A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Classification and sensitivity analysis of a proposed primary metabolic reaction network for Streptomyces lividans

Constructing a metabolic flux analysis model is in principle fairly straightforward. However, there are a number of mathematical pitfalls. First, dependent reactions are a recurring problem and, second, the choice of reactions to measure may not be straight-forward. A method for systematic identification of dependent reactions and a thorough reactions classification procedure is presented. A well-defined stoichiometric presentation can provide significant insight into metabolic control mechanisms. Two methods for analyzing the impact of perturbations in the measured fluxes on the remaining metabolism and the impact of changes in biomass composition on the calculated metabolic reactions is developed. A metabolic reaction network proposed for Streptomyces lividans is used as an example to demonstrate the outlined analysis. It is concluded that oxygen utilization has the highest influence on the pathway fluxes and that realistic perturbations in the biomass composition do not significantly alter the flux patterns.     

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization,confidence bounds,and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.     

Ensemble modeling of metabolic networks

Complete modeling of metabolic networks is desirable, but it is difficult to accomplish because of the lack of kinetics. As a step toward this goal, we have developed an approach to build an ensemble of dynamic models that reach the same steady state. The models in the ensemble are based on the same mechanistic framework at the elementary reaction level, including known regulations, and span the space of all kinetics allowable by thermodynamics. This ensemble allows for the examination of possible phenotypes of the network upon perturbations, such as changes in enzyme expression levels. The size of the ensemble is reduced by acquiring data for such perturbation phenotypes. If the mechanistic framework is approximately accurate, the ensemble converges to a smaller set of models and becomes more predictive. This approach bypasses the need for detailed characterization of kinetic parameters and arrives at a set of models that describes relevant phenotypes upon enzyme perturbations.     

A kinetic model describes metabolic response to perturbations and distribution of flux control in the benzenoid network of Petunia hybrida

In recent years there has been much interest in the genetic enhancement of plant metabolism; however, attempts at genetic modification are often unsuccessful due to an incomplete understanding of network dynamics and their regulatory properties. Kinetic modeling of plant metabolic networks can provide predictive information on network control and response to genetic perturbations, which allow estimation of flux at any concentration of intermediate or enzyme in the system. In this research, a kinetic model of the benzenoid network was developed to simulate whole network responses to different concentrations of supplied phenylalanine (Phe) in petunia flowers and capture flux redistributions caused by genetic manipulations. Kinetic parameters were obtained by network decomposition and non‐linear least squares optimization of data from petunia flowers supplied with either 75 or 150 mm ²H₅‐Phe. A single set of kinetic parameters simultaneously accommodated labeling and pool size data obtained for all endogenous and emitted volatiles at the two concentrations of supplied ²H₅‐Phe. The generated kinetic model was validated using flowers from transgenic petunia plants in which benzyl CoA:benzyl alcohol/phenylethanol benzoyltransferase (BPBT) was down‐regulated via RNAi. The determined in vivo kinetic parameters were used for metabolic control analysis, in which flux control coefficients were calculated for fluxes around the key branch point at Phe and revealed that phenylacetaldehyde synthase activity is the primary controlling factor for the phenylacetaldehyde branch of the benzenoid network. In contrast, control of flux through the β‐oxidative and non‐β‐oxidative pathways is highly distributed.     

Metabolic flux control analysis of branch points: an improved approach to obtain flux control coefficients from large perturbation data

An overview of published approaches for the metabolic flux control analysis of branch points revealed that often not all fundamental constraints on the flux control coefficients have been taken into account. This has led to contradictory statements in literature on the minimum number of large perturbation experiments required to estimate the complete set of flux control coefficients C(J) for a metabolic branch point. An improved calculation procedure, based on approximate Lin-log reaction kinetics, is proposed, providing explicit analytical solutions of steady state fluxes and metabolite concentrations as a function of large changes in enzyme levels. The obtained solutions allow direct calculation of elasticity ratios from experimental data and subsequently all C(J)-values from the unique relation between elasticity ratio's and flux control coefficients. This procedure ensures that the obtained C(J)-values satisfy all fundamental constraints. From these it follows that for a three enzyme branch point only one characterised or two uncharacterised large flux perturbations are sufficient to obtain all C(J)- values. The improved calculation procedure is illustrated with four experimental cases.     

Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

Ensemble Modeling for Aromatic Production in Escherichia coli

Ensemble Modeling (EM) is a recently developed method for metabolic modeling, particularly for utilizing the effect of enzyme tuning data on the production of a specific compound to refine the model. This approach is used here to investigate the production of aromatic products in Escherichia coli. Instead of using dynamic metabolite data to fit a model, the EM approach uses phenotypic data (effects of enzyme overexpression or knockouts on the steady state production rate) to screen possible models. These data are routinely generated during strain design. An ensemble of models is constructed that all reach the same steady state and are based on the same mechanistic framework at the elementary reaction level. The behavior of the models spans the kinetics allowable by thermodynamics. Then by using existing data from the literature for the overexpression of genes coding for transketolase (Tkt), transaldolase (Tal), and phosphoenolpyruvate synthase (Pps) to screen the ensemble, we arrive at a set of models that properly describes the known enzyme overexpression phenotypes. This subset of models becomes more predictive as additional data are used to refine the models. The final ensemble of models demonstrates the characteristic of the cell that Tkt is the first rate controlling step, and correctly predicts that only after Tkt is overexpressed does an increase in Pps increase the production rate of aromatics. This work demonstrates that EM is able to capture the result of enzyme overexpression on aromatic producing bacteria by successfully utilizing routinely generated enzyme tuning data to guide model learning.     

