Dynamic Metabolic Model Research Articles

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.

Identifying Key In Silico Knockout for Enhancement of Limonene Yield Through Dynamic Metabolic Modelling.

Living cells display dynamic and complex behaviors. To understand their response and to infer novel insights not possible with traditional reductionist approaches, over the last few decades various computational modelling methodologies have been developed. In this chapter, we focus on modelling the dynamic metabolic response, using linear and nonlinear ordinary differential equations, of an engineered Escherichia coli MG1655 strain with plasmid pJBEI-6409 that produces limonene. We show the systems biology steps involved from collecting time-series data of living cells, to dynamic model creation and fitting the model with experimental responses using COPASI software.

CHOmpact: A reduced metabolic model of Chinese hamster ovary cells with enhanced interpretability.

Metabolic modeling has emerged as a key tool for the characterization of biopharmaceutical cell culture processes. Metabolic models have also been instrumental in identifying genetic engineering targets and developing feeding strategies that optimize the growth and productivity of Chinese hamster ovary (CHO) cells. Despite their success, metabolic models of CHO cells still present considerable challenges. Genome-scale metabolic models (GeMs) of CHO cells are very large (>6000 reactions) and are difficult to constrain to yield physiologically consistent flux distributions. The large scale of GeMs also makes the interpretation of their outputs difficult. To address these challenges, we have developed CHOmpact, a reduced metabolic network that encompasses 101 metabolites linked through 144 reactions. Our compact reaction network allows us to deploy robust, nonlinear optimization and ensure that the computed flux distributions are physiologically consistent. Furthermore, our CHOmpact model delivers enhanced interpretability of simulation results and has allowed us to identify the mechanisms governing shifts in the anaplerotic consumption of asparagine and glutamate as well as an important mechanism of ammonia detoxification within mitochondria. CHOmpact, thus, addresses key challenges of large-scale metabolic models and will serve as a platform to develop dynamic metabolic models for the control and optimization of biopharmaceutical cell culture processes.

Towards Autonomous Process Control—Digital Twin for HIV-Gag VLP Production in HEK293 Cells Using a Dynamic Metabolic Model

Despite intensive research over the last three decades, it has not yet been possible to bring an effective vaccine against human immunodeficiency virus (HIV) and the resulting acquired immunodeficiency syndrome (AIDS) to market. Virus-like particles (VLP) are a promising approach for efficient and effective vaccination and could play an important role in the fight against HIV. For example, HEK293 (human embryo kidney) cells can be used to produce virus-like particles. In this context, given the quality-by-design (QbD) concept for manufacturing, a digital twin is of great importance for the production of HIV-Gag-formed VLPs. In this work, a dynamic metabolic model for the production of HIV-Gag VLPs was developed and validated. The model can represent the VLP production as well as the consumption or formation of all important substrates and metabolites. Thus, in combination with already described process analytical technology (PAT) methods, the final step towards the implementation of a digital twin for process development and design, as well as process automation, was completed.

Towards Autonomous Process Control – Digital Twin for Antibody and VLP Manufacturing Using a Dynamic Metabolic Model

Towards Autonomous Process Control – Digital Twin for Antibody and VLP Manufacturing Using a Dynamic Metabolic Model

Towards Autonomous Process Control—Digital Twin for CHO Cell-Based Antibody Manufacturing Using a Dynamic Metabolic Model

The development of new biologics is becoming more challenging due to global competition and increased requirements for process understanding and assured quality in regulatory approval. As a result, there is a need for predictive, mechanistic process models. These reduce the resources and time required in process development, generating understanding, expanding the possible operating space, and providing the basis for a digital twin for automated process control. Monoclonal antibodies are an important representative of industrially produced biologics that can be used for a wide range of applications. In this work, the validation of a mechanistic process model with respect to sensitivity, as well as accuracy and precision, is presented. For the investigated process conditions, the concentration of glycine, phenylalanine, tyrosine, and glutamine have been identified as significant influencing factors for product formation via statistical evaluation. Cell growth is, under the investigated process conditions, significantly dependent on the concentration of glucose within the investigated design space. Other significant amino acids were identified. A Monte Carlo simulation was used to simulate the cultivation run with an optimized medium resulting from the sensitivity analysis. The precision of the model was shown to have a 95% confidence interval. The model shown here includes the implementation of cell death in addition to models described in the literature.

