Dynamic flux balance analysis of diauxic growth in Escherichia coli

A systems-wide understanding of photosynthetic acclimation in algae and higher plants

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology.

Emergence of microbial diversity due to cross-feeding interactions in a spatial model of gut microbial metabolism

Background

The human gut contains approximately 10¹⁴ bacteria, belonging to hundreds of different species. Together, these microbial species form a complex food web that can break down nutrient sources that our own digestive enzymes cannot handle, including complex polysaccharides, producing short chain fatty acids and additional metabolites, e.g., vitamin K. Microbial diversity is important for colonic health: Changes in the composition of the microbiota have been associated with inflammatory bowel disease, diabetes, obesity and Crohn’s disease, and make the microbiota more vulnerable to infestation by harmful species, e.g., Clostridium difficile. To get a grip on the controlling factors of microbial diversity in the gut, we here propose a multi-scale, spatiotemporal dynamic flux-balance analysis model to study the emergence of metabolic diversity in a spatial gut-like, tubular environment. The model features genome-scale metabolic models (GEM) of microbial populations, resource sharing via extracellular metabolites, and spatial population dynamics and evolution.

Results

In this model, cross-feeding interactions emerge readily, despite the species’ ability to metabolize sugars autonomously. Interestingly, the community requires cross-feeding for producing a realistic set of short-chain fatty acids from an input of glucose, If we let the composition of the microbial subpopulations change during invasion of adjacent space, a complex and stratified microbiota evolves, with subspecies specializing on cross-feeding interactions via a mechanism of compensated trait loss. The microbial diversity and stratification collapse if the flux through the gut is enhanced to mimic diarrhea.

Conclusions

In conclusion, this in silico model is a helpful tool in systems biology to predict and explain the controlling factors of microbial diversity in the gut. It can be extended to include, e.g., complex nutrient sources, and host-microbiota interactions via the intestinal wall.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0430-4) contains supplementary material, which is available to authorized users.

Dynamic flux balance analysis with nonlinear objective function

Dynamic flux balance analysis (DFBA) extends flux balance analysis and enables the combined simulation of both intracellular and extracellular environments of microbial cultivation processes. A DFBA model contains two coupled parts, a dynamic part at the upper level (extracellular environment) and an optimization part at the lower level (intracellular environment). Both parts are coupled through substrate uptake and product secretion rates. This work proposes a Karush-Kuhn-Tucker condition based solution approach for DFBA models, which have a nonlinear objective function in the lower-level part. To solve this class of DFBA models an extreme-ray-based reformulation is proposed to ensure certain regularity of the lower-level optimization problem. The method is introduced by utilizing two simple example networks and then applied to a realistic model of central carbon metabolism of wild-type Corynebacterium glutamicum.

Community metabolic modeling approaches to understanding the gut microbiome: Bridging biochemistry and ecology

Interest in the human microbiome is at an all time high. The number of human microbiome studies is growing exponentially, as are reported associations between microbial communities and disease. However, we have not been able to translate the ever-growing amount of microbiome sequence data into better health. To do this, we need a practical means of transforming a disease-associated microbiome into a health-associated microbiome. This will require a framework that can be used to generate predictions about community dynamics within the microbiome under different conditions, predictions that can be tested and validated. In this review, using the gut microbiome to illustrate, we describe two classes of model that are currently being used to generate predictions about microbial community dynamics: ecological models and metabolic models. We outline the strengths and weaknesses of each approach and discuss the insights into the gut microbiome that have emerged from modeling thus far. We then argue that the two approaches can be combined to yield a community metabolic model, which will supply the framework needed to move from high-throughput omics data to testable predictions about how prebiotic, probiotic, and nutritional interventions affect the microbiome. We are confident that with a suitable model, researchers and clinicians will be able to harness the stream of sequence data and begin designing strategies to make targeted alterations to the microbiome and improve health.

Model-based quantification of metabolic interactions from dynamic microbial-community data

An important challenge in microbial ecology is to infer metabolic-exchange fluxes between growing microbial species from community-level data, concerning species abundances and metabolite concentrations. Here we apply a model-based approach to integrate such experimental data and thereby infer metabolic-exchange fluxes. We designed a synthetic anaerobic co-culture of Clostridium acetobutylicum and Wolinella succinogenes that interact via interspecies hydrogen transfer and applied different environmental conditions for which we expected the metabolic-exchange rates to change. We used stoichiometric models of the metabolism of the two microorganisms that represents our current physiological understanding and found that this understanding - the model - is sufficient to infer the identity and magnitude of the metabolic-exchange fluxes and it suggested unexpected interactions. Where the model could not fit all experimental data, it indicates specific requirement for further physiological studies. We show that the nitrogen source influences the rate of interspecies hydrogen transfer in the co-culture. Additionally, the model can predict the intracellular fluxes and optimal metabolic exchange rates, which can point to engineering strategies. This study therefore offers a realistic illustration of the strengths and weaknesses of model-based integration of heterogenous data that makes inference of metabolic-exchange fluxes possible from community-level experimental data.

