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Model validation and selection in metabolic flux analysis and flux balance analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both methods use metabolic reaction network models of metabolism operating at steady state so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. These fluxes can shed light on basic biology and have been successfully used to inform metabolic engineering strategies. Several approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to compare alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, such as the quantification of flux estimate uncertainty, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ 2 -test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how adopting robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology.

59 BASIC BIOLOGICAL SCIENCES↗

Integrative teaching of metabolic modeling and flux analysis with interactive python modules

Abstract The modeling of rates of biochemical reactions—fluxes—in metabolic networks is widely used for both basic biological research and biotechnological applications. A number of different modeling methods have been developed to estimate and predict fluxes, including kinetic and constraint‐based (Metabolic Flux Analysis and flux balance analysis) approaches. Although different resources exist for teaching these methods individually, to‐date no resources have been developed to teach these approaches in an integrative way that equips learners with an understanding of each modeling paradigm, how they relate to one another, and the information that can be gleaned from each. We have developed a series of modeling simulations in Python to teach kinetic modeling, metabolic control analysis, 13C‐metabolic flux analysis, and flux balance analysis. These simulations are presented in a series of interactive notebooks with guided lesson plans and associated lecture notes. Learners assimilate key principles using models of simple metabolic networks by running simulations, generating and using data, and making and validating predictions about the effects of modifying model parameters. We used these simulations as the hands‐on computer laboratory component of a four‐day metabolic modeling workshop and participant survey results showed improvements in learners' self‐assessed competence and confidence in understanding and applying metabolic modeling techniques after having attended the workshop. The resources provided can be incorporated in their entirety or individually into courses and workshops on bioengineering and metabolic modeling at the undergraduate, graduate, or postgraduate level.

Kaste, Joshua A. M.↗

A High-Quality Genome-Scale Model for Rhodococcus opacus Metabolism

Rhodococcus opacus is a bacterium that has a high tolerance to aromatic compounds and can produce significant amounts of triacylglycerol (TAG). Here, we present iGR1773, the first genome-scale model (GSM) of R. opacus PD630 metabolism based on its genomic sequence and associated data. The model includes 1773 genes, 3025 reactions, and 1956 metabolites, was developed in a reproducible manner using CarveMe, and was evaluated through Metabolic Model tests (MEMOTE). We combine the model with two Constraint-Based Reconstruction and Analysis (COBRA) methods that use transcriptomics data to predict growth rates and fluxes: E-Flux2 and SPOT (Simplified Pearson Correlation with Transcriptomic data). Growth rates are best predicted by E-Flux2. Flux profiles are more accurately predicted by E-Flux2 than flux balance analysis (FBA) and parsimonious FBA (pFBA), when compared to 44 central carbon fluxes measured by 13C-Metabolic Flux Analysis (13C-MFA). Under glucose-fed conditions, E-Flux2 presents an R2 value of 0.54, while predictions based on pFBA had an inferior R2 of 0.28. We attribute this improved performance to the extra activity information provided by the transcriptomics data. For phenol-fed metabolism, in which the substrate first enters the TCA cycle, E-Flux2’s flux predictions display a high R2 of 0.96 while pFBA showed an R2 of 0.93. We also show that glucose metabolism and phenol metabolism function with similar relative ATP maintenance costs. These findings demonstrate that iGR1773 can help the metabolic engineering community predict aromatic substrate utilization patterns and perform computational strain design.

Roell, Garrett W.↗

BayFlux v1.0

This is an open source software library for performing Bayesian genome scale 13C Metabolic Flux Analysis (Bayesian 13C MFA). This is a new type of metabolic modeling that quantifies flux in a probabilistic manner at the genome scale.

Garcia Martin, Hector↗

maranasgroup/yeastsMFA

The parameterization of kinetic models requires measurement of fluxes and/or metabolite levels for a base strain and a few genetic perturbations thereof. Unlike stoichiometric models that are mostly invariant to the specific strain, it remains unclear whether kinetic models constructed for different strains of the same species have similar or significantly different kinetic parameters. This important question underpins the applicability range and prediction limits of kinetic reconstructions. To this end, herein we parameterize two separate large-scale kinetic models using K-FIT with genome-wide coverage corresponding to two distinct strains of Saccharomyces cerevisiae: CEN.PK 113-7D strain (model k-sacce306-CENPK), and growth-deficient BY4741 (isogenic to S288c; model k-sacce306-BY4741). The metabolic network for each model contains 306 reactions, 230 metabolites, and 119 substrate-level regulatory interactions. The two models (for CEN.PK and BY4741) recapitulate, within one standard deviation, 77% and 75% of the fitted dataset fluxes, respectively, determined by 13C metabolic flux analysis for wild-type and eight single-gene knockout mutants of each strain. Strain-specific kinetic parameterization results indicate that key enzymes in the TCA cycle, glycolysis, and arginine and proline metabolism drive the metabolic differences between these two strains of S. cerevisiae. Our results suggest that although kinetic models cannot be readily used across strains as stoichiometric models, they can capture species-specific information through the kinetic parameterization process.

