Dynamic Flux Balance Model Research Articles

A coupled metabolic flux/compartmental hydrodynamic model for large-scale aerated bioreactors

Spatial variation of microorganism populations in stirred-tank bioreactors, caused by the interactions of complex multiphase flows and microorganism metabolism, results in undesirable performance characteristics and significant challenges in scale-up activities. In this work, a novel modelling approach is developed to investigate these coupled processes in bioreactors, which involves the integration of a computational fluid dynamics-informed compartmental hydrodynamic and a dynamic flux balance (DFB) model. This coupling poses significant computational challenges especially when dealing with transient scenarios. To tackle these challenges we developed a fast point-location algorithm to solve the DFB model at different bioreactor locations. To validate the presented modelling approach, a binary search tree-based metabolic model for E. coli was developed and integrated with a flow-informed compartmental model of a large-scale four-impeller aerated bioreactor in fed-batch operation. The model results exhibit favorable agreement with the concentration profiles reported in literature for both lab-scale and industrial scale bioreactors. Furthermore, the ability of the approach to deal with transient scenarios permitted to study the effect of oxygen closed loop control responses and the occurrence of oscillatory behaviour which were crucial to explain part of the data.

Biophysical metabolic modeling of complex bacterial colony morphology.

Microbial colony growth is shaped by the physics of biomass propagation and nutrient diffusion, and by the metabolic reactions that organisms activate as a function of the surrounding environment. While microbial colonies have been explored using minimal models of growth and motility, full integration of biomass propagation and metabolism is still lacking. Here, building upon our framework for Computation of Microbial Ecosystems in Time and Space (COMETS), we combine dynamic flux balance modeling of metabolism with collective biomass propagation and demographic fluctuations to provide nuanced simulations of E. coli colonies. Simulations produced realistic colony morphology, consistent with our experiments. They characterize the transition between smooth and furcated colonies and the decay of genetic diversity. Furthermore, we demonstrate that under certain conditions, biomass can accumulate along "metabolic rings" that are reminiscent of coffee-stain rings, but have a completely different origin. Our approach is a key step towards predictive microbial ecosystems modeling.

A Method for tackling multiplicity in dynamic flux balance models by an ellipsoidal reflection operation

Dynamic Flux Balance Models (DFBM) can describe the evolution of metabolites’ concentrations with time by solving a linear programming (LP) problem at each time interval. However, since multiple solutions of the LP commonly exist, different trajectories can be obtained. An interior-point based method (weighted primal–dual method) proposed in a previous study that picks a specific solution from multiple solutions of LP is computationally expensive for a large metabolic network. In this research, we propose an alternative computationally efficient method based on an ellipsoidal reflection mathematical operation. The method is applied to different examples to demonstrate the algorithm and its computational efficiency and then for modeling the fermentation of B. pertussis resulting in excellent computational performance and accurate fitting of experimental dynamic data.

Online estimation using dynamic flux balance model and multiparametric programming

An approach is proposed for online estimation of bounds on metabolite’s concentrations based on limited measurements and Dynamic Flux Balance Models (DFBM) which use linear programming (LP) to model the evolution of metabolites with time. A Weighted primal-dual method to address the multiplicity of solutions of DFBMs is combined with multiparametric nonlinear programming (mpNLP) for set membership estimation. The set membership estimation (SME) approach is used to propagate the uncertainty onto metabolites’ concentrations over time. By only measuring biomass concentration and culture volume, bounds of metabolites’ concentrations can be estimated online by SME during the fermentation. The proposed algorithm is applied to batch and fed-batch fermentation of E. coli.

Set Membership Estimation with Dynamic Flux Balance Models

Dynamic flux balance models (DFBM) are used in this study to infer metabolite concentrations that are difficult to measure online. The concentrations are estimated based on few available measurements. To account for uncertainty in initial conditions the DFBM is converted into a variable structure system based on a multiparametric linear programming (mpLP) where different regions of the state space are described by correspondingly different state space models. Using this variable structure system, a special set membership-based estimation approach is proposed to estimate unmeasured concentrations from few available measurements. For unobservable concentrations, upper and lower bounds are estimated. The proposed set membership estimation was applied to batch fermentation of E. coli based on DFBM.

A method for tackling primal multiplicity of solutions of dynamic flux balance models

A method is presented to tackle primal multiplicity of Dynamic flux balance analysis (DFBA) which is a Linear Programming (LP) based modeling approach that assumes that the cell distributes fluxes such as to maximize a specific biological objective. When the LP problem has multiple optima, the LP solvers usually only report the first optimum that it is reached which may not fit well the experimental data. To tackle this primal multiplicity problem, the weighted primal-dual method with auxiliary parameters is used to calculate a unique time trajectory for a given set of initial conditions. Through tuning of these auxiliary parameters, a unique optimal solution can be obtained and calibrated to fit available experimental data. Beyond its capability to tackle multiplicity, the algorithm is shown to significantly improve the prediction of some metabolites in a case study of the fed-batch fermentation of Bordetella pertussis.

