Flux-dependent graphs for metabolic networks

Integration of graph neural networks and genome-scale metabolic models for predicting gene essentiality

Genome-scale metabolic models are powerful tools for understanding cellular physiology. Flux balance analysis (FBA), in particular, is an optimization-based approach widely employed for predicting metabolic phenotypes. In model microbes such as Escherichia coli, FBA has been successful at predicting essential genes, i.e. those genes that impair survival when deleted. A central assumption in this approach is that both wild type and deletion strains optimize the same fitness objective. Although the optimality assumption may hold for the wild type metabolic network, deletion strains are not subject to the same evolutionary pressures and knock-out mutants may steer their metabolism to meet other objectives for survival. Here, we present FlowGAT, a hybrid FBA-machine learning strategy for predicting essentiality directly from wild type metabolic phenotypes. The approach is based on graph-structured representation of metabolic fluxes predicted by FBA, where nodes correspond to enzymatic reactions and edges quantify the propagation of metabolite mass flow between a reaction and its neighbours. We integrate this information into a graph neural network that can be trained on knock-out fitness assay data. Comparisons across different model architectures reveal that FlowGAT predictions for E. coli are close to those of FBA for several growth conditions. This suggests that essentiality of enzymatic genes can be predicted by exploiting the inherent network structure of metabolism. Our approach demonstrates the benefits of combining the mechanistic insights afforded by genome-scale models with the ability of deep learning to infer patterns from complex datasets.

Metabolic Connectome and Its Role in the Prediction, Diagnosis, and Treatment of Complex Diseases

The interconnectivity of advanced biological systems is essential for their proper functioning. In modern connectomics, biological entities such as proteins, genes, RNA, DNA, and metabolites are often represented as nodes, while the physical, biochemical, or functional interactions between them are represented as edges. Among these entities, metabolites are particularly significant as they exhibit a closer relationship to an organism's phenotype compared to genes or proteins. Moreover, the metabolome has the ability to amplify small proteomic and transcriptomic changes, even those from minor genomic changes. Metabolic networks, which consist of complex systems comprising hundreds of metabolites and their interactions, play a critical role in biological research by mediating energy conversion and chemical reactions within cells. This review provides an introduction to common metabolic network models and their construction methods. It also explores the diverse applications of metabolic networks in elucidating disease mechanisms, predicting and diagnosing diseases, and facilitating drug development. Additionally, it discusses potential future directions for research in metabolic networks. Ultimately, this review serves as a valuable reference for researchers interested in metabolic network modeling, analysis, and their applications.

A Machine Learning Approach for Predicting Essentiality of Metabolic Genes

The identification of essential genes is a key challenge in systems and synthetic biology, particularly for engineering metabolic pathways that convert feedstocks into valuable products. Assessment of gene essentiality at a genome scale requires large and costly growth assays of knockout strains. Here we describe a strategy to predict the essentiality of metabolic genes using binary classification algorithms. The approach combines elements from genome-scale metabolic models, directed graphs, and machine learning into a predictive model that can be trained on small knockout data. We demonstrate the efficacy of this approach using the most complete metabolic model of Escherichia coli and various machine learning algorithms for binary classification.

Robustness and Complexity of Directed and Weighted Metabolic Hypergraphs

Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here, we propose a directed hypergraph with edge-dependent vertex weight as a novel framework to represent metabolic networks. This hypergraph-based representation captures higher-order interactions among metabolites and reactions, as well as the directionalities of reactions and stoichiometric weights, preserving all essential information. Within this framework, we propose the communicability and the search information as metrics to quantify the robustness and complexity of directed hypergraphs. We explore the implications of network directionality on these measures and illustrate a practical example by applying them to a small-scale E. coli core model. Additionally, we compare the robustness and the complexity of 30 different models of metabolism, connecting structural and biological properties. Our findings show that antibiotic resistance is associated with high structural robustness, while the complexity can distinguish between eukaryotic and prokaryotic organisms.

A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

Elementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, it has long been recognized that optimization-based approaches may fail to uniquely identify EFM weights and return different feasible solutions across objective functions and solvers. Here we show that, for flux networks only involving single molecule transformations, these problems can be avoided by imposing a Markovian constraint on EFM weights. Our Markovian constraint guarantees a unique solution to the flux decomposition problem, and that solution is arguably more biophysically plausible than other solutions. We describe an algorithm for computing Markovian EFM weights via steady state analysis of a certain discrete-time Markov chain, based on the flux network, which we call the cycle-history Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer's disease patients. Our method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.

Immuno-metabolic signaling in leishmaniasis: insights gained from mathematical modeling

Motivation

Leishmaniasis is a global concern especially in underdeveloped and developing subtropical and tropical regions. The extent of infectivity in host is majorly dependent on functional polarization of macrophages. Classically activated M1 macrophage can eliminate parasite through production of iNOS and alternatively activated M2 macrophages can promote parasite growth through by providing shelter and nutrients to parasite. The biological processes involved in immune signaling and metabolism of host and parasite might be responsible for deciding fate of parasite.