Clostridioides difficile 630Δerm in silico and in vivo - quantitative growth and extensive polysaccharide secretion

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.

Dynamic genome-scale metabolic modeling of the yeast Pichia pastoris

BACKGROUND

Pichia pastoris shows physiological advantages in producing recombinant proteins, compared to other commonly used cell factories. This yeast is mostly grown in dynamic cultivation systems, where the cell's environment is continuously changing and many variables influence process productivity. In this context, a model capable of explaining and predicting cell behavior for the rational design of bioprocesses is highly desirable. Currently, there are five genome-scale metabolic reconstructions of P. pastoris which have been used to predict extracellular cell behavior in stationary conditions.

RESULTS

In this work, we assembled a dynamic genome-scale metabolic model for glucose-limited, aerobic cultivations of Pichia pastoris. Starting from an initial model structure for batch and fed-batch cultures, we performed pre/post regression diagnostics to ensure that model parameters were identifiable, significant and sensitive. Once identified, the non-relevant ones were iteratively fixed until a priori robust modeling structures were found for each type of cultivation. Next, the robustness of these reduced structures was confirmed by calibrating the model with new datasets, where no sensitivity, identifiability or significance problems appeared in their parameters. Afterwards, the model was validated for the prediction of batch and fed-batch dynamics in the studied conditions. Lastly, the model was employed as a case study to analyze the metabolic flux distribution of a fed-batch culture and to unravel genetic and process engineering strategies to improve the production of recombinant Human Serum Albumin (HSA). Simulation of single knock-outs indicated that deviation of carbon towards cysteine and tryptophan formation improves HSA production. The deletion of methylene tetrahydrofolate dehydrogenase could increase the HSA volumetric productivity by 630%. Moreover, given specific bioprocess limitations and strain characteristics, the model suggests that implementation of a decreasing specific growth rate during the feed phase of a fed-batch culture results in a 25% increase of the volumetric productivity of the protein.

CONCLUSION

In this work, we formulated a dynamic genome scale metabolic model of Pichia pastoris that yields realistic metabolic flux distributions throughout dynamic cultivations. The model can be calibrated with experimental data to rationally propose genetic and process engineering strategies to improve the performance of a P. pastoris strain of interest.

Wine microbiome: A dynamic world of microbial interactions

Most fermented products are generated by a mixture of microbes. These microbial consortia perform various biological activities responsible for the nutritional, hygienic, and aromatic qualities of the product. Wine is no exception. Substantial yeast and bacterial biodiversity is observed on grapes, and in both must and wine. The diverse microorganisms present interact throughout the winemaking process. The interactions modulate the hygienic and sensorial properties of the wine. Many studies have been conducted to elucidate the nature of these interactions, with the aim of establishing better control of the two fermentations occurring during wine processing. However, wine is a very complex medium making such studies difficult. In this review, we present the current state of research on microbial interactions in wines. We consider the different kinds of interactions between different microorganisms together with the consequences of these interactions. We underline the major challenges to obtaining a better understanding of how microbes interact. Finally, strategies and methodologies that may help unravel microbe interactions in wine are suggested.

Metabolic network modeling with model organisms

Flux balance analysis (FBA) with genome-scale metabolic network models (GSMNM) allows systems level predictions of metabolism in a variety of organisms. Different types of predictions with different accuracy levels can be made depending on the applied experimental constraints ranging from measurement of exchange fluxes to the integration of gene expression data. Metabolic network modeling with model organisms has pioneered method development in this field. In addition, model organism GSMNMs are useful for basic understanding of metabolism, and in the case of animal models, for the study of metabolic human diseases. Here, we discuss GSMNMs of most highly used model organisms with the emphasis on recent reconstructions.

Efficient estimation of the maximum metabolic productivity of batch systems

BACKGROUND

Production of chemicals from engineered organisms in a batch culture involves an inherent trade-off between productivity, yield, and titer. Existing strategies for strain design typically focus on designing mutations that achieve the highest yield possible while maintaining growth viability. While these methods are computationally tractable, an optimum productivity could be achieved by a dynamic strategy in which the intracellular division of resources is permitted to change with time. New methods for the design and implementation of dynamic microbial processes, both computational and experimental, have therefore been explored to maximize productivity. However, solving for the optimal metabolic behavior under the assumption that all fluxes in the cell are free to vary is a challenging numerical task. Previous studies have therefore typically focused on simpler strategies that are more feasible to implement in practice, such as the time-dependent control of a single flux or control variable.

