Semi-Automatic Detection of Errors in Genome-Scale Metabolic Models

Background

Genome-Scale Metabolic Models (GSMMs) are used for numerous tasks requiring computational estimates of metabolic fluxes, from predicting novel drug targets to engineering microbes to produce valuable compounds. A key limiting step in most applications of GSMMs is ensuring their representation of the target organism's metabolism is complete and accurate. Identifying and visualizing errors in GSMMs is complicated by the fact that they contain thousands of densely interconnected reactions. Furthermore, many errors in GSMMs only become apparent when considering pathways of connected reactions collectively, as opposed to examining reactions individually.

Results

We present Metabolic Accuracy Check and Analysis Workflow (MACAW), a collection of algorithms for detecting errors in GSMMs. The relative frequencies of errors we detect in manually curated GSMMs appear to reflect the different approaches used to curate them. Changing the method used to automatically create a GSMM from a particular organism's genome can have a larger impact on the kinds of errors in the resulting GSMM than using the same method with a different organism's genome. Our algorithms are particularly capable of identifying errors that are only apparent at the pathway level, including loops, and nontrivial cases of dead ends.

Conclusions

MACAW is capable of identifying inaccuracies of varying severity in a wide range of GSMMs. Correcting these errors can measurably improve the predictive capacity of a GSMM. The relative prevalence of each type of error we identify in a large collection of GSMMs could help shape future efforts for further automation of error correction and GSMM creation.

LooplessFluxSampler: an efficient toolbox for sampling the loopless flux solution space of metabolic models

BACKGROUND

Uniform random sampling of mass-balanced flux solutions offers an unbiased appraisal of the capabilities of metabolic networks. Unfortunately, it is impossible to avoid thermodynamically infeasible loops in flux samples when using convex samplers on large metabolic models. Current strategies for randomly sampling the non-convex loopless flux space display limited efficiency and lack theoretical guarantees.

RESULTS

Here, we present LooplessFluxSampler, an efficient algorithm for exploring the loopless mass-balanced flux solution space of metabolic models, based on an Adaptive Directions Sampling on a Box (ADSB) algorithm. ADSB is rooted in the general Adaptive Direction Sampling (ADS) framework, specifically the Parallel ADS, for which theoretical convergence and irreducibility results are available for sampling from arbitrary distributions. By sampling directions that adapt to the target distribution, ADSB traverses more efficiently the sample space achieving faster mixing than other methods. Importantly, the presented algorithm is guaranteed to target the uniform distribution over convex regions, and it provably converges on the latter distribution over more general (non-convex) regions provided the sample can have full support.

CONCLUSIONS

LooplessFluxSampler enables scalable statistical inference of the loopless mass-balanced solution space of large metabolic models. Grounded in a theoretically sound framework, this toolbox provides not only efficient but also reliable results for exploring the properties of the almost surely non-convex loopless flux space. Finally, LooplessFluxSampler includes a Markov Chain diagnostics suite for assessing the quality of the final sample and the performance of the algorithm.

Flux Balance Analysis of Mammalian Cell Systems

Flux balance analysis (FBA) is a computational methodology to model and analyze the metabolic behavior of cells. In this chapter, we break down the key steps for formulating an FBA model and other FBA-derived methodologies in the context of mammalian cell biology, including strain design, developing cell line-specific models, and conducting flux sampling. We provide annotated COBRApy code for each step to show how it would work in practice.

Characterising the metabolic rewiring of extremely slow growing Komagataella phaffii

Retentostat cultivations have enabled investigations into substrate-limited near-zero growth for a number of microbes. Quantitative physiology at these near-zero growth conditions has been widely discussed, yet characterisation of the fluxome is relatively under-reported. We investigated the rewiring of metabolism in the transition of a recombinant protein-producing strain of Komagataella phaffii to glucose-limited near-zero growth rates. We used cultivation data from a 200-fold range of growth rates and comprehensive biomass composition data to integrate growth rate dependent biomass equations, generated using a number of different approaches, into a K. phaffii genome-scale metabolic model. Here, we show that a non-growth-associated maintenance value of 0.65 mmol ATP g CDW - 1 h - 1 and a growth-associated maintenance value of 108 mmol ATP g CDW - 1 lead to accurate growth rate predictions. In line with its role as energy source, metabolism is rewired to increase the yield of ATP per glucose. This includes a reduction of flux through the pentose phosphate pathway, and a greater utilisation of glycolysis and the TCA cycle. Interestingly, we observed activity of an external, non-proton translocating NADH dehydrogenase in addition to the malate-aspartate shuttle. Regardless of the method used for the generation of biomass equations, a similar, yet different, growth rate dependent rewiring was predicted. As expected, these differences between the different methods were clearer at higher growth rates, where the biomass equation provides a much greater constraint than at slower growth rates. When placed on an increasingly limited glucose diet, the metabolism of K. phaffii adapts, enabling it to continue to drive critical processes sustaining its high viability at near-zero growth rates.

