Construction of an E. Coli genome-scale atom mapping model for MFA calculations

Metabolic flux analysis (MFA) has so far been restricted to lumped networks lacking many important pathways, partly due to the difficulty in automatically generating isotope mapping matrices for genome-scale metabolic networks. Here we introduce a procedure that uses a compound matching algorithm based on the graph theoretical concept of pattern recognition along with relevant reaction information to automatically generate genome-scale atom mappings which trace the path of atoms from reactants to products for every reaction. The procedure is applied to the iAF1260 metabolic reconstruction of Escherichia coli yielding the genome-scale isotope mapping model imPR90068. This model maps 90,068 non-hydrogen atoms that span all 2,077 reactions present in iAF1260 (previous largest mapping model included 238 reactions). The expanded scope of the isotope mapping model allows the complete tracking of labeled atoms through pathways such as cofactor and prosthetic group biosynthesis and histidine metabolism. An EMU representation of imPR90068 is also constructed and made available.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

Rational design of 13C-labeling experiments for metabolic flux analysis in mammalian cells

ABSTRACT: BACKGROUND: 13C-Metabolic flux analysis (13C-MFA) is a standard technique to probe cellular metabolism and elucidate in vivo metabolic fluxes. 13C-Tracer selection is an important step in conducting 13C-MFA, however, current methods are restricted to trial-and-error approaches, which commonly focus on an arbitrary subset of the tracer design space. To systematically probe the complete tracer design space, especially for complex systems such as mammalian cells, there is a pressing need for new rational approaches to identify optimal tracers. RESULTS: Recently, we introduced a new framework for optimal 13C-tracer design based on elementary metabolite units (EMU) decomposition, in which a measured metabolite is decomposed into a linear combination of so-called EMU basis vectors. In this contribution, we applied the EMU method to a realistic network model of mammalian metabolism with lactate as the measured metabolite. The method was used to select optimal tracers for the two free fluxes in the system, the oxidative pentose phosphate pathway (oxPPP) flux and anaplerosis by pyruvate carboxylase (PC). Our approach was based on sensitivity analysis of EMU basis vector coefficients with respect to free fluxes. Through efficient grouping of coefficient sensitivities, simple tracer selection rules were derived for high-resolution quantification of the fluxes in the mammalian network model. The approach resulted in a significant reduction of the number of possible tracers and the feasible tracers were evaluated using numerical simulations. Two optimal, novel tracers were identified that have not been previously considered for 13C-MFA of mammalian cells, specifically [2,3,4,5,6-13C]glucose for elucidating oxPPP flux and [3,4-13C]glucose for elucidating PC flux. We demonstrate that 13C-glutamine tracers perform poorly in this system in comparison to the optimal glucose tracers. CONCLUSIONS: In this work, we have demonstrated that optimal tracer design does not need to be a pure simulation-based trial-and-error process; rather, rational insights into tracer design can be gained through the application of the EMU basis vector methodology. Using this approach, rational labeling rules can be established a priori to guide the selection of optimal 13C-tracers for high-resolution flux elucidation in complex metabolic network models.     

An elementary metabolite unit (EMU) based method of isotopically nonstationary flux analysis

Nonstationary metabolic flux analysis (NMFA) is at present a very computationally intensive exercise, especially for large reaction networks. We applied elementary metabolite unit (EMU) theory to NMFA, dramatically reducing computational difficulty. We also introduced block decoupling, a new method that systematically and comprehensively divides EMU systems of equations into smaller subproblems to further reduce computational difficulty. These improvements led to a 5000-fold reduction in simulation times, enabling an entirely new and more complicated set of problems to be analyzed with NMFA. We simulated a series of nonstationary and stationary GC/MS measurements for a large E. coli network that was then used to estimate parameters and their associated confidence intervals. We found that fluxes could be successfully estimated using only nonstationary labeling data and external flux measurements. Addition of near-stationary and stationary time points increased the precision of most parameters. Contrary to prior reports, the precision of nonstationary estimates proved to be comparable to the precision of estimates based solely on stationary data. Finally, we applied EMU-based NMFA to experimental nonstationary measurements taken from brown adipocytes and successfully estimated fluxes and some metabolite concentrations. By using NFMA instead of traditional MFA, the experiment required only 6 h instead of 50 (the time necessary for most metabolite labeling to reach 99% of isotopic steady state).     

