Lethality and synthetic lethality in the genome-wide metabolic network of Escherichia coli

Understanding flux switching in metabolic networks through an analysis of synthetic lethals

Biological systems are robust and redundant. The redundancy can manifest as alternative metabolic pathways. Synthetic double lethals are pairs of reactions that, when deleted simultaneously, abrogate cell growth. However, removing one reaction allows the rerouting of metabolites through alternative pathways. Little is known about these hidden linkages between pathways. Understanding them in the context of pathogens is useful for therapeutic innovations. We propose a constraint-based optimisation approach to identify inter-dependencies between metabolic pathways. It minimises rerouting between two reaction deletions, corresponding to a synthetic lethal pair, and outputs the set of reactions vital for metabolic rewiring, known as the synthetic lethal cluster. We depict the results for different pathogens and show that the reactions span across metabolic modules, illustrating the complexity of metabolism. Finally, we demonstrate how the two classes of synthetic lethals play a role in metabolic networks and influence the different properties of a synthetic lethal cluster.

Machine learning for the advancement of genome-scale metabolic modeling

Constraint-based modeling (CBM) has evolved as the core systems biology tool to map the interrelations between genotype, phenotype, and external environment. The recent advancement of high-throughput experimental approaches and multi-omics strategies has generated a plethora of new and precise information from wide-ranging biological domains. On the other hand, the continuously growing field of machine learning (ML) and its specialized branch of deep learning (DL) provide essential computational architectures for decoding complex and heterogeneous biological data. In recent years, both multi-omics and ML have assisted in the escalation of CBM. Condition-specific omics data, such as transcriptomics and proteomics, helped contextualize the model prediction while analyzing a particular phenotypic signature. At the same time, the advanced ML tools have eased the model reconstruction and analysis to increase the accuracy and prediction power. However, the development of these multi-disciplinary methodological frameworks mainly occurs independently, which limits the concatenation of biological knowledge from different domains. Hence, we have reviewed the potential of integrating multi-disciplinary tools and strategies from various fields, such as synthetic biology, CBM, omics, and ML, to explore the biochemical phenomenon beyond the conventional biological dogma. How the integrative knowledge of these intersected domains has improved bioengineering and biomedical applications has also been highlighted. We categorically explained the conventional genome-scale metabolic model (GEM) reconstruction tools and their improvement strategies through ML paradigms. Further, the crucial role of ML and DL in omics data restructuring for GEM development has also been briefly discussed. Finally, the case-study-based assessment of the state-of-the-art method for improving biomedical and metabolic engineering strategies has been elaborated. Therefore, this review demonstrates how integrating experimental and in silico strategies can help map the ever-expanding knowledge of biological systems driven by condition-specific cellular information. This multiview approach will elevate the application of ML-based CBM in the biomedical and bioengineering fields for the betterment of society and the environment.

Development and applications of genome-scale metabolic network models

The genome-scale metabolic network model is an effective tool for characterizing the gene-protein-response relationship in the entire metabolic pathway of an organism. By combining various algorithms, the genome-scale metabolic network model can effectively simulate the influence of a specific environment on the physiological state of cells, optimize the culture conditions of strains, and predict the targets of genetic modification to achieve targeted modification of strains. In this review, we summarize the whole process of model building, sort out the various tools that may be involved in the model building process, and explain the role of various algorithms in model analysis. In addition, we also summarized the application of GSMM in network characteristics, cell phenotypes, metabolic engineering, etc. Finally, we discuss the current challenges facing GSMM.

Extreme Antagonism Arising from Gene-Environment Interactions

Antagonistic interactions in biological systems, which occur when one perturbation blunts the effect of another, are typically interpreted as evidence that the two perturbations impact the same cellular pathway or function. Yet, this interpretation ignores extreme antagonistic interactions wherein an otherwise deleterious perturbation compensates for the function lost because of a prior perturbation. Here, we report on gene-environment interactions involving genetic mutations that are deleterious in a permissive environment but beneficial in a specific environment that restricts growth. These extreme antagonistic interactions constitute gene-environment analogs of synthetic rescues previously observed for gene-gene interactions. Our approach uses two independent adaptive evolution steps to address the lack of experimental methods to systematically identify such extreme interactions. We apply the approach to Escherichia coli by successively adapting it to defined glucose media without and with the antibiotic rifampicin. The approach identified multiple mutations that are beneficial in the presence of rifampicin and deleterious in its absence. The analysis of transcription shows that the antagonistic adaptive mutations repress a stringent response-like transcriptional program, whereas nonantagonistic mutations have an opposite transcriptional profile. Our approach represents a step toward the systematic characterization of extreme antagonistic gene-drug interactions, which can be used to identify targets to select against antibiotic resistance.

