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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.↗

Systematic comparison of local approaches for isotopically nonstationary metabolic flux analysis

Quantification of reaction fluxes of metabolic networks can help us understand how the integration of different metabolic pathways determine cellular functions. Yet, intracellular fluxes cannot be measured directly but are estimated with metabolic flux analysis (MFA) that relies on the patterns of isotope labeling of metabolites in the network. For metabolic systems, typical for plants, where all potentially labeled atoms effectively have only one source atom pool, only isotopically nonstationary MFA can provide information about intracellular fluxes. There are several global approaches that implement MFA for an entire metabolic network and estimate, at once, a steady-state flux distribution for all reactions with identifiable fluxes in the network. In contrast, local approaches deal with estimation of fluxes for a subset of reactions, with smaller data demand for flux estimation. Here we present a systematic comparative review and benchmarking of the existing local approaches for isotopically nonstationary MFA. The comparison is conducted with respect to the required data and underlying computational problems solved on a synthetic network example. Furthermore, we benchmark the performance of these approaches in estimating fluxes for a subset of reactions using data obtained from the simulation of nitrogen fluxes in the Arabidopsis thaliana core metabolism. The findings pinpoint practical aspects that need to be considered when applying local approaches for flux estimation in large-scale plant metabolic networks.

59 BASIC BIOLOGICAL SCIENCES↗

Chapter 14: Dynamic Flux Analysis: An Experimental Approach of Fluxomics

Metabolic flux analysis represents an essential perspective to understand cellular physiology and offers quantitative information to guide pathway engineering. A valuable approach for experimental elucidation of metabolic flux is dynamic flux analysis, which estimates the relative or absolute flow rates through a series of metabolic intermediates in a given pathway. It is based on kinetic isotope labeling experiments, liquid chromatography-mass spectrometry (LC-MS), and computational analysis that relate kinetic isotope trajectories of metabolites to pathway activity. Herein, we illustrate the mathematic principles underlying the dynamic flux analysis and mainly focus on describing the experimental procedures for data generation. This protocol is exemplified using cyanobacterial metabolism as an example, for which reliable labeling data for central carbon metabolites can be acquired quantitatively. This protocol is applicable to other microbial systems as well and can be readily adapted to address different metabolic processes.

BASIC BIOLOGICAL SCIENCES↗

Isotopically nonstationary metabolic flux analysis of plants: recent progress and future opportunities

Metabolic flux analysis (MFA) is a valuable tool for quantifying cellular phenotypes and to guide plant metabolic engineering. By introducing stable isotopic tracers and employing mathematical models, MFA can quantify the rates of metabolic reactions through biochemical pathways. Recent applications of isotopically nonstationary MFA (INST–MFA) to plants have elucidated nonintuitive metabolism in leaves under optimal and stress conditions, described coupled fluxes for fast–growing algae, and produced a synergistic multi–organ flux map that is a first in MFA for any biological system. Finally, these insights could not be elucidated through other approaches and show the potential of INST–MFA to correct an oversimplified understanding of plant metabolism.

59 BASIC BIOLOGICAL SCIENCES↗

Mechanisms of metabolic adaptation in the duckweed Lemna gibba: an integrated metabolic, transcriptomic and flux analysis

Abstract Background Duckweeds are small, rapidly growing aquatic flowering plants. Due to their ability for biomass production at high rates they represent promising candidates for biofuel feedstocks. Duckweeds are also excellent model organisms because they can be maintained in well-defined liquid media, usually reproduce asexually, and because genomic resources are becoming increasingly available. To demonstrate the utility of duckweed for integrated metabolic studies, we examined the metabolic adaptation of growing Lemna gibba cultures to different nutritional conditions. Results To establish a framework for quantitative metabolic research in duckweeds we derived a central carbon metabolism network model of Lemna gibba based on its draft genome. Lemna gibba fronds were grown with nitrate or glutamine as nitrogen source. The two conditions were compared by quantification of growth kinetics, metabolite levels, transcript abundance, as well as by 13 C-metabolic flux analysis. While growing with glutamine, the fronds grew 1.4 times faster and accumulated more protein and less cell wall components compared to plants grown on nitrate. Characterization of photomixotrophic growth by 13 C-metabolic flux analysis showed that, under both metabolic growth conditions, the Calvin-Benson-Bassham cycle and the oxidative pentose-phosphate pathway are highly active, creating a futile cycle with net ATP consumption. Depending on the nitrogen source, substantial reorganization of fluxes around the tricarboxylic acid cycle took place, leading to differential formation of the biosynthetic precursors of the Asp and Gln families of proteinogenic amino acids. Despite the substantial reorganization of fluxes around the tricarboxylic acid cycle, flux changes could largely not be associated with changes in transcripts. Conclusions Through integrated analysis of growth rate, biomass composition, metabolite levels, and metabolic flux, we show that Lemna gibba is an excellent system for quantitative metabolic studies in plants. Our study showed that Lemna gibba adjusts to different nitrogen sources by reorganizing central metabolism. The observed disconnect between gene expression regulation and metabolism underscores the importance of metabolic flux analysis as a tool in such studies.