State-of the-Art Constraint-Based Modeling of Microbial Metabolism: From Basics to Context-Specific Models with a Focus on Methanotrophs

Methanotrophy is the ability of an organism to capture and utilize the greenhouse gas, methane, as a source of energy-rich carbon. Over the years, significant progress has been made in understanding of mechanisms for methane utilization, mostly in bacterial systems, including the key metabolic pathways, regulation and the impact of various factors (iron, copper, calcium, lanthanum, and tungsten) on cell growth and methane bioconversion. The implementation of -omics approaches provided vast amount of heterogeneous data that require the adaptation or development of computational tools for a system-wide interrogative analysis of methanotrophy. The genome-scale mathematical modeling of its metabolism has been envisioned as one of the most productive strategies for the integration of muti-scale data to better understand methane metabolism and enable its biotechnological implementation. Herein, we provide an overview of various computational strategies implemented for methanotrophic systems. We highlight functional capabilities as well as limitations of the most popular web resources for the reconstruction, modification and optimization of the genome-scale metabolic models for methane-utilizing bacteria.

Improving pathway prediction accuracy of constraints-based metabolic network models by treating enzymes as microcompartments

Metabolic network models have become increasingly precise and accurate as the most widespread and practical digital representations of living cells. The prediction functions were significantly expanded by integrating cellular resources and abiotic constraints in recent years. However, if unreasonable modeling methods were adopted due to a lack of consideration of biological knowledge, the conflicts between stoichiometric and other constraints, such as thermodynamic feasibility and enzyme resource availability, would lead to distorted predictions. In this work, we investigated a prediction anomaly of EcoETM, a constraints-based metabolic network model, and introduced the idea of enzyme compartmentalization into the analysis process. Through rational combination of reactions, we avoid the false prediction of pathway feasibility caused by the unrealistic assumption of free intermediate metabolites. This allowed us to correct the pathway structures of l-serine and l-tryptophan. A specific analysis explains the application method of the EcoETM-like model and demonstrates its potential and value in correcting the prediction results in pathway structure by resolving the conflict between different constraints and incorporating the evolved roles of enzymes as reaction compartments. Notably, this work also reveals the trade-off between product yield and thermodynamic feasibility. Our work is of great value for the structural improvement of constraints-based models.

A reactive species reactions module for integration into genome-scale metabolic models for improved insights: Application to cancer

Reactive species (RS) play significant roles in many disease contexts. Despite their crucial roles in diseases including cancer, the RS are not adequately modeled in the genome-scale metabolic (GSM) models, which are used to understand cell metabolism in disease contexts. We have developed a scalable RS reactions module that can be integrated with any Recon 3D-derived human metabolic model, or after fine-tuning, with any metabolic model. With RS-integration, the GSM models of three cancers (basal-like triple negative breast cancer (TNBC), high grade serous ovarian carcinoma (HGSOC) and colorectal cancer (CRC)) built from Recon 3D, precisely highlighted the increases/decreases in fluxes (dysregulation) occurring in important pathways of these cancers. These dysregulations were not prominent in the standard cancer models without the RS module. Further, the results from these RS-integrated cancer GSM models suggest the following decreasing order in the ease of ferroptosis-targeting to treat the cancers: TNBC > HGSOC > CRC.

Cardinality optimization in constraint-based modelling: application to human metabolism

MOTIVATION

Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution.

RESULTS

By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction.

AVAILABILITY AND IMPLEMENTATION

Open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.

How reliable are Chinese hamster ovary (CHO) cell genome-scale metabolic models?

Genome-scale metabolic models (GEMs) possess the power to revolutionize bioprocess and cell line engineering workflows thanks to their ability to predict and understand whole-cell metabolism in silico. Despite this potential, it is currently unclear how accurately GEMs can capture both intracellular metabolic states and extracellular phenotypes. Here, we investigate this knowledge gap to determine the reliability of current Chinese hamster ovary (CHO) cell metabolic models. We introduce a new GEM, iCHO2441, and create CHO-S and CHO-K1 specific GEMs. These are compared against iCHO1766, iCHO2048, and iCHO2291. Model predictions are assessed via comparison with experimentally measured growth rates, gene essentialities, amino acid auxotrophies, and 13 C intracellular reaction rates. Our results highlight that all CHO cell models are able to capture extracellular phenotypes and intracellular fluxes, with the updated GEM outperforming the original CHO cell GEM. Cell line-specific models were able to better capture extracellular phenotypes but failed to improve intracellular reaction rate predictions in this case. Ultimately, this work provides an updated CHO cell GEM to the community and lays a foundation for the development and assessment of next-generation flux analysis techniques, highlighting areas for model improvements.

Reconciliation and evolution of Penicillium rubens genome-scale metabolic networks-What about specialised metabolism?

In recent years, genome sequencing of filamentous fungi has revealed a high proportion of specialised metabolites with growing pharmaceutical interest. However, detecting such metabolites through in silico genome analysis does not necessarily guarantee their expression under laboratory conditions. However, one plausible strategy for enabling their production lies in modifying the growth conditions. Devising a comprehensive experimental design testing in different culture environments is time-consuming and expensive. Therefore, using in silico modelling as a preliminary step, such as Genome-Scale Metabolic Network (GSMN), represents a promising approach to predicting and understanding the observed specialised metabolite production in a given organism. To address these questions, we reconstructed a new high-quality GSMN for the Penicillium rubens Wisconsin 54-1255 strain, a commonly used model organism. Our reconstruction, iPrub22, adheres to current convention standards and quality criteria, incorporating updated functional annotations, orthology searches with different GSMN templates, data from previous reconstructions, and manual curation steps targeting primary and specialised metabolites. With a MEMOTE score of 74% and a metabolic coverage of 45%, iPrub22 includes 5,192 unique metabolites interconnected by 5,919 reactions, of which 5,033 are supported by at least one genomic sequence. Of the metabolites present in iPrub22, 13% are categorised as belonging to specialised metabolism. While our high-quality GSMN provides a valuable resource for investigating known phenotypes expressed in P. rubens, our analysis identifies bottlenecks related, in particular, to the definition of what is a specialised metabolite, which requires consensus within the scientific community. It also points out the necessity of accessible, standardised and exhaustive databases of specialised metabolites. These questions must be addressed to fully unlock the potential of natural product production in P. rubens and other filamentous fungi. Our work represents a foundational step towards the objective of rationalising the production of natural products through GSMN modelling.