Dinh, Hoang↗

maranasgroup/k-sacce306

The parameterization of kinetic models requires measurement of fluxes and/or metabolite levels for a base strain and a few genetic perturbations thereof. Unlike stoichiometric models that are mostly invariant to the specific strain, it remains unclear whether kinetic models constructed for different strains of the same species have similar or significantly different kinetic parameters. This important question underpins the applicability range and prediction limits of kinetic reconstructions. To this end, herein we parameterize two separate large-scale kinetic models using K-FIT with genome-wide coverage corresponding to two distinct strains of Saccharomyces cerevisiae: CEN.PK 113-7D strain (model k-sacce306-CENPK), and growth-deficient BY4741 (isogenic to S288c; model k-sacce306-BY4741). The metabolic network for each model contains 306 reactions, 230 metabolites, and 119 substrate-level regulatory interactions. The two models (for CEN.PK and BY4741) recapitulate, within one standard deviation, 77% and 75% of the fitted dataset fluxes, respectively, determined by 13C metabolic flux analysis for wild-type and eight single-gene knockout mutants of each strain. Strain-specific kinetic parameterization results indicate that key enzymes in the TCA cycle, glycolysis, and arginine and proline metabolism drive the metabolic differences between these two strains of S. cerevisiae. Our results suggest that although kinetic models cannot be readily used across strains as stoichiometric models, they can capture species-specific information through the kinetic parameterization process.

Dinh, Hoang↗

Creating multifunctional synthetic lichen platforms for sustainable biosynthesis of biofuel precursors

In this project, we were creating a sustainable platform for biofuel production, utilizing carbon-fixing autotrophs to supply oxygen and organic substrates to heterotrophic partners, which in turn produce carbon dioxide to feed the autotrophs. This symbiotic lichen community could lower the input cost, optimize metabolic exchanges and improve the generation of biofuel precursors through multi-omics driven genetic engineering. The cyanobacteria Synechococcus elongatus (S. elongatus) was used as the primary autotroph to provide oxygen and organic substrates, especially sucrose, to a co-culture system. The strain with overexpression of sucrose transporter cscB demonstrated a significant increase in sucrose production under salt stress as what we expected. We also implemented 13C metabolic flux analysis on the sucrose secreting strain S. elongatus cscB-NaCl. Next, transporters proteins like glutamate exporter mscCG from Corynebacterium glutamicum was overexpressed in S. elongatus to improve metabolite exchange.

Betenbaugh, Michael↗

13 C-metabolic flux analysis of Clostridium ljungdahlii illuminates its core metabolism under mixotrophic culture conditions

Carbon dioxide-fixing acetogenic bacteria (acetogens) utilizing the Wood-Ljungdahl Pathway (WLP) play an important role in CO 2 fixation in the biosphere and in the development of biological processes – alone or in cocultures, under both autotrophic and mixotrophic conditions – for production of chemicals and fuels. To date, limited work has been reported in experimentally validating and quantifying reaction fluxes of their core metabolic pathways. Here, the core metabolic model of the acetogen Clostridium ljungdahlii was interrogated using 13 C-metabolic flux analysis ( 13 C-MFA), which required the development of a new defined culture medium. Autotrophic, heterotrophic, and mixotrophic growth in defined medium was possible by adding 1 mM methionine to replace yeast extract. Our 13 C-MFA found an incomplete TCA cycle and inactive core pathways/reactions, notably those of the oxidative pentose phosphate pathway, Entner-Doudoroff pathway, and malate dehydrogenase. 13 C-MFA during mixotrophic growth using the parallel tracers [1– 13 C]fructose, [1,2– 13 C]fructose, [1,2,3– 13 C]fructose, and [U– 13 C]asparagine found that externally supplied CO 2 contributed the majority of carbon consumed. All internally-produced CO 2 from the catabolism of asparagine and fructose was consumed by the WLP. While glycolysis of fructose was active, it was not a major contributor to overall production of ATP, NADH, and acetyl-CoA. Gluconeogenic reactions were active despite the availability of organic carbon. Asparagine was catabolized equally via conversion to threonine and subsequent cleavage to produce acetaldehyde and glycine, and via deamination to fumarate and then the anaplerotic conversion of malate to pyruvate. Both pathways for asparagine catabolism produced acetyl-CoA, either directly via pyruvate or indirectly via the WLP. Cofactor stoichiometry based on our data predicted an essentially zero flux through the ferredoxin-dependent transhydrogenase (Nfn) reaction. Instead, nearly all of NADPH generated from the hydrogenase reaction was consumed by the WLP. Reduced ferredoxin produced by the hydrogenase reaction and glycolysis was mostly used for ATP generation via the RNF/ATPase system, with the remainder consumed by the WLP. NADH produced by RNF/ATPase was entirely consumed via the WLP.