59 BASIC BIOLOGICAL SCIENCES↗

Leonid Storm Flux Analysis From One Leonid MAC Video AL50R

A detailed meteor flux analysis is presented of a seventeen-minute portion of one videotape, collected on November 18, 1999, during the Leonid Multi-instrument Aircraft Campaign. The data was recorded around the peak of the Leonid meteor storm using an intensified CCD camera pointed towards the low southern horizon. Positions of meteors on the sky were measured. These measured meteor distributions were compared to a Monte Carlo simulation, which is a new approach to parameter estimation for mass ratio and flux. Comparison of simulated flux versus observed flux levels, seen between 1:50:00 and 2:06:41 UT, indicate a magnitude population index of r = 1.8 +/- 0.1 and mass ratio of s = 1.64 +/- 0.06. The average spatial density of the material contributing to the Leonid storm peak is measured at 0.82 +/- 0.19 particles per square kilometer per hour for particles of at least absolute visual magnitude +6.5. Clustering analysis of the arrival times of Leonids impacting the earth's atmosphere over the total observing interval shows no enhancement or clumping down to time scales of the video frame rate. This indicates a uniformly random temporal distribution of particles in the stream encountered during the 1999 epoch. Based on the observed distribution of meteors on the sky and the model distribution, recommendations am made for the optimal pointing directions for video camera meteor counts during future ground and airborne missions.

Gural, Peter S.↗

Walking the ‘design–build–test–learn’ cycle: flux analysis and genetic engineering reveal the pliability of plant central metabolism

Oilseeds are of great economic importance for food and animal feed and their contribution to renewable energy production. Soybean seeds (Glycine max (L.) Merr.) contain c. 40% protein, 20% oil, and 30% carbohydrate (Song et al., 2023). Due to the massive scale of soybean production worldwide, even small improvements in seed protein and oil content make economic sense (Song et al., 2023). Successful manipulation of seed composition largely depends on a thorough understanding of the processes and pathways involved in the biosynthesis of fatty acids and amino acids, which are the building blocks of lipids and proteins. Rational engineering of the synthesis of storage reserves, that is, the rerouting of metabolic flux in central metabolism, is difficult to accomplish due to the complexity of the central metabolic network, the intricate regulation of its enzymes at multiple levels, and the often-unpredictable effects of genetic manipulation (Sweetlove et al., 2017). Therefore, the advancement of our understanding of central metabolism and its control of carbon partitioning requires following an iterative ‘design–build–test–learn’ (DBTL) cycle (Lin & Eudes, 2020) where metabolic flux analysis and hypothesis testing by transgenic approaches are important components. Previous metabolic studies on soybeans using isotopic tracers and metabolic flux analysis have provided insight into how lipid and protein biosynthesis occurs simultaneously during seed development (Allen et al., 2009; Allen & Young, 2013; Kambhampati et al., 2021). In an article published in this issue of New Phytologist, Morley et al. (2023; 1834–1851) put the insights they have gained into the delivery of metabolic precursors and energy cofactors to oil synthesis to the test and arrive at a successful metabolic engineering design. They show that an increase in seed oil content in soybeans can be achieved by overexpression of malic enzyme (ME) during seed development. Malic enzyme refers to a class of decarboxylating malate dehydrogenase enzymes that oxidize malate with NAD + or NADP + as redox cofactor while generating pyruvate and CO 2 . Like higher plants in general, soybean has distinct NADH- or NADPH-producing ME isoforms localized to the cytosol, plastid, or mitochondria (Gerrard Wheeler et al., 2016). As Morley et al. show, an increase in seed oil can be achieved in particular when a NADP+-dependent enzyme isoform (EC 1.1.1.40) is overexpressed in the plastid. Given the complex compartmentalization of pyruvate, malate, and redox metabolism (Fig. 1), increased oil production appears to depend on additional pyruvate and reducing equivalents being produced in the same compartment where de novo fatty acid biosynthesis occurs: the plastid.