Using high-throughput data and dynamic flux balance modeling techniques to identify points of constraint in xylose utilization in Saccharomyces cerevisiae

Several enzymes and cofactors have been identified as contributing to the slow utilization of xylose by xylose-fermenting strains of Saccharomyces cerevisiae. However, there has been no consensus on which of these possible bottlenecks are the most important to address. A previous strain characterization study from our lab suggested that insufficient NAD+ limits fermentation and may be the most important bottleneck affecting utilization of xylose for the production of ethanol. The development and validation of a genome scale dynamic flux balance model would help to verify the existence and extent of this and other metabolic bottlenecks and suggest solutions to guide future strain development thereby minimizing bottleneck impact on process economics. A dynamic flux balance model was developed to identify bottlenecks in several strains of S. cerevisiae, both with wild-type pentose phosphate pathway expression and with the pathway over expressed. ZWF1 was found to be limiting in the oxidative portion of the pentose phosphate pathway under oxygen replete conditions. This pathway is used to regenerate NADPH. Under oxygen limiting conditions, respiration of xylose was limited by the lack of oxygen as a terminal electron acceptor. Ethanol production was also limited under these conditions due to the inability to balance NAD+/NADH. The model suggests the use of the anaplerotic glyoxylate pathway to improve NAD+/NADH balance, increasing ethanol production by 50% while producing succinate as a coproduct at upwards of 20 g/l. In the production of high value chemicals from biomass, the use of the respiratory metabolism is a waste of feedstock carbon. Bottlenecks previously identified in the oxidative pentose phosphate pathway are currently only relevant under oxygen-replete conditions and cannot impact the partitioning of carbon between the respiratory and fermentative pathways. Focusing future efforts on the non-respiratory balancing of NAD+/NADH, perhaps through the glyoxylate pathway, would improve the economics of ethanol production both directly and through coproduct formation.

Adaptive predictive control of bioprocesses with constraint-based modeling and estimation

Control of biotechnological processes is currently recipe-based with insufficient ability to handle possible uncertainties, which results in suboptimal production processes. To address this problem, model-based optimization and control approaches can be implemented to derive optimal control strategies. However, for reliable performance of model-based control, it is crucial to use flexible and adaptive control strategies which address biological variability while compensating for uncertainties. In this work, we present an approach for adaptive control of a bioprocess based on dynamic flux balance models. A previously developed bilevel approach for bioprocess optimization is implemented inside a model predictive control (MPC) routine. To account for model uncertainties, a moving horizon estimation algorithm is combined with the MPC in order to estimate uncertain parameters of the underlying model online for different metabolic modes. We apply this method to maximize the productivity of a target metabolite under microaerobic conditions by adapting the degree of oxygen-limitation online.

A Dynamic Multi-Tissue Flux Balance Model Captures Carbon and Nitrogen Metabolism and Optimal Resource Partitioning During Arabidopsis Growth.

Plant metabolism is highly adapted in response to its surrounding for acquiring limiting resources. In this study, a dynamic flux balance modeling framework with a multi-tissue (leaf and root) diel genome-scale metabolic model of Arabidopsis thaliana was developed and applied to investigate the reprogramming of plant metabolism through multiple growth stages under different nutrient availability. The framework allowed the modeling of optimal partitioning of resources and biomass in leaf and root over diel phases. A qualitative flux map of carbon and nitrogen metabolism was identified which was consistent across growth phases under both nitrogen rich and limiting conditions. Results from the model simulations suggested distinct metabolic roles in nitrogen metabolism played by enzymes with different cofactor specificities. Moreover, the dynamic model was used to predict the effect of physiological or environmental perturbation on the growth of Arabidopsis leaves and roots.

Optimizing performance of semi-continuous cell culture in an ambr15™ microbioreactor using dynamic flux balance modeling.

The ambr bioreactors are single-use microbioreactors for cell line development and process optimization. With operating conditions for large-scale biopharmaceutical production properly scaled down, microbioreactors such as the ambr15™ can potentially be used to predict the effect of process changes such as modified media or different cell lines. While there have been some recent studies evaluating the ambr15™ technology as a scale-down model for fed-batch operations, little has been reported for semi-continuous or continuous operation. Gassing rates and dilution rates in the ambr15™ were varied in this study to attempt to replicate performance of a perfusion process at the 5L scale. At both scales, changes to metabolite production and consumption, and cell growth rate and therapeutic protein production were measured. Conditions were identified in the ambr15™ bioreactor that produced metabolic shifts and specific metabolic and protein production rates that are characteristic of the corresponding 5L perfusion process. A dynamic flux balance (DFB) model was employed to understand and predict the metabolic changes observed. The DFB model predicted trends observed experimentally, including lower specific glucose consumption and a switch from lactate production to consumption when dissolved CO2 was maintained at higher levels in the broth. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 34:420-431, 2018.