MinReact: a systematic approach for identifying minimal metabolic networks

MOTIVATION

Genome-scale metabolic models are widely constructed and studied for understanding various design principles underlying metabolism, predominantly redundancy. Metabolic networks are highly redundant and it is possible to minimize the metabolic networks into smaller networks that retain the functionality of the original network.

RESULTS

Here, we establish a new method, MinReact that systematically removes reactions from a given network to identify minimal reactome(s). We show that our method identifies smaller minimal reactomes than existing methods and also scales well to larger metabolic networks. Notably, our method exploits known aspects of network structure and redundancy to identify multiple minimal metabolic networks. We illustrate the utility of MinReact by identifying multiple minimal networks for 77 organisms from the BiGG database. We show that these multiple minimal reactomes arise due to the presence of compensatory reactions/pathways. We further employed MinReact for a case study to identify the minimal reactomes of different organisms in both glucose and xylose minimal environments. Identification of minimal reactomes of these different organisms elucidate that they exhibit varying levels of redundancy. A comparison of the minimal reactomes on glucose and xylose illustrates that the differences in the reactions required to sustain growth on either medium. Overall, our algorithm provides a rapid and reliable way to identify minimal subsets of reactions that are essential for survival, in a systematic manner.

AVAILABILITY AND IMPLEMENTATION

Algorithm is available from https://github.com/RamanLab/MinReact.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Understanding the evolution of functional redundancy in metabolic networks

Motivation

Metabolic networks have evolved to reduce the disruption of key metabolic pathways by the establishment of redundant genes/reactions. Synthetic lethals in metabolic networks provide a window to study these functional redundancies. While synthetic lethals have been previously studied in different organisms, there has been no study on how the synthetic lethals are shaped during adaptation/evolution.

Results

To understand the adaptive functional redundancies that exist in metabolic networks, we here explore a vast space of ‘random’ metabolic networks evolved on a glucose environment. We examine essential and synthetic lethal reactions in these random metabolic networks, evaluating over 39 billion phenotypes using an efficient algorithm previously developed in our lab, Fast-SL. We establish that nature tends to harbour higher levels of functional redundancies compared with random networks. We then examined the propensity for different reactions to compensate for one another and show that certain key metabolic reactions that are necessary for growth in a particular growth medium show much higher redundancies, and can partner with hundreds of different reactions across the metabolic networks that we studied. We also observe that certain redundancies are unique to environments while some others are observed in all environments. Interestingly, we observe that even very diverse reactions, such as those belonging to distant pathways, show synthetic lethality, illustrating the distributed nature of robustness in metabolism. Our study paves the way for understanding the evolution of redundancy in metabolic networks, and sheds light on the varied compensation mechanisms that serve to enhance robustness.

Supplementary information

Supplementary data are available at Bioinformatics online.

Identification of critical connectors in the directed reaction-centric graphs of microbial metabolic networks

BACKGROUND

Detection of central nodes in asymmetrically directed biological networks depends on centrality metrics quantifying individual nodes' importance in a network. In topological analyses on metabolic networks, various centrality metrics have been mostly applied to metabolite-centric graphs. However, centrality metrics including those not depending on high connections are largely unexplored for directed reaction-centric graphs.

RESULTS

We applied directed versions of centrality metrics to directed reaction-centric graphs of microbial metabolic networks. To investigate the local role of a node, we developed a novel metric, cascade number, considering how many nodes are closed off from information flow when a particular node is removed. High modularity and scale-freeness were found in the directed reaction-centric graphs and betweenness centrality tended to belong to densely connected modules. Cascade number and bridging centrality identified cascade subnetworks controlling local information flow and irreplaceable bridging nodes between functional modules, respectively. Reactions highly ranked with bridging centrality and cascade number tended to be essential, compared to reactions that other central metrics detected.

CONCLUSIONS

We demonstrate that cascade number and bridging centrality are useful to identify key reactions controlling local information flow in directed reaction-centric graphs of microbial metabolic networks. Knowledge about the local flow connectivity and connections between local modules will contribute to understand how metabolic pathways are assembled.

Evolutionary design principles in metabolism

Microorganisms are ubiquitous and adapt to various dynamic environments to sustain growth. These adaptations accumulate, generating new traits forming the basis of evolution. Organisms adapt at various levels, such as gene regulation, signalling, protein-protein interactions and metabolism. Of these, metabolism forms the integral core of an organism for maintaining the growth and function of a cell. Therefore, studying adaptations in metabolic networks is crucial to understand the emergence of novel metabolic capabilities. Metabolic networks, composed of enzyme-catalysed reactions, exhibit certain repeating paradigms or design principles that arise out of different selection pressures. In this review, we discuss the design principles that are known to exist in metabolic networks, such as functional redundancy, modularity, flux coupling and exaptations. We elaborate on the studies that have helped gain insights highlighting the interplay of these design principles and adaptation. Further, we discuss how evolution plays a role in exploiting such paradigms to enhance the robustness of organisms. Looking forward, we predict that with the availability of ever-increasing numbers of bacterial, archaeal and eukaryotic genomic sequences, novel design principles will be identified, expanding our understanding of these paradigms shaped by varied evolutionary processes.

