Constraint-based Modeling Research Articles

Sensitivities in protein allocation models reveal distribution of metabolic capacity and flux control.

Expanding on constraint-based metabolic models, protein allocation models (PAMs) enhance flux predictions by accounting for protein resource allocation in cellular metabolism. Yet, to this date, there are no dedicated methods for analyzing and understanding the growth-limiting factors in simulated phenotypes in PAMs. Here, we introduce a systematic framework for identifying the most sensitive enzyme concentrations (sEnz) in PAMs. The framework exploits the primal and dual formulations of these models to derive sensitivity coefficients based on relations between variables, constraints, and the objective function. This approach enhances our understanding of the growth-limiting factors of metabolic phenotypes under specific environmental or genetic conditions. Compared to other traditional methods for calculating sensitivities, sEnz requires substantially less computation time and facilitates more intuitive comparison and analysis of sensitivities. The sensitivities calculated by sEnz cover enzymes, reactions and protein sectors, enabling a holistic overview of the factors influencing metabolism. When applied to an Escherichia coli PAM, sEnz revealed major pathways and enzymes driving overflow metabolism. Overall, sEnz offers a computational efficient framework for understanding PAM predictions and unravelling the factors governing a particular metabolic phenotype. sEnz is implemented in the modular toolbox for the generation and analysis of PAMs in Python (PAModelpy; v.0.0.3.3), available on Pypi (https://pypi.org/project/PAModelpy/). The source code together with all other python scripts and notebooks are available on GitHub (https://github.com/iAMB-RWTH-Aachen/PAModelpy). Supplementary data are available at Bioinformatics online.

MitoMAMMAL: a genome scale model of mammalian mitochondria predicts cardiac and BAT metabolism

Abstract Motivation Mitochondria perform several essential functions in order to maintain cellular homeostasis and mitochondrial metabolism is inherently flexible to allow correct function in a wide range of tissues. Dysregulated mitochondrial metabolism can therefore affect different tissues in different ways which presents experimental challenges in understanding the pathology of mitochondrial diseases. System-level metabolic modelling is therefore useful in gaining in-depth insights into tissue-specific mitochondrial metabolism, yet despite the mouse being a common model organism used in research, there is currently no mouse specific mitochondrial metabolic model available. Results In this work, building upon the similarity between human and mouse mitochondrial metabolism, we have created mitoMammal, a genome-scale metabolic model that contains human and mouse specific gene-product reaction rules. MitoMammal is therefore able to model mouse and human mitochondrial metabolism. To demonstrate this feature, using an adapted E-Flux algorithm, we first integrated proteomic data extracted from mitochondria of isolated mouse cardiomyocytes and mouse brown adipocyte tissue. We then integrated transcriptomic data from in vitro differentiated human brown adipose cells and modelled the context specific metabolism using flux balance analysis. In all three simulations, mitoMammal made mostly accurate, and some novel predictions relating to energy metabolism in the context of cardiomyocytes and brown adipocytes. This demonstrates its usefulness in research relating to cardiac disease and diabetes in both mouse and human contexts. Availability and implementation MitoMammal is formatted in SBML3. The code required for constraint-based modelling used in this work is implemented in Python 3 and is available as a Jupyter Notebook. The mitoMammal metabolic model, along with Jupyter notebooks and data used in this work are available at: https://gitlab.com/habermann_lab/mitomammal. Supplementary Information Supplementary data are available at Bioinformatics Advances online.

Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes.