RESULTS

This work presents an efficient method for the calculation of a maximum theoretical productivity of a batch culture system using a dynamic optimization framework. The proposed method follows traditional assumptions of dynamic flux balance analysis: first, that internal metabolite fluxes are governed by a pseudo-steady state, and secondly that external metabolite fluxes are dynamically bounded. The optimization is achieved via collocation on finite elements, and accounts explicitly for an arbitrary number of flux changes. The method can be further extended to calculate the complete Pareto surface of productivity as a function of yield. We apply this method to succinate production in two engineered microbial hosts, Escherichia coli and Actinobacillus succinogenes, and demonstrate that maximum productivities can be more than doubled under dynamic control regimes.

CONCLUSIONS

The maximum theoretical yield is a measure that is well established in the metabolic engineering literature and whose use helps guide strain and pathway selection. We present a robust, efficient method to calculate the maximum theoretical productivity: a metric that will similarly help guide and evaluate the development of dynamic microbial bioconversions. Our results demonstrate that nearly optimal yields and productivities can be achieved with only two discrete flux stages, indicating that near-theoretical productivities might be achievable in practice.

The use of genome-scale metabolic network reconstruction to predict fluxes and equilibrium composition of N-fixing versus C-fixing cells in a diazotrophic cyanobacterium, Trichodesmium erythraeum

Background

Computational, genome based predictions of organism phenotypes has enhanced the ability to investigate the biological phenomena that help organisms survive and respond to their environments. In this study, we have created the first genome-scale metabolic network reconstruction of the nitrogen fixing cyanobacterium T. erythraeum and used genome-scale modeling approaches to investigate carbon and nitrogen fluxes as well as growth and equilibrium population composition.

Results

We created a genome-scale reconstruction of T. erythraeum with 971 reactions, 986 metabolites, and 647 unique genes. We then used data from previous studies as well as our own laboratory data to establish a biomass equation and two distinct submodels that correspond to the two cell types formed by T. erythraeum. We then use flux balance analysis and flux variability analysis to generate predictions for how metabolism is distributed to account for the unique productivity of T. erythraeum. Finally, we used in situ data to constrain the model, infer time dependent population compositions and metabolite production using dynamic Flux Balance Analysis. We find that our model predicts equilibrium compositions similar to laboratory measurements, approximately 15.5% diazotrophs for our model versus 10-20% diazotrophs reported in literature. We also found that equilibrium was the most efficient mode of growth and that equilibrium was stoichiometrically mediated. Moreover, the model predicts that nitrogen leakage is an essential condition of optimality for T. erythraeum; cells leak approximately 29.4% total fixed nitrogen when growing at the optimal growth rate, which agrees with values observed in situ.

Conclusion

The genome-metabolic network reconstruction allows us to use constraints based modeling approaches to predict growth and optimal cellular composition in T. erythraeum colonies. Our predictions match both in situ and laboratory data, indicating that stoichiometry of metabolic reactions plays a large role in the differentiation and composition of different cell types. In order to realize the full potential of the model, advance modeling techniques which account for interactions between colonies, the environment and surrounding species need to be developed.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0383-z) contains supplementary material, which is available to authorized users.

Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.

Can microbes compete with cows for sustainable protein production - A feasibility study on high quality protein

An increasing population and their increased demand for high-protein diets will require dramatic changes in the food industry, as limited resources and environmental issues will make animal derived foods and proteins, gradually more unsustainable to produce. To explore alternatives to animal derived proteins, an economic model was built around the genome-scale metabolic network of E. coli to study the feasibility of recombinant protein production as a food source. Using a novel model, we predicted which microbial production strategies are optimal for economic return, by capturing the tradeoff between the market prices of substrates, product output and the efficiency of microbial production. A case study with the food protein, Bovine Alpha Lactalbumin was made to evaluate the upstream economic feasibilities. Simulations with different substrate profiles at maximum productivity were used to explore the feasibility of recombinant Bovine Alpha Lactalbumin production coupled with market prices of utilized materials. We found that recombinant protein production could be a feasible food source and an alternative to traditional sources.

Genome scale metabolic modeling of cancer

Cancer cells reprogram metabolism to support rapid proliferation and survival. Energy metabolism is particularly important for growth and genes encoding enzymes involved in energy metabolism are frequently altered in cancer cells. A genome scale metabolic model (GEM) is a mathematical formalization of metabolism which allows simulation and hypotheses testing of metabolic strategies. It has successfully been applied to many microorganisms and is now used to study cancer metabolism. Generic models of human metabolism have been reconstructed based on the existence of metabolic genes in the human genome. Cancer specific models of metabolism have also been generated by reducing the number of reactions in the generic model based on high throughput expression data, e.g. transcriptomics and proteomics. Targets for drugs and bio markers for diagnostics have been identified using these models. They have also been used as scaffolds for analysis of high throughput data to allow mechanistic interpretation of changes in expression. Finally, GEMs allow quantitative flux predictions using flux balance analysis (FBA). Here we critically review the requirements for successful FBA simulations of cancer cells and discuss the symmetry between the methods used for modeling of microbial and cancer metabolism. GEMs have great potential for translational research on cancer and will therefore become of increasing importance in the future.

