Minimal cut sets (MCSs) have emerged as an important branch of constraint-based metabolic modeling, offering a versatile framework for analyzing and engineering metabolic networks. Over the past two decades, MCSs have evolved from a theoretical concept into a powerful tool for identifying tailored metabolic intervention strategies and studying robustness and failure modes of metabolic networks. Successful (experimental) applications range from designing highly efficient microbial cell factories to targeting cancer cell metabolism. This review highlights key conceptual and algorithmic advancements that have transformed MCSs into a flexible methodology applicable to metabolic models of any size. It also provides a comprehensive overview of their applications and concludes with a perspective on future research directions. The review aims to equip both newcomers and experts with the knowledge needed to effectively leverage MCSs for metabolic network analysis and design, therapeutic targeting, and beyond.

SUMMARY: Computational metabolomics workflows have revolutionized the untargeted metabolomics field. However, the organization and prioritization of metabolite features remains a laborious process. Organizing metabolomics data is often done through mass fragmentation-based spectral similarity grouping, resulting in feature sets that also represent an intuitive and scientifically meaningful first stage of analysis in untargeted metabolomics. Exploiting such feature sets, feature-set testing has emerged as an approach that is widely used in genomics and targeted metabolomics pathway enrichment analyses. It allows for formally combining groupings with statistical testing into more meaningful pathway enrichment conclusions. Here, we present msFeaST (mass spectral Feature Set Testing), a feature-set testing and visualization workflow for LC-MS/MS untargeted metabolomics data. Feature-set testing involves statistically assessing differential abundance patterns for groups of features across experimental conditions. We developed msFeaST to make use of spectral similarity-based feature groupings generated using k-medoids clustering, where the resulting clusters serve as a proxy for grouping structurally similar features with potential biosynthesis pathway relationships. Spectral clustering done in this way allows for feature group-wise statistical testing using the globaltest package, which provides high power to detect small concordant effects via joint modeling and reduced multiplicity adjustment penalties. Hence, msFeaST provides interactive integration of the semi-quantitative experimental information with mass-spectral structural similarity information, enhancing the prioritization of features and feature sets during exploratory data analysis. AVAILABILITY AND IMPLEMENTATION: The msFeaST workflow is freely available through https://github.com/kevinmildau/msFeaST and built to work on MacOS and Linux systems.

SUMMARY: PyCoMo is a python package for quick and easy generation of genome-scale compartmentalized community metabolic models that are compliant with current openCOBRA file formats. The resulting models can be used to predict (i) the maximum growth rate at a given abundance profile, (ii) the feasible community compositions at a given growth rate, and (iii) all exchange metabolites and cross-feeding interactions in a community metabolic model independent of the abundance profile; we demonstrate PyCoMo's capability by analysing methane production in a previously published simplified biogas community metabolic model. AVAILABILITY AND IMPLEMENTATION: PyCoMo is freely available under an MIT licence at http://github.com/univieCUBE/PyCoMo, the Python Package Index, and Zenodo.

Genome-scale metabolic models (GSMMs) offer a holistic view of biochemical reaction networks, enabling in-depth analyses of metabolism across species and tissues in multiple conditions. However, comparing GSMMs Against each other poses challenges as current dimensionality reduction algorithms or clustering methods lack mechanistic interpretability, and often rely on subjective assumptions. Here, we propose a new approach utilizing logisitic principal component analysis (LPCA) that efficiently clusters GSMMs while singling out mechanistic differences in terms of reactions and pathways that drive the categorization. We applied LPCA to multiple diverse datasets, including GSMMs of 222 Escherichia-strains, 343 budding yeasts (Saccharomycotina), 80 human tissues, and 2943 Firmicutes strains. Our findings demonstrate LPCA's effectiveness in preserving microbial phylogenetic relationships and discerning human tissue-specific metabolic profiles, exhibiting comparable performance to traditional methods like t-distributed stochastic neighborhood embedding (t-SNE) and Jaccard coefficients. Moreover, the subsystems and associated reactions identified by LPCA align with existing knowledge, underscoring its reliability in dissecting GSMMs and uncovering the underlying drivers of separation.