The increasing availability of enzyme turnover number measurements from experiments and of turnover number predictions from deep learning models prompts the use of these enzyme parameters in precise metabolic engineering. Yet, there is no computational approach that allows the prediction of metabolic engineering strategies that rely on the modification of turnover numbers. It is also unclear if modifications of turnover numbers without alterations in the host's transcriptional regulatory machinery suffice to increase the production of chemicals of interest. Here, we present a constraint-based modeling approach, termed Overcoming Kinetic rate Obstacles (OKO), that uses enzyme-constrained metabolic models to predict in silico strategies to increase the production of a given chemical, while ensuring specified cell growth. We demonstrate that the application of OKO to enzyme-constrained metabolic models of Escherichia coli and Saccharomyces cerevisiae results in strategies that can at least double the production of over 40 compounds with little penalty to growth. Interestingly, we show that the overproduction of compounds of interest does not entail only an increase in the values of turnover numbers. Lastly, we demonstrate that a refinement of OKO, allowing also for manipulation of enzyme abundance, facilitates the usage of the available compendia and deep learning models of turnover numbers in the design of precise metabolic engineering strategies. Our results expand the usage of genome-scale metabolic models toward the identification of targets for protein engineering, allowing their direct usage in the generation of innovative metabolic engineering designs for various biotechnological applications.

Defining Golden Batches in Biomanufacturing Processes From Internal Metabolic Activity to Detect Process Changes That May Affect Product Quality.

Cellular metabolism plays a role in the observed variability of a drug substance's Critical Quality Attributes (CQAs) made by biomanufacturing processes. Therefore, here we describe a new approach for monitoring biomanufacturing processes that measures a set of metabolic reaction rates (named Critical Metabolic Parameters (CMP) in addition to the macroscopic process conditions currently being used as Critical Process Parameters (CPP) for biomanufacturing. Constraint-based systems biology models like Flux Balance Analysis (FBA) are used to estimate metabolic reaction rates, and metabolic rates are used as inputs for multivariate Batch Evolution Models (BEM). Metabolic activity was reproducible among batches and could be monitored to detect a deliberately induced macroscopic process shift (i.e., temperature change). The CMP approach has the potential to enable "golden batches" in biomanufacturing processes to be defined from the internal metabolic activity and to aid in detecting process changes that may impact the quality of the product. Overall, the data suggested that monitoring of metabolic activity has promise for biomanufacturing process control.

Integrating Molecular Perspectives: Strategies for Comprehensive Multi-Omics Integrative Data Analysis and Machine Learning Applications in Transcriptomics, Proteomics, and Metabolomics.

With the advent of high-throughput technologies, the field of omics has made significant strides in characterizing biological systems at various levels of complexity. Transcriptomics, proteomics, and metabolomics are the three most widely used omics technologies, each providing unique insights into different layers of a biological system. However, analyzing each omics data set separately may not provide a comprehensive understanding of the subject under study. Therefore, integrating multi-omics data has become increasingly important in bioinformatics research. In this article, we review strategies for integrating transcriptomics, proteomics, and metabolomics data, including co-expression analysis, metabolite-gene networks, constraint-based models, pathway enrichment analysis, and interactome analysis. We discuss combined omics integration approaches, correlation-based strategies, and machine learning techniques that utilize one or more types of omics data. By presenting these methods, we aim to provide researchers with a better understanding of how to integrate omics data to gain a more comprehensive view of a biological system, facilitating the identification of complex patterns and interactions that might be missed by single-omics analyses.

CRISPRi-mediated metabolic switch enables concurrent aerobic and synthetic anaerobic fermentations in engineered consortium

Replacing petrochemicals with compounds from bio-based manufacturing processes remains an important part of the global effort to move towards a sustainable future. However, achieving economic viability requires both optimized cell factories and innovative processes. Here, we address this challenge by developing a fermentation platform, which enables two concurrent fermentations in one bioreactor. We first construct a xylitol producing Escherichia coli strain in which CRISPRi-mediated gene silencing is used to switch the metabolism from aerobic to anaerobic, even when the bacteria are under oxic conditions. The switch also decouples growth from production, which further increases the yield. The strain produces acetate as a byproduct, which is subsequently metabolized under oxic conditions by a secondary E. coli strain. Through constraint-based metabolic modelling this strain is designed to co-valorize glucose and the excreted acetate to a secondary product. This unique syntrophic consortium concept facilitates the implementation of “two fermentations in one go”, where the concurrent fermentation displays similar titers and productivities as compared to two separate single strain fermentations.