Identification of active constraints in dynamic flux balance analysis

This study deals with the calibration of dynamic metabolic flux models that are formulated as the maximization of an objective subject to constraints. Two approaches were applied for identifying the constraints from data. In the first approach a minimal active number of limiting constraints is found based on data that are assumed to be bounded within sets whereas, in the second approach, the limiting constraints are found based on parametric sensitivity analysis. The ability of these approaches to finding the active limiting constraints was verified through their application to two case studies: an in-silico (simulated) data-based study describing the growth of E. coli and an experimental data-based study for Bordetella pertussis (B. pertussis). © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 33:26-36, 2017.

A multi-scale, multi-disciplinary approach for assessing the technological, economic and environmental performance of bio-based chemicals

In recent years, bio-based chemicals have gained interest as a renewable alternative to petrochemicals. However, there is a significant need to assess the technological, biological, economic and environmental feasibility of bio-based chemicals, particularly during the early research phase. Recently, the Multi-scale framework for Sustainable Industrial Chemicals (MuSIC) was introduced to address this issue by integrating modelling approaches at different scales ranging from cellular to ecological scales. This framework can be further extended by incorporating modelling of the petrochemical value chain and the de novo prediction of metabolic pathways connecting existing host metabolism to desirable chemical products. This multi-scale, multi-disciplinary framework for quantitative assessment of bio-based chemicals will play a vital role in supporting engineering, strategy and policy decisions as we progress towards a sustainable chemical industry.

Metabolic modeling of a chronic wound biofilm consortium predicts spatial partitioning of bacterial species

Background

Chronic wounds are often colonized by consortia comprised of different bacterial species growing as biofilms on a complex mixture of wound exudate. Bacteria growing in biofilms exhibit phenotypes distinct from planktonic growth, often rendering the application of antibacterial compounds ineffective. Computational modeling represents a complementary tool to experimentation for generating fundamental knowledge and developing more effective treatment strategies for chronic wound biofilm consortia.

Results

We developed spatiotemporal models to investigate the multispecies metabolism of a biofilm consortium comprised of two common chronic wound isolates: the aerobe Pseudomonas aeruginosa and the facultative anaerobe Staphylococcus aureus. By combining genome-scale metabolic reconstructions with partial differential equations for metabolite diffusion, the models were able to provide both temporal and spatial predictions with genome-scale resolution. The models were used to analyze the metabolic differences between single species and two species biofilms and to demonstrate the tendency of the two bacteria to spatially partition in the multispecies biofilm as observed experimentally. Nutrient gradients imposed by supplying glucose at the bottom and oxygen at the top of the biofilm induced spatial partitioning of the two species, with S. aureus most concentrated in the anaerobic region and P. aeruginosa present only in the aerobic region. The two species system was predicted to support a maximum biofilm thickness much greater than P. aeruginosa alone but slightly less than S. aureus alone, suggesting an antagonistic metabolic effect of P. aeruginosa on S. aureus. When each species was allowed to enhance its growth through consumption of secreted metabolic byproducts assuming identical uptake kinetics, the competitiveness of P. aeruginosa was further reduced due primarily to the more efficient lactate metabolism of S. aureus. Lysis of S. aureus by a small molecule inhibitor secreted from P. aeruginosa and/or P. aeruginosa aerotaxis were predicted to substantially increase P. aeruginosa competitiveness in the aerobic region, consistent with in vitro experimental studies.

Conclusions

Our biofilm modeling approach allows the prediction of individual species metabolism and interspecies interactions in both time and space with genome-scale resolution. This study yielded new insights into the multispecies metabolism of a chronic wound biofilm, in particular metabolic factors that may lead to spatial partitioning of the two bacterial species. We believe that P. aeruginosa lysis of S. aureus combined with nutrient competition is a particularly relevant scenario for which model predictions could be tested experimentally.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0334-8) contains supplementary material, which is available to authorized users.

Metabolic modelling in a dynamic evolutionary framework predicts adaptive diversification of bacteria in a long-term evolution experiment

BACKGROUND

Predicting adaptive trajectories is a major goal of evolutionary biology and useful for practical applications. Systems biology has enabled the development of genome-scale metabolic models. However, analysing these models via flux balance analysis (FBA) cannot predict many evolutionary outcomes including adaptive diversification, whereby an ancestral lineage diverges to fill multiple niches. Here we combine in silico evolution with FBA and apply this modelling framework, evoFBA, to a long-term evolution experiment with Escherichia coli.

