Dynamic flux balance analysis of diauxic growth in Escherichia coli

Network-level allosteric effects are elucidated by detailing how ligand-binding events modulate utilization of catalytic potentials

Allosteric regulation has traditionally been described by mathematically-complex allosteric rate laws in the form of ratios of polynomials derived from the application of simplifying kinetic assumptions. Alternatively, an approach that explicitly describes all known ligand-binding events requires no simplifying assumptions while allowing for the computation of enzymatic states. Here, we employ such a modeling approach to examine the "catalytic potential" of an enzyme-an enzyme's capacity to catalyze a biochemical reaction. The catalytic potential is the fundamental result of multiple ligand-binding events that represents a "tug of war" among the various regulators and substrates within the network. This formalism allows for the assessment of interacting allosteric enzymes and development of a network-level understanding of regulation. We first define the catalytic potential and use it to characterize the response of three key kinases (hexokinase, phosphofructokinase, and pyruvate kinase) in human red blood cell glycolysis to perturbations in ATP utilization. Next, we examine the sensitivity of the catalytic potential by using existing personalized models, finding that the catalytic potential allows for the identification of subtle but important differences in how individuals respond to such perturbations. Finally, we explore how the catalytic potential can help to elucidate how enzymes work in tandem to maintain a homeostatic state. Taken together, this work provides an interpretation and visualization of the dynamic interactions and network-level effects of interacting allosteric enzymes.

A Review of Dynamic Modeling Approaches and Their Application in Computational Strain Optimization for Metabolic Engineering

Mathematical modeling is a key process to describe the behavior of biological networks. One of the most difficult challenges is to build models that allow quantitative predictions of the cells' states along time. Recently, this issue started to be tackled through novel in silico approaches, such as the reconstruction of dynamic models, the use of phenotype prediction methods, and pathway design via efficient strain optimization algorithms. The use of dynamic models, which include detailed kinetic information of the biological systems, potentially increases the scope of the applications and the accuracy of the phenotype predictions. New efforts in metabolic engineering aim at bridging the gap between this approach and other different paradigms of mathematical modeling, as constraint-based approaches. These strategies take advantage of the best features of each method, and deal with the most remarkable limitation—the lack of available experimental information—which affects the accuracy and feasibility of solutions. Parameter estimation helps to solve this problem, but adding more computational cost to the overall process. Moreover, the existing approaches include limitations such as their scalability, flexibility, convergence time of the simulations, among others. The aim is to establish a trade-off between the size of the model and the level of accuracy of the solutions. In this work, we review the state of the art of dynamic modeling and related methods used for metabolic engineering applications, including approaches based on hybrid modeling. We describe approaches developed to undertake issues regarding the mathematical formulation and the underlying optimization algorithms, and that address the phenotype prediction by including available kinetic rate laws of metabolic processes. Then, we discuss how these have been used and combined as the basis to build computational strain optimization methods for metabolic engineering purposes, how they lead to bi-level schemes that can be used in the industry, including a consideration of their limitations.

Consistency of cybernetic variables with gene expression profiles: A more rigorous test

Diauxic growth of Escherichia coli is driven by a host of internal, complex regulatory actions. In this classic scenario of cellular control, the cell employs a rational algorithm to modulate its metabolism in a competitive fashion. Cybernetic models of metabolism, whose development now spans three decades, were first formulated to describe regulation of cells in complex, multi-substrate environments. They modeled this scenario using the hypothesis that the formation of the enzymatic machinery is regulated to maximize a return on investment. While this assumption is made on the basis of logical arguments rooted in evolutionary principles, little effort has been taken to validate if enzymes are truly synthesized in the same fashion that is predicted by cybernetic variables. This work revisits the original cybernetic models describing diauxic growth and compares their predictions of enzyme synthesis control with time series gene expression data in microarray and qRT-PCR formats. Three separate studies are made for two different strains of E. coli. The first is for the growth of E. coli BW25113 on a mixture of glucose and acetate, whose gene expression changes are metered by microarray. Another is also for the sequential consumption of glucose and acetate but involves strain MG1655 and employs qRT-PCR. The final is for E. coli MG1655 on glucose and lactose. By demonstrating how cybernetic variables for induced enzyme synthesis mimic the behavior of transcriptional data, a strong argument for using cybernetic models is made. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:858-867, 2018.

Putting primary metabolism into perspective to obtain better fruits

Background

One of the key goals of fruit biology is to understand the factors that influence fruit growth and quality, ultimately with a view to manipulating them for improvement of fruit traits.

Scope

Primary metabolism, which is not only essential for growth but is also a major component of fruit quality, is an obvious target for improvement. However, metabolism is a moving target that undergoes marked changes throughout fruit growth and ripening.

Conclusions

Agricultural practice and breeding have successfully improved fruit metabolic traits, but both face the complexity of the interplay between development, metabolism and the environment. Thus, more fundamental knowledge is needed to identify further strategies for the manipulation of fruit metabolism. Nearly two decades of post-genomics approaches involving transcriptomics, proteomics and/or metabolomics have generated a lot of information about the behaviour of fruit metabolic networks. Today, the emergence of modelling tools is providing the opportunity to turn this information into a mechanistic understanding of fruits, and ultimately to design better fruits. Since high-quality data are a key requirement in modelling, a range of must-have parameters and variables is proposed.

