Dynamic flux balance analysis of diauxic growth in Escherichia coli

Addressing uncertainty in genome-scale metabolic model reconstruction and analysis

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

Dynamic Allocation of Carbon Storage and Nutrient-Dependent Exudation in a Revised Genome-Scale Model of Prochlorococcus

Microbial life in the oceans impacts the entire marine ecosystem, global biogeochemistry and climate. The marine cyanobacterium Prochlorococcus, an abundant component of this ecosystem, releases a significant fraction of the carbon fixed through photosynthesis, but the amount, timing and molecular composition of released carbon are still poorly understood. These depend on several factors, including nutrient availability, light intensity and glycogen storage. Here we combine multiple computational approaches to provide insight into carbon storage and exudation in Prochlorococcus. First, with the aid of a new algorithm for recursive filling of metabolic gaps (ReFill), and through substantial manual curation, we extended an existing genome-scale metabolic model of Prochlorococcus MED4. In this revised model (iSO595), we decoupled glycogen biosynthesis/degradation from growth, thus enabling dynamic allocation of carbon storage. In contrast to standard implementations of flux balance modeling, we made use of forced influx of carbon and light into the cell, to recapitulate overflow metabolism due to the decoupling of photosynthesis and carbon fixation from growth during nutrient limitation. By using random sampling in the ensuing flux space, we found that storage of glycogen or exudation of organic acids are favored when the growth is nitrogen limited, while exudation of amino acids becomes more likely when phosphate is the limiting resource. We next used COMETS to simulate day-night cycles and found that the model displays dynamic glycogen allocation and exudation of organic acids. The switch from photosynthesis and glycogen storage to glycogen depletion is associated with a redistribution of fluxes from the Entner-Doudoroff to the Pentose Phosphate pathway. Finally, we show that specific gene knockouts in iSO595 exhibit dynamic anomalies compatible with experimental observations, further demonstrating the value of this model as a tool to probe the metabolic dynamic of Prochlorococcus.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Opportunities and Challenges for Microbial Synthesis of Fatty Acid-Derived Chemicals (FACs)

Global warming and uneven distribution of fossil fuels worldwide concerns have spurred the development of alternative, renewable, sustainable, and environmentally friendly resources. From an engineering perspective, biosynthesis of fatty acid-derived chemicals (FACs) is an attractive and promising solution to produce chemicals from abundant renewable feedstocks and carbon dioxide in microbial chassis. However, several factors limit the viability of this process. This review first summarizes the types of FACs and their widely applications. Next, we take a deep look into the microbial platform to produce FACs, give an outlook for the platform development. Then we discuss the bottlenecks in metabolic pathways and supply possible solutions correspondingly. Finally, we highlight the most recent advances in the fast-growing model-based strain design for FACs biosynthesis.

A dynamic multi-tissue model to study human metabolism

Metabolic modeling enables the study of human metabolism in healthy and in diseased conditions, e.g., the prediction of new drug targets and biomarkers for metabolic diseases. To accurately describe blood and urine metabolite dynamics, the integration of multiple metabolically active tissues is necessary. We developed a dynamic multi-tissue model, which recapitulates key properties of human metabolism at the molecular and physiological level based on the integration of transcriptomics data. It enables the simulation of the dynamics of intra-cellular and extra-cellular metabolites at the genome scale. The predictive capacity of the model is shown through the accurate simulation of different healthy conditions (i.e., during fasting, while consuming meals or during exercise), and the prediction of biomarkers for a set of Inborn Errors of Metabolism with a precision of 83%. This novel approach is useful to prioritize new biomarkers for many metabolic diseases, as well as for the integration of various types of personal omics data, towards the personalized analysis of blood and urine metabolites.

Cooperative metabolic resource allocation in spatially-structured systems

Natural selection has shaped the evolution of cells and multi-cellular organisms such that social cooperation can often be preferred over an individualistic approach to metabolic regulation. This paper extends a framework for dynamic metabolic resource allocation based on the maximum entropy principle to spatiotemporal models of metabolism with cooperation. Much like the maximum entropy principle encapsulates 'bet-hedging' behaviour displayed by organisms dealing with future uncertainty in a fluctuating environment, its cooperative extension describes how individuals adapt their metabolic resource allocation strategy to further accommodate limited knowledge about the welfare of others within a community. The resulting theory explains why local regulation of metabolic cross-feeding can fulfil a community-wide metabolic objective if individuals take into consideration an ensemble measure of total population performance as the only form of global information. The latter is likely supplied by quorum sensing in microbial systems or signalling molecules such as hormones in multi-cellular eukaryotic organisms.

Understanding the host-microbe interactions using metabolic modeling

The human gut harbors an enormous number of symbiotic microbes, which is vital for human health. However, interactions within the complex microbiota community and between the microbiota and its host are challenging to elucidate, limiting development in the treatment for a variety of diseases associated with microbiota dysbiosis. Using in silico simulation methods based on flux balance analysis, those interactions can be better investigated. Flux balance analysis uses an annotated genome-scale reconstruction of a metabolic network to determine the distribution of metabolic fluxes that represent the complete metabolism of a bacterium in a certain metabolic environment such as the gut. Simulation of a set of bacterial species in a shared metabolic environment can enable the study of the effect of numerous perturbations, such as dietary changes or addition of a probiotic species in a personalized manner. This review aims to introduce to experimental biologists the possible applications of flux balance analysis in the host-microbiota interaction field and discusses its potential use to improve human health. Video abstract.