MOTIVATION: Characterizing all steady-state flux distributions in metabolic models remains limited to small models due to the explosion of possibilities. Often it is sufficient to look only at all possible overall conversions a cell can catalyze ignoring the details of intracellular metabolism. Such a characterization is achieved by elementary conversion modes (ECMs), which can be conveniently computed with ecmtool. However, currently, ecmtool is memory intensive, and it cannot be aided appreciably by parallelization. RESULTS: We integrate mplrs-a scalable parallel vertex enumeration method-into ecmtool. This speeds up computation, drastically reduces memory requirements and enables ecmtool's use in standard and high-performance computing environments. We show the new capabilities by enumerating all feasible ECMs of the near-complete metabolic model of the minimal cell JCVI-syn3.0. Despite the cell's minimal character, the model gives rise to 4.2×109 ECMs and still contains several redundant sub-networks. AVAILABILITY AND IMPLEMENTATION: ecmtool is available at https://github.com/SystemsBioinformatics/ecmtool. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Chromatographic peak picking is among the first steps in data processing workflows of raw LC-HRMS datasets in untargeted metabolomics applications. Its performance is crucial for the holistic detection of all metabolic features as well as their relative quantification for statistical analysis and metabolite identification. Random noise, non-baseline separated compounds and unspecific background signals complicate this task. RESULTS: A machine-learning-based approach entitled PeakBot was developed for detecting chromatographic peaks in LC-HRMS profile-mode data. It first detects all local signal maxima in a chromatogram, which are then extracted as super-sampled standardized areas (retention-time versus m/z). These are subsequently inspected by a custom-trained convolutional neural network that forms the basis of PeakBot's architecture. The model reports if the respective local maximum is the apex of a chromatographic peak or not as well as its peak center and bounding box. In training and independent validation datasets used for development, PeakBot achieved a high performance with respect to discriminating between chromatographic peaks and background signals (accuracy of 0.99). For training the machine-learning model a minimum of 100 reference features are needed to learn their characteristics to achieve high-quality peak-picking results for detecting such chromatographic peaks in an untargeted fashion. PeakBot is implemented in python (3.8) and uses the TensorFlow (2.5.0) package for machine-learning related tasks. It has been tested on Linux and Windows OSs. AVAILABILITY AND IMPLEMENTATION: The package is available free of charge for non-commercial use (CC BY-NC-SA). It is available at https://github.com/christophuv/PeakBot. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Untargeted metabolomics data analysis is highly labour intensive and can be severely frustrated by both experimental noise and redundant features. Homologous polymer series is a particular case of features that can either represent large numbers of noise features or alternatively represent features of interest with large peak redundancy. Here, we present homologueDiscoverer, an R package that allows for the targeted and untargeted detection of homologue series as well as their evaluation and management using interactive plots and simple local database functionalities. AVAILABILITY AND IMPLEMENTATION: homologueDiscoverer is freely available at GitHub https://github.com/kevinmildau/homologueDiscoverer. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Metabolomic time course analyses of biofluids are highly relevant for clinical diagnostics. However, many sampling methods suffer from unknown sample sizes, commonly known as size effects. This prevents absolute quantification of biomarkers. Recently, several mathematical post acquisition normalization methods have been developed to overcome these problems either by exploiting already known pharmacokinetic information or by statistical means. Here we present an improved normalization method, MIX, that combines the advantages of both approaches. It couples two normalization terms, one based on a pharmacokinetic model (PKM) and the other representing a popular statistical approach, probabilistic quotient normalization (PQN), in a single model. To test the performance of MIX, we generated synthetic data closely resembling real finger sweat metabolome measurements. We show that MIX normalization successfully tackles key weaknesses of the individual strategies: it (i) reduces the risk of overfitting with PKM, and (ii), contrary to PQN, it allows to compute sample volumes. Finally, we validate MIX by using real finger sweat as well as blood plasma metabolome data and demonstrate that MIX allows to better and more robustly correct for size effects. In conclusion, the MIX method improves the reliability and robustness of quantitative biomarker detection in finger sweat and other biofluids, paving the way for biomarker discovery and hypothesis generation from metabolomic time course data.

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass "reaction", which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed "without cancellations". In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.

BACKGROUND: Elementary flux mode (EFM) analysis is a well-established, yet computationally challenging approach to characterize metabolic networks. Standard algorithms require huge amounts of memory and lack scalability which limits their application to single servers and consequently limits a comprehensive analysis to medium-scale networks. Recently, Avis et al. developed mplrs-a parallel version of the lexicographic reverse search (lrs) algorithm, which, in principle, enables an EFM analysis on high-performance computing environments (Avis and Jordan. mplrs: a scalable parallel vertex/facet enumeration code. arXiv:1511.06487 , 2017). Here we test its applicability for EFM enumeration. RESULTS: We developed EFMlrs, a Python package that gives users access to the enumeration capabilities of mplrs. EFMlrs uses COBRApy to process metabolic models from sbml files, performs loss-free compressions of the stoichiometric matrix, and generates suitable inputs for mplrs as well as efmtool, providing support not only for our proposed new method for EFM enumeration but also for already established tools. By leveraging COBRApy, EFMlrs also allows the application of additional reaction boundaries and seamlessly integrates into existing workflows. CONCLUSION: We show that due to mplrs's properties, the algorithm is perfectly suited for high-performance computing (HPC) and thus offers new possibilities for the unbiased analysis of substantially larger metabolic models via EFM analyses. EFMlrs is an open-source program that comes together with a designated workflow and can be easily installed via pip.