13C metabolic flux analysis↗

Computational Framework for Machine-Learning-Enabled 13 C Fluxomics

13 C metabolic flux analysis (MFA) has emerged as a powerful tool for synthetic biology. This optimization-based approach suffers long computation time and unstable solutions depending on the initial guess. Here, we develop a machine-learning-based framework for 13 C fluxomics. Specifically, training and test data sets are generated by metabolic network decomposition and flux sampling, in which flux ratios at metabolic nodes and simulated labeling patterns of metabolites are used as training targets and features, respectively. To improve prediction accuracy and simplify the model, automated processes are developed for flux ratio selection based on solvability and feature screening based on importance. We found that predictive performance can be significantly improved using both amino acids and central carbon metabolites in comparison with amino acids alone. Together with measured external fluxes, the predicted flux ratios determine the mass balance system, yielding global flux distributions. This approach is validated by flux estimation using both simulated and experimental data in comparison with canonical 13 C MFA. The approach represents a reliable fluxomics method readily applicable to high-throughput metabolic phenotyping, which highlights the advances of intelligent learning algorithms in synthetic biology, specifically in the Test and Learn stage of the Design-Build-Test-Learn cycle.

13C metabolic flux analysis↗

Analyzing Mass Spectrometry Imaging Data of 13C-Labeled Phospholipids in Camelina sativa and Thlaspi arvense (Pennycress) Embryos

The combination of 13C-isotopic labeling and mass spectrometry imaging (MSI) offers an approach to analyze metabolic flux in situ. However, combining isotopic labeling and MSI presents technical challenges ranging from sample preparation, label incorporation, data collection, and analysis. Isotopic labeling and MSI individually create large, complex data sets, and this is compounded when both methods are combined. Therefore, analyzing isotopically labeled MSI data requires streamlined procedures to support biologically meaningful interpretations. Using currently available software and techniques, here we describe a workflow to analyze 13C-labeled isotopologues of the membrane lipid and storage oil lipid intermediate―phosphatidylcholine (PC). Our results with embryos of the oilseed crops, Camelina sativa and Thlaspi arvense (pennycress), demonstrated greater 13C-isotopic labeling in the cotyledons of developing embryos compared with the embryonic axis. Greater isotopic enrichment in PC molecular species with more saturated and longer chain fatty acids suggest different flux patterns related to fatty acid desaturation and elongation pathways. The ability to evaluate MSI data of isotopically labeled plant embryos will facilitate the potential to investigate spatial aspects of metabolic flux in situ.

metabolomics↗

Re-Programing Glucose Catabolism in the Microalga Chlorella sorokiniana under Light Condition

The microalga Chlorella sorokiniana has attracted much attention for lipid production and wastewater treatment. It can perform photosynthesis and organic carbon utilization concurrently. To understand its phototrophic metabolism, a biomass compositional analysis, a 13 C metabolic flux analysis, and metabolite pool size analyses were performed. Under dark condition, the oxidative pentose phosphate pathway (OPP) was the major route for glucose catabolism (88% carbon flux) and a cyclic OPP–glycolytic route for glucose catabolism was formed. Under light condition, fluxes in the glucose catabolism, tricarboxylic acid (TCA) cycle, and anaplerotic reaction (CO 2 fixation via phosphoenolpyruvate carboxylase) were all suppressed. Meanwhile, the RuBisCO reaction became active and the ratio of its carbon fixation to glucose carbon utilization was determined as 7:100. Moreover, light condition significantly reduced the pool sizes of sugar phosphate metabolites (such as E4P, F6P, and S7P) and promoted biomass synthesis (which reached 0.155 h –1 ). In addition, light condition increased glucose consumption rates, leading to higher ATP and NADPH production and a higher protein content (43% vs. 30%) in the biomass during the exponential growth phase.

13C-MFA↗

Daylength variation affects growth, photosynthesis, leaf metabolism, partitioning, and metabolic fluxes

Abstract Daylength, a seasonal and latitudinal variable, exerts a substantial impact on plant growth. However, the relationship between daylength and growth is nonproportional, suggesting the existence of adaptive mechanisms. Thus, our study aimed to comprehensively investigate the adaptive strategies employed by plants in response to daylength variation. We grew false flax (Camelina sativa) plants, a model oilseed crop, under long-day (LD) and short-day (SD) conditions and used growth measurements, gas exchange measurements, and isotopic labeling techniques, including 13C, 14C, and 2H2O, to determine responses to different daylengths. Our findings revealed that daylength influences various growth parameters, photosynthetic physiology, carbon partitioning, metabolic fluxes, and metabolite levels. SD plants employed diverse mechanisms to compensate for reduced CO2 fixation in the shorter photoperiod. These mechanisms included enhanced photosynthetic rates and reduced respiration in the light (RL), leading to increased shoot investment. Additionally, SD plants exhibited reduced rates of the glucose 6-phosphate (G6P) shunt and greater partitioning of sugars into starch, thereby sustaining carbon availability during the longer night. Isotopic labeling results further demonstrated substantial alterations in the partitioning of amino acids and TCA cycle intermediates between rapidly and slowly turning over pools. Overall, the results point to multiple developmental, physiological, and metabolic ways in which plants adapt to different daylengths to maintain growth.

59 BASIC BIOLOGICAL SCIENCES↗