Resource allocation modeling for autonomous prediction of plant cell phenotypes

Predicting the plant cell response in complex environmental conditions is a challenge in plant biology. Here we developed a resource allocation model of cellular and molecular scale for the leaf photosynthetic cell of Arabidopsis thaliana, based on the Resource Balance Analysis (RBA) constraint-based modeling framework. The RBA model contains the metabolic network and the major macromolecular processes involved in the plant cell growth and survival and localized in cellular compartments. We simulated the model for varying environmental conditions of temperature, irradiance, partial pressure of CO2 and O2, and compared RBA predictions to known resource distributions and quantitative phenotypic traits such as the relative growth rate, the C:N ratio, and finally to the empirical characteristics of CO2 fixation given by the well-established Farquhar model. In comparison to other standard constraint-based modeling methods like Flux Balance Analysis, the RBA model makes accurate quantitative predictions without the need for empirical constraints. Altogether, we show that RBA significantly improves the autonomous prediction of plant cell phenotypes in complex environmental conditions, and provides mechanistic links between the genotype and the phenotype of the plant cell.

Prediction and integration of metabolite-protein interactions with genome-scale metabolic models

Metabolites, as small molecules, can act not only as substrates to enzymes, but also as effectors of activity of proteins with different functions, thereby affecting various cellular processes. While several experimental techniques have started to catalogue the metabolite-protein interactions (MPIs) present in different cellular contexts, characterizing the functional relevance of MPIs remains a challenging problem. Computational approaches from the constrained-based modeling framework allow for predicting MPIs and integrating their effects in the in silico analysis of metabolic and physiological phenotypes, like cell growth. Here, we provide a classification of all existing constraint-based approaches that predict and integrate MPIs using genome-scale metabolic networks as input. In addition, we benchmark the performance of the approaches to predict MPIs in a comparative study using different features extracted from the model structure and predicted metabolic phenotypes with the state-of-the-art metabolic networks of Escherichia coli and Saccharomyces cerevisiae. Lastly, we provide an outlook for future, feasible directions to expand the consideration of MPIs in constraint-based modeling approaches with wide biotechnological applications.

Fuzzy optimization for identifying antiviral targets for treating SARS-CoV-2 infection in the heart

In this paper, a fuzzy hierarchical optimization framework is proposed for identifying potential antiviral targets for treating severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in the heart. The proposed framework comprises four objectives for evaluating the elimination of viral biomass growth and the minimization of side effects during treatment. In the application of the framework, Dulbecco's modified eagle medium (DMEM) and Ham's medium were used as uptake nutrients on an antiviral target discovery platform. The prediction results from the framework reveal that most of the antiviral enzymes in the aforementioned media are involved in fatty acid metabolism and amino acid metabolism. However, six enzymes involved in cholesterol biosynthesis in Ham's medium and three enzymes involved in glycolysis in DMEM are unable to eliminate the growth of the SARS-CoV-2 biomass. Three enzymes involved in glycolysis, namely BPGM, GAPDH, and ENO1, in DMEM combine with the supplemental uptake of L-cysteine to increase the cell viability grade and metabolic deviation grade. Moreover, six enzymes involved in cholesterol biosynthesis reduce and fail to reduce viral biomass growth in a culture medium if a cholesterol uptake reaction does not occur and occurs in this medium, respectively.

Model Validation and Selection in Metabolic Flux Analysis and Flux Balance Analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both of these methods use metabolic reaction network models of metabolism operating at steady state, so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. A number of approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to decide on and/or discriminate between alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ2-test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how the adoption of robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology in particular.

Co-feeding enhances the yield of methyl ketones

The biotechnological production of methyl ketones is a sustainable alternative to fossil-derived chemical production. To date, the best host for microbial production of methyl ketones is a genetically engineered Pseudomonas taiwanensis VLB120 ∆6 pProd strain, achieving yields of 101 mgg-1 on glucose in batch cultivations. For competitiveness with the petrochemical production pathway, however, higher yields are necessary. Co-feeding can improve the yield by fitting the carbon-to-energy ratio to the organism and the target product. In this work, we developed co-feeding strategies for P. taiwanensis VLB120 ∆6 pProd by combined metabolic modeling and experimental work. In a first step, we conducted flux balance analysis with an expanded genome-scale metabolic model of iJN1463 and found ethanol as the most promising among five cosubstrates. Next, we performed cultivations with ethanol and found the highest reported yield in batch production of methyl ketones with P. taiwanensis VLB120 to date, namely, 154 mg g-1 methyl ketones. However, ethanol is toxic to the cell, which reflects in a lower substrate consumption and lower product concentrations when compared to production on glucose. Hence, we propose cofeeding ethanol with glucose and find that, indeed, higher concentrations than in ethanol-fed cultivation (0.84 g Laq-1 with glucose and ethanol as opposed to 0.48 g Laq-1 with only ethanol) were achieved, with a yield of 85 mg g-1. In a last step, comparing experimental with computational results suggested the potential for improving the methyl ketone yield by fed-batch cultivation, in which cell growth and methyl ketone production are separated into two phases employing optimal ethanol to glucose ratios.