RESULTS

Simulations predicted the adaptive diversification that occurred in one experimental population and generated hypotheses about the mechanisms that promoted coexistence of the diverged lineages. We experimentally tested and, on balance, verified these mechanisms, showing that diversification involved niche construction and character displacement through differential nutrient uptake and altered metabolic regulation.

CONCLUSION

The evoFBA framework represents a promising new way to model biochemical evolution, one that can generate testable predictions about evolutionary and ecosystem-level outcomes.

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

BACKGROUND

Photosynthetic 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.

RESULTS

In 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 [Formula: see text]-carotene density by factors of about 2.5 and 2.1, respectively.

CONCLUSIONS

The analysis shows that a model-based approach can be used to develop and significantly improve biotechnological processes for biofuels and pigments.

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures-Systems biology-based interpretation using genome-scale metabolic flux balance model and multivariate data analysis

Genome-scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745-753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome-scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163-1173, 2016.

Transition of an Anaerobic Escherichia coli Culture to Aerobiosis: Balancing mRNA and Protein Levels in a Demand-Directed Dynamic Flux Balance Analysis

The facultative anaerobic bacterium Escherichia coli is frequently forced to adapt to changing environmental conditions. One important determinant for metabolism is the availability of oxygen allowing a more efficient metabolism. Especially in large scale bioreactors, the distribution of oxygen is inhomogeneous and individual cells encounter frequent changes. This might contribute to observed yield losses during process upscaling. Short-term gene expression data exist of an anaerobic E. coli batch culture shifting to aerobic conditions. The data reveal temporary upregulation of genes that are less efficient in terms of energy conservation than the genes predicted by conventional flux balance analyses. In this study, we provide evidence for a positive correlation between metabolic fluxes and gene expression. We then hypothesize that the more efficient enzymes are limited by their low expression, restricting flux through their reactions. We define a demand that triggers expression of the demanded enzymes that we explicitly include in our model. With these features we propose a method, demand-directed dynamic flux balance analysis, dddFBA, bringing together elements of several previously published methods. The introduction of additional flux constraints proportional to gene expression provoke a temporary demand for less efficient enzymes, which is in agreement with the transient upregulation of these genes observed in the data. In the proposed approach, the applied objective function of growth rate maximization together with the introduced constraints triggers expression of metabolically less efficient genes. This finding is one possible explanation for the yield losses observed in large scale bacterial cultivations where steady oxygen supply cannot be warranted.

The steady-state assumption in oscillating and growing systems

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods.

Model-based dietary optimization for late-stage, levodopa-treated, Parkinson's disease patients

Levodopa has been the gold standard for Parkinson’s disease treatment for more than 40 years. Its bioavailability is hindered by dietary amino acids, leading to fluctuations in the motor response particularly in late-stage (stage 3 and 4 on Hoehn and Yahr scale) patients. The routine dietary intervention consists of low-protein (<0.8 g/kg) diets or the redistribution of daily protein allowance to the last meal. Computational modeling was used to examine the fluctuation of gastrointestinal levodopa absorption under consideration of the diet by (i) identifying the group of patients that could benefit from dietary interventions, (ii) comparing existing diet recommendations for their impact on levodopa bioavailability, and (iii) suggesting a mechanism-based dietary intervention. We developed a multiscale computational model consisting of an ordinary differential equations-based advanced compartmentalized absorption and transit (ACAT) gut model and metabolic genome-scale small intestine epithelial cell model. We used this model to investigate complex spatiotemporal relationship between dietary amino acids and levodopa absorption. Our model predicted an improvement in bioavailability, as reflected by blood concentrations of levodopa with protein redistribution diet by 34% compared with a low-protein diet and by 11% compared with the ante cibum (a.c.) administration. These results are consistent with the reported better outcome in late-stage patients. A systematic analysis of the effect of different amino acids in the diet suggested that a serine-rich diet could improve the bioavailability by 22% compared with the a.c. administration. In addition, the slower gastric emptying rate in PD patients exacerbates the loss of levodopa due to competition. Optimizing dietary recommendations in quantity, composition, and intake time holds the promise to improve levodopa efficiency and patient’s quality of life based on highly detailed, mechanistic models of gut physiology endowed with improved extrapolative properties, thus paving the way for precision medical treatment.

A simple strategy guides the complex metabolic regulation in Escherichia coli

A way to decipher the complexity of the cellular metabolism is to study the effect of different external perturbations. Through an analysis over a sufficiently large set of gene knockouts and growing conditions, one aims to find a unifying principle that governs the metabolic regulation. For instance, it is known that the cessation of the microorganism proliferation after a gene deletion is only transient. However, we do not know the guiding principle that determines the partial or complete recovery of the growth rate, the corresponding redistribution of the metabolic fluxes and the possible different phenotypes. In spite of this large variety in the observed metabolic adjustments, we show that responses of E. coli to several different perturbations can always be derived from a sequence of greedy and myopic resilencings. This simple mechanism provides a detailed explanation for the experimental dynamics both at cellular (proliferation rate) and molecular level (¹³C-determined fluxes), also in case of appearance of multiple phenotypes. As additional support, we identified an example of a simple network motif that is capable of implementing this myopic greediness in the regulation of the metabolism.

