Dynamic flux balance analysis of diauxic growth in Escherichia coli

Mathematical Modeling of Cellular Metabolism

Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

Genome-scale modelling of microbial metabolism with temporal and spatial resolution

Most natural microbial systems have evolved to function in environments with temporal and spatial variations. A major limitation to understanding such complex systems is the lack of mathematical modelling frameworks that connect the genomes of individual species and temporal and spatial variations in the environment to system behaviour. The goal of this review is to introduce the emerging field of spatiotemporal metabolic modelling based on genome-scale reconstructions of microbial metabolism. The extension of flux balance analysis (FBA) to account for both temporal and spatial variations in the environment is termed spatiotemporal FBA (SFBA). Following a brief overview of FBA and its established dynamic extension, the SFBA problem is introduced and recent progress is described. Three case studies are reviewed to illustrate the current state-of-the-art and possible future research directions are outlined. The author posits that SFBA is the next frontier for microbial metabolic modelling and a rapid increase in methods development and system applications is anticipated.

Synthetic Ecology of Microbes: Mathematical Models and Applications

As the indispensable role of natural microbial communities in many aspects of life on Earth is uncovered, the bottom-up engineering of synthetic microbial consortia with novel functions is becoming an attractive alternative to engineering single-species systems. Here, we summarize recent work on synthetic microbial communities with a particular emphasis on open challenges and opportunities in environmental sustainability and human health. We next provide a critical overview of mathematical approaches, ranging from phenomenological to mechanistic, to decipher the principles that govern the function, dynamics and evolution of microbial ecosystems. Finally, we present our outlook on key aspects of microbial ecosystems and synthetic ecology that require further developments, including the need for more efficient computational algorithms, a better integration of empirical methods and model-driven analysis, the importance of improving gene function annotation, and the value of a standardized library of well-characterized organisms to be used as building blocks of synthetic communities.

Modeling and Simulation of Optimal Resource Management during the Diurnal Cycle in Emiliania huxleyi by Genome-Scale Reconstruction and an Extended Flux Balance Analysis Approach

The coccolithophorid unicellular alga Emiliania huxleyi is known to form large blooms, which have a strong effect on the marine carbon cycle. As a photosynthetic organism, it is subjected to a circadian rhythm due to the changing light conditions throughout the day. For a better understanding of the metabolic processes under these periodically-changing environmental conditions, a genome-scale model based on a genome reconstruction of the E. huxleyi strain CCMP 1516 was created. It comprises 410 reactions and 363 metabolites. Biomass composition is variable based on the differentiation into functional biomass components and storage metabolites. The model is analyzed with a flux balance analysis approach called diurnal flux balance analysis (diuFBA) that was designed for organisms with a circadian rhythm. It allows storage metabolites to accumulate or be consumed over the diurnal cycle, while keeping the structure of a classical FBA problem. A feature of this approach is that the production and consumption of storage metabolites is not defined externally via the biomass composition, but the result of optimal resource management adapted to the diurnally-changing environmental conditions. The model in combination with this approach is able to simulate the variable biomass composition during the diurnal cycle in proximity to literature data.

Elucidating temporal resource allocation and diurnal dynamics in phototrophic metabolism using conditional FBA

The computational analysis of phototrophic growth using constraint-based optimization requires to go beyond current time-invariant implementations of flux-balance analysis (FBA). Phototrophic organisms, such as cyanobacteria, rely on harvesting the sun’s energy for the conversion of atmospheric CO2 into organic carbon, hence their metabolism follows a strongly diurnal lifestyle. We describe the growth of cyanobacteria in a periodic environment using a new method called conditional FBA. Our approach enables us to incorporate the temporal organization and conditional dependencies into a constraint-based description of phototrophic metabolism. Specifically, we take into account that cellular processes require resources that are themselves products of metabolism. Phototrophic growth can therefore be formulated as a time-dependent linear optimization problem, such that optimal growth requires a differential allocation of resources during different times of the day. Conditional FBA then allows us to simulate phototrophic growth of an average cell in an environment with varying light intensity, resulting in dynamic time-courses for all involved reaction fluxes, as well as changes in biomass composition over a diurnal cycle. Our results are in good agreement with several known facts about the temporal organization of phototrophic growth and have implications for further analysis of resource allocation problems in phototrophic metabolism.

