Essentiality and damage in metabolic networks

A biochemical network modeling of a whole-cell

All cellular processes can be ultimately understood in terms of respective fundamental biochemical interactions between molecules, which can be modeled as networks. Very often, these molecules are shared by more than one process, therefore interconnecting them. Despite this effect, cellular processes are usually described by separate networks with heterogeneous levels of detail, such as metabolic, protein-protein interaction, and transcription regulation networks. Aiming at obtaining a unified representation of cellular processes, we describe in this work an integrative framework that draws concepts from rule-based modeling. In order to probe the capabilities of the framework, we used an organism-specific database and genomic information to model the whole-cell biochemical network of the Mycoplasma genitalium organism. This modeling accounted for 15 cellular processes and resulted in a single component network, indicating that all processes are somehow interconnected. The topological analysis of the network showed structural consistency with biological networks in the literature. In order to validate the network, we estimated gene essentiality by simulating gene deletions and compared the results with experimental data available in the literature. We could classify 212 genes as essential, being 95% of them consistent with experimental results. Although we adopted a relatively simple organism as a case study, we suggest that the presented framework has the potential for paving the way to more integrated studies of whole organisms leading to a systemic analysis of cells on a broader scale. The modeling of other organisms using this framework could provide useful large-scale models for different fields of research such as bioengineering, network biology, and synthetic biology, and also provide novel tools for medical and industrial applications.

Computing Minimum Reaction Modifications in a Boolean Metabolic Network

In metabolic network modification, we newly add enzymes or/and knock-out genes to maximize the biomass production with minimum side-effect. Although this problem has been studied for various problem settings via mathematical models including flux balance analysis, elementary mode, and Boolean models, some important problem settings still remain to be studied. In this paper, we consider the Boolean Reaction Modification (BRM) problem, where a host metabolic network and a reference metabolic network are given in the Boolean model. The host network initially produces some toxic compounds and cannot produce some necessary compounds, but the reference network can produce the necessary compounds, and we should minimize the total number of removed reactions from the host network and added reactions from the reference network so that the toxic compounds are not producible, but the necessary compounds are producible in the resulting host network. We developed integer linear programming (ILP)-based methods for BRM, and compared them with OptStrain and SimOptStrain. The results show that our method performed better for reducing the total number of added and removed reactions, while OptStrain and SimOptStrain performed better for optimizing the production of the target compound. Our developed software is freely available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/solBRM/solBRM.html ".

Discovery of Boolean metabolic networks: integer linear programming based approach

Background

Traditional drug discovery methods focused on the efficacy of drugs rather than their toxicity. However, toxicity and/or lack of efficacy are produced when unintended targets are affected in metabolic networks. Thus, identification of biological targets which can be manipulated to produce the desired effect with minimum side-effects has become an important and challenging topic. Efficient computational methods are required to identify the drug targets while incurring minimal side-effects.

Results

In this paper, we propose a graph-based computational damage model that summarizes the impact of enzymes on compounds in metabolic networks. An efficient method based on Integer Linear Programming formalism is then developed to identify the optimal enzyme-combination so as to minimize the side-effects. The identified target enzymes for known successful drugs are then verified by comparing the results with those in the existing literature.

Conclusions

Side-effects reduction plays a crucial role in the study of drug development. A graph-based computational damage model is proposed and the theoretical analysis states the captured problem is NP-completeness. The proposed approaches can therefore contribute to the discovery of drug targets. Our developed software is available at “http://hkumath.hku.hk/~wkc/APBC2018-metabolic-network.zip”.

Computing smallest intervention strategies for multiple metabolic networks in a boolean model

This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online.

Computational Methods for Modification of Metabolic Networks

In metabolic engineering, modification of metabolic networks is an important biotechnology and a challenging computational task. In the metabolic network modification, we should modify metabolic networks by newly adding enzymes or/and knocking-out genes to maximize the biomass production with minimum side-effect. In this mini-review, we briefly review constraint-based formalizations for Minimum Reaction Cut (MRC) problem where the minimum set of reactions is deleted so that the target compound becomes non-producible from the view point of the flux balance analysis (FBA), elementary mode (EM), and Boolean models. Minimum Reaction Insertion (MRI) problem where the minimum set of reactions is added so that the target compound newly becomes producible is also explained with a similar formalization approach. The relation between the accuracy of the models and the risk of overfitting is also discussed.

Integer programming-based method for designing synthetic metabolic networks by Minimum Reaction Insertion in a Boolean model

In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html."

Flux balance impact degree: a new definition of impact degree to properly treat reversible reactions in metabolic networks

MOTIVATION

Metabolic pathways are complex systems of chemical reactions taking place in every living cell to degrade substrates and synthesize molecules needed for life. Modeling the robustness of these networks with respect to the dysfunction of one or several reactions is important to understand the basic principles of biological network organization, and to identify new drug targets. While several approaches have been proposed for that purpose, they are computationally too intensive to analyze large networks, and do not properly handle reversible reactions.

RESULTS

We propose a new model-the flux balance impact degree-to model the robustness of large metabolic networks with respect to gene knock-out. We formulate the computation of the impact of one or several reaction blocking as linear programs, and propose efficient strategies to solve them. We show that the proposed method better predicts the phenotypic impact of single gene deletions on Escherichia coli than existing methods.