Fine-tuning mitochondrial activity in Yarrowia lipolytica for citrate overproduction

Yarrowia lipolytica is a non-conventional yeast with promising industrial potentials for lipids and citrate production. It is also widely used for studying mitochondrial respiration due to a respiratory chain like those of mammalian cells. In this study we used a genome-scale model (GEM) of Y. lipolytica metabolism and performed a dynamic Flux Balance Analysis (dFBA) algorithm to analyze and identify metabolic levers associated with citrate optimization. Analysis of fluxes at stationary growth phase showed that carbon flux derived from glucose is rewired to citric acid production and lipid accumulation, whereas the oxidative phosphorylation (OxPhos) shifted to the alternative respiration mode through alternative oxidase (AOX) protein. Simulations of optimized citrate secretion flux resulted in a pronounced lipid oxidation along with reactive oxygen species (ROS) generation and AOX flux inhibition. Then, we experimentally challenged AOX inhibition by adding n-Propyl Gallate (nPG), a specific AOX inhibitor, on Y. lipolytica batch cultures at stationary phase. Our results showed a twofold overproduction of citrate (20.5 g/L) when nPG is added compared to 10.9 g/L under control condition (no nPG addition). These results suggest that ROS management, especially through AOX activity, has a pivotal role on citrate/lipid flux balance in Y. lipolytica. All taken together, we thus provide for the first time, a key for the understanding of a predominant metabolic mechanism favoring citrate overproduction in Y. lipolytica at the expense of lipids accumulation.

Metabolic modelling approaches for describing and engineering microbial communities

Microbes do not live in isolation but in microbial communities. The relevance of microbial communities is increasing due to growing awareness of their influence on a huge number of environmental, health and industrial processes. Hence, being able to control and engineer the output of both natural and synthetic communities would be of great interest. However, most of the available methods and biotechnological applications involving microorganisms, both in vivo and in silico, have been developed in the context of isolated microbes. In vivo microbial consortia development is extremely difficult and costly because it implies replicating suitable environments in the wet-lab. Computational approaches are thus a good, cost-effective alternative to study microbial communities, mainly via descriptive modelling, but also via engineering modelling. In this review we provide a detailed compilation of examples of engineered microbial communities and a comprehensive, historical revision of available computational metabolic modelling methods to better understand, and rationally engineer wild and synthetic microbial communities.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Insights into the role of energy source in hormesis through diauxic growth of bacteria in mixed cultivation systems

Hormesis, a biphasic dose-response relationship characterized by low-dose stimulation and high-dose inhibition, has been reported to be closely related to energy sources in cultivation systems. However, few studies have clarified how the energy source influences hormesis. In this study, based on the typical diauxic patterns of Escherichia coli (E. coli) growth in mixed cultivation media containing 1.0 g L^-1 glucose and Luria-Bertani broth, the hormetic response of sulfonamides (SAs) to E. coli growth was investigated under this diauxic growth condition to thoroughly explain the close relationship between hormesis and energy sources in cultivation systems. The results indicated that SAs trigger time-dependent hormetic effects on E. coli growth over the span of 24 h, in which the biphasic dose-response occurs only during the second lag and the earlier stage of the second log phase of diauxic growth. Mechanistic exploration reveals that SAs can bind with adenylate cyclase at a low dose and dihydropteroate synthase at a high dose, respectively, activating the stimulatory and inhibitory signaling pathway to influence carbon catabolite repression in diauxic growth, which can interfere with the metabolism of tryptone and yeast extract to ultimately trigger hormesis. Moreover, the stimulatory and inhibitory effects of SAs are changed by the variations in metabolic status at different growth phases, resulting in time-dependent hormesis. This study proposes an induced mechanistic explanation of hormesis in mixed cultivation media based on the energy source's metabolism, which may not only reflect the generalizability of hormesis but also further promote its application in production activities.

Inferring composition and function of the human gut microbiome in time and space: A review of genome-scale metabolic modelling tools

The human gut hosts a complex community of microorganisms that directly influences gastrointestinal physiology, playing a central role in human health. Because of its importance, the metabolic interplay between the gut microbiome and host metabolism has gained special interest. While there has been great progress in the field driven by metagenomics and experimental studies, the mechanisms underpinning microbial composition and interactions in the microbiome remain poorly understood. Genome-scale metabolic models are mathematical structures capable of describing the metabolic potential of microbial cells. They are thus suitable tools for probing the metabolic properties of microbial communities. In this review, we discuss the most recent and relevant genome-scale metabolic modelling tools for inferring the composition, interactions, and ultimately, biological function of the constituent species of a microbial community with special emphasis in the gut microbiota. Particular attention is given to constraint-based metabolic modelling methods as well as hybrid agent-based methods for capturing the interactions and behavior of the community in time and space. Finally, we discuss the challenges hindering comprehensive modelling of complex microbial communities and its application for the in-silico design of microbial consortia with therapeutic functions.

Reconstructing organisms in silico: genome-scale models and their emerging applications

Escherichia coli is considered to be the best-known microorganism given the large number of published studies detailing its genes, its genome and the biochemical functions of its molecular components. This vast literature has been systematically assembled into a reconstruction of the biochemical reaction networks that underlie E. coli's functions, a process which is now being applied to an increasing number of microorganisms. Genome-scale reconstructed networks are organized and systematized knowledge bases that have multiple uses, including conversion into computational models that interpret and predict phenotypic states and the consequences of environmental and genetic perturbations. These genome-scale models (GEMs) now enable us to develop pan-genome analyses that provide mechanistic insights, detail the selection pressures on proteome allocation and address stress phenotypes. In this Review, we first discuss the overall development of GEMs and their applications. Next, we review the evolution of the most complete GEM that has been developed to date: the E. coli GEM. Finally, we explore three emerging areas in genome-scale modelling of microbial phenotypes: collections of strain-specific models, metabolic and macromolecular expression models, and simulation of stress responses.

Effect of plasma-induced oxidative stress on the glycolysis pathway of Escherichia coli

Antibiotic resistance is one of the world's most urgent public health problems. Due to its antibacterial properties, cold atmospheric plasma (CAP) may serve as an alternative method to antibiotics. It is claimed that oxidative stress caused by CAP is the main reason of bacteria inactivation. In this work, we computationally investigated the effect of plasma-induced oxidation on various glycolysis metabolites, by monitoring the production of the biomass. We observed that in addition to the significant reduction in biomass production, the rate of some reactions has increased. These reactions produce anti-oxidant products, showing the bacterial defense mechanism to escape the oxidative damage. Nevertheless, the simulations show that the plasma-induced oxidation effect is much stronger than the defense mechanism, causing killing of the bacteria.

Genome-Scale Metabolic Modeling for Unraveling Molecular Mechanisms of High Threat Pathogens

Pathogens give rise to a wide range of diseases threatening global health and hence drawing public health agencies' attention to establish preventative and curative solutions. Genome-scale metabolic modeling is ever increasingly used tool for biomedical applications including the elucidation of antibiotic resistance, virulence, single pathogen mechanisms and pathogen-host interaction systems. With this approach, the sophisticated cellular system of metabolic reactions inside the pathogens as well as between pathogen and host cells are represented in conjunction with their corresponding genes and enzymes. Along with essential metabolic reactions, alternate pathways and fluxes are predicted by performing computational flux analyses for the growth of pathogens in a very short time. The genes or enzymes responsible for the essential metabolic reactions in pathogen growth are regarded as potential drug targets, as a priori guide to researchers in the pharmaceutical field. Pathogens alter the key metabolic processes in infected host, ultimately the objective of these integrative constraint-based context-specific metabolic models is to provide novel insights toward understanding the metabolic basis of the acute and chronic processes of infection, revealing cellular mechanisms of pathogenesis, identifying strain-specific biomarkers and developing new therapeutic approaches including the combination drugs. The reaction rates predicted during different time points of pathogen development enable us to predict active pathways and those that only occur during certain stages of infection, and thus point out the putative drug targets. Among others, fatty acid and lipid syntheses reactions are recent targets of new antimicrobial drugs. Genome-scale metabolic models provide an improved understanding of how intracellular pathogens utilize the existing microenvironment of the host. Here, we reviewed the current knowledge of genome-scale metabolic modeling in pathogen cells as well as pathogen host interaction systems and the promising applications in the extension of curative strategies against pathogens for global preventative healthcare.

From sequence to information

Today massive amounts of sequenced metagenomic and metatranscriptomic data from different ecological niches and environmental locations are available. Scientific progress depends critically on methods that allow extracting useful information from the various types of sequence data. Here, we will first discuss types of information contained in the various flavours of biological sequence data, and how this information can be interpreted to increase our scientific knowledge and understanding. We argue that a mechanistic understanding of biological systems analysed from different perspectives is required to consistently interpret experimental observations, and that this understanding is greatly facilitated by the generation and analysis of dynamic mathematical models. We conclude that, in order to construct mathematical models and to test mechanistic hypotheses, time-series data are of critical importance. We review diverse techniques to analyse time-series data and discuss various approaches by which time-series of biological sequence data have been successfully used to derive and test mechanistic hypotheses. Analysing the bottlenecks of current strategies in the extraction of knowledge and understanding from data, we conclude that combined experimental and theoretical efforts should be implemented as early as possible during the planning phase of individual experiments and scientific research projects.

This article is part of the theme issue ‘Integrative research perspectives on marine conservation’.

The era of big data: Genome-scale modelling meets machine learning

With omics data being generated at an unprecedented rate, genome-scale modelling has become pivotal in its organisation and analysis. However, machine learning methods have been gaining ground in cases where knowledge is insufficient to represent the mechanisms underlying such data or as a means for data curation prior to attempting mechanistic modelling. We discuss the latest advances in genome-scale modelling and the development of optimisation algorithms for network and error reduction, intracellular constraining and applications to strain design. We further review applications of supervised and unsupervised machine learning methods to omics datasets from microbial and mammalian cell systems and present efforts to harness the potential of both modelling approaches through hybrid modelling.

Modeling a co-culture of Clostridium autoethanogenum and Clostridium kluyveri to increase syngas conversion to medium-chain fatty-acids

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We model a co-culture of C. autoethanogenum and C. kluyveri for syngas fermentation.

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Biomass species ratio affects ethanol and acetate profiles in the co-culture.

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The model predicts that addition of succinate increases caproate production.

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Genetic interventions  in C. autoethanogenum could increase caproate production.

Microbial fermentation of synthesis gas (syngas) is becoming more attractive for sustainable production of commodity chemicals. To date, syngas fermentation focuses mainly on the use of Clostridium species for the production of small organic molecules such as ethanol and acetate. The co-cultivation of syngas-fermenting microorganisms with chain-elongating bacteria can expand the range of possible products, allowing, for instance, the production of medium-chain fatty acids (MCFA) and alcohols from syngas. To explore these possibilities, we report herein a genome-scale, constraint-based metabolic model to describe growth of a co-culture of Clostridium autoethanogenum and Clostridium kluyveri on syngas for the production of valuable compounds. Community flux balance analysis was used to gain insight into the metabolism of the two strains and their interactions, and to reveal potential strategies enabling production of butyrate and hexanoate.

The model suggests that one strategy to optimize the production of medium-chain fatty-acids from syngas would be the addition of succinate. According to the prediction, addition of succinate would increase the pool of crotonyl-CoA and the ethanol/acetate uptake ratio in C. kluyveri, resulting in a flux of up to 60% of electrons into hexanoate. Another potential way to further optimize butyrate and hexanoate production would be an increase of C. autoethanogenum ethanol production. Blocking either acetaldehyde dehydrogenase or formate dehydrogenase (ferredoxin) activity or formate transport, in the C. autoethanogenum metabolic model could potentially lead to an up to 150% increase in ethanol production.

Reconstruction and analysis of genome-scale metabolic model of weak Crabtree positive yeast Lachancea kluyveri

Lachancea kluyveri, a weak Crabtree positive yeast, has been extensively studied for its unique URC pyrimidine catabolism pathway. It produces more biomass than Saccharomyces cerevisiae due to the underlying weak Crabtree effect and resorts to fermentation only in oxygen limiting conditions that renders it as a suitable industrial host. The yeast also produces ethyl acetate as a major overflow metabolite in aerobic conditions. Here, we report the first genome-scale metabolic model, iPN730, of L. kluyveri comprising of 1235 reactions, 1179 metabolites, and 730 genes distributed in 8 compartments. The in silico viability in different media conditions and the growth characteristics in various carbon sources show good agreement with experimental data. Dynamic flux balance analysis describes the growth dynamics, substrate utilization and product formation kinetics in various oxygen-limited conditions. We have also demonstrated the effect of switching carbon sources on the production of ethyl acetate under varying oxygen uptake rates. A phenotypic phase plane analysis described the energetic cost penalty of ethyl acetate and ethanol production on the specific growth rate of L. kluyveri. We generated the context specific models of L. kluyveri growing on uracil or ammonium salts as the sole nitrogen source. Differential flux calculated using flux variability analysis helped us in highlighting pathways like purine, histidine, riboflavin and pyrimidine metabolism associated with uracil degradation. The genome-scale metabolic construction of L. kluyveri will provide a better understanding of metabolism behind ethyl acetate production as well as uracil catabolism (pyrimidine degradation) pathway. iPN730 is an addition to genome-scale metabolic models of non-conventional yeasts that will facilitate system-wide omics analysis to understand fungal metabolic diversity.

Modeling tissue-relevant Caenorhabditis elegans metabolism at network, pathway, reaction, and metabolite levels

Metabolism is a highly compartmentalized process that provides building blocks for biomass generation during development, homeostasis, and wound healing, and energy to support cellular and organismal processes. In metazoans, different cells and tissues specialize in different aspects of metabolism. However, studying the compartmentalization of metabolism in different cell types in a whole animal and for a particular stage of life is difficult. Here, we present MEtabolic models Reconciled with Gene Expression (MERGE), a computational pipeline that we used to predict tissue-relevant metabolic function at the network, pathway, reaction, and metabolite levels based on single-cell RNA-sequencing (scRNA-seq) data from the nematode Caenorhabditis elegans. Our analysis recapitulated known tissue functions in C. elegans, captured metabolic properties that are shared with similar tissues in human, and provided predictions for novel metabolic functions. MERGE is versatile and applicable to other systems. We envision this work as a starting point for the development of metabolic network models for individual cells as scRNA-seq continues to provide higher-resolution gene expression data.

Dynamic co-culture metabolic models reveal the fermentation dynamics, metabolic capacities and interplays of cheese starter cultures

In this study, we have investigated the cheese starter culture as a microbial community through a question: can the metabolic behaviour of a co-culture be explained by the characterized individual organism that constituted the co-culture? To address this question, the dairy-origin lactic acid bacteria Lactococcus lactis subsp. cremoris, Lactococcus lactis subsp. lactis, Streptococcus thermophilus and Leuconostoc mesenteroides, commonly used in cheese starter cultures, were grown in pure and four different co-cultures. We used a dynamic metabolic modelling approach based on the integration of the genome-scale metabolic networks of the involved organisms to simulate the co-cultures. The strain-specific kinetic parameters of dynamic models were estimated using the pure culture experiments and they were subsequently applied to co-culture models. Biomass, carbon source, lactic acid and most of the amino acid concentration profiles simulated by the co-culture models fit closely to the experimental results and the co-culture models explained the mechanisms behind the dynamic microbial abundance. We then applied the co-culture models to estimate further information on the co-cultures that could not be obtained by the experimental method used. This includes estimation of the profile of various metabolites in the co-culture medium such as flavour compounds produced and the individual organism level metabolic exchange flux profiles, which revealed the potential metabolic interactions between organisms in the co-cultures.

Regulatory dynamic enzyme-cost flux balance analysis: A unifying framework for constraint-based modeling

Integrated modeling of metabolism and gene regulation continues to be a major challenge in computational biology. While there exist approaches like regulatory flux balance analysis (rFBA), dynamic flux balance analysis (dFBA), resource balance analysis (RBA) or dynamic enzyme-cost flux balance analysis (deFBA) extending classical flux balance analysis (FBA) in various directions, there have been no constraint-based methods so far that allow predicting the dynamics of metabolism taking into account both macromolecule production costs and regulatory events. In this paper, we introduce a new constraint-based modeling framework named regulatory dynamic enzyme-cost flux balance analysis (r-deFBA), which unifies dynamic modeling of metabolism, cellular resource allocation and transcriptional regulation in a hybrid discrete-continuous setting. With r-deFBA, we can predict discrete regulatory states together with the continuous dynamics of reaction fluxes, external substrates, enzymes, and regulatory proteins needed to achieve a cellular objective such as maximizing biomass over a time interval. The dynamic optimization problem underlying r-deFBA can be reformulated as a mixed-integer linear optimization problem, for which there exist efficient solvers.

A review of methods for the reconstruction and analysis of integrated genome-scale models of metabolism and regulation

The current survey aims to describe the main methodologies for extending the reconstruction and analysis of genome-scale metabolic models and phenotype simulation with Flux Balance Analysis mathematical frameworks, via the integration of Transcriptional Regulatory Networks and/or gene expression data. Although the surveyed methods are aimed at improving phenotype simulations obtained from these models, the perspective of reconstructing integrated genome-scale models of metabolism and gene expression for diverse prokaryotes is still an open challenge.

Minimizing the number of optimizations for efficient community dynamic flux balance analysis

Dynamic flux balance analysis uses a quasi-steady state assumption to calculate an organism's metabolic activity at each time-step of a dynamic simulation, using the well-known technique of flux balance analysis. For microbial communities, this calculation is especially costly and involves solving a linear constrained optimization problem for each member of the community at each time step. However, this is unnecessary and inefficient, as prior solutions can be used to inform future time steps. Here, we show that a basis for the space of internal fluxes can be chosen for each microbe in a community and this basis can be used to simulate forward by solving a relatively inexpensive system of linear equations at most time steps. We can use this solution as long as the resulting metabolic activity remains within the optimization problem's constraints (i.e. the solution to the linear system of equations remains a feasible to the linear program). As the solution becomes infeasible, it first becomes a feasible but degenerate solution to the optimization problem, and we can solve a different but related optimization problem to choose an appropriate basis to continue forward simulation. We demonstrate the efficiency and robustness of our method by comparing with currently used methods on a four species community, and show that our method requires at least 91% fewer optimizations to be solved. For reproducibility, we prototyped the method using Python. Source code is available at https://github.com/jdbrunner/surfin_fba.

Modeling microbial cross-feeding at intermediate scale portrays community dynamics and species coexistence

Social interaction between microbes can be described at many levels of details: from the biochemistry of cell-cell interactions to the ecological dynamics of populations. Choosing an appropriate level to model microbial communities without losing generality remains a challenge. Here we show that modeling cross-feeding interactions at an intermediate level between genome-scale metabolic models of individual species and consumer-resource models of ecosystems is suitable to experimental data. We applied our modeling framework to three published examples of multi-strain Escherichia coli communities with increasing complexity: uni-, bi-, and multi-directional cross-feeding of either substitutable metabolic byproducts or essential nutrients. The intermediate-scale model accurately fit empirical data and quantified metabolic exchange rates that are hard to measure experimentally, even for a complex community of 14 amino acid auxotrophies. By studying the conditions of species coexistence, the ecological outcomes of cross-feeding interactions, and each community’s robustness to perturbations, we extracted new quantitative insights from these three published experimental datasets. Our analysis provides a foundation to quantify cross-feeding interactions from experimental data, and highlights the importance of metabolic exchanges in the dynamics and stability of microbial communities.

The behavior of microbial communities such as the human microbiome is hard to predict by its species composition alone. Our efforts to engineer microbiomes—for example to improve human health—would benefit from mathematical models that accurately describe how microbes exchange metabolites with each other and how their environment shapes these exchanges. But what is an appropriate level of details for those models? We propose an intermediate level to model metabolic exchanges between microbes. We show that these models can accurately describe population dynamics in three laboratory communities and predicts their stability in response to perturbations such as changes in the nutrients available in the medium that they grow on. Our work suggests that a highly detailed metabolic network model is unnecessary for extracting ecological insights from experimental data and improves mathematical models so that one day we may be able to predict the behavior of real-world communities such as the human microbiome.

Application of Systems Engineering Principles and Techniques in Biological Big Data Analytics: A Review

In the past few decades, we have witnessed tremendous advancements in biology, life sciences and healthcare. These advancements are due in no small part to the big data made available by various high-throughput technologies, the ever-advancing computing power, and the algorithmic advancements in machine learning. Specifically, big data analytics such as statistical and machine learning has become an essential tool in these rapidly developing fields. As a result, the subject has drawn increased attention and many review papers have been published in just the past few years on the subject. Different from all existing reviews, this work focuses on the application of systems, engineering principles and techniques in addressing some of the common challenges in big data analytics for biological, biomedical and healthcare applications. Specifically, this review focuses on the following three key areas in biological big data analytics where systems engineering principles and techniques have been playing important roles: the principle of parsimony in addressing overfitting, the dynamic analysis of biological data, and the role of domain knowledge in biological data analytics.

A unifying modelling formalism for the integration of stoichiometric and kinetic models

Current research on systems and synthetic biology relies heavily on mathematical models of the systems under study. The usefulness of such models depends on the quantity and quality of biological data, and on the availability of appropriate modelling formalisms that can gather and accommodate such data so that they can be exploited properly. Given our incomplete knowledge of biological systems and the fact that they consist of many subsystems, biological data are usually uncertain and heterogeneous. These facts hinder the use of mathematical models and computational methods. In the scope of dynamic biological systems, e.g. metabolic networks, this difficulty can be overcome by the novel modelling formalism of flexible nets (FNs). We show that an FN can combine, in a natural way, a stoichiometric model and a kinetic model. Moreover, the resulting net admits nonlinear dynamics and can be analysed in both transient and steady states.

Metabolic multistability and hysteresis in a model aerobe-anaerobe microbiome community

Major changes in the microbiome are associated with health and disease. Some microbiome states persist despite seemingly unfavorable conditions, such as the proliferation of aerobe-anaerobe communities in oxygen-exposed environments in wound infections or small intestinal bacterial overgrowth. Mechanisms underlying transitions into and persistence of these states remain unclear. Using two microbial taxa relevant to the human microbiome, we combine genome-scale mathematical modeling, bioreactor experiments, transcriptomics, and dynamical systems theory to show that multistability and hysteresis (MSH) is a mechanism describing the shift from an aerobe-dominated state to a resilient, paradoxically persistent aerobe-anaerobe state. We examine the impact of changing oxygen and nutrient regimes and identify changes in metabolism and gene expression that lead to MSH and associated multi-stable states. In such systems, conceptual causation-correlation connections break and MSH must be used for analysis. Using MSH to analyze microbiome dynamics will improve our conceptual understanding of stability of microbiome states and transitions between states.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

Towards model-driven characterization and manipulation of plant lipid metabolism

Plant lipids have versatile applications and provide essential fatty acids in human diet. Therefore, there has been a growing interest to better characterize the genetic basis, regulatory networks, and metabolic pathways that shape lipid quantity and composition. Addressing these issues is challenging due to context-specificity of lipid metabolism integrating environmental, developmental, and tissue-specific cues. Here we systematically review the known metabolic pathways and regulatory interactions that modulate the levels of storage lipids in oilseeds. We argue that the current understanding of lipid metabolism provides the basis for its study in the context of genome-wide plant metabolic networks with the help of approaches from constraint-based modeling and metabolic flux analysis. The focus is on providing a comprehensive summary of the state-of-the-art of modeling plant lipid metabolic pathways, which we then contrast with the existing modeling efforts in yeast and microalgae. We then point out the gaps in knowledge of lipid metabolism, and enumerate the recent advances of using genome-wide association and quantitative trait loci mapping studies to unravel the genetic regulations of lipid metabolism. Finally, we offer a perspective on how advances in the constraint-based modeling framework can propel further characterization of plant lipid metabolism and its rational manipulation.

Simulating the evolutionary trajectories of metabolic pathways for insect symbionts in the genus Sodalis

Insect-bacterial symbioses are ubiquitous, but there is still much to uncover about how these relationships establish, persist and evolve. The tsetse endosymbiont Sodalis glossinidius displays intriguing metabolic adaptations to its microenvironment, but the process by which this relationship evolved remains to be elucidated. The recent chance discovery of the free-living species of the genus Sodalis, Sodalis praecaptivus, provides a serendipitous starting point from which to investigate the evolution of this symbiosis. Here, we present a flux balance model for S. praecaptivus and empirically verify its predictions. Metabolic modelling is used in combination with a multi-objective evolutionary algorithm to explore the trajectories that S. glossinidius may have undertaken from this starting point after becoming internalized. The order in which key genes are lost is shown to influence the evolved populations, providing possible targets for future in vitro genetic manipulation. This method provides a detailed perspective on possible evolutionary trajectories for S. glossinidius in this fundamental process of evolutionary and ecological change.

Using automated reasoning to explore the metabolism of unconventional organisms: a first step to explore host-microbial interactions

Systems modelled in the context of molecular and cellular biology are difficult to represent with a single calibrated numerical model. Flux optimisation hypotheses have shown tremendous promise to accurately predict bacterial metabolism but they require a precise understanding of metabolic reactions occurring in the considered species. Unfortunately, this information may not be available for more complex organisms or non-cultured microorganisms such as those evidenced in microbiomes with metagenomic techniques. In both cases, flux optimisation techniques may not be applicable to elucidate systems functioning. In this context, we describe how automatic reasoning allows relevant features of an unconventional biological system to be identified despite a lack of data. A particular focus is put on the use of Answer Set Programming, a logic programming paradigm with combinatorial optimisation functionalities. We describe its usage to over-approximate metabolic responses of biological systems and solve gap-filling problems. In this review, we compare steady-states and Boolean abstractions of metabolic models and illustrate their complementarity via applications to the metabolic analysis of macro-algae. Ongoing applications of this formalism explore the emerging field of systems ecology, notably elucidating interactions between a consortium of microbes and a host organism. As the first step in this field, we will illustrate how the reduction in microbiotas according to expected metabolic phenotypes can be addressed with gap-filling problems.

μBialSim: Constraint-Based Dynamic Simulation of Complex Microbiomes

Microbial communities are pervasive in the natural environment, associated with many hosts, and of increasing importance in biotechnological applications. The complexity of these microbial systems makes the underlying mechanisms driving their dynamics difficult to identify. While experimental meta-OMICS techniques are routinely applied to record the inventory and activity of microbiomes over time, it remains difficult to obtain quantitative predictions based on such data. Mechanistic, quantitative mathematical modeling approaches hold the promise to both provide predictive power and shed light on cause-effect relationships driving these dynamic systems. We introduce μbialSim (pronounced "microbial sim"), a dynamic Flux-Balance-Analysis-based (dFBA) numerical simulator which is able to predict the time course in terms of composition and activity of microbiomes containing 100s of species in batch or chemostat mode. Activity of individual species is simulated by using separate FBA models which have access to a common pool of compounds, allowing for metabolite exchange. A novel augmented forward Euler method ensures numerical accuracy by temporarily reducing the time step size when compound concentrations decrease rapidly due to high compound affinities and/or the presence of many consuming species. We present three exemplary applications of μbialSim: a batch culture of a hydrogenotrophic archaeon, a syntrophic methanogenic biculture, and a 773-species human gut microbiome which exhibits a complex and dynamic pattern of metabolite exchange. Focusing on metabolite exchange as the main interaction type, μbialSim allows for the mechanistic simulation of microbiomes at their natural complexity. Simulated trajectories can be used to contextualize experimental meta-OMICS data and to derive hypotheses on cause-effect relationships driving community dynamics based on scenario simulations. μbialSim is implemented in Matlab and relies on the COBRA Toolbox or CellNetAnalyzer for FBA calculations. The source code is available under the GNU General Public License v3.0 at https://git.ufz.de/UMBSysBio/microbialsim.