Calibration and analysis of genome-based models for microbial ecology

Microbial ecosystem modeling is complicated by the large number of unknown parameters and the lack of appropriate calibration tools. Here we present a novel computational framework for modeling microbial ecosystems, which combines genome-based model construction with statistical analysis and calibration to experimental data. Using this framework, we examined the dynamics of a community of Escherichia coli strains that emerged in laboratory evolution experiments, during which an ancestral strain diversified into two coexisting ecotypes. We constructed a microbial community model comprising the ancestral and the evolved strains, which we calibrated using separate monoculture experiments. Simulations reproduced the successional dynamics in the evolution experiments, and pathway activation patterns observed in microarray transcript profiles. Our approach yielded detailed insights into the metabolic processes that drove bacterial diversification, involving acetate cross-feeding and competition for organic carbon and oxygen. Our framework provides a missing link towards a data-driven mechanistic microbial ecology.

Integrating Kinetic Model of E. coli with Genome Scale Metabolic Fluxes Overcomes Its Open System Problem and Reveals Bistability in Central Metabolism

An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi-‘omics’ steady state data and a genome-scale metabolic network model. We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population.

Metabolic modeling predicts metabolite changes in Mycobacterium tuberculosis

BACKGROUND

Mycobacterium tuberculosis (MTB) is the causal agent of the disease tuberculosis (TB). Metabolic adaptations are thought to be critical to the survival of MTB during pathogenesis. Computational tools that can be used to study MTB metabolism in silico and prioritize resource-intensive experimental work could significantly accelerate research.

RESULTS

We have developed E-Flux-MFC, an enhancement of our original E-Flux method that enables the prediction of changes in the production of external and internal metabolites corresponding to gene expression measurements. We have used this method to simulate the changes in the metabolic state of Mycobacterium tuberculosis (MTB). We have validated the accuracy of E-Flux-MFC for predicting changes in lipids and metabolites during a hypoxia time course using previously published metabolomics and transcriptomics data. We have further validated the accuracy of the method for predicting changes in MTB lipids following the deletion and induction of two well-studied transcription factors (TFs). We have applied the method to predict the metabolic impact of the induction of each of the approximately 180 MTB TFs using a previously generated and publically available expression data set.

CONCLUSIONS

E-flux-MFC can be used to study global changes in MTB metabolites from gene expression data associated with environmental and genetic perturbations. The application of this method to a data set of MTB TF perturbations provides a resource for studying the large number of TFs whose functions remain unknown. Most TFs impact metabolites indirectly through the propagation of gene expression changes through the regulatory network rather than through their direct regulons. E-Flux-MFC is also applicable to any organism for which accurate metabolic models are available.

Metabolic Adaptation Processes That Converge to Optimal Biomass Flux Distributions

In simple organisms like E.coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E.coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

In modeling metabolic networks, concepts like biomass optimization are often used to determine flux distributions of simple organisms such as E.coli. Although they often give good results in practice, they normally rely on heuristic considerations like “evolution has tuned metabolic fluxes to optimize growth, hence optimizing growth gives reasonable fluxes”. The main result of this paper is to show that metabolic adaptation naturally leads to optimal growth, in the sense that the flux distribution associated to optimal growth is the dominant attractor of the fitness landscape of the metabolic adaptation process.

A Single Dynamic Metabolic Model Can Describe mAb Producing CHO Cell Batch and Fed-Batch Cultures on Different Culture Media

CHO cell culture high productivity relies on optimized culture medium management under fed-batch or perfused chemostat strategies enabling high cell densities. In this work, a dynamic metabolic model for CHO cells was further developed, calibrated and challenged using datasets obtained under four different culture conditions, including two batch and two fed-batch cultures comparing two different culture media. The recombinant CHO-DXB11 cell line producing the EG2-hFc monoclonal antibody was studied. Quantification of extracellular substrates and metabolites concentration, viable cell density, monoclonal antibody concentration and intracellular concentration of metabolite intermediates of glycolysis, pentose-phosphate and TCA cycle, as well as of energetic nucleotides, were obtained for model calibration. Results suggest that a single model structure with a single set of kinetic parameter values is efficient at simulating viable cell behavior in all cases under study, estimating the time course of measured and non-measured intracellular and extracellular metabolites. Model simulations also allowed performing dynamic metabolic flux analysis, showing that the culture media and the fed-batch strategies tested had little impact on flux distribution. This work thus paves the way to an in silico platform allowing to assess the performance of different culture media and fed-batch strategies.