A metabolic modeling-based framework for predicting trophic dependencies in native rhizobiomes of crop plants.

The exchange of metabolites (i.e., metabolic interactions) between bacteria in the rhizosphere determines various plant-associated functions. Systematically understanding the metabolic interactions in the rhizosphere, as well as in other types of microbial communities, would open the door to the optimization of specific predefined functions of interest, and therefore to the harnessing of the functionality of various types of microbiomes. However, mechanistic knowledge regarding the gathering and interpretation of these interactions is limited. Here, we present a framework utilizing genomics and constraint-based modeling approaches, aiming to interpret the hierarchical trophic interactions in the soil environment. 243 genome scale metabolic models of bacteria associated with a specific disease-suppressive vs disease-conducive apple rhizospheres were drafted based on genome-resolved metagenomes, comprising an in silico native microbial community. Iteratively simulating microbial community members' growth in a metabolomics-based apple root-like environment produced novel data on potential trophic successions, used to form a network of communal trophic dependencies. Network-based analyses have characterized interactions associated with beneficial vs non-beneficial microbiome functioning, pinpointing specific compounds and microbial species as potential disease supporting and suppressing agents. This framework provides a means for capturing trophic interactions and formulating a range of testable hypotheses regarding the metabolic capabilities of microbial communities within their natural environment. Essentially, it can be applied to different environments and biological landscapes, elucidating the conditions for the targeted manipulation of various microbiomes, and the execution of countless predefined functions.

Updating assembly parameters for spacecraft assembly process state changes: based on data fusion method

Thermal protection systems (TPSs) are important components of reusable spacecraft, and their assembly quality has a crucial impact on flight safety. Owing to the complex assembly process and variable states of spacecraft thermal protection systems, assembly parameters may vary under different assembly states. Therefore, to obtain assembly parameters accurately and efficiently under different assembly states, in this study, 3D point cloud data and fiber optic sensor data were fused to develop an assembly parameter update method for assembly process state changes. Firstly, based on the measured data of thermal protection components and load-bearing structure, the gap, flush and matching parameters solution model are proposed. Secondly, to address the deformation problem of the load-bearing structure caused by changes in assembly status, a fusion method based on laser scanning and sensor detection was devised to achieve deformation prediction of the assembly structure during the assembly process. Thirdly, based on the assembly parameter solution model and point cloud prediction model, a constraint-based assembly parameter optimisation model was established, and an improved quantum particle swarm optimisation (LQPSO) algorithm was employed to achieve assembly parameter updates oriented toward changes in assembly status. Finally, an experimental system for array-based thermal protection structure simulation was established to validate the proposed method. The results show that the proposed parameter update method can achieve ideal results for different assembly state simulation components.

A hierarchy of metabolite exchanges in metabolic models of microbial species and communities.

The metabolic network of an organism can be analyzed as a constraint-based model. This analysis can be biased, optimizing an objective such as growth rate, or unbiased, aiming to describe the full feasible space of metabolic fluxes through pathway analysis or random flux sampling. In particular, pathway analysis can decompose the flux space into fundamental and formally defined metabolic pathways. Unbiased methods scale poorly with network size due to combinatorial explosion, but a promising approach to improve scalability is to focus on metabolic subnetworks, e.g., cells' metabolite exchanges with each other and the environment, rather than the full metabolic networks. Here, we applied pathway enumeration and flux sampling to metabolite exchanges in microbial species and a microbial community, using models ranging from central carbon metabolism to genome-scale and focusing on pathway definitions that allow direct targeting of subnetworks such as metabolite exchanges (elementary conversion modes, elementary flux patterns, and minimal pathways). Enumerating growth-supporting metabolite exchanges, we found that metabolite exchanges from different pathway definitions were related through a hierarchy, and we show that this hierarchical relationship between pathways holds for metabolic networks and subnetworks more generally. Metabolite exchange frequencies, defined as the fraction of pathways in which each metabolite was exchanged, were similar across pathway definitions, with a few specific exchanges explaining large differences in pathway counts. This indicates that biological interpretation of predicted metabolite exchanges is robust to the choice of pathway definition, and it suggests strategies for more scalable pathway analysis. Our results also signal wider biological implications, facilitating detailed and interpretable analysis of metabolite exchanges and other subnetworks in fields such as metabolic engineering and synthetic biology.

