A scientific workflow framework for 13C metabolic flux analysis

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 χ2 -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.

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.

Measuring metabolic reaction fluxes in living cells is difficult, yet important. The gold standard is to label extracellular metabolites with ¹³C, to use mass spectrometry to find out where the ¹³C-atoms ends up, and finally use mathematical modelling to calculate how quickly each reaction must have flowed, for the ¹³C-atoms to end up like that. This measurement thus relies on usage of the right mathematical model, which must be selected among various candidate models. In this manuscript, we present a new way to do this model selection step, utilizing validation data. Using an adopted approach to calculate the uncertainty of model predictions, we identify new validation experiments, which are neither too similar, nor too dissimilar, compared to the previous training data. The model candidate that is best at predicting this new validation data is the one chosen. Tests on simulated data where the true model is known, shows that the validation-based method is robust when the magnitude of the error in the measurement uncertainty is unknown, something that conventional methods are not. This improvement is important since true uncertainties can be difficult to estimate for these data. Finally, we demonstrate how the new method can be used on real data, to identify fluxes and important reactions.

Metabolic flux analysis of the neural cell glycocalyx reveals differential utilization of monosaccharides

Saccharides in our diet are major sources of carbon for the formation of biomass such as proteins, lipids, nucleic acids and glycans. Among the dietary monosaccharides, glucose occupies a central role in metabolism, but human blood contains regulated levels of other monosaccharides as well. Their influence on metabolism and how they are utilized have not been explored thoroughly. Applying metabolic flux analysis on glycan synthesis can reveal the pathways that supply glycosylation precursors and provide a snapshot of the metabolic state of the cell. In this study, we traced the incorporation of six 13C uniformly labeled monosaccharides in the N-glycans, O-glycans and glycosphingolipids of both pluripotent and neural NTERA-2 cells. We gathered detailed isotopologue data for hundreds of glycoconjugates using mass spectrometry methods. The contributions of de novo synthesis and direct incorporation pathways for glucose, mannose, fructose, galactose, N-acetylglucosamine and fucose were determined based on their isotope incorporation. Co-feeding studies revealed that fructose incorporation is drastically decreased by the presence of glucose, while mannose and galactose were much less affected. Furthermore, increased sialylation slowed down the turnover of glycans, but fucosylation attenuated this effect. Our results demonstrated that exogenous monosaccharide utilization can vary markedly depending on the cell differentiation state and monosaccharide availability, and that the incorporation of carbons can also differ among different glycan structures. We contend that the analysis of metabolic isotope labeling of glycans can yield new insights about cell metabolism.

The Design of FluxML: A Universal Modeling Language for 13C Metabolic Flux Analysis

¹³C metabolic flux analysis (MFA) is the method of choice when a detailed inference of intracellular metabolic fluxes in living organisms under metabolic quasi-steady state conditions is desired. Being continuously developed since two decades, the technology made major contributions to the quantitative characterization of organisms in all fields of biotechnology and health-related research. ¹³C MFA, however, stands out from other "-omics sciences," in that it requires not only experimental-analytical data, but also mathematical models and a computational toolset to infer the quantities of interest, i.e., the metabolic fluxes. At present, these models cannot be conveniently exchanged between different labs. Here, we present the implementation-independent model description language FluxML for specifying ¹³C MFA models. The core of FluxML captures the metabolic reaction network together with atom mappings, constraints on the model parameters, and the wealth of data configurations. In particular, we describe the governing design processes that shaped the FluxML language. We demonstrate the utility of FluxML to represent many contemporary experimental-analytical requirements in the field of ¹³C MFA. The major aim of FluxML is to offer a sound, open, and future-proof language to unambiguously express and conserve all the necessary information for model re-use, exchange, and comparison. Along with FluxML, several powerful computational tools are supplied for easy handling, but also to maintain a maximum of flexibility. Altogether, the FluxML collection is an "all-around carefree package" for ¹³C MFA modelers. We believe that FluxML improves scientific productivity as well as transparency and therewith contributes to the efficiency and reproducibility of computational modeling efforts in the field of ¹³C MFA.

Towards an Understanding of Energy Impairment in Huntington's Disease Brain

This review systematically examines the evidence for shifts in flux through energy generating biochemical pathways in Huntington’s disease (HD) brains from humans and model systems. Compromise of the electron transport chain (ETC) appears not to be the primary or earliest metabolic change in HD pathogenesis. Rather, compromise of glucose uptake facilitates glucose flux through glycolysis and may possibly decrease flux through the pentose phosphate pathway (PPP), limiting subsequent NADPH and GSH production needed for antioxidant protection. As a result, oxidative damage to key glycolytic and tricarboxylic acid (TCA) cycle enzymes further restricts energy production so that while basal needs may be met through oxidative phosphorylation, those of excessive stimulation cannot. Energy production may also be compromised by deficits in mitochondrial biogenesis, dynamics or trafficking. Restrictions on energy production may be compensated for by glutamate oxidation and/or stimulation of fatty acid oxidation. Transcriptional dysregulation generated by mutant huntingtin also contributes to energetic disruption at specific enzymatic steps. Many of the alterations in metabolic substrates and enzymes may derive from normal regulatory feedback mechanisms and appear oscillatory. Fine temporal sequencing of the shifts in metabolic flux and transcriptional and expression changes associated with mutant huntingtin expression remain largely unexplored and may be model dependent. Differences in disease progression among HD model systems at the time of experimentation and their varying states of metabolic compensation may explain conflicting reports in the literature. Progressive shifts in metabolic flux represent homeostatic compensatory mechanisms that maintain the model organism through presymptomatic and symptomatic stages.

Computational Approaches on Stoichiometric and Kinetic Modeling for Efficient Strain Design

Engineering biological systems that are capable of overproducing products of interest is the ultimate goal of any biotechnology application. To this end, stoichiometric (or steady state) and kinetic models are increasingly becoming available for a variety of organisms including prokaryotes, eukaryotes, and microbial communities. This ever-accelerating pace of such model reconstructions has also spurred the development of optimization-based strain design techniques. This chapter highlights a number of such frameworks developed in recent years in order to generate testable hypotheses (in terms of genetic interventions), thus addressing the challenges in metabolic engineering. In particular, three major methods are covered in detail including two methods for designing strains (i.e., one stoichiometric model-based and the other by integrating kinetic information into a stoichiometric model) and one method for analyzing microbial communities.

Recent advances in high-throughput 13C-fluxomics

The rise of high throughput (HT) strain engineering tools accompanying the area of synthetic biology is supporting the generation of a large number of microbial cell factories. A current bottleneck in process development is our limited capacity to rapidly analyze the metabolic state of the engineered strains, and in particular their intracellular fluxes. HT ¹³C-fluxomics workflows have not yet become commonplace, despite the existence of several HT tools at each of the required stages. This includes cultivation and sampling systems, analytics for isotopic analysis, and software for data processing and flux calculation. Here, we review recent advances in the field and highlight bottlenecks that must be overcome to allow the emergence of true HT ¹³C-fluxomics workflows.