Advances in the integration of transcriptional regulatory information into genome-scale metabolic models

A major goal of systems biology is to build predictive computational models of cellular metabolism. Availability of complete genome sequences and wealth of legacy biochemical information has led to the reconstruction of genome-scale metabolic networks in the last 15 years for several organisms across the three domains of life. Due to paucity of information on kinetic parameters associated with metabolic reactions, the constraint-based modelling approach, flux balance analysis (FBA), has proved to be a vital alternative to investigate the capabilities of reconstructed metabolic networks. In parallel, advent of high-throughput technologies has led to the generation of massive amounts of omics data on transcriptional regulation comprising mRNA transcript levels and genome-wide binding profile of transcriptional regulators. A frontier area in metabolic systems biology has been the development of methods to integrate the available transcriptional regulatory information into constraint-based models of reconstructed metabolic networks in order to increase the predictive capabilities of computational models and understand the regulation of cellular metabolism. Here, we review the existing methods to integrate transcriptional regulatory information into constraint-based models of metabolic networks.

Metabolic Network Modeling of Microbial Interactions in Natural and Engineered Environmental Systems

We review approaches to characterize metabolic interactions within microbial communities using Stoichiometric Metabolic Network (SMN) models for applications in environmental and industrial biotechnology. SMN models are computational tools used to evaluate the metabolic engineering potential of various organisms. They have successfully been applied to design and optimize the microbial production of antibiotics, alcohols and amino acids by single strains. To date however, such models have been rarely applied to analyze and control the metabolism of more complex microbial communities. This is largely attributed to the diversity of microbial community functions, metabolisms, and interactions. Here, we firstly review different types of microbial interaction and describe their relevance for natural and engineered environmental processes. Next, we provide a general description of the essential methods of the SMN modeling workflow including the steps of network reconstruction, simulation through Flux Balance Analysis (FBA), experimental data gathering, and model calibration. Then we broadly describe and compare four approaches to model microbial interactions using metabolic networks, i.e., (i) lumped networks, (ii) compartment per guild networks, (iii) bi-level optimization simulations, and (iv) dynamic-SMN methods. These approaches can be used to integrate and analyze diverse microbial physiology, ecology and molecular community data. All of them (except the lumped approach) are suitable for incorporating species abundance data but so far they have been used only to model simple communities of two to eight different species. Interactions based on substrate exchange and competition can be directly modeled using the above approaches. However, interactions based on metabolic feedbacks, such as product inhibition and synthropy require extensions to current models, incorporating gene regulation and compounding accumulation mechanisms. SMN models of microbial interactions can be used to analyze complex “omics” data and to infer and optimize metabolic processes. Thereby, SMN models are suitable to capitalize on advances in high-throughput molecular and metabolic data generation. SMN models are starting to be applied to describe microbial interactions during wastewater treatment, in-situ bioremediation, microalgae blooms methanogenic fermentation, and bioplastic production. Despite their current challenges, we envisage that SMN models have future potential for the design and development of novel growth media, biochemical pathways and synthetic microbial associations.

Dynamic metabolic models in context: biomass backtracking

Mathematical modeling has proven to be a powerful tool to understand and predict functional and regulatory properties of metabolic processes. High accuracy dynamic modeling of individual pathways is thereby opposed by simplified but genome scale constraint based approaches. A method that links these two powerful techniques would greatly enhance predictive power but is so far lacking. We present biomass backtracking, a workflow that integrates the cellular context in existing dynamic metabolic models via stoichiometrically exact drain reactions based on a genome scale metabolic model. With comprehensive examples, for different species and environmental contexts, we show the importance and scope of applications and highlight the improvement compared to common boundary formulations in existing metabolic models. Our method allows for the contextualization of dynamic metabolic models based on all available information. We anticipate this to greatly increase their accuracy and predictive power for basic research and also for drug development and industrial applications.

Genome scale models of yeast: towards standardized evaluation and consistent omic integration

Genome scale models (GEMs) have enabled remarkable advances in systems biology, acting as functional databases of metabolism, and as scaffolds for the contextualization of high-throughput data. In the case of Saccharomyces cerevisiae (budding yeast), several GEMs have been published and are currently used for metabolic engineering and elucidating biological interactions. Here we review the history of yeast's GEMs, focusing on recent developments. We study how these models are typically evaluated, using both descriptive and predictive metrics. Additionally, we analyze the different ways in which all levels of omics data (from gene expression to flux) have been integrated in yeast GEMs. Relevant conclusions and current challenges for both GEM evaluation and omic integration are highlighted.