Controlled Measurement and Comparative Analysis of Cellular Components in E. coli Reveals Broad Regulatory Changes in Response to Glucose Starvation

How do bacteria regulate their cellular physiology in response to starvation? Here, we present a detailed characterization of Escherichia coli growth and starvation over a time-course lasting two weeks. We have measured multiple cellular components, including RNA and proteins at deep genomic coverage, as well as lipid modifications and flux through central metabolism. Our study focuses on the physiological response of E. coli in stationary phase as a result of being starved for glucose, not on the genetic adaptation of E. coli to utilize alternative nutrients. In our analysis, we have taken advantage of the temporal correlations within and among RNA and protein abundances to identify systematic trends in gene regulation. Specifically, we have developed a general computational strategy for classifying expression-profile time courses into distinct categories in an unbiased manner. We have also developed, from dynamic models of gene expression, a framework to characterize protein degradation patterns based on the observed temporal relationships between mRNA and protein abundances. By comparing and contrasting our transcriptomic and proteomic data, we have identified several broad physiological trends in the E. coli starvation response. Strikingly, mRNAs are widely down-regulated in response to glucose starvation, presumably as a strategy for reducing new protein synthesis. By contrast, protein abundances display more varied responses. The abundances of many proteins involved in energy-intensive processes mirror the corresponding mRNA profiles while proteins involved in nutrient metabolism remain abundant even though their corresponding mRNAs are down-regulated.

Bacteria frequently experience starvation conditions in their natural environments. Yet how they modify their physiology in response to these conditions remains poorly understood. Here, we performed a detailed, two-week starvation experiment in E. coli. We exhaustively monitored changes in cellular components, such as RNA and protein abundances, over time. We subsequently compared and contrasted these measurements using novel computational approaches we developed specifically for analyzing gene-expression time-course data. Using these approaches, we could identify systematic trends in the E. coli starvation response. In particular, we found that cells systematically limit mRNA and protein production, degrade proteins involved in energy-intensive processes, and maintain or increase the amount of proteins involved in energy production. Thus, the bacteria assume a cellular state in which their ongoing energy use is limited while they are poised to take advantage of any nutrients that may become available.

Improved metabolite profile smoothing for flux estimation

As genome-scale metabolic models become more sophisticated and dynamic, one significant challenge in using these models is to effectively integrate increasingly prevalent systems-scale metabolite profiling data into them. One common data processing step when integrating metabolite data is to smooth experimental time course measurements: the smoothed profiles can be used to estimate metabolite accumulation (derivatives), and thus the flux distribution of the metabolic model. However, this smoothing step is susceptible to the (often significant) noise in experimental measurements, limiting the accuracy of downstream model predictions. Here, we present several improvements to current approaches for smoothing metabolite time course data using defined functions. First, we use a biologically-inspired mathematical model function taken from transcriptional profiling and clustering literature that captures the dynamics of many biologically relevant transient processes. We demonstrate that it is competitive with, and often superior to, previously described fitting schemas, and may serve as an effective single option for data smoothing in metabolic flux applications. We also implement a resampling-based approach to buffer out sensitivity to specific data sets and allow for more accurate fitting of noisy data. We found that this method, as well as the addition of parameter space constraints, yielded improved estimates of concentrations and derivatives (fluxes) in previously described fitting functions. These methods have the potential to improve the accuracy of existing and future dynamic metabolic models by allowing for the more effective integration of metabolite profiling data.