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

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

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems

Background

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed.

Results

In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics.

Conclusion

The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0584-8) contains supplementary material, which is available to authorized users.

Dynamic elementary mode modelling of non-steady state flux data

BACKGROUND

A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.

RESULTS

Two methods are introduced here: dynamic elementary mode analysis (dynEMA) and dynamic elementary mode regression discriminant analysis (dynEMR-DA). The former is an extension of the recently proposed principal elementary mode analysis (PEMA) method from steady state to non-steady state scenarios. The latter is a discriminant model that permits to identify which dynEMs behave strongly different depending on the experimental conditions. Two case studies of Saccharomyces cerevisiae, with fluxes derived from simulated and real concentration data sets, are presented to highlight the benefits of this dynamic modelling.

CONCLUSIONS

This methodology permits to analyse metabolic fluxes at early stages with the aim of i) creating reduced dynamic models of flux data, ii) combining many experiments in a single biologically meaningful model, and iii) identifying the metabolic pathways that drive the organism from one state to another when changing the environmental conditions.

Metabolic model-based analysis of the emergence of bacterial cross-feeding via extensive gene loss

Background

Metabolic dependencies between microbial species have a significant impact on the assembly and activity of microbial communities. However, the evolutionary origins of such dependencies and the impact of metabolic and genomic architecture on their emergence are not clear.

Results

To address these questions, we developed a novel framework, coupling a reductive evolution model with a multi-species genome-scale metabolic model to simulate the evolution of two-species microbial communities. Simulating thousands of independent evolutionary trajectories, we surprisingly found that under certain environmental and evolutionary settings metabolic dependencies emerged frequently even though our model does not include explicit selection for cooperation. Evolved dependencies involved cross-feeding of a diverse set of metabolites, reflecting constraints imposed by metabolic network architecture. We additionally found metabolic ‘missed opportunities’, wherein species failed to capitalize on metabolites made available by their partners. Examining the genes deleted in each evolutionary trajectory and the deletion timing further revealed both genome-wide properties and specific metabolic mechanisms associated with species interaction.

Conclusion

Our findings provide insight into the evolution of cooperative interaction among microbial species and a unique view into the way such relationships emerge.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0588-4) contains supplementary material, which is available to authorized users.

Estimation of time-varying growth, uptake and excretion rates from dynamic metabolomics data

Motivation

Technological advances in metabolomics have made it possible to monitor the concentration of extracellular metabolites over time. From these data, it is possible to compute the rates of uptake and excretion of the metabolites by a growing cell population, providing precious information on the functioning of intracellular metabolism. The computation of the rate of these exchange reactions, however, is difficult to achieve in practice for a number of reasons, notably noisy measurements, correlations between the concentration profiles of the different extracellular metabolites, and discontinuties in the profiles due to sudden changes in metabolic regime.

Results

We present a method for precisely estimating time-varying uptake and excretion rates from time-series measurements of extracellular metabolite concentrations, specifically addressing all of the above issues. The estimation problem is formulated in a regularized Bayesian framework and solved by a combination of extended Kalman filtering and smoothing. The method is shown to improve upon methods based on spline smoothing of the data. Moreover, when applied to two actual datasets, the method recovers known features of overflow metabolism in Escherichia coli and Lactococcus lactis, and provides evidence for acetate uptake by L. lactis after glucose exhaustion. The results raise interesting perspectives for further work on rate estimation from measurements of intracellular metabolites.

Availability and implementation

The Matlab code for the estimation method is available for download at https://team.inria.fr/ibis/rate-estimation-software/, together with the datasets.

Supplementary information

Supplementary data are available at Bioinformatics online.

Optimization of bioprocess productivity based on metabolic-genetic network models with bilevel dynamic programming

One of the main goals of metabolic engineering is to obtain high levels of a microbial product through genetic modifications. To improve the productivity of such a process, the dynamic implementation of metabolic engineering strategies has been proven to be more beneficial compared to static genetic manipulations in which the gene expression is not controlled over time, by resolving the trade-off between growth and production. In this work, a bilevel optimization framework based on constraint-based models is applied to identify an optimal strategy for dynamic genetic and process level manipulations to increase productivity. The dynamic enzyme-cost flux balance analysis (deFBA) as underlying metabolic network model captures the network dynamics and enables the analysis of temporal regulation in the metabolic-genetic network. We apply our computational framework to maximize ethanol productivity in a batch process with Escherichia coli. The results highlight the importance of integrating the genetic level and enzyme production and degradation processes for obtaining optimal dynamic gene and process manipulations.

Review and perspective on mathematical modeling of microbial ecosystems

Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial 'who is there?'