59 BASIC BIOLOGICAL SCIENCES↗

Metabolic flux analysis in leaf metabolism quantifies the link between photorespiration and one carbon metabolism

Photorespiration is the second largest carbon flux in most leaves and is integrated into metabolism broadly including one-carbon (C 1 ) metabolism. Photorespiratory intermediates such as serine and others may serve as sources of C 1 units, but it is unclear to what degree this happens in vivo, whether altered photorespiration changes flux to C 1 metabolism, and if so through which intermediates. To clarify these questions, we quantified carbon flux from photorespiration to C 1 metabolism using 13 CO 2 labelling and isotopically non-stationary metabolic flux analysis in Arabidopsis thaliana under different O 2 concentrations which modulate photorespiration. The results revealed that ~5.8% of assimilated carbon passes to C 1 metabolism under ambient photorespiratory conditions, but this flux greatly decreases under limited photorespiration. Furthermore, the primary carbon flux from photorespiration to C 1 metabolism is through serine. Our results provide fundamental insight into how photorespiration is integrated into C 1 metabolism, with possible implications for C 1 metabolic response to climate change.

Photosynthesis↗

Quantifying the propagation of parametric uncertainty on flux balance analysis

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

59 BASIC BIOLOGICAL SCIENCES↗

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↗

Adapting isotopic tracer and metabolic flux analysis approaches to study C1 metabolism

Single-carbon (C1, or one-carbon) substrates are promising feedstocks for sustainable biofuel and biochemical production. Crucial to the goal of engineering C1-utilizing strains for improved production is a quantitative understanding of the organization, regulation and rates of the reactions that underpin C1 metabolism. 13 C Metabolic flux analysis (MFA) is a well-established platform for interrogating these questions with multi-carbon substrates, and uses the differential labeling of metabolites that results from feeding a substrate with position-specific incorporation of 13 C in order to infer quantitative fluxes and pathway topology. Furthermore, adapting isotopic tracer approaches to C1 metabolism, where position-specific substrate labeling is impossible, requires additional experimental considerations. Here we review recent studies that have developed isotopic tracer approaches to overcome the challenge of uniform metabolite labeling and provide quantitative insight into C1 metabolism.

59 BASIC BIOLOGICAL SCIENCES↗

The metabolic origins of non-photorespiratory CO 2 release during photosynthesis: a metabolic flux analysis

Respiration in the light (R L ) releases CO 2 in photosynthesizing leaves and is a phenomenon that occurs independently from photorespiration. Since R L lowers net carbon fixation, understanding R L could help improve plant carbon-use efficiency and models of crop photosynthesis. Although R L was identified more than 75 years ago, its biochemical mechanisms remain unclear. To identify reactions contributing to R L , we mapped metabolic fluxes in photosynthesizing source leaves of the oilseed crop and model plant camelina (Camelina sativa). We performed a flux analysis using isotopic labeling patterns of central metabolites during 13 CO 2 labeling time course, gas exchange, and carbohydrate production rate experiments. To quantify the contributions of multiple potential CO 2 sources with statistical and biological confidence, we increased the number of metabolites measured and reduced biological and technical heterogeneity by using single mature source leaves and quickly quenching metabolism by directly injecting liquid N 2 ; we then compared the goodness-of-fit between these data and data from models with alternative metabolic network structures and constraints. Our analysis predicted that R L releases 5.2 μmol CO2 g –1 FW h –1 of CO 2 , which is relatively consistent with a value of 9.3 μmol CO 2 g –1 FW h –1 measured by CO 2 gas exchange. The results indicated that ≤10% of R L results from TCA cycle reactions, which are widely considered to dominate R L . Further analysis of the results indicated that oxidation of glucose-6-phosphate to pentose phosphate via 6-phosphogluconate (the G6P/OPP shunt) can account for >% of CO 2 released by R L .

59 BASIC BIOLOGICAL SCIENCES↗

PET-FBA: A lightweight enzyme allocation and thermodynamics-constrained flux analysis approach to explore Escherichia coli metabolic adaptation to intracellular acidification

Escherichia coli employs diverse strategies to adapt to acidic environments that disrupt enzyme activity and the thermodynamic feasibility of essential reactions. To understand the impact of pH stress on cell metabolism, we present the PET-FBA (pH-, Enzyme protein allocation-, and Thermodynamics-constrained Flux Balance Analysis) framework. PET-FBA extends genome-scale modeling by integrating enzyme protein costs and reaction Gibbs free energy changes. Additionally, by incorporating pH-dependent enzyme kinetics in response to intracellular acidification, this framework enables the simulation of E. coli's metabolic adjustments across varying external pH levels. The model's accuracy is validated by comparing in silico growth simulations with experimental measurements under both anaerobic and aerobic conditions, as well as in silico gene knockouts of essential genes. By explicitly incorporating pH effects, our model accurately replicates the metabolic shift towards lactate production as the primary fermentation product at low pH in anaerobic conditions. This shift is only predicted when enzyme kinetics are dynamically adjusted as a function of pH. Further analysis revealed that this shift can be attributed to the reduced protein efficiency of the acetyl-CoA branch compared to lactate dehydrogenase under acidic stress, which then becomes crucial for maintaining NAD regeneration and cell growth at low pH. Furthermore, we identified strategies for enhancing cell growth under acidic anaerobic conditions by improving the enzyme activity of lactate dehydrogenase and pyruvate formate lyase, which increases NAD production efficiency and reduces enzyme protein allocation costs. Designed as a lightweight yet versatile framework, PET-FBA enables efficient genome-scale metabolic analysis. Using E. coli as a model system, our framework provides a systematic approach to understanding metabolic responses to environmental stress, pinpointing key metabolic bottlenecks, and identifying potential targets for strain optimization.