Multi-scale exploration of the technical, economic, and environmental dimensions of bio-based chemical production

In recent years, bio-based chemicals have gained traction as a sustainable alternative to petrochemicals. However, despite rapid advances in metabolic engineering and synthetic biology, there remain significant economic and environmental challenges. In order to maximize the impact of research investment in a new bio-based chemical industry, there is a need for assessing the technological, economic, and environmental potentials of combinations of biomass feedstocks, biochemical products, bioprocess technologies, and metabolic engineering approaches in the early phase of development of cell factories. To address this issue, we have developed a comprehensive Multi-scale framework for modeling Sustainable Industrial Chemicals production (MuSIC), which integrates modeling approaches for cellular metabolism, bioreactor design, upstream/downstream processes and economic impact assessment. We demonstrate the use of the MuSIC framework in a case study where two major polymer precursors (1,3-propanediol and 3-hydroxypropionic acid) are produced from two biomass feedstocks (corn-based glucose and soy-based glycerol) through 66 proposed biosynthetic pathways in two host organisms (Escherichia coli and Saccharomyces cerevisiae). The MuSIC framework allows exploration of tradeoffs and interactions between economy-scale objectives (e.g. profit maximization, emission minimization), constraints (e.g. land-use constraints) and process- and cell-scale technology choices (e.g. strain design or oxygenation conditions). We demonstrate that economy-scale assessment can be used to guide specific strain design decisions in metabolic engineering, and that these design decisions can be affected by non-intuitive dependencies across multiple scales.

Metabolic network modeling of microbial communities

Genome-scale metabolic network reconstructions and constraint-based analyses are powerful methods that have the potential to make functional predictions about microbial communities. Genome-scale metabolic networks are used to characterize the metabolic functions of microbial communities via several techniques including species compartmentalization, separating species-level and community-level objectives, dynamic analysis, the 'enzyme-soup' approach, multiscale modeling, and others. There are many challenges in the field, including a need for tools that accurately assign high-level omics signals to individual community members, the need for improved automated network reconstruction methods, and novel algorithms for integrating omics data and engineering communities. As technologies and modeling frameworks improve, we expect that there will be corresponding advances in the fields of ecology, health science, and microbial community engineering.

Metabolic modeling of synthesis gas fermentation in bubble column reactors

BACKGROUND

A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors.

RESULTS

We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst. Our modeling approach involved combining a genome-scale reconstruction of C. ljungdahlii metabolism with multiphase transport equations that govern convective and dispersive processes within the spatially varying column. The reactor model was spatially discretized to yield a large set of ordinary differential equations (ODEs) in time with embedded linear programs (LPs) and solved using the MATLAB based code DFBAlab. Simulations were performed to analyze the effects of important process and cellular parameters on key measures of reactor performance including ethanol titer, ethanol-to-acetate ratio, and CO and H2 conversions.

CONCLUSIONS

Our computational study demonstrated that mathematical modeling provides a complementary tool to experimentation for understanding, predicting, and optimizing syngas fermentation reactors. These model predictions could guide future cellular and process engineering efforts aimed at alleviating bottlenecks to biochemical production in syngas bubble column reactors.

Dynamic metabolic flux analysis using B-splines to study the effects of temperature shift on CHO cell metabolism

Metabolic flux analysis (MFA) is widely used to estimate intracellular fluxes. Conventional MFA, however, is limited to continuous cultures and the mid-exponential growth phase of batch cultures. Dynamic MFA (DMFA) has emerged to characterize time-resolved metabolic fluxes for the entire culture period. Here, the linear DMFA approach was extended using B-spline fitting (B-DMFA) to estimate mass balanced fluxes. Smoother fits were achieved using reduced number of knots and parameters. Additionally, computation time was greatly reduced using a new heuristic algorithm for knot placement. B-DMFA revealed that Chinese hamster ovary cells shifted from 37 °C to 32 °C maintained a constant IgG volume-specific productivity, whereas the productivity for the controls peaked during mid-exponential growth phase and declined afterward. The observed 42% increase in product titer at 32 °C was explained by a prolonged cell growth with high cell viability, a larger cell volume and a more stable volume-specific productivity.

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New dynamic MFA framework using B-spline (B-DMFA) generates smooth fit.

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B-DMFA performs better than linear DMFA when fitting fast dynamic changes.

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Heuristic algorithm for knot placement dramatically reduced computation time.

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Temperature shifted cultures maintain a constant IgG volume specific productivity.

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CHO cells shifted to 32 °C have a 42% higher IgG titer due to larger cell volume.