Selection of tracers for 13C-metabolic flux analysis using elementary metabolite units (EMU) basis vector methodology

Metabolic flux analysis (MFA) is a powerful technique for elucidating in vivo fluxes in microbial and mammalian systems. A key step in (13)C-MFA is the selection of an appropriate isotopic tracer to observe fluxes in a proposed network model. Despite the importance of MFA in metabolic engineering and beyond, current approaches for tracer experiment design are still largely based on trial-and-error. The lack of a rational methodology for selecting isotopic tracers prevents MFA from achieving its full potential. Here, we introduce a new technique for tracer experiment design based on the concept of elementary metabolite unit (EMU) basis vectors. We demonstrate that any metabolite in a network model can be expressed as a linear combination of so-called EMU basis vectors, where the corresponding coefficients indicate the fractional contribution of the EMU basis vector to the product metabolite. The strength of this approach is the decoupling of substrate labeling, i.e. the EMU basis vectors, from the dependence on free fluxes, i.e. the coefficients. In this work, we demonstrate that flux observability inherently depends on the number of independent EMU basis vectors and the sensitivities of coefficients with respect to free fluxes. Specifically, the number of independent EMU basis vectors places hard limits on how many free fluxes can be determined in a model. This constraint is used as a guide for selecting feasible substrate labeling. In three example models, we demonstrate that by maximizing the number of independent EMU basis vectors the observability of a system is improved. Inspection of sensitivities of coefficients with respect to free fluxes provides additional constraints for proper selection of tracers. The present contribution provides a fresh perspective on an important topic in metabolic engineering, and gives practical guidelines and design principles for a priori selection of isotopic tracers for (13)C-MFA studies.     

Identification of genome-scale metabolic network models using experimentally measured flux profiles

Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.     

Multidimensional Dynamics of the Proteome in the Neurodegenerative and Aging Mammalian Brain

The amount of any given protein in the brain is determined by the rates of its synthesis and destruction, which are regulated by different cellular mechanisms. Here, we combine metabolic labeling in live mice with global proteomic profiling to simultaneously quantify both the flux and amount of proteins in mouse models of neurodegeneration. In multiple models, protein turnover increases were associated with increasing pathology. This method distinguishes changes in protein expression mediated by synthesis from those mediated by degradation. In the App^NL-F knockin mouse model of Alzheimer’s disease, increased turnover resulted from imbalances in both synthesis and degradation, converging on proteins associated with synaptic vesicle recycling (Dnm1, Cltc, Rims1) and mitochondria (Fis1, Ndufv1). In contrast to disease models, aging in wild-type mice caused a widespread decrease in protein recycling associated with a decrease in autophagic flux. Overall, this simple multidimensional approach enables a comprehensive mapping of proteome dynamics and identifies affected proteins in mouse models of disease and other live animal test settings.     

Literature mining supports a next-generation modeling approach to predict cellular byproduct secretion

The metabolic byproducts secreted by growing cells can be easily measured and provide a window into the state of a cell; they have been essential to the development of microbiology, cancer biology, and biotechnology. Progress in computational modeling of cells has made it possible to predict metabolic byproduct secretion with bottom-up reconstructions of metabolic networks. However, owing to a lack of data, it has not been possible to validate these predictions across a wide range of strains and conditions. Through literature mining, we were able to generate a database of Escherichia coli strains and their experimentally measured byproduct secretions. We simulated these strains in six historical genome-scale models of E. coli, and we report that the predictive power of the models has increased as they have expanded in size and scope. The latest genome-scale model of metabolism correctly predicts byproduct secretion for 35/89 (39%) of designs. The next-generation genome-scale model of metabolism and gene expression (ME-model) correctly predicts byproduct secretion for 40/89 (45%) of designs, and we show that ME-model predictions could be further improved through kinetic parameterization. We analyze the failure modes of these simulations and discuss opportunities to improve prediction of byproduct secretion.     

Interplay between Constraints,Objectives, and Optimality for Genome-Scale Stoichiometric Models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.     