Chinese hamster ovary (CHO) cells are the leading platform for the production of biopharmaceuticals with human-like glycosylation. The standard practice for cell line generation relies on trial and error approaches such as adaptive evolution and high-throughput screening, which typically take several months. Metabolic modeling could aid in designing better producer cell lines and thus shorten development times. The genome-scale metabolic model (GSMM) of CHO can accurately predict growth rates. However, in order to predict rational engineering strategies it also needs to accurately predict intracellular fluxes. In this work we evaluated the agreement between the fluxes predicted by parsimonious flux balance analysis (pFBA) using the CHO GSMM and a wide range of 13C metabolic flux data from literature. While glycolytic fluxes were predicted relatively well, the fluxes of tricarboxylic acid (TCA) cycle were vastly underestimated due to too low energy demand. Inclusion of computationally estimated maintenance energy significantly improved the overall accuracy of intracellular flux predictions. Maintenance energy was therefore determined experimentally by running continuous cultures at different growth rates and evaluating their respective energy consumption. The experimentally and computationally determined maintenance energy were in good agreement. Additionally, we compared alternative objective functions (minimization of uptake rates of seven nonessential metabolites) to the biomass objective. While the predictions of the uptake rates were quite inaccurate for most objectives, the predictions of the intracellular fluxes were comparable to the biomass objective function.

Motivation: Elementary flux mode (EFM) analysis allows an unbiased description of metabolic networks in terms of minimal pathways (involving a minimal set of reactions). To date, the enumeration of EFMs is impracticable in genome-scale metabolic models. In a complementary approach, we introduce the concept of a flux tope (FT), involving a maximal set of reactions (with fixed directions), which allows one to study the coordination of reaction directions in metabolic networks and opens a new way for EFM enumeration. Results: A FT is a (nontrivial) subset of the flux cone specified by fixing the directions of all reversible reactions. In a consistent metabolic network (without unused reactions), every FT contains a 'maximal pathway', carrying flux in all reactions. This decomposition of the flux cone into FTs allows the enumeration of EFMs (of individual FTs) without increasing the problem dimension by reaction splitting. To develop a mathematical framework for FT analysis, we build on the concepts of sign vectors and hyperplane arrangements. Thereby, we observe that FT analysis can be applied also to flux optimization problems involving additional (inhomogeneous) linear constraints. For the enumeration of FTs, we adapt the reverse search algorithm and provide an efficient implementation. We demonstrate that (biomass-optimal) FTs can be enumerated in genome-scale metabolic models of B.cuenoti and E.coli, and we use FTs to enumerate EFMs in models of M.genitalium and B.cuenoti. Availability and implementation: The source code is freely available at https://github.com/mpgerstl/FTA. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Knockout strategies, particularly the concept of constrained minimal cut sets (cMCSs), are an important part of the arsenal of tools used in manipulating metabolic networks. Given a specific design, cMCSs can be calculated even in genome-scale networks. We would however like to find not only the optimal intervention strategy for a given design but the best possible design too. Our solution (PSOMCS) is to use particle swarm optimization (PSO) along with the direct calculation of cMCSs from the stoichiometric matrix to obtain optimal designs satisfying multiple objectives. RESULTS: To illustrate the working of PSOMCS, we apply it to a toy network. Next we show its superiority by comparing its performance against other comparable methods on a medium sized E. coli core metabolic network. PSOMCS not only finds solutions comparable to previously published results but also it is orders of magnitude faster. Finally, we use PSOMCS to predict knockouts satisfying multiple objectives in a genome-scale metabolic model of E. coli and compare it with OptKnock and RobustKnock. CONCLUSIONS: PSOMCS finds competitive knockout strategies and designs compared to other current methods and is in some cases significantly faster. It can be used in identifying knockouts which will force optimal desired behaviors in large and genome scale metabolic networks. It will be even more useful as larger metabolic models of industrially relevant organisms become available.

