potential growth and biomass conditions, we compute an upper bound estimate on the model's prediction accuracy (R=0.54). The model's network‐based predictive ability outperforms predictions obtained using genomic features of individual genes, reflecting the effect of selection imposed by metabolic stoichiometric constraints. Thus, while the timing of gene loss might be expected to be a completely stochastic evolutionary process, remarkably, we find that metabolic considerations, on their own, make a marked 40% contribution to determining when such losses occur.     

The metabolic flux phenotype of heterotrophic Arabidopsis cells reveals a complex response to changes in nitrogen supply

The extent to which individual plants utilise nitrate and ammonium, the two principal nitrogen sources in the rhizosphere, is variable and many species require a balance between the two forms for optimal growth. The effects of nitrate and ammonium on gene expression, enzyme activity and metabolite composition have been documented extensively with the aim of understanding the way in which plant cells respond to the different forms of nitrogen, but ultimately the impact of these changes on the organisation and operation of the central metabolic network can only be addressed by analysing the fluxes supported by the network. Accordingly steady‐state metabolic flux analysis was used to define the metabolic phenotype of a heterotrophic Arabidopsis thaliana cell culture grown in Murashige and Skoog and ammonium‐free media, treatments that influenced growth and biomass composition. Fluxes through the central metabolic network were deduced from the redistribution of label into metabolic intermediates and end products observed when cells were labelled with [1‐¹³C]‐, [2‐¹³C]‐ or [¹³C₆]glucose, in tandem with ¹⁴C‐measurements of the net accumulation of biomass. Analysis of the flux maps showed that: (i) flux through the oxidative pentose phosphate pathway varied independently of the reductant demand for biosynthesis, (ii) non‐plastidic processes made a significant and variable contribution to the provision of reducing power for the plastid, and (iii) the inclusion of ammonium in the growth medium increased cell maintenance costs, in agreement with the futile cycling model of ammonium toxicity. These conclusions highlight the complexity of the metabolic response to a change in nitrogen nutrition.     

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.     

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.