QUESTION

An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment. Mathematical models with their abstraction capability are essential to capture the underlying phenomena and connect the different scales at which these systems act. Differential equation models and constraint-based stoichiometric models are deterministic approaches that can successfully provide a macroscopic description of the outcome from microscopic behaviors. In this mini-review, we present classical and recent applications of these modeling methods and illustrate the potential of their integration. Indeed, approaches that can capture multiple scales are needed in order to understand emergent patterns in ecosystems and their dynamics regulated by different spatio-temporal phenomena. We finally discuss promising examples of methods proposing the integration of differential equations with constraint-based stoichiometric models and argue that more work is needed in this direction.

Integration of genome-scale metabolic networks into whole-body PBPK models shows phenotype-specific cases of drug-induced metabolic perturbation

Drug-induced perturbations of the endogenous metabolic network are a potential root cause of cellular toxicity. A mechanistic understanding of such unwanted side effects during drug therapy is therefore vital for patient safety. The comprehensive assessment of such drug-induced injuries requires the simultaneous consideration of both drug exposure at the whole-body and resulting biochemical responses at the cellular level. We here present a computational multi-scale workflow that combines whole-body physiologically based pharmacokinetic (PBPK) models and organ-specific genome-scale metabolic network (GSMN) models through shared reactions of the xenobiotic metabolism. The applicability of the proposed workflow is illustrated for isoniazid, a first-line antibacterial agent against Mycobacterium tuberculosis, which is known to cause idiosyncratic drug-induced liver injuries (DILI). We combined GSMN models of a human liver with N-acetyl transferase 2 (NAT2)-phenotype-specific PBPK models of isoniazid. The combined PBPK-GSMN models quantitatively describe isoniazid pharmacokinetics, as well as intracellular responses, and changes in the exometabolome in a human liver following isoniazid administration. Notably, intracellular and extracellular responses identified with the PBPK-GSMN models are in line with experimental and clinical findings. Moreover, the drug-induced metabolic perturbations are distributed and attenuated in the metabolic network in a phenotype-dependent manner. Our simulation results show that a simultaneous consideration of both drug pharmacokinetics at the whole-body and metabolism at the cellular level is mandatory to explain drug-induced injuries at the patient level. The proposed workflow extends our mechanistic understanding of the biochemistry underlying adverse events and may be used to prevent drug-induced injuries in the future.

The genotype of a patient determines the extent of drug-induced metabolic perturbations on the endogenous cellular network of the liver. A team around Lars Kuepfer at Germany’s RWTH Aachen University developed a computational workflow that links drug pharmacokinetics at the whole-body level with a cellular network of the liver. The authors used the competitive cofactor and energy demands in endogenous and drug metabolism to establish a multi-scale model for the antibiotic isoniazid. Their model quantitatively describes how isoniazid pharmacokinetics alter the intracellular liver biochemistry and the utilization of extracellular metabolites in different patient genotypes. The study outlines how a mechanistic understanding of genotype-dependent drug-induced metabolic perturbations may help to explain diverging incidence rates of toxic events in different patient subgroups. This could reduce the occurrence of toxic side effects during drug treatments in the future.

Genome-scale fluxes predicted under the guidance of enzyme abundance using a novel hyper-cube shrink algorithm

Motivation

One of the long-expected goals of genome-scale metabolic modelling is to evaluate the influence of the perturbed enzymes on flux distribution. Both ordinary differential equation (ODE) models and constraint-based models, like Flux balance analysis (FBA), lack the capacity to perform metabolic control analysis (MCA) for large-scale networks.

Results

In this study, we developed a hyper-cube shrink algorithm (HCSA) to incorporate the enzymatic properties into the FBA model by introducing a pseudo reaction V constrained by enzymatic parameters. Our algorithm uses the enzymatic information quantitatively rather than qualitatively. We first demonstrate the concept by applying HCSA to a simple three-node network, whereby we obtained a good correlation between flux and enzyme abundance. We then validate its prediction by comparison with ODE and with a synthetic network producing voilacein and analogues in Saccharomyces cerevisiae. We show that HCSA can mimic the state-state results of ODE. Finally, we show its capability of predicting the flux distribution in genome-scale networks by applying it to sporulation in yeast. We show the ability of HCSA to operate without biomass flux and perform MCA to determine rate-limiting reactions.

Availability and implementation

Algorithm was implemented by Matlab and C ++. The code is available at https://github.com/kekegg/HCSA.

Contact

xiezhengwei@hsc.pku.edu.cn or qi@pku.edu.cn.

Supplementary information

Supplementary data are available at Bioinformatics online.

The spatial and metabolic basis of colony size variation

Spatial structure impacts microbial growth and interactions, with ecological and evolutionary consequences. It is therefore important to quantitatively understand how spatial proximity affects interactions in different environments. We tested how proximity influences colony size when either Escherichia coli or Salmonella enterica are grown on various carbon sources. The importance of colony location changed with species and carbon source. Spatially explicit, genome-scale metabolic modeling recapitulated observed colony size variation. Competitors that determine territory size, according to Voronoi diagrams, were the most important drivers of variation in colony size. However, the relative importance of different competitors changed through time. Further, the effect of location increased when colonies took up resources quickly relative to the diffusion of limiting resources. These analyses made it apparent that the importance of location was smaller than expected for experiments with S. enterica growing on glucose. The accumulation of toxic byproducts appeared to limit the growth of large colonies and reduced variation in colony size. Our work provides an experimentally and theoretically grounded understanding of how location interacts with metabolism and diffusion to influence microbial interactions.