ONE-SENTENCE SUMMARY

By combining computational and experimental work, we demonstrate that feeding ethanol in addition to glucose improves the yield of biotechnologically produced methyl ketones.

Linear programming based gene expression model (LPM-GEM) predicts the carbon source for Bacillus subtilis

BACKGROUND

Elucidating cellular metabolism led to many breakthroughs in biotechnology, synthetic biology, and health sciences. To date, deriving metabolic fluxes by ¹³C tracer experiments is the most prominent approach for studying metabolic fluxes quantitatively, often with high accuracy and precision. However, the technique has a high demand for experimental resources. Alternatively, flux balance analysis (FBA) has been employed to estimate metabolic fluxes without labeling experiments. It is less informative but can benefit from the low costs and low experimental efforts and gain flux estimates in experimentally difficult conditions. Methods to integrate relevant experimental data have been emerged to improve FBA flux estimations. Data from transcription profiling is often selected since it is easy to generate at the genome scale, typically embedded by a discretization of differential and non-differential expressed genes coding for the respective enzymes.

RESULT

We established the novel method Linear Programming based Gene Expression Model (LPM-GEM). LPM-GEM linearly embeds gene expression into FBA constraints. We implemented three strategies to reduce thermodynamically infeasible loops, which is a necessary prerequisite for such an omics-based model building. As a case study, we built a model of B. subtilis grown in eight different carbon sources. We obtained good flux predictions based on the respective transcription profiles when validating with ¹³C tracer based metabolic flux data of the same conditions. We could well predict the specific carbon sources. When testing the model on another, unseen dataset that was not used during training, good prediction performance was also observed. Furthermore, LPM-GEM outperformed a well-established model building methods.

CONCLUSION

Employing LPM-GEM integrates gene expression data efficiently. The method supports gene expression-based FBA models and can be applied as an alternative to estimate metabolic fluxes when tracer experiments are inappropriate.

Toward modeling metabolic state from single-cell transcriptomics

Background

Single-cell metabolic studies bring new insights into cellular function, which can often not be captured on other omics layers. Metabolic information has wide applicability, such as for the study of cellular heterogeneity or for the understanding of drug mechanisms and biomarker development. However, metabolic measurements on single-cell level are limited by insufficient scalability and sensitivity, as well as resource intensiveness, and are currently not possible in parallel with measuring transcript state, commonly used to identify cell types. Nevertheless, because omics layers are strongly intertwined, it is possible to make metabolic predictions based on measured data of more easily measurable omics layers together with prior metabolic network knowledge.

Scope of Review

We summarize the current state of single-cell metabolic measurement and modeling approaches, motivating the use of computational techniques. We review three main classes of computational methods used for prediction of single-cell metabolism: pathway-level analysis, constraint-based modeling, and kinetic modeling. We describe the unique challenges arising when transitioning from bulk to single-cell modeling. Finally, we propose potential model extensions and computational methods that could be leveraged to achieve these goals.

Major Conclusions

Single-cell metabolic modeling is a rising field that provides a new perspective for understanding cellular functions. The presented modeling approaches vary in terms of input requirements and assumptions, scalability, modeled metabolic layers, and newly gained insights. We believe that the use of prior metabolic knowledge will lead to more robust predictions and will pave the way for mechanistic and interpretable machine-learning models.

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Single-cell RNA sequencing and prior metabolic knowledge enable metabolic predictions.

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When compared to bulk, single-cell modeling is linked to unique insights and challenges.

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Computational modelling approaches differ in applicability and newly provided insights.

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The use of prior metabolic knowledge paves the way for mechanistic machine-learning.

Engineering Escherichia coli for the utilization of ethylene glycol

Background

A considerable challenge in the development of bioprocesses for producing chemicals and fuels has been the high cost of feedstocks relative to oil prices, making it difficult for these processes to compete with their conventional petrochemical counterparts. Hence, in the absence of high oil prices in the near future, there has been a shift in the industry to produce higher value compounds such as fragrances for cosmetics. Yet, there is still a need to address climate change and develop biotechnological approaches for producing large market, lower value chemicals and fuels.

