Dynamic flux balance analysis of diauxic growth in Escherichia coli

A peptide-based method for 13C Metabolic Flux Analysis in microbial communities

The study of intracellular metabolic fluxes and inter-species metabolite exchange for microbial communities is of crucial importance to understand and predict their behaviour. The most authoritative method of measuring intracellular fluxes, ¹³C Metabolic Flux Analysis (¹³C MFA), uses the labeling pattern obtained from metabolites (typically amino acids) during ¹³C labeling experiments to derive intracellular fluxes. However, these metabolite labeling patterns cannot easily be obtained for each of the members of the community. Here we propose a new type of ¹³C MFA that infers fluxes based on peptide labeling, instead of amino acid labeling. The advantage of this method resides in the fact that the peptide sequence can be used to identify the microbial species it originates from and, simultaneously, the peptide labeling can be used to infer intracellular metabolic fluxes. Peptide identity and labeling patterns can be obtained in a high-throughput manner from modern proteomics techniques. We show that, using this method, it is theoretically possible to recover intracellular metabolic fluxes in the same way as through the standard amino acid based ¹³C MFA, and quantify the amount of information lost as a consequence of using peptides instead of amino acids. We show that by using a relatively small number of peptides we can counter this information loss. We computationally tested this method with a well-characterized simple microbial community consisting of two species.

Microbial communities underlie a variety of important biochemical processes ranging from underground cave formation to gold mining or the onset of obesity. Metabolic fluxes describe how carbon and energy flow through the microbial community and therefore provide insights that are rarely captured by other techniques, such as metatranscriptomics or metaproteomics. The most authoritative method to measure fluxes for pure cultures consists of feeding the cells a labeled carbon source and deriving the fluxes from the ensuing metabolite labeling pattern (typically amino acids). Since we cannot easily separate cells of metabolite for each species in a community, this approach is not generally applicable to microbial communities. Here we present a method to derive fluxes from the labeling of peptides, instead of amino acids. This approach has the advantage that peptides can be assigned to each species in a community in a high-throughput fashion through modern proteomic methods. We show that, by using this method, it is theoretically possible to recover the same amount of information as through the standard approach, if enough peptides are used. We computationally tested this method with a well-characterized simple microbial community consisting of two species.

Clarifying the regulation of NO/N2O production in Nitrosomonas europaea during anoxic-oxic transition via flux balance analysis of a metabolic network model

The metabolic mechanism regulating the production of nitric and nitrous oxide (NO, N2O) in ammonia oxidizing bacteria (AOB) was characterized by flux balance analysis (FBA) of a stoichiometric metabolic network (SMN) model. The SMN model was created using 51 reactions and 44 metabolites of the energy metabolism in Nitrosomonas europaea, a widely studied AOB. FBA of model simulations provided estimates for reaction rates and yield ratios of intermediate metabolites, substrates, and products. These estimates matched well, deviating on average by 15% from values for 17 M yield ratios reported for non-limiting oxygen and ammonium concentrations. A sensitivity analysis indicated that the reactions catalysed by cytochromes aa3 and P460 principally regulate the pathways of NO and N2O production (hydroxylamine oxidoreductase mediated and nitrifier denitrification). FBA of simulated N. europaea exposure to oxic-anoxic-oxic transition indicated that NO and N2O production primarily resulted from an intracellular imbalance between the production and consumption of electron equivalents during NH3 oxidation, and that NO and N2O are emitted when the sum of their production rates is greater than half the rate of NO oxidation by cytochrome P460.

DRUM: a new framework for metabolic modeling under non-balanced growth. Application to the carbon metabolism of unicellular microalgae

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.

Computational approaches to metabolic engineering utilizing systems biology and synthetic biology

Metabolic engineering modifies cellular function to address various biochemical applications. Underlying metabolic engineering efforts are a host of tools and knowledge that are integrated to enable successful outcomes. Concurrent development of computational and experimental tools has enabled different approaches to metabolic engineering. One approach is to leverage knowledge and computational tools to prospectively predict designs to achieve the desired outcome. An alternative approach is to utilize combinatorial experimental tools to empirically explore the range of cellular function and to screen for desired traits. This mini-review focuses on computational systems biology and synthetic biology tools that can be used in combination for prospective in silico strain design.

Emergent biosynthetic capacity in simple microbial communities

Microbes have an astonishing capacity to transform their environments. Yet, the metabolic capacity of a single species is limited and the vast majority of microorganisms form complex communities and join forces to exhibit capabilities far exceeding those achieved by any single species. Such enhanced metabolic capacities represent a promising route to many medical, environmental, and industrial applications and call for the development of a predictive, systems-level understanding of synergistic microbial capacity. Here we present a comprehensive computational framework, integrating high-quality metabolic models of multiple species, temporal dynamics, and flux variability analysis, to study the metabolic capacity and dynamics of simple two-species microbial ecosystems. We specifically focus on detecting emergent biosynthetic capacity--instances in which a community growing on some medium produces and secretes metabolites that are not secreted by any member species when growing in isolation on that same medium. Using this framework to model a large collection of two-species communities on multiple media, we demonstrate that emergent biosynthetic capacity is highly prevalent. We identify commonly observed emergent metabolites and metabolic reprogramming patterns, characterizing typical mechanisms of emergent capacity. We further find that emergent secretion tends to occur in two waves, the first as soon as the two organisms are introduced, and the second when the medium is depleted and nutrients become limited. Finally, aiming to identify global community determinants of emergent capacity, we find a marked association between the level of emergent biosynthetic capacity and the functional/phylogenetic distance between community members. Specifically, we demonstrate a "Goldilocks" principle, where high levels of emergent capacity are observed when the species comprising the community are functionally neither too close, nor too distant. Taken together, our results demonstrate the potential to design and engineer synthetic communities capable of novel metabolic activities and point to promising future directions in environmental and clinical bioengineering.

Variability of metabolite levels is linked to differential metabolic pathways in Arabidopsis's responses to abiotic stresses

Constraint-based approaches have been used for integrating data in large-scale metabolic networks to obtain insights into metabolism of various organisms. Due to the underlying steady-state assumption, these approaches are usually not suited for making predictions about metabolite levels. Here, we ask whether we can make inferences about the variability of metabolite levels from a constraint-based analysis based on the integration of transcriptomics data. To this end, we analyze time-resolved transcriptomics and metabolomics data from Arabidopsis thaliana under a set of eight different light and temperature conditions. In a previous study, the gene expression data have already been integrated in a genome-scale metabolic network to predict pathways, termed modulators and sustainers, which are differentially regulated with respect to a biochemically meaningful data-driven null model. Here, we present a follow-up analysis which bridges the gap between flux- and metabolite-centric methods. One of our main findings demonstrates that under certain environmental conditions, the levels of metabolites acting as substrates in modulators or sustainers show significantly lower temporal variations with respect to the remaining measured metabolites. This observation is discussed within the context of a systems-view of plasticity and robustness of metabolite contents and pathway fluxes. Our study paves the way for investigating the existence of similar principles in other species for which both genome-scale networks and high-throughput metabolomics data of high quality are becoming increasingly available.

Method for finding metabolic properties based on the general growth law. Liver examples. A general framework for biological modeling

We propose a method for finding metabolic parameters of cells, organs and whole organisms, which is based on the earlier discovered general growth law. Based on the obtained results and analysis of available biological models, we propose a general framework for modeling biological phenomena and discuss how it can be used in Virtual Liver Network project. The foundational idea of the study is that growth of cells, organs, systems and whole organisms, besides biomolecular machinery, is influenced by biophysical mechanisms acting at different scale levels. In particular, the general growth law uniquely defines distribution of nutritional resources between maintenance needs and biomass synthesis at each phase of growth and at each scale level. We exemplify the approach considering metabolic properties of growing human and dog livers and liver transplants. A procedure for verification of obtained results has been introduced too. We found that two examined dogs have high metabolic rates consuming about 0.62 and 1 gram of nutrients per cubic centimeter of liver per day, and verified this using the proposed verification procedure. We also evaluated consumption rate of nutrients in human livers, determining it to be about 0.088 gram of nutrients per cubic centimeter of liver per day for males, and about 0.098 for females. This noticeable difference can be explained by evolutionary development, which required females to have greater liver processing capacity to support pregnancy. We also found how much nutrients go to biomass synthesis and maintenance at each phase of liver and liver transplant growth. Obtained results demonstrate that the proposed approach can be used for finding metabolic characteristics of cells, organs, and whole organisms, which can further serve as important inputs and constraints for many applications in biology (such as protein expression), biotechnology (synthesis of substances), and medicine.

Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics

The interspecies exchange of metabolites plays a key role in the spatiotemporal dynamics of microbial communities. This raises the question of whether ecosystem-level behavior of structured communities can be predicted using genome-scale metabolic models for multiple organisms. We developed a modeling framework that integrates dynamic flux balance analysis with diffusion on a lattice and applied it to engineered communities. First, we predicted and experimentally confirmed the species ratio to which a two-species mutualistic consortium converges and the equilibrium composition of a newly engineered three-member community. We next identified a specific spatial arrangement of colonies, which gives rise to what we term the "eclipse dilemma": does a competitor placed between a colony and its cross-feeding partner benefit or hurt growth of the original colony? Our experimentally validated finding that the net outcome is beneficial highlights the complex nature of metabolic interactions in microbial communities while at the same time demonstrating their predictability.

Promise and reality in the expanding field of network interaction analysis: metabolic networks

In the last few decades, metabolic networks revealed their capabilities as powerful tools to analyze the cellular metabolism. Many research fields (eg, metabolic engineering, diagnostic medicine, pharmacology, biochemistry, biology and physiology) improved the understanding of the cell combining experimental assays and metabolic network-based computations. This process led to the rise of the “systems biology” approach, where the theory meets experiments and where two complementary perspectives cooperate in the study of biological phenomena. Here, the reconstruction of metabolic networks is presented, along with established and new algorithms to improve the description of cellular metabolism. Then, advantages and limitations of modeling algorithms and network reconstruction are discussed.

Systematic evaluation of methods for integration of transcriptomic data into constraint-based models of metabolism

Constraint-based models of metabolism are a widely used framework for predicting flux distributions in genome-scale biochemical networks. The number of published methods for integration of transcriptomic data into constraint-based models has been rapidly increasing. So far the predictive capability of these methods has not been critically evaluated and compared. This work presents a survey of recently published methods that use transcript levels to try to improve metabolic flux predictions either by generating flux distributions or by creating context-specific models. A subset of these methods is then systematically evaluated using published data from three different case studies in E. coli and S. cerevisiae. The flux predictions made by different methods using transcriptomic data are compared against experimentally determined extracellular and intracellular fluxes (from 13C-labeling data). The sensitivity of the results to method-specific parameters is also evaluated, as well as their robustness to noise in the data. The results show that none of the methods outperforms the others for all cases. Also, it is observed that for many conditions, the predictions obtained by simple flux balance analysis using growth maximization and parsimony criteria are as good or better than those obtained using methods that incorporate transcriptomic data. We further discuss the differences in the mathematical formulation of the methods, and their relation to the results we have obtained, as well as the connection to the underlying biological principles of metabolic regulation.

d-OptCom: Dynamic multi-level and multi-objective metabolic modeling of microbial communities

Most microbial communities change with time in response to changes and/or perturbations in environmental conditions. Temporal variations in interspecies metabolic interactions within these communities can significantly affect their structure and function. Here, we introduce d-OptCom, an extension of the OptCom procedure, for the dynamic metabolic modeling of microbial communities. It enables capturing the temporal dynamics of biomass concentration of the community members and extracellular concentration of the shared metabolites, while integrating species- and community-level fitness functions. The applicability of d-OptCom was demonstrated by modeling the dynamic co-growth of auxotrophic mutant pairs of E. coli and by computationally assessing the dynamics and composition of a uranium-reducing community comprised of Geobacter sulfurreducens, Rhodoferax ferrireducens, and Shewanella oneidensis. d-OptCom was also employed to examine the impact of lactate vs acetate addition on the relative abundance of uranium-reducing species. These studies highlight the importance of simultaneously accounting for both species- and community-level fitness functions when modeling microbial communities, and demonstrate that the incorporation of uptake kinetic information can substantially improve the prediction of interspecies flux trafficking. Overall, this study paves the way for the dynamic multi-level and multi-objective analysis of microbial ecosystems.

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

Toward quantitative understanding on microbial community structure and functioning: a modeling-centered approach using degradation of marine oil spills as example

Molecular ecology approaches are rapidly advancing our insights into the microorganisms involved in the degradation of marine oil spills and their metabolic potentials. Yet, many questions remain open: how do oil-degrading microbial communities assemble in terms of functional diversity, species abundances and organization and what are the drivers? How do the functional properties of microorganisms scale to processes at the ecosystem level? How does mass flow among species, and which factors and species control and regulate fluxes, stability and other ecosystem functions? Can generic rules on oil-degradation be derived, and what drivers underlie these rules? How can we engineer oil-degrading microbial communities such that toxic polycyclic aromatic hydrocarbons are degraded faster? These types of questions apply to the field of microbial ecology in general. We outline how recent advances in single-species systems biology might be extended to help answer these questions. We argue that bottom-up mechanistic modeling allows deciphering the respective roles and interactions among microorganisms. In particular constraint-based, metagenome-derived community-scale flux balance analysis appears suited for this goal as it allows calculating degradation-related fluxes based on physiological constraints and growth strategies, without needing detailed kinetic information. We subsequently discuss what is required to make these approaches successful, and identify a need to better understand microbial physiology in order to advance microbial ecology. We advocate the development of databases containing microbial physiological data. Answering the posed questions is far from trivial. Oil-degrading communities are, however, an attractive setting to start testing systems biology-derived models and hypotheses as they are relatively simple in diversity and key activities, with several key players being isolated and a high availability of experimental data and approaches.

k-OptForce: integrating kinetics with flux balance analysis for strain design

Computational strain design protocols aim at the system-wide identification of intervention strategies for the enhanced production of biochemicals in microorganisms. Existing approaches relying solely on stoichiometry and rudimentary constraint-based regulation overlook the effects of metabolite concentrations and substrate-level enzyme regulation while identifying metabolic interventions. In this paper, we introduce k-OptForce, which integrates the available kinetic descriptions of metabolic steps with stoichiometric models to sharpen the prediction of intervention strategies for improving the bio-production of a chemical of interest. It enables identification of a minimal set of interventions comprised of both enzymatic parameter changes (for reactions with available kinetics) and reaction flux changes (for reactions with only stoichiometric information). Application of k-OptForce to the overproduction of L-serine in E. coli and triacetic acid lactone (TAL) in S. cerevisiae revealed that the identified interventions tend to cause less dramatic rearrangements of the flux distribution so as not to violate concentration bounds. In some cases the incorporation of kinetic information leads to the need for additional interventions as kinetic expressions render stoichiometry-only derived interventions infeasible by violating concentration bounds, whereas in other cases the kinetic expressions impart flux changes that favor the overproduction of the target product thereby requiring fewer direct interventions. A sensitivity analysis on metabolite concentrations shows that the required number of interventions can be significantly affected by changing the imposed bounds on metabolite concentrations. Furthermore, k-OptForce was capable of finding non-intuitive interventions aiming at alleviating the substrate-level inhibition of key enzymes in order to enhance the flux towards the product of interest, which cannot be captured by stoichiometry-alone analysis. This study paves the way for the integrated analysis of kinetic and stoichiometric models and enables elucidating system-wide metabolic interventions while capturing regulatory and kinetic effects.

A model comparison study of the flowering time regulatory network in Arabidopsis

Background

Several dynamic models of a gene regulatory network of the light-induced floral transition process in Arabidopsis have been developed to capture the behavior of gene transcription and infer predictions based on experimental observations. It has been proven that the models can make accurate and novel predictions, which generate testable hypotheses.

Two major issues were addressed in this study. First, construction of dynamic models for gene regulatory networks requires the use of mathematic modeling that comprises equations of a large number of parameters. Second, the binding mechanism of the transcription factor with DNA is another factor that requires detailed modeling. The first issue was tackled by adopting an optimization algorithm, and the second was addressed by comparing the performance of three alternative modeling approaches, namely the S-system, the Michaelis-Menten model and the Mass-action model. The efficiencies of parameter estimation and modeling performance were calculated based on least square error (O(p)), mean relative error (MRE) and Akaike Information Criterion (AIC).

Results

We compared three models to describe gene regulation of the flowering transition process in Arabidopsis. The Mass-action model is the simplest and has the least parameters. It is therefore less computation-intensive with the smallest AIC value. The disadvantage, however, is that it assumes the system is simply a second order reaction which is not the case in our study. The Michaelis-Menten model also assumes the system is homogeneous and ignores the intracellular protein transport process. The S-system model has the best performance and it does describe the diffusion effects. A disadvantage of the S-system is that it involves the most parameters. The largest AIC value also implies an over-fitting may occur in parameter estimation.

Conclusions

Three dynamic models were adopted to describe the dynamics of the gene regulatory network of the flowering transition process in Arabidopsis. Based on MRE, the least square error and global sensitivity analysis, the S-system has the best performance. However, the fact that it has the highest AIC suggests an over-fitting may occur in parameter estimation. The result of this study may need to be applied carefully when modeling complex gene regulatory networks.

Stoichiometric modelling of microbial metabolism

Stoichiometric models describe cellular biochemistry with systems of linear equations. The models which are fundamentally based on the steady-state assumption are comparatively easy to construct and can be applied to networks up to genome scale. Fluxes are inherent variables in stoichiometric models and linear optimization can be used to identify intracellular flux distributions. Great caution, however, has to be paid to the selection of the specific objective function which inevitably implies the existence of a specific global cellular rationale. On the other hand, stoichiometric models provide an analytical platform for contextualization of experimental data. Equally important, the stoichiometric models can be used for structural analyses of metabolic networks as such supporting for example rational model-driven strategies in metabolic engineering.

Recent progress in engineering human-associated microbiomes

Recent progress in molecular biology and genetics opens up the possibility of engineering a variety of biological systems, from single-cellular to multicellular organisms. The consortia of microbes that reside on the human body, the human-associated microbiota, are particularly interesting as targets for forward engineering and manipulation due to their relevance in health and disease. New technologies in analysis and perturbation of the human microbiota will lead to better diagnostic and therapeutic strategies against diseases of microbial origin or pathogenesis. Here, we discuss recent advances that are bringing us closer to realizing the true potential of an engineered human-associated microbial community.

Incorporation of flexible objectives and time-linked simulation with flux balance analysis

We present two modifications of the flux balance analysis (FBA) metabolic modeling framework which relax implicit assumptions of the biomass reaction. Our flexible flux balance analysis (flexFBA) objective removes the fixed proportion between reactants, and can therefore produce a subset of biomass reactants. Our time-linked flux balance analysis (tFBA) simulation removes the fixed proportion between reactants and byproducts, and can therefore describe transitions between metabolic steady states. Used together, flexFBA and tFBA model a time scale shorter than the regulatory and growth steady state encoded by the biomass reaction. This combined short-time FBA method is intended for integrated modeling applications to enable detailed and dynamic depictions of microbial physiology such as whole-cell modeling. For example, when modeling Escherichia coli, it avoids artifacts caused by low-copy-number enzymes in single-cell models with kinetic bounds. Even outside integrated modeling contexts, the detailed predictions of flexFBA and tFBA complement existing FBA techniques. We show detailed metabolite production of in silico knockouts used to identify when correct essentiality predictions are made for the wrong reason.

Optimal control of gene expression for fast proteome adaptation to environmental change

Bacterial populations growing in a changing world must adjust their proteome composition in response to alterations in the environment. Rapid proteome responses to growth medium changes are expected to increase the average growth rate and fitness value of these populations. Little is known about the dynamics of proteome change, e.g., whether bacteria use optimal strategies of gene expression for rapid proteome adjustments and if there are lower bounds to the time of proteome adaptation in response to growth medium changes. To begin answering these types of questions, we modeled growing bacteria as stoichiometrically coupled networks of metabolic pathways. These are balanced during steady-state growth in a constant environment but are initially unbalanced after rapid medium shifts due to a shortage of enzymes required at higher concentrations in the new environment. We identified an optimal strategy for rapid proteome adjustment in the absence of protein degradation and found a lower bound to the time of proteome adaptation after medium shifts. This minimal time is determined by the ratio between the Kullback-Leibler distance from the pre- to the postshift proteome and the postshift steady-state growth rate. The dynamics of optimally controlled proteome adaptation has a simple analytical solution. We used detailed numerical modeling to demonstrate that realistic bacterial control systems can emulate this optimal strategy for rapid proteome adaptation. Our results may provide a conceptual link between the physiology and population genetics of growing bacteria.

Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.

MC3: a steady-state model and constraint consistency checker for biochemical networks

Background

Stoichiometric models provide a structural framework for analyzing steady-state cellular behavior. Models are developed either through augmentations of existing models or more recently through automatic reconstruction tools. There is currently no standardized practice or method for validating the properties of a model before placing it in the public domain. Considerable effort is often required to understand a model’s inconsistencies before its reuse within new research efforts.

Results

We present a review of common issues in stoichiometric models typically uncovered during pathway analysis and constraint-based optimization, and we detail succinct and efficient ways to find them. We present MC³, Model and Constraint Consistency Checker, a computational tool that can be used for two purposes: (a) identifying potential connectivity and topological issues for a given stoichiometric matrix, S, and (b) flagging issues that arise during constraint-based optimization. The MC³ tool includes three distinct checking components. The first examines the results of computing the basis for the null space for Sv = 0; the second uses connectivity analysis; and the third utilizes Flux Variability Analysis. MC³ takes as input a stoichiometric matrix and flux constraints, and generates a report summarizing issues.

Conclusions

We report the results of applying MC³ to published models for several systems including Escherichia coli, an adipocyte cell, a Chinese Hamster Ovary cell, and Leishmania major. Several issues with no prior documentation are identified. MC³ provides a standalone MATLAB-based comprehensive tool for model validation, a task currently performed either ad hoc or implemented in part within other computational tools.

Flux balance analysis of Chlorella sp. FC2 IITG under photoautotrophic and heterotrophic growth conditions

Quantification of carbon flux distribution in the metabolic network of microalgae remains important to understand the complex interplay between energy metabolism, carbon fixation, and assimilation pathways. This is even more relevant with respect to cyclic metabolism of microalgae under light-dark cycle. In the present study, flux balance analysis (FBA) was carried out for an indigenous isolate Chlorella sp. FC2 IITG under photoautotrophic and heterotrophic growth conditions. A shift in intracellular flux distribution was predicted during transition from nutrient sufficient phase to nutrient starvation phase of growth. Further, dynamic flux analysis (dFBA) was carried out to capture light-dark metabolism over discretized pseudo steady state time intervals. Our key findings include the following: (i) unlike heterotrophic condition, oxidative pentose phosphate (PP) pathway, and Krebs cycle were relatively inactive under photoautotrophic growth; (ii) in both growth conditions, while transhydrogenation reaction was highly active, glyoxalate shunt was found to be nonoperative; (iii) flux distribution during transition period was marked with up regulation of carbon flux toward nongrowth associated (NGA) maintenance energy, oxidative phosphorylation, and photophosphorylation; (iv) redirection of carbon flux from polysaccharide and neutral lipid resulted in up regulation of Krebs cycle flux in the dark phase; (v) elevated glycolytic and acetyl-CoA flux were coupled with induction of neutral lipid during light cycle of the growth; (vi) significantly active photophosphorylation in the light phase was able to satisfy cellular energy requirement without need of oxidative PP pathway; and (vi) unlike static FBA, dFBA predicted an unaltered NGA maintenance energy of 1.5 mmol g(-1) DCW h(-1).

Novel multiscale modeling tool applied to Pseudomonas aeruginosa biofilm formation

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.

Multiscale metabolic modeling: dynamic flux balance analysis on a whole-plant scale

Plant metabolism is characterized by a unique complexity on the cellular, tissue, and organ levels. On a whole-plant scale, changing source and sink relations accompanying plant development add another level of complexity to metabolism. With the aim of achieving a spatiotemporal resolution of source-sink interactions in crop plant metabolism, a multiscale metabolic modeling (MMM) approach was applied that integrates static organ-specific models with a whole-plant dynamic model. Allowing for a dynamic flux balance analysis on a whole-plant scale, the MMM approach was used to decipher the metabolic behavior of source and sink organs during the generative phase of the barley (Hordeum vulgare) plant. It reveals a sink-to-source shift of the barley stem caused by the senescence-related decrease in leaf source capacity, which is not sufficient to meet the nutrient requirements of sink organs such as the growing seed. The MMM platform represents a novel approach for the in silico analysis of metabolism on a whole-plant level, allowing for a systemic, spatiotemporally resolved understanding of metabolic processes involved in carbon partitioning, thus providing a novel tool for studying yield stability and crop improvement.

Synthetic biology of cyanobacteria: unique challenges and opportunities

Photosynthetic organisms, and especially cyanobacteria, hold great promise as sources of renewably-produced fuels, bulk and specialty chemicals, and nutritional products. Synthetic biology tools can help unlock cyanobacteria's potential for these functions, but unfortunately tool development for these organisms has lagged behind that for S. cerevisiae and E. coli. While these organisms may in many cases be more difficult to work with as “chassis” strains for synthetic biology than certain heterotrophs, the unique advantages of autotrophs in biotechnology applications as well as the scientific importance of improved understanding of photosynthesis warrant the development of these systems into something akin to a “green E. coli.” In this review, we highlight unique challenges and opportunities for development of synthetic biology approaches in cyanobacteria. We review classical and recently developed methods for constructing targeted mutants in various cyanobacterial strains, and offer perspective on what genetic tools might most greatly expand the ability to engineer new functions in such strains. Similarly, we review what genetic parts are most needed for the development of cyanobacterial synthetic biology. Finally, we highlight recent methods to construct genome-scale models of cyanobacterial metabolism and to use those models to measure properties of autotrophic metabolism. Throughout this paper, we discuss some of the unique challenges of a diurnal, autotrophic lifestyle along with how the development of synthetic biology and biotechnology in cyanobacteria must fit within those constraints.

Analysis and design of a genetic circuit for dynamic metabolic engineering

Recent advances in synthetic biology have equipped us with new tools for bioprocess optimization at the genetic level. Previously, we have presented an integrated in silico design for the dynamic control of gene expression based on a density-sensing unit and a genetic toggle switch. In the present paper, analysis of a serine-producing Escherichia coli mutant shows that an instantaneous ON-OFF switch leads to a maximum theoretical productivity improvement of 29.6% compared to the mutant. To further the design, global sensitivity analysis is applied here to a mathematical model of serine production in E. coli coupled with a genetic circuit. The model of the quorum sensing and the toggle switch involves 13 parameters of which 3 are identified as having a significant effect on serine concentration. Simulations conducted in this reduced parameter space further identified the optimal ranges for these 3 key parameters to achieve productivity values close to the maximum theoretical values. This analysis can now be used to guide the experimental implementation of a dynamic metabolic engineering strategy and reduce the time required to design the genetic circuit components.

Basic concepts and principles of stoichiometric modeling of metabolic networks

Metabolic networks supply the energy and building blocks for cell growth and maintenance. Cells continuously rewire their metabolic networks in response to changes in environmental conditions to sustain fitness. Studies of the systemic properties of metabolic networks give insight into metabolic plasticity and robustness, and the ability of organisms to cope with different environments. Constraint-based stoichiometric modeling of metabolic networks has become an indispensable tool for such studies. Herein, we review the basic theoretical underpinnings of constraint-based stoichiometric modeling of metabolic networks. Basic concepts, such as stoichiometry, chemical moiety conservation, flux modes, flux balance analysis, and flux solution spaces, are explained with simple, illustrative examples. We emphasize the mathematical definitions and their network topological interpretations.

Flux balance analysis of cyanobacterial metabolism: the metabolic network of Synechocystis sp. PCC 6803

Cyanobacteria are versatile unicellular phototrophic microorganisms that are highly abundant in many environments. Owing to their capability to utilize solar energy and atmospheric carbon dioxide for growth, cyanobacteria are increasingly recognized as a prolific resource for the synthesis of valuable chemicals and various biofuels. To fully harness the metabolic capabilities of cyanobacteria necessitates an in-depth understanding of the metabolic interconversions taking place during phototrophic growth, as provided by genome-scale reconstructions of microbial organisms. Here we present an extended reconstruction and analysis of the metabolic network of the unicellular cyanobacterium Synechocystis sp. PCC 6803. Building upon several recent reconstructions of cyanobacterial metabolism, unclear reaction steps are experimentally validated and the functional consequences of unknown or dissenting pathway topologies are discussed. The updated model integrates novel results with respect to the cyanobacterial TCA cycle, an alleged glyoxylate shunt, and the role of photorespiration in cellular growth. Going beyond conventional flux-balance analysis, we extend the computational analysis to diurnal light/dark cycles of cyanobacterial metabolism.

Community flux balance analysis for microbial consortia at balanced growth

A central focus in studies of microbial communities is the elucidation of the relationships between genotype, phenotype, and dynamic community structure. Here, we present a new computational method called community flux balance analysis (cFBA) to study the metabolic behavior of microbial communities. cFBA integrates the comprehensive metabolic capacities of individual microorganisms in terms of (genome-scale) stoichiometric models of metabolism, and the metabolic interactions between species in the community and abiotic processes. In addition, cFBA considers constraints deriving from reaction stoichiometry, reaction thermodynamics, and the ecosystem. cFBA predicts for communities at balanced growth the maximal community growth rate, the required rates of metabolic reactions within and between microbes and the relative species abundances. In order to predict species abundances and metabolic activities at the optimal community growth rate, a nonlinear optimization problem needs to be solved. We outline the methodology of cFBA and illustrate the approach with two examples of microbial communities. These examples illustrate two useful applications of cFBA. Firstly, cFBA can be used to study how specific biochemical limitations in reaction capacities cause different types of metabolic limitations that microbial consortia can encounter. In silico variations of those maximal capacities allow for a global view of the consortium responses to various metabolic and environmental constraints. Secondly, cFBA is very useful for comparing the performance of different metabolic cross-feeding strategies to either find one that agrees with experimental data or one that is most efficient for the community of microorganisms.

Single-cell dynamics reveals sustained growth during diauxic shifts

Stochasticity in gene regulation has been characterized extensively, but how it affects cellular growth and fitness is less clear. We study the growth of E. coli cells as they shift from glucose to lactose metabolism, which is characterized by an obligatory growth arrest in bulk experiments that is termed the lag phase. Here, we follow the growth dynamics of individual cells at minute-resolution using a single-cell assay in a microfluidic device during this shift, while also monitoring lac expression. Mirroring the bulk results, the majority of cells displays a growth arrest upon glucose exhaustion, and resume when triggered by stochastic lac expression events. However, a significant fraction of cells maintains a high rate of elongation and displays no detectable growth lag during the shift. This ability to suppress the growth lag should provide important selective advantages when nutrients are scarce. Trajectories of individual cells display a highly non-linear relation between lac expression and growth, with only a fraction of fully induced levels being sufficient for achieving near maximal growth. A stochastic molecular model together with measured dependencies between nutrient concentration, lac expression level, and growth accurately reproduces the observed switching distributions. The results show that a growth arrest is not obligatory in the classic diauxic shift, and underscore that regulatory stochasticity ought to be considered in terms of its impact on growth and survival.

Applications of analysis of dynamic adaptations in parameter trajectories

Metabolic profiling in combination with pathway-based analyses and computational modelling are becoming increasingly important in clinical and preclinical research. Modelling multi-factorial, progressive diseases requires the integration of molecular data at the metabolome, proteome and transcriptome levels. Also the dynamic interaction of organs and tissues needs to be considered. The processes involved cover time scales that are several orders of magnitude different. We report applications of a computational approach to bridge the scales and different levels of biological detail. Analysis of dynamic adaptations in parameter trajectories (ADAPTs) aims to investigate phenotype transitions during disease development and after a therapeutic intervention. ADAPT is based on a time-dependent evolution of model parameters to describe the dynamics of metabolic adaptations. The progression of metabolic adaptations is predicted by identifying necessary dynamic changes in the model parameters to describe the transition between experimental data obtained during different stages. To get a better understanding of the concept, the ADAPT approach is illustrated in a theoretical study. Its application in research on progressive changes in lipoprotein metabolism is also discussed.

Dynamic metabolic modeling of a microaerobic yeast co-culture: predicting and optimizing ethanol production from glucose/xylose mixtures

BACKGROUND

A key step in any process that converts lignocellulose to biofuels is the efficient fermentation of both hexose and pentose sugars. The co-culture of respiratory-deficient Saccharomyces cerevisiae and wild-type Scheffersomyces stipitis has been identified as a promising system for microaerobic ethanol production because S. cerevisiae only consumes glucose while S. stipitis efficiently converts xylose to ethanol.

RESULTS

To better predict how these two yeasts behave in batch co-culture and to optimize system performance, a dynamic flux balance model describing co-culture metabolism was developed from genome-scale metabolic reconstructions of the individual organisms. First a dynamic model was developed for each organism by estimating substrate uptake kinetic parameters from batch pure culture data and evaluating model extensibility to different microaerobic growth conditions. The co-culture model was constructed by combining the two individual models assuming a cellular objective of total growth rate maximization. To obtain accurate predictions of batch co-culture data collected at different microaerobic conditions, the S. cerevisiae maximum glucose uptake rate was reduced from its pure culture value to account for more efficient S. stipitis glucose uptake in co-culture. The dynamic co-culture model was used to predict the inoculum concentration and aeration level that maximized batch ethanol productivity. The model predictions were validated with batch co-culture experiments performed at the optimal conditions. Furthermore, the dynamic model was used to predict how engineered improvements to the S. stipitis xylose transport system could improve co-culture ethanol production.

CONCLUSIONS

These results demonstrate the utility of the dynamic co-culture metabolic model for guiding process and metabolic engineering efforts aimed at increasing microaerobic ethanol production from glucose/xylose mixtures.

Multi-scale modeling for sustainable chemical production

With recent advances in metabolic engineering, it is now technically possible to produce a wide portfolio of existing petrochemical products from biomass feedstock. In recent years, a number of modeling approaches have been developed to support the engineering and decision-making processes associated with the development and implementation of a sustainable biochemical industry. The temporal and spatial scales of modeling approaches for sustainable chemical production vary greatly, ranging from metabolic models that aid the design of fermentative microbial strains to material and monetary flow models that explore the ecological impacts of all economic activities. Research efforts that attempt to connect the models at different scales have been limited. Here, we review a number of existing modeling approaches and their applications at the scales of metabolism, bioreactor, overall process, chemical industry, economy, and ecosystem. In addition, we propose a multi-scale approach for integrating the existing models into a cohesive framework. The major benefit of this proposed framework is that the design and decision-making at each scale can be informed, guided, and constrained by simulations and predictions at every other scale. In addition, the development of this multi-scale framework would promote cohesive collaborations across multiple traditionally disconnected modeling disciplines to achieve sustainable chemical production.

Dynamic strain scanning optimization: an efficient strain design strategy for balanced yield, titer, and productivity. DySScO strategy for strain design

Background

In recent years, constraint-based metabolic models have emerged as an important tool for metabolic engineering; a number of computational algorithms have been developed for identifying metabolic engineering strategies where the production of the desired chemical is coupled with the growth of the organism. A caveat of the existing algorithms is that they do not take the bioprocess into consideration; as a result, while the product yield can be optimized using these algorithms, the product titer and productivity cannot be optimized. In order to address this issue, we developed the Dynamic Strain Scanning Optimization (DySScO) strategy, which integrates the Dynamic Flux Balance Analysis (dFBA) method with existing strain algorithms.

Results

In order to demonstrate the effective of the DySScO strategy, we applied this strategy to the design of Escherichia coli strains targeted for succinate and 1,4-butanediol production respectively. We evaluated consequences of the tradeoff between growth yield and product yield with respect to titer and productivity, and showed that the DySScO strategy is capable of producing strains that balance the product yield, titer, and productivity. In addition, we evaluated the economic viability of the designed strain, and showed that the economic performance of a strain can be strongly affected by the price difference between the product and the feedstock.

Conclusion

Our study demonstrated that the DySScO strategy is a useful computational tool for designing microbial strains with balanced yield, titer, and productivity, and has potential applications in evaluating the economic performance of the design strains.

Mechanistic analysis of multi-omics datasets to generate kinetic parameters for constraint-based metabolic models

BACKGROUND

Constraint-based modeling uses mass balances, flux capacity, and reaction directionality constraints to predict fluxes through metabolism. Although transcriptional regulation and thermodynamic constraints have been integrated into constraint-based modeling, kinetic rate laws have not been extensively used.

RESULTS

In this study, an in vivo kinetic parameter estimation problem was formulated and solved using multi-omic data sets for Escherichia coli. To narrow the confidence intervals for kinetic parameters, a series of kinetic model simplifications were made, resulting in fewer kinetic parameters than the full kinetic model. These new parameter values are able to account for flux and concentration data from 20 different experimental conditions used in our training dataset. Concentration estimates from the simplified kinetic model were within one standard deviation for 92.7% of the 790 experimental measurements in the training set. Gibbs free energy changes of reaction were calculated to identify reactions that were often operating close to or far from equilibrium. In addition, enzymes whose activities were positively or negatively influenced by metabolite concentrations were also identified. The kinetic model was then used to calculate the maximum and minimum possible flux values for individual reactions from independent metabolite and enzyme concentration data that were not used to estimate parameter values. Incorporating these kinetically-derived flux limits into the constraint-based metabolic model improved predictions for uptake and secretion rates and intracellular fluxes in constraint-based models of central metabolism.

CONCLUSIONS

This study has produced a method for in vivo kinetic parameter estimation and identified strategies and outcomes of kinetic model simplification. We also have illustrated how kinetic constraints can be used to improve constraint-based model predictions for intracellular fluxes and biomass yield and identify potential metabolic limitations through the integrated analysis of multi-omics datasets.

Systematic applications of metabolomics in metabolic engineering

The goals of metabolic engineering are well-served by the biological information provided by metabolomics: information on how the cell is currently using its biochemical resources is perhaps one of the best ways to inform strategies to engineer a cell to produce a target compound. Using the analysis of extracellular or intracellular levels of the target compound (or a few closely related molecules) to drive metabolic engineering is quite common. However, there is surprisingly little systematic use of metabolomics datasets, which simultaneously measure hundreds of metabolites rather than just a few, for that same purpose. Here, we review the most common systematic approaches to integrating metabolite data with metabolic engineering, with emphasis on existing efforts to use whole-metabolome datasets. We then review some of the most common approaches for computational modeling of cell-wide metabolism, including constraint-based models, and discuss current computational approaches that explicitly use metabolomics data. We conclude with discussion of the broader potential of computational approaches that systematically use metabolomics data to drive metabolic engineering.

Temporal expression-based analysis of metabolism

Metabolic flux is frequently rerouted through cellular metabolism in response to dynamic changes in the intra- and extra-cellular environment. Capturing the mechanisms underlying these metabolic transitions in quantitative and predictive models is a prominent challenge in systems biology. Progress in this regard has been made by integrating high-throughput gene expression data into genome-scale stoichiometric models of metabolism. Here, we extend previous approaches to perform a Temporal Expression-based Analysis of Metabolism (TEAM). We apply TEAM to understanding the complex metabolic dynamics of the respiratorily versatile bacterium Shewanella oneidensis grown under aerobic, lactate-limited conditions. TEAM predicts temporal metabolic flux distributions using time-series gene expression data. Increased predictive power is achieved by supplementing these data with a large reference compendium of gene expression, which allows us to take into account the unique character of the distribution of expression of each individual gene. We further propose a straightforward method for studying the sensitivity of TEAM to changes in its fundamental free threshold parameter θ, and reveal that discrete zones of distinct metabolic behavior arise as this parameter is changed. By comparing the qualitative characteristics of these zones to additional experimental data, we are able to constrain the range of θ to a small, well-defined interval. In parallel, the sensitivity analysis reveals the inherently difficult nature of dynamic metabolic flux modeling: small errors early in the simulation propagate to relatively large changes later in the simulation. We expect that handling such “history-dependent” sensitivities will be a major challenge in the future development of dynamic metabolic-modeling techniques.

Understanding the dynamic response of microorganisms to environmental changes is a major challenge in systems biology. In many cases, these responses manifest themselves through changes in gene transcription, which then propagate to adjust flow through metabolism. Here, we implement a Temporal Expression-based Analysis of Metabolism (TEAM) by dynamically integrating a genome-scale model of the metabolism of S. oneidensis with high-throughput measurements of gene expression and growth data. TEAM recapitulates the complex cascade of secretion and re-uptake of intermediary carbon sources that S. oneidensis exhibits in the experimental data. We show that these complicated metabolic behaviors are best captured when TEAM explicitly accounts for each gene's unique transcriptional signature. Furthermore, by way of a newly proposed sensitivity analysis, we reveal and study the inherent difficulty of dynamic metabolic flux modeling: small changes early in a simulation can easily spread and lead to significant changes towards the end of it. We expect that further development of robust dynamic flux balance methods will need to overcome such “history-dependent” sensitivities in order to achieve increased predictive accuracy.