Use of genetic and chemical synthetic lethality as probes of complexity in bacterial cell systems

Different conditions and genomic contexts are known to have an impact on gene essentiality and interactions. Synthetic lethal interactions occur when a combination of perturbations, either genetic or chemical, result in a more profound fitness defect than expected based on the effect of each perturbation alone. Synthetic lethality in bacterial systems has long been studied; however, during the past decade, the emerging fields of genomics and chemical genomics have led to an increase in the scale and throughput of these studies. Here, we review the concepts of genomics and chemical genomics in the context of synthetic lethality and their revolutionary roles in uncovering novel biology such as the characterization of genes of unknown function and in antibacterial drug discovery. We provide an overview of the methodologies, examples and challenges of both genetic and chemical synthetic lethal screening platforms. Finally, we discuss how to apply genetic and chemical synthetic lethal approaches to rationalize the synergies of drugs, screen for new and improved antibacterial therapies and predict drug mechanism of action.

Metabolic Model Reconstruction and Analysis of an Artificial Microbial Ecosystem

Microbial communities are widespread in the environment, and to isolate and identify species or to determine relations among microorganisms, some 'omics methods like metagenomics, proteomics, and metabolomics have been used. When combined with various 'omics data, models known as artificial microbial ecosystems (AME) are powerful methods that can make functional predictions about microbial communities. Reconstruction of an AME model is the first step for model analysis. Many techniques have been applied to the construction of AME models, e.g., the compartmentalization approach, community objectives method, and dynamic analysis approach. Of these approaches, species compartmentalization is the most relevant to genetics. Besides, some algorithms have been developed for the analysis of AME models. In this chapter, we present a general protocol for the use of the species compartmentalization method to reconstruct a model of microbial communities. Then, the analysis of an AME is discussed.

Biconnectivity of the cellular metabolism: A cross-species study and its implication for human diseases

The maintenance of stability during perturbations is essential for living organisms, and cellular networks organize multiple pathways to enable elements to remain connected and communicate, even when some pathways are broken. Here, we evaluated the biconnectivity of the metabolic networks of 506 species in terms of the clustering coefficients and the largest biconnected components (LBCs), wherein a biconnected component (BC) indicates a set of nodes in which every pair is connected by more than one path. Via comparison with the rewired networks, we illustrated how biconnectivity in cellular metabolism is achieved on small and large scales. Defining the biconnectivity of individual metabolic compounds by counting the number of species in which the compound belonged to the LBC, we demonstrated that biconnectivity is significantly correlated with the evolutionary age and functional importance of a compound. The prevalence of diseases associated with each metabolic compound quantifies the compounds vulnerability, i.e., the likelihood that it will cause a metabolic disorder. Moreover, the vulnerability depends on both the biconnectivity and the lethality of the compound. This fact can be used in drug discovery and medical treatments.

Genetic redundancy is prevalent within the 6.7 Mb Sinorhizobium meliloti genome

Biological pathways are frequently identified via a genetic loss-of-function approach. While this approach has proven to be powerful, it is imperfect as illustrated by well-studied pathways continuing to have missing steps. One potential limiting factor is the masking of phenotypes through genetic redundancy. The prevalence of genetic redundancy in bacterial species has received little attention, although isolated examples of functionally redundant gene pairs exist. Here, we made use of a strain of Sinorhizobium meliloti whose genome was reduced by 45 % through the complete removal of a megaplasmid and a chromid (3 Mb of the 6.7 Mb genome was removed) to begin quantifying the level of genetic redundancy within a large bacterial genome. A mutagenesis of the strain with the reduced genome identified a set of transposon insertions precluding growth of this strain on minimal medium. Transfer of these mutations to the wild-type background revealed that 10-15 % of these chromosomal mutations were located within duplicated genes, as they did not prevent growth of cells with the full genome. The functionally redundant genes were involved in a variety of metabolic pathways, including central carbon metabolism, transport, and amino acid biosynthesis. These results indicate that genetic redundancy may be prevalent within large bacterial genomes. Failing to account for redundantly encoded functions in loss-of-function studies will impair our understanding of a broad range of biological processes and limit our ability to use synthetic biology in the construction of designer cell factories.

Evolution of regulatory networks towards adaptability and stability in a changing environment

Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which evolve by selectively rewiring links towards enhancing adaptability to a changing environment and stability against dynamical perturbations. We find that sparse and heterogeneous connectivity patterns emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks. The characteristic scaling behavior of stability reflects the balance between robustness and flexibility. The scaling of fluctuation in the perturbation spread shows a dynamic crossover, which is analyzed by investigating separately the stochasticity of internal dynamics and the network structure differences depending on the evolution pathways. Our study delineates how the ambivalent pressure of evolution shapes biological networks, which can be helpful for studying general complex systems interacting with environments.

Metabolic flux analysis of Escherichia coli knockouts: lessons from the Keio collection and future outlook

Cellular metabolic and regulatory systems are of fundamental interest to biologists and engineers. Incomplete understanding of these complex systems remains an obstacle to progress in biotechnology and metabolic engineering. An established method for obtaining new information on network structure, regulation and dynamics is to study the cellular system following a perturbation such as a genetic knockout. The Keio collection of all viable Escherichia coli single-gene knockouts is facilitating a systematic investigation of the regulation and metabolism of E. coli. Of all omics measurements available, the metabolic flux profile (the fluxome) provides the most direct and relevant representation of the cellular phenotype. Recent advances in (13)C-metabolic flux analysis are now permitting highly precise and accurate flux measurements for investigating cellular systems and guiding metabolic engineering efforts.

Phase transition in the biconnectivity of scale-free networks

In information-transport and biological systems, sometimes there is more than one pathway between two nodes, so that there is a backup in case one pathway becomes defective. The size of such biconnected nodes can be an important measure of the robustness of a system. The giant biconnected components of diverse real-world networks suggest the importance of scale-free topology in biconnectivity. Thus, here, we consider the critical behavior of the largest biconnected component (BC) as links are added and form a random scale-free network. The critical exponents β((BC)) and β((SC)) associated with the order parameter of the percolation transition of the biconnected component and the single-connected component (SC), respectively, are compared. We obtain a ratio β((BC))/β((SC))=λ-1 for 2<λ<3 and 2 for λ>3, where λ is the exponent of the degree distribution in scale-free networks. We also determine the finite-size scaling behavior of the order parameter analytically and numerically.

Basic and applied uses of genome-scale metabolic network reconstructions of Escherichia coli

The genome-scale model (GEM) of metabolism in the bacterium Escherichia coli K-12 has been in development for over a decade and is now in wide use. GEM-enabled studies of E. coli have been primarily focused on six applications: (1) metabolic engineering, (2) model-driven discovery, (3) prediction of cellular phenotypes, (4) analysis of biological network properties, (5) studies of evolutionary processes, and (6) models of interspecies interactions. In this review, we provide an overview of these applications along with a critical assessment of their successes and limitations, and a perspective on likely future developments in the field. Taken together, the studies performed over the past decade have established a genome-scale mechanistic understanding of genotype-phenotype relationships in E. coli metabolism that forms the basis for similar efforts for other microbial species. Future challenges include the expansion of GEMs by integrating additional cellular processes beyond metabolism, the identification of key constraints based on emerging data types, and the development of computational methods able to handle such large-scale network models with sufficient accuracy.

Characterizing criticality of proteins by systems dynamics: Escherichia coli central carbon metabolism as a working example

Background

Systems biology calls for studying system-level properties of genes and proteins rather than their individual chemical/biological properties, regarding the bio-molecules as system components. By characterizing how critical the components are to the system and classifying them accordingly, we can study the underlying complex mechanisms, facilitating researches in drug target selection, metabolic engineering, complex disease, etc. Up to date, most studies aiming at this goal are confined to the topology-based or flux-analysis approaches. However, proteins have tertiary structures and specific functions, especially in metabolic systems. Thus topological properties such as connectivity, path length, etc., are not good surrogates for protein properties. Also, the manner of individual sensitivity analysis in most flux-analysis approaches cannot reveal the simultaneous impacts on collateral components as well as the overall impact on the system, thus lacking in system-level perspective.

Results

In the present work, we developed a method to directly assess protein system-level properties based on system dynamics and in silico knockouts, regarding to the conceptual term "criticality". Applying the method to E. coli central carbon metabolic system, we found that multiple enzymes including phosphoglycerate kinase, enolase, transketolase-b, etc., had critical roles in the system in terms of both system states and dynamical stability. In contrast, another set of enzymes including glucose-6-phosphate isomerise, pyruvate kinase, phosphoglucomutase, etc., exerted very little influences when deleted. The finding is consistent with experimental characterization of metabolic essentiality and other studies on E. coli gene essentiality and functions. We also found that enzymes could affect distant metabolites or enzymes even greater than a close neighbour and asymmetry in system-level properties of enzymes catalyzing alternative pathways could give rise to local flux compensation.

Conclusions

Our method creates a different angle for evaluating protein criticality to a biological system from the conventional methodologies. Moreover, the method leads to consistent results with experimental references, showing its efficiency in studying protein system-level properties. Besides working on metabolic systems, the application of the method can be extended to other kinds of bio-systems to reveal the constitutive/functional properties of system building blocks.

Branching process approach for Boolean bipartite networks of metabolic reactions

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR logic gates. We reduce the bipartite network into a unipartite network by integrating out OR gates and obtain the effective branching ratio for the remaining AND gates. Then the standard BP approach is applied to the reduced network, and the avalanche-size distribution is obtained. We test the BP results with simulations on the model networks and two microbial metabolic networks, demonstrating the usefulness of the BP approach.

Constraints-based stoichiometric analysis of hypoxic stress on steroidogenesis in fathead minnows, Pimephales promelas

In this study, an in silico genome-scale metabolic model of steroidogenesis was used to investigate the effects of hypoxic stress on steroid hormone productions in fish. Adult female fathead minnows (Pimephales promelas) were exposed to hypoxia for 7 days with fish sub-sampled on days 1, 3 and 7 of exposure. At each time point, selected steroid enzyme gene expressions and steroid hormone productions were quantified in ovaries. Fold changes in steroid enzyme gene expressions were used to qualitatively scale transcript enzyme reaction constraints (akin to the range of an enzyme’s catalytic activity) in the in silico model. Subsequently, in silico predicted steroid hormone productions were qualitatively compared with experimental results. Key findings were as follows. (1) In silico gene deletion analysis identified highly conserved ‘essential’ genes required for steroid hormone productions. These agreed well (75%) with literature-published genes downregulated in vertebrates (fish and mammal) exposed to hypoxia. (2) Quantification of steroid hormones produced ex vivo from ovaries showed a significant reduction for 17β-estradiol and 17α,20β-dihydroxypregnenone production after 24 h (day 1) of exposure. This lowered 17β-estradiol production was concomitant with downregulation of cyp19a1a gene expression in ovaries. In silico predictions showed agreement with experimentation by predicting effects on estrogen (17β-estradiol and estrone) production. (3) Stochastic sampling of in silico reactions indicated that cholesterol uptake and catalysis to pregnenolone along with estrogen methyltransferase and glucuronidation reactions were also impacted by hypoxia. Taken together, this in silico analysis introduces a powerful model for pathway analysis that can lend insights on the effects of various stressor scenarios on metabolic functions.

Applications of system-level models of metabolism for analysis of bacterial physiology and identification of new drug targets

For nearly all of the 20th century, biologists gained considerable insights into the fundamental principles of cellular dynamics by examining select modules of biochemical processes. This form of analysis provides detailed information about the workings of the examined pathways. However, any attempt to alter the normal function of bacteria (perhaps for industrial or medicinal goals) requires a detailed global understanding of cellular mechanisms. The reductionist mode of analysis cannot provide the required information for developing the needed perspective on the complex interactions of biochemical pathways. Thankfully, the increasing availability of microbial genomic, transcriptomic, proteomic and other high-throughput data permits system-level analyses of microbiology. During the past two decades, systems biologists have developed constraint-based genome-scale models (GSM) of metabolism for a variety of pathogens. These models are important tools for assessing the metabolic capabilities of various genotypes. Simultaneously, new computational methods have been developed that use these network reconstructions to answer an array of important immunological questions. The objective of this article is to briefly review some of the uses of GSMs for studying bacterial metabolism under different conditions and to discuss how the calculated solutions can be used for rational design of drugs.

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.

Centralized modularity of N-linked glycosylation pathways in mammalian cells

Glycosylation is a highly complex process to produce a diverse repertoire of cellular glycans that are attached to proteins and lipids. Glycans are involved in fundamental biological processes, including protein folding and clearance, cell proliferation and apoptosis, development, immune responses, and pathogenesis. One of the major types of glycans, N-linked glycans, is formed by sequential attachments of monosaccharides to proteins by a limited number of enzymes. Many of these enzymes can accept multiple N-linked glycans as substrates, thereby generating a large number of glycan intermediates and their intermingled pathways. Motivated by the quantitative methods developed in complex network research, we investigated the large-scale organization of such N-linked glycosylation pathways in mammalian cells. The N-linked glycosylation pathways are extremely modular, and are composed of cohesive topological modules that directly branch from a common upstream pathway of glycan synthesis. This unique structural property allows the glycan production between modules to be controlled by the upstream region. Although the enzymes act on multiple glycan substrates, indicating cross-talk between modules, the impact of the cross-talk on the module-specific enhancement of glycan synthesis may be confined within a moderate range by transcription-level control. The findings of the present study provide experimentally-testable predictions for glycosylation processes, and may be applicable to therapeutic glycoprotein engineering.

Genome-scale gene/reaction essentiality and synthetic lethality analysis

Synthetic lethals are to pairs of non-essential genes whose simultaneous deletion prohibits growth. One can extend the concept of synthetic lethality by considering gene groups of increasing size where only the simultaneous elimination of all genes is lethal, whereas individual gene deletions are not. We developed optimization-based procedures for the exhaustive and targeted enumeration of multi-gene (and by extension multi-reaction) lethals for genome-scale metabolic models. Specifically, these approaches are applied to iAF1260, the latest model of Escherichia coli, leading to the complete identification of all double and triple gene and reaction synthetic lethals as well as the targeted identification of quadruples and some higher-order ones. Graph representations of these synthetic lethals reveal a variety of motifs ranging from hub-like to highly connected subgraphs providing a birds-eye view of the avenues available for redirecting metabolism and uncovering complex patterns of gene utilization and interdependence. The procedure also enables the use of falsely predicted synthetic lethals for metabolic model curation. By analyzing the functional classifications of the genes involved in synthetic lethals, we reveal surprising connections within and across clusters of orthologous group functional classifications.

Systems-level approaches for identifying and analyzing genetic interaction networks in Escherichia coli and extensions to other prokaryotes

Molecular interactions define the functional organization of the cell. Epistatic (genetic, or gene-gene) interactions, one of the most informative and commonly encountered forms of functional relationships, are increasingly being used to map process architecture in model eukaryotic organisms. In particular, 'systems-level' screens in yeast and worm aimed at elucidating genetic interaction networks have led to the generation of models describing the global modular organization of gene products and protein complexes within a cell. However, comparable data for prokaryotic organisms have not been available. Given its ease of growth and genetic manipulation, the Gram-negative bacterium Escherichia coli appears to be an ideal model system for performing comprehensive genome-scale examinations of genetic redundancy in bacteria. In this review, we highlight emerging experimental and computational techniques that have been developed recently to examine functional relationships and redundancy in E. coli at a systems-level, and their potential application to prokaryotes in general. Additionally, we have scanned PubMed abstracts and full-text published articles to manually curate a list of approximately 200 previously reported synthetic sick or lethal genetic interactions in E. coli derived from small-scale experimental studies.

Inferring minimal feasible metabolic networks of Escherichia coli

Since the organism contains many redundant reactions, the minimal feasible metabolic network that contains the basic growth function is not the collection of reactions that associate the essential genes. To identify minimal metabolic reaction set is a challenging work in theoretical approach. A new method is presented here to identify the smallest required reaction set of growth-sustaining metabolic networks. The content and number of the minimal reactions for growth are variable in different random processes. Though the different carbon sources also vary the content of the reactions in the minimal metabolic networks, most essential reactions locate in the same metabolic subsystems, such as cofactor and prosthetic group biosynthesis, cell envelope biosynthesis, and membrane lipid metabolism.

Genome-scale analysis to the impact of gene deletion on the metabolism of E. coli: constraint-based simulation approach

Background

Genome-scale models of metabolism have only been analyzed with the constraint-based modelling philosophy. Some gene deletion studies on in silico organism models at genome-scale have been made, but most of them were from the aspects of distinguishing lethal and non-lethal genes or growth rate. The impact of gene deletion on flux redistribution, the functions and characters of key genes, and the performance of different reactions in entire gene deletion still lack research.

Results

Three main researches have been done into the metabolism of E. coli in gene deletion. The first work was about finding key genes and subsystems: First, by calculating the deletion impact p of whole 1261 genes, one by one, on the metabolic flux redistribution of E. coli_iAF1260, we can find that p is more detailed in describing the change of organism's metabolism. Next, we sought out 195 important (high-p) genes, and they are more than essential genes (growth rate f becomes zero if deleting). So we speculated that under some circumstances and when an important gene is deleted, a big change in the metabolic system of E. coli has taken place and E. coli may use other reaction ways to strive to live. Further, by determining the functional subsystems to which 195 key genes belong, we found that their distribution to subsystems was not even and most of them were related to just three subsystems and that all of the 8 important but not essential genes appear just in "Oxidative Phosphorylation". Our second work was about p's three characters: We analyzed the correlation between p and d (connection degree of one gene) and the correlation between p and v_gene (flux sum controlled by one gene), and found that both of them are not of linear correlation, but the correlation between p and f is of highly linear correlation. The third work was about highly-affected reactions: We found 16 reactions with more than 2000 Rg value (measuring the impact that a reaction is gotten in the whole 1261 gene deletion). We speculated that highly-affected reactions involve in the metabolism of basic biomasses.

Conclusion

To sum up, these results we obtained have biological significances and our researches will shed new light on the future researches.

Spontaneous reaction silencing in metabolic optimization

Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances. Yet, the mechanisms as well as the range of conditions and phenotypes associated with this behavior remain very poorly understood. Here we predict computationally and analytically that any organism evolving to maximize growth rate, ATP production, or any other linear function of metabolic fluxes tends to significantly reduce the number of active metabolic reactions compared to typical nonoptimal states. The reduced number appears to be constant across the microbial species studied and just slightly larger than the minimum number required for the organism to grow at all. We show that this massive spontaneous reaction silencing is triggered by the irreversibility of a large fraction of the metabolic reactions and propagates through the network as a cascade of inactivity. Our results help explain existing experimental data on intracellular flux measurements and the usage of latent pathways, shedding new light on microbial evolution, robustness, and versatility for the execution of specific biochemical tasks. In particular, the identification of optimal reaction activity provides rigorous ground for an intriguing knockout-based method recently proposed for the synthetic recovery of metabolic function.

Cellular growth and other integrated metabolic functions are manifestations of the coordinated interconversion of a large number of chemical compounds. But what is the relation between such whole-cell behaviors and the activity pattern of the individual biochemical reactions? In this study, we have used flux balance-based methods and reconstructed networks of Helicobacter pylori, Staphylococcus aureus, Escherichia coli, and Saccharomyces cerevisiae to show that a cell seeking to optimize a metabolic objective, such as growth, has a tendency to spontaneously inactivate a significant number of its metabolic reactions, while all such reactions are recruited for use in typical suboptimal states. The mechanisms governing this behavior not only provide insights into why numerous genes can often be disabled without affecting optimal growth but also lay a foundation for the recently proposed synthetic rescue of metabolic function in which the performance of suboptimally operating cells can be enhanced by disabling specific metabolic reactions. Our findings also offer explanation for another experimentally observed behavior, in which some inactive reactions are temporarily activated following a genetic or environmental perturbation. The latter is of utmost importance given that nonoptimal and transient metabolic behaviors are arguably common in natural environments.

The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli

The number and scope of methods developed to interrogate and use metabolic network reconstructions has significantly expanded over the past 15 years. In particular, Escherichia coli metabolic network reconstruction has reached the genome scale and been utilized to address a broad spectrum of basic and practical applications in five main categories: metabolic engineering, model-directed discovery, interpretations of phenotypic screens, analysis of network properties and studies of evolutionary processes. Spurred on by these accomplishments, the field is expected to move forward and further broaden the scope and content of network reconstructions, develop new and novel in silico analysis tools, and expand in adaptation to uses of proximal and distal causation in biology. Taken together, these efforts will solidify a mechanistic genotype-phenotype relationship for microbial metabolism.

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114-120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases. We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.

Metabolite essentiality elucidates robustness of Escherichia coli metabolism

Complex biological systems are very robust to genetic and environmental changes at all levels of organization. Many biological functions of Escherichia coli metabolism can be sustained against single-gene or even multiple-gene mutations by using redundant or alternative pathways. Thus, only a limited number of genes have been identified to be lethal to the cell. In this regard, the reaction-centric gene deletion study has a limitation in understanding the metabolic robustness. Here, we report the use of flux-sum, which is the summation of all incoming or outgoing fluxes around a particular metabolite under pseudo-steady state conditions, as a good conserved property for elucidating such robustness of E. coli from the metabolite point of view. The functional behavior, as well as the structural and evolutionary properties of metabolites essential to the cell survival, was investigated by means of a constraints-based flux analysis under perturbed conditions. The essential metabolites are capable of maintaining a steady flux-sum even against severe perturbation by actively redistributing the relevant fluxes. Disrupting the flux-sum maintenance was found to suppress cell growth. This approach of analyzing metabolite essentiality provides insight into cellular robustness and concomitant fragility, which can be used for several applications, including the development of new drugs for treating pathogens.

Characterization of protein-interaction networks in tumors

BACKGROUND

Analyzing differential-gene-expression data in the context of protein-interaction networks (PINs) yields information on the functional cellular status. PINs can be formally represented as graphs, and approximating PINs as undirected graphs allows the network properties to be characterized using well-established graph measures. This paper outlines features of PINs derived from 29 studies on differential gene expression in cancer. For each study the number of differentially regulated genes was determined and used as a basis for PIN construction utilizing the Online Predicted Human Interaction Database.

RESULTS

Graph measures calculated for the largest subgraph of a PIN for a given differential-gene-expression data set comprised properties reflecting the size, distribution, biological relevance, density, modularity, and cycles. The values of a distinct set of graph measures, namely Closeness Centrality, Graph Diameter, Index of Aggregation, Assortative Mixing Coefficient, Connectivity, Sum of the Wiener Number, modified Vertex Distance Number, and Eigenvalues differed clearly between PINs derived on the basis of differential gene expression data sets characterizing malignant tissue and PINs derived on the basis of randomly selected protein lists.

CONCLUSION

Cancer PINs representing differentially regulated genes are larger than those of randomly selected protein lists, indicating functional dependencies among protein lists that can be identified on the basis of transcriptomics experiments. However, the prevalence of hub proteins was not increased in the presence of cancer. Interpretation of such graphs in the context of robustness may yield novel therapies based on synthetic lethality that are more effective than focusing on single-action drugs for cancer treatment.