Perception and regulatory principles of microbial growth control

Fast growth represents an effective strategy for microbial organisms to survive in competitive environments. To accomplish this task, cells must adapt their metabolism to changing nutrient conditions in a way that maximizes their growth rate. However, the regulation of the growth related metabolic pathways can be fundamentally different among microbes. We therefore asked whether growth control by perception of the cell’s intracellular metabolic state can give rise to higher growth than by direct perception of extracellular nutrient availability. To answer this question, we created a simplified dynamical computer model of a cellular metabolic network whose regulation was inferred by an optimization approach. We used this model for a competing species experiment, where a species with extracellular nutrient perception competes against one with intracellular nutrient perception by evaluating their respective average growth rate. We found that the intracellular perception is advantageous under situations where the up and down regulation of pathways cannot follow the fast changing nutrient availability in the environment. In this case, optimal regulation ignores any other nutrients except the most preferential ones, in agreement with the phenomenon of catabolite repression in prokaryotes. The corresponding metabolic pathways remain activated, despite environmental fluctuations. Therefore, the cell can take up preferential nutrients as soon as they are available without any prior regulation. As a result species that rely on intracellular perception gain a relevant fitness advantage in fluctuating nutrient environments, which enables survival by outgrowing competitors.

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.

Unraveling interactions in microbial communities - from co-cultures to microbiomes

Microorganisms do not exist in isolation in the environment. Instead, they form complex communities among themselves as well as with their hosts. Different forms of interactions not only shape the composition of these communities but also define how these communities are established and maintained. The kinds of interaction a bacterium can employ are largely encoded in its genome. This allows us to deploy a genomescale modeling approach to understand, and ultimately predict, the complex and intertwined relationships in which microorganisms engage. So far, most studies on microbial communities have been focused on synthetic co-cultures and simple communities. However, recent advances in molecular and computational biology now enable bottom up methods to be deployed for complex microbial communities from the environment to provide insight into the intricate and dynamic interactions in which microorganisms are engaged. These methods will be applicable for a wide range of microbial communities involved in industrial processes, as well as understanding, preserving and reconditioning natural microbial communities present in soil, water, and the human microbiome.

Systems modeling approaches for microbial community studies: from metagenomics to inference of the community structure

Microbial communities play important roles in health, industrial applications and earth's ecosystems. With current molecular techniques we can characterize these systems in unprecedented detail. However, such methods provide little mechanistic insight into how the genetic properties and the dynamic couplings between individual microorganisms give rise to their dynamic activities. Neither do they give insight into what we call “the community state”, that is the fluxes and concentrations of nutrients within the community. This knowledge is a prerequisite for rational control and intervention in microbial communities. Therefore, the inference of the community structure from experimental data is a major current challenge. We will argue that this inference problem requires mathematical models that can integrate heterogeneous experimental data with existing knowledge. We propose that two types of models are needed. Firstly, mathematical models that integrate existing genomic, physiological, and physicochemical information with metagenomics data so as to maximize information content and predictive power. This can be achieved with the use of constraint-based genome-scale stoichiometric modeling of community metabolism which is ideally suited for this purpose. Next, we propose a simpler coarse-grained model, which is tailored to solve the inference problem from the experimental data. This model unambiguously relate to the more detailed genome-scale stoichiometric models which act as heterogeneous data integrators. The simpler inference models are, in our opinion, key to understanding microbial ecosystems, yet until now, have received remarkably little attention. This has led to the situation where the modeling of microbial communities, using only genome-scale models is currently more a computational, theoretical exercise than a method useful to the experimentalist.

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.

Spatially-resolved metabolic cooperativity within dense bacterial colonies

Background

The exchange of metabolites and the reprogramming of metabolism in response to shifting microenvironmental conditions can drive subpopulations of cells within colonies toward divergent behaviors. Understanding the interactions of these subpopulations—their potential for competition as well as cooperation—requires both a metabolic model capable of accounting for a wide range of environmental conditions, and a detailed dynamic description of the cells’ shared extracellular space.

Results

Here we show that a cell’s position within an in silicoEscherichia coli colony grown on glucose minimal agar can drastically affect its metabolism: “pioneer” cells at the outer edge engage in rapid growth that expands the colony, while dormant cells in the interior separate two spatially distinct subpopulations linked by a cooperative form of acetate crossfeeding that has so far gone unnoticed. Our hybrid simulation technique integrates 3D reaction-diffusion modeling with genome-scale flux balance analysis (FBA) to describe the position-dependent metabolism and growth of cells within a colony. Our results are supported by imaging experiments involving strains of fluorescently-labeled E. coli. The spatial patterns of fluorescence within these experimental colonies identify cells with upregulated genes associated with acetate crossfeeding and are in excellent agreement with the predictions. Furthermore, the height-to-width ratios of both the experimental and simulated colonies are in good agreement over a growth period of 48 hours.