Introducing an Optimization- and explicit Runge-Kutta- based Approach to Perform Dynamic Flux Balance Analysis

In this work we introduce the generalized Optimization- and explicit Runge-Kutta-based Approach (ORKA) to perform dynamic Flux Balance Analysis (dFBA), which is numerically more accurate and computationally tractable than existing approaches. ORKA is applied to a four-tissue (leaf, root, seed, and stem) model of Arabidopsis thaliana, p-ath773, uniquely capturing the core-metabolism of several stages of growth from seedling to senescence at hourly intervals. Model p-ath773 has been designed to show broad agreement with published plant-scale properties such as mass, maintenance, and senescence, yet leaving reaction-level behavior unconstrainted. Hence, it serves as a framework to study the reaction-level behavior necessary for observed plant-scale behavior. Two such case studies of reaction-level behavior include the lifecycle progression of sulfur metabolism and the diurnal flow of water throughout the plant. Specifically, p-ath773 shows how transpiration drives water flow through the plant and how water produced by leaf tissue metabolism may contribute significantly to transpired water. Investigation of sulfur metabolism elucidates frequent cross-compartment exchange of a standing pool of amino acids which is used to regulate the proton flow. Overall, p-ath773 and ORKA serve as scaffolds for dFBA-based lifecycle modeling of plants and other systems to further broaden the scope of in silico metabolic investigation.

Dynamic Metabolic Analysis of Cupriavidus necator DSM545 Producing Poly(3-hydroxybutyric acid) from Glycerol

Cupriavidus necator DSM 545 can utilise glycerol to synthesise poly(3-hydroxybutyric acid) under unbalanced growth conditions, i.e., nitrogen limitation. To improve poly(3-hydroxybutyric acid) (PHB) batch production by C. necator through model-guided bioprocessing or genetic engineering, insights into the dynamic effect of the fermentation conditions on cell metabolism are crucial. In this work, we have used dynamic flux balance analysis (DFBA), a constrained-based stoichiometric modelling approach, to study the metabolic change associated with PHB synthesis during batch cultivation. The model employs the ‘minimisation of all fluxes’ as cellular objectives and measured extracellular fluxes as additional constraints. The mass balance constraints are further adjusted based on thermodynamic considerations. The resultant flux distribution profiles characterise the evolution of metabolic states due to adaptation to dynamic extracellular conditions and provide further insights towards improvements that can be implemented to enhance PHB productivity.

Dynamic metabolic resource allocation based on the maximum entropy principle

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

Dynamic Flux Balance Analysis to Evaluate the Strain Production Performance on Shikimic Acid Production in Escherichia coli

Flux balance analysis (FBA) is used to improve the microbial production of useful compounds. However, a large gap often exists between the FBA solution and the experimental yield, because of growth and byproducts. FBA has been extended to dynamic FBA (dFBA), which is applicable to time-varying processes, such as batch or fed-batch cultures, and has significantly contributed to metabolic and cultural engineering applications. On the other hand, the performance of the experimental strains has not been fully evaluated. In this study, we applied dFBA to the production of shikimic acid from glucose in Escherichia coli, to evaluate the production performance of the strain as a case study. The experimental data of glucose consumption and cell growth were used as FBA constraints. Bi-level FBA optimization with maximized growth and shikimic acid production were the objective functions. Results suggest that the shikimic acid concentration in the high-shikimic-acid-producing strain constructed in the experiment reached up to 84% of the maximum value by simulation. Thus, this method can be used to evaluate the performance of strains and estimate the milestones of strain improvement.

Modeling Plant Metabolism: From Network Reconstruction to Mechanistic Models

Mathematical modeling of plant metabolism enables the plant science community to understand the organization of plant metabolism, obtain quantitative insights into metabolic functions, and derive engineering strategies for manipulation of metabolism. Among the various modeling approaches, metabolic pathway analysis can dissect the basic functional modes of subsections of core metabolism, such as photorespiration, and reveal how classical definitions of metabolic pathways have overlapping functionality. In the many studies using constraint-based modeling in plants, numerous computational tools are currently available to analyze large-scale and genome-scale metabolic networks. For ¹³C-metabolic flux analysis, principles of isotopic steady state have been used to study heterotrophic plant tissues, while nonstationary isotope labeling approaches are amenable to the study of photoautotrophic and secondary metabolism. Enzyme kinetic models explore pathways in mechanistic detail, and we discuss different approaches to determine or estimate kinetic parameters. In this review, we describe recent advances and challenges in modeling plant metabolism.

Biochemical Characteristics and a Genome-Scale Metabolic Model of an Indian Euryhaline Cyanobacterium with High Polyglucan Content

Marine cyanobacteria are promising microbes to capture and convert atmospheric CO₂ and light into biomass and valuable industrial bio-products. Yet, reports on metabolic characteristics of non-model cyanobacteria are scarce. In this report, we show that an Indian euryhaline Synechococcus sp. BDU 130192 has biomass accumulation comparable to a model marine cyanobacterium and contains approximately double the amount of total carbohydrates, but significantly lower protein levels compared to Synechococcus sp. PCC 7002 cells. Based on its annotated chromosomal genome sequence, we present a genome scale metabolic model (GSMM) of this cyanobacterium, which we have named as iSyn706. The model includes 706 genes, 908 reactions, and 900 metabolites. The difference in the flux balance analysis (FBA) predicted flux distributions between Synechococcus sp. PCC 7002 and Synechococcus sp. BDU130192 strains mimicked the differences in their biomass compositions. Model-predicted oxygen evolution rate for Synechococcus sp. BDU130192 was found to be close to the experimentally-measured value. The model was analyzed to determine the potential of the strain for the production of various industrially-useful products without affecting growth significantly. This model will be helpful to researchers interested in understanding the metabolism as well as to design metabolic engineering strategies for the production of industrially-relevant compounds.

Quantitative analysis of amino acid metabolism in liver cancer links glutamate excretion to nucleotide synthesis

We used a combination of experimental measurements and computer simulations to understand how liver cancer cells rewire their metabolism to grow faster. We observed that glutamate is excreted by the cells, and our simulations suggest that this occurs because glutamate is formed in excess in the cytoplasm, when cells rapidly synthesize nucleotides, which are required for growth. Meanwhile, glutamate that is formed in the mitochondria is, on the other hand, not excreted. Treating glutamate as two distinct pools, a cytosolic and a mitochondrial, is useful to better understand why many cancer cells rapidly consume glutamine, the precursor of glutamate. The results point toward potential drug targets that could be used to reduce growth of liver cancer cells.

Many cancer cells consume glutamine at high rates; counterintuitively, they simultaneously excrete glutamate, the first intermediate in glutamine metabolism. Glutamine consumption has been linked to replenishment of tricarboxylic acid cycle (TCA) intermediates and synthesis of adenosine triphosphate (ATP), but the reason for glutamate excretion is unclear. Here, we dynamically profile the uptake and excretion fluxes of a liver cancer cell line (HepG2) and use genome-scale metabolic modeling for in-depth analysis. We find that up to 30% of the glutamine is metabolized in the cytosol, primarily for nucleotide synthesis, producing cytosolic glutamate. We hypothesize that excreting glutamate helps the cell to increase the nucleotide synthesis rate to sustain growth. Indeed, we show experimentally that partial inhibition of glutamate excretion reduces cell growth. Our integrative approach thus links glutamine addiction to glutamate excretion in cancer and points toward potential drug targets.

Metabolic Efficiency of Sugar Co-Metabolism and Phenol Degradation in Alicyclobacillus acidocaldarius for Improved Lignocellulose Processing

Substrate availability plays a key role in dictating metabolic strategies. Most microorganisms consume carbon/energy sources in a sequential, preferential order. The presented study investigates metabolic strategies of Alicyclobacillus acidocaldarius, a thermoacidophilic bacterium that has been shown to co-utilize glucose and xylose, as well as degrade phenolic compounds. An existing metabolic model was expanded to include phenol degradation and was analyzed with both metabolic pathway and constraint-based analysis methods. Elementary flux mode analysis was used in conjunction with resource allocation theory to investigate ecologically optimal metabolic pathways for different carbon substrate combinations. Additionally, a dynamic version of flux balance analysis was used to generate time-resolved simulations of growth on phenol and xylose. Results showed that availability of xylose along with glucose did not predict enhanced growth efficiency beyond that of glucose alone, but did predict some differences in pathway utilization and byproduct profiles. In contrast, addition of phenol as a co-substrate with xylose predicted lower growth efficiency. Dynamic simulations predicted co-consumption of xylose and phenol in a similar pattern as previously reported experiments. Altogether, this work serves as a case study for combining both elementary flux mode and flux balance analyses to probe unique metabolic features, and also demonstrates the versatility of A. acidocaldarius for lignocellulosic biomass processing applications.

LK-DFBA: a linear programming-based modeling strategy for capturing dynamics and metabolite-dependent regulation in metabolism

BACKGROUND

The systems-scale analysis of cellular metabolites, "metabolomics," provides data ideal for applications in metabolic engineering. However, many of the computational tools for strain design are built around Flux Balance Analysis (FBA), which makes assumptions that preclude direct integration of metabolomics data into the underlying models. Finding a way to retain the advantages of FBA's linear structure while relaxing some of its assumptions could allow us to account for metabolite levels and metabolite-dependent regulation in strain design tools built from FBA, improving the accuracy of predictions made by these tools. We designed, implemented, and characterized a modeling strategy based on Dynamic FBA (DFBA), called Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), to satisfy these specifications. Our strategy adds constraints describing the dynamics and regulation of metabolism that are strictly linear. We evaluated LK-DFBA against alternative modeling frameworks using simulated noisy data from a small in silico model and a larger model of central carbon metabolism in E. coli, and compared each framework's ability to recapitulate the original system.

RESULTS

In the smaller model, we found that we could use regression from a dynamic flux estimation (DFE) with an optional non-linear parameter optimization to reproduce metabolite concentration dynamic trends more effectively than an ordinary differential equation model with generalized mass action rate laws when tested under realistic data sampling frequency and noise levels. We observed detrimental effects across all tested modeling approaches when metabolite time course data were missing, but found these effects to be smaller for LK-DFBA in most cases. With the E. coli model, we produced qualitatively reasonable results with similar properties to the smaller model and explored two different parameterization structures that yield trade-offs in computation time and accuracy.

CONCLUSIONS

LK-DFBA allows for calculation of metabolite concentrations and considers metabolite-dependent regulation while still retaining many computational advantages of FBA. This provides the proof-of-principle for a new metabolic modeling framework with the potential to create genome-scale dynamic models and the potential to be applied in strain engineering tools that currently use FBA.