Exploring the metabolic profile of A. baumannii for antimicrobial development using genome-scale modeling.

With the emergence of multidrug-resistant bacteria, the World Health Organization published a catalog of microorganisms urgently needing new antibiotics, with the carbapenem-resistant Acinetobacter baumannii designated as "critical". Such isolates, frequently detected in healthcare settings, pose a global pandemic threat. One way to facilitate a systemic view of bacterial metabolism and allow the development of new therapeutics is to apply constraint-based modeling. Here, we developed a versatile workflow to build high-quality and simulation-ready genome-scale metabolic models. We applied our workflow to create a metabolic model for A. baumannii and validated its predictive capabilities using experimental nutrient utilization and gene essentiality data. Our analysis showed that our model iACB23LX could recapitulate cellular metabolic phenotypes observed during in vitro experiments, while positive biomass production rates were observed and experimentally validated in various growth media. We further defined a minimal set of compounds that increase A. baumannii's cellular biomass and identified putative essential genes with no human counterparts, offering new candidates for future antimicrobial development. Finally, we assembled and curated the first collection of metabolic reconstructions for distinct A. baumannii strains and analyzed their growth characteristics. The presented models are in a standardized and well-curated format, enhancing their usability for multi-strain network reconstruction.

Constraint-based modelling predicts metabolic signatures of low and high-grade serous ovarian cancer

Ovarian cancer is an aggressive, heterogeneous disease, burdened with late diagnosis and resistance to chemotherapy. Clinical features of ovarian cancer could be explained by investigating its metabolism, and how the regulation of specific pathways links to individual phenotypes. Ovarian cancer is of particular interest for metabolic research due to its heterogeneous nature, with five distinct subtypes having been identified, each of which may display a unique metabolic signature. To elucidate metabolic differences, constraint-based modelling (CBM) represents a powerful technology, inviting the integration of ‘omics’ data, such as transcriptomics. However, many CBM methods have not prioritised accurate growth rate predictions, and there are very few ovarian cancer genome-scale studies. Here, a novel method for CBM has been developed, employing the genome-scale model Human1 and flux balance analysis, enabling the integration of in vitro growth rates, transcriptomics data and media conditions to predict the metabolic behaviour of cells. Using low- and high-grade ovarian cancer, subtype-specific metabolic differences have been predicted, which have been supported by publicly available CRISPR-Cas9 data from the Cancer Cell Line Encyclopaedia and an extensive literature review. Metabolic drivers of aggressive, invasive phenotypes, as well as pathways responsible for increased chemoresistance in low-grade cell lines have been suggested. Experimental gene dependency data has been used to validate areas of the pentose phosphate pathway as essential for low-grade cellular growth, highlighting potential vulnerabilities for this ovarian cancer subtype.

A physical constraint-based machine learning model for shale oil production prediction

Shale oil has become a crucial unconventional resource, bolstering energy supply security, and it is important to accurately predict shale oil production dynamics. However, traditional prediction methods are faced with the challenges of large data fluctuations and numerous interference factors, which make accurate prediction difficult. This paper introduces a deep learning approach, specifically a physical constraint-based convolutional neural network combined with long short-term memory and attention mechanism (CNN-LSTM-AM), to predict shale oil production dynamics. Initially, the correlation analysis method is used to analyze the correlation strengths of features with the prediction target, and the data that are most strongly correlated with the daily oil production are screened out and preprocessed. Key features are then extracted; that is, the CNN layer's output is fed into the LSTM layer, the output of which informs a fully connected layer for time-series production predictions. The model integrates an AM to concentrate on vital data aspects. In the “five-linear flow” formula, the imbibition is hard-coded into the shale oil production prediction model. Physical constraints are introduced into the model. Data driven and empirical formulas are used to introduce a loss function as a constraint condition in the training process of a machine learning model to improve the interpretability and predictive ability of the model. During the tuning phase, Bayesian optimization is used to fine-tune the model's hyperparameters. Shapley additive explanation and accumulated local effects analyses are used to further assess and quantify the significance of the essential parameters, thus optimizing the prediction effectiveness.

