Dynamic Flux Balance Analysis Research Articles

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 2.8g/L with the increase of gas recycle ratio from 0 to 30 at the empty bed residence time of 60 .

Cross-regulation between proteome reallocation and metabolic flux redistribution governs bacterial growth transition kinetics

Bacteria need to adjust their metabolism and protein synthesis simultaneously to adapt to changing nutrient conditions. It’s still a grand challenge to predict how cells coordinate such adaptation due to the cross-regulation between the metabolic fluxes and the protein synthesis. Here we developed a dynamic Constrained Allocation Flux Balance Analysis method (dCAFBA), which integrates flux-controlled proteome allocation and protein limited flux balance analysis. This framework can predict the redistribution dynamics of metabolic fluxes without requiring detailed enzyme parameters. We reveal that during nutrient up-shifts, the calculated metabolic fluxes change in agreement with experimental measurements of enzyme protein dynamics. During nutrient down-shifts, we uncover a switch of metabolic bottleneck from carbon uptake proteins to metabolic enzymes, which disrupts the coordination between metabolic flux and their enzyme abundance. Our method provides a quantitative framework to investigate cellular metabolism under varying environments and reveals insights into bacterial adaptation strategies.

Dynamic flux balance analysis of high cell density fed-batch culture of Escherichia coli BL21 (DE3) with mass spectrometry-based spent media analysis.

Dynamic flux balance analysis (FBA) allows estimation of intracellular reaction rates using organism-specific genome-scale metabolic models (GSMM) and by assuming instantaneous pseudo-steady states for processes that are inherently dynamic. This technique is well-suited for industrial bioprocesses employing complex media characterized by a hierarchy of substrate uptake and product secretion. However, knowledge of exchange rates of many components of the media would be required to obtain meaningful results. Here, we performed spent media analysis using mass spectrometry coupled with liquid and gas chromatography for a fed-batch, high-cell density cultivation of Escherichia coli BL21(DE3) expressing a recombinant protein. Time course measurements thus obtained for 246 metabolites were converted to instantaneous exchange rates. These were then used as constraints for dynamic FBA using a previously reported GSMM, thus providing insights into how the flux map evolves through the process. Changes in tri-carboxylic acid cycle fluxes correlated with the increased demand for energy during recombinant protein production. The results show how amino acids act as hubs for the synthesis of other cellular metabolites. Our results provide a deeper understanding of an industrial bioprocess and will have implications in further optimizing the process.

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

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

Dynamic flux balance analysis of 1,3-propanediol production by clostridium butyricum fermentation.

To study the relationship between the yield of 1,3-propanediol (1,3-PDO) and the flux change of the Clostridium butyricum metabolic pathway, an optimized calculation method based on dynamic flux balance analysis was used by combining genome-scale flux balance analysis with a kinetic model. A more comprehensive and extensive metabolic pathway was obtained by optimization calculations. The primary extended branches include: the dihydroxyacetone node, which enters the pentose phosphate pathway; the α-oxoglutarate node, which has synthetic metabolic pathways for glutamic acid and amino acids; and the serine and homocysteine nodes, which produce cystathionine before homocysteine enters the methionine cycle pathway. According to the expanded metabolic network, the flux distribution of key nodes in the metabolic pathway and the relationship between the flux distribution ratio of nodes and the yield of 1,3-PDO were analyzed. At the dihydroxyacetone node, the flux of dihydroxyacetone converted to dihydroxyacetone phosphate was positively correlated with the yield of 1,3-PDO. As an important intermediate product, the flux change in the metabolic pathway of α-oxoglutarate reacting with amino acids to produce glutamic acid is positively correlated with the yield. When pyruvate was used as the central node to convert into lactic acid and α-oxoglutarate, the proportion of branch flux was negatively correlated with the yield of 1,3-PDO. These studies provide a theoretical basis for the optimization and further study of the metabolic pathway of C. butyricum.

Computational assessment of lipid production in Rhodosporidium toruloidesin 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 toruloideswas 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.

‘Social’ versus ‘asocial’ cells—dynamic competition flux balance analysis

In multicellular organisms cells compete for resources or growth factors. If any one cell type wins, the co-existence of diverse cell types disappears. Existing dynamic Flux Balance Analysis (dFBA) does not accommodate changes in cell density caused by competition. Therefore we here develop ‘dynamic competition Flux Balance Analysis’ (dcFBA). With total biomass synthesis as objective, lower-growth-yield cells were outcompeted even when cells synthesized mutually required nutrients. Signal transduction between cells established co-existence, which suggests that such ‘socialness’ is required for multicellularity. Whilst mutants with increased specific growth rate did not outgrow the other cell types, loss of social characteristics did enable a mutant to outgrow the other cells. We discuss that ‘asocialness’ rather than enhanced growth rates, i.e., a reduced sensitivity to regulatory factors rather than enhanced growth rates, may characterize cancer cells and organisms causing ecological blooms. Therapies reinforcing cross-regulation may therefore be more effective than those targeting replication rates.

Model predictive control of a fermenter using dynamic flux balance analysis coupled with convolutional neural networks

Flux balance analysis-based models are increasingly used in bioprocess control and optimization. Unlike unstructured models, flux balance analysis-based models investigate the genome-scale network reconstructions of the microorganisms under study. Although these models are accurate, they pose computational cost challenges in rigorous optimization tasks or online optimal control strategies. In this work, we develop low-computational cost hybrid models by using deep convolutional neural networks to surrogate the problem/model. Furthermore, to address the computational challenges associated with optimal control of flux balance analysis-based models, we propose a successive linearization scheme that incorporates a Laguerre function-based model predictive control strategy coupled with a Luenberger-like observer. To investigate the effectiveness of the proposed method, optimal control of a fed-batch process is considered. Results show the acceptable accuracy of the proposed hybrid model and control scheme while reducing the computational cost significantly.

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.

Assumptions on decision making and environment can yield multiple steady states in microbial community models

BackgroundMicrobial community simulations using genome scale metabolic networks (GSMs) are relevant for many application areas, such as the analysis of the human microbiome. Such simulations rely on assumptions about the culturing environment, affecting if the culture may reach a metabolically stationary state with constant microbial concentrations. They also require assumptions on decision making by the microbes: metabolic strategies can be in the interest of individual community members or of the whole community. However, the impact of such common assumptions on community simulation results has not been investigated systematically.ResultsHere, we investigate four combinations of assumptions, elucidate how they are applied in literature, provide novel mathematical formulations for their simulation, and show how the resulting predictions differ qualitatively. Our results stress that different assumption combinations give qualitatively different predictions on microbial coexistence by differential substrate utilization. This fundamental mechanism is critically under explored in the steady state GSM literature with its strong focus on coexistence states due to crossfeeding (division of labor). Furthermore, investigating a realistic synthetic community, where the two involved strains exhibit no growth in isolation, but grow as a community, we predict multiple modes of cooperation, even without an explicit cooperation mechanism.ConclusionsSteady state GSM modelling of microbial communities relies both on assumed decision making principles and environmental assumptions. In principle, dynamic flux balance analysis addresses both. In practice, our methods that address the steady state directly may be preferable, especially if the community is expected to display multiple steady states.

A Holistic Approach from Systems Biology Reveals the Direct Influence of the Quorum-Sensing Phenomenon on Pseudomonas aeruginosa Metabolism to Pyoverdine Biosynthesis.

Computational modeling and simulation of biological systems have become valuable tools for understanding and predicting cellular performance and phenotype generation. This work aimed to construct, model, and dynamically simulate the virulence factor pyoverdine (PVD) biosynthesis in Pseudomonas aeruginosa through a systemic approach, considering that the metabolic pathway of PVD synthesis is regulated by the quorum-sensing (QS) phenomenon. The methodology comprised three main stages: (i) Construction, modeling, and validation of the QS gene regulatory network that controls PVD synthesis in P. aeruginosa strain PAO1; (ii) construction, curating, and modeling of the metabolic network of P. aeruginosa using the flux balance analysis (FBA) approach; (iii) integration and modeling of these two networks into an integrative model using the dynamic flux balance analysis (DFBA) approximation, followed, finally, by an in vitro validation of the integrated model for PVD synthesis in P. aeruginosa as a function of QS signaling. The QS gene network, constructed using the standard System Biology Markup Language, comprised 114 chemical species and 103 reactions and was modeled as a deterministic system following the kinetic based on mass action law. This model showed that the higher the bacterial growth, the higher the extracellular concentration of QS signal molecules, thus emulating the natural behavior of P. aeruginosa PAO1. The P. aeruginosa metabolic network model was constructed based on the iMO1056 model, the P. aeruginosa PAO1 strain genomic annotation, and the metabolic pathway of PVD synthesis. The metabolic network model included the PVD synthesis, transport, exchange reactions, and the QS signal molecules. This metabolic network model was curated and then modeled under the FBA approximation, using biomass maximization as the objective function (optimization problem, a term borrowed from the engineering field). Next, chemical reactions shared by both network models were chosen to combine them into an integrative model. To this end, the fluxes of these reactions, obtained from the QS network model, were fixed in the metabolic network model as constraints of the optimization problem using the DFBA approximation. Finally, simulations of the integrative model (CCBM1146, comprising 1123 reactions and 880 metabolites) were run using the DFBA approximation to get (i) the flux profile for each reaction, (ii) the bacterial growth profile, (iii) the biomass profile, and (iv) the concentration profiles of metabolites of interest such as glucose, PVD, and QS signal molecules. The CCBM1146 model showed that the QS phenomenon directly influences the P. aeruginosa metabolism to PVD biosynthesis as a function of the change in QS signal intensity. The CCBM1146 model made it possible to characterize and explain the complex and emergent behavior generated by the interactions between the two networks, which would have been impossible to do by studying each system's individual components or scales separately. This work is the first in silico report of an integrative model comprising the QS gene regulatory network and the metabolic network of P. aeruginosa.

Dynamic genome-scale modeling of Saccharomyces cerevisiae unravels mechanisms for ester formation during alcoholic fermentation.

Fermentation employing Saccharomyces cerevisiae has produced alcoholic beverages and bread for millennia. More recently, S. cerevisiae has been used to manufacture specific metabolites for the food, pharmaceutical, and cosmetic industries. Among the most important of these metabolites are compounds associated with desirable aromas and flavors, including higher alcohols and esters. Although the physiology of yeast has been well-studied, its metabolic modulation leading to aroma production in relevant industrial scenarios such as winemaking is still unclear. Here we ask what are the underlying metabolic mechanisms that explain the conserved and varying behavior of different yeasts regarding aroma formation under enological conditions? We employed dynamic flux balance analysis (dFBA) to answer this key question using the latest genome-scale metabolic model (GEM) of S. cerevisiae. The model revealed several conserved mechanisms among wine yeasts, for example, acetate ester formation is dependent on intracellular metabolic acetyl-CoA/CoA levels, and the formation of ethyl esters facilitates the removal of toxic fatty acids from cells using CoA. Species-specific mechanisms were also found, such as a preference for the shikimate pathway leading to more 2-phenylethanol production in the Opale strain as well as strain behavior varying notably during the carbohydrate accumulation phase and carbohydrate accumulation inducing redox restrictions during a later cell growth phase for strain Uvaferm. In conclusion, our new metabolic model of yeast under enological conditions revealed key metabolic mechanisms in wine yeasts, which will aid future research strategies to optimize their behavior in industrial settings.

Developing a metabolic model‐based fed‐batch feeding strategy for Pichia pastoris fermentation through fine‐tuning of the methanol utilization pathway

Pichia pastoris is a commonly used microbial host for recombinant protein production. It is mostly cultivated in fed-batch mode, in which the environment of the cell is continuously changing. Hence, it is vital to understand the influence of feeding strategy parameters on the intracellular reaction network to fine-tune bioreactor performance. This study used dynamic flux balance analysis (DFBA) integrated with transcriptomics data to simulate the recombinant P. pastoris (Muts ) growth during the induction phase for three fed-batch strategies, conducted at constant specific growth rates (μ-stat). The induction phase was split into equal time intervals, and the correlated reactions with protein yield were identified in the three fed-batch strategies using the Pearson correlation coefficient. Subsequently, principal component analysis (PCA) was applied to cluster induction phase time intervals and identify the role of correlated reactions on metabolic differentiation of time intervals. It was found that increasing fluxes through the methanol dissimilation pathway increased protein yield. By adding a methanol assimilation pathway inhibitor (HgCl2 ) to the shake flask medium growing on glycerol: methanol mixture (10%: 90%, v/v), the protein titre increased by 60%. As per DFBA, the higher the methanol to biomass flux ratio (Rmeoh/Δx ), the higher the protein yield. Finally, a novel feeding strategy was developed to increase the amount of Rmeoh/Δx compared to the three feeding strategies. The concentration of recombinant human growth hormone (rhGH), used as the model protein, increased by 16% compared to the optimal culture result obtained previously (800 mg L-1 to 928 mg L-1 ), while production yield improved by 85% (24.8 mg gDCW -1 to 46 mg gDCW -1 ).

Elucidating dynamic anaerobe metabolism with HRMAS 13C NMR and genome-scale modeling

Anaerobic microbial metabolism drives critical functions within global ecosystems, host–microbiota interactions, and industrial applications, yet remains ill-defined. Here we advance a versatile approach to elaborate cellular metabolism in obligate anaerobes using the pathogen Clostridioides difficile, an amino acid and carbohydrate-fermenting Clostridia. High-resolution magic angle spinning nuclear magnetic resonance (NMR) spectroscopy of C. difficile, grown with fermentable 13C substrates, informed dynamic flux balance analysis (dFBA) of the pathogen’s genome-scale metabolism. Analyses identified dynamic recruitment of oxidative and supporting reductive pathways, with integration of high-flux amino acid and glycolytic metabolism at alanine’s biosynthesis to support efficient energy generation, nitrogen handling and biomass generation. Model predictions informed an approach leveraging the sensitivity of 13C NMR spectroscopy to simultaneously track cellular carbon and nitrogen flow from [U-13C]glucose and [15N]leucine, confirming the formation of [13C,15N]alanine. Findings identify metabolic strategies used by C. difficile to support its rapid colonization and expansion in gut ecosystems.

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.

Nonlinear programming reformulation of dynamic flux balance analysis models

Dynamic flux balance analysis (dFBA) models are very popular in systems biology because of the many possible applications. dFBA consists of dynamic mass balance equations that describe the concentration of external metabolites and an optimization model to compute the internal flux distribution of the cell. Here, we applied a nonlinear programming formulation for solving dFBA models. The ODE system is discretized using the orthogonal collocation technique and the optimization problem is replaced by its first-order optimality conditions. In addition, an adaptive mesh scheme is applied to improve performance by efficiently handling changes in the active set of constraints. This formulation ensures total differentiability of the model, which can be solved by large-scale solvers and take advantage of automatic differentiation packages. The new approach presents results equivalent to state-of-the-art methods and outperforms them in dynamic optimization problems by avoiding calling an external solver to handle the embedded optimization model.

SimDFBA: A framework for bioprocess simulation and development

Many efforts have been made to model bio-processes and investigate the main effective parameters using conventional known softwares. The main shortcoming of such models is that the bioreactor is considered a black box. Such simplification causes uncertainty in following different metabolic pathways of microorganisms. This study presents a new method for simulating bio-processes by integrating available conventional simulation softwares such as ASPEN PLUS and MATLAB. The former is used to simulate common process equipment, and the latter is employed to model Bio-reactor. Besides, the Bio-reactor is modeled mathematically with Dynamic Flux Balance Analysis (DFBA) concept using the metabolic network reconstruction model. This framework will simultaneously provide a rigorous basic model of both upstream and downstream equipment. This approach can also be used as a toolbox to implement process optimization and modern control strategies on the bio-processes. A syngas fermentation bioprocess case study was chosen to implement the new framework.

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 modelling enables deciphering ethanol metabolism via the acrylate pathway in the propionate-producer Anaerotignum neopropionicum

BackgroundMicrobial production of propionate from diluted streams of ethanol (e.g., deriving from syngas fermentation) is a sustainable alternative to the petrochemical production route. Yet, few ethanol-fermenting propionigenic bacteria are known, and understanding of their metabolism is limited. Anaerotignum neopropionicum is a propionate-producing bacterium that uses the acrylate pathway to ferment ethanol and CO2 to propionate and acetate. In this work, we used computational and experimental methods to study the metabolism of A. neopropionicum and, in particular, the pathway for conversion of ethanol into propionate.ResultsOur work describes iANEO_SB607, the first genome-scale metabolic model (GEM) of A. neopropionicum. The model was built combining the use of automatic tools with an extensive manual curation process, and it was validated with experimental data from this and published studies. The model predicted growth of A. neopropionicum on ethanol, lactate, sugars and amino acids, matching observed phenotypes. In addition, the model was used to implement a dynamic flux balance analysis (dFBA) approach that accurately predicted the fermentation profile of A. neopropionicum during batch growth on ethanol. A systematic analysis of the metabolism of A. neopropionicum combined with model simulations shed light into the mechanism of ethanol fermentation via the acrylate pathway, and revealed the presence of the electron-transferring complexes NADH-dependent reduced ferredoxin:NADP+ oxidoreductase (Nfn) and acryloyl-CoA reductase-EtfAB, identified for the first time in this bacterium.ConclusionsThe realisation of the GEM iANEO_SB607 is a stepping stone towards the understanding of the metabolism of the propionate-producer A. neopropionicum. With it, we have gained insight into the functioning of the acrylate pathway and energetic aspects of the cell, with focus on the fermentation of ethanol. Overall, this study provides a basis to further exploit the potential of propionigenic bacteria as microbial cell factories.