Conclusions

Our modeling paradigm can accurately reproduce a number of known features of E. coli colony growth, as well as predict a novel one that had until now gone unrecognized. The acetate crossfeeding we see has a direct analogue in a form of lactate crossfeeding observed in certain forms of cancer, and we anticipate future application of our methodology to models of tissues and tumors.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0155-1) contains supplementary material, which is available to authorized users.

Computational Studies of the Intestinal Host-Microbiota Interactome

A large and growing body of research implicates aberrant immune response and compositional shifts of the intestinal microbiota in the pathogenesis of many intestinal disorders. The molecular and physical interaction between the host and the microbiota, known as the host-microbiota interactome, is one of the key drivers in the pathophysiology of many of these disorders. This host-microbiota interactome is a set of dynamic and complex processes, and needs to be treated as a distinct entity and subject for study. Disentangling this complex web of interactions will require novel approaches, using a combination of data-driven bioinformatics with knowledge-driven computational modeling. This review describes the computational approaches for investigating the host-microbiota interactome, with emphasis on the human intestinal tract and innate immunity, and highlights open challenges and existing gaps in the computation methodology for advancing our knowledge about this important facet of human health.

Integration of transcriptomics and metabolomics data specifies the metabolic response of Chlamydomonas to rapamycin treatment

Flux phenotypes predicted by constraint-based methods can be refined by the inclusion of heterogeneous data. While recent advances facilitate the integration of transcriptomics and proteomics data, purely stoichiometry-based approaches for the prediction of flux phenotypes by considering metabolomics data are lacking. Here we propose a constraint-based method, termed TREM-Flux, for integrating time-resolved metabolomics and transcriptomics data. We demonstrate the applicability of TREM-Flux in the dissection of the metabolic response of Chlamydomonas reinhardtii to rapamycin treatment by integrating the expression levels of 982 genes and the content of 45 metabolites obtained from two growth conditions. The findings pinpoint cysteine and methionine metabolism to be most affected by the rapamycin treatment. Our study shows that the integration of time-resolved unlabeled metabolomics data in addition to transcriptomics data can specify the metabolic pathways involved in the system's response to a studied treatment.

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.

Succinate Overproduction: A Case Study of Computational Strain Design Using a Comprehensive Escherichia coli Kinetic Model

Computational strain-design prediction accuracy has been the focus for many recent efforts through the selective integration of kinetic information into metabolic models. In general, kinetic model prediction quality is determined by the range and scope of genetic and/or environmental perturbations used during parameterization. In this effort, we apply the k-OptForce procedure on a kinetic model of E. coli core metabolism constructed using the Ensemble Modeling (EM) method and parameterized using multiple mutant strains data under aerobic respiration with glucose as the carbon source. Minimal interventions are identified that improve succinate yield under both aerobic and anaerobic conditions to test the fidelity of model predictions under both genetic and environmental perturbations. Under aerobic condition, k-OptForce identifies interventions that match existing experimental strategies while pointing at a number of unexplored flux re-directions such as routing glyoxylate flux through the glycerate metabolism to improve succinate yield. Many of the identified interventions rely on the kinetic descriptions that would not be discoverable by a purely stoichiometric description. In contrast, under fermentative (anaerobic) condition, k-OptForce fails to identify key interventions including up-regulation of anaplerotic reactions and elimination of competitive fermentative products. This is due to the fact that the pathways activated under anaerobic condition were not properly parameterized as only aerobic flux data were used in the model construction. This study shed light on the importance of condition-specific model parameterization and provides insight on how to augment kinetic models so as to correctly respond to multiple environmental perturbations.

Principles and practice of lipidomics

The technical advances in mass spectrometry, particularly the development of (ultra)-high-resolution/mass accuracy measurement capabilities in combination with refinement of soft ionization techniques, have increased the application and success of lipidomics to answer biological questions in relation to lipid metabolism. Together with other omics technologies, lipidomics has become an important tool to practice systems biology as lipids comprise a very significant part of the metabolome and play pleiotropic roles in cellular functions. As an increasing number of disorders are linked to lipid metabolism, lipidomics is used to search for biomarkers, understand disease mechanism and follow the efficacy of therapeutic options. This review provides a first introduction to the major methodological strategies currently used for mass spectrometry-based lipidomics and associated data pre-processing and analysis.