Evaluating the feasibility of medium-chain oleochemical synthesis using microbial chain elongation.

In this work, the authors use constraint-based metabolic modelling and enzyme cost minimization to assess the feasibility of using metabolic engineering to expand the product spectrum of anaerobic chain elongating bacteria.

Epigenetic control of metabolic identity across cell types.

Constraint-based network modelling is a powerful tool for analysing cellular metabolism at genomic scale. Here, we conducted an integrative analysis of metabolic networks reconstructed from RNA-seq data with paired epigenomic data from the EpiATLAS resource of the International Human Epigenome Consortium (IHEC). Applying a state-of-the-art contextualisation algorithm, we reconstructed metabolic networks across 1,555 samples corresponding to 58 tissues and cell types. Analysis of these networks revealed the distribution of metabolic functionalities across human cell types and provides a compendium of human metabolic activity. This integrative approach allowed us to define, across tissues and cell types, i) reactions that fulfil the basic metabolic processes (core metabolism), and ii) cell type-specific functions (unique metabolism), that shape the metabolic identity of a cell or a tissue. Integration with EpiATLAS-derived cell type-specific gene-level chromatin states and enhancer-gene interactions identified enhancers, transcription factors, and key nodes controlling core and unique metabolism. Transport and first reactions of pathways were enriched for high expression, active chromatin state, and Polycomb-mediated repression in cell types where pathways are inactive, suggesting that key nodes are targets of repression. This integrative analysis forms the basis for identifying regulation points that control metabolic identity in human cells.

Transporter annotations are holding up progress in metabolic modeling

Mechanistic, constraint-based models of microbial isolates or communities are a staple in the metabolic analysis toolbox, but predictions about microbe-microbe and microbe-environment interactions are only as good as the accuracy of transporter annotations. A number of hurdles stand in the way of comprehensive functional assignments for membrane transporters. These include general or non-specific substrate assignments, ambiguity in the localization, directionality and reversibility of a transporter, and the many-to-many mapping of substrates, transporters and genes. In this perspective, we summarize progress in both experimental and computational approaches used to determine the function of transporters and consider paths forward that integrate both. Investment in accurate, high-throughput functional characterization is needed to train the next-generation of predictive tools toward genome-scale metabolic network reconstructions that better predict phenotypes and interactions. More reliable predictions in this domain will benefit fields ranging from personalized medicine to metabolic engineering to microbial ecology.

Including glutamine in a resource allocation model of energy metabolism in cancer and yeast cells

Energy metabolism is crucial for all living cells, especially during fast growth or stress scenarios. Many cancer and activated immune cells (Warburg effect) or yeasts (Crabtree effect) mostly rely on aerobic glucose fermentation leading to lactate or ethanol, respectively, to generate ATP. In recent years, several mathematical models have been proposed to explain the Warburg effect on theoretical grounds. Besides glucose, glutamine is a very important substrate for eukaryotic cells—not only for biosynthesis, but also for energy metabolism. Here, we present a minimal constraint-based stoichiometric model for explaining both the classical Warburg effect and the experimentally observed respirofermentation of glutamine (WarburQ effect). We consider glucose and glutamine respiration as well as the respective fermentation pathways. Our resource allocation model calculates the ATP production rate, taking into account enzyme masses and, therefore, pathway costs. While our calculation predicts glucose fermentation to be a superior energy-generating pathway in human cells, different enzyme characteristics in yeasts reduce this advantage, in some cases to such an extent that glucose respiration is preferred. The latter is observed for the fungal pathogen Candida albicans, which is a known Crabtree-negative yeast. Further, optimization results show that glutamine is a valuable energy source and important substrate under glucose limitation, in addition to its role as a carbon and nitrogen source of biomass in eukaryotic cells. In conclusion, our model provides insights that glutamine is an underestimated fuel for eukaryotic cells during fast growth and infection scenarios and explains well the observed parallel respirofermentation of glucose and glutamine in several cell types.