K-FIT: An accelerated kinetic parameterization algorithm using steady-state fluxomic data

Kinetic models predict the metabolic flows by directly linking metabolite concentrations and enzyme levels to reaction fluxes. Robust parameterization of organism-level kinetic models that faithfully reproduce the effect of different genetic or environmental perturbations remains an open challenge due to the intractability of existing algorithms. This paper introduces Kinetics-based Fluxomics Integration Tool (K-FIT), a robust kinetic parameterization workflow that leverages a novel decomposition approach to identify steady-state fluxes in response to genetic perturbations followed by a gradient-based update of kinetic parameters until predictions simultaneously agree with the fluxomic data in all perturbed metabolic networks. The applicability of K-FIT to large-scale models is demonstrated by parameterizing an expanded kinetic model for E. coli (307 reactions and 258 metabolites) using fluxomic data from six mutants. The achieved thousand-fold speed-up afforded by K-FIT over meta-heuristic approaches is transformational enabling follow-up robustness of inference analyses and optimal design of experiments to inform metabolic engineering strategies.     

Optimal re-design of primary metabolism in Escherichia coli using linlog kinetics

This paper examines the validity of the linlog approach, which was recently developed in our laboratory, by comparison of two different kinetic models for the metabolic network of Escherichia coli. The first model is a complete mechanistic model; the second is an approximative model in which linlog kinetics are applied. The parameters of the linlog model (elasticities) are derived from the mechanistic model. Three different optimization cases are examined. In all cases, the objective is to calculate the enzyme levels that maximize a certain flux while keeping the total amount of enzyme constant and preventing large changes of metabolite concentrations. For an average variation of metabolite levels of 10% and individual changes of a factor 2, the predicted enzyme levels, metabolite concentrations and fluxes of both models are highly similar. This similarity holds for changes in enzyme level of a factor 4-6 and for changes in fluxes up to a factor 6. In all three cases, the predicted optimal enzyme levels could neither have been found by intuition-based approaches, nor on basis of flux control coefficients. This demonstrates that kinetic models are essential tools in Metabolic Engineering. In this respect, the linlog approach is a valuable extension of MCA, since it allows construction of kinetic models, based on MCA parameters, that can be used for constrained optimization problems and are valid for large changes of metabolite and enzyme levels.     

基于酶约束的代谢网络模型研究进展及其应用

基因组尺度代谢网络模型已经成功地应用于指导代谢工程改造,但由于传统通量平衡分析法仅考虑化学计量学和反应方向约束,模拟得到的是理论最优结果,对一些现象如代谢溢流、底物层级利用等无法准确描述。近年来人们通过在代谢网络模型中引入新的蛋白量、热力学等约束发展了新的约束优化计算方法,可以更准确真实地模拟细胞在不同条件下的代谢行为。文中主要对近年来提出的多种酶约束模型进行评述,对酶约束引入的基本思路、酶约束的数学方程表示及优化目标设定、引入酶约束后对代谢通量计算结果的影响及酶约束模型在代谢工程菌种改造中的应用等进行了全面深入的介绍,并提出了已有各种方法存在的主要问题,展望了相关方法的未来发展方向。通过引入新的约束,代谢网络模型能够更精确模拟和预测细胞在环境和基因扰动下的代谢行为,为代谢工程菌种改造提供更准确可靠的指导。     

Development of a mathematical model for evaluating the dynamics of normal and apoptotic Chinese hamster ovary cells

A metabolic flux based methodology was developed for modeling the metabolism of a Chinese hamster ovary cell line. The elimination of insignificant fluxes resulted in a simplified metabolic network which was the basis for modeling the significant metabolites. Employing kinetic rate expressions for growing and non-growing subpopulations, a logistic model was developed for cell growth and dynamic models were formulated to describe culture composition and monoclonal antibody (MAb) secretion. The model was validated for a range of nutrient concentrations. Good agreement was obtained between model predictions and experimental data. The ultimate goal of this study is to establish a comprehensive dynamic model which may be used for model-based optimization of the cell culture for MAb production in both batch and fed-batch systems.     