Optimal density of bacterial cells

A substantial fraction of the bacterial cytosol is occupied by catalysts and their substrates. While a higher volume density of catalysts and substrates might boost biochemical fluxes, the resulting molecular crowding can slow down diffusion, perturb the reactions' Gibbs free energies, and reduce the catalytic efficiency of proteins. Due to these tradeoffs, dry mass density likely possesses an optimum that facilitates maximal cellular growth and that is interdependent on the cytosolic molecule size distribution. Here, we analyze the balanced growth of a model cell, accounting systematically for crowding effects on reaction kinetics. Its optimal cytosolic volume occupancy depends on the nutrient-dependent resource allocation into large ribosomal vs. small metabolic macromolecules, reflecting a tradeoff between the saturation of metabolic enzymes, favoring larger occupancies with higher encounter rates, and the inhibition of the ribosomes, favoring lower occupancies with unhindered diffusion of tRNAs. Our predictions across growth rates are quantitatively consistent with the experimentally observed reduction in volume occupancy on rich media compared to minimal media in E. coli. Strong deviations from optimal cytosolic occupancy only lead to minute reductions in growth rate, which are nevertheless evolutionarily relevant due to large bacterial population sizes. In sum, cytosolic density variation in bacterial cells appears to be consistent with an optimality principle of cellular efficiency.

Phenotype-specific estimation of metabolic fluxes using gene expression data

A cell's genome influences its metabolism via the expression of enzyme-related genes, but transcriptome and fluxome are not perfectly correlated as post-transcriptional mechanisms also regulate reaction's kinetics. Here, we addressed the question: given a transcriptome, how unobserved mechanisms of reaction kinetics should be systematically accounted for when inferring the fluxome? To infer the most likely and least biased fluxome, we present Pheflux, a constraint-based model maximizing Shannon's entropy of fluxes per mRNA. Benchmarked against ¹³C fluxes of yeast and bacteria, Pheflux accurately estimates the carbon core metabolism. We applied Pheflux to thousands of normal and tumor cell transcriptomes obtained from The Cancer Genome Atlas. Pheflux showed statistically significantly higher glucose yields on lactate in breast, kidney, and bronchus-lung tumoral cells than their normal counterparts. Results are consistent with the Warburg effect, a hallmark of cancer metabolism, suggesting that Pheflux can be efficiently used to study the metabolism of eukaryotic cells.

Constraint-Based Reconstruction and Analyses of Metabolic Models: Open-Source Python Tools and Applications to Cancer

The influence of metabolism on signaling, epigenetic markers, and transcription is highly complex yet important for understanding cancer physiology. Despite the development of high-resolution multi-omics technologies, it is difficult to infer metabolic activity from these indirect measurements. Fortunately, genome-scale metabolic models and constraint-based modeling provide a systems biology framework to investigate the metabolic states and define the genotype-phenotype associations by integrations of multi-omics data. Constraint-Based Reconstruction and Analysis (COBRA) methods are used to build and simulate metabolic networks using mathematical representations of biochemical reactions, gene-protein reaction associations, and physiological and biochemical constraints. These methods have led to advancements in metabolic reconstruction, network analysis, perturbation studies as well as prediction of metabolic state. Most computational tools for performing these analyses are written for MATLAB, a proprietary software. In order to increase accessibility and handle more complex datasets and models, community efforts have started to develop similar open-source tools in Python. To date there is a comprehensive set of tools in Python to perform various flux analyses and visualizations; however, there are still missing algorithms in some key areas. This review summarizes the availability of Python software for several components of COBRA methods and their applications in cancer metabolism. These tools are evolving rapidly and should offer a readily accessible, versatile way to model the intricacies of cancer metabolism for identifying cancer-specific metabolic features that constitute potential drug targets.

The topology of genome-scale metabolic reconstructions unravels independent modules and high network flexibility

The topology of metabolic networks is recognisably modular with modules weakly connected apart from sharing a pool of currency metabolites. Here, we defined modules as sets of reversible reactions isolated from the rest of metabolism by irreversible reactions except for the exchange of currency metabolites. Our approach identifies topologically independent modules under specific conditions associated with different metabolic functions. As case studies, the E.coli iJO1366 and Human Recon 2.2 genome-scale metabolic models were split in 103 and 321 modules respectively, displaying significant correlation patterns in expression data. Finally, we addressed a fundamental question about the metabolic flexibility conferred by reversible reactions: “Of all Directed Topologies (DTs) defined by fixing directions to all reversible reactions, how many are capable of carrying flux through all reactions?”. Enumeration of the DTs for iJO1366 model was performed using an efficient depth-first search algorithm, rejecting infeasible DTs based on mass-imbalanced and loopy flux patterns. We found the direction of 79% of reversible reactions must be defined before all directions in the network can be fixed, granting a high degree of flexibility.