A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism.

RMBNToolbox: random models for biochemical networks

BACKGROUND

There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models.

RESULTS

We present a computational toolbox for generating random biochemical network models which mimic real biochemical networks. The toolbox is called Random Models for Biochemical Networks. The toolbox works in the Matlab environment, and it makes it possible to generate various network structures, stoichiometries, kinetic laws for reactions, and parameters therein. The generation can be based on statistical rules and distributions, and more detailed information of real biochemical networks can be used in situations where it is known. The toolbox can be easily extended. The resulting network models can be exported in the format of Systems Biology Markup Language.

CONCLUSION

While more information is accumulating on biochemical networks, random networks can be used as an intermediate step towards their better understanding. Random networks make it possible to study the effects of various network characteristics to the overall behavior of the network. Moreover, the construction of artificial network models provides the ground truth data needed in the validation of various computational methods in the fields of parameter estimation and data analysis.

Plasticity of genetic interactions in metabolic networks of yeast

Why are most genes dispensable? The impact of gene deletions may depend on the environment (plasticity), the presence of compensatory mechanisms (mutational robustness), or both. Here, we analyze the interaction between these two forces by exploring the condition-dependence of synthetic genetic interactions that define redundant functions and alternative pathways. We performed systems-level flux balance analysis of the yeast (Saccharomyces cerevisiae) metabolic network to identify genetic interactions and then tested the model's predictions with in vivo gene-deletion studies. We found that the majority of synthetic genetic interactions are restricted to certain environmental conditions, partly because of the lack of compensation under some (but not all) nutrient conditions. Moreover, the phylogenetic cooccurrence of synthetically interacting pairs is not significantly different from random expectation. These findings suggest that these gene pairs have at least partially independent functions, and, hence, compensation is only a byproduct of their evolutionary history. Experimental analyses that used multiple gene deletion strains not only confirmed predictions of the model but also showed that investigation of false predictions may both improve functional annotation within the model and also lead to the discovery of higher-order genetic interactions. Our work supports the view that functional redundancy may be more apparent than real, and it offers a unified framework for the evolution of environmental adaptation and mutational robustness.

Fractality in complex networks: critical and supercritical skeletons

Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a box-covering algorithm that is a modified version of the original algorithm introduced by Song [Nature (London) 433, 392 (2005)]; this algorithm enables easy implementation. Fractal networks are viewed as comprising a skeleton and shortcuts. The skeleton, embedded underneath the original network, is a special type of spanning tree based on the edge betweenness centrality; it provides a scaffold for the fractality of the network. When the skeleton is regarded as a branching tree, it exhibits a plateau in the mean branching number as a function of the distance from a root. For nonfractal networks, on the other hand, the mean branching number decays to zero without forming a plateau. Based on these observations, we construct a fractal network model by combining a random branching tree and local shortcuts. The scaffold branching tree can be either critical or supercritical, depending on the small worldness of a given network. For the network constructed from the critical (supercritical) branching tree, the average number of vertices within a given box grows with the lateral size of the box according to a power-law (an exponential) form in the cluster-growing method. The critical and supercritical skeletons are observed in protein interaction networks and the World Wide Web, respectively. The distribution of box masses, i.e., the number of vertices within each box, follows a power law Pm(M) approximately M(-eta). The exponent eta depends on the box lateral size l(B). For small values of l(B), eta is equal to the degree exponent gamma of a given scale-free network, whereas eta approaches the exponent tau=gamma/(gamma-1) as l(B) increases, which is the exponent of the cluster-size distribution of the random branching tree. Finally, we study the perimeter H(alpha) of a given box alpha, i.e., the number of edges connected to different boxes from a given box alpha as a function of the box mass M(B,alpha). It is obtained that the average perimeter over the boxes with box mass M(B) is likely to scale as <H(M(B))> approximately M(B), irrespective of the box size l(B).

Biological context networks: a mosaic view of the interactome

Network models are a fundamental tool for the visualization and analysis of molecular interactions occurring in biological systems. While broadly illuminating the molecular machinery of the cell, graphical representations of protein interaction networks mask complex patterns of interaction that depend on temporal, spatial, or condition-specific contexts. In this paper, we introduce a novel graph construct called a biological context network that explicitly captures these changing patterns of interaction from one biological context to another. We consider known gene ontology biological process and cellular component annotations as a proxy for context, and show that aggregating small process-specific protein interaction sub-networks leads to the emergence of observed scale-free properties. The biological context model also provides the basis for characterizing proteins in terms of several context-specific measures, including ‘interactive promiscuity,' which identifies proteins whose interacting partners vary from one context to another. We show that such context-sensitive measures are significantly better predictors of knockout lethality than node degree, reaching better than 70% accuracy among the top scoring proteins.

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.