Results

In this work, we study ethylene glycol (EG), a novel feedstock that we believe has promise to address this challenge. We engineer Escherichia coli (E. coli) to consume EG and examine glycolate production as a case study for chemical production. Using a combination of modeling and experimental studies, we identify oxygen concentration as an important metabolic valve in the assimilation and use of EG as a substrate. Two oxygen-based strategies are thus developed and tested in fed-batch bioreactors. Ultimately, the best glycolate production strategy employed a target respiratory quotient leading to the highest observed fermentation performance. With this strategy, a glycolate titer of 10.4 g/L was reached after 112 h of production time in a fed-batch bioreactor. Correspondingly, a yield of 0.8 g/g from EG and productivity of 0.1 g/L h were measured during the production stage. Our modeling and experimental results clearly suggest that oxygen concentration is an important factor in the assimilation and use of EG as a substrate. Finally, our use of metabolic modeling also sheds light on the intracellular distribution through central metabolism, implicating flux to 2-phosphoglycerate as the primary route for EG assimilation.

Conclusion

Overall, our work suggests that EG could provide a renewable starting material for commercial biosynthesis of fuels and chemicals that may achieve economic parity with petrochemical feedstocks while sequestering carbon dioxide.

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

Background

The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS² approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS² approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations.

Results

In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS² approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables.

Conclusions

Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Systematically gap-filling the genome-scale metabolic model of CHO cells

OBJECTIVE

Chinese hamster ovary (CHO) cells are the leading cell factories for producing recombinant proteins in the biopharmaceutical industry. In this regard, constraint-based metabolic models are useful platforms to perform computational analysis of cell metabolism. These models need to be regularly updated in order to include the latest biochemical data of the cells, and to increase their predictive power. Here, we provide an update to iCHO1766, the metabolic model of CHO cells.

RESULTS

We expanded the existing model of Chinese hamster metabolism with the help of four gap-filling approaches, leading to the addition of 773 new reactions and 335 new genes. We incorporated these into an updated genome-scale metabolic network model of CHO cells, named iCHO2101. In this updated model, the number of reactions and pathways capable of carrying flux is substantially increased.

CONCLUSIONS

The present CHO model is an important step towards more complete metabolic models of CHO cells.

Genome-scale metabolic reconstruction of the non-model yeast Issatchenkia orientalis SD108 and its application to organic acids production

Many platform chemicals can be produced from renewable biomass by microorganisms, with organic acids making up a large fraction. Intolerance to the resulting low pH growth conditions, however, remains a challenge for the industrial production of organic acids by microorganisms. Issatchenkia orientalis SD108 is a promising host for industrial production because it is tolerant to acidic conditions as low as pH 2.0. With the goal to systematically assess the metabolic capabilities of this non-model yeast, we developed a genome-scale metabolic model for I. orientalis SD108 spanning 850 genes, 1826 reactions, and 1702 metabolites. In order to improve the model’s quantitative predictions, organism-specific macromolecular composition and ATP maintenance requirements were determined experimentally and implemented. We examined its network topology, including essential genes and flux coupling analysis and drew comparisons with the Yeast 8.3 model for Saccharomyces cerevisiae. We explored the carbon substrate utilization and examined the organism’s production potential for the industrially-relevant succinic acid, making use of the OptKnock framework to identify gene knockouts which couple production of the targeted chemical to biomass production. The genome-scale metabolic model iIsor850 is a data-supported curated model which can inform genetic interventions for overproduction.

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Genome-scale metabolic model iIsor850 describes metabolism of I. orientalis SD108.

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Customized biomass reaction highlights differences with S. cerevisiae.

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Chemostat data elucidate growth-associated ATP maintenance.

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Substrate utilization and CRISPR/Cas9 gene knockout phenotypes validate model.

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Model pinpoints candidate gene deletions coupling succinic acid production to growth.

Regulatory dynamic enzyme-cost flux balance analysis: A unifying framework for constraint-based modeling

Integrated modeling of metabolism and gene regulation continues to be a major challenge in computational biology. While there exist approaches like regulatory flux balance analysis (rFBA), dynamic flux balance analysis (dFBA), resource balance analysis (RBA) or dynamic enzyme-cost flux balance analysis (deFBA) extending classical flux balance analysis (FBA) in various directions, there have been no constraint-based methods so far that allow predicting the dynamics of metabolism taking into account both macromolecule production costs and regulatory events. In this paper, we introduce a new constraint-based modeling framework named regulatory dynamic enzyme-cost flux balance analysis (r-deFBA), which unifies dynamic modeling of metabolism, cellular resource allocation and transcriptional regulation in a hybrid discrete-continuous setting. With r-deFBA, we can predict discrete regulatory states together with the continuous dynamics of reaction fluxes, external substrates, enzymes, and regulatory proteins needed to achieve a cellular objective such as maximizing biomass over a time interval. The dynamic optimization problem underlying r-deFBA can be reformulated as a mixed-integer linear optimization problem, for which there exist efficient solvers.

Metabolic Network Reconstructions to Predict Drug Targets and Off-Target Effects

The drug development pipeline has stalled because of the difficulty in identifying new drug targets while minimizing off-target effects. Computational methods, such as the use of metabolic network reconstructions, may provide a cost-effective platform to test new hypotheses for drug targets and prevent off-target effects. Here, we summarize available methods to identify drug targets and off-target effects using either reaction-centric, gene-centric, or metabolite-centric approaches with genome-scale metabolic network reconstructions.

Inferring Metabolic Flux from Time-Course Metabolomics

The metabolic activity of a mammalian cell changes dynamically over time and is tied to the changing metabolic demands of cellular processes such as cell differentiation and proliferation. While experimental tools like time-course metabolomics and flux tracing can measure the dynamics of a few pathways, they are unable to infer fluxes at the whole network level. To address this limitation, we have developed the Dynamic Flux Activity (DFA) algorithm, a genome-scale modeling approach that uses time-course metabolomics to predict dynamic flux rewiring during transitions between metabolic states. This chapter provides a protocol for applying DFA to characterize the dynamic metabolic activity of various cancer cell lines.

Advanced Modeling of Cellular Proliferation: Toward a Multi-scale Framework Coupling Cell Cycle to Metabolism by Integrating Logical and Constraint-Based Models

Biological functions require a coherent cross talk among multiple layers of regulation within the cell. Computational efforts that aim to understand how these layers are integrated across spatial, temporal, and functional scales represent a challenge in Systems Biology. We have developed a computational, multi-scale framework that couples cell cycle and metabolism networks in the budding yeast cell. Here we describe the methodology at the basis of this framework, which integrates on off-the-shelf logical (Boolean) models of a minimal yeast cell cycle with a constraint-based model of metabolism (i.e., the Yeast 7 metabolic network reconstruction). Models are implemented in Python code using the BooleanNet and COBRApy packages, respectively, and are connected through the Boolean logic. The methodology allows for incorporation of interaction data, and validation through -omics data. Furthermore, evolutionary strategies may be incorporated to explore regulatory structures underlying coherent cross talks among regulatory layers.

Systematic assessment of secondary bile acid metabolism in gut microbes reveals distinct metabolic capabilities in inflammatory bowel disease

BACKGROUND

The human gut microbiome performs important functions in human health and disease. A classic example for host-gut microbial co-metabolism is host biosynthesis of primary bile acids and their subsequent deconjugation and transformation by the gut microbiome. To understand these system-level host-microbe interactions, a mechanistic, multi-scale computational systems biology approach that integrates the different types of omic data is needed. Here, we use a systematic workflow to computationally model bile acid metabolism in gut microbes and microbial communities.

RESULTS

Therefore, we first performed a comparative genomic analysis of bile acid deconjugation and biotransformation pathways in 693 human gut microbial genomes and expanded 232 curated genome-scale microbial metabolic reconstructions with the corresponding reactions (available at https://vmh.life ). We then predicted the bile acid biotransformation potential of each microbe and in combination with other microbes. We found that each microbe could produce maximally six of the 13 secondary bile acids in silico, while microbial pairs could produce up to 12 bile acids, suggesting bile acid biotransformation being a microbial community task. To investigate the metabolic potential of a given microbiome, publicly available metagenomics data from healthy Western individuals, as well as inflammatory bowel disease patients and healthy controls, were mapped onto the genomes of the reconstructed strains. We constructed for each individual a large-scale personalized microbial community model that takes into account strain-level abundances. Using flux balance analysis, we found considerable variation in the potential to deconjugate and transform primary bile acids between the gut microbiomes of healthy individuals. Moreover, the microbiomes of pediatric inflammatory bowel disease patients were significantly depleted in their bile acid production potential compared with that of controls. The contributions of each strain to overall bile acid production potential across individuals were found to be distinct between inflammatory bowel disease patients and controls. Finally, bottlenecks limiting secondary bile acid production potential were identified in each microbiome model.

CONCLUSIONS

This large-scale modeling approach provides a novel way of analyzing metagenomics data to accelerate our understanding of the metabolic interactions between the host and gut microbiomes in health and diseases states. Our models and tools are freely available to the scientific community.

DynamicME: dynamic simulation and refinement of integrated models of metabolism and protein expression

BACKGROUND

Genome-scale models of metabolism and macromolecular expression (ME models) enable systems-level computation of proteome allocation coupled to metabolic phenotype.