Genome-scale metabolic reconstructions represent all biochemical reactions that an organism can accomplish. These reconstructions are complex and often difficult to study in great detail. A way to overcome this limitation is to focus on specific pathways or subsystems. We present a novel method to identify metabolic modules based on the network topology. The method relies on reaction directions and ignores currency metabolites, which artificially connect distant metabolic reactions. In this way, topologically independent modules are built, where inputs and outputs are controlled by irreversible reactions. The method is automatic and unbiased, and, the result is a set of condition specific modules with defined metabolic functions. As a proof-of-concept we generated biologically relevant modules for the E.coli and Human genome-scale metabolic reconstructions supported by transcriptomic data. Finally, we applied the novel approach to study the network flexibility conferred by reversible reactions. In the case of the E. coli model, we found that the direction of 79% of structurally reversible reactions (those not directionally constrained by surrounding irreversible reactions) must be fixed to determine all the reaction directions in the network. Therefore, reversible reactions operate practically independent of each other.

Integrative Genome-Scale Metabolic Modeling Reveals Versatile Metabolic Strategies for Methane Utilization in Methylomicrobium album BG8

Methylomicrobium album BG8 is an aerobic methanotrophic bacterium with promising features as a microbial cell factory for the conversion of methane to value-added chemicals. However, the lack of a genome-scale metabolic model (GEM) of M. album BG8 has hindered the development of systems biology and metabolic engineering of this methanotroph. To fill this gap, a high-quality GEM was constructed to facilitate a system-level understanding of the biochemistry of M. album BG8. Flux balance analysis, constrained with time-series data derived from experiments with various levels of methane, oxygen, and biomass, was used to investigate the metabolic states that promote the production of biomass and the excretion of carbon dioxide, formate, and acetate. The experimental and modeling results indicated that M. album BG8 requires a ratio of ∼1.5:1 between the oxygen- and methane-specific uptake rates for optimal growth. Integrative modeling revealed that at ratios of  >2:1 oxygen-to-methane uptake flux, carbon dioxide and formate were the preferred excreted compounds, while at ratios of <1.5:1 acetate accounted for a larger fraction of the total excreted flux. Our results showed a coupling between biomass production and the excretion of carbon dioxide that was linked to the ratio between the oxygen- and methane-specific uptake rates. In contrast, acetate excretion was experimentally detected during exponential growth only when the initial biomass concentration was increased. A relatively lower growth rate was also observed when acetate was produced in the exponential phase, suggesting a trade-off between biomass and acetate production.

IMPORTANCE A genome-scale metabolic model (GEM) is an integrative platform that enables the incorporation of a wide range of experimental data. It is used to reveal system-level metabolism and, thus, clarify the link between the genotype and phenotype. The lack of a GEM for Methylomicrobium album BG8, an aerobic methane-oxidizing bacterium, has hindered its use in environmental and industrial biotechnology applications. The diverse metabolic states indicated by the GEM developed in this study demonstrate the versatility in the methane metabolic processes used by this strain. The integrative GEM presented here will aid the implementation of the design-build-test-learn paradigm in the metabolic engineering of M. album BG8. This advance will facilitate the development of a robust methane bioconversion platform and help to mitigate methane emissions from environmental systems.

Flux balance analysis of the ammonia-oxidizing bacterium Nitrosomonas europaea ATCC19718 unravels specific metabolic activities while degrading toxic compounds

The ammonia-oxidizing bacterium Nitrosomonas europaea has been widely recognized as an important player in the nitrogen cycle as well as one of the most abundant members in microbial communities for the treatment of industrial or sewage wastewater. Its natural metabolic versatility and extraordinary ability to degrade environmental pollutants (e.g., aromatic hydrocarbons such as benzene and toluene) enable it to thrive under various harsh environmental conditions. Constraint-based metabolic models constructed from genome sequences enable quantitative insight into the central and specialized metabolism within a target organism. These genome-scale models have been utilized to understand, optimize, and design new strategies for improved bioprocesses. Reduced modeling approaches have been used to elucidate Nitrosomonas europaea metabolism at a pathway level. However, genome-scale knowledge about the simultaneous oxidation of ammonia and pollutant metabolism of N. europaea remains limited. Here, we describe the reconstruction, manual curation, and validation of the genome-scale metabolic model for N. europaea, iGC535. This reconstruction is the most accurate metabolic model for a nitrifying organism to date, reaching an average prediction accuracy of over 90% under several growth conditions. The manually curated model can predict phenotypes under chemolithotrophic and chemolithoorganotrophic conditions while oxidating methane and wastewater pollutants. Calculated flux distributions under different trophic conditions show that several key pathways are affected by the type of carbon source available, including central carbon metabolism and energy production.

