Constraints-based models: regulation of gene expression reduces the steady-state solution space

On the representativeness and stability of a set of EFMs

MOTIVATION

Elementary flux modes are a well-known tool for analyzing metabolic networks. The whole set of elementary flux modes (EFMs) cannot be computed in most genome-scale networks due to their large cardinality. Therefore, different methods have been proposed to compute a smaller subset of EFMs that can be used for studying the structure of the network. These latter methods pose the problem of studying the representativeness of the calculated subset. In this article, we present a methodology to tackle this problem.

RESULTS

We have introduced the concept of stability for a particular network parameter and its relation to the representativeness of the EFM extraction method studied. We have also defined several metrics to study and compare the EFM biases. We have applied these techniques to compare the relative behavior of previously proposed methods in two case studies. Furthermore, we have presented a new method for the EFM computation (PiEFM), which is more stable (less biased) than previous ones, has suitable representativeness measures, and exhibits better variability in the extracted EFMs.

AVAILABILITY AND IMPLEMENTATION

Software and additional material are freely available at https://github.com/biogacop/PiEFM.

Totoro: Identifying Active Reactions During the Transient State for Metabolic Perturbations

Motivation: The increasing availability of metabolomic data and their analysis are improving the understanding of cellular mechanisms and how biological systems respond to different perturbations. Currently, there is a need for novel computational methods that facilitate the analysis and integration of increasing volume of available data.

Results: In this paper, we present Totoro a new constraint-based approach that integrates quantitative non-targeted metabolomic data of two different metabolic states into genome-wide metabolic models and predicts reactions that were most likely active during the transient state. We applied Totoro to real data of three different growth experiments (pulses of glucose, pyruvate, succinate) from Escherichia coli and we were able to predict known active pathways and gather new insights on the different metabolisms related to each substrate. We used both the E. coli core and the iJO1366 models to demonstrate that our approach is applicable to both smaller and larger networks.

Availability:Totoro is an open source method (available at https://gitlab.inria.fr/erable/totoro) suitable for any organism with an available metabolic model. It is implemented in C++ and depends on IBM CPLEX which is freely available for academic purposes.

Protocol for condition-dependent metabolite yield prediction using the TRIMER pipeline

This protocol explains the pipeline for condition-dependent metabolite yield prediction using Transcription Regulation Integrated with MEtabolic Regulation (TRIMER). TRIMER targets metabolic engineering applications via a hybrid model integrating transcription factor (TF)-gene regulatory network (TRN) with a Bayesian network (BN) inferred from transcriptomic expression data to effectively regulate metabolic reactions. For E. coli and yeast, TRIMER achieves reliable knockout phenotype and flux predictions from the deletion of one or more TFs at the genome scale.

For complete details on the use and execution of this protocol, please refer to Niu et al. (2021).

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TRIMER is a package for transcription-regulated metabolic predictions

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Global dependency modeling by Bayesian network enables condition-dependent prediction

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We present the step-by-step TRIMER implementation for metabolic engineering

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We demonstrate the analyses for E. coli and yeast mutants

TRIMER: Transcription Regulation Integrated with Metabolic Regulation

There has been extensive research in predictive modeling of genome-scale metabolic reaction networks. Living systems involve complex stochastic processes arising from interactions among different biomolecules. For more accurate and robust prediction of target metabolic behavior under different conditions, not only metabolic reactions but also the genetic regulatory relationships involving transcription factors (TFs) affecting these metabolic reactions should be modeled. We have developed a modeling and simulation pipeline enabling the analysis of Transcription Regulation Integrated with Metabolic Regulation: TRIMER. TRIMER utilizes a Bayesian network (BN) inferred from transcriptomes to model the transcription factor regulatory network. TRIMER then infers the probabilities of the gene states relevant to the metabolism of interest, and predicts the metabolic fluxes and their changes that result from the deletion of one or more transcription factors at the genome scale. We demonstrate TRIMER’s applicability to both simulated and experimental data and provide performance comparison with other existing approaches.

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TRIMER models transcription-regulated metabolism using Bayesian network modeling;

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TRIMER integrates prior knowledge (regulatory interaction) with data (expression);

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TRIMER enables metabolic behavior prediction for general knockout strategies;

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TRIMER includes a simulator as an evaluation platform for similar hybrid models;

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TRIMER reliably predicts metabolite yields for both simulated and experimental data.

A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)

Genome-scale stoichiometric modeling of metabolism has become a standard systems biology tool for modeling cellular physiology and growth. Extensions of this approach are emerging as a valuable avenue for predicting, understanding and designing microbial communities. Computation of microbial ecosystems in time and space (COMETS) extends dynamic flux balance analysis to generate simulations of multiple microbial species in molecularly complex and spatially structured environments. Here we describe how to best use and apply the most recent version of COMETS, which incorporates a more accurate biophysical model of microbial biomass expansion upon growth, evolutionary dynamics and extracellular enzyme activity modules. In addition to a command-line option, COMETS includes user-friendly Python and MATLAB interfaces compatible with the well-established COBRA models and methods, as well as comprehensive documentation and tutorials. This protocol provides a detailed guideline for installing, testing and applying COMETS to different scenarios, generating simulations that take from a few minutes to several days to run, with broad applicability to microbial communities across biomes and scales.

Answer Set Programming for Computing Constraints-Based Elementary Flux Modes: Application to Escherichia coli Core Metabolism

Elementary Flux Modes (EFMs) provide a rigorous basis to systematically characterize the steady state, cellular phenotypes, as well as metabolic network robustness and fragility. However, the number of EFMs typically grows exponentially with the size of the metabolic network, leading to excessive computational demands, and unfortunately, a large fraction of these EFMs are not biologically feasible due to system constraints. This combinatorial explosion often prevents the complete analysis of genome-scale metabolic models. Traditionally, EFMs are computed by the double description method, an efficient algorithm based on matrix calculation; however, only a few constraints can be integrated into this computation. They must be monotonic with regard to the set inclusion of the supports; otherwise, they must be treated in post-processing and thus do not save computational time. We present aspefm, a hybrid computational tool based on Answer Set Programming (ASP) and Linear Programming (LP) that permits the computation of EFMs while implementing many different types of constraints. We apply our methodology to the Escherichia coli core model, which contains 226×106 EFMs. In considering transcriptional and environmental regulation, thermodynamic constraints, and resource usage considerations, the solution space is reduced to 1118 EFMs that can be computed directly with aspefm. The solution set, for E. coli growth on O2 gradients spanning fully aerobic to anaerobic, can be further reduced to four optimal EFMs using post-processing and Pareto front analysis.

Recent advances in constraint and machine learning-based metabolic modeling by leveraging stoichiometric balances, thermodynamic feasibility and kinetic law formalisms

Understanding the governing principles behind organisms' metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.

Flux Coupling and the Objective Functions' Length in EFMs

Structural analysis of constraint-based metabolic network models attempts to find the network's properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

A review of methods for the reconstruction and analysis of integrated genome-scale models of metabolism and regulation

The current survey aims to describe the main methodologies for extending the reconstruction and analysis of genome-scale metabolic models and phenotype simulation with Flux Balance Analysis mathematical frameworks, via the integration of Transcriptional Regulatory Networks and/or gene expression data. Although the surveyed methods are aimed at improving phenotype simulations obtained from these models, the perspective of reconstructing integrated genome-scale models of metabolism and gene expression for diverse prokaryotes is still an open challenge.

Simulating the evolutionary trajectories of metabolic pathways for insect symbionts in the genus Sodalis

Insect-bacterial symbioses are ubiquitous, but there is still much to uncover about how these relationships establish, persist and evolve. The tsetse endosymbiont Sodalis glossinidius displays intriguing metabolic adaptations to its microenvironment, but the process by which this relationship evolved remains to be elucidated. The recent chance discovery of the free-living species of the genus Sodalis, Sodalis praecaptivus, provides a serendipitous starting point from which to investigate the evolution of this symbiosis. Here, we present a flux balance model for S. praecaptivus and empirically verify its predictions. Metabolic modelling is used in combination with a multi-objective evolutionary algorithm to explore the trajectories that S. glossinidius may have undertaken from this starting point after becoming internalized. The order in which key genes are lost is shown to influence the evolved populations, providing possible targets for future in vitro genetic manipulation. This method provides a detailed perspective on possible evolutionary trajectories for S. glossinidius in this fundamental process of evolutionary and ecological change.

Computing irreversible minimal cut sets in genome-scale metabolic networks via flux cone projection

MOTIVATION

Minimal cut sets (MCSs) for metabolic networks are sets of reactions which, if they are removed from the network, prevent a target reaction from carrying flux. To compute MCSs different methods exist, which may fail to find sufficiently many MCSs for larger genome-scale networks.

RESULTS

Here we introduce irreversible minimal cut sets (iMCSs). These are MCSs that consist of irreversible reactions only. The advantage of iMCSs is that they can be computed by projecting the flux cone of the metabolic network on the set of irreversible reactions, which usually leads to a smaller cone. Using oriented matroid theory, we show how the projected cone can be computed efficiently and how this can be applied to find iMCSs even in large genome-scale networks.

AVAILABILITY AND IMPLEMENTATION

Software is freely available at https://sourceforge.net/projects/irreversibleminimalcutsets/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

MOOMIN - Mathematical explOration of 'Omics data on a MetabolIc Network

MOTIVATION

Analysis of differential expression of genes is often performed to understand how the metabolic activity of an organism is impacted by a perturbation. However, because the system of metabolic regulation is complex and all changes are not directly reflected in the expression levels, interpreting these data can be difficult.

RESULTS

In this work, we present a new algorithm and computational tool that uses a genome-scale metabolic reconstruction to infer metabolic changes from differential expression data. Using the framework of constraint-based analysis, our method produces a qualitative hypothesis of a change in metabolic activity. In other words, each reaction of the network is inferred to have increased, decreased, or remained unchanged in flux. In contrast to similar previous approaches, our method does not require a biological objective function and does not assign on/off activity states to genes. An implementation is provided and it is available online. We apply the method to three published datasets to show that it successfully accomplishes its two main goals: confirming or rejecting metabolic changes suggested by differentially expressed genes based on how well they fit in as parts of a coordinated metabolic change, as well as inferring changes in reactions whose genes did not undergo differential expression.

AVAILABILITY AND IMPLEMENTATION

github.com/htpusa/moomin.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Integration of probabilistic regulatory networks into constraint-based models of metabolism with applications to Alzheimer's disease

Background

Mathematical models of biological networks can provide important predictions and insights into complex disease. Constraint-based models of cellular metabolism and probabilistic models of gene regulatory networks are two distinct areas that have progressed rapidly in parallel over the past decade. In principle, gene regulatory networks and metabolic networks underly the same complex phenotypes and diseases. However, systematic integration of these two model systems remains a fundamental challenge.

Results

In this work, we address this challenge by fusing probabilistic models of gene regulatory networks into constraint-based models of metabolism. The novel approach utilizes probabilistic reasoning in BN models of regulatory networks serves as the “glue” that enables a natural interface between the two systems. Probabilistic reasoning is used to predict and quantify system-wide effects of perturbation to the regulatory network in the form of constraints for flux variability analysis. In this setting, both regulatory and metabolic networks inherently account for uncertainty. Applications leverage constraint-based metabolic models of brain metabolism and gene regulatory networks parameterized by gene expression data from the hippocampus to investigate the role of the HIF-1 pathway in Alzheimer’s disease. Integrated models support HIF-1A as effective target to reduce the effects of hypoxia in Alzheimer’s disease. However, HIF-1A activation is far less effective in shifting metabolism when compared to brain metabolism in healthy controls.

Conclusions

The direct integration of probabilistic regulatory networks into constraint-based models of metabolism provides novel insights into how perturbations in the regulatory network may influence metabolic states. Predictive modeling of enzymatic activity can be facilitated using probabilistic reasoning, thereby extending the predictive capacity of the network. This framework for model integration is generalizable to other systems.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2872-8) contains supplementary material, which is available to authorized users.

Extreme pathway analysis reveals the organizing rules of metabolic regulation

Cellular systems shift metabolic states by adjusting gene expression and enzyme activities to adapt to physiological and environmental changes. Biochemical and genetic studies are identifying how metabolic regulation affects the selection of metabolic phenotypes. However, how metabolism influences its regulatory architecture still remains unexplored. We present a new method of extreme pathway analysis (the minimal set of conically independent metabolic pathways) to deduce regulatory structures from pure pathway information. Applying our method to metabolic networks of human red blood cells and Escherichia coli, we shed light on how metabolic regulation are organized by showing which reactions within metabolic networks are more prone to transcriptional or allosteric regulation. Applied to a human genome-scale metabolic system, our method detects disease-associated reactions. Thus, our study deepens the understanding of the organizing principle of cellular metabolic regulation and may contribute to metabolic engineering, synthetic biology, and disease treatment.

Thermodynamic constraints for identifying elementary flux modes

Metabolic pathway analysis is a key method to study metabolism and the elementary flux modes (EFMs) is one major concept allowing one to analyze the network in terms of minimal pathways. Their practical use has been hampered by the combinatorial explosion of their number in large systems. The EFMs give the possible pathways at steady state, but the real pathways are limited by biological constraints. In this review, we display three different methods that integrate thermodynamic constraints in terms of Gibbs free energy in the EFMs computation.

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.

Identification of metabolic pathways using pathfinding approaches: a systematic review

Metabolic pathways have become increasingly available for various microorganisms. Such pathways have spurred the development of a wide array of computational tools, in particular, mathematical pathfinding approaches. This article can facilitate the understanding of computational analysis of metabolic pathways in genomics. Moreover, stoichiometric and pathfinding approaches in metabolic pathway analysis are discussed. Three major types of studies are elaborated: stoichiometric identification models, pathway-based graph analysis and pathfinding approaches in cellular metabolism. Furthermore, evaluation of the outcomes of the pathways with mathematical benchmarking metrics is provided. This review would lead to better comprehension of metabolism behaviors in living cells, in terms of computed pathfinding approaches.

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

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

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

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

Data-driven integration of genome-scale regulatory and metabolic network models

Microbes are diverse and extremely versatile organisms that play vital roles in all ecological niches. Understanding and harnessing microbial systems will be key to the sustainability of our planet. One approach to improving our knowledge of microbial processes is through data-driven and mechanism-informed computational modeling. Individual models of biological networks (such as metabolism, transcription, and signaling) have played pivotal roles in driving microbial research through the years. These networks, however, are highly interconnected and function in concert-a fact that has led to the development of a variety of approaches aimed at simulating the integrated functions of two or more network types. Though the task of integrating these different models is fraught with new challenges, the large amounts of high-throughput data sets being generated, and algorithms being developed, means that the time is at hand for concerted efforts to build integrated regulatory-metabolic networks in a data-driven fashion. In this perspective, we review current approaches for constructing integrated regulatory-metabolic models and outline new strategies for future development of these network models for any microbial system.

Critical assessment of genome-scale metabolic networks: the need for a unified standard

Genome-scale metabolic networks have been reconstructed for several organisms. These metabolic networks provide detailed information about the metabolism inside the cells, coupled with the genomic, proteomic and thermodynamic information. These networks are widely simulated using 'constraint-based' modelling techniques and find applications ranging from strain improvement for metabolic engineering to prediction of drug targets in pathogenic organisms. Components of these metabolic networks are represented in multiple file formats and also using different markup languages, with varying levels of annotations; this leads to inconsistencies and increases the complexities in comparing and analysing reconstructions on multiple platforms. In this work, we critically examine nearly 100 published genome-scale metabolic networks and their corresponding constraint-based models and discuss various issues with respect to model quality. One of the major concerns is the lack of annotations using standard identifiers that can uniquely describe several components such as metabolites, genes, proteins and reactions. We also find that many models do not have complete information regarding constraints on reactions fluxes and objective functions for carrying out simulations. Overall, our analysis highlights the need for a widely acceptable standard for representing constraint-based models. A rigorous standard can help in streamlining the process of reconstruction and improve the quality of reconstructed metabolic models.

Insights into pH-induced metabolic switch by flux balance analysis

Lactate accumulation in mammalian cell culture is known to impede cellular growth and productivity. The control of lactate formation and consumption in a hybridoma cell line was achieved by pH alteration during the early exponential growth phase. In particular, lactate consumption was induced even at high glucose concentrations at pH 6.8, whereas highly increased production of lactate was obtained at pH 7.8. Consequently, constraint-based metabolic flux analysis was used to examine pH-induced metabolic states in the same growth state. We demonstrated that lactate influx at pH 6.8 led cells to maintain high fluxes in the TCA cycle and malate-aspartate shuttle resulting in a high ATP production rate. In contrast, under increased pH conditions, less ATP was generated and different ATP sources were utilized. Gene expression analysis led to the conclusion that lactate formation at high pH was enabled by gluconeogenic pathways in addition to facilitated glucose uptake. The obtained results provide new insights into the influence of pH on cellular metabolism, and are of importance when considering pH heterogeneities typically present in large scale industrial bioreactors.

Computational prediction of essential metabolic genes using constraint-based approaches

In this chapter, we describe the application of constraint-based modeling to predict the impact of gene deletions on a metabolic phenotype. The metabolic reactions taking place inside cells form large networks, which have been reconstructed at a genome-scale for several organisms at increasing levels of detail. By integrating mathematical modeling techniques with biochemical principles, constraint-based approaches enable predictions of metabolite fluxes and growth under specific environmental conditions or for genetically modified microorganisms. Similar to the experimental knockout of a gene, predicting the essentiality of a metabolic gene for a phenotype further allows to generate hypotheses on its biological function and design of genetic engineering strategies for biotechnological applications. Here, we summarize the principles of constraint-based approaches and provide a detailed description of the procedure to predict the essentiality of metabolic genes with respect to a specific metabolic function. We exemplify the approach by predicting the essentiality of reactions in the citric acid cycle for the production of glucose from fatty acids.

Understanding carbon catabolite repression in Escherichia coli using quantitative models

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

MIRA: mutual information-based reporter algorithm for metabolic networks

MOTIVATION

Discovering the transcriptional regulatory architecture of the metabolism has been an important topic to understand the implications of transcriptional fluctuations on metabolism. The reporter algorithm (RA) was proposed to determine the hot spots in metabolic networks, around which transcriptional regulation is focused owing to a disease or a genetic perturbation. Using a z-score-based scoring scheme, RA calculates the average statistical change in the expression levels of genes that are neighbors to a target metabolite in the metabolic network. The RA approach has been used in numerous studies to analyze cellular responses to the downstream genetic changes. In this article, we propose a mutual information-based multivariate reporter algorithm (MIRA) with the goal of eliminating the following problems in detecting reporter metabolites: (i) conventional statistical methods suffer from small sample sizes, (ii) as z-score ranges from minus to plus infinity, calculating average scores can lead to canceling out opposite effects and (iii) analyzing genes one by one, then aggregating results can lead to information loss. MIRA is a multivariate and combinatorial algorithm that calculates the aggregate transcriptional response around a metabolite using mutual information. We show that MIRA's results are biologically sound, empirically significant and more reliable than RA.

RESULTS

We apply MIRA to gene expression analysis of six knockout strains of Escherichia coli and show that MIRA captures the underlying metabolic dynamics of the switch from aerobic to anaerobic respiration. We also apply MIRA to an Autism Spectrum Disorder gene expression dataset. Results indicate that MIRA reports metabolites that highly overlap with recently found metabolic biomarkers in the autism literature. Overall, MIRA is a promising algorithm for detecting metabolic drug targets and understanding the relation between gene expression and metabolic activity.

AVAILABILITY AND IMPLEMENTATION

The code is implemented in C# language using .NET framework. Project is available upon request.

Comparison on extreme pathways reveals nature of different biological processes

Background

Constraint-based reconstruction and analysis (COBRA) is used for modeling genome-scale metabolic networks (MNs). In a COBRA model, extreme pathways (ExPas) are the edges of its conical solution space, which is formed by all viable steady-state flux distributions. ExPa analysis has been successfully applied to MNs to reveal their phenotypic capabilities and properties. Recently, the COBRA framework has been extended to transcriptional regulatory networks (TRNs) and transcriptional and translational networks (TTNs), so efforts are needed to determine whether ExPa analysis is also effective on these two types of networks.

Results

In this paper, the ExPas resulting from the COBRA models of E.coli's MN, TRN and TTN were horizontally compared from 5 aspects: (1) Total number and the ratio of their amount to reaction amount; (2) Length distribution; (3) Reaction participation; (4) Correlated reaction sets (CoSets); (5) interconnectivity degree. Significant discrepancies in above properties were observed during the comparison, which reveals the biological natures of different biological processes. Besides, by demonstrating the application of ExPa analysis on E.coli, we provide a practical guidance of an improved approach to compute ExPas on COBRA models of TRNs.

Conclusions

ExPas of E.coli's MN, TRN and TTN have different properties, which are strongly connected with various biological natures of biochemical networks, such as topological structure, specificity and redundancy. Our study shows that ExPas are biologically meaningful on the newborn models and suggests the effectiveness of ExPa analysis on them.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

Dissecting the energy metabolism in Mycoplasma pneumoniae through genome-scale metabolic modeling

A new genome-scale metabolic reconstruction of M. pneumonia is used in combination with external metabolite measurement and protein abundance measurements to quantitatively explore the energy metabolism of this genome-reduce human pathogen.

We established a detailed biomass composition for M. pneumoniae, thus allowing for growth simulations.

Using our metabolic model, we corrected the metabolic network topology and the functional annotation of key metabolic enzymes.

M. pneumoniae, unlike other laboratory-grown bacteria, uses a high fraction of energy (up to 89%) for cellular maintenance and not for growth.

Simulating different growth conditions as well as single and double mutant phenotypes, we analyzed pathway connectivity and the impact of gene deletions on the growth performance of M. pneumoniae, highlighting the limited adaptive capabilities of this minimal model organism.

Mycoplasma pneumoniae, a threatening pathogen with a minimal genome, is a model organism for bacterial systems biology for which substantial experimental information is available. With the goal of understanding the complex interactions underlying its metabolism, we analyzed and characterized the metabolic network of M. pneumoniae in great detail, integrating data from different omics analyses under a range of conditions into a constraint-based model backbone. Iterating model predictions, hypothesis generation, experimental testing, and model refinement, we accurately curated the network and quantitatively explored the energy metabolism. In contrast to other bacteria, M. pneumoniae uses most of its energy for maintenance tasks instead of growth. We show that in highly linear networks the prediction of flux distributions for different growth times allows analysis of time-dependent changes, albeit using a static model. By performing an in silico knock-out study as well as analyzing flux distributions in single and double mutant phenotypes, we demonstrated that the model accurately represents the metabolism of M. pneumoniae. The experimentally validated model provides a solid basis for understanding its metabolic regulatory mechanisms.

Genome-level transcription data of Yersinia pestis analyzed with a new metabolic constraint-based approach

Background

Constraint-based computational approaches, such as flux balance analysis (FBA), have proven successful in modeling genome-level metabolic behavior for conditions where a set of simple cellular objectives can be clearly articulated. Recently, the necessity to expand the current range of constraint-based methods to incorporate high-throughput experimental data has been acknowledged by the proposal of several methods. However, these methods have rarely been used to address cellular metabolic responses to some relevant perturbations such as antimicrobial or temperature-induced stress. Here, we present a new method for combining gene-expression data with FBA (GX-FBA) that allows modeling of genome-level metabolic response to a broad range of environmental perturbations within a constraint-based framework. The method uses mRNA expression data to guide hierarchical regulation of cellular metabolism subject to the interconnectivity of the metabolic network.

Results

We applied GX-FBA to a genome-scale model of metabolism in the gram negative bacterium Yersinia pestis and analyzed its metabolic response to (i) variations in temperature known to induce virulence, and (ii) antibiotic stress. Without imposition of any a priori behavioral constraints, our results show strong agreement with reported phenotypes. Our analyses also lead to novel insights into how Y. pestis uses metabolic adjustments to counter different forms of stress.

Conclusions

Comparisons of GX-FBA predicted metabolic states with fluxomic measurements and different reported post-stress phenotypes suggest that mass conservation constraints and network connectivity can be an effective representative of metabolic flux regulation in constraint-based models. We believe that our approach will be of aid in the in silico evaluation of cellular goals under different conditions and can be used for a variety of analyses such as identification of potential drug targets and their action.

Understanding regulation of metabolism through feasibility analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.

Analysis of metabolic subnetworks by flux cone projection

Background

Analysis of elementary modes (EMs) is proven to be a powerful constraint-based method in the study of metabolic networks. However, enumeration of EMs is a hard computational task. Additionally, due to their large number, EMs cannot be simply used as an input for subsequent analysis. One possibility is to limit the analysis to a subset of interesting reactions. However, analysing an isolated subnetwork can result in finding incorrect EMs which are not part of any steady-state flux distribution of the original network. The ideal set to describe the reaction activity in a subnetwork would be the set of all EMs projected to the reactions of interest. Recently, the concept of "elementary flux patterns" (EFPs) has been proposed. Each EFP is a subset of the support (i.e., non-zero elements) of at least one EM.

Results

We introduce the concept of ProCEMs (Projected Cone Elementary Modes). The ProCEM set can be computed by projecting the flux cone onto a lower-dimensional subspace and enumerating the extreme rays of the projected cone. In contrast to EFPs, ProCEMs are not merely a set of reactions, but projected EMs. We additionally prove that the set of EFPs is included in the set of ProCEM supports. Finally, ProCEMs and EFPs are compared for studying substructures of biological networks.

Conclusions

We introduce the concept of ProCEMs and recommend its use for the analysis of substructures of metabolic networks for which the set of EMs cannot be computed.

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.

Modelling osmotic stress by Flux Balance Analysis at the genomic scale

Predictive microbiology for food safety is still primarily based on empirical models describing the effect of the environmental conditions of the food on the kinetics of the growth of foodborne pathogens. One way to make these models more mechanistic is to use systems biology methods such as Flux Balance Analysis (FBA). FBA consists of evaluating the possible fluxes through the metabolic reactions taking place in a cell. Using this method, the specific growth rate of Escherichia coli can be predicted by assuming, as an objective function, that the cells maximise their biomass production during balanced growth. Whilst this works under favourable environmental conditions, our simulations show that this objective function is not sufficient to explain the decrease of the growth rate due to osmotic stress. One feature of the FBA models is that the parameters and objective function in general refer to chemostat experiments where the carbon source is the main limiting factor. This may be relevant to some foods where the carbon to nitrogen balance is limiting but, in general, it is the physico-chemical conditions which are the most stringent. We therefore need to examine the effect of such constraints on the fluxes and/or modify the objective function, or to elaborate the metabolic model by taking into account other functional levels of the cell in order to develop mechanistic predictive models for osmotic stress conditions.

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.

Bacterial growth rate reflects a bottleneck in resource allocation

BACKGROUND

Growth rate management in fast-growing bacteria is currently an active research area. In spite of the huge progress made in our understanding of the molecular mechanisms controlling the growth rate, fundamental questions concerning its intrinsic limitations are still relevant today. In parallel, systems biology claims that mathematical models could shed light on these questions.

METHODS

This review explores some possible reasons for the limitation of the growth rate in fast-growing bacteria, using a systems biology approach based on constraint-based modeling methods.

RESULTS

Recent experimental results and a new constraint-based modelling method named Resource Balance Analysis (RBA) reveal the existence of constraints on resource allocation between biological processes in bacterial cells. In this context, the distribution of a finite amount of resources between the metabolic network and the ribosomes limits the growth rate, which implies the existence of a bottleneck between these two processes. Any mechanism for saving resources increases the growth rate.

GENERAL SIGNIFICANCE

Consequently, the emergence of genetic regulation of metabolic pathways, e.g. catabolite repression, could then arise as a means to minimise the protein cost, i.e. maximising growth performance while minimising the resource allocation. This article is part of a Special Issue entitled Systems Biology of Microorganisms.

Expanding a dynamic flux balance model of yeast fermentation to genome-scale

Background

Yeast is considered to be a workhorse of the biotechnology industry for the production of many value-added chemicals, alcoholic beverages and biofuels. Optimization of the fermentation is a challenging task that greatly benefits from dynamic models able to accurately describe and predict the fermentation profile and resulting products under different genetic and environmental conditions. In this article, we developed and validated a genome-scale dynamic flux balance model, using experimentally determined kinetic constraints.

Results

Appropriate equations for maintenance, biomass composition, anaerobic metabolism and nutrient uptake are key to improve model performance, especially for predicting glycerol and ethanol synthesis. Prediction profiles of synthesis and consumption of the main metabolites involved in alcoholic fermentation closely agreed with experimental data obtained from numerous lab and industrial fermentations under different environmental conditions. Finally, fermentation simulations of genetically engineered yeasts closely reproduced previously reported experimental results regarding final concentrations of the main fermentation products such as ethanol and glycerol.

Conclusion

A useful tool to describe, understand and predict metabolite production in batch yeast cultures was developed. The resulting model, if used wisely, could help to search for new metabolic engineering strategies to manage ethanol content in batch fermentations.

Integration of metabolic reactions and gene regulation

Metabolic reactions and gene regulation are two primary processes of cells. In response to environmental changes cells often adjust the regulatory programs and shift the metabolic states. An integrative investigation and modeling of these two processes would improve our understanding about the cellular systems and may generate substantial impacts in medicine, agriculture, environmental protection, and energy production. We review the studies of the various aspects of the crosstalk between metabolic reactions and gene regulation, including models, empirical evidence, and available databases.

The application of flux balance analysis in systems biology

An increasing number of genome-scale reconstructions of intracellular biochemical networks are being generated. Coupled with these stoichiometric models, several systems-based approaches for probing these reconstructions in silico have been developed. One such approach, called flux balance analysis (FBA), has been effective at predicting systemic phenotypes in the form of fluxes through a reaction network. FBA employs a linear programming (LP) strategy to generate a flux distribution that is optimized toward a particular 'objective,' subject to a set of underlying physicochemical and thermodynamic constraints. Although classical FBA assumes steady-state conditions, several extensions have been proposed in recent years to constrain the allowable flux distributions and enable characterization of dynamic profiles even with minimal kinetic information. Furthermore, FBA coupled with techniques for measuring fluxes in vivo has facilitated integration of computational and experimental approaches, and is allowing pursuit of rational hypothesis-driven research. Ultimately, as we will describe in this review, studying intracellular reaction fluxes allows us to understand network structure and function and has broad applications ranging from metabolic engineering to drug discovery.

Genome-scale metabolic networks

During the last decade, models have been developed to characterize cellular metabolism at the level of an entire metabolic network. The main concept that underlies whole-network metabolic modeling is the identification and mathematical definition of constraints. Here, we review large-scale metabolic network modeling, in particular, stoichiometric- and constraint-based approaches. Although many such models have been reconstructed, few networks have been extensively validated and tested experimentally, and we focus on these. We describe how metabolic networks can be represented using stoichiometric matrices and well-defined constraints on metabolic fluxes. We then discuss relatively successful approaches, including flux balance analysis (FBA), pathway analysis, and common extensions or modifications to these approaches. Finally, we describe techniques for integrating these approaches with models of other biological processes.

Predicting metabolic fluxes using gene expression differences as constraints

A standard approach to estimate intracellular fluxes on a genome-wide scale is flux-balance analysis (FBA), which optimizes an objective function subject to constraints on (relations between) fluxes. The performance of FBA models heavily depends on the relevance of the formulated objective function and the completeness of the defined constraints. Previous studies indicated that FBA predictions can be improved by adding regulatory on/off constraints. These constraints were imposed based on either absolute or relative gene expression values. We provide a new algorithm that directly uses regulatory up/down constraints based on gene expression data in FBA optimization (tFBA). Our assumption is that if the activity of a gene drastically changes from one condition to the other, the flux through the reaction controlled by that gene will change accordingly. We allow these constraints to be violated, to account for posttranscriptional control and noise in the data. These up/down constraints are less stringent than the on/off constraints as previously proposed. Nevertheless, we obtain promising predictions, since many up/down constraints can be enforced. The potential of the proposed method, tFBA, is demonstrated through the analysis of fluxes in yeast under nine different cultivation conditions, between which approximately 5,000 regulatory up/down constraints can be defined. We show that changes in gene expression are predictive for changes in fluxes. Additionally, we illustrate that flux distributions obtained with tFBA better fit transcriptomics data than previous methods. Finally, we compare tFBA and FBA predictions to show that our approach yields more biologically relevant results.

An automated phenotype-driven approach (GeneForce) for refining metabolic and regulatory models

Integrated constraint-based metabolic and regulatory models can accurately predict cellular growth phenotypes arising from genetic and environmental perturbations. Challenges in constructing such models involve the limited availability of information about transcription factor—gene target interactions and computational methods to quickly refine models based on additional datasets. In this study, we developed an algorithm, GeneForce, to identify incorrect regulatory rules and gene-protein-reaction associations in integrated metabolic and regulatory models. We applied the algorithm to refine integrated models of Escherichia coli and Salmonella typhimurium, and experimentally validated some of the algorithm's suggested refinements. The adjusted E. coli model showed improved accuracy (∼80.0%) for predicting growth phenotypes for 50,557 cases (knockout mutants tested for growth in different environmental conditions). In addition to identifying needed model corrections, the algorithm was used to identify native E. coli genes that, if over-expressed, would allow E. coli to grow in new environments. We envision that this approach will enable the rapid development and assessment of genome-scale metabolic and regulatory network models for less characterized organisms, as such models can be constructed from genome annotations and cis-regulatory network predictions.

Computational models of biological networks are useful for explaining experimental observations and predicting phenotypic behaviors. The construction of genome-scale metabolic and regulatory models is still a labor-intensive process, even with the availability of genome sequences and high-throughput datasets. Since our knowledge about biological systems is incomplete, these models are iteratively refined and validated as we discover new connections in biological networks, and eliminate inconsistencies between model predictions and experimental observations. To enable researchers to quickly determine what causes discrepancies between observed phenotypes and model predictions, we developed a new approach (GeneForce) that automatically corrects integrated metabolic and transcriptional regulatory network models. To illustrate the utility of the approach, we applied the developed method to well-curated models of E. coli metabolism and regulation. We found that the approach significantly improved the accuracy of phenotype predictions and suggested changes needed to the metabolic and/or regulatory models. We also used the approach to identify rescue non-growth phenotypes and to evaluate the conservation of transcriptional regulatory interactions between E. coli and S. typhimurium. The developed approach helps reconcile discrepancies between model predictions and experimental data by hypothesizing required network changes, and helps facilitate the development of new genome-scale models.

Using effective subnetworks to predict selected properties of gene networks

BACKGROUND

Difficulties associated with implementing gene therapy are caused by the complexity of the underlying regulatory networks. The forms of interactions between the hundreds of genes, proteins, and metabolites in these networks are not known very accurately. An alternative approach is to limit consideration to genes on the network. Steady state measurements of these influence networks can be obtained from DNA microarray experiments. However, since they contain a large number of nodes, the computation of influence networks requires a prohibitively large set of microarray experiments. Furthermore, error estimates of the network make verifiable predictions impossible.

METHODOLOGY/PRINCIPAL FINDINGS

Here, we propose an alternative approach. Rather than attempting to derive an accurate model of the network, we ask what questions can be addressed using lower dimensional, highly simplified models. More importantly, is it possible to use such robust features in applications? We first identify a small group of genes that can be used to affect changes in other nodes of the network. The reduced effective empirical subnetwork (EES) can be computed using steady state measurements on a small number of genetically perturbed systems. We show that the EES can be used to make predictions on expression profiles of other mutants, and to compute how to implement pre-specified changes in the steady state of the underlying biological process. These assertions are verified in a synthetic influence network. We also use previously published experimental data to compute the EES associated with an oxygen deprivation network of E.coli, and use it to predict gene expression levels on a double mutant. The predictions are significantly different from the experimental results for less than of genes.

CONCLUSIONS/SIGNIFICANCE

The constraints imposed by gene expression levels of mutants can be used to address a selected set of questions about a gene network.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

Gradient descent optimization in gene regulatory pathways

Background

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. Elucidating the architecture and dynamics of large scale gene regulatory networks is an important goal in systems biology. The knowledge of the gene regulatory networks further gives insights about gene regulatory pathways. This information leads to many potential applications in medicine and molecular biology, examples of which are identification of metabolic pathways, complex genetic diseases, drug discovery and toxicology analysis. High-throughput technologies allow studying various aspects of gene regulatory networks on a genome-wide scale and we will discuss recent advances as well as limitations and future challenges for gene network modeling. Novel approaches are needed to both infer the causal genes and generate hypothesis on the underlying regulatory mechanisms.

Methodology

In the present article, we introduce a new method for identifying a set of optimal gene regulatory pathways by using structural equations as a tool for modeling gene regulatory networks. The method, first of all, generates data on reaction flows in a pathway. A set of constraints is formulated incorporating weighting coefficients. Finally the gene regulatory pathways are obtained through optimization of an objective function with respect to these weighting coefficients. The effectiveness of the present method is successfully tested on ten gene regulatory networks existing in the literature. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. The results compare favorably with earlier experimental results. The validated pathways point to a combination of previously documented and novel findings.

Conclusions

We show that our method can correctly identify the causal genes and effectively output experimentally verified pathways. The present method has been successful in deriving the optimal regulatory pathways for all the regulatory networks considered. The biological significance and applicability of the optimal pathways has also been discussed. Finally the usefulness of the present method on genetic engineering is depicted with an example.

Modeling with a view to target identification in metabolic engineering: a critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy.