DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis

Coupling flux balance analysis with reactive transport modeling through machine learning for rapid and stable simulation of microbial metabolic switching

Integrating genome-scale metabolic networks with reactive transport models (RTMs) provides a detailed description of the dynamic changes in microbial growth and metabolism. Despite promising demonstrations in the past, computational inefficiency has been pointed out as a critical issue to overcome because it requires repeated application of linear programming (LP) to obtain flux balance analysis (FBA) solutions in every time step and spatial grid. To address this challenge, we propose a new simulation method where we train and validate artificial neural networks (ANNs) using randomly sampled FBA solutions and incorporate the resulting surrogate FBA model (represented as algebraic equations) into RTMs as source/sink terms. We demonstrate the efficiency of our method via a case study of Shewanella oneidensis MR-1. During aerobic growth on lactate, S. oneidensis produces metabolic byproducts (such as pyruvate and acetate), which are subsequently consumed as alternative carbon sources when the preferred nutrients are depleted. To effectively simulate these complex dynamics, we used a cybernetic approach that models metabolic switches as the outcome of dynamic competition among multiple growth options. In both zero-dimensional batch and one-dimensional column configurations, the ANN-based surrogate models achieved substantial reduction of computational time by several orders of magnitude compared to the original LP-based FBA models. Moreover, the ANN models produced robust solutions without any special measures to prevent numerical instability. These developments significantly promote our ability to utilize genome-scale networks in complex, multi-physics, and multi-dimensional ecosystem modeling.

An integrated multiphase dynamic genome-scale model explains batch fermentations led by species of the Saccharomyces genus

During batch fermentation, a variety of compounds are synthesized, as microorganisms undergo distinct growth phases: lag, exponential, growth-no-growth transition, stationary, and decay. A detailed understanding of the metabolic pathways involved in these phases is crucial for optimizing the production of target compounds. Dynamic flux balance analysis (dFBA) offers insight into the dynamics of metabolic pathways. However, explaining secondary metabolism remains a challenge. A multiphase and multi-objective dFBA scheme (MPMO model) has been proposed for this purpose. However, its formulation is discontinuous, changing from phase to phase; its accuracy in predicting intracellular fluxes is hampered by the lack of a mechanistic link between phases; and its simulation requires considerable computational effort. To address these limitations, we combine a novel model with a genome-scale model to predict the distribution of intracellular fluxes throughout batch fermentation. This integrated multiphase continuous model (IMC) has a unique formulation over time, and it incorporates empirical regulatory descriptions to automatically identify phase transitions and incorporates the hypotheses that yeasts might vary their cellular objective over time to adapt to the changing environment. We validated the predictive capacity of the IMC model by comparing its predictions with intracellular metabolomics data for Saccharomyces uvarum during batch fermentation. The model aligns well with the data, confirming its predictive capabilities. Notably, the IMC model accurately predicts trehalose accumulation, which was enforced in the MPMO model. We further demonstrate the generalizability of the IMC model, explaining the dynamics of primary and secondary metabolism of three Saccharomyces species. The model provides biological insights consistent with the literature and metabolomics data, establishing it as a valuable tool for exploring the dynamics of novel fermentation processes.IMPORTANCEThis work presents an integrated multiphase continuous dynamic genome-scale model (IMC model) for batch fermentation, a crucial process widely used in industry to produce biofuels, enzymes, pharmaceuticals, and food products or ingredients. The IMC model integrates a continuous kinetic model with a genome-scale model to address the critical limitations of existing dynamic flux balance analysis schemes, such as the difficulty of explaining secondary metabolism, the lack of mechanistic links between growth phases, or the high computational demands. The model also introduces the hypothesis that cells adapt the FBA objective over time. The IMC improves the accuracy of intracellular flux predictions and simplifies the implementation process with a unique dFBA formulation over time. Its ability to predict both primary and secondary metabolism dynamics in different Saccharomyces species underscores its versatility and robustness. Furthermore, its alignment with empirical metabolomics data validates its predictive power, offering valuable insights into metabolic processes during batch fermentation. These advances pave the way for optimizing fermentation processes, potentially leading to more efficient production of target compounds and novel biotechnological applications.

Revealing novel protein interaction partners of glyphosate in Escherichia coli

Despite all debates about its safe use, glyphosate remains the most widely applied active ingredient in herbicide products, with renewed approval in the European Union until 2033. Non-target organisms are commonly exposed to glyphosate as a matter of its mode of application, with its broader environmental and biological impacts remaining under investigation. Glyphosate displays structural similarity to phosphoenolpyruvate (PEP), thereby competitively inhibiting the 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS), crucial for the synthesis of aromatic amino acids in plants, fungi, bacteria, and archaea. Most microbes, including the gut bacterium Escherichia coli (E. coli), possess a glyphosate-sensitive class I EPSPS, making them vulnerable to glyphosate's effects. Yet, little is known about glyphosate's interactions with other bacterial proteins or its broader modes of action at the proteome level. Here, we employed a quantitative proteomics and thermal proteome profiling (TPP) approach to identify novel protein binding partners of glyphosate in the E. coli proteome. Glyphosate exposure significantly altered amino acid synthesizing pathways. The abundance of shikimate pathway proteins was increased, suggesting a compensatory mechanism. Extracellular riboflavin concentrations were elevated upon glyphosate exposure, while intracellular levels remained stable. Beyond the target enzyme EPSPS, thermal proteome profiling indicated an effect of glyphosate on the thermal stability of certain proteins, including AroH and ProA, indicating interactions. Similar to the competitive binding between PEP and glyphosate at EPSPS, one reason for the interaction of AroH and ProA with the herbicide could be a high structural similarity between their substrates and glyphosate. Overall, glyphosate induced metabolic disturbances in E. coli, extending beyond its primary target, thereby providing new insights into glyphosate's broader impact on microbial systems.

Flux balance analysis of metabolic networks for efficient engineering of microbial cell factories

Metabolic engineering principles have long been applied to explore the metabolic networks of complex microbial cell factories under a variety of environmental constraints for effective deployment of the microorganisms in the optimal production of biochemicals like biofuels, polymers, amino acids, recombinant proteins. One of the methodologies used for analyzing microbial metabolic networks is the Flux Balance Analysis (FBA), which employs applications of optimization techniques for forecasting biomass growth and metabolic flux distribution of industrially important products under specified environmental conditions. The in silico flux simulations are instrumental for designing the production-specific microbial cell factories. However, FBA has some inherent limitations. The present review emphasizes how the incorporation of additional kinetic, thermodynamic, expression and regulatory constraints and integration of omics data into the classical FBA platform improve the prediction accuracy of FBA. A programmed comparison of the simulated data with the experimental observations is presented for supporting the claim. The review further accounts for the successful implementation of classical FBA in biotechnological applications and identifies areas in which classical FBA fails to make correct predictions. The analysis of the predictive capabilities of the different FBA strategies presented here is expected to help researchers in finding new avenues in engineering highly efficient microbial metabolic pathways and identify the key metabolic bottlenecks during the process. Based on the appropriate metabolic network design, fermentation engineers will be able to effectively design the bioreactors and optimize large-scale biochemical production through suitable pathway modifications.

Review on computer-assisted biosynthetic capacities elucidation to assess metabolic interactions and communication within microbial communities

Microbial communities thrive through interactions and communication, which are challenging to study as most microorganisms are not cultivable. To address this challenge, researchers focus on the extracellular space where communication events occur. Exometabolomics and interactome analysis provide insights into the molecules involved in communication and the dynamics of their interactions. Advances in sequencing technologies and computational methods enable the reconstruction of taxonomic and functional profiles of microbial communities using high-throughput multi-omics data. Network-based approaches, including community flux balance analysis, aim to model molecular interactions within and between communities. Despite these advances, challenges remain in computer-assisted biosynthetic capacities elucidation, requiring continued innovation and collaboration among diverse scientists. This review provides insights into the current state and future directions of computer-assisted biosynthetic capacities elucidation in studying microbial communities.

Machine learning for the advancement of genome-scale metabolic modeling

Constraint-based modeling (CBM) has evolved as the core systems biology tool to map the interrelations between genotype, phenotype, and external environment. The recent advancement of high-throughput experimental approaches and multi-omics strategies has generated a plethora of new and precise information from wide-ranging biological domains. On the other hand, the continuously growing field of machine learning (ML) and its specialized branch of deep learning (DL) provide essential computational architectures for decoding complex and heterogeneous biological data. In recent years, both multi-omics and ML have assisted in the escalation of CBM. Condition-specific omics data, such as transcriptomics and proteomics, helped contextualize the model prediction while analyzing a particular phenotypic signature. At the same time, the advanced ML tools have eased the model reconstruction and analysis to increase the accuracy and prediction power. However, the development of these multi-disciplinary methodological frameworks mainly occurs independently, which limits the concatenation of biological knowledge from different domains. Hence, we have reviewed the potential of integrating multi-disciplinary tools and strategies from various fields, such as synthetic biology, CBM, omics, and ML, to explore the biochemical phenomenon beyond the conventional biological dogma. How the integrative knowledge of these intersected domains has improved bioengineering and biomedical applications has also been highlighted. We categorically explained the conventional genome-scale metabolic model (GEM) reconstruction tools and their improvement strategies through ML paradigms. Further, the crucial role of ML and DL in omics data restructuring for GEM development has also been briefly discussed. Finally, the case-study-based assessment of the state-of-the-art method for improving biomedical and metabolic engineering strategies has been elaborated. Therefore, this review demonstrates how integrating experimental and in silico strategies can help map the ever-expanding knowledge of biological systems driven by condition-specific cellular information. This multiview approach will elevate the application of ML-based CBM in the biomedical and bioengineering fields for the betterment of society and the environment.

Modeling Microbial Communities: Perspective and Challenges

Microbial communities are immensely important due to their widespread presence and profound impact on various facets of life. Understanding these complex systems necessitates mathematical modeling, a powerful tool for simulating and predicting microbial community behavior. This review offers a critical analysis of metabolic modeling and highlights key areas that would greatly benefit from broader discussion and collaboration. Moreover, we explore the challenges and opportunities linked to the intricate nature of these communities, spanning data generation, modeling, and validation. We are confident that ongoing advancements in modeling techniques, such as machine learning, coupled with interdisciplinary collaborations, will unlock the full potential of microbial communities across diverse applications.

Revealing the dynamics and mechanisms of bacterial interactions in cheese production with metabolic modelling

Cheese taste and flavour properties result from complex metabolic processes occurring in microbial communities. A deeper understanding of such mechanisms makes it possible to improve both industrial production processes and end-product quality through the design of microbial consortia. In this work, we caracterise the metabolism of a three-species community consisting of Lactococcus lactis, Lactobacillus plantarum and Propionibacterium freudenreichii during a seven-week cheese production process. Using genome-scale metabolic models and omics data integration, we modeled and calibrated individual dynamics using monoculture experiments, and coupled these models to capture the metabolism of the community. This model accurately predicts the dynamics of the community, enlightening the contribution of each microbial species to organoleptic compound production. Further metabolic exploration revealed additional possible interactions between the bacterial species. This work provides a methodological framework for the prediction of community-wide metabolism and highlights the added value of dynamic metabolic modeling for the comprehension of fermented food processes.

Convex Representation of Metabolic Networks with Michaelis-Menten Kinetics

Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis-Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.

A dynamic model of growth phase of bio-conversion of methane to polyhydroxybutyrate using dynamic flux balance analysis

Biological conversion of waste methane to biodegradable plastics is a way of reducing their production cost. This study addresses the computational modeling of the growth phase reactor of the process of polyhydroxybutyrate production. The model was used for investigating the effect of gas recycling and inlet gas retention time on the reactor performance. The model was run by the use of a genome-scale metabolic network of Methylocystis hirsuta in a dynamic flux balance analysis framework. The reactor has been modeled for two separate feeding scenarios: a pure methane feed and a biogas feed. The mass transfer coefficient parameter was predicted as a function of superficial gas velocities by the regression of data from published experiments. The results show an increase of removal efficiency by 38% and biomass concentration by 2.8 g/L with the increase of gas recycle ratio from 0 to 30 at the empty bed residence time of 60  min .

Microbial interactions from a new perspective: reinforcement learning reveals new insights into microbiome evolution

MOTIVATION

Microbes are essential part of all ecosystems, influencing material flow and shaping their surroundings. Metabolic modeling has been a useful tool and provided tremendous insights into microbial community metabolism. However, current methods based on flux balance analysis (FBA) usually fail to predict metabolic and regulatory strategies that lead to long-term survival and stability especially in heterogenous communities.

RESULTS

Here, we introduce a novel reinforcement learning algorithm, Self-Playing Microbes in Dynamic FBA, which treats microbial metabolism as a decision-making process, allowing individual microbial agents to evolve by learning and adapting metabolic strategies for enhanced long-term fitness. This algorithm predicts what microbial flux regulation policies will stabilize in the dynamic ecosystem of interest in the presence of other microbes with minimal reliance on predefined strategies. Throughout this article, we present several scenarios wherein our algorithm outperforms existing methods in reproducing outcomes, and we explore the biological significance of these predictions.

AVAILABILITY AND IMPLEMENTATION

The source code for this article is available at: https://github.com/chan-csu/SPAM-DFBA.

Computational assessment of lipid production in Rhodosporidium toruloides in two-stage and one-stage batch bioprocesses

Oleaginous yeasts are promising platforms for microbial lipids production as a renewable and sustainable alternative to vegetable oils in biodiesel production. In this paper, a thorough in silico assessment of lipid production in batch cultivation by Rhodosporidium toruloides was developed. By means of dynamic flux balance analysis, the traditional two-stage bioprocess (TSB) performed by the native strain was contrasted with one-stage bioprocess (OSB) using four designed strains obtained by gene knockout strategies. Lipid titer, yield, content, and productivity were analyzed at different initial C/N ratios as relevant performance indicators used in bioprocesses. By weighting these indicators, a global lipid efficiency metric (GLEM) was defined to consider different scenarios. Under simulated conditions, designed strains for lipid overproduction in OSB outperformed the TSB in terms of lipid title (up to threefold), lipid yield (up to 2.4-fold), lipid content (up to 2.8-fold, with a maximum of 76%), and productivity (up to 1.3-fold), depending on C/N ratios. Using these efficiency parameters and the proposed GLEM, the process of selecting the most suitable candidates for lipid production could be carried out before experimental assays. This methodology holds the potential to be extended to other oleaginous microorganisms and diverse strain design techniques.

Inferring microbial interactions with their environment from genomic and metagenomic data

Microbial communities assemble through a complex set of interactions between microbes and their environment, and the resulting metabolic impact on the host ecosystem can be profound. Microbial activity is known to impact human health, plant growth, water quality, and soil carbon storage which has lead to the development of many approaches and products meant to manipulate the microbiome. In order to understand, predict, and improve microbial community engineering, genome-scale modeling techniques have been developed to translate genomic data into inferred microbial dynamics. However, these techniques rely heavily on simulation to draw conclusions which may vary with unknown parameters or initial conditions, rather than more robust qualitative analysis. To better understand microbial community dynamics using genome-scale modeling, we provide a tool to investigate the network of interactions between microbes and environmental metabolites over time. Using our previously developed algorithm for simulating microbial communities from genome-scale metabolic models (GSMs), we infer the set of microbe-metabolite interactions within a microbial community in a particular environment. Because these interactions depend on the available environmental metabolites, we refer to the networks that we infer as metabolically contextualized, and so name our tool MetConSIN: Metabolically Contextualized Species Interaction Networks.

Microbiome distribution modeling using gradient descent strategies for mock, in vitro and clinical community distributions

The human gut is home to a complex array of microorganisms interacting with the host and each other, forming a community known as the microbiome. This community has been linked to human health and disease, but understanding the underlying interactions is still challenging for researchers. Standard studies typically use high-throughput sequencing to analyze microbiome distribution in patient samples. Recent advancements in meta-omic data analysis have enabled computational modeling strategies to integrate this information into an in silico model. However, there is a need for improved parameter fitting and data integration features in microbial community modeling. This study proposes a novel alternative strategy utilizing state-of-the-art dynamic flux balance analysis (dFBA) to provide a simple protocol enabling accurate replication of abundance data composition through dynamic parameter estimation and integration of metagenomic data. We used a recurrent optimization algorithm to replicate community distributions from three different sources: mock, in vitro, and clinical microbiome. Our results show an accuracy of 98% and 96% when using in vitro and clinical bacterial abundance distributions, respectively. The proposed modeling scheme allowed us to observe the evolution of metabolites. It could provide a deeper understanding of metabolic interactions while taking advantage of the high contextualization features of GEM schemes to fit the study case. The proposed modeling scheme could improve the approach in cases where external factors determine specific bacterial distributions, such as drug intake.

From Spatial-Temporal Multiscale Modeling to Application: Bridging the Valley of Death in Industrial Biotechnology

The Valley of Death confronts industrial biotechnology with a significant challenge to the commercialization of products. Fortunately, with the integration of computation, automation and artificial intelligence (AI) technology, the industrial biotechnology accelerates to cross the Valley of Death. The Fourth Industrial Revolution (Industry 4.0) has spurred advanced development of intelligent biomanufacturing, which has evolved the industrial structures in line with the worldwide trend. To achieve this, intelligent biomanufacturing can be structured into three main parts that comprise digitalization, modeling and intellectualization, with modeling forming a crucial link between the other two components. This paper provides an overview of mechanistic models, data-driven models and their applications in bioprocess development. We provide a detailed elaboration of the hybrid model and its applications in bioprocess engineering, including strain design, process control and optimization, as well as bioreactor scale-up. Finally, the challenges and opportunities of biomanufacturing towards Industry 4.0 are also discussed.

A study of a diauxic growth experiment using an expanded dynamic flux balance framework

Flux balance analysis (FBA) remains one of the most used methods for modeling the entirety of cellular metabolism, and a range of applications and extensions based on the FBA framework have been generated. Dynamic flux balance analysis (dFBA), the expansion of FBA into the time domain, still has issues regarding accessibility limiting its widespread adoption and application, such as a lack of a consistently rigid formalism and tools that can be applied without expert knowledge. Recent work has combined dFBA with enzyme-constrained flux balance analysis (decFBA), which has been shown to greatly improve accuracy in the comparison of computational simulations and experimental data, but such approaches generally do not take into account the fact that altering the enzyme composition of a cell is not an instantaneous process. Here, we have developed a decFBA method that explicitly takes enzyme change constraints (ecc) into account, decFBAecc. The resulting software is a simple yet flexible framework for using genome-scale metabolic modeling for simulations in the time domain that has full interoperability with the COBRA Toolbox 3.0. To assess the quality of the computational predictions of decFBAecc, we conducted a diauxic growth fermentation experiment with Escherichia coli BW25113 in glucose minimal M9 medium. The comparison of experimental data with dFBA, decFBA and decFBAecc predictions demonstrates how systematic analyses within a fixed constraint-based framework can aid the study of model parameters. Finally, in explaining experimentally observed phenotypes, our computational analysis demonstrates the importance of non-linear dependence of exchange fluxes on medium metabolite concentrations and the non-instantaneous change in enzyme composition, effects of which have not previously been accounted for in constraint-based analysis.

Basin-scale biogeography of marine phytoplankton reflects cellular-scale optimization of metabolism and physiology

Extensive microdiversity within Prochlorococcus, the most abundant marine cyanobacterium, occurs at scales from a single droplet of seawater to ocean basins. To interpret the structuring role of variations in genetic potential, as well as metabolic and physiological acclimation, we developed a mechanistic constraint-based modeling framework that incorporates the full suite of genes, proteins, metabolic reactions, pigments, and biochemical compositions of 69 sequenced isolates spanning the Prochlorococcus pangenome. Optimizing each strain to the local, observed physical and chemical environment along an Atlantic Ocean transect, we predicted variations in strain-specific patterns of growth rate, metabolic configuration, and physiological state, defining subtle niche subspaces directly attributable to differences in their encoded metabolic potential. Predicted growth rates covaried with observed ecotype abundances, affirming their significance as a measure of fitness and inferring a nonlinear density dependence of mortality. Our study demonstrates the potential to interpret global-scale ecosystem organization in terms of cellular-scale processes.

Enhancement of Ethanol Production Using a Hybrid of Firefly Algorithm and Dynamic Flux Balance Analysis

Many high-demand industrial products are generated by microorganisms, including fuels, food, vitamins, and other chemicals. Metabolic engineering is the method of circumventing cellular control to manufacture a desirable product or to create a new product that the host cells do not normally need to produce. One of the objectives of microorganism metabolic engineering is to maximise the production of a desired product. However, owing to the structure of the regulatory cellular and metabolic network, identifying specific genes to be knocked out is difficult. The development of optimization algorithms often confronts issues such as easily trapping in local maxima and handling multivariate and multimodal functions inefficiently. To predict the gene knockout list that can generate high yields of desired product, a hybrid of Firefly Algorithm and Dynamic Flux Balance Analysis (FADFBA) is proposed. This paper focuses on the ethanol production of Escherichia coli (E. coli). The findings of the experiments include gene lists, ethanol production, growth rate, and the performance of FADFBA.

Genome-Scale Metabolic Modeling Enables In-Depth Understanding of Big Data

Genome-scale metabolic models (GEMs) enable the mathematical simulation of the metabolism of archaea, bacteria, and eukaryotic organisms. GEMs quantitatively define a relationship between genotype and phenotype by contextualizing different types of Big Data (e.g., genomics, metabolomics, and transcriptomics). In this review, we analyze the available Big Data useful for metabolic modeling and compile the available GEM reconstruction tools that integrate Big Data. We also discuss recent applications in industry and research that include predicting phenotypes, elucidating metabolic pathways, producing industry-relevant chemicals, identifying drug targets, and generating knowledge to better understand host-associated diseases. In addition to the up-to-date review of GEMs currently available, we assessed a plethora of tools for developing new GEMs that include macromolecular expression and dynamic resolution. Finally, we provide a perspective in emerging areas, such as annotation, data managing, and machine learning, in which GEMs will play a key role in the further utilization of Big Data.

Harmonics, evolutionary generators, DANCE, and HEAR-functional dimensions

Evolution of the major kingdoms of life has spanned over the last 4 billion years on Earth. Studies of the process comprise different fields of study with alternative perspectives. This paper focuses on mathematic unification of the subject area; enriching an engineering based structure to advance our understanding of pathways which lead to distinct constructs in life, furthering geographic bordering processes with biological context. Application of logistic regression requires partitioning of variance within cellular and molecular systems; use of higher mathematic technique (multi-objective genetic algorithm) generates variance within the different scales of evolution, the result of which is analogous with the Fisher equation model of gene distribution within populations. Laboratory and field studies were integrated to illustrate emergence in evolutionary processes in the terrestrial/soil environment. Nematological field and laboratory trials validate the existence of triangular relationships within biological communities; further harmonic constants between interacting species may be found with emergent consequence. We distinguish different strategical groupings in the soil community, with the core groupings recognized with Meloidogyne spp. illustrating positive (emergent) growth; Radopholus similis (neutral growth), and Helicotylenchus pseudorobustus (negative growth). The patterns of emergent systems are shown in the extremes of Morocco's dynamic soil environment. Fuzzy classification methods: Mamdani, Takugi-Sugeno-Kang; additional novel DANCE (Differential Algorithmic Network Centered Emergence) and functional expressions HEAR (Harmonic Evolutionary Algorithmic Resilience), are recommended to give a basis for development of constructs covering different categories of life.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

Knowledge extraction from literature and enzyme sequences complements FBA analysis in metabolic engineering

Flux balance analysis (FBA) using genome-scale metabolic model (GSM) is a useful method for improving the bio-production of useful compounds. However, FBA often does not impose important constraints such as nutrients uptakes, by-products excretions and gases (oxygen and carbon dioxide) transfers. Furthermore, important information on metabolic engineering such as enzyme amounts, activities, and characteristics caused by gene expression and enzyme sequences is basically not included in GSM. Therefore, simple FBA is often not sufficient to search for metabolic manipulation strategies that are useful for improving the production of target compounds. In this study, we proposed a method using literature and enzyme search to complement the FBA-based metabolic manipulation strategies. As a case study, this method was applied to shikimic acid production by Corynebacterium glutamicum to verify its usefulness. As unique strategies in literature-mining, overexpression of the transcriptional regulator SugR and gene disruption related to by-products productions were complemented. In the search for alternative enzyme sequences, it was suggested that those candidates are searched for from various species based on features captured by deep learning, which are not simply homologous to amino acid sequences of the base enzymes.

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.

Dynamic metabolic modelling predicts efficient acetogen-gut bacterium cocultures for CO-to-butyrate conversion

AIMS

While gas-fermenting acetogens have been engineered to secrete non-native metabolites such as butyrate, acetate remains the most thermodynamically favourable product. An alternative to metabolic engineering is to exploit native capabilities for CO-to-acetate conversion by coculturing an acetogen with a second bacterium that provides efficient acetate-butyrate conversion.

METHODS AND RESULTS

We used dynamic metabolic modelling to computationally evaluate the CO-to-butyrate conversion capabilities of candidate coculture systems by exploiting the diversity of human gut bacteria for anaerobic synthesis of butyrate from acetate and ethanol. A preliminary screening procedure based on flux balance analysis was developed to identify 48 gut bacteria which satisfied minimal growth rate and acetate-to-butyrate conversion requirements when cultured on minimal medium containing acetate and a simple sugar not consumed by the paired acetogen. A total of 170 acetogen/gut bacterium/sugar combinations were dynamically simulated for continuous growth using a 70/30 CO/CO₂ feed gas mixture and minimal medium computationally determined for each combination.

CONCLUSIONS

While coculture systems involving the acetogens Eubacterium limosum or Blautia producta yielded low butyrate productivities and CO-to-ethanol conversion had minimal impact on system performance, dynamic simulations predicted a large number of promising coculture designs with Clostridium ljungdahlii or C. autoethanogenum as the CO-to-acetate converter. Pairings with the gut bacterium Clostridium hylemonae or Roseburia hominis were particularly promising due to their ability to generate high butyrate productivities over a range of dilution rates with a variety of sugars. The higher specific acetate secretion rate of C. ljungdahlii proved more beneficial than the elevated growth rate of C. autoethanogenum for coculture butyrate productivity.

SIGNIFICANCE AND IMPACT OF THE STUDY

Our study demonstrated that metabolic modelling could provide useful insights into coculture design that can guide future experimental studies. More specifically, our predictions generated several favourable designs, which could serve as the first coculture systems realized experimentally.

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.

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.

Predicting Nash equilibria for microbial metabolic interactions

MOTIVATION

Microbial metabolic interactions impact ecosystems, human health and biotechnology profoundly. However, their determination remains elusive, invoking an urgent need for predictive models seamlessly integrating metabolism with evolutionary principles that shape community interactions.

RESULTS

Inspired by the evolutionary game theory, we formulated a bi-level optimization framework termed NECom for which any feasible solutions are Nash equilibria of microbial community metabolic models with/without an outer-level (community) objective function. Distinct from discrete matrix games, NECom models the continuous interdependent strategy space of metabolic fluxes. We showed that NECom successfully predicted several classical games in the context of metabolic interactions that were falsely or incompletely predicted by existing methods, including prisoner's dilemma, snowdrift and cooperation. The improved capability originates from the novel formulation to prevent 'forced altruism' hidden in previous static algorithms while allowing for sensing all potential metabolite exchanges to determine evolutionarily favorable interactions between members, a feature missing in dynamic methods. The results provided insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites and demonstrated similarities and differences between games in the continuous metabolic flux space and matrix games. NECom was then applied to a reported algae-yeast co-culture system that shares typical cross-feeding features of lichen, a model system of mutualism. 488 growth conditions corresponding to 3,221 experimental data points were simulated. Without training any parameters using the data, NECom is more predictive of species' growth rates given uptake rates compared with flux balance analysis with an overall 63.5% and 81.7% reduction in root-mean-square error for the two species.

AVAILABILITY

Simulation code and data are available at https://github.com/Jingyi-Cai/NECom.git.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Automated engineering of synthetic metabolic pathways for efficient biomanufacturing

Metabolic engineering involves the engineering and optimization of processes from single-cell to fermentation in order to increase production of valuable chemicals for health, food, energy, materials and others. A systems approach to metabolic engineering has gained traction in recent years thanks to advances in strain engineering, leading to an accelerated scaling from rapid prototyping to industrial production. Metabolic engineering is nowadays on track towards a truly manufacturing technology, with reduced times from conception to production enabled by automated protocols for DNA assembly of metabolic pathways in engineered producer strains. In this review, we discuss how the success of the metabolic engineering pipeline often relies on retrobiosynthetic protocols able to identify promising production routes and dynamic regulation strategies through automated biodesign algorithms, which are subsequently assembled as embedded integrated genetic circuits in the host strain. Those approaches are orchestrated by an experimental design strategy that provides optimal scheduling planning of the DNA assembly, rapid prototyping and, ultimately, brings forward an accelerated Design-Build-Test-Learn cycle and the overall optimization of the biomanufacturing process. Achieving such a vision will address the increasingly compelling demand in our society for delivering valuable biomolecules in an affordable, inclusive and sustainable bioeconomy.

Quantitative models of nitrogen-fixing organisms

Nitrogen-fixing organisms are of importance to the environment, providing bioavailable nitrogen to the biosphere. Quantitative models have been used to complement the laboratory experiments and in situ measurements, where such evaluations are difficult or costly. Here, we review the current state of the quantitative modeling of nitrogen-fixing organisms and ways to enhance the bridge between theoretical and empirical studies.

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.

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.

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.

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.

Understanding the metabolism of the tetralin degrader Sphingopyxis granuli strain TFA through genome-scale metabolic modelling

Sphingopyxis granuli strain TFA is an α-proteobacterium that belongs to the sphingomonads, a group of bacteria well-known for its degradative capabilities and oligotrophic metabolism. Strain TFA is the only bacterium in which the mineralisation of the aromatic pollutant tetralin has been completely characterized at biochemical, genetic, and regulatory levels and the first Sphingopyxis characterised as facultative anaerobe. Here we report additional metabolic features of this α-proteobacterium using metabolic modelling and the functional integration of genomic and transcriptomic data. The genome-scale metabolic model (GEM) of strain TFA, which has been manually curated, includes information on 743 genes, 1114 metabolites and 1397 reactions. This represents the largest metabolic model for a member of the Sphingomonadales order thus far. The predictive potential of this model was validated against experimentally calculated growth rates on different carbon sources and under different growth conditions, including both aerobic and anaerobic metabolisms. Moreover, new carbon and nitrogen sources were predicted and experimentally validated. The constructed metabolic model was used as a platform for the incorporation of transcriptomic data, generating a more robust and accurate model. In silico flux analysis under different metabolic scenarios highlighted the key role of the glyoxylate cycle in the central metabolism of strain TFA.

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.

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.

Dynamic metabolic modelling of overproduced protein secretion in Streptomyces lividans using adaptive DFBA

BACKGROUND

Streptomyces lividans is an appealing host for the production of proteins of biotechnological interest due to its relaxed exogenous DNA restriction system and its ability to secrete proteins directly to the medium through the major Sec or the minor Tat routes. Often, protein secretion displays non-uniform time-dependent patterns. Understanding the associated metabolic changes is a crucial step to engineer protein production. Dynamic Flux Balance Analysis (DFBA) allows the study of the interactions between a modelled organism and its environment over time. Existing methods allow the specification of initial model and environment conditions, but do not allow introducing arbitrary modifications in the course of the simulation. Living organisms, however, display unexpected adaptive metabolic behaviours in response to unpredictable changes in their environment. Engineering the secretion of products of biotechnological interest has systematically proven especially difficult to model using DFBA. Accurate time-dependent modelling of complex and/or arbitrary, adaptive metabolic processes demands an extended approach to DFBA.

RESULTS

In this work, we introduce Adaptive DFBA, a novel, versatile simulation approach that permits inclusion of changes in the organism or the environment at any time in the simulation, either arbitrary or interactively responsive to environmental changes. This approach extends traditional DFBA to allow steering arbitrarily complex simulations of metabolic dynamics. When applied to Sec- or Tat-dependent secretion of overproduced proteins in S. lividans, Adaptive DFBA can overcome the limitations of traditional DFBA to reproduce experimental data on plasmid-free, plasmid bearing and secretory protein overproducing S. lividans TK24, and can yield useful insights on the behaviour of systems with limited experimental knowledge such as agarase or amylase overproduction in S. lividans TK21.

CONCLUSIONS

Adaptive DFBA has allowed us to overcome DFBA limitations and to generate more accurate models of the metabolism during the overproduction of secretory proteins in S. lividans, improving our understanding of the underlying processes. Adaptive DFBA is versatile enough to permit dynamical metabolic simulations of arbitrarily complex biotechnological processes.

Fast uncertainty quantification for dynamic flux balance analysis using non-smooth polynomial chaos expansions

We present a novel surrogate modeling method that can be used to accelerate the solution of uncertainty quantification (UQ) problems arising in nonlinear and non-smooth models of biological systems. In particular, we focus on dynamic flux balance analysis (DFBA) models that couple intracellular fluxes, found from the solution of a constrained metabolic network model of the cellular metabolism, to the time-varying nature of the extracellular substrate and product concentrations. DFBA models are generally computationally expensive and present unique challenges to UQ, as they entail dynamic simulations with discrete events that correspond to switches in the active set of the solution of the constrained intracellular model. The proposed non-smooth polynomial chaos expansion (nsPCE) method is an extension of traditional PCE that can effectively capture singularities in the DFBA model response due to the occurrence of these discrete events. The key idea in nsPCE is to use a model of the singularity time to partition the parameter space into two elements on which the model response behaves smoothly. Separate PCE models are then fit in both elements using a basis-adaptive sparse regression approach that is known to scale well with respect to the number of uncertain parameters. We demonstrate the effectiveness of nsPCE on a DFBA model of an E. coli monoculture that consists of 1075 reactions and 761 metabolites. We first illustrate how traditional PCE is unable to handle problems of this level of complexity. We demonstrate that over 800-fold savings in computational cost of uncertainty propagation and Bayesian estimation of parameters in the substrate uptake kinetics can be achieved by using the nsPCE surrogates in place of the full DFBA model simulations. We then investigate the scalability of the nsPCE method by utilizing it for global sensitivity analysis and maximum a posteriori estimation in a synthetic metabolic network problem with a larger number of parameters related to both intracellular and extracellular quantities.