42 ENGINEERING↗

Uses of Multi-Objective Flux Analysis for Optimization of Microbial Production of Secondary Metabolites

Secondary metabolites are not essential for the growth of microorganisms, but they play a critical role in how microbes interact with their surroundings. In addition to this important ecological role, secondary metabolites also have a variety of agricultural, medicinal, and industrial uses, and thus the examination of secondary metabolism of plants and microbes is a growing scientific field. While the chemical production of certain secondary metabolites is possible, industrial-scale microbial production is a green and economically attractive alternative. This is even more true, given the advances in bioengineering that allow us to alter the workings of microbes in order to increase their production of compounds of interest. This type of engineering requires detailed knowledge of the “chassis” organism’s metabolism. Since the resources and the catalytic capacity of enzymes in microbes is finite, it is important to examine the tradeoffs between various bioprocesses in an engineered system and alter its working in a manner that minimally perturbs the robustness of the system while allowing for the maximum production of a product of interest. The in silico multi-objective analysis of metabolism using genome-scale models is an ideal method for such examinations.

59 BASIC BIOLOGICAL SCIENCES↗

Heat Flux Analysis From IR Imaging on Proto-MPEX

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a linear device used to develop the source and heating concept for MPEX, an experiment to study plasma–material interactions for future fusion reactors. This paper highlights recent analysis and results on Proto-MPEX using an infrared (IR) camera, a key tool for imaging heat fluxes measured at the material target. The target heat fluxes are crucial to understanding the source and heating concepts. The recent analysis includes the application of homography and 3-D finite-element methods to provide between-shot measurements of the 2-D target heat flux profile. The IR camera inferred heat flux is shown to correlate with Langmuir probe inferred heat fluxes for a range of parameters in helicon only and helicon + electron cyclotron heated discharges. Results show both desirable central and undesirable edge heat flux for helicon source and electron heating on the target. These heat flux measurements are shown to be important for better understanding of the source and heating physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Root system architecture and environmental flux analysis in mature crops using 3D root mesocosms

Current methods of root sampling typically only obtain small or incomplete sections of root systems and do not capture their true complexity. To facilitate the visualization and analysis of full-sized plant root systems in 3-dimensions, we developed customized mesocosm growth containers. While highly scalable, the design presented here uses an internal volume of 45 ft 3 (1.27 m 3 ), suitable for large crop and bioenergy grass root systems to grow largely unconstrained. Furthermore, they allow for the excavation and preservation of 3-dimensional root system architecture (RSA), and facilitate the collection of time-resolved subterranean environmental data. Sensor arrays monitoring matric potential, temperature and CO 2 levels are buried in a grid formation at various depths to assess environmental fluxes at regular intervals. Methods of 3D data visualization of fluxes were developed to allow for comparison with root system architectural traits. Following harvest, the recovered root system can be digitally reconstructed in 3D through photogrammetry, which is an inexpensive method requiring only an appropriate studio space and a digital camera. We developed a pipeline to extract features from the 3D point clouds, or from derived skeletons that include point cloud voxel number as a proxy for biomass, total root system length, volume, depth, convex hull volume and solidity as a function of depth. Ground-truthing these features with biomass measurements from manually dissected root systems showed a high correlation. We evaluated switchgrass, maize, and sorghum root systems to highlight the capability for species wide comparisons. We focused on two switchgrass ecotypes, upland (VS16) and lowland (WBC3), in identical environments to demonstrate widely different root system architectures that may be indicative of core differences in their rhizoeconomic foraging strategies. Finally, we imposed a strong physiological water stress and manipulated the growth medium to demonstrate whole root system plasticity in response to environmental stimuli. Hence, these new “3D Root Mesocosms” and accompanying computational analysis provides a new paradigm for study of mature crop systems and the environmental fluxes that shape them.

59 BASIC BIOLOGICAL SCIENCES↗