Nitrosomonas europaea catalyzes the first step of the nitrification process (ammonia to nitrite). It has been recognized as one of the most important members of microbial communities of wastewater treatment processes. Genome-scale models are powerful tools in process optimization since they can predict the organism’s behavior under different growth conditions. The final genome-scale model of N. europaea ATCC19718, iGC535, can predict growth and oxygen uptake rates with 90.52% accuracy under chemolithotrophic and chemolitoorganotrophic conditions. Moreover, iGC535 can predict the simultaneous oxidation of ammonia and wastewater pollutants, such as benzene, toluene, phenol and, chlorobenzene. iGC535 represents the most comprehensive knowledge-base for a nitrifying organism available to date. The genome-scale model reconstructed in this work brings us closer to understanding N. europaea’s role in a community with other nitrifying bacteria.

Simulating single-cell metabolism using a stochastic flux-balance analysis algorithm

Stochasticity from gene expression in single cells is known to drive metabolic heterogeneity at the level of cellular populations, which is understood to have important consequences for issues such as microbial drug tolerance and treatment of human diseases like cancer. Despite considerable advancements in profiling the genomes, transcriptomes, and proteomes of single cells, it remains difficult to experimentally characterize their metabolism at the genome scale. Computational methods could bridge this gap toward a systems understanding of single-cell biology. To address this challenge, we developed stochastic simulation algorithm with flux-balance analysis embedded (SSA-FBA), a computational framework for simulating the stochastic dynamics of the metabolism of individual cells using genome-scale metabolic models with experimental estimates of gene expression and enzymatic reaction rate parameters. SSA-FBA extends the constraint-based modeling formalism of metabolic network modeling to the single-cell regime, enabling simulation when experimentation is intractable. We also developed an efficient implementation of SSA-FBA that leverages the topology of embedded flux-balance analysis models to significantly reduce the computational cost of simulation. As a preliminary case study, we built a reduced single-cell model of Mycoplasma pneumoniae and used SSA-FBA to illustrate the role of stochasticity on the dynamics of metabolism at the single-cell level.

Microbial regulation of hexokinase 2 links mitochondrial metabolism and cell death in colitis

Hexokinases (HK) catalyze the first step of glycolysis limiting its pace. HK2 is highly expressed in gut epithelium, contributes to immune responses, and is upregulated during inflammation. We examined the microbial regulation of HK2 and its impact on inflammation using mice lacking HK2 in intestinal epithelial cells (Hk2ΔIEC). Hk2ΔIEC mice were less susceptible to acute colitis. Analyzing the epithelial transcriptome from Hk2ΔIEC mice during colitis and using HK2-deficient intestinal organoids and Caco-2 cells revealed reduced mitochondrial respiration and epithelial cell death in the absence of HK2. The microbiota strongly regulated HK2 expression and activity. The microbially derived short-chain fatty acid (SCFA) butyrate repressed HK2 expression via histone deacetylase 8 (HDAC8) and reduced mitochondrial respiration in wild-type but not in HK2-deficient Caco-2 cells. Butyrate supplementation protected wild-type but not Hk2ΔIEC mice from colitis. Our findings define a mechanism how butyrate promotes intestinal homeostasis and suggest targeted HK2-inhibition as therapeutic avenue for inflammation.

A Standardized Brain Molecular Atlas: A Resource for Systems Modeling and Simulation

Accurate molecular concentrations are essential for reliable analyses of biochemical networks and the creation of predictive models for molecular and systems biology, yet protein and metabolite concentrations used in such models are often poorly constrained or irreproducible. Challenges of using data from different sources include conflicts in nomenclature and units, as well as discrepancies in experimental procedures, data processing and implementation of the model. To obtain a consistent estimate of protein and metabolite levels, we integrated and normalized data from a large variety of sources to calculate Adjusted Molecular Concentrations. We found a high degree of reproducibility and consistency of many molecular species across brain regions and cell types, consistent with tight homeostatic regulation. We demonstrated the value of this normalization with differential protein expression analyses related to neurodegenerative diseases, brain regions and cell types. We also used the results in proof-of-concept simulations of brain energy metabolism. The standardized Brain Molecular Atlas overcomes the obstacles of missing or inconsistent data to support systems biology research and is provided as a resource for biomolecular modeling.

Metabolism perturbation Causedby the overexpression of carbon monoxide dehydrogenase/Acetyl-CoA synthase gene complex accelerated gas to acetate conversion rate ofEubacterium limosumKIST612

Microbial conversion of carbon monoxide (CO) to acetate is a promising upcycling strategy for carbon sequestration. Herein, we demonstrate that CO conversion and acetate production rates of Eubacterium limosum KIST612 strain can be improved by in silico prediction and in vivo assessment. The mimicked CO metabolic model of KIST612 predicted that overexpressing the CO dehydrogenase (CODH) increases CO conversion and acetate production rates. To validate the prediction, we constructed mutant strains overexpressing CODH gene cluster and measured their CO conversion and acetate production rates. A mutant strain (ELM031) co-overexpressing CODH, coenzyme CooC2 and ACS showed a 3.1 × increased specific CO oxidation rate as well as 1.4 × increased specific acetate production rate, compared to the wild type strain. The transcriptional and translational data with redox balance analysis showed that ELM031 has enhanced reducing potential from up-regulation of ferredoxin and related metabolism directly linked to energy conservation.