Elementary flux modes (EFMs) emerged as a formal concept to describe metabolic pathways and have become an established tool for constraint-based modeling and metabolic network analysis. EFMs are characteristic (support-minimal) vectors of the flux cone that contains all feasible steady-state flux vectors of a given metabolic network. EFMs account for (homogeneous) linear constraints arising from reaction irreversibilities and the assumption of steady state; however, other (inhomogeneous) linear constraints, such as minimal and maximal reaction rates frequently used by other constraint-based techniques (such as flux balance analysis [FBA]), cannot be directly integrated. These additional constraints further restrict the space of feasible flux vectors and turn the flux cone into a general flux polyhedron in which the concept of EFMs is not directly applicable anymore. For this reason, there has been a conceptual gap between EFM-based (pathway) analysis methods and linear optimization (FBA) techniques, as they operate on different geometric objects. One approach to overcome these limitations was proposed ten years ago and is based on the concept of elementary flux vectors (EFVs). Only recently has the community started to recognize the potential of EFVs for metabolic network analysis. In fact, EFVs exactly represent the conceptual development required to generalize the idea of EFMs from flux cones to flux polyhedra. This work aims to present a concise theoretical and practical introduction to EFVs that is accessible to a broad audience. We highlight the close relationship between EFMs and EFVs and demonstrate that almost all applications of EFMs (in flux cones) are possible for EFVs (in flux polyhedra) as well. In fact, certain properties can only be studied with EFVs. Thus, we conclude that EFVs provide a powerful and unifying framework for constraint-based modeling of metabolic networks.

MOTIVATION: Robustness, the ability of biological networks to uphold their functionality in spite of perturbations, is a key characteristic of all living systems. Although several theoretical approaches have been developed to formalize robustness, it still eludes an exact quantification. Here, we present a rigorous and quantitative approach for the structural robustness of metabolic networks by measuring their ability to tolerate random reaction (or gene) knockouts. RESULTS: In analogy to reliability theory, based on an explicit consideration of all possible knockout sets, we exactly quantify the probability of failure for a given network function (e.g. growth). This measure can be computed if the network's minimal cut sets (MSCs) are known. We show that even in genome-scale metabolic networks the probability of (network) failure can be reliably estimated from MSCs with lowest cardinalities. We demonstrate the applicability of our theory by analyzing the structural robustness of multiple Enterobacteriaceae and Blattibacteriaceae and show a dramatically low structural robustness for the latter. We find that structural robustness develops from the ability to proliferate in multiple growth environments consistent with experimentally found knowledge. CONCLUSION: The probability of (network) failure provides thus a reliable and easily computable measure of structural robustness and redundancy in (genome-scale) metabolic networks. AVAILABILITY AND IMPLEMENTATION: Source code is available under the GNU General Public License at https://github.com/mpgerstl/networkRobustnessToolbox CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Isotope tracer experiments are an invaluable technique to analyze and study the metabolism of biological systems. However, isotope labeling experiments are often affected by naturally abundant isotopes especially in cases where mass spectrometric methods make use of derivatization. The correction of these additive interferences--in particular for complex isotopic systems--is numerically challenging and still an emerging field of research. When positional information is generated via collision-induced dissociation, even more complex calculations for isotopic interference correction are necessary. So far, no freely available tools can handle tandem mass spectrometry data. We present isotope correction toolbox, a program that corrects tandem mass isotopomer data from tandem mass spectrometry experiments. Isotope correction toolbox is written in the multi-platform programming language Perl and, therefore, can be used on all commonly available computer platforms. AVAILABILITY AND IMPLEMENTATION: Source code and documentation can be freely obtained under the Artistic License or the GNU General Public License from: https://github.com/jungreuc/isotope_correction_toolbox/ CONTACT: {[email protected],[email protected]} SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

UNLABELLED: : Elementary flux modes (EFMs) are important structural tools for the analysis of metabolic networks. It is known that many topologically feasible EFMs are biologically irrelevant. Therefore, tools are needed to find the relevant ones. We present thermodynamic tEFM analysis (tEFMA) which uses the cellular metabolome to avoid the enumeration of thermodynamically infeasible EFMs. Specifically, given a metabolic network and a not necessarily complete metabolome, tEFMA efficiently returns the full set of thermodynamically feasible EFMs consistent with the metabolome. Compared with standard approaches, tEFMA strongly reduces the memory consumption and the overall runtime. Thus tEFMA provides a new way to analyze unbiasedly hitherto inaccessible large-scale metabolic networks. AVAILABILITY AND IMPLEMENTATION: https://github.com/mpgerstl/tEFMA CONTACT: : [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Constrained minimal cut sets (cMCSs) have recently been introduced as a framework to enumerate minimal genetic intervention strategies for targeted optimization of metabolic networks. Two different algorithmic schemes (adapted Berge algorithm and binary integer programming) have been proposed to compute cMCSs from elementary modes. However, in their original formulation both algorithms are not fully comparable. RESULTS: Here we show that by a small extension to the integer program both methods become equivalent. Furthermore, based on well-known preprocessing procedures for integer programming we present efficient preprocessing steps which can be used for both algorithms. We then benchmark the numerical performance of the algorithms in several realistic medium-scale metabolic models. The benchmark calculations reveal (i) that these preprocessing steps can lead to an enormous speed-up under both algorithms, and (ii) that the adapted Berge algorithm outperforms the binary integer approach. CONCLUSIONS: Generally, both of our new implementations are by at least one order of magnitude faster than other currently available implementations.