RESULTS

We develop DynamicME, an algorithm enabling time-course simulation of cell metabolism and protein expression. DynamicME correctly predicted the substrate utilization hierarchy on a mixed carbon substrate medium. We also found good agreement between predicted and measured time-course expression profiles. ME models involve considerably more parameters than metabolic models (M models). We thus generate an ensemble of models (each model having its rate constants perturbed), and then analyze the models by identifying archetypal time-course metabolite concentration profiles. Furthermore, we use a metaheuristic optimization method to calibrate ME model parameters using time-course measurements such as from a (fed-) batch culture. Finally, we show that constraints on protein concentration dynamics ("inertia") alter the metabolic response to environmental fluctuations, including increased substrate-level phosphorylation and lowered oxidative phosphorylation.

CONCLUSIONS

Overall, DynamicME provides a novel method for understanding proteome allocation and metabolism under complex and transient environments, and to utilize time-course cell culture data for model-based interpretation or model refinement.

Dynamic Network Modeling of Stem Cell Metabolism

Stem cell metabolism is intrinsically tied to stem cell pluripotency and function. Yet, understanding metabolic rewiring in stem cells has been challenging due to the complex and highly interconnected nature of the metabolic network. Genome-scale metabolic network models are increasingly used to holistically model the metabolic behavior of various cells and tissues using transcriptomics data. However, these powerful approaches that model steady-state behavior have limited utility for studying dynamic stem cell state transitions. To address this complexity, we recently developed the dynamic flux activity (DFA) approach; DFA is a genome-scale modeling approach that uses time-course metabolic data to predict metabolic flux rewiring. This protocol outlines the steps for modeling steady-state and dynamic metabolic behavior using transcriptomics and time-course metabolomics data, respectively. Using data from naive and primed pluripotent stem cells, we demonstrate how we can use genome-scale modeling and DFA to comprehensively characterize the metabolic differences between these states.

Escher-FBA: a web application for interactive flux balance analysis

Background

Flux balance analysis (FBA) is a widely-used method for analyzing metabolic networks. However, most existing tools that implement FBA require downloading software and writing code. Furthermore, FBA generates predictions for metabolic networks with thousands of components, so meaningful changes in FBA solutions can be difficult to identify. These challenges make it difficult for beginners to learn how FBA works.

Results

To meet this need, we present Escher-FBA, a web application for interactive FBA simulations within a pathway visualization. Escher-FBA allows users to set flux bounds, knock out reactions, change objective functions, upload metabolic models, and generate high-quality figures without downloading software or writing code. We provide detailed instructions on how to use Escher-FBA to replicate several FBA simulations that generate real scientific hypotheses.

Conclusions

We designed Escher-FBA to be as intuitive as possible so that users can quickly and easily understand the core concepts of FBA. The web application can be accessed at https://sbrg.github.io/escher-fba.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0607-5) contains supplementary material, which is available to authorized users.

rate) optimization in constraint-based modeling and applications in metabolic engineering

BACKGROUND

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing.

RESULTS

We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli.

CONCLUSIONS

We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements.

The FASTCORE Family: For the Fast Reconstruction of Compact Context-Specific Metabolic Networks Models

The FASTCORE family is a family of algorithms that are mainly used to build context-specific models but can also be applied to other tasks such as gapfilling and consistency testing. The FASTCORE family has very low computational demands with running times that are several orders of magnitude lower than its main competitors. Furthermore, the models built by the FASTCORE family have a better resolution power (defined as the ability to capture metabolic variations between different tissues, cell types, or contexts) than models from other algorithms.

Coupling Fluxes, Enzymes, and Regulation in Genome-Scale Metabolic Models

Genome-scale models have expanded beyond their metabolic origins. Multiple modeling frameworks are required to combine metabolism with enzymatic networks, transcription, translation, and regulation. Mathematical programming offers a powerful set of tools for tackling these "multi-modality" models, although special attention must be paid to the connections between modeling types. This chapter reviews common methods for combining metabolic and discrete logical models into a single mathematical programming framework. Best practices, caveats, and recommendations are presented for the most commonly used software packages. Methods for troubleshooting large sets of logical rules are also discussed.

Quantitative systems pharmacology and the personalized drug-microbiota-diet axis

Precision medicine is an emerging paradigm that aims at maximizing the benefits and minimizing the adverse effects of drugs. Realistic mechanistic models are needed to understand and limit heterogeneity in drug responses. While pharmacokinetic models describe in detail a drug's absorption and metabolism, they generally do not account for individual variations in response to environmental influences, in addition to genetic variation. For instance, the human gut microbiota metabolizes drugs and is modulated by diet, and it exhibits significant variation among individuals. However, the influence of the gut microbiota on drug failure or drug side effects is under-researched. Here, we review recent advances in computational modeling approaches that could contribute to a better, mechanism-based understanding of drug–microbiota–diet interactions and their contribution to individual drug responses. By integrating systems biology and quantitative systems pharmacology with microbiology and nutrition, the conceptually and technologically demand for novel approaches could be met to enable the study of individual variability, thereby providing breakthrough support for progress in precision medicine.

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The response to drug treatment is highly variable among individuals.

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Pharmacokinetic models have been used to accelerate drug discovery but do not account for a person's diet and gut microbiota.

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Here, we propose combining constraint-based and pharmacokinetic modeling to capture also dietary and gut microbial metabolism.

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Such integrated models will enable the individual-specific prediction of drug response.

Glycosylation flux analysis reveals dynamic changes of intracellular glycosylation flux distribution in Chinese hamster ovary fed-batch cultures

N-linked glycosylation of proteins has both functional and structural significance. Importantly, the glycan structure of a therapeutic protein influences its efficacy, pharmacokinetics, pharmacodynamics and immunogenicity. In this work, we developed glycosylation flux analysis (GFA) for predicting intracellular production and consumption rates (fluxes) of glycoforms, and applied this analysis to CHO fed-batch immunoglobulin G (IgG) production using two different media compositions, with and without additional manganese feeding. The GFA is based on a constraint-based modeling of the glycosylation network, employing a pseudo steady state assumption. While the glycosylation fluxes in the network are balanced at each time point, the GFA allows the fluxes to vary with time by way of two scaling factors: (1) an enzyme-specific factor that captures the temporal changes among glycosylation reactions catalysed by the same enzyme, and (2) the cell specific productivity factor that accounts for the dynamic changes in the IgG production rate. The GFA of the CHO fed-batch cultivations showed that regardless of the media composition, galactosylation fluxes decreased with the cultivation time more significantly than the other glycosylation reactions. Furthermore, the GFA showed that the addition of Mn, a cofactor of galactosyltransferase, has the effect of increasing the galactosylation fluxes but only during the beginning of the cultivation period. The results thus demonstrated the power of the GFA in delineating the dynamic alterations of the glycosylation fluxes by local (enzyme-specific) and global (cell specific productivity) factors.

Development of a Framework for Metabolic Pathway Analysis-Driven Strain Optimization Methods

Genome-scale metabolic models (GSMMs) have become important assets for rational design of compound overproduction using microbial cell factories. Most computational strain optimization methods (CSOM) using GSMMs, while useful in metabolic engineering, rely on the definition of questionable cell objectives, leading to some bias. Metabolic pathway analysis approaches do not require an objective function. Though their use brings immediate advantages, it has mostly been restricted to small scale models due to computational demands. Additionally, their complex parameterization and lack of intuitive tools pose an important challenge towards making these widely available to the community. Recently, MCSEnumerator has extended the scale of these methods, namely regarding enumeration of minimal cut sets, now able to handle GSMMs. This work proposes a tool implementing this method as a Java library and a plugin within the OptFlux metabolic engineering platform providing a friendly user interface. A standard enumeration problem and pipeline applicable to GSMMs is proposed, making use by the community simpler. To highlight the potential of these approaches, we devised a case study for overproduction of succinate, providing a phenotype analysis of a selected strategy and comparing robustness with a selected solution from a bi-level CSOM.

A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks

Background

Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement.

Results

Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways.

Conclusions

Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1412-z) contains supplementary material, which is available to authorized users.

Literature mining supports a next-generation modeling approach to predict cellular byproduct secretion

The metabolic byproducts secreted by growing cells can be easily measured and provide a window into the state of a cell; they have been essential to the development of microbiology, cancer biology, and biotechnology. Progress in computational modeling of cells has made it possible to predict metabolic byproduct secretion with bottom-up reconstructions of metabolic networks. However, owing to a lack of data, it has not been possible to validate these predictions across a wide range of strains and conditions. Through literature mining, we were able to generate a database of Escherichia coli strains and their experimentally measured byproduct secretions. We simulated these strains in six historical genome-scale models of E. coli, and we report that the predictive power of the models has increased as they have expanded in size and scope. The latest genome-scale model of metabolism correctly predicts byproduct secretion for 35/89 (39%) of designs. The next-generation genome-scale model of metabolism and gene expression (ME-model) correctly predicts byproduct secretion for 40/89 (45%) of designs, and we show that ME-model predictions could be further improved through kinetic parameterization. We analyze the failure modes of these simulations and discuss opportunities to improve prediction of byproduct secretion.

solveME: fast and reliable solution of nonlinear ME models

Background

Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.

Results

Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.

Conclusions

Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1240-1) contains supplementary material, which is available to authorized users.

Computational Modeling of Human Metabolism and Its Application to Systems Biomedicine

Modern high-throughput techniques offer immense opportunities to investigate whole-systems behavior, such as those underlying human diseases. However, the complexity of the data presents challenges in interpretation, and new avenues are needed to address the complexity of both diseases and data. Constraint-based modeling is one formalism applied in systems biology. It relies on a genome-scale reconstruction that captures extensive biochemical knowledge regarding an organism. The human genome-scale metabolic reconstruction is increasingly used to understand normal cellular and disease states because metabolism is an important factor in many human diseases. The application of human genome-scale reconstruction ranges from mere querying of the model as a knowledge base to studies that take advantage of the model's topology and, most notably, to functional predictions based on cell- and condition-specific metabolic models built based on omics data.An increasing number and diversity of biomedical questions are being addressed using constraint-based modeling and metabolic models. One of the most successful biomedical applications to date is cancer metabolism, but constraint-based modeling also holds great potential for inborn errors of metabolism or obesity. In addition, it offers great prospects for individualized approaches to diagnostics and the design of disease prevention and intervention strategies. Metabolic models support this endeavor by providing easy access to complex high-throughput datasets. Personalized metabolic models have been introduced. Finally, constraint-based modeling can be used to model whole-body metabolism, which will enable the elucidation of metabolic interactions between organs and disturbances of these interactions as either causes or consequence of metabolic diseases. This chapter introduces constraint-based modeling and describes some of its contributions to systems biomedicine.

Modeling and Simulation Tools: From Systems Biology to Systems Medicine

Modeling is an integral component of modern biology. In this chapter we look into the role of the model, as it pertains to Systems Medicine, and the software that is required to instantiate and run it. We do this by comparing the development, implementation, and characteristics of tools that have been developed to work with two divergent methodologies: Systems Biology and Pharmacometrics. From the Systems Biology perspective we consider the concept of "Software as a Medical Device" and what this may imply for the migration of research-oriented, simulation software into the domain of human health.In our second perspective, we see how in practice hundreds of computational tools already accompany drug discovery and development at every stage of the process. Standardized exchange formats are required to streamline the model exchange between tools, which would minimize translation errors and reduce the required time. With the emergence, almost 15 years ago, of the SBML standard, a large part of the domain of interest is already covered and models can be shared and passed from software to software without recoding them. Until recently the last stage of the process, the pharmacometric analysis used in clinical studies carried out on subject populations, lacked such an exchange medium. We describe a new emerging exchange format in Pharmacometrics which covers the non-linear mixed effects models, the standard statistical model type used in this area. By interfacing these two formats the entire domain can be covered by complementary standards and subsequently the according tools.

Quantitative prediction of genome-wide resource allocation in bacteria

Predicting resource allocation between cell processes is the primary step towards decoding the evolutionary constraints governing bacterial growth under various conditions. Quantitative prediction at genome-scale remains a computational challenge as current methods are limited by the tractability of the problem or by simplifying hypotheses. Here, we show that the constraint-based modeling method Resource Balance Analysis (RBA), calibrated using genome-wide absolute protein quantification data, accurately predicts resource allocation in the model bacterium Bacillus subtilis for a wide range of growth conditions. The regulation of most cellular processes is consistent with the objective of growth rate maximization except for a few suboptimal processes which likely integrate more complex objectives such as coping with stressful conditions and survival. As a proof of principle by using simulations, we illustrated how calibrated RBA could aid rational design of strains for maximizing protein production, offering new opportunities to investigate design principles in prokaryotes and to exploit them for biotechnological applications.

Co-evolution of strain design methods based on flux balance and elementary mode analysis

More than a decade ago, the first genome-scale metabolic models for two of the most relevant microbes for biotechnology applications, Escherichia coli and Saccaromyces cerevisiae, were published. Shortly after followed the publication of OptKnock, the first strain design method using bilevel optimization to couple cellular growth with the production of a target product. This initiated the development of a family of strain design methods based on the concept of flux balance analysis. Another family of strain design methods, based on the concept of elementary mode analysis, has also been growing. Although the computation of elementary modes is hindered by computational complexity, recent breakthroughs have allowed applying elementary mode analysis at the genome scale. Here we review and compare strain design methods and look back at the last 10 years of in silico strain design with constraint-based models. We highlight some features of the different approaches and discuss the utilization of these methods in successful in vivo metabolic engineering applications.

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Computational strain design methods are divided into two main families.

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We trace the evolutionary history of these two families.

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Surveyed successful cases of model-guided strain design for industrial applications.

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Most proposed methods have not yet been tested in real applications.

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Agreement between in silico and in vivo results shows potential of tested methods.

Development and application of efficient pathway enumeration algorithms for metabolic engineering applications

Metabolic Engineering (ME) aims to design microbial cell factories towards the production of valuable compounds. In this endeavor, one important task relates to the search for the most suitable heterologous pathway(s) to add to the selected host. Different algorithms have been developed in the past towards this goal, following distinct approaches spanning constraint-based modeling, graph-based methods and knowledge-based systems based on chemical rules. While some of these methods search for pathways optimizing specific objective functions, here the focus will be on methods that address the enumeration of pathways that are able to convert a set of source compounds into desired targets and their posterior evaluation according to different criteria. Two pathway enumeration algorithms based on (hyper)graph-based representations are selected as the most promising ones and are analyzed in more detail: the Solution Structure Generation and the Find Path algorithms. Their capabilities and limitations are evaluated when designing novel heterologous pathways, by applying these methods on three case studies of synthetic ME related to the production of non-native compounds in E. coli and S. cerevisiae: 1-butanol, curcumin and vanillin. Some targeted improvements are implemented, extending both methods to address limitations identified that impair their scalability, improving their ability to extract potential pathways over large-scale databases. In all case-studies, the algorithms were able to find already described pathways for the production of the target compounds, but also alternative pathways that can represent novel ME solutions after further evaluation.

Double and multiple knockout simulations for genome-scale metabolic network reconstructions

Background

Constraint-based modeling of genome-scale metabolic network reconstructions has become a widely used approach in computational biology. Flux coupling analysis is a constraint-based method that analyses the impact of single reaction knockouts on other reactions in the network.

Results

We present an extension of flux coupling analysis for double and multiple gene or reaction knockouts, and develop corresponding algorithms for an in silico simulation. To evaluate our method, we perform a full single and double knockout analysis on a selection of genome-scale metabolic network reconstructions and compare the results.

Software

A prototype implementation of double knockout simulation is available at http://hoverboard.io/L4FC.

Prediction of intracellular metabolic states from extracellular metabolomic data

Metabolic models can provide a mechanistic framework to analyze information-rich omics data sets, and are increasingly being used to investigate metabolic alternations in human diseases. An expression of the altered metabolic pathway utilization is the selection of metabolites consumed and released by cells. However, methods for the inference of intracellular metabolic states from extracellular measurements in the context of metabolic models remain underdeveloped compared to methods for other omics data. Herein, we describe a workflow for such an integrative analysis emphasizing on extracellular metabolomics data. We demonstrate, using the lymphoblastic leukemia cell lines Molt-4 and CCRF-CEM, how our methods can reveal differences in cell metabolism. Our models explain metabolite uptake and secretion by predicting a more glycolytic phenotype for the CCRF-CEM model and a more oxidative phenotype for the Molt-4 model, which was supported by our experimental data. Gene expression analysis revealed altered expression of gene products at key regulatory steps in those central metabolic pathways, and literature query emphasized the role of these genes in cancer metabolism. Moreover, in silico gene knock-outs identified unique control points for each cell line model, e.g., phosphoglycerate dehydrogenase for the Molt-4 model. Thus, our workflow is well-suited to the characterization of cellular metabolic traits based on extracellular metabolomic data, and it allows the integration of multiple omics data sets into a cohesive picture based on a defined model context.

Characterizing metabolic pathway diversification in the context of perturbation size

Cell metabolism is an important platform for sustainable biofuel, chemical and pharmaceutical production but its complexity presents a major challenge for scientists and engineers. Although in silico strains have been designed in the past with predicted performances near the theoretical maximum, real-world performance is often sub-optimal. Here, we simulate how strain performance is impacted when subjected to many randomly varying perturbations, including discrepancies between gene expression and in vivo flux, osmotic stress, and substrate uptake perturbations due to concentration gradients in bioreactors. This computational study asks whether robust performance can be achieved by adopting robustness-enhancing mechanisms from naturally evolved organisms-in particular, redundancy. Our study shows that redundancy, typically perceived as a ubiquitous robustness-enhancing strategy in nature, can either improve or undermine robustness depending on the magnitude of the perturbations. We also show that the optimal number of redundant pathways used can be predicted for a given perturbation size.

Optimal cofactor swapping can increase the theoretical yield for chemical production in Escherichia coli and Saccharomyces cerevisiae

Maintaining cofactor balance is a critical function in microorganisms, but often the native cofactor balance does not match the needs of an engineered metabolic flux state. Here, an optimization procedure is utilized to identify optimal cofactor-specificity "swaps" for oxidoreductase enzymes utilizing NAD(H) or NADP(H) in the genome-scale metabolic models of Escherichia coli and Saccharomyces cerevisiae. The theoretical yields of all native carbon-containing molecules are considered, as well as theoretical yields of twelve heterologous production pathways in E. coli. Swapping the cofactor specificity of central metabolic enzymes (especially GAPD and ALCD2x) is shown to increase NADPH production and increase theoretical yields for native products in E. coli and yeast--including L-aspartate, L-lysine, L-isoleucine, L-proline, L-serine, and putrescine--and non-native products in E. coli-including 1,3-propanediol, 3-hydroxybutyrate, 3-hydroxypropanoate, 3-hydroxyvalerate, and styrene.

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.