The view of microbes as energy converters illustrates the trade-off between growth rate and yield

The application of thermodynamics to microbial growth has a long tradition that originated in the middle of the 20th century. This approach reflects the view that self-replication is a thermodynamic process that is not fundamentally different from mechanical thermodynamics. The key distinction is that a free energy gradient is not converted into mechanical (or any other form of) energy but rather into new biomass. As such, microbes can be viewed as energy converters that convert a part of the energy contained in environmental nutrients into chemical energy that drives self-replication. Before the advent of high-throughput sequencing technologies, only the most central metabolic pathways were known. However, precise measurement techniques allowed for the quantification of exchanged extracellular nutrients and heat of growing microbes with their environment. These data, together with the absence of knowledge of metabolic details, drove the development of so-called black-box models, which only consider the observable interactions of a cell with its environment and neglect all details of how exactly inputs are converted into outputs. Now, genome sequencing and genome-scale metabolic models (GEMs) provide us with unprecedented detail about metabolic processes inside the cell. However, mostly due to computational complexity issues, the derived modelling approaches make surprisingly little use of thermodynamic concepts. Here, we review classical black-box models and modern approaches that integrate thermodynamics into GEMs. We also illustrate how the description of microbial growth as an energy converter can help to understand and quantify the trade-off between microbial growth rate and yield.

Probabilistic thermodynamic analysis of metabolic networks

MOTIVATION

Random sampling of metabolic fluxes can provide a comprehensive description of the capabilities of a metabolic network. However, current sampling approaches do not model thermodynamics explicitly, leading to inaccurate predictions of an organism's potential or actual metabolic operations.

RESULTS

We present a probabilistic framework combining thermodynamic quantities with steady-state flux constraints to analyze the properties of a metabolic network. It includes methods for probabilistic metabolic optimization and for joint sampling of thermodynamic and flux spaces. Applied to a model of Escherichia coli, we use the methods to reveal known and novel mechanisms of substrate channeling, and to accurately predict reaction directions and metabolite concentrations. Interestingly, predicted flux distributions are multimodal, leading to discrete hypotheses on E.coli's metabolic capabilities.

AVAILABILITY AND IMPLEMENTATION

Python and MATLAB packages available at https://gitlab.com/csb.ethz/pta.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Metabolic flux from the chloroplast provides signals controlling photosynthetic acclimation to cold in Arabidopsis thaliana

Photosynthesis is especially sensitive to environmental conditions, and the composition of the photosynthetic apparatus can be modulated in response to environmental change, a process termed photosynthetic acclimation. Previously, we identified a role for a cytosolic fumarase, FUM2 in acclimation to low temperature in Arabidopsis thaliana. Mutant lines lacking FUM2 were unable to acclimate their photosynthetic apparatus to cold. Here, using gas exchange measurements and metabolite assays of acclimating and non-acclimating plants, we show that acclimation to low temperature results in a change in the distribution of photosynthetically fixed carbon to different storage pools during the day. Proteomic analysis of wild-type Col-0 Arabidopsis and of a fum2 mutant, which was unable to acclimate to cold, indicates that extensive changes occurring in response to cold are affected in the mutant. Metabolic and proteomic data were used to parameterize metabolic models. Using an approach called flux sampling, we show how the relative export of triose phosphate and 3-phosphoglycerate provides a signal of the chloroplast redox state that could underlie photosynthetic acclimation to cold.

Metabolic flux configuration determination using information entropy

Constraint-based models use steady-state mass balances to define a solution space of flux configurations, which can be narrowed down by measuring as many fluxes as possible. Due to loops and redundant pathways, this process typically yields multiple alternative solutions. To address this ambiguity, flux sampling can estimate the probability distribution of each flux, or a flux configuration can be singled out by further minimizing the sum of fluxes according to the assumption that cellular metabolism favors states where enzyme-related costs are economized. However, flux sampling is susceptible to artifacts introduced by thermodynamically infeasible cycles and is it not clear if the economy of fluxes assumption (EFA) is universally valid. Here, we formulated a constraint-based approach, MaxEnt, based on the principle of maximum entropy, which in this context states that if more than one flux configuration is consistent with a set of experimentally measured fluxes, then the one with the minimum amount of unwarranted assumptions corresponds to the best estimation of the non-observed fluxes. We compared MaxEnt predictions to Escherichia coli and Saccharomyces cerevisiae publicly available flux data. We found that the mean square error (MSE) between experimental and predicted fluxes by MaxEnt and EFA-based methods are three orders of magnitude lower than the median of 1,350,000 MSE values obtained using flux sampling. However, only MaxEnt and flux sampling correctly predicted flux through E. coli’s glyoxylate cycle, whereas EFA-based methods, in general, predict no flux cycles. We also tested MaxEnt predictions at increasing levels of overflow metabolism. We found that MaxEnt accuracy is not affected by overflow metabolism levels, whereas the EFA-based methods show a decreasing performance. These results suggest that MaxEnt is less sensitive than flux sampling to artifacts introduced by thermodynamically infeasible cycles and that its predictions are less susceptible to overfitting than EFA-based methods.

A Genome-Scale Insight into the Effect of Shear Stress During the Fed-Batch Production of Clavulanic Acid by Streptomyces Clavuligerus

Streptomyces clavuligerus is a filamentous Gram-positive bacterial producer of the β-lactamase inhibitor clavulanic acid. Antibiotics biosynthesis in the Streptomyces genus is usually triggered by nutritional and environmental perturbations. In this work, a new genome scale metabolic network of Streptomyces clavuligerus was reconstructed and used to study the experimentally observed effect of oxygen and phosphate concentrations on clavulanic acid biosynthesis under high and low shear stress. A flux balance analysis based on experimental evidence revealed that clavulanic acid biosynthetic reaction fluxes are favored in conditions of phosphate limitation, and this is correlated with enhanced activity of central and amino acid metabolism, as well as with enhanced oxygen uptake. In silico and experimental results show a possible slowing down of tricarboxylic acid (TCA) due to reduced oxygen availability in low shear stress conditions. In contrast, high shear stress conditions are connected with high intracellular oxygen availability favoring TCA activity, precursors availability and clavulanic acid (CA) production.

Genome-Scale Metabolic Model of Xanthomonas phaseoli pv. manihotis: An Approach to Elucidate Pathogenicity at the Metabolic Level

Xanthomonas phaseoli pv. manihotis (Xpm) is the causal agent of cassava bacterial blight, the most important bacterial disease in this crop. There is a paucity of knowledge about the metabolism of Xanthomonas and its relevance in the pathogenic process, with the exception of the elucidation of the xanthan biosynthesis route. Here we report the reconstruction of the genome-scale model of Xpm metabolism and the insights it provides into plant-pathogen interactions. The model, iXpm1556, displayed 1,556 reactions, 1,527 compounds, and 890 genes. Metabolic maps of central amino acid and carbohydrate metabolism, as well as xanthan biosynthesis of Xpm, were reconstructed using Escher (https://escher.github.io/) to guide the curation process and for further analyses. The model was constrained using the RNA-seq data of a mutant of Xpm for quorum sensing (QS), and these data were used to construct context-specific models (CSMs) of the metabolism of the two strains (wild type and QS mutant). The CSMs and flux balance analysis were used to get insights into pathogenicity, xanthan biosynthesis, and QS mechanisms. Between the CSMs, 653 reactions were shared; unique reactions belong to purine, pyrimidine, and amino acid metabolism. Alternative objective functions were used to demonstrate a trade-off between xanthan biosynthesis and growth and the re-allocation of resources in the process of biosynthesis. Important features altered by QS included carbohydrate metabolism, NAD(P)+ balance, and fatty acid elongation. In this work, we modeled the xanthan biosynthesis and the QS process and their impact on the metabolism of the bacterium. This model will be useful for researchers studying host-pathogen interactions and will provide insights into the mechanisms of infection used by this and other Xanthomonas species.

A biochemically-interpretable machine learning classifier for microbial GWAS

Current machine learning classifiers have successfully been applied to whole-genome sequencing data to identify genetic determinants of antimicrobial resistance (AMR), but they lack causal interpretation. Here we present a metabolic model-based machine learning classifier, named Metabolic Allele Classifier (MAC), that uses flux balance analysis to estimate the biochemical effects of alleles. We apply the MAC to a dataset of 1595 drug-tested Mycobacterium tuberculosis strains and show that MACs predict AMR phenotypes with accuracy on par with mechanism-agnostic machine learning models (isoniazid AUC = 0.93) while enabling a biochemical interpretation of the genotype-phenotype map. Interpretation of MACs for three antibiotics (pyrazinamide, para-aminosalicylic acid, and isoniazid) recapitulates known AMR mechanisms and suggest a biochemical basis for how the identified alleles cause AMR. Extending flux balance analysis to identify accurate sequence classifiers thus contributes mechanistic insights to GWAS, a field thus far dominated by mechanism-agnostic results.

Current machine learning classifiers have been applied to whole-genome sequencing data to identify determinants of antimicrobial resistance, but they lack interpretability. Here the authors present a metabolic machine learning classifier that uses flux balance analysis to estimate the biochemical effects of alleles.

Single-Cell RNA Sequencing Maps Endothelial Metabolic Plasticity in Pathological Angiogenesis

Endothelial cell (EC) metabolism is an emerging target for anti-angiogenic therapy in tumor angiogenesis and choroidal neovascularization (CNV), but little is known about individual EC metabolic transcriptomes. By single-cell RNA sequencing 28,337 murine choroidal ECs (CECs) and sprouting CNV-ECs, we constructed a taxonomy to characterize their heterogeneity. Comparison with murine lung tumor ECs (TECs) revealed congruent marker gene expression by distinct EC phenotypes across tissues and diseases, suggesting similar angiogenic mechanisms. Trajectory inference predicted that differentiation of venous to angiogenic ECs was accompanied by metabolic transcriptome plasticity. ECs displayed metabolic transcriptome heterogeneity during cell-cycle progression and in quiescence. Hypothesizing that conserved genes are important, we used an integrated analysis, based on congruent transcriptome analysis, CEC-tailored genome-scale metabolic modeling, and gene expression meta-analysis in cross-species datasets, followed by in vitro and in vivo validation, to identify SQLE and ALDH18A1 as previously unknown metabolic angiogenic targets.

Large-scale kinetic metabolic models of Pseudomonas putida KT2440 for consistent design of metabolic engineering strategies

BACKGROUND

Pseudomonas putida is a promising candidate for the industrial production of biofuels and biochemicals because of its high tolerance to toxic compounds and its ability to grow on a wide variety of substrates. Engineering this organism for improved performances and predicting metabolic responses upon genetic perturbations requires reliable descriptions of its metabolism in the form of stoichiometric and kinetic models.

RESULTS

In this work, we developed kinetic models of P. putida to predict the metabolic phenotypes and design metabolic engineering interventions for the production of biochemicals. The developed kinetic models contain 775 reactions and 245 metabolites. Furthermore, we introduce here a novel set of constraints within thermodynamics-based flux analysis that allow for considering concentrations of metabolites that exist in several compartments as separate entities. We started by a gap-filling and thermodynamic curation of iJN1411, the genome-scale model of P. putida KT2440. We then systematically reduced the curated iJN1411 model, and we created three core stoichiometric models of different complexity that describe the central carbon metabolism of P. putida. Using the medium complexity core model as a scaffold, we generated populations of large-scale kinetic models for two studies. In the first study, the developed kinetic models successfully captured the experimentally observed metabolic responses to several single-gene knockouts of a wild-type strain of P. putida KT2440 growing on glucose. In the second study, we used the developed models to propose metabolic engineering interventions for improved robustness of this organism to the stress condition of increased ATP demand.

CONCLUSIONS

The study demonstrates the potential and predictive capabilities of the kinetic models that allow for rational design and optimization of recombinant P. putida strains for improved production of biofuels and biochemicals. The curated genome-scale model of P. putida together with the developed large-scale stoichiometric and kinetic models represents a significant resource for researchers in industry and academia.

Microenvironmental cooperation promotes early spread and bistability of a Warburg-like phenotype

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Such a behaviour turns out to be linked to the re-cycling of overflow products by non-aberrant cells. Quantitative insight on the overall emerging picture is provided by a spatially homogeneous version of the model.

Erroneous energy-generating cycles in published genome scale metabolic networks: Identification and removal

Energy metabolism is central to cellular biology. Thus, genome-scale models of heterotrophic unicellular species must account appropriately for the utilization of external nutrients to synthesize energy metabolites such as ATP. However, metabolic models designed for flux-balance analysis (FBA) may contain thermodynamically impossible energy-generating cycles: without nutrient consumption, these models are still capable of charging energy metabolites (such as ADP→ATP or NADP⁺→NADPH). Here, we show that energy-generating cycles occur in over 85% of metabolic models without extensive manual curation, such as those contained in the ModelSEED and MetaNetX databases; in contrast, such cycles are rare in the manually curated models of the BiGG database. Energy generating cycles may represent model errors, e.g., erroneous assumptions on reaction reversibilities. Alternatively, part of the cycle may be thermodynamically feasible in one environment, while the remainder is thermodynamically feasible in another environment; as standard FBA does not account for thermodynamics, combining these into an FBA model allows erroneous energy generation. The presence of energy-generating cycles typically inflates maximal biomass production rates by 25%, and may lead to biases in evolutionary simulations. We present efficient computational methods (i) to identify energy generating cycles, using FBA, and (ii) to identify minimal sets of model changes that eliminate them, using a variant of the GlobalFit algorithm.

Genome-scale metabolic models are routinely used to simulate the growth of unicellular organisms, and are likely to become an important tool in the medical sciences. The most popular method employed for this task is flux balance analysis (FBA), a simplified mathematical description able to describe the simultaneous activity of hundreds of biochemical reactions. Cellular functions are often dependent on the availability of sufficient energy, and thus a correct representation of energy metabolism appears crucial to metabolic modeling. However, we found that the majority of FBA models generated directly from genome sequences, as well as a minority of carefully curated models, are capable of generating energy out of thin air. These models charge energy metabolites such as ATP without any nutrient uptake. We named the corresponding sets of reactions “erroneous energy generating cycles” (EGCs) and developed a high-throughput algorithm for their identification. We found EGCs in 238 (68%) of 350 metabolic models from three different databases. We developed a second, fully automated method for EGC removal. Simulations on the corrected models typically showed growth rates that were 25% slower than in the original models, demonstrating the importance of checking metabolic model reconstructions for EGCs.

Fast-SNP: a fast matrix pre-processing algorithm for efficient loopless flux optimization of metabolic models

Motivation: Computation of steady-state flux solutions in large metabolic models is routinely performed using flux balance analysis based on a simple LP (Linear Programming) formulation. A minimal requirement for thermodynamic feasibility of the flux solution is the absence of internal loops, which are enforced using ‘loopless constraints’. The resulting loopless flux problem is a substantially harder MILP (Mixed Integer Linear Programming) problem, which is computationally expensive for large metabolic models.

Results: We developed a pre-processing algorithm that significantly reduces the size of the original loopless problem into an easier and equivalent MILP problem. The pre-processing step employs a fast matrix sparsification algorithm—Fast- sparse null-space pursuit (SNP)—inspired by recent results on SNP. By finding a reduced feasible ‘loop-law’ matrix subject to known directionalities, Fast-SNP considerably improves the computational efficiency in several metabolic models running different loopless optimization problems. Furthermore, analysis of the topology encoded in the reduced loop matrix enabled identification of key directional constraints for the potential permanent elimination of infeasible loops in the underlying model. Overall, Fast-SNP is an effective and simple algorithm for efficient formulation of loop-law constraints, making loopless flux optimization feasible and numerically tractable at large scale.

Availability and Implementation: Source code for MATLAB including examples is freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization uses Gurobi, CPLEX or GLPK (the latter is included with the algorithm).

Contact:lars.nielsen@uq.edu.au

Supplementary information:Supplementary data are available at Bioinformatics online.