Dynamic Flux Balance Analysis Using DFBAlab

Bioprocesses are of critical importance in several industries such as the food and pharmaceutical industries. Despite their importance and widespread application, bioprocess models remain rather simplistic and based on unstructured models. These simple models have limitations, making it very difficult to model complex bioprocesses. With dynamic flux balance analysis (DFBA) more comprehensive bioprocess models can be obtained. DFBA simulations are difficult to carry out because they result in dynamic systems with linear programs embedded. Therefore, the use of DFBA as a modeling tool has been limited. With DFBAlab, a MATLAB code that performs efficient and reliable DFBA simulations, the use of DFBA as a modeling tool has become more accessible. Here, we illustrate with an example how to implement bioprocess models in DFBAlab.

Computational Approaches on Stoichiometric and Kinetic Modeling for Efficient Strain Design

Engineering biological systems that are capable of overproducing products of interest is the ultimate goal of any biotechnology application. To this end, stoichiometric (or steady state) and kinetic models are increasingly becoming available for a variety of organisms including prokaryotes, eukaryotes, and microbial communities. This ever-accelerating pace of such model reconstructions has also spurred the development of optimization-based strain design techniques. This chapter highlights a number of such frameworks developed in recent years in order to generate testable hypotheses (in terms of genetic interventions), thus addressing the challenges in metabolic engineering. In particular, three major methods are covered in detail including two methods for designing strains (i.e., one stoichiometric model-based and the other by integrating kinetic information into a stoichiometric model) and one method for analyzing microbial communities.

Computational Methods to Assess the Production Potential of Bio-Based Chemicals

Elevated costs and long implementation times of bio-based processes for producing chemicals represent a bottleneck for moving to a bio-based economy. A prospective analysis able to elucidate economically and technically feasible product targets at early research phases is mandatory. Computational tools can be implemented to explore the biological and technical spectrum of feasibility, while constraining the operational space for desired chemicals. In this chapter, two different computational tools for assessing potential for bio-based production of chemicals from different perspectives are described in detail. The first tool is GEM-Path: an algorithm to compute all structurally possible pathways from one target molecule to the host metabolome. The second tool is a framework for Modeling Sustainable Industrial Chemicals production (MuSIC), which integrates modeling approaches for cellular metabolism, bioreactor design, upstream/downstream processes, and economic impact assessment. Integrating GEM-Path and MuSIC will play a vital role in supporting early phases of research efforts and guide the policy makers with decisions, as we progress toward planning a sustainable chemical industry.

Optimization of Multi-Omic Genome-Scale Models: Methodologies, Hands-on Tutorial, and Perspectives

Genome-scale metabolic models are valuable tools for assessing the metabolic potential of living organisms. Being downstream of gene expression, metabolism is increasingly being used as an indicator of the phenotypic outcome for drugs and therapies. We here present a review of the principal methods used for constraint-based modelling in systems biology, and explore how the integration of multi-omic data can be used to improve phenotypic predictions of genome-scale metabolic models. We believe that the large-scale comparison of the metabolic response of an organism to different environmental conditions will be an important challenge for genome-scale models. Therefore, within the context of multi-omic methods, we describe a tutorial for multi-objective optimization using the metabolic and transcriptomics adaptation estimator (METRADE), implemented in MATLAB. METRADE uses microarray and codon usage data to model bacterial metabolic response to environmental conditions (e.g., antibiotics, temperatures, heat shock). Finally, we discuss key considerations for the integration of multi-omic networks into metabolic models, towards automatically extracting knowledge from such models.

From Genes to Ecosystems in Microbiology: Modeling Approaches and the Importance of Individuality

Models are important tools in microbial ecology. They can be used to advance understanding by helping to interpret observations and test hypotheses, and to predict the effects of ecosystem management actions or a different climate. Over the past decades, biological knowledge and ecosystem observations have advanced to the molecular and in particular gene level. However, microbial ecology models have changed less and a current challenge is to make them utilize the knowledge and observations at the genetic level. We review published models that explicitly consider genes and make predictions at the population or ecosystem level. The models can be grouped into three general approaches, i.e., metabolic flux, gene-centric and agent-based. We describe and contrast these approaches by applying them to a hypothetical ecosystem and discuss their strengths and weaknesses. An important distinguishing feature is how variation between individual cells (individuality) is handled. In microbial ecosystems, individual heterogeneity is generated by a number of mechanisms including stochastic interactions of molecules (e.g., gene expression), stochastic and deterministic cell division asymmetry, small-scale environmental heterogeneity, and differential transport in a heterogeneous environment. This heterogeneity can then be amplified and transferred to other cell properties by several mechanisms, including nutrient uptake, metabolism and growth, cell cycle asynchronicity and the effects of age and damage. For example, stochastic gene expression may lead to heterogeneity in nutrient uptake enzyme levels, which in turn results in heterogeneity in intracellular nutrient levels. Individuality can have important ecological consequences, including division of labor, bet hedging, aging and sub-optimality. Understanding the importance of individuality and the mechanism(s) underlying it for the specific microbial system and question investigated is essential for selecting the optimal modeling strategy.