Efficient control of population structure in model organism association mapping

Genomewide association mapping in model organisms such as inbred mouse strains is a promising approach for the identification of risk factors related to human diseases. However, genetic association studies in inbred model organisms are confronted by the problem of complex population structure among strains. This induces inflated false positive rates, which cannot be corrected using standard approaches applied in human association studies such as genomic control or structured association. Recent studies demonstrated that mixed models successfully correct for the genetic relatedness in association mapping in maize and Arabidopsis panel data sets. However, the currently available mixed-model methods suffer from computational inefficiency. In this article, we propose a new method, efficient mixed-model association (EMMA), which corrects for population structure and genetic relatedness in model organism association mapping. Our method takes advantage of the specific nature of the optimization problem in applying mixed models for association mapping, which allows us to substantially increase the computational speed and reliability of the results. We applied EMMA to in silico whole-genome association mapping of inbred mouse strains involving hundreds of thousands of SNPs, in addition to Arabidopsis and maize data sets. We also performed extensive simulation studies to estimate the statistical power of EMMA under various SNP effects, varying degrees of population structure, and differing numbers of multiple measurements per strain. Despite the limited power of inbred mouse association mapping due to the limited number of available inbred strains, we are able to identify significantly associated SNPs, which fall into known QTL or genes identified through previous studies while avoiding an inflation of false positives. An R package implementation and webserver of our EMMA method are publicly available.     

Identification of optimal measurement sets for complete flux elucidation in metabolic flux analysis experiments

Metabolic flux analysis (MFA) methods use external flux and isotopic measurements to quantify the magnitude of metabolic flows in metabolic networks. A key question in this analysis is choosing a set of measurements that is capable of yielding a unique flux distribution (identifiability). In this article, we introduce an optimization-based framework that uses incidence structure analysis to determine the smallest (or most cost-effective) set of measurements leading to complete flux elucidation. This approach relies on an integer linear programming formulation OptMeas that allows for the measurement of external fluxes and the complete (or partial) enumeration of the isotope forms of metabolites without requiring any of these to be chosen in advance. We subsequently query and refine the measurement sets suggested by OptMeas for identifiability and optimality. OptMeas is first tested on small to medium-size demonstration examples. It is subsequently applied to a large-scale E. coli isotopomer mapping model with more than 17,000 isotopomers. A number of additional measurements are identified leading to maximum flux elucidation in an amorphadiene producing E. coli strain.     

Metabolic flux balance analysis and the in silicoanalysis of Escherichia coliK-12 gene deletions

Background

Genome sequencing and bioinformatics are producing detailed lists of the molecular components contained in many prokaryotic organisms. From this 'parts catalogue' of a microbial cell, in silicorepresentations of integrated metabolic functions can be constructed and analyzed using flux balance analysis (FBA). FBA is particularly well-suited to study metabolic networks based on genomic, biochemical, and strain specific information.

Results

Herein, we have utilized FBA to interpret and analyze the metabolic capabilities of Escherichia coli. We have computationally mapped the metabolic capabilities of E. coliusing FBA and examined the optimal utilization of the E. colimetabolic pathways as a function of environmental variables. We have used an in silicoanalysis to identify seven gene products of central metabolism (glycolysis, pentose phosphate pathway, TCA cycle, electron transport system) essential for aerobic growth of E. colion glucose minimal media, and 15 gene products essential for anaerobic growth on glucose minimal media. The in silico tpi ^-, zwf, and pta ^-mutant strains were examined in more detail by mapping the capabilities of these in silicoisogenic strains.

Conclusions

We found that computational models of E. colimetabolism based on physicochemical constraints can be used to interpret mutant behavior. These in silicaresults lead to a further understanding of the complex genotype-phenotype relation. Supplementary information: 10.1186/1471-2105-1-1     

Kinetic isotope effects significantly influence intracellular metabolite 13C labeling patterns and flux determination

Rigorous mathematical modeling of carbon-labeling experiments allows estimation of fluxes through the pathways of central carbon metabolism, yielding powerful information for basic scientific studies as well as for a wide range of applications. However, the mathematical models that have been developed for flux determination from ¹³C labeling data have commonly neglected the influence of kinetic isotope effects on the distribution of ¹³C label in intracellular metabolites, as these effects have often been assumed to be inconsequential. We have used measurements of the ¹³C isotope effects on the pyruvate dehydrogenase enzyme from the literature to model isotopic fractionation at the pyruvate node and quantify the modeling errors expected to result from the assumption that isotope effects are negligible. We show that under some conditions kinetic isotope effects have a significant impact on the ¹³C labeling patterns of intracellular metabolites, and the errors associated with neglecting isotope effects in ¹³C-metabolic flux analysis models can be comparable in size to measurement errors associated with GC–MS. Thus, kinetic isotope effects must be considered in any rigorous assessment of errors in ¹³C labeling data, goodness-of-fit between model and data, confidence intervals of estimated metabolic fluxes, and statistical significance of differences between estimated metabolic flux distributions.     

Interpreting metabolic complexity via isotope-assisted metabolic flux analysis

Isotope-assisted metabolic flux analysis (iMFA) is a powerful method to mathematically determine the metabolic fluxome from experimental isotope labeling data and a metabolic network model. While iMFA was originally developed for industrial biotechnological applications, it is increasingly used to analyze eukaryotic cell metabolism in physiological and pathological states. In this review, we explain how iMFA estimates the intracellular fluxome, including data and network model (inputs), the optimization-based data fitting (process), and the flux map (output). We then describe how iMFA enables analysis of metabolic complexities and discovery of metabolic pathways. Our goal is to expand the use of iMFA in metabolism research, which is essential to maximizing the impact of metabolic experiments and continuing to advance iMFA and biocomputational techniques.     

CONSTRICTOR: Constraint Modification Provides Insight into Design of Biochemical Networks

Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique in silico strains, each representing an “expression state”, or a combination of gene expression levels required to achieve the overproduction target. The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.     

Validation-based model selection for 13C metabolic flux analysis with uncertain measurement errors

Accurate measurements of metabolic fluxes in living cells are central to metabolism research and metabolic engineering. The gold standard method is model-based metabolic flux analysis (MFA), where fluxes are estimated indirectly from mass isotopomer data with the use of a mathematical model of the metabolic network. A critical step in MFA is model selection: choosing what compartments, metabolites, and reactions to include in the metabolic network model. Model selection is often done informally during the modelling process, based on the same data that is used for model fitting (estimation data). This can lead to either overly complex models (overfitting) or too simple ones (underfitting), in both cases resulting in poor flux estimates. Here, we propose a method for model selection based on independent validation data. We demonstrate in simulation studies that this method consistently chooses the correct model in a way that is independent on errors in measurement uncertainty. This independence is beneficial, since estimating the true magnitude of these errors can be difficult. In contrast, commonly used model selection methods based on the χ²-test choose different model structures depending on the believed measurement uncertainty; this can lead to errors in flux estimates, especially when the magnitude of the error is substantially off. We present a new approach for quantification of prediction uncertainty of mass isotopomer distributions in other labelling experiments, to check for problems with too much or too little novelty in the validation data. Finally, in an isotope tracing study on human mammary epithelial cells, the validation-based model selection method identified pyruvate carboxylase as a key model component. Our results argue that validation-based model selection should be an integral part of MFA model development.     

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.     

13C metabolic flux analysis of three divergent extremely thermophilic bacteria: Geobacillus sp. LC300, Thermus thermophilus HB8, and Rhodothermus marinus DSM 4252

Thermophilic organisms are being increasingly investigated and applied in metabolic engineering and biotechnology. The distinct metabolic and physiological characteristics of thermophiles, including broad substrate range and high uptake rates, coupled with recent advances in genetic tool development, present unique opportunities for strain engineering. However, poor understanding of the cellular physiology and metabolism of thermophiles has limited the application of systems biology and metabolic engineering tools to these organisms. To address this concern, we applied high resolution ¹³C metabolic flux analysis to quantify fluxes for three divergent extremely thermophilic bacteria from separate phyla: Geobacillus sp. LC300, Thermus thermophilus HB8, and Rhodothermus marinus DSM 4252. We performed 18 parallel labeling experiments, using all singly labeled glucose tracers for each strain, reconstructed and validated metabolic network models, measured biomass composition, and quantified precise metabolic fluxes for each organism. In the process, we resolved many uncertainties regarding gaps in pathway reconstructions and elucidated how these organisms maintain redox balance and generate energy. Overall, we found that the metabolisms of the three thermophiles were highly distinct, suggesting that adaptation to growth at high temperatures did not favor any particular set of metabolic pathways. All three strains relied heavily on glycolysis and TCA cycle to generate key cellular precursors and cofactors. None of the investigated organisms utilized the Entner-Doudoroff pathway and only one strain had an active oxidative pentose phosphate pathway. Taken together, the results from this study provide a solid foundation for future model building and engineering efforts with these and related thermophiles.