Diverse classes of constraints enable broader applicability of a linear programming-based dynamic metabolic modeling framework

Current metabolic modeling tools suffer from a variety of limitations, from scalability to simplifying assumptions, that preclude their use in many applications. We recently created a modeling framework, Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), that addresses a key gap: capturing metabolite dynamics and regulation while retaining a potentially scalable linear programming structure. Key to this framework’s success are the linear kinetics and regulatory constraints imposed on the system. However, while the linearity of these constraints reduces computational complexity, it may not accurately capture the behavior of many biochemical systems. Here, we developed three new classes of LK-DFBA constraints to better model interactions between metabolites and the reactions they regulate. We tested these new approaches on several synthetic and biological systems, and also performed the first-ever comparison of LK-DFBA predictions to experimental data. We found that no single constraint approach was optimal across all systems examined, and systems with the same topological structure but different parameters were often best modeled by different types of constraints. However, we did find that when genetic perturbations were implemented in the systems, the optimal constraint approach typically remained the same as for the wild-type regardless of the model topology or parameterization, indicating that just a single wild-type dataset could allow identification of the ideal constraint to enable model predictivity for a given system. These results suggest that the availability of multiple constraint approaches will allow LK-DFBA to model a wider range of metabolic systems.

An MIQP framework for metabolic pathways optimisation and dynamic flux analysis

Dynamic flux analysis methods have been widely used for deciphering complex metabolic fluxes transients. However, many of them require frequent experimental measurements and are ineffective in dealing with under-determined metabolic reaction networks. In this study, we addressed these challenges by (i) integrating a macroscale kinetic model with its dynamic metabolic flux model to enable flux simulation over the entire time course for batch operation, and (ii) constructing a single-level mixed-integer quadratic program (MIQP) to automatically identify the shortest metabolic pathways from substrate inflow to biosynthesis of biomass and desired bioproducts. To demonstrate the advantages of the proposed framework, a X. dendrorhous fermentation process for astaxanthin production was utilised as the case study. It is found that the current framework is able to efficiently identify essential pathways and reduce the size of the original metabolic network by 70% with negligible computational cost. Furthermore, the modelling consistency, robustness, and limitation of this framework were thoroughly investigated. This research provides a new avenue for efficient in-silico design, analysis, and gene knockout of microbial strains for bioproduct synthesis.

Exploring dynamic metabolomics data with multiway data analysis: a simulation study

BackgroundAnalysis of dynamic metabolomics data holds the promise to improve our understanding of underlying mechanisms in metabolism. For example, it may detect changes in metabolism due to the onset of a disease. Dynamic or time-resolved metabolomics data can be arranged as a three-way array with entries organized according to a subjects mode, a metabolites mode and a time mode. While such time-evolving multiway data sets are increasingly collected, revealing the underlying mechanisms and their dynamics from such data remains challenging. For such data, one of the complexities is the presence of a superposition of several sources of variation: induced variation (due to experimental conditions or inborn errors), individual variation, and measurement error. Multiway data analysis (also known as tensor factorizations) has been successfully used in data mining to find the underlying patterns in multiway data. To explore the performance of multiway data analysis methods in terms of revealing the underlying mechanisms in dynamic metabolomics data, simulated data with known ground truth can be studied.ResultsWe focus on simulated data arising from different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, and a human cholesterol model. We generate data with induced variation as well as individual variation. Systematic experiments are performed to demonstrate the advantages and limitations of multiway data analysis in analyzing such dynamic metabolomics data and their capacity to disentangle the different sources of variations. We choose to use simulations since we want to understand the capability of multiway data analysis methods which is facilitated by knowing the ground truth.ConclusionOur numerical experiments demonstrate that despite the increasing complexity of the studied dynamic metabolic models, tensor factorization methods CANDECOMP/PARAFAC(CP) and Parallel Profiles with Linear Dependences (Paralind) can disentangle the sources of variations and thereby reveal the underlying mechanisms and their dynamics.

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

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. 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. 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. 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.

Selection of a Minimal Suboptimal Set of EFMs for Dynamic Metabolic Modelling

Mathematical modelling supports the understanding of basic biological mechanisms and is the basis for bioprocess simulation, prediction, control and optimization. Dynamic macroscopic models can be derived from the concept of elementary flux modes (EFMs), which provide a comprehensive representation of all possible pathways through a metabolic network. As the number of EFMs drastically increases with the size of the metabolic network, a procedure to reduce the number of EFMs and select the most informative ones is required. For this purpose, this study proposes a methodology to select a minimal suboptimal set of elementary flux modes allowing the development of reduced macroscopic models. The algorithm is divided into two steps. First, the concept behind the cosine-similarity algorithm is extended for a large number of EFMs to cut the initial set by removing all the collinear modes. Next, the algorithm is used to extract only the most informative modes from the reduced set by means of a series of optimization problems. The algorithm performance is illustrated with datasets from hybridoma cultures in batch and perfusion modes, and two metabolic networks with different levels of description.

Evaluation of Single Sample Network Inference Methods for Metabolomics-Based Systems Medicine.

Networks and network analyses are fundamental tools of systems biology. Networks are built by inferring pair-wise relationships among biological entities from a large number of samples such that subject-specific information is lost. The possibility of constructing these sample (individual)-specific networks from single molecular profiles might offer new insights in systems and personalized medicine and as a consequence is attracting more and more research interest. In this study, we evaluated and compared LIONESS (Linear Interpolation to Obtain Network Estimates for Single Samples) and ssPCC (single sample network based on Pearson correlation) in the metabolomics context of metabolite–metabolite association networks. We illustrated and explored the characteristics of these two methods on (i) simulated data, (ii) data generated from a dynamic metabolic model to simulate real-life observed metabolite concentration profiles, and (iii) 22 metabolomic data sets and (iv) we applied single sample network inference to a study case pertaining to the investigation of necrotizing soft tissue infections to show how these methods can be applied in metabolomics. We also proposed some adaptations of the methods that can be used for data exploration. Overall, despite some limitations, we found single sample networks to be a promising tool for the analysis of metabolomics data.

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

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

Differential suitability of reactive oxygen species and the role of glutathione in regulating paradoxical behavior in gliomas: A mathematical perspective.

Manipulative strategies of ROS in cancer are often exhibited as changes in the redox and thiol ratio of the cells. Cellular responses to oxidative insults are generated in response to these changes which are triggered due to the rerouting of the metabolic framework to maintain survival under stress. However, mechanisms of these metabolic re-routing are not clearly understood and remained debatable. In the present work, we have designed a context-based dynamic metabolic model to establish that the coordinated functioning of glutathione peroxidase (GTHP), glutathione oxidoreductase (GTHO) and NADPH oxidase (NOX) is crucial in determining cancerous transformation, specifically in gliomas. Further, we propose that the puzzling duality of ROS (represented by changes in h2o2 in the present model) in exhibiting varying cellular fates can be determined by considering simultaneous changes in nadph/nadp+ and gsh/gssg that occur during the reprogramming of metabolic reactions. This will be helpful in determining the pro-apoptotic or anti-apoptotic fate of gliomas and can be useful in designing effective pro-oxidant and/or anti-oxidant therapeutic approaches against gliomas.

Robust estimation and economic predictive control for dynamic metabolic flux systems under probabilistic uncertainty

A novel formulation is proposed for propagating parametric uncertainty for Dynamic Metabolic Flux models involving the solution of Linear Programming (LP) problems. The propagation approach is based on the calculation of all possible active sets of constraints at each time interval. Then, a tree-based approach is used to propagate the uncertainty onto the worst case of each active set where each branch of the tree corresponds to an active set of constraints. Each branch is assigned a relative probability according to the relative hypervolume occupied by the active set solutions in the parameter space. The approach is applied for the robust estimation of the Ecoli fermentation process and for the design of a robust economic predictive controller for this system. The proposed method is found to be significantly more efficient as compared with other uncertainty propagation approaches such as Monte Carlo (MC) simulations.

Dynamic metabolic resource allocation based on the maximum entropy principle.

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

On the Use of Correlation and MI as a Measure of Metabolite-Metabolite Association for Network Differential Connectivity Analysis.

Metabolite differential connectivity analysis has been successful in investigating potential molecular mechanisms underlying different conditions in biological systems. Correlation and Mutual Information (MI) are two of the most common measures to quantify association and for building metabolite—metabolite association networks and to calculate differential connectivity. In this study, we investigated the performance of correlation and MI to identify significantly differentially connected metabolites. These association measures were compared on (i) 23 publicly available metabolomic data sets and 7 data sets from other fields, (ii) simulated data with known correlation structures, and (iii) data generated using a dynamic metabolic model to simulate real-life observed metabolite concentration profiles. In all cases, we found more differentially connected metabolites when using correlation indices as a measure for association than MI. We also observed that different MI estimation algorithms resulted in difference in performance when applied to data generated using a dynamic model. We concluded that there is no significant benefit in using MI as a replacement for standard Pearson’s or Spearman’s correlation when the application is to quantify and detect differentially connected metabolites.

Dynamic Modeling of CHO Cell Metabolism Using the Hybrid Cybernetic Approach With a Novel Elementary Mode Analysis Strategy.

Chinese hamster ovary (CHO) cell culture has a major importance on the production of biopharmaceuticals, including recombinant therapeutic proteins such as monoclonal antibodies (MAb). Mathematical modeling of biological systems can successfully assess metabolism complexity while providing logical and systematic methods for relevant genetic target and culture parameter identification toward cell growth and productivity improvements. Most modeling approaches on CHO cells have been performed under stationary constraints, and only a few dynamic models have been presented on simplified reaction sets, due to substantial overparameterization problems. The hybrid cybernetic modeling (HCM) approach has been recently used to describe the dynamic behavior by incorporating regulation between different metabolic states by elementary mode participation control, with sets of equations evaluated by objective functions. However, as metabolic networks evaluated are constructed toward a genomic scale, and cell compartmentalization is considered, identification of the active set becomes more difficult as EM number exponentially grows. Thus, the development of robust approaches for EM active set selection and analysis with smaller computational requirements is required to impulse the use of cybernetic modeling on larger up to genome-scale networks. In this report, a novel elementary mode selection strategy, based on a polar representation of the convex solution space is presented and coupled to a cybernetic approach to model the dynamic physiologic and metabolic behavior of CHO-S cell cultures. The proposed Polar Space Yield Analysis (PSYA) was compared to other reported elementary mode selection approaches derived from Common Metabolic Objective Analysis (CMOA) used in Flux Balance Analysis (FBA), Yield Space Analysis (YSA), and Lumped Yield Space Analysis (LYSA). For this purpose, exponential growth phase dynamic metabolic models were calculated using kinetic rate equations based on previously modeled growth parameters. Finally, complete culture dynamic metabolic flux models were constructed using the HCM approach with selected elementary mode sets. The yield space elementary mode- and the polar space elementary mode- hybrid cybernetic models presented the best fits and performances. Also, a flux reaction perturbation prediction approach based on the polar yield solution space resulted useful for metabolic network flux distribution capability analysis and identification of potential genetic modifications targets.

Metabolic pathway analysis and dynamic macroscopic model development for lovastatin production by Monascus purpureus using metabolic footprinting concept

Understanding and modeling of the metabolic pathway of a cell by probing the fraction of extracellular metabolites is gaining much interest in biological reactions. This communication deals with metabolic footprinting technique to understand the effect of static- and shake-culture conditions on the production of lovastatin by Monascus purpureus by probing the predominant exometabolites. A strong glycolytic flux pattern was observed in the shake culture of M. purpureus that resulted in the accumulation of tricarboxylic acids such as, citric acid, succinic acid, and oxalic acid, apart from glycerol and ethanol. Interestingly, those exometabolites were most probably utilized for enhanced production of lovastatin in shake culture after 10 days of fermentation. This suggests a correlation with the higher production of lovastatin in shake culture compared to that of in static-culture. The predominant metabolic network was developed from metabolic footprinting technique. Metabolic flux analysis was performed to check the consistency of the proposed metabolic cascade. A reduced dynamic metabolic model was developed from eight elementary macro-reactions. Predicted specific substrate utilization and product excretion rates have also been correlated well with the experimental observations, which validate the proposed metabolic pathway developed from metabolic footprinting data.

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

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.