Advances and perspectives in computational prediction of microbial gene essentiality

The minimal subset of genes required for cellular growth, survival and viability of an organism are classified as essential genes. Knowledge of essential genes gives insight into the core structure and functioning of a cell. This might lead to more efficient antimicrobial drug discovery, to elucidation of the correlations between genotype and phenotype, and a better understanding of the minimal requirements for a (synthetic) cell. Traditionally, constructing a catalog of essential genes for a given microbe involved costly and time-consuming laboratory experiments. While experimental methods have produced abundant gene essentiality data for model organisms like Escherichia coli and Bacillus subtilis, the knowledge generated cannot automatically be extrapolated to predict essential genes in all bacteria. In addition, essential genes identified in the laboratory are by definition 'conditionally essential', as they are essential under the specified experimental conditions: these might not resemble conditions in the microorganisms' natural habitat(s). Also, large-scale experimental assaying for essential genes is not always feasible because of the time investment required to setup these assays. The ability to rapidly and precisely identify essential genes in silico is therefore important and has great potential for applications in medicine, biotechnology and basic biological research. Here, we review the advances made in the use of computational methods to predict microbial gene essentiality, perspectives for the future of these techniques and the possible practical applications of essential genes.

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

In the continuous mode of cell culture, a constant flow carrying fresh media replaces culture fluid, cells, nutrients and secreted metabolites. Here we present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. We derive a number of consequences from the model that are independent of parameter values. The ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties. This conclusion is robust even in the presence of multi-stability, which is explained in our model by a negative feedback loop due to toxic byproduct accumulation. A complex landscape of steady states emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced.

Combining metabolomics and network analysis to improve tacrolimus production in Streptomyces tsukubaensis using different exogenous feedings

Tacrolimus is widely used as an immunosuppressant in the treatment of various autoimmune diseases. However, the low fermentation yield of tacrolimus has thus far restricted its industrial applications. To solve this problem, the time-series response mechanisms of the intracellular metabolism that were highly correlated with tacrolimus biosynthesis were investigated using different exogenous feeding strategies in S. tsukubaensis. The metabolomic datasets, which contained 93 metabolites, were subjected to weighted correlation network analysis (WGCNA), and eight distinct metabolic modules and seven hub metabolites were identified to be specifically associated with tacrolimus biosynthesis. The analysis of metabolites within each metabolic module suggested that the pentose phosphate pathway (PPP), shikimate and aspartate pathway might be the main limiting factors in the rapid synthesis phase of tacrolimus accumulation. Subsequently, all possible key-limiting steps in the above metabolic pathways were further screened using a genome-scale metabolic network model (GSMM) of S. tsukubaensis. Based on the prediction results, two newly identified targets (aroC and dapA) were overexpressed experimentally, and both of the engineered strains showed higher tacrolimus production. Moreover, the best strain, HT-aroC/dapA, that was engineered to simultaneously enhanced chorismate and lysine biosynthesis was able to produce 128.19 mg/L tacrolimus, 1.64-fold higher than control (78.26 mg/L). These findings represent a valuable addition to our understanding of tacrolimus accumulation in S. tsukubaensis, and pave the way to further production improvements.

Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

Constraint-based stoichiometric modelling from single organisms to microbial communities

Microbial communities are ubiquitously found in Nature and have direct implications for the environment, human health and biotechnology. The species composition and overall function of microbial communities are largely shaped by metabolic interactions such as competition for resources and cross-feeding. Although considerable scientific progress has been made towards mapping and modelling species-level metabolism, elucidating the metabolic exchanges between microorganisms and steering the community dynamics remain an enormous scientific challenge. In view of the complexity, computational models of microbial communities are essential to obtain systems-level understanding of ecosystem functioning. This review discusses the applications and limitations of constraint-based stoichiometric modelling tools, and in particular flux balance analysis (FBA). We explain this approach from first principles and identify the challenges one faces when extending it to communities, and discuss the approaches used in the field in view of these challenges. We distinguish between steady-state and dynamic FBA approaches extended to communities. We conclude that much progress has been made, but many of the challenges are still open.

Parametric studies of metabolic cooperativity in Escherichia coli colonies: Strain and geometric confinement effects

Characterizing the complex spatial and temporal interactions among cells in a biological system (i.e. bacterial colony, microbiome, tissue, etc.) remains a challenge. Metabolic cooperativity in these systems can arise due to the subtle interplay between microenvironmental conditions and the cells' regulatory machinery, often involving cascades of intra- and extracellular signalling molecules. In the simplest of cases, as demonstrated in a recent study of the model organism Escherichia coli, metabolic cross-feeding can arise in monoclonal colonies of bacteria driven merely by spatial heterogeneity in the availability of growth substrates; namely, acetate, glucose and oxygen. Another recent study demonstrated that even closely related E. coli strains evolved different glucose utilization and acetate production capabilities, hinting at the possibility of subtle differences in metabolic cooperativity and the resulting growth behavior of these organisms. Taking a first step towards understanding the complex spatio-temporal interactions within microbial populations, we performed a parametric study of E. coli growth on an agar substrate and probed the dependence of colony behavior on: 1) strain-specific metabolic characteristics, and 2) the geometry of the underlying substrate. To do so, we employed a recently developed multiscale technique named 3D dynamic flux balance analysis which couples reaction-diffusion simulations with iterative steady-state metabolic modeling. Key measures examined include colony growth rate and shape (height vs. width), metabolite production/consumption and concentration profiles, and the emergence of metabolic cooperativity and the fractions of cell phenotypes. Five closely related strains of E. coli, which exhibit large variation in glucose consumption and organic acid production potential, were studied. The onset of metabolic cooperativity was found to vary substantially between these five strains by up to 10 hours and the relative fraction of acetate utilizing cells within the colonies varied by a factor of two. Additionally, growth with six different geometries designed to mimic those that might be found in a laboratory, a microfluidic device, and inside a living organism were considered. Geometries were found to have complex, often nonlinear effects on colony growth and cross-feeding with "hard" features resulting in larger effect than "soft" features. These results demonstrate that strain-specific features and spatial constraints imposed by the growth substrate can have significant effects even for microbial populations as simple as isogenic E. coli colonies.

Overflow metabolism and growth cessation in Clostridium thermocellum DSM1313 during high cellulose loading fermentations

As a model thermophilic bacterium for the production of second-generation biofuels, the metabolism of Clostridium thermocellum has been widely studied. However, most studies have characterized C. thermocellum metabolism for growth at relatively low substrate concentrations. This outlook is not industrially relevant, however, as commercial viability requires substrate loadings of at least 100 g/L cellulosic materials. Recently, a wild-type C. thermocellum DSM1313 was cultured on high cellulose loading batch fermentations and reported to produce a wide range of fermentative products not seen at lower substrate concentrations, opening the door for a more in-depth analysis of how this organism will behave in industrially relevant conditions. In this work, we elucidated the interconnectedness of overflow metabolism and growth cessation in C. thermocellum during high cellulose loading batch fermentations (100 g/L). Metabolic flux and thermodynamic analyses suggested that hydrogen and formate accumulation perturbed the complex redox metabolism and limited conversion of pyruvate to acetyl-CoA conversion, likely leading to overflow metabolism and growth cessation in C. thermocellum. Pyruvate formate lyase (PFL) acts as an important redox valve and its flux is inhibited by formate accumulation. Finally, we demonstrated that manipulation of fermentation conditions to alleviate hydrogen accumulation could dramatically alter the fate of pyruvate, providing valuable insight into process design for enhanced C. thermocellum production of chemicals and biofuels. Biotechnol. Bioeng. 2017;114: 2592-2604. © 2017 Wiley Periodicals, Inc.

Plant genome-scale reconstruction: from single cell to multi-tissue modelling and omics analyses

In this review, we present the latest developments in plant systems biology with particular emphasis on plant genome-scale reconstructions and multi-omics analyses. Understanding multicellular metabolism is far from trivial and 'omics' data are difficult to interpret in the absence of a systems framework. 'Omics' data appropriately integrated with genome-scale reconstructions and modelling facilitates our understanding of how individual components interact and influence overall cell, tissue or organisms function. Here we present examples of how plant metabolic reconstructions and modelling are used as a systems-based framework for improving our understanding of the plant metabolic processes in single cells and multiple tissues.

A multiscale, model-based analysis of the multi-tissue interplay underlying blood glucose regulation in type I diabetes

A multiscale model for blood glucose regulation in diabetes type I patients is constructed by integrating detailed metabolic network models for fat, liver and muscle cells into a whole body physiologically-based pharmacokinetic/pharmacodynamic (pBPK/PD) model. The blood glucose regulation PBPK/PD model simulates the distribution and metabolization of glucose, insulin and glucagon on an organ and whole body level. The genome-scale metabolic networks in contrast describe intracellular reactions. The developed multiscale model is fitted to insulin, glucagon and glucose measurements of a 48h clinical trial featuring 6 subjects and is subsequently used to simulate (in silico) the influence of geneknockouts and drug-induced enzyme inhibitions on whole body blood glucose levels. Simulations of diabetes associated gene knockouts and impaired cellular glucose metabolism, resulted in elevated whole body blood-glucose levels, but also in a metabolic shift within the cell's reaction network. Such multiscale models have the potential to be employed in the exploration of novel drug-targets or to be integrated into control algorithms for artificial pancreas systems.

redGEM: Systematic reduction and analysis of genome-scale metabolic reconstructions for development of consistent core metabolic models

Genome-scale metabolic reconstructions have proven to be valuable resources in enhancing our understanding of metabolic networks as they encapsulate all known metabolic capabilities of the organisms from genes to proteins to their functions. However the complexity of these large metabolic networks often hinders their utility in various practical applications. Although reduced models are commonly used for modeling and in integrating experimental data, they are often inconsistent across different studies and laboratories due to different criteria and detail, which can compromise transferability of the findings and also integration of experimental data from different groups. In this study, we have developed a systematic semi-automatic approach to reduce genome-scale models into core models in a consistent and logical manner focusing on the central metabolism or subsystems of interest. The method minimizes the loss of information using an approach that combines graph-based search and optimization methods. The resulting core models are shown to be able to capture key properties of the genome-scale models and preserve consistency in terms of biomass and by-product yields, flux and concentration variability and gene essentiality. The development of these “consistently-reduced” models will help to clarify and facilitate integration of different experimental data to draw new understanding that can be directly extendable to genome-scale models.

