Regulation of gene expression in flux balance models of metabolism

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.

Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks

MOTIVATION

Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion.

RESULTS

In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks.

CONTACT

joshua.chan@connect.polyu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Systems biology of the qa gene cluster in Neurospora crassa

An ensemble of genetic networks that describe how the model fungal system, Neurospora crassa, utilizes quinic acid (QA) as a sole carbon source has been identified previously. A genetic network for QA metabolism involves the genes, qa-1F and qa-1S, that encode a transcriptional activator and repressor, respectively and structural genes, qa-2, qa-3, qa-4, qa-x, and qa-y. By a series of 4 separate and independent, model-guided, microarray experiments a total of 50 genes are identified as QA-responsive and hypothesized to be under QA-1F control and/or the control of a second QA-responsive transcription factor (NCU03643) both in the fungal binuclear Zn(II)2Cys6 cluster family. QA-1F regulation is not sufficient to explain the quantitative variation in expression profiles of the 50 QA-responsive genes. QA-responsive genes include genes with products in 8 mutually connected metabolic pathways with 7 of them one step removed from the tricarboxylic (TCA) Cycle and with 7 of them one step removed from glycolysis: (1) starch and sucrose metabolism; (2) glycolysis/glucanogenesis; (3) TCA Cycle; (4) butanoate metabolism; (5) pyruvate metabolism; (6) aromatic amino acid and QA metabolism; (7) valine, leucine, and isoleucine degradation; and (8) transport of sugars and amino acids. Gene products both in aromatic amino acid and QA metabolism and transport show an immediate response to shift to QA, while genes with products in the remaining 7 metabolic modules generally show a delayed response to shift to QA. The additional QA-responsive cutinase transcription factor-1β (NCU03643) is found to have a delayed response to shift to QA. The series of microarray experiments are used to expand the previously identified genetic network describing the qa gene cluster to include all 50 QA-responsive genes including the second transcription factor (NCU03643). These studies illustrate new methodologies from systems biology to guide model-driven discoveries about a core metabolic network involving carbon and amino acid metabolism in N. crassa.

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.

Technologies and approaches to elucidate and model the virulence program of salmonella

Salmonella is a primary cause of enteric diseases in a variety of animals. During its evolution into a pathogenic bacterium, Salmonella acquired an elaborate regulatory network that responds to multiple environmental stimuli within host animals and integrates them resulting in fine regulation of the virulence program. The coordinated action by this regulatory network involves numerous virulence regulators, necessitating genome-wide profiling analysis to assess and combine efforts from multiple regulons. In this review we discuss recent high-throughput analytic approaches used to understand the regulatory network of Salmonella that controls virulence processes. Application of high-throughput analyses have generated large amounts of data and necessitated the development of computational approaches for data integration. Therefore, we also cover computer-aided network analyses to infer regulatory networks, and demonstrate how genome-scale data can be used to construct regulatory and metabolic systems models of Salmonella pathogenesis. Genes that are coordinately controlled by multiple virulence regulators under infectious conditions are more likely to be important for pathogenesis. Thus, reconstructing the global regulatory network during infection or, at the very least, under conditions that mimic the host cellular environment not only provides a bird's eye view of Salmonella survival strategy in response to hostile host environments but also serves as an efficient means to identify novel virulence factors that are essential for Salmonella to accomplish systemic infection in the host.

Ecosystems biology of microbial metabolism

The metabolic capabilities of many environmentally and medically important microbes can be quantitatively explored using systems biology approaches to metabolic networks. Yet, as we learn more about the complex microbe-microbe and microbe-environment interactions in microbial communities, it is important to understand whether and how system-level approaches can be extended to the ecosystem level. Here we summarize recent work that addresses these challenges at multiple scales, starting from two-species natural and synthetic ecology models, up to biosphere-level approaches. Among the many fascinating open challenges in this field is whether the integration of high throughput sequencing methods and mathematical models will help us capture emerging principles of ecosystem-level metabolic organization and evolution.

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.

Elimination of thermodynamically infeasible loops in steady-state metabolic models

The constraint-based reconstruction and analysis (COBRA) framework has been widely used to study steady-state flux solutions in genome-scale metabolic networks. One shortcoming of current COBRA methods is the possible violation of the loop law in the computed steady-state flux solutions. The loop law is analogous to Kirchhoff's second law for electric circuits, and states that at steady state there can be no net flux around a closed network cycle. Although the consequences of the loop law have been known for years, it has been computationally difficult to work with. Therefore, the resulting loop-law constraints have been overlooked. Here, we present a general mixed integer programming approach called loopless COBRA (ll-COBRA), which can be used to eliminate all steady-state flux solutions that are incompatible with the loop law. We apply this approach to improve flux predictions on three common COBRA methods: flux balance analysis, flux variability analysis, and Monte Carlo sampling of the flux space. Moreover, we demonstrate that the imposition of loop-law constraints with ll-COBRA improves the consistency of simulation results with experimental data. This method provides an additional constraint for many COBRA methods, enabling the acquisition of more realistic simulation results.

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.

Use of genome-scale metabolic models in evolutionary systems biology

One of the major aims of the nascent field of evolutionary systems biology is to test evolutionary hypotheses that are not only realistic from a population genetic point of view but also detailed in terms of molecular biology mechanisms. By providing a mapping between genotype and phenotype for hundreds of genes, genome-scale systems biology models of metabolic networks have already provided valuable insights into the evolution of metabolic gene contents and phenotypes of yeast and other microbial species. Here we review the recent use of these computational models to predict the fitness effect of mutations, genetic interactions, evolutionary outcomes, and to decipher the mechanisms of mutational robustness. While these studies have demonstrated that even simplified models of biochemical reaction networks can be highly informative for evolutionary analyses, they have also revealed the weakness of this modeling framework to quantitatively predict mutational effects, a challenge that needs to be addressed for future progress in evolutionary systems biology.

Genome-scale metabolic models of Saccharomyces cerevisiae

Systematic analysis of Saccharomyces cerevisiae metabolic functions and pathways has been the subject of extensive studies and established in many aspects. With the reconstruction of the yeast genome-scale metabolic (GSM) network and in silico simulation of the GSM model, the nature of the underlying cellular processes can be tested and validated with the increasing metabolic knowledge. GSM models are also being exploited in fundamental research studies and industrial applications. In this chapter, the principle concepts for construction, simulation and validation of GSM models, progressive applications of the yeast GSM models, and future perspectives are described. This will support and encourage researchers who are interested in systemic analysis of yeast metabolism and systems biology.

Improving the iMM904 S. cerevisiae metabolic model using essentiality and synthetic lethality data

BACKGROUND

Saccharomyces cerevisiae is the first eukaryotic organism for which a multi-compartment genome-scale metabolic model was constructed. Since then a sequence of improved metabolic reconstructions for yeast has been introduced. These metabolic models have been extensively used to elucidate the organizational principles of yeast metabolism and drive yeast strain engineering strategies for targeted overproductions. They have also served as a starting point and a benchmark for the reconstruction of genome-scale metabolic models for other eukaryotic organisms. In spite of the successive improvements in the details of the described metabolic processes, even the recent yeast model (i.e., iMM904) remains significantly less predictive than the latest E. coli model (i.e., iAF1260). This is manifested by its significantly lower specificity in predicting the outcome of grow/no grow experiments in comparison to the E. coli model.

RESULTS

In this paper we make use of the automated GrowMatch procedure for restoring consistency with single gene deletion experiments in yeast and extend the procedure to make use of synthetic lethality data using the genome-scale model iMM904 as a basis. We identified and vetted using literature sources 120 distinct model modifications including various regulatory constraints for minimal and YP media. The incorporation of the suggested modifications led to a substantial increase in the fraction of correctly predicted lethal knockouts (i.e., specificity) from 38.84% (87 out of 224) to 53.57% (120 out of 224) for the minimal medium and from 24.73% (45 out of 182) to 40.11% (73 out of 182) for the YP medium. Synthetic lethality predictions improved from 12.03% (16 out of 133) to 23.31% (31 out of 133) for the minimal medium and from 6.96% (8 out of 115) to 13.04% (15 out of 115) for the YP medium.

CONCLUSIONS

Overall, this study provides a roadmap for the computationally driven correction of multi-compartment genome-scale metabolic models and demonstrates the value of synthetic lethals as curation agents.

A computational tool for the simulation and optimization of microbial strains accounting integrated metabolic/regulatory information

BACKGROUND AND SCOPE

Recently, a number of methods and tools have been proposed to allow the use of genome-scale metabolic models for the phenotype simulation and optimization of microbial strains, within the field of Metabolic Engineering (ME). One of the limitations of most of these algorithms and tools is the fact that only metabolic information is taken into account, disregarding knowledge on regulatory events.

IMPLEMENTATION AND PERFORMANCES

This work proposes a novel software tool that implements methods for the phenotype simulation and optimization of microbial strains using integrated models, encompassing both metabolic and regulatory information. This tool is developed as a plug-in that runs over OptFlux, a computational platform that aims to be a reference tool for the ME community.

AVAILABILITY

The plug-in is made available in the OptFlux web site (www.optflux.org) together with examples and documentation.

Genome-scale metabolic modeling of a clostridial co-culture for consolidated bioprocessing

An alternative consolidated bioprocessing approach is the use of a co-culture containing cellulolytic and solventogenic clostridia. It has been demonstrated that the rate of cellulose utilization in the co-culture of Clostridium acetobutylicum and Clostridium cellulolyticum is improved compared to the mono-culture of C. cellulolyticum, suggesting the presence of syntrophy between these two species. However, the metabolic interactions in the co-culture are not well understood. To understand the metabolic interactions in the co-culture, we developed a genome-scale metabolic model of C. cellulolyticum comprising of 431 genes, 621 reactions, and 603 metabolites. The C. cellulolyticum model can successfully predict the chemostat growth and byproduct secretion with cellulose as the substrate. However, a growth arrest phenomenon, which occurs in batch cultures of C. cellulolyticum at cellulose concentrations higher than 6.7 g/L, cannot be predicted by dynamic flux balance analysis due to the lack of understanding of the underlying mechanism. These genome-scale metabolic models of the pure cultures have also been integrated using a community modeling framework to develop a dynamic model of metabolic interactions in the co-culture. Co-culture simulations suggest that cellobiose inhibition cannot be the main factor that is responsible for improved cellulose utilization relative to mono-culture of C. cellulolyticum.

The virus as metabolic engineer

Recent genome-wide screens of host genetic requirements for viral infection have reemphasized the critical role of host metabolism in enabling the production of viral particles. In this review, we highlight the metabolic aspects of viral infection found in these studies, and focus on the opportunities these requirements present for metabolic engineers. In particular, the objectives and approaches that metabolic engineers use are readily comparable to the behaviors exhibited by viruses during infection. As a result, metabolic engineers have a unique perspective that could lead to novel and effective methods to combat viral infection.

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.

Probabilistic integrative modeling of genome-scale metabolic and regulatory networks in Escherichia coli and Mycobacterium tuberculosis

Prediction of metabolic changes that result from genetic or environmental perturbations has several important applications, including diagnosing metabolic disorders and discovering novel drug targets. A cardinal challenge in obtaining accurate predictions is the integration of transcriptional regulatory networks with the corresponding metabolic network. We propose a method called probabilistic regulation of metabolism (PROM) that achieves this synthesis and enables straightforward, automated, and quantitative integration of high-throughput data into constraint-based modeling, making it an ideal tool for constructing genome-scale regulatory-metabolic network models for less-studied organisms. PROM introduces probabilities to represent gene states and gene-transcription factor interactions. By using PROM, we constructed an integrated regulatory-metabolic network for the model organism, Escherichia coli, and demonstrated that our method based on automated inference is more accurate and comprehensive than the current state of the art, which is based on manual curation of literature. After validating the approach, we used PROM to build a genome-scale integrated metabolic-regulatory model for Mycobacterium tuberculosis, a critically important human pathogen. This study incorporated data from more than 1,300 microarrays, 2,000 transcription factor-target interactions regulating 3,300 metabolic reactions, and 1,905 KO phenotypes for E. coli and M. tuberculosis. PROM identified KO phenotypes with accuracies as high as 95%, and predicted growth rates quantitatively with correlation of 0.95. Importantly, PROM represents the successful integration of a top-down reconstructed, statistically inferred regulatory network with a bottom-up reconstructed, biochemically detailed metabolic network, bridging two important classes of systems biology models that are rarely combined quantitatively.

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.

Characterization of growth and metabolism of the haloalkaliphile Natronomonas pharaonis

Natronomonas pharaonis is an archaeon adapted to two extreme conditions: high salt concentration and alkaline pH. It has become one of the model organisms for the study of extremophilic life. Here, we present a genome-scale, manually curated metabolic reconstruction for the microorganism. The reconstruction itself represents a knowledge base of the haloalkaliphile's metabolism and, as such, would greatly assist further investigations on archaeal pathways. In addition, we experimentally determined several parameters relevant to growth, including a characterization of the biomass composition and a quantification of carbon and oxygen consumption. Using the metabolic reconstruction and the experimental data, we formulated a constraints-based model which we used to analyze the behavior of the archaeon when grown on a single carbon source. Results of the analysis include the finding that Natronomonas pharaonis, when grown aerobically on acetate, uses a carbon to oxygen consumption ratio that is theoretically near-optimal with respect to growth and energy production. This supports the hypothesis that, under simple conditions, the microorganism optimizes its metabolism with respect to the two objectives. We also found that the archaeon has a very low carbon efficiency of only about 35%. This inefficiency is probably due to a very low P/O ratio as well as to the other difficulties posed by its extreme environment.

Extremophiles are organisms that thrive in physically or geochemically extreme conditions that are detrimental, even lethal, to the majority of life on Earth. Natronomonas pharaonis is one that has been able to adapt to both high salt concentration and an alkaline pH. In this study, we investigate the chemical reactions that occur within the microorganism, collectively referred to as its metabolic network, that allow it to convert the nutrients in its environment to biomass and energy. Specifically, we reconstructed the network by collecting evidence for the existence of reactions from the literature, and then supplemented them with computational approaches, for example by searching the genome of Natronomonas pharaonis for genes that could potentially encode analogs of known enzymes from other organisms. Finally, with the network in hand, we developed a computational model which we used to simulate growth. Among other results, we found indications that Natronomonas pharaonis regulates its metabolism such that energy production and growth are maximized. Despite this however, we also found that Natronomonas pharaonis is only able to incorporate a very small fraction of the total carbon that it consumes (approximately 35%), likely in no small part due to the difficulties posed by its environment.

Network integration meets network dynamics

Molecular interaction networks provide a window on the workings of the cell. However, combining various types of networks into one coherent large-scale dynamic model remains a formidable challenge. A recent paper in BMC Systems Biology describes a promising step in this direction.

Utilizing elementary mode analysis, pathway thermodynamics, and a genetic algorithm for metabolic flux determination and optimal metabolic network design

BACKGROUND

Microbial hosts offer a number of unique advantages when used as production systems for both native and heterologous small-molecules. These advantages include high selectivity and benign environmental impact; however, a principal drawback is low yield and/or productivity, which limits economic viability. Therefore a major challenge in developing a microbial production system is to maximize formation of a specific product while sustaining cell growth. Tools to rationally reconfigure microbial metabolism for these potentially conflicting objectives remain limited. Exhaustively exploring combinations of genetic modifications is both experimentally and computationally inefficient, and can become intractable when multiple gene deletions or insertions need to be considered. Alternatively, the search for desirable gene modifications may be solved heuristically as an evolutionary optimization problem. In this study, we combine a genetic algorithm and elementary mode analysis to develop an optimization framework for evolving metabolic networks with energetically favorable pathways for production of both biomass and a compound of interest.

RESULTS

Utilization of thermodynamically-weighted elementary modes for flux reconstruction of E. coli central metabolism revealed two clusters of EMs with respect to their Delta Gp degrees. For proof of principle testing, the algorithm was applied to ethanol and lycopene production in E. coli. The algorithm was used to optimize product formation, biomass formation, and product and biomass formation simultaneously. Predicted knockouts often matched those that have previously been implemented experimentally for improved product formation. The performance of a multi-objective genetic algorithm showed that it is better to couple the two objectives in a single objective genetic algorithm.

CONCLUSION

A computationally tractable framework is presented for the redesign of metabolic networks for maximal product formation combining elementary mode analysis (a form of convex analysis), pathway thermodynamics, and a genetic algorithm to optimize the production of two industrially-relevant products, ethanol and lycopene, from E. coli. The designed algorithm can be applied to any small-scale model of cellular metabolism theoretically utilizing any substrate and applied towards the production of any product.

Descriptive and predictive applications of constraint-based metabolic models

Constraint-based models of metabolism are becoming available for an increasing number of organisms. These models can be used in combination with existing experimental data to describe the behavior of an organism and to analyze experimental observations in the context of a model. Such a descriptive application of the models can also allow for the integration of various types of data. Additionally, these models can be used in a predictive fashion to hypothesize the outcomes of new experiments. Comparing model predictions with experimental results allows for the iterative improvement of developed models and increases our understanding of the organism being studied. A number of recent examples of both descriptive and predictive applications of constraint-based models are discussed.

Metabolic modeling and analysis of the metabolic switch in Streptomyces coelicolor

BACKGROUND

The transition from exponential to stationary phase in Streptomyces coelicolor is accompanied by a major metabolic switch and results in a strong activation of secondary metabolism. Here we have explored the underlying reorganization of the metabolome by combining computational predictions based on constraint-based modeling and detailed transcriptomics time course observations.

RESULTS

We reconstructed the stoichiometric matrix of S. coelicolor, including the major antibiotic biosynthesis pathways, and performed flux balance analysis to predict flux changes that occur when the cell switches from biomass to antibiotic production. We defined the model input based on observed fermenter culture data and used a dynamically varying objective function to represent the metabolic switch. The predicted fluxes of many genes show highly significant correlation to the time series of the corresponding gene expression data. Individual mispredictions identify novel links between antibiotic production and primary metabolism.

CONCLUSION

Our results show the usefulness of constraint-based modeling for providing a detailed interpretation of time course gene expression data.

Accomplishments in genome-scale in silico modeling for industrial and medical biotechnology

Driven by advancements in high-throughput biological technologies and the growing number of sequenced genomes, the construction of in silico models at the genome scale has provided powerful tools to investigate a vast array of biological systems and applications. Here, we review comprehensively the uses of such models in industrial and medical biotechnology, including biofuel generation, food production, and drug development. While the use of in silico models is still in its early stages for delivering to industry, significant initial successes have been achieved. For the cases presented here, genome-scale models predict engineering strategies to enhance properties of interest in an organism or to inhibit harmful mechanisms of pathogens. Going forward, genome-scale in silico models promise to extend their application and analysis scope to become a trans-formative tool in biotechnology.

Systematic development of hybrid cybernetic models: application to recombinant yeast co-consuming glucose and xylose

The hybrid cybernetic modeling approach of Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) views the substrate uptake flux in microorganisms as being distributed in a regulated way among different elementary modes (EMs) of a metabolic network, which intracellular fluxes related to the uptake rates by the pseudo-steady-state approximation on intracellular metabolites. While the conceptual development has been demonstrated by Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) using a rather simple example (i.e., Escherichia coli metabolizing a single substrate), its extension to a larger scale network involving multiple substrates results in serious overparameterization (which implies an excessive number of parameters relative to the measurements available to determine them). Through the case study of recombinant Saccharomyces yeast co-consuming glucose and xylose, we present a systematic way of formulating a minimal order hybrid cybernetic model (HCM) for a general metabolic network. The overparameterization problem mostly arising from a large number of EMs is avoided using a model reduction technique developed by Song and Ramkrishna (Song and Ramkrishna [2009a] Biotechnol. Bioeng. 102(2):554-568) where an original set of EMs is condensed to a much smaller subset. Detailed discussions follow on the issue of determining the minimal set of active modes needed for the description of the simultaneous consumption of multiple substrates. The developed HCM is compared with other metabolic models: macroscopic bioreaction models (Provost et al. [2006] Bioprocess Biosyt. Eng. 29(5-6):349-366), and dynamic flux balance analysis. It is shown that the HCM outperforms the other two as validated using various sets of fermentation data. The difference among the models is more dramatic in a situation such as the sequential utilization of glucose and xylose, which is observed under realistic fermentation conditions.

Interpreting expression data with metabolic flux models: predicting Mycobacterium tuberculosis mycolic acid production

Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.

Metabolic adaptation after whole genome duplication

Whole genome duplications (WGDs) have been hypothesized to be responsible for major transitions in evolution. However, the effects of WGD and subsequent gene loss on cellular behavior and metabolism are still poorly understood. Here we develop a genome scale evolutionary model to study the dynamics of gene loss and metabolic adaptation after WGD. Using the metabolic network of Saccharomyces cerevisiae as an example, we primarily study the outcome of WGD on yeast as it currently is. However, similar results were obtained using a recontructed hypothetical metabolic network of the pre-WGD ancestor. We show that the retention of genes in duplicate in the model, corresponds nicely with those retained in duplicate after the ancestral WGD in S. cerevisiae. Also, we observe that transporter and glycolytic genes have a higher probability to be retained in duplicate after WGD and subsequent gene loss, both in the model as in S. cerevisiae, which leads to an increase in glycolytic flux after WGD. Furthermore, the model shows that WGD leads to better adaptation than small-scale duplications, in environments for which duplication of a whole pathway instead of single reactions is needed to increase fitness. This is indeed the case for adaptation to high glucose levels. Thus, our model confirms the hypothesis that WGD has been important in the adaptation of yeast to the new, glucose-rich environment that arose after the appearance of angiosperms. Moreover, the model shows that WGD is almost always detrimental on the short term in environments to which the lineage is preadapted, but can have immediate fitness benefits in "new" environments. This explains why WGD, while pivotal in the evolution of many lineages and an apparent "easy" genetic operator, occurs relatively rarely.

Optimal metabolic regulation using a constraint-based model

Regulation of metabolic enzymes plays a crucial role in the maintenance of metabolic homeostasis, and in the capacity of living systems to undergo physiological adaptation under multiple environmental conditions. Metabolic regulation is achieved through a complex interplay of transcriptional and post-transcriptional mechanisms, some of which have been experimentally characterized for specific pathways and organisms. Many of the details, however, including the values of most kinetic parameters, have proven difficult to elucidate. Hence, understanding the principles that underlie metabolic regulation strategies constitutes an ongoing challenge. In the context of genome-scale steady state models of metabolic networks, it has been shown that evolution may drive metabolic networks towards reaching computationally predictable optimal states, such as maximal growth capacity. Here we develop a new computational approach based on the hypothesis that the regulatory systems operating on metabolic networks have evolved towards an optimal architecture as well. Specifically, we hypothesize that the topology of metabolic regulation networks has been selected for optimally maintaining the system balanced around one or more steady states. Based on these hypotheses, we use methods related to flux balance analysis to construct a model of metabolic regulation based primarily on a metabolic network's topology, bypassing the requirement for the details of all kinetic parameters. This model predicts an optimal regulatory network of metabolic interactions that can resolve perturbations to a given steady state in a metabolic system. We explore the ability of the model to predict optimal regulatory responses in both a simple toy network and in a fragment of the well-described glycolysis pathway.

Can the whole be less than the sum of its parts? Pathway analysis in genome-scale metabolic networks using elementary flux patterns

Elementary modes represent a valuable concept in the analysis of metabolic reaction networks. However, they can only be computed in medium-size systems, preventing application to genome-scale metabolic models. In consequence, the analysis is usually constrained to a specific part of the known metabolism, and the remaining system is modeled using abstractions like exchange fluxes and external species. As we show by the analysis of a model of the central metabolism of Escherichia coli that has been previously analyzed using elementary modes, the choice of these abstractions heavily impacts the pathways that are detected, and the results are biased by the knowledge of the metabolic capabilities of the network by the user. In order to circumvent these problems, we introduce the concept of elementary flux patterns, which explicitly takes into account possible steady-state fluxes through a genome-scale metabolic network when analyzing pathways through a subsystem. By being similar to elementary mode analysis, our concept now allows for the application of many elementary-mode-based tools to genome-scale metabolic networks. We present an algorithm to compute elementary flux patterns and analyze a model of the tricarboxylic acid cycle and adjacent reactions in E. coli. Thus, we detect several pathways that can be used as alternative routes to some central metabolic pathways. Finally, we give an outlook on further applications like the computation of minimal media, the development of knockout strategies, and the analysis of combined genome-scale networks.

Functional states of the genome-scale Escherichia coli transcriptional regulatory system

A transcriptional regulatory network (TRN) constitutes the collection of regulatory rules that link environmental cues to the transcription state of a cell's genome. We recently proposed a matrix formalism that quantitatively represents a system of such rules (a transcriptional regulatory system [TRS]) and allows systemic characterization of TRS properties. The matrix formalism not only allows the computation of the transcription state of the genome but also the fundamental characterization of the input-output mapping that it represents. Furthermore, a key advantage of this “pseudo-stoichiometric” matrix formalism is its ability to easily integrate with existing stoichiometric matrix representations of signaling and metabolic networks. Here we demonstrate for the first time how this matrix formalism is extendable to large-scale systems by applying it to the genome-scale Escherichia coli TRS. We analyze the fundamental subspaces of the regulatory network matrix (R) to describe intrinsic properties of the TRS. We further use Monte Carlo sampling to evaluate the E. coli transcription state across a subset of all possible environments, comparing our results to published gene expression data as validation. Finally, we present novel in silico findings for the E. coli TRS, including (1) a gene expression correlation matrix delineating functional motifs; (2) sets of gene ontologies for which regulatory rules governing gene transcription are poorly understood and which may direct further experimental characterization; and (3) the appearance of a distributed TRN structure, which is in stark contrast to the more hierarchical organization of metabolic networks.

Cells are comprised of genomic information that encodes for proteins, the basic building blocks underlying all biological processes. A transcriptional regulatory system (TRS) connects a cell's environmental cues to its genome and in turn determines which genes are turned “on” in response to these cues. Consequently, TRSs control which proteins of an intracellular biochemical reaction network are present. These systems have been mathematically described, often through Boolean expressions that represent the activation or inhibition of gene transcription in response to various inputs. We recently developed a matrix formalism that extends these approaches and facilitates a quantitative representation of the Boolean logic underlying a TRS. We demonstrated on small-scale TRSs that this matrix representation is advantageous in that it facilitates the calculation of unique properties of a given TRS. Here we apply this matrix formalism to the genome-scale Escherichia coli TRS, demonstrating for the first time the predictive power of the approach at a large scale. We use the matrix-based model of E. coli transcriptional regulation to generate novel findings about the system, including new functional motifs; sets of genes whose regulation is poorly understood; and features of the TRS structure.

Understanding virulence mechanisms in M. tuberculosis infection via a circuit-based simulation framework

Tuberculosis (TB), caused by the bacterium Mycobacterium tuberculosis (Mtb), is a growing international health crisis. Mtb is able to persist in host tissues in a non-replicating persistent (NRP) or latent state. This presents a challenge in the treatment of TB. Latent TB can re-activate in 10% of individuals with normal immune systems, higher for those with compromised immune systems. A quantitative understanding of latency-associated virulence mechanisms may help researchers develop more effective methods to battle the spread and reduce TB associated fatalities. Leveraging BioXyce's ability to simulate whole-cell and multi-cellular systems we are developing a circuit-based framework to investigate the impact of pathogenicity-associated pathways on the latency/reactivation phase of tuberculosis infection. We discuss efforts to simulate metabolic pathways that potentially impact the ability of Mtb to persist within host immune cells. We demonstrate how simulation studies can provide insight regarding the efficacy of potential anti-TB agents on biological networks critical to Mtb pathogenicity using a systems chemical biology approach.

Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation

Background

Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.

Results

We show that the use of Monte Carlo sampling of the steady-state flux space of a cell-scale metabolic system in conjunction with Principal Component Analysis and eigenvector rotation results in a low-dimensional and biochemically interpretable decomposition of the steady flux states of the system. This decomposition comes in the form of a low number of small reaction sets whose flux variability accounts for nearly all of the flux variability in the entire system. This result indicates an underlying simplicity and implies that the regulation of a relatively low number of reaction sets can essentially determine the flux state of the entire network in the given growth environment.

Conclusion

We demonstrate how our top-down analysis of networks can be used to determine key regulatory requirements independent of specific parameters and mechanisms. Our approach complements the reductionist approach to elucidation of regulatory mechanisms and facilitates the development of our understanding of global regulatory strategies in biological networks.

Harnessing nature's toolbox: regulatory elements for synthetic biology

Synthetic biologists seek to engineer complex biological systems composed of modular elements. Achieving higher complexity in engineered biological organisms will require manipulating numerous systems of biological regulation: transcription; RNA interactions; protein signalling; and metabolic fluxes, among others. Exploiting the natural modularity at each level of biological regulation will promote the development of standardized tools for designing biological systems.

Genome-scale models of bacterial metabolism: reconstruction and applications

Genome-scale metabolic models bridge the gap between genome-derived biochemical information and metabolic phenotypes in a principled manner, providing a solid interpretative framework for experimental data related to metabolic states, and enabling simple in silico experiments with whole-cell metabolism. Models have been reconstructed for almost 20 bacterial species, so far mainly through expert curation efforts integrating information from the literature with genome annotation. A wide variety of computational methods exploiting metabolic models have been developed and applied to bacteria, yielding valuable insights into bacterial metabolism and evolution, and providing a sound basis for computer-assisted design in metabolic engineering. Recent advances in computational systems biology and high-throughput experimental technologies pave the way for the systematic reconstruction of metabolic models from genomes of new species, and a corresponding expansion of the scope of their applications. In this review, we provide an introduction to the key ideas of metabolic modeling, survey the methods, and resources that enable model reconstruction and refinement, and chart applications to the investigation of global properties of metabolic systems, the interpretation of experimental results, and the re-engineering of their biochemical capabilities.

Flux balance analysis: interrogating genome-scale metabolic networks

Flux balance analysis (FBA) is a computational method to analyze reconstructions of biochemical networks. FBA requires the formulation of a biochemical network in a precise mathematical framework called a stoichiometric matrix. An objective function is defined (e.g., growth rate) toward which the system is assumed to be optimized. In this chapter, we present the methodology, theory, and common pitfalls of the application of FBA.

Genome-scale model for Clostridium acetobutylicum: Part I. Metabolic network resolution and analysis

A genome-scale metabolic network reconstruction for Clostridium acetobutylicum (ATCC 824) was carried out using a new semi-automated reverse engineering algorithm. The network consists of 422 intracellular metabolites involved in 552 reactions and includes 80 membrane transport reactions. The metabolic network illustrates the reliance of clostridia on the urea cycle, intracellular L-glutamate solute pools, and the acetylornithine transaminase for amino acid biosynthesis from the 2-oxoglutarate precursor. The semi-automated reverse engineering algorithm identified discrepancies in reaction network databases that are major obstacles for fully automated network-building algorithms. The proposed semi-automated approach allowed for the conservation of unique clostridial metabolic pathways, such as an incomplete TCA cycle. A thermodynamic analysis was used to determine the physiological conditions under which proposed pathways (e.g., reverse partial TCA cycle and reverse arginine biosynthesis pathway) are feasible. The reconstructed metabolic network was used to create a genome-scale model that correctly characterized the butyrate kinase knock-out and the asolventogenic M5 pSOL1 megaplasmid degenerate strains. Systematic gene knock-out simulations were performed to identify a set of genes encoding clostridial enzymes essential for growth in silico.

Modelling and analysis of gene regulatory networks

Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.

Incorporation of enzyme concentrations into FBA and identification of optimal metabolic pathways

Background

In the present article, we propose a method for determining optimal metabolic pathways in terms of the level of concentration of the enzymes catalyzing various reactions in the entire metabolic network. The method, first of all, generates data on reaction fluxes in a pathway based on steady state condition. A set of constraints is formulated incorporating weighting coefficients corresponding to concentration of enzymes catalyzing reactions in the pathway. Finally, the rate of yield of the target metabolite, starting with a given substrate, is maximized in order to identify an optimal pathway through these weighting coefficients.

Results

The effectiveness of the present method is demonstrated on two synthetic systems existing in the literature, two pentose phosphate, two glycolytic pathways, core carbon metabolism and a large network of carotenoid biosynthesis pathway of various organisms belonging to different phylogeny. A comparative study with the existing extreme pathway analysis also forms a part of this investigation. Biological relevance and validation of the results are provided. Finally, the impact of the method on metabolic engineering is explained with a few examples.

Conclusions

The method may be viewed as determining an optimal set of enzymes that is required to get an optimal metabolic pathway. Although it is a simple one, it has been able to identify a carotenoid biosynthesis pathway and the optimal pathway of core carbon metabolic network that is closer to some earlier investigations than that obtained by the extreme pathway analysis. Moreover, the present method has identified correctly optimal pathways for pentose phosphate and glycolytic pathways. It has been mentioned using some examples how the method can suitably be used in the context of metabolic engineering.

Integrating metabolic, transcriptional regulatory and signal transduction models in Escherichia coli

MOTIVATION

The effort to build a whole-cell model requires the development of new modeling approaches, and in particular, the integration of models for different types of processes, each of which may be best described using different representation. Flux-balance analysis (FBA) has been useful for large-scale analysis of metabolic networks, and methods have been developed to incorporate transcriptional regulation (regulatory FBA, or rFBA). Of current interest is the integration of these approaches with detailed models based on ordinary differential equations (ODEs).

RESULTS

We developed an approach to modeling the dynamic behavior of metabolic, regulatory and signaling networks by combining FBA with regulatory Boolean logic, and ordinary differential equations. We use this approach (called integrated FBA, or iFBA) to create an integrated model of Escherichia coli which combines a flux-balance-based, central carbon metabolic and transcriptional regulatory model with an ODE-based, detailed model of carbohydrate uptake control. We compare the predicted Escherichia coli wild-type and single gene perturbation phenotypes for diauxic growth on glucose/lactose and glucose/glucose-6-phosphate with that of the individual models. We find that iFBA encapsulates the dynamics of three internal metabolites and three transporters inadequately predicted by rFBA. Furthermore, we find that iFBA predicts different and more accurate phenotypes than the ODE model for 85 of 334 single gene perturbation simulations, as well for the wild-type simulations. We conclude that iFBA is a significant improvement over the individual rFBA and ODE modeling paradigms.

AVAILABILITY

All MATLAB files used in this study are available at http://www.simtk.org/home/ifba/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments

Background

Metabolic fluxes provide invaluable insight on the integrated response of a cell to environmental stimuli or genetic modifications. Current computational methods for estimating the metabolic fluxes from ¹³C isotopomer measurement data rely either on manual derivation of analytic equations constraining the fluxes or on the numerical solution of a highly nonlinear system of isotopomer balance equations. In the first approach, analytic equations have to be tediously derived for each organism, substrate or labelling pattern, while in the second approach, the global nature of an optimum solution is difficult to prove and comprehensive measurements of external fluxes to augment the ¹³C isotopomer data are typically needed.

Results

We present a novel analytic framework for estimating metabolic flux ratios in the cell from ¹³C isotopomer measurement data. In the presented framework, equation systems constraining the fluxes are derived automatically from the model of the metabolism of an organism. The framework is designed to be applicable with all metabolic network topologies, ¹³C isotopomer measurement techniques, substrates and substrate labelling patterns.

By analyzing nuclear magnetic resonance (NMR) and mass spectrometry (MS) measurement data obtained from the experiments on glucose with the model micro-organisms Bacillus subtilis and Saccharomyces cerevisiae we show that our framework is able to automatically produce the flux ratios discovered so far by the domain experts with tedious manual analysis. Furthermore, we show by in silico calculability analysis that our framework can rapidly produce flux ratio equations – as well as predict when the flux ratios are unobtainable by linear means – also for substrates not related to glucose.

Conclusion

The core of ¹³C metabolic flux analysis framework introduced in this article constitutes of flow and independence analysis of metabolic fragments and techniques for manipulating isotopomer measurements with vector space techniques. These methods facilitate efficient, analytic computation of the ratios between the fluxes of pathways that converge to a common junction metabolite. The framework can been seen as a generalization and formalization of existing tradition for computing metabolic flux ratios where equations constraining flux ratios are manually derived, usually without explicitly showing the formal proofs of the validity of the equations.