Combining metabolic evolution and systematic fed-batch optimization for efficient single-cell oil production from sugarcane bagasse

We developed in this study an efficient production process of SCO from sugarcane bagasse hydrolysates using Y. lipolytica. We described a dynamic flux balance model strategy based on a genome-scale metabolic model of Y. lipolytica and SCO fermentation kinetics that applied for rational design of optimized fed-batch process with high single cell oil accumulation. Furthermore, metabolic evolution approach with buoyancy screening was implemented for selecting a high lipid producing yeast strain. The efficient conversion process combined model-based fed-batch process design and evolution-based strain optimization enabling high SCO titer of 45 g/L and 0.25 g-SCO/g-glucose yield from hydrolysates, a 6-fold improvement in titer and 1.4-fold improvement in yield over batch wild-type process. Through this combinatorial optimization effort, we demonstrated the cost-effective, lignocellulose-based SCO process that could meet techno-economic feasibility providing a sustainable alternative to vegetative oils for biofuels and oleochemicals synthesis.

Applications of Polynomial Chaos Expansions in optimization and control of bioreactors based on dynamic metabolic flux balance models

This work proposes model based approaches for on-line or off-line economic optimization of batch reactors in the presence of model error (uncertainty). Polynomial Chaos Expansions are used as an effective and computationally efficient tool to propagate the error in model parameters into the optimizations’ cost functions. The computational efficiency of the proposed uncertainty propagation approach is essential for the implementation of the on-line approach that takes into account feedback corrections. The role of feedback, as applied in the on-line formulation, is proved to be instrumental for reducing conservatism of the optimization results. The proposed approaches can serve to design recipes for maximizing productivity in batch, fed-batch or perfusion operation of bioreactors.

Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae.

BackgroundPhotosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process.ResultsIn this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions. The modeling approach is based on dynamic flux balance analysis (DFBA) and includes regulatory models to predict the accumulation of pigment molecules. The accuracy of the model predictions is validated through independent experimental data followed by a subsequent model-based fed-batch optimization. In our experimentally validated fed-batch optimization study we increase biomass and upbeta-carotene density by factors of about 2.5 and 2.1, respectively.ConclusionsThe analysis shows that a model-based approach can be used to develop and significantly improve biotechnological processes for biofuels and pigments.

Nonlinear model predictive control of fed-batch fermentations using dynamic flux balance models

Fed-batch fermentation is an important production technology in the biochemical industry. Using fed-batch Saccharomyces cerevisiae fermentation as a prototypical example, we developed a general methodology for nonlinear model predictive control of fed-batch bioreactors described by dynamic flux balance models. The control objective was to maximize ethanol production at a fixed final batch time by adjusting the glucose feeding rate and the aerobic–anaerobic switching time. Effectiveness of the closed-loop implementation was evaluated by comparing the relative performance of NMPC and the open-loop optimal controller. NMPC was able to compensate for structural errors in the intracellular model and parametric errors in the substrate uptake kinetics and cellular energetics by increasing ethanol production between 8.0% and 14.7% compared with the open-loop operating policy. Minimal degradation in NMPC performance was observed when the biomass, glucose, and ethanol concentration and liquid volume measurements were corrupted with Gaussian white noise. NMPC based on the dynamic flux balance model was shown to improve ethanol production compared to the same NMPC formulation based on a simpler unstructured model. To our knowledge, this study represents the first attempt to utilize a dynamic flux balance model within a nonlinear model-based control scheme.

Dynamic flux balancing elucidates NAD(P)H production as limiting response to furfural inhibition in Saccharomyces cerevisiae.

Achieving efficient and economical lignocellulose-based bioprocess requires a robust organism tolerant to furfural, a major inhibitory compound present in lignocellulosic hydrolysate. The aim of this study was to develop a model that could generate quantitative descriptions of cell metabolism for elucidating the cell's adaptive response to furfural. Such a modelling tool could provide strategies for the design of more robust cells. A dynamic flux balance (dFBA) model of Saccharomyces cerevisiae was created by coupling a kinetic fermentation model with a previously published genome-scale stoichiometric model. The dFBA model was used for studying intracellular and extracellular flux responses to furfural perturbations under steady state and dynamic conditions. The predicted effects of furfural on dynamic flux profiles agreed well with previously published experimental results. The model showed that the yeast cell adjusts its metabolism in response to furfural challenge by increasing fluxes through the pentose phosphate pathway, TCA cycle, and proline and serine biosynthesis in order to meet the high demand of NAD(P)H cofactors. The model described here can be used to aid in systematic optimization of the yeast, as well as of the fermentation process, for efficient lignocellulosic ethanol production.