Reduced models are used commonly to understand the metabolism of organisms and to integrate experimental data for many different studies such as physiology, fluxomics and metabolomics. Without consistent or clear criteria on how these reduced models are actually developed, it is difficult to ensure that they reflect the detailed knowledge that is kept in genome scale metabolic network models (GEMs). The redGEM algorithm presented here allows us to systematically develop consistently reduced metabolic models from their genome-scale counterparts. We applied redGEM for the construction of a core model for E. coli central carbon metabolism. We constructed the core model irJO1366 based on the latest genome-scale E. coli metabolic reconstruction (iJO1366). irJO1366 contains the central carbon pathways and other immediate pathways that must be connected to them for consistency with the iJO1366. irJO1366 can be used to understand metabolism of the organism and also to provide guidance for metabolic engineering purposes. The algorithm is also designed to be modular so that heterologous reactions or pathways can be appended to the core model akin to a “plug-and-play”, synthetic biology approach. The algorithm is applicable to any compartmentalized or non-compartmentalized GEM.

More than just a gut feeling: constraint-based genome-scale metabolic models for predicting functions of human intestinal microbes

The human gut is colonized with a myriad of microbes, with substantial interpersonal variation. This complex ecosystem is an integral part of the gastrointestinal tract and plays a major role in the maintenance of homeostasis. Its dysfunction has been correlated to a wide array of diseases, but the understanding of causal mechanisms is hampered by the limited amount of cultured microbes, poor understanding of phenotypes, and the limited knowledge about interspecies interactions. Genome-scale metabolic models (GEMs) have been used in many different fields, ranging from metabolic engineering to the prediction of interspecies interactions. We provide showcase examples for the application of GEMs for gut microbes and focus on (i) the prediction of minimal, synthetic, or defined media; (ii) the prediction of possible functions and phenotypes; and (iii) the prediction of interspecies interactions. All three applications are key in understanding the role of individual species in the gut ecosystem as well as the role of the microbiota as a whole. Using GEMs in the described fashions has led to designs of minimal growth media, an increased understanding of microbial phenotypes and their influence on the host immune system, and dietary interventions to improve human health. Ultimately, an increased understanding of the gut ecosystem will enable targeted interventions in gut microbial composition to restore homeostasis and appropriate host-microbe crosstalk.

A Diverse Community To Study Communities: Integration of Experiments and Mathematical Models To Study Microbial Consortia

The last few years have seen the advancement of high-throughput experimental techniques that have produced an extraordinary amount of data. Bioinformatics and statistical analyses have become instrumental to interpreting the information coming from, e.g., sequencing data and often motivate further targeted experiments. The broad discipline of “computational biology” extends far beyond the well-established field of bioinformatics, but it is our impression that more theoretical methods such as the use of mathematical models are not yet as well integrated into the research studying microbial interactions. The empirical complexity of microbial communities presents challenges that are difficult to address with in vivo/in vitro approaches alone, and with microbiology developing from a qualitative to a quantitative science, we see stronger opportunities arising for interdisciplinary projects integrating theoretical approaches with experiments. Indeed, the addition of in silico experiments, i.e., computational simulations, has a discovery potential that is, unfortunately, still largely underutilized and unrecognized by the scientific community. This minireview provides an overview of mathematical models of natural ecosystems and emphasizes that one critical point in the development of a theoretical description of a microbial community is the choice of problem scale. Since this choice is mostly dictated by the biological question to be addressed, in order to employ theoretical models fully and successfully it is vital to implement an interdisciplinary view at the conceptual stages of the experimental design.

Computational modelling of genome-scale metabolic networks and its application to CHO cell cultures

Genome-scale metabolic models (GEMs) have become increasingly important in recent years. Currently, GEMs are the most accurate in silico representation of the genotype-phenotype link. They allow us to study complex networks from the systems perspective. Their application may drastically reduce the amount of experimental and clinical work, improve diagnostic tools and increase our understanding of complex biological phenomena. GEMs have also demonstrated high potential for the optimisation of bio-based production of recombinant proteins. Herein, we review the basic concepts, methods, resources and software tools used for the reconstruction and application of GEMs. We overview the evolution of the modelling efforts devoted to the metabolism of Chinese Hamster Ovary (CHO) cells. We present a case study on CHO cell metabolism under different amino acid depletions. This leads us to the identification of the most influential as well as essential amino acids in selected CHO cell lines.