Multiscale Model of Mycobacterium tuberculosis Infection Maps Metabolite and Gene Perturbations to Granuloma Sterilization Predictions

Granulomas are a hallmark of tuberculosis. Inside granulomas, the pathogen Mycobacterium tuberculosis may enter a metabolically inactive state that is less susceptible to antibiotics. Understanding M. tuberculosis metabolism within granulomas could contribute to reducing the lengthy treatment required for tuberculosis and provide additional targets for new drugs. Two key adaptations of M. tuberculosis are a nonreplicating phenotype and accumulation of lipid inclusions in response to hypoxic conditions. To explore how these adaptations influence granuloma-scale outcomes in vivo, we present a multiscale in silico model of granuloma formation in tuberculosis. The model comprises host immunity, M. tuberculosis metabolism, M. tuberculosis growth adaptation to hypoxia, and nutrient diffusion. We calibrated our model to in vivo data from nonhuman primates and rabbits and apply the model to predict M. tuberculosis population dynamics and heterogeneity within granulomas. We found that bacterial populations are highly dynamic throughout infection in response to changing oxygen levels and host immunity pressures. Our results indicate that a nonreplicating phenotype, but not lipid inclusion formation, is important for long-term M. tuberculosis survival in granulomas. We used virtual M. tuberculosis knockouts to predict the impact of both metabolic enzyme inhibitors and metabolic pathways exploited to overcome inhibition. Results indicate that knockouts whose growth rates are below ∼66% of the wild-type growth rate in a culture medium featuring lipid as the only carbon source are unable to sustain infections in granulomas. By mapping metabolite- and gene-scale perturbations to granuloma-scale outcomes and predicting mechanisms of sterilization, our method provides a powerful tool for hypothesis testing and guiding experimental searches for novel antituberculosis interventions.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Network-based metabolic analysis and microbial community modeling

Network inference is being applied to studies of microbial ecology to visualize and characterize microbial communities. Network representations can allow examination of the underlying organizational structure of a microbial community, and identification of key players or environmental conditions that influence community assembly and stability. Microbial co-association networks provide information on the dynamics of community structure as a function of time or other external variables. Community metabolic networks can provide a mechanistic link between species through identification of metabolite exchanges and species specific resource requirements. When used together, co-association networks and metabolic networks can provide a more in-depth view of the hidden rules that govern the stability and dynamics of microbial communities.

Visualization of Metabolic Interaction Networks in Microbial Communities Using VisANT 5.0

The complexity of metabolic networks in microbial communities poses an unresolved visualization and interpretation challenge. We address this challenge in the newly expanded version of a software tool for the analysis of biological networks, VisANT 5.0. We focus in particular on facilitating the visual exploration of metabolic interaction between microbes in a community, e.g. as predicted by COMETS (Computation of Microbial Ecosystems in Time and Space), a dynamic stoichiometric modeling framework. Using VisANT's unique metagraph implementation, we show how one can use VisANT 5.0 to explore different time-dependent ecosystem-level metabolic networks. In particular, we analyze the metabolic interaction network between two bacteria previously shown to display an obligate cross-feeding interdependency. In addition, we illustrate how a putative minimal gut microbiome community could be represented in our framework, making it possible to highlight interactions across multiple coexisting species. We envisage that the "symbiotic layout" of VisANT can be employed as a general tool for the analysis of metabolism in complex microbial communities as well as heterogeneous human tissues. VisANT is freely available at: http://visant.bu.edu and COMETS at http://comets.bu.edu.

Challenges in microbial ecology: building predictive understanding of community function and dynamics

The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth's soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model–experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved.

Multiscale Metabolic Modeling of C4 Plants: Connecting Nonlinear Genome-Scale Models to Leaf-Scale Metabolism in Developing Maize Leaves

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, we suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data, and we demonstrate that our method predicts fluxes that achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems.

A Strategy for Functional Interpretation of Metabolomic Time Series Data in Context of Metabolic Network Information

The functional connection of experimental metabolic time series data with biochemical network information is an important, yet complex, issue in systems biology. Frequently, experimental analysis of diurnal, circadian, or developmental dynamics of metabolism results in a comprehensive and multidimensional data matrix comprising information about metabolite concentrations, protein levels, and/or enzyme activities. While, irrespective of the type of organism, the experimental high-throughput analysis of the transcriptome, proteome, and metabolome has become a common part of many systems biological studies, functional data integration in a biochemical and physiological context is still challenging. Here, an approach is presented which addresses the functional connection of experimental time series data with biochemical network information which can be inferred, for example, from a metabolic network reconstruction. Based on a time-continuous and variance-weighted regression analysis of experimental data, metabolic functions, i.e., first-order derivatives of metabolite concentrations, were related to time-dependent changes in other biochemically relevant metabolic functions, i.e., second-order derivatives of metabolite concentrations. This finally revealed time points of perturbed dependencies in metabolic functions indicating a modified biochemical interaction. The approach was validated using previously published experimental data on a diurnal time course of metabolite levels, enzyme activities, and metabolic flux simulations. To support and ease the presented approach of functional time series analysis, a graphical user interface including a test data set and a manual is provided which can be run within the numerical software environment Matlab®.

Spatiotemporal modeling of microbial metabolism

BACKGROUND

Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.

RESULTS

We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution.

CONCLUSIONS

Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems.

Constraint Based Modeling Going Multicellular

Constraint based modeling has seen applications in many microorganisms. For example, there are now established methods to determine potential genetic modifications and external interventions to increase the efficiency of microbial strains in chemical production pipelines. In addition, multiple models of multicellular organisms have been created including plants and humans. While initially the focus here was on modeling individual cell types of the multicellular organism, this focus recently started to switch. Models of microbial communities, as well as multi-tissue models of higher organisms have been constructed. These models thereby can include different parts of a plant, like root, stem, or different tissue types in the same organ. Such models can elucidate details of the interplay between symbiotic organisms, as well as the concerted efforts of multiple tissues and can be applied to analyse the effects of drugs or mutations on a more systemic level. In this review we give an overview of the recent development of multi-tissue models using constraint based techniques and the methods employed when investigating these models. We further highlight advances in combining constraint based models with dynamic and regulatory information and give an overview of these types of hybrid or multi-level approaches.

Simulating Serial-Target Antibacterial Drug Synergies Using Flux Balance Analysis

Flux balance analysis (FBA) is an increasingly useful approach for modeling the behavior of metabolic systems. However, standard FBA modeling of genetic knockouts cannot predict drug combination synergies observed between serial metabolic targets, even though such synergies give rise to some of the most widely used antibiotic treatments. Here we extend FBA modeling to simulate responses to chemical inhibitors at varying concentrations, by diverting enzymatic flux to a waste reaction. This flux diversion yields very similar qualitative predictions to prior methods for single target activity. However, we find very different predictions for combinations, where flux diversion, which mimics the kinetics of competitive metabolic inhibitors, can explain serial target synergies between metabolic enzyme inhibitors that we confirmed in Escherichia coli cultures. FBA flux diversion opens the possibility for more accurate genome-scale predictions of drug synergies, which can be used to suggest treatments for infections and other diseases.

Metabolic engineering with multi-objective optimization of kinetic models

Kinetic models have a great potential for metabolic engineering applications. They can be used for testing which genetic and regulatory modifications can increase the production of metabolites of interest, while simultaneously monitoring other key functions of the host organism. This work presents a methodology for increasing productivity in biotechnological processes exploiting dynamic models. It uses multi-objective dynamic optimization to identify the combination of targets (enzymatic modifications) and the degree of up- or down-regulation that must be performed in order to optimize a set of pre-defined performance metrics subject to process constraints. The capabilities of the approach are demonstrated on a realistic and computationally challenging application: a large-scale metabolic model of Chinese Hamster Ovary cells (CHO), which are used for antibody production in a fed-batch process. The proposed methodology manages to provide a sustained and robust growth in CHO cells, increasing productivity while simultaneously increasing biomass production, product titer, and keeping the concentrations of lactate and ammonia at low values. The approach presented here can be used for optimizing metabolic models by finding the best combination of targets and their optimal level of up/down-regulation. Furthermore, it can accommodate additional trade-offs and constraints with great flexibility.

Cyanobacterial Biofuels: Strategies and Developments on Network and Modeling

Cyanobacteria, the phototrophic microorganisms, have attracted much attention recently as a promising source for environmentally sustainable biofuels production. However, barriers for commercial markets of cyanobacteria-based biofuels concern the economic feasibility. Miscellaneous strategies for improving the production performance of cyanobacteria have thus been developed. Among these, the simple ad hoc strategies resulting in failure to optimize fully cell growth coupled with desired product yield are explored. With the advancement of genomics and systems biology, a new paradigm toward systems metabolic engineering has been recognized. In particular, a genome-scale metabolic network reconstruction and modeling is a crucial systems-based tool for whole-cell-wide investigation and prediction. In this review, the cyanobacterial genome-scale metabolic models, which offer a system-level understanding of cyanobacterial metabolism, are described. The main process of metabolic network reconstruction and modeling of cyanobacteria are summarized. Strategies and developments on genome-scale network and modeling through the systems metabolic engineering approach are advanced and employed for efficient cyanobacterial-based biofuels production.