Results

Using systems biology approach, we constructed two mathematical models and inter-regulatory immune-metabolic networks of M1 and M2 state, through which we identified crucial components that are associated with these phenotypes. We also demonstrated how parasite may modulate M1 phenotype for its growth and proliferation and transition to M2 state. Through our previous findings as well as from recent findings we could identify SHP-1 as a key component in regulating the immune-metabolic characterization of M2 macrophage. By targeting SHP-1 at cellular level, it might be possible to modulate immuno-metabolic mechanism and thereby control parasite survival.

Availability and implementation

Mathematical modeling is implemented as a workflow and the models are deposited in BioModel database. FactoMineR is available at: https://github.com/cran/FactoMineR/tree/master.

Metaboverse enables automated discovery and visualization of diverse metabolic regulatory patterns

Metabolism is intertwined with various cellular processes, including controlling cell fate, influencing tumorigenesis, participating in stress responses and more. Metabolism is a complex, interdependent network, and local perturbations can have indirect effects that are pervasive across the metabolic network. Current analytical and technical limitations have long created a bottleneck in metabolic data interpretation. To address these shortcomings, we developed Metaboverse, a user-friendly tool to facilitate data exploration and hypothesis generation. Here we introduce algorithms that leverage the metabolic network to extract complex reaction patterns from data. To minimize the impact of missing measurements within the network, we introduce methods that enable pattern recognition across multiple reactions. Using Metaboverse, we identify a previously undescribed metabolite signature that correlated with survival outcomes in early stage lung adenocarcinoma patients. Using a yeast model, we identify metabolic responses suggesting an adaptive role of citrate homeostasis during mitochondrial dysfunction facilitated by the citrate transporter, Ctp1. We demonstrate that Metaboverse augments the user's ability to extract meaningful patterns from multi-omics datasets to develop actionable hypotheses.

Flows of Substances in Networks and Network Channels: Selected Results and Applications

This review paper is devoted to a brief overview of results and models concerning flows in networks and channels of networks. First of all, we conduct a survey of the literature in several areas of research connected to these flows. Then, we mention certain basic mathematical models of flows in networks that are based on differential equations. We give special attention to several models for flows of substances in channels of networks. For stationary cases of these flows, we present probability distributions connected to the substance in the nodes of the channel for two basic models: the model of a channel with many arms modeled by differential equations and the model of a simple channel with flows of substances modeled by difference equations. The probability distributions obtained contain as specific cases any probability distribution of a discrete random variable that takes values of 0,1,…. We also mention applications of the considered models, such as applications for modeling migration flows. Special attention is given to the connection of the theory of stationary flows in channels of networks and the theory of the growth of random networks.

Searching for the Metabolic Signature of Cancer: A Review from Warburg's Time to Now

This review focuses on the evolving understanding that we have of tumor cell metabolism, particularly glycolytic and oxidative metabolism, and traces back its evolution through time. This understanding has developed since the pioneering work of Otto Warburg, but the understanding of tumor cell metabolism continues to be hampered by misinterpretation of his work. This has contributed to the use of the new concepts of metabolic switch and metabolic reprogramming， that are out of step with reality. The Warburg effect is often considered to be a hallmark of cancer, but is it really? More generally, is there a metabolic signature of cancer? We draw the conclusion that the signature of cancer cannot be reduced to a single factor, but is expressed at the tissue level in terms of the capacity of cells to dynamically explore a vast metabolic landscape in the context of significant environmental heterogeneities.

Emerging landscape of molecular interaction networks: Opportunities, challenges and prospects

Network biology finds application in interpreting molecular interaction networks and providing insightful inferences using graph theoretical analysis of biological systems. The integration of computational bio-modelling approaches with different hybrid network-based techniques provides additional information about the behaviour of complex systems. With increasing advances in high-throughput technologies in biological research, attempts have been made to incorporate this information into network structures, which has led to a continuous update of network biology approaches over time. The newly minted centrality measures accommodate the details of omics data and regulatory network structure information. The unification of graph network properties with classical mathematical and computational modelling approaches and technologically advanced approaches like machine-learning- and artificial intelligence-based algorithms leverages the potential application of these techniques. These computational advances prove beneficial and serve various applications such as essential gene prediction, identification of drug–disease interaction and gene prioritization. Hence, in this review, we have provided a comprehensive overview of the emerging landscape of molecular interaction networks using graph theoretical approaches. With the aim to provide information on the wide range of applications of network biology approaches in understanding the interaction and regulation of genes, proteins, enzymes and metabolites at different molecular levels, we have reviewed the methods that utilize network topological properties, emerging hybrid network-based approaches and applications that integrate machine learning techniques to analyse molecular interaction networks. Further, we have discussed the applications of these approaches in biomedical research with a note on future prospects.