Genome-scale modeling of human metabolism – a systems biology approach

Altered metabolism is linked to the appearance of various human diseases and a better understanding of disease-associated metabolic changes may lead to the identification of novel prognostic biomarkers and the development of new therapies. Genome-scale metabolic models (GEMs) have been employed for studying human metabolism in a systematic manner, as well as for understanding complex human diseases. In the past decade, such metabolic models – one of the fundamental aspects of systems biology – have started contributing to the understanding of the mechanistic relationship between genotype and phenotype. In this review, we focus on the construction of the Human Metabolic Reaction database, the generation of healthy cell type- and cancer-specific GEMs using different procedures, and the potential applications of these developments in the study of human metabolism and in the identification of metabolic changes associated with various disorders. We further examine how in silico genome-scale reconstructions can be employed to simulate metabolic flux distributions and how high-throughput omics data can be analyzed in a context-dependent fashion. Insights yielded from this mechanistic modeling approach can be used for identifying new therapeutic agents and drug targets as well as for the discovery of novel biomarkers. Finally, recent advancements in genome-scale modeling and the future challenge of developing a model of whole-body metabolism are presented. The emergent contribution of GEMs to personalized and translational medicine is also discussed.     

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.     

Continuous modeling of metabolic networks with gene regulation in yeast and in vivo determination of rate parameters

A continuous model of a metabolic network including gene regulation to simulate metabolic fluxes during batch cultivation of yeast Saccharomyces cerevisiae was developed. The metabolic network includes reactions of glycolysis, gluconeogenesis, glycerol and ethanol synthesis and consumption, the tricarboxylic acid cycle, and protein synthesis. Carbon sources considered were glucose and then ethanol synthesized during growth on glucose. The metabolic network has 39 fluxes, which represent the action of 50 enzymes and 64 genes and it is coupled with a gene regulation network which defines enzyme synthesis (activities) and incorporates regulation by glucose (enzyme induction and repression), modeled using ordinary differential equations. The model includes enzyme kinetics, equations that follow both mass-action law and transport as well as inducible, repressible, and constitutive enzymes of metabolism. The model was able to simulate a fermentation of S. cerevisiae during the exponential growth phase on glucose and the exponential growth phase on ethanol using only one set of kinetic parameters. All fluxes in the continuous model followed the behavior shown by the metabolic flux analysis (MFA) obtained from experimental results. The differences obtained between the fluxes given by the model and the fluxes determined by the MFA do not exceed 25% in 75% of the cases during exponential growth on glucose, and 20% in 90% of the cases during exponential growth on ethanol. Furthermore, the adjustment of the fermentation profiles of biomass, glucose, and ethanol were 95%, 95%, and 79%, respectively. With these results the simulation was considered successful. A comparison between the simulation of the continuous model and the experimental data of the diauxic yeast fermentation for glucose, biomass, and ethanol, shows an extremely good match using the parameters found. The small discrepancies between the fluxes obtained through MFA and those predicted by the differential equations, as well as the good match between the profiles of glucose, biomass, and ethanol, and our simulation, show that this simple model, that does not rely on complex kinetic expressions, is able to capture the global behavior of the experimental data. Also, the determination of parameters using a straightforward minimization technique using data at only two points in time was sufficient to produce a relatively accurate model. Thus, even with a small amount of experimental data (rates and not concentrations) it was possible to estimate the parameters minimizing a simple objective function. The method proposed allows the obtention of reasonable parameters and concentrations in a system with a much larger number of unknowns than equations. Hence a contribution of this study is to present a convenient way to find in vivo rate parameters to model metabolic and genetic networks under different conditions.     

Inferring Metabolic States in Uncharacterized Environments Using Gene-Expression Measurements

The large size of metabolic networks entails an overwhelming multiplicity in the possible steady-state flux distributions that are compatible with stoichiometric constraints. This space of possibilities is largest in the frequent situation where the nutrients available to the cells are unknown. These two factors: network size and lack of knowledge of nutrient availability, challenge the identification of the actual metabolic state of living cells among the myriad possibilities. Here we address this challenge by developing a method that integrates gene-expression measurements with genome-scale models of metabolism as a means of inferring metabolic states. Our method explores the space of alternative flux distributions that maximize the agreement between gene expression and metabolic fluxes, and thereby identifies reactions that are likely to be active in the culture from which the gene-expression measurements were taken. These active reactions are used to build environment-specific metabolic models and to predict actual metabolic states. We applied our method to model the metabolic states of Saccharomyces cerevisiae growing in rich media supplemented with either glucose or ethanol as the main energy source. The resulting models comprise about 50% of the reactions in the original model, and predict environment-specific essential genes with high sensitivity. By minimizing the sum of fluxes while forcing our predicted active reactions to carry flux, we predicted the metabolic states of these yeast cultures that are in large agreement with what is known about yeast physiology. Most notably, our method predicts the Crabtree effect in yeast cells growing in excess glucose, a long-known phenomenon that could not have been predicted by traditional constraint-based modeling approaches. Our method is of immediate practical relevance for medical and industrial applications, such as the identification of novel drug targets, and the development of biotechnological processes that use complex, largely uncharacterized media, such as biofuel production.     

Towards Kinetic Modeling of Global Metabolic Networks: Methylobacterium extorquens AM1 Growth as Validation

Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, gluconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concentrations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K’s and K’eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.