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

BackgroundStreptomyces 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.ResultsIn 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.ConclusionsAdaptive 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.

To investigate the relationship between the yield of 1,3-propanediol (1,3-PD) and the flux variation in metabolic pathways of Klebsiella pneumoniae, an optimized calculation method was constructed on basis of dynamic flux balance analysis by combining genome-scale flux balance analysis with a kinetic model of extracellular metabolites. Through optimizing calculations, a more completely expanded metabolic pathway was obtained, which includes the previously reported metabolic pathway and additional three pathways or site: a pentose phosphate pathway (PPP) elicited at the dihydroxyacetone (DHA) node to provide more reducing equivalents; a branch of synthetic amino acids at the 3-phosphoglycerate (3PG) node; and the α-ketoglutarate site in the tricarboxylic acid (TCA) cycle leading to anabolic pathways for glutamate and other amino acids. On this basis, the relationships between the dynamic flux distribution of the important nodes in the metabolic pathway and the yield of 1,3-propanediol were analyzed. First, dynamic flux change from DHA to the PPP is positively correlated with the yield. Second, variation in flux in the TCA cycle is also positively correlated with the yield of 1,3-propanediol. In addition, the influence of the feedback loop formed by the cofactor tetrahydrofolate on the flux change of TCA in the amino acid anabolic pathway was examined. These results are of important reference value and have guiding significance for the extension of the glycerol metabolism pathway in K. pneumoniae, the rational transformation of genetic engineering in bacteria, and the optimization of metabolic pathways for industrial production.

BackgroundFlux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.ResultsHere, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.ConclusionsOur methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.

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

Mathematical Modeling of a Raceway Pond System for Biofuels Production

BackgroundGenome-wide reconstructions of metabolism opened the way to thorough investigations of cell metabolism for health care and industrial purposes. However, the predictions offered by Flux Balance Analysis (FBA) can be strongly affected by the choice of flux boundaries, with particular regard to the flux of reactions that sink nutrients into the system. To mitigate possible errors introduced by a poor selection of such boundaries, a rational approach suggests to focus the modeling efforts on the pivotal ones.MethodsIn this work, we present a methodology for the automatic identification of the key fluxes in genome-wide constraint-based models, by means of variance-based sensitivity analysis. The goal is to identify the parameters for which a small perturbation entails a large variation of the model outcomes, also referred to as sensitive parameters. Due to the high number of FBA simulations that are necessary to assess sensitivity coefficients on genome-wide models, our method exploits a master-slave methodology that distributes the computation on massively multi-core architectures. We performed the following steps: (1) we determined the putative parameterizations of the genome-wide metabolic constraint-based model, using Saltelli’s method; (2) we applied FBA to each parameterized model, distributing the massive amount of calculations over multiple nodes by means of MPI; (3) we then recollected and exploited the results of all FBA runs to assess a global sensitivity analysis.ResultsWe show a proof-of-concept of our approach on latest genome-wide reconstructions of human metabolism Recon2.2 and Recon3D. We report that most sensitive parameters are mainly associated with the intake of essential amino acids in Recon2.2, whereas in Recon 3D they are associated largely with phospholipids. We also illustrate that in most cases there is a significant contribution of higher order effects.ConclusionOur results indicate that interaction effects between different model parameters exist, which should be taken into account especially at the stage of calibration of genome-wide models, supporting the importance of a global strategy of sensitivity analysis.

In this work, a reduced form of dynamic flux balance model based on artificial neural networks for batch and fed-batch fermentation of xylose-utilizing engineered Saccharomyces cerevisiae RWB 218 is developed. The intracellular description of carbon metabolism in the model is simulated by a multilayer-perceptron (MLP) network. First, this hybrid model is compared to the full mechanistic dynamic flux balance analysis (DFBA) in terms of accuracy and computational time regarding available experimental data on anaerobic batch cultivation. Afterwards, it is used in a model-based sequential dynamic optimization procedure in order to maximize ethanol productivity. The initial liquid volume charged in the bioreactor, the feed flow rates in aerobic and anaerobic conditions, the final batch time, and the switching time from aerobic to anaerobic conditions are considered as decision variables. Differential evolution (DE), as a robust and efficient optimization method, is employed to solve the problem for several glucose mass fractions in the feed stream. The results show that in similar conditions a small deviation in each operating parameter from its optimal value may lead to considerable decrease in ethanol productivity.

For biogas-producing continuous stirred tank reactors, an increase in dilution rate increases the methane production rate as long as substrate input can be converted fully. However, higher dilution rates necessitate higher specific microbial growth rates, which are assumed to have a strong impact on the apparent microbial biomass yield due to cellular maintenance. To test this, we operated two reactors at 37°C in parallel at dilution rates of 0.18 and 0.07 days-1 (hydraulic retention times of 5.5 and 14 days, doubling times of 3.9 and 9.9 days in steady state) with identical inoculum and a mixture of volatile fatty acids as sole carbon sources. We evaluated the performance of the Anaerobic Digestion Model No. 1 (ADM1), a thermodynamic black box approach (TBA), and dynamic flux balance analysis (dFBA), to describe the experimental observations. All models overestimated the impact of dilution rate on the apparent microbial biomass yield when using default parameter values. Based on our analysis, a maintenance coefficient value below 0.2 kJ per carbon mole of microbial biomass per hour should be used for the TBA, corresponding to 0.12 mmol ATP per gram dry weight per hour for dFBA, which strongly deviates from the value of 9.8 kJ Cmol h-1 that has been suggested to apply to all anaerobic microorganisms at 37°C. We hypothesized that a decrease in dilution rate might select taxa with minimized maintenance expenditure. However, no major differences in the dominating taxa between the reactors were observed based on amplicon sequencing of 16S rRNA genes and terminal restriction fragment length polymorphism analysis of mcrA genes. Surprisingly, Methanosaeta dominated over Methanosarcina even at a dilution rate of 0.18 days-1, which contradicts previous model expectations. Furthermore, only 23–49% of the bacterial reads could be assigned to known syntrophic fatty acid oxidizers, indicating that unknown members of this functional group remain to be discovered. In conclusion, microbial maintenance was found to be much lower for acetogenesis and methanogenesis than previously assumed, likely due to the exceptionally low growth rates in anaerobic digestion. This finding might also be relevant for other microbial systems operating at similarly low growth rates.

Hybrid neural modeling framework for simulation and optimization of diauxie-involved fed-batch fermentative succinate production

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.

In this study, we present a hybrid modeling framework that integrates piecewise Partial Least Squares (PLS) regression with Dynamic Flux Balance Analysis (dFBA) to simulate and optimize Chinese Hamster Ovary (CHO) cell fed-batch culture. Twenty-four Ambr15 experiments were conducted to systematically vary feed and inoculum compositions. Time-resolved metabolite, biomass, and Monoclonal antibodies (mAb) concentrations were collected and modeled. The hybrid model achieved high prediction accuracy (Normalized Mean Squared Error (NMSE) < 0.15 for most metabolites) and provided interpretable flux profiles. Multivariate analysis revealed consistent metabolic signatures tied to media formulation, where specific feed–inoculum combinations drove shifts in glycolysis, TCA cycle flux, and nitrogen metabolism. These insights demonstrate the model’s capacity to capture key metabolic adaptations and support data-driven media optimization in CHO cell culture. • A piecewise hybrid model developed and validated for CHO fed-batch culture. • Bioreactor experiments were performed with 24 different media blends. • A balanced production\consumption of key metabolites results in higher mAb titer. • Specific feed–inoculum blends drive shifts in glycolytic and TCA cycle fluxes. • Hybrid model results in good predictions for varying media composition (NMSE<0.15).

Antibiotic‐associated infections with Clostridioides difficile are a severe and often lethal risk for hospitalized patients, and can also affect populations without these classical risk factors. For a rational design of therapeutical concepts, a better knowledge of the metabolism of the pathogen is crucial. Metabolic modeling can provide a simulation of quantitative growth and usage of metabolic pathways, leading to a deeper understanding of the organism. Here, we present an elaborate genome‐scale metabolic model of C. difficile 630Δerm. The model iHD992 includes experimentally determined product and substrate uptake rates and is able to simulate the energy metabolism and quantitative growth of C. difficile. Dynamic flux balance analysis was used for time‐resolved simulations of the quantitative growth in two different media. The model predicts oxidative Stickland reactions and glucose degradation as main sources of energy, while the resulting reduction potential is mostly used for acetogenesis via the Wood–Ljungdahl pathway. Initial modeling experiments did not reproduce the observed growth behavior before the production of large quantities of a previously unknown polysaccharide was detected. Combined genome analysis and laboratory experiments indicated that the polysaccharide is an acetylated glucose polymer. Time‐resolved simulations showed that polysaccharide secretion was coupled to growth even during unstable glucose uptake in minimal medium. This is accomplished by metabolic shifts between active glycolysis and gluconeogenesis which were also observed in laboratory experiments.

Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.

Genetic modifications, such as gene knockout technique, have become mainstream in metabolic engineering to produce desired amount of targeted metabolites through reconstruction of the metabolic networks. The production, however, does not often achieve desirable outcome. To this end, in-silico methods have been applied to predict potential metabolic network response and optimise production. Previous methods working on relational modelling framework, such as OptKnock and OptGene, however, failed at handling its multivariable and multimodal functions optimization algorithms. This paper proposes hybridising bacterial foraging optimizationg algorithm (BFO) and dynamic flux balance analysis (DFBA) to overcome problems in OptKnock and OptGene with a nature-inspired algorithm and also to couple kinematic variables in the model to predict production of succinate in E.coli model. In-silico results showed that by knocking out genes identifed by BFODFBA, production rate of succinate is better as when compared to OptKnock and OptGene.KeywordsBacterial foraging algorithmDynamic flux balance analysisGene knockoutMetabolic engineering Escherichia coli

Streptomyces clavuligerus is the main industrial producer of clavulanic acid (CA), a potent β-lactamase inhibitor. However, the metabolic interplay linking amino acid utilization, nitrogen regulation, and CA biosynthesis remains poorly understood, particularly under complex medium conditions. The genome-scale metabolic model iLT1021 was used to simulate the dynamic metabolism of S. clavuligerus cultivated in GLYCAS-5 medium. Dynamic flux balance analysis (dFBA) captured the transition from primary to secondary metabolism, while robustness analysis and amino acid network topology identified key metabolic control nodes. Integration of dFBA with experimental exometabolome data revealed a clear temporal pattern of amino acid consumption: glutamate, aspartate, and serine were rapidly depleted during exponential growth, whereas histidine and tryptophan were consumed later, coinciding with the onset of CA biosynthesis. Glutamate and glutamine emerged as central nitrogen carriers connecting the α-ketoglutarate and Arg-Orn pathways. Robustness analysis indicated that Arg and Orn enhanced CA fluxes, while Lys and Val had inhibitory effects. Under nitrogen limitation, accumulation of fructose-1,6-bisphosphate and reduced TCA activity reflected a redirection of carbon toward CA precursors. This study provides the first genome-scale dynamic modeling of S. clavuligerus in a complex medium, demonstrating that amino acid availability and their temporal utilization pattern govern the metabolic switch from growth to CA biosynthesis. This integrative framework helps to interpret the metabolic behavior of S. clavuligerus growth in complex medium, offering valuable insights into nutrient regulation and secondary metabolism in filamentous bacteria.