Computational System Level Approaches for Discerning Reciprocal Regulation of IL10 and IL12 in Leishmaniasis

IL12 and IL10 are two of the major cytokines which control the fate of Leishmaniasis. This paper presents two models healthy state and diseased state which shows how secretion of IL12 is responsible for parasite elimination and IL10 can jeopardize the parasite elimination and promote its survival. Epigenetic modification in the host IL12 and IL10 promoter can decide the fate of parasites. It was observed that reciprocal relationship exists between IL12 and IL10 and that is majorly controlled by a transcription factor NFAT5 from Rel family of transcription factors. By targeting this transcription factor at the cellular level, it might be possible to modulate the release of powerful pro-inflammatory cytokines, thereby reducing parasite survival. The mathematical models developed here serves as a step towards finding a key component that can pave a way for therapeutic investigation.

Organic waste conversion through anaerobic digestion: A critical insight into the metabolic pathways and microbial interactions

Anaerobic digestion is a promising method for energy recovery through conversion of organic waste to biogas and other industrial valuables. However, to tap the full potential of anaerobic digestion, deciphering the microbial metabolic pathway activities and their underlying bioenergetics is required. In addition, the behavior of organisms in consortia along with the analytical abilities to kinetically measure their metabolic interactions will allow rational optimization of the process. This review aims to explore the metabolic bottlenecks of the microbial communities adopting latest advances of profiling and ¹³C tracer-based analysis using state of the art analytical platforms (GC, GC-MS, LC-MS, NMR). The review summarizes the phases of anaerobic digestion, the role of microbial communities, key process parameters of significance, syntrophic microbial interactions and the bottlenecks that are critical for optimal bioenergetics and enhanced production of valuables. Considerations into the designing of efficient synthetic microbial communities as well as the latest advances in capturing their metabolic cross talk will be highlighted. The review further explores how the presence of additives and inhibiting factors affect the metabolic pathways. The critical insight into the reaction mechanism covered in this review may be helpful to optimize and upgrade the anaerobic digestion system.

Controlling network ensembles

The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of uncertainty. Here, we investigate the minimum energy control of network ensembles, which may take one of a number of possible realizations. We ensure the controller derived can perform the desired control with a tunable amount of accuracy and we study how the control energy and the overall control cost scale with the number of possible realizations. Our focus is in characterizing the solution of the optimal control problem in the limit in which the systems are drawn from a continuous distribution, and in particular, how to properly pose the weighting terms in the objective function. We verify the theory in three examples of interest: a unidirectional chain network with uncertain edge weights and self-loop weights, a network where each edge weight is drawn from a given distribution, and the Jacobian of the dynamics corresponding to the cell signaling network of autophagy in the presence of uncertain parameters.

Application of the control usually requires complete knowledge of the system, which is rare for biological networks characterized by uncertainty. Klickstein et al. propose an optimal control for uncertain systems represented by network ensembles where only weight distributions for edges are known.

MetNet: A two-level approach to reconstructing and comparing metabolic networks

Metabolic pathway comparison and interaction between different species can detect important information for drug engineering and medical science. In the literature, proposals for reconstructing and comparing metabolic networks present two main problems: network reconstruction requires usually human intervention to integrate information from different sources and, in metabolic comparison, the size of the networks leads to a challenging computational problem. We propose to automatically reconstruct a metabolic network on the basis of KEGG database information. Our proposal relies on a two-level representation of the huge metabolic network: the first level is graph-based and depicts pathways as nodes and relations between pathways as edges; the second level represents each metabolic pathway in terms of its reactions content. The two-level representation complies with the KEGG database, which decomposes the metabolism of all the different organisms into “reference” pathways in a standardised way. On the basis of this two-level representation, we introduce some similarity measures for both levels. They allow for both a local comparison, pathway by pathway, and a global comparison of the entire metabolism. We developed a tool, MetNet, that implements the proposed methodology. MetNet makes it possible to automatically reconstruct the metabolic network of two organisms selected in KEGG and to compare their two networks both quantitatively and visually. We validate our methodology by presenting some experiments performed with MetNet.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

Physicochemical and metabolic constraints for thermodynamics-based stoichiometric modelling under mesophilic growth conditions

Metabolic engineering in the post-genomic era is characterised by the development of new methods for metabolomics and fluxomics, supported by the integration of genetic engineering tools and mathematical modelling. Particularly, constraint-based stoichiometric models have been widely studied: (i) flux balance analysis (FBA) (in silico), and (ii) metabolic flux analysis (MFA) (in vivo). Recent studies have enabled the incorporation of thermodynamics and metabolomics data to improve the predictive capabilities of these approaches. However, an in-depth comparison and evaluation of these methods is lacking. This study presents a thorough analysis of two different in silico methods tested against experimental data (metabolomics and ¹³C-MFA) for the mesophile Escherichia coli. In particular, a modified version of the recently published matTFA toolbox was created, providing a broader range of physicochemical parameters. Validating against experimental data allowed the determination of the best physicochemical parameters to perform the TFA (Thermodynamics-based Flux Analysis). An analysis of flux pattern changes in the central carbon metabolism between ¹³C-MFA and TFA highlighted the limited capabilities of both approaches for elucidating the anaplerotic fluxes. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA. Finally, this study emphasised the need for standardisation in the fluxomics community: novel approaches are frequently released but a thorough comparison with currently accepted methods is not always performed.

Biotechnology has benefitted from the development of high throughput methods characterising living systems at different levels (e.g. concerning genes or proteins), allowing the industrial production of chemical commodities. Recently, focus has been placed on determining reaction rates (or metabolic fluxes) in the metabolic network of certain microorganisms, in order to identify bottlenecks hindering their exploitation. Two main approaches are commonly used, termed metabolic flux analysis (MFA) and flux balance analysis (FBA), based on measuring and estimating fluxes, respectively. While the influence of thermodynamics in living systems was accepted several decades ago, its application to study biochemical networks has only recently been enabled. In this sense, a multitude of different approaches constraining well-established modelling methods with thermodynamics has been suggested. However, physicochemical parameters are generally not properly adjusted to the experimental conditions, which might affect their predictive capabilities. In this study, we have explored the reliability of currently available tools by investigating the impact of varying said parameters in the simulation of metabolic fluxes and metabolite concentration values. Additionally, our in-depth analysis allowed us to highlight limitations and potential solutions that should be considered in future studies.

Identifying naturally occurring communities of primary care providers in the English National Health Service in London

OBJECTIVES

Primary Care Networks (PCNs) are a new organisational hierarchy with wide-ranging responsibilities introduced in the National Health Service (NHS) Long Term Plan. The vision is that PCNs should represent 'natural' communities of general practices (GP practices) collaborating at scale and covering a geography that fits well with practices, other healthcare providers and local communities. Our study aims to identify natural communities of GP practices based on patient registration patterns using Markov Multiscale Community Detection, an unsupervised network-based clustering technique to create catchments for these communities.

DESIGN

Retrospective observational study using Hospital Episode Statistics - patient-level administrative records of attendances to hospital.

SETTING

General practices in the 32 Clinical Commissioning Groups of Greater London PARTICIPANTS: All adult patients resident in and registered to a GP practice in Greater London that had one or more outpatient encounters at NHS hospitals between 1^st April 2017 and 31^st March 2018.

MAIN OUTCOME MEASURES

The allocation of GP practices in Greater London to PCNs based on the registrations of patients resident in each Lower Layer Super Output Area (LSOA) of Greater London. The population size and coverage of each proposed PCN.

RESULTS

3 428 322 unique patients attended 1334 GPs in 4835 LSOAs in Greater London. Our model grouped 1291 GPs (96.8%) and 4721 LSOAs (97.6%) into 165 mutually exclusive PCNs. Median PCN list size was 53 490, with a lower quartile of 38 079 patients and an upper quartile of 72 982 patients. A median of 70.1% of patients attended a GP within their allocated PCN, ranging from 44.6% to 91.4%.

CONCLUSIONS

With PCNs expected to take a role in population health management and with community providers expected to reconfigure around them, it is vital to recognise how PCNs represent their communities. Our method may be used by policymakers to understand the populations and geography shared between networks.

Systems Genetics for Mechanistic Discovery in Heart Diseases

Cardiovascular diseases are the leading cause of death worldwide. Complex diseases with highly heterogenous disease progression among patient populations, cardiovascular diseases feature multifactorial contributions from both genetic and environmental stressors. Despite significant effort utilizing multiple approaches from molecular biology to genome-wide association studies, the genetic landscape of cardiovascular diseases, particularly for the nonfamilial forms of heart failure, is still poorly understood. In the past decade, systems-level approaches based on omics technologies have become an important approach for the study of complex traits in large populations. These advances create opportunities to integrate genetic variation with other biological layers to identify and prioritize candidate genes, understand pathogenic pathways, and elucidate gene-gene and gene-environment interactions. In this review, we will highlight some of the recent progress made using systems genetics approaches to uncover novel mechanisms and molecular bases of cardiovascular pathophysiological manifestations. The key technology and data analysis platforms necessary to implement systems genetics will be described, and the current major challenges and future directions will also be discussed. For complex cardiovascular diseases, such as heart failure, systems genetics represents a powerful strategy to obtain mechanistic insights and to develop individualized diagnostic and therapeutic regiments, paving the way for precision cardiovascular medicine.