Heterogeneous oxygen availability affects the titer and topology but not the fidelity of plasmid DNA produced by Escherichia coli

Background

Dissolved oxygen tension (DOT) is hardly constant and homogenously distributed in a bioreactor, which can have a negative impact in the metabolism and product synthesis. However, the effects of DOT on plasmid DNA (pDNA) production and quality have not been thoroughly investigated. In the present study, the effects of aerobic (DOT ≥30% air sat.), microaerobic (constant DOT = 3% air sat.) and oscillatory DOT (from 0 to 100% air sat.) conditions on pDNA production, quality and host performance were characterized.

Results

Microaerobic conditions had little effect on pDNA production, supercoiled fraction and sequence fidelity. By contrast, oscillatory DOT caused a 22% decrease in pDNA production compared with aerobic cultures. Although in aerobic cultures the pDNA supercoiled fraction was 98%, it decreased to 80% under heterogeneous DOT conditions. The different oxygen availabilities had no effect on the fidelity of the produced pDNA. The estimated metabolic fluxes indicated substantial differences at the level of the pentose phosphate pathway and TCA cycle under different conditions. Cyclic changes in fermentative pathway fluxes, as well as fast shifts in the fluxes through cytochromes, were also estimated. Model-based genetic modifications that can potentially improve the process performance are suggested.

Conclusions

DOT heterogeneities strongly affected cell performance, pDNA production and topology. This should be considered when operating or scaling-up a bioreactor with deficient mixing. Constant microaerobic conditions affected the bacterial metabolism but not the amount or quality of pDNA. Therefore, pDNA production in microaerobic cultures may be an alternative for bioreactor operation at higher oxygen transfer rates.

Electronic supplementary material

The online version of this article (doi:10.1186/s12896-017-0378-x) contains supplementary material, which is available to authorized users.

Engineering biological systems using automated biofoundries

Engineered biological systems such as genetic circuits and microbial cell factories have promised to solve many challenges in the modern society. However, the artisanal processes of research and development are slow, expensive, and inconsistent, representing a major obstacle in biotechnology and bioengineering. In recent years, biological foundries or biofoundries have been developed to automate design-build-test engineering cycles in an effort to accelerate these processes. This review summarizes the enabling technologies for such biofoundries as well as their early successes and remaining challenges.

Clostridium butyricum maximizes growth while minimizing enzyme usage and ATP production: metabolic flux distribution of a strain cultured in glycerol

BACKGROUND

The increase in glycerol obtained as a byproduct of biodiesel has encouraged the production of new industrial products, such as 1,3-propanediol (PDO), using biotechnological transformation via bacteria like Clostridium butyricum. However, despite the increasing role of Clostridium butyricum as a bio-production platform, its metabolism remains poorly modeled.

RESULTS

We reconstructed iCbu641, the first genome-scale metabolic (GSM) model of a PDO producer Clostridium strain, which included 641 genes, 365 enzymes, 891 reactions, and 701 metabolites. We found an enzyme expression prediction of nearly 84% after comparison of proteomic data with flux distribution estimation using flux balance analysis (FBA). The remaining 16% corresponded to enzymes directionally coupled to growth, according to flux coupling findings (FCF). The fermentation data validation also revealed different phenotype states that depended on culture media conditions; for example, Clostridium maximizes its biomass yield per enzyme usage under glycerol limitation. By contrast, under glycerol excess conditions, Clostridium grows sub-optimally, maximizing biomass yield while minimizing both enzyme usage and ATP production. We further evaluated perturbations in the GSM model through enzyme deletions and variations in biomass composition. The GSM predictions showed no significant increase in PDO production, suggesting a robustness to perturbations in the GSM model. We used the experimental results to predict that co-fermentation was a better alternative than iCbu641 perturbations for improving PDO yields.

CONCLUSIONS

The agreement between the predicted and experimental values allows the use of the GSM model constructed for the PDO-producing Clostridium strain to propose new scenarios for PDO production, such as dynamic simulations, thereby reducing the time and costs associated with experimentation.

Dynamic metabolic modeling of heterotrophic and mixotrophic microalgal growth on fermentative wastes

Microalgae are promising microorganisms for the production of numerous molecules of interest, such as pigments, proteins or triglycerides that can be turned into biofuels. Heterotrophic or mixotrophic growth on fermentative wastes represents an interesting approach to achieving higher biomass concentrations, while reducing cost and improving the environmental footprint. Fermentative wastes generally consist of a blend of diverse molecules and it is thus crucial to understand microalgal metabolism in such conditions, where switching between substrates might occur. Metabolic modeling has proven to be an efficient tool for understanding metabolism and guiding the optimization of biomass or target molecule production. Here, we focused on the metabolism of Chlorella sorokiniana growing heterotrophically and mixotrophically on acetate and butyrate. The metabolism was represented by 172 metabolic reactions. The DRUM modeling framework with a mildly relaxed quasi-steady-state assumption was used to account for the switching between substrates and the presence of light. Nine experiments were used to calibrate the model and nine experiments for the validation. The model efficiently predicted the experimental data, including the transient behavior during heterotrophic, autotrophic, mixotrophic and diauxic growth. It shows that an accurate model of metabolism can now be constructed, even in dynamic conditions, with the presence of several carbon substrates. It also opens new perspectives for the heterotrophic and mixotrophic use of microalgae, especially for biofuel production from wastes.