Structural constraints limit the regime of optimal flux in autocatalytic reaction networks

Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks remains elusive. In this work, we present a theoretical framework that allows specific bounds on the thermodynamic affinity and on the concentrations of autocatalysts in mass-action autocatalytic networks. These bounds can be obtained solely from the stoichiometry of the underlying chemical reaction network, and are independent from the numerical values of kinetic parameters. This property holds in the specific regime where all the fluxes of the network are tightly coupled and maximal. Our method is applicable to large networks, and can be used to complement constraints-based modeling methods of metabolic networks, which typically do not provide predictions about thermodynamic properties or concentration ranges of metabolites.

Constraint-based Model for Energy Optimization Management of Parallel Pumping Systems with Demand Variability

Constraint-based Model for Energy Optimization Management of Parallel Pumping Systems with Demand Variability

Educational models for cognition: Methodology of modeling intellectual skills for intelligent tutoring systems

Automation of teaching people new skills requires modeling of human reasoning because human cognition involves active reasoning over the new subject domain to acquire skills that will later become automatic. The article presents Thought Process Trees — a language for modeling human reasoning that was created to facilitate the development of intelligent tutoring systems, which can perform the same reasoning that is expected of a student and find deficiencies in their line of thinking, providing explanatory messages and allowing them to learn from performance errors. The methodology of building trees which better reflect human learning is discussed, with examples of design choices during the modeling process and their consequences. The characteristics of educational modeling that impact building subject-domain models for intelligent tutoring systems are discussed. The trees were formalized and served as a basis for developing a framework for constructing intelligent tutoring systems. This significantly lowered the time required to build and debug a constraint-based subject-domain model. The framework has already been used to develop five intelligent tutoring systems and their prototypes and is being used to develop more of them.

GEM-based computational modeling for exploring metabolic interactions in a microbial community.

Microbial communities play fundamental roles in every complex ecosystem, such as soil, sea and the human body. The stability and diversity of the microbial community depend precisely on the composition of the microbiota. Any change in the composition of these communities affects microbial functions. An important goal of studying the interactions between species is to understand the behavior of microbes and their responses to perturbations. These interactions among species are mediated by the exchange of metabolites within microbial communities. We developed a computational model for the microbial community that has a separate compartment for exchanging metabolites. This model can predict possible metabolites that cause competition, commensalism, and mutual interactions between species within a microbial community. Our constraint-based community metabolic modeling approach provides insights to elucidate the pattern of metabolic interactions for each common metabolite between two microbes. To validate our approach, we used a toy model and a syntrophic co-culture of Desulfovibrio vulgaris and Methanococcus maripaludis, as well as another in co-culture between Geobacter sulfurreducens and Rhodoferax ferrireducens. For a more general evaluation, we applied our algorithm to the honeybee gut microbiome, composed of seven species, and the epiphyte strain Pantoea eucalypti 299R. The epiphyte strain Pe299R has been previously studied and cultured with six different phyllosphere bacteria. Our algorithm successfully predicts metabolites, which imply mutualistic, competitive, or commensal interactions. In contrast to OptCom, MRO, and MICOM algorithms, our COMMA algorithm shows that the potential for competitive interactions between an epiphytic species and Pe299R is not significant. These results are consistent with the experimental measurements of population density and reproductive success of the Pe299R strain.