Genome-scale metabolic network reconstruction

Bacterial metabolism is an important source of novel products/processes for everyday life and strong efforts are being undertaken to discover and exploit new usable substances of microbial origin. Computational modeling and in silico simulations are powerful tools in this context since they allow the exploration and a deeper understanding of bacterial metabolic circuits. Many approaches exist to quantitatively simulate chemical reaction fluxes within the whole microbial metabolism and, regardless of the technique of choice, metabolic model reconstruction is the first step in every modeling pipeline. Reconstructing a metabolic network consists in drafting the list of the biochemical reactions that an organism can carry out together with information on cellular boundaries, a biomass assembly reaction, and exchange fluxes with the external environment. Building up models able to represent the different functional cellular states is universally recognized as a tricky task that requires intensive manual effort and much additional information besides genome sequence. In this chapter we present a general protocol for metabolic reconstruction in bacteria and the main challenges encountered during this process.

Integration of metabolomics data into metabolic networks

Metabolite levels together with their corresponding metabolic fluxes are integrative outcomes of biochemical transformations and regulatory processes and they can be used to characterize the response of biological systems to genetic and/or environmental changes. However, while changes in transcript or to some extent protein levels can usually be traced back to one or several responsible genes, changes in fluxes and particularly changes in metabolite levels do not follow such rationale and are often the outcome of complex interactions of several components. The increasing quality and coverage of metabolomics technologies have fostered the development of computational approaches for integrating metabolic read-outs with large-scale models to predict the physiological state of a system. Constraint-based approaches, relying on the stoichiometry of the considered reactions, provide a modeling framework amenable to analyses of large-scale systems and to the integration of high-throughput data. Here we review the existing approaches that integrate metabolomics data in variants of constrained-based approaches to refine model reconstructions, to constrain flux predictions in metabolic models, and to relate network structural properties to metabolite levels. Finally, we discuss the challenges and perspectives in the developments of constraint-based modeling approaches driven by metabolomics data.

MetDFBA: incorporating time-resolved metabolomics measurements into dynamic flux balance analysis

This paper presents MetDFBA, a new approach incorporating experimental metabolomics time-series into constraint-based modeling. The method can be used for hypothesis testing and predicting dynamic flux profiles.

Using a genome-scale metabolic model of Enterococcus faecalis V583 to assess amino acid uptake and its impact on central metabolism

Increasing antibiotic resistance in pathogenic bacteria necessitates the development of new medication strategies. Interfering with the metabolic network of the pathogen can provide novel drug targets but simultaneously requires a deeper and more detailed organism-specific understanding of the metabolism, which is often surprisingly sparse. In light of this, we reconstructed a genome-scale metabolic model of the pathogen Enterococcus faecalis V583. The manually curated metabolic network comprises 642 metabolites and 706 reactions. We experimentally determined metabolic profiles of E. faecalis grown in chemically defined medium in an anaerobic chemostat setup at different dilution rates and calculated the net uptake and product fluxes to constrain the model. We computed growth-associated energy and maintenance parameters and studied flux distributions through the metabolic network. Amino acid auxotrophies were identified experimentally for model validation and revealed seven essential amino acids. In addition, the important metabolic hub of glutamine/glutamate was altered by constructing a glutamine synthetase knockout mutant. The metabolic profile showed a slight shift in the fermentation pattern toward ethanol production and increased uptake rates of multiple amino acids, especially l-glutamine and l-glutamate. The model was used to understand the altered flux distributions in the mutant and provided an explanation for the experimentally observed redirection of the metabolic flux. We further highlighted the importance of gene-regulatory effects on the redirection of the metabolic fluxes upon perturbation. The genome-scale metabolic model presented here includes gene-protein-reaction associations, allowing a further use for biotechnological applications, for studying essential genes, proteins, or reactions, and the search for novel drug targets.

DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis

BACKGROUND

Dynamic Flux Balance Analysis (DFBA) is a dynamic simulation framework for biochemical processes. DFBA can be performed using different approaches such as static optimization (SOA), dynamic optimization (DOA), and direct approaches (DA). Few existing simulators address the theoretical and practical challenges of nonunique exchange fluxes or infeasible linear programs (LPs). Both are common sources of failure and inefficiencies for these simulators.

RESULTS

DFBAlab, a MATLAB-based simulator that uses the LP feasibility problem to obtain an extended system and lexicographic optimization to yield unique exchange fluxes, is presented. DFBAlab is able to simulate complex dynamic cultures with multiple species rapidly and reliably, including differential-algebraic equation (DAE) systems. In addition, DFBAlab's running time scales linearly with the number of species models. Three examples are presented where the performance of COBRA, DyMMM and DFBAlab are compared.

CONCLUSIONS

Lexicographic optimization is used to determine unique exchange fluxes which are necessary for a well-defined dynamic system. DFBAlab does not fail during numerical integration due to infeasible LPs. The extended system obtained through the LP feasibility problem in DFBAlab provides a penalty function that can be used in optimization algorithms.

Understanding carbon catabolite repression in Escherichia coli using quantitative models

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolized. Although this system is one of the paradigms of the regulation of gene expression in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell that are responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signaling, and that are subject to global physical and physiological constraints, has motivated important modeling efforts over the past four decades, especially in the enterobacterium Escherichia coli. Different hypotheses concerning the dynamic functioning of the system have been explored by a variety of modeling approaches. We review these studies and summarize their contributions to the quantitative understanding of CCR, focusing on diauxic growth in E. coli. Moreover, we propose a highly simplified representation of diauxic growth that makes it possible to bring out the salient features of the models proposed in the literature and confront and compare the explanations they provide.

CONSTRICTOR: constraint modification provides insight into design of biochemical networks

Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique in silico strains, each representing an “expression state”, or a combination of gene expression levels required to achieve the overproduction target. The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

Predictive sulfur metabolism - a field in flux

The key role of sulfur metabolites in response to biotic and abiotic stress in plants, as well as their importance in diet and health has led to a significant interest and effort in trying to understand and manipulate the production of relevant compounds. Metabolic engineering utilizes a set of theoretical tools to help rationally design modifications that enhance the production of a desired metabolite. Such approaches have proven their value in bacterial systems, however, the paucity of success stories to date in plants, suggests that challenges remain. Here, we review the most commonly used methods for understanding metabolic flux, focusing on the sulfur assimilatory pathway. We highlight known issues with both experimental and theoretical approaches, as well as presenting recent methods for integrating different modeling strategies, and progress toward an understanding of flux at the whole plant level.

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Dynamic flux balance analysis for synthetic microbial communities

Dynamic flux balance analysis (DFBA) is an extension of classical flux balance analysis that allows the dynamic effects of the extracellular environment on microbial metabolism to be predicted and optimised. Recently this computational framework has been extended to microbial communities for which the individual species are known and genome-scale metabolic reconstructions are available. In this review, the authors provide an overview of the emerging DFBA approach with a focus on two case studies involving the conversion of mixed hexose/pentose sugar mixtures by synthetic microbial co-culture systems. These case studies illustrate the key requirements of the DFBA approach, including the incorporation of individual species metabolic reconstructions, formulation of extracellular mass balances, identification of substrate uptake kinetics, numerical solution of the coupled linear program/differential equations and model adaptation for common, suboptimal growth conditions and identified species interactions. The review concludes with a summary of progress to date and possible directions for future research.

Optimal control analysis of the dynamic growth behavior of microorganisms

Understanding the growth behavior of microorganisms using modeling and optimization techniques is an active area of research in the fields of biochemical engineering and systems biology. In this paper, we propose a general modeling framework, based on Monod model, to model the growth of microorganisms. Utilizing the general framework, we formulate an optimal control problem with the objective of maximizing a long-term cellular goal and solve it analytically under various constraints for the growth of microorganisms in a two substrate batch environment. We investigate the relation between long term and short term cellular goals and show that the objective of maximizing cellular concentration at a fixed final time is equivalent to maximization of instantaneous growth rate. We then establish the mathematical connection between the generalized framework and optimal and cybernetic modeling frameworks and derive generalized governing dynamic equations for optimal and cybernetic models. We finally illustrate the influence of various constraints in the cybernetic modeling framework on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms.