Comparison of metabolic states using genome-scale metabolic models.

Genome-scale metabolic models (GEMs) are comprehensive knowledge bases of cellular metabolism and serve as mathematical tools for studying biological phenotypes and metabolic states or conditions in various organisms and cell types. Given the sheer size and complexity of human metabolism, selecting parameters for existing analysis methods such as metabolic objective functions and model constraints is not straightforward in human GEMs. In particular, comparing several conditions in large GEMs to identify condition- or disease-specific metabolic features is challenging. In this study, we showcase a scalable, model-driven approach for an in-depth investigation and comparison of metabolic states in large GEMs which enables identifying the underlying functional differences. Using a combination of flux space sampling and network analysis, our approach enables extraction and visualisation of metabolically distinct network modules. Importantly, it does not rely on known or assumed objective functions. We apply this novel approach to extract the biochemical differences in adipocytes arising due to unlimited vs blocked uptake of branched-chain amino acids (BCAAs, considered as biomarkers in obesity) using a human adipocyte GEM (iAdipocytes1809). The biological significance of our approach is corroborated by literature reports confirming our identified metabolic processes (TCA cycle and Fatty acid metabolism) to be functionally related to BCAA metabolism. Additionally, our analysis predicts a specific altered uptake and secretion profile indicating a compensation for the unavailability of BCAAs. Taken together, our approach facilitates determining functional differences between any metabolic conditions of interest by offering a versatile platform for analysing and comparing flux spaces of large metabolic networks.

Integrating systemic and molecular levels to infer key drivers sustaining metabolic adaptations.

Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.

Genome Scale-Differential Flux Analysis reveals deregulation of lung cell metabolism on SARS-CoV-2 infection.

The COVID-19 pandemic is posing an unprecedented threat to the whole world. In this regard, it is absolutely imperative to understand the mechanism of metabolic reprogramming of host human cells by SARS-CoV-2. A better understanding of the metabolic alterations would aid in design of better therapeutics to deal with COVID-19 pandemic. We developed an integrated genome-scale metabolic model of normal human bronchial epithelial cells (NHBE) infected with SARS-CoV-2 using gene-expression and macromolecular make-up of the virus. The reconstructed model predicts growth rates of the virus in high agreement with the experimental measured values. Furthermore, we report a method for conducting genome-scale differential flux analysis (GS-DFA) in context-specific metabolic models. We apply the method to the context-specific model and identify severely affected metabolic modules predominantly comprising of lipid metabolism. We conduct an integrated analysis of the flux-altered reactions, host-virus protein-protein interaction network and phospho-proteomics data to understand the mechanism of flux alteration in host cells. We show that several enzymes driving the altered reactions inferred by our method to be directly interacting with viral proteins and also undergoing differential phosphorylation under diseased state. In case of SARS-CoV-2 infection, lipid metabolism particularly fatty acid oxidation, cholesterol biosynthesis and beta-oxidation cycle along with arachidonic acid metabolism are predicted to be most affected which confirms with clinical metabolomics studies. GS-DFA can be applied to existing repertoire of high-throughput proteomic or transcriptomic data in diseased condition to understand metabolic deregulation at the level of flux.

Validity of natural isotope abundance correction for metabolic flux analysis.

A pervasive issue in stable isotope tracing and metabolic flux analysis is the presence of naturally occurring isotopes such as 13C. For mass isotopomer distributions (MIDs) measured by mass spectrometry, it is common practice to correct for natural occurrence of isotopes within metabolites of interest using a linear transform based on binomial distributions. The resulting corrected MIDs are often used to fit metabolic network models and infer metabolic fluxes, which implicitly assumes that corrected MIDs will yield the same flux solution as the actual observed MIDs. Although this assumption can be empirically verified in special cases by simulation studies, there seems to be no published proof of this important property for the general case. In this paper, we prove that this property holds for the case of noise-free MID data obtained at steady state. On the other hand, for noisy MID data, the flux solution will generally differ between the two representations. These results provide a theoretical foundation for the common practice of MID correction in metabolic flux analysis.

Dynamic metabolic resource allocation based on the maximum entropy principle.

Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle of maximum entropy. These concepts both generalise and unify prior approaches to dynamic metabolic modelling by establishing a smooth interpolation between dynamic flux balance analysis and dynamic metabolic models without regulation. The resulting theory is successful in describing 'bet-hedging' strategies employed by cell populations dealing with uncertainty in a fluctuating environment, including heterogenous resource investment, accumulation of reserves in growth-limiting conditions, and the observed behaviour of yeast growing in batch and continuous cultures. The maximum entropy principle is also shown to yield an optimal control law consistent with partitioning resources between elementary flux mode families, which has important practical implications for model reduction, selection, and simulation.

A Pareto approach to resolve the conflict between information gain and experimental costs: Multiple-criteria design of carbon labeling experiments.

Science revolves around the best way of conducting an experiment to obtain insightful results. Experiments with maximal information content can be found by computational experimental design (ED) strategies that identify optimal conditions under which to perform the experiment. Several criteria have been proposed to measure the information content, each emphasizing different aspects of the design goal, i.e., reduction of uncertainty. Where experiments are complex or expensive, second sight is at the budget governing the achievable amount of information. In this context, the design objectives cost and information gain are often incommensurable, though dependent. By casting the ED task into a multiple-criteria optimization problem, a set of trade-off designs is derived that approximates the Pareto-frontier which is instrumental for exploring preferable designs. In this work, we present a computational methodology for multiple-criteria ED of information-rich experiments that accounts for virtually any set of design criteria. The methodology is implemented for the case of 13C metabolic flux analysis (MFA), which is arguably the most expensive type among the 'omics' technologies, featuring dozens of design parameters (tracer composition, analytical platform, measurement selection etc.). Supported by an innovative visualization scheme, we demonstrate with two realistic showcases that the use of multiple criteria reveals deep insights into the conflicting interplay between information carriers and cost factors that are not amendable to single-objective ED. For instance, tandem mass spectrometry turns out as best-in-class with respect to information gain, while it delivers this information quality cheaper than the other, routinely applied analytical technologies. Therewith, our Pareto approach to ED offers the investigator great flexibilities in the conception phase of a study to balance costs and benefits.

Dynamic flux balance analysis with nonlinear objective function.

Dynamic flux balance analysis (DFBA) extends flux balance analysis and enables the combined simulation of both intracellular and extracellular environments of microbial cultivation processes. A DFBA model contains two coupled parts, a dynamic part at the upper level (extracellular environment) and an optimization part at the lower level (intracellular environment). Both parts are coupled through substrate uptake and product secretion rates. This work proposes a Karush-Kuhn-Tucker condition based solution approach for DFBA models, which have a nonlinear objective function in the lower-level part. To solve this class of DFBA models an extreme-ray-based reformulation is proposed to ensure certain regularity of the lower-level optimization problem. The method is introduced by utilizing two simple example networks and then applied to a realistic model of central carbon metabolism of wild-type Corynebacterium glutamicum.

Assessment of FBA Based Gene Essentiality Analysis in Cancer with a Fast Context-Specific Network Reconstruction Method.

MOTIVATION: Gene Essentiality Analysis based on Flux Balance Analysis (FBA-based GEA) is a promising tool for the identification of novel metabolic therapeutic targets in cancer. The reconstruction of cancer-specific metabolic networks, typically based on gene expression data, constitutes a sensible step in this approach. However, to our knowledge, no extensive assessment on the influence of the reconstruction process on the obtained results has been carried out to date. RESULTS: In this article, we aim to study context-specific networks and their FBA-based GEA results for the identification of cancer-specific metabolic essential genes. To that end, we used gene expression datasets from the Cancer Cell Line Encyclopedia (CCLE), evaluating the results obtained in 174 cancer cell lines. In order to more clearly observe the effect of cancer-specific expression data, we did the same analysis using randomly generated expression patterns. Our computational analysis showed some essential genes that are fairly common in the reconstructions derived from both gene expression and randomly generated data. However, though of limited size, we also found a subset of essential genes that are very rare in the randomly generated networks, while recurrent in the sample derived networks, and, thus, would presumably constitute relevant drug targets for further analysis. In addition, we compare the in-silico results to high-throughput gene silencing experiments from Project Achilles with conflicting results, which leads us to raise several questions, particularly the strong influence of the selected biomass reaction on the obtained results. Notwithstanding, using previous literature in cancer research, we evaluated the most relevant of our targets in three different cancer cell lines, two derived from Gliobastoma Multiforme and one from Non-Small Cell Lung Cancer, finding that some of the predictions are in the right track.

Rapid Prediction of Bacterial Heterotrophic Fluxomics Using Machine Learning and Constraint Programming.

13C metabolic flux analysis (13C-MFA) has been widely used to measure in vivo enzyme reaction rates (i.e., metabolic flux) in microorganisms. Mining the relationship between environmental and genetic factors and metabolic fluxes hidden in existing fluxomic data will lead to predictive models that can significantly accelerate flux quantification. In this paper, we present a web-based platform MFlux (http://mflux.org) that predicts the bacterial central metabolism via machine learning, leveraging data from approximately 100 13C-MFA papers on heterotrophic bacterial metabolisms. Three machine learning methods, namely Support Vector Machine (SVM), k-Nearest Neighbors (k-NN), and Decision Tree, were employed to study the sophisticated relationship between influential factors and metabolic fluxes. We performed a grid search of the best parameter set for each algorithm and verified their performance through 10-fold cross validations. SVM yields the highest accuracy among all three algorithms. Further, we employed quadratic programming to adjust flux profiles to satisfy stoichiometric constraints. Multiple case studies have shown that MFlux can reasonably predict fluxomes as a function of bacterial species, substrate types, growth rate, oxygen conditions, and cultivation methods. Due to the interest of studying model organism under particular carbon sources, bias of fluxome in the dataset may limit the applicability of machine learning models. This problem can be resolved after more papers on 13C-MFA are published for non-model species.

Robustness analysis of elementary flux modes generated by column generation.

Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA, when the errors are only in measurements and bounded by an interval, the robust problem can be stated as a convex quadratic programming (QP) problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem, thereby avoiding explicit enumeration of EFMs. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicates that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.

On dynamically generating relevant elementary flux modes in a metabolic network using optimization.

Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.

Software applications for flux balance analysis.

Flux balance analysis (FBA) is a widely used computational method for characterizing and engineering intrinsic cellular metabolism. The increasing number of its successful applications and growing popularity are possibly attributable to the availability of specific software tools for FBA. Each tool has its unique features and limitations with respect to operational environment, user-interface and supported analysis algorithms. Presented herein is an in-depth evaluation of currently available FBA applications, focusing mainly on usability, functionality, graphical representation and inter-operability. Overall, most of the applications are able to perform basic features of model creation and FBA simulation. COBRA toolbox, OptFlux and FASIMU are versatile to support advanced in silico algorithms to identify environmental and genetic targets for strain design. SurreyFBA, WEbcoli, Acorn, FAME, GEMSiRV and MetaFluxNet are the distinct tools which provide the user friendly interfaces in model handling. In terms of software architecture, FBA-SimVis and OptFlux have the flexible environments as they enable the plug-in/add-on feature to aid prospective functional extensions. Notably, an increasing trend towards the implementation of more tailored e-services such as central model repository and assistance to collaborative efforts was observed among the web-based applications with the help of advanced web-technologies. Furthermore, most recent applications such as the Model SEED, FAME, MetaFlux and MicrobesFlux have even included several routines to facilitate the reconstruction of genome-scale metabolic models. Finally, a brief discussion on the future directions of FBA applications was made for the benefit of potential tool developers.

Software applications toward quantitative metabolic flux analysis and modeling.

Metabolites and their pathways are central for adaptation and survival. Metabolic modeling elucidates in silico all the possible flux pathways (flux balance analysis, FBA) and predicts the actual fluxes under a given situation, further refinement of these models is possible by including experimental isotopologue data. In this review, we initially introduce the key theoretical concepts and different analysis steps in the modeling process before comparing flux calculation and metabolite analysis programs such as C13, BioOpt, COBRA toolbox, Metatool, efmtool, FiatFlux, ReMatch, VANTED, iMAT and YANA. Their respective strengths and limitations are discussed and compared to alternative software. While data analysis of metabolites, calculation of metabolic fluxes, pathways and their condition-specific changes are all possible, we highlight the considerations that need to be taken into account before deciding on a specific software. Current challenges in the field include the computation of large-scale networks (in elementary mode analysis), regulatory interactions and detailed kinetics, and these are discussed in the light of powerful new approaches.