A dynamic flux balance model and bottleneck identification of glucose, xylose, xylulose co-fermentation in Saccharomyces cerevisiae

A combination of batch fermentations and genome scale flux balance analysis were used to identify and quantify the rate limiting reactions in the xylulose transport and utilization pathway. Xylulose phosphorylation by xylulokinase was identified as limiting in wild type Saccharomyces cerevisiae, but transport became limiting when xylulokinase was upregulated. Further experiments showed xylulose transport through the HXT family of non-specific glucose transporters. A genome scale flux balance model was developed which included an improved variable sugar uptake constraint controlled by HXT expression. Model predictions closely matched experimental xylulose utilization rates suggesting the combination of transport and xylulokinase constraints is sufficient to explain xylulose utilization limitation in S. cerevisiae.

In silico analysis of bioethanol overproduction by genetically modified microorganisms in coculture fermentation.

Lignocellulosic biomass is an attractive sustainable carbon source for fermentative production of bioethanol. In this context, use of microbial consortia consisting of substrate-selective microbes is advantageous as it eliminates the negative impacts of glucose catabolite repression. In this study, a detailed in silico analysis of bioethanol production from glucose-xylose mixtures of various compositions by coculture fermentation of xylose-selective Escherichia coli strain ZSC113 and glucose-selective wild-type Saccharomyces cerevisiae is presented. Dynamic flux balance models based on available genome-scale metabolic networks of the microorganisms have been used to analyze bioethanol production and the maximization of ethanol productivity is addressed by computing optimal aerobic-anaerobic switching times. A set of genetic engineering strategies for ethanol overproduction by E. coli strain ZSC113 have been evaluated for their efficiency in the context of batch coculture process. Finally, simulations are carried out to determine the pairs of genetically modified E. coli strain ZSC113 and S. cerevisiae that significantly enhance ethanol productivity in batch coculture fermentation.

Robust nonlinear predictive control for a bioreactor based on a Dynamic Metabolic Flux Balance model

A robust economic nonlinear predictive controller is proposed for batch biochemical processes. The algorithm is based on a dynamic metabolic flux modeling (DFBM) approach that has gained increasing acceptance in the pharmaceutical industry. Since DFBM models are formulated as LP (linear programming) problems, the corresponding robust economic optimal control solution results in a bi-level optimization consisting of maximizing an economic objective subject to the LP based model. To address robustness the DFBM model is represented by using a Polynomial Chaos Expansion model which allows quick propagation of the uncertainty in parameters onto the cost function to be optimized by the controller. The performance of the robust algorithm is applied to E.coli batch fermentation and it is found to be computationally efficient and superior to the nominal (non-robust) predictive controller.

In silico analysis of bioethanol production from glucose/xylose mixtures during fed-batch fermentation of co-culture and mono-culture systems

This study presents a detailed in silico analysis of bioethanol production from glucose/xylose mixtures of various compositions by fed-batch co-culture and mono-culture fermentation of specialized microbes. The mono-culture consists of recombinant Saccharomyces cerevisise that can metabolize both hexose and pentose sugars while the co-culture system consists of substrate-selective microbes. Dynamic flux balance models based on available genome-scale reconstructions of the microorganisms have been used to analyze bioethanol production in fed-batch culture with constant feed rates and the maximization of ethanol productivity is addressed by computing optimal aerobic-anaerobic switching times. The simulation results clearly point to the superior performance of fed-batch fermentation of microbial co-culture against fed-batch fermentation of mono-culture for bioethanol production from glucose/xylose mixtures. A set of potential genetic engineering strategies for enhancement of S. cerevisiae and Escherichia coli strains performance have been identified. Such in silico predictions using genome-scale models provide valuable guidance for conducting in vivo metabolic engineering experiments.

Dynamic flux balance analysis of batch fermentation: effect of genetic manipulations on ethanol production

In silico optimization of bioethanol production from lignocellulosic biomasses is investigated by combining process systems engineering approach and systems biology approach. Lignocellulosic biomass is an attractive sustainable carbon source for fermentative production of bioethanol. For enhanced ethanol production, metabolic engineering of wild-type strains-that can metabolize both hexose and pentose sugars or microbial consortia consisting of substrate-selective microbes-may be advantageous. This study presents a detailed in silico analysis of bioethanol production from glucose-xylose mixtures of various compositions by batch mono-culture and co-culture fermentation of specialized microbes. Dynamic flux balance models based on available genome-scale reconstructions of the microorganisms have been used to analyze bioethanol production, and the maximization of ethanol productivity is addressed by computing optimal aerobic-anaerobic switching times. Effects of ten metabolic engineering strategies that have been suggested in the literature for ethanol overproduction, have been evaluated for their efficiency in enhancing the ethanol productivity in the context of batch mono-culture and co-culture processes.