AVAILABILITY

https://sunflower.kuicr.kyoto-u.ac.jp/∼tyoyo/fbid/index.html

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Studying protein-protein interaction networks: a systems view on diseases

In order to better understand several cellular processes, it is helpful to study how various components make up the system. This systems perspective is supported by several modelling tools including network analysis. Networks of protein-protein interactions (PPI networks) offer a way to depict, visualize and quantify the functioning and relative importance of particular proteins in cell function. The toolkit of network analysis ranges from the local indices describing individual proteins (as network nodes) to global indicators of system architecture, describing the total interaction system (as the whole network). We briefly introduce some of these network indices and present a case study where the connectedness and potential functional relationships between certain disease proteins are inferred. We argue that network analysis can be used, in general, to improve databases, to infer novel functions, to quantify positional importance and to support predictions in pathogenesis studies. The systems perspective and network analysis can be of particular importance in studying diseases with complex molecular processes.

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.

Representation, simulation, and hypothesis generation in graph and logical models of biological networks

This chapter presents a discussion of metabolic modeling from graph theory and logical modeling perspectives. These perspectives are closely related and focus on the coarse structure of metabolism, rather than the finer details of system behavior. The models have been used as background knowledge for hypothesis generation by Robot Scientists using yeast as a model eukaryote, where experimentation and machine learning are used to identify additional knowledge to improve the metabolic model. The logical modeling concept is being adapted to cell signaling and transduction biological networks.

Investigating the validity of current network analysis on static conglomerate networks by protein network stratification

Background

A molecular network perspective forms the foundation of systems biology. A common practice in analyzing protein-protein interaction (PPI) networks is to perform network analysis on a conglomerate network that is an assembly of all available binary interactions in a given organism from diverse data sources. Recent studies on network dynamics suggested that this approach might have ignored the dynamic nature of context-dependent molecular systems.

Results

In this study, we employed a network stratification strategy to investigate the validity of the current network analysis on conglomerate PPI networks. Using the genome-scale tissue- and condition-specific proteomics data in Arabidopsis thaliana, we present here the first systematic investigation into this question. We stratified a conglomerate A. thaliana PPI network into three levels of context-dependent subnetworks. We then focused on three types of most commonly conducted network analyses, i.e., topological, functional and modular analyses, and compared the results from these network analyses on the conglomerate network and five stratified context-dependent subnetworks corresponding to specific tissues.

Conclusions

We found that the results based on the conglomerate PPI network are often significantly different from those of context-dependent subnetworks corresponding to specific tissues or conditions. This conclusion depends neither on relatively arbitrary cutoffs (such as those defining network hubs or bottlenecks), nor on specific network clustering algorithms for module extraction, nor on the possible high false positive rates of binary interactions in PPI networks. We also found that our conclusions are likely to be valid in human PPI networks. Furthermore, network stratification may help resolve many controversies in current research of systems biology.

Reconstruction and validation of RefRec: a global model for the yeast molecular interaction network

Molecular interaction networks establish all cell biological processes. The networks are under intensive research that is facilitated by new high-throughput measurement techniques for the detection, quantification, and characterization of molecules and their physical interactions. For the common model organism yeast Saccharomyces cerevisiae, public databases store a significant part of the accumulated information and, on the way to better understanding of the cellular processes, there is a need to integrate this information into a consistent reconstruction of the molecular interaction network. This work presents and validates RefRec, the most comprehensive molecular interaction network reconstruction currently available for yeast. The reconstruction integrates protein synthesis pathways, a metabolic network, and a protein-protein interaction network from major biological databases. The core of the reconstruction is based on a reference object approach in which genes, transcripts, and proteins are identified using their primary sequences. This enables their unambiguous identification and non-redundant integration. The obtained total number of different molecular species and their connecting interactions is approximately 67,000. In order to demonstrate the capacity of RefRec for functional predictions, it was used for simulating the gene knockout damage propagation in the molecular interaction network in approximately 590,000 experimentally validated mutant strains. Based on the simulation results, a statistical classifier was subsequently able to correctly predict the viability of most of the strains. The results also showed that the usage of different types of molecular species in the reconstruction is important for accurate phenotype prediction. In general, the findings demonstrate the benefits of global reconstructions of molecular interaction networks. With all the molecular species and their physical interactions explicitly modeled, our reconstruction is able to serve as a valuable resource in additional analyses involving objects from multiple molecular -omes. For that purpose, RefRec is freely available in the Systems Biology Markup Language format.

Identifying essential genes in bacterial metabolic networks with machine learning methods

Background

Identifying essential genes in bacteria supports to identify potential drug targets and an understanding of minimal requirements for a synthetic cell. However, experimentally assaying the essentiality of their coding genes is resource intensive and not feasible for all bacterial organisms, in particular if they are infective.

Results

We developed a machine learning technique to identify essential genes using the experimental data of genome-wide knock-out screens from one bacterial organism to infer essential genes of another related bacterial organism. We used a broad variety of topological features, sequence characteristics and co-expression properties potentially associated with essentiality, such as flux deviations, centrality, codon frequencies of the sequences, co-regulation and phyletic retention. An organism-wise cross-validation on bacterial species yielded reliable results with good accuracies (area under the receiver-operator-curve of 75% - 81%). Finally, it was applied to drug target predictions for Salmonella typhimurium. We compared our predictions to the viability of experimental knock-outs of S. typhimurium and identified 35 enzymes, which are highly relevant to be considered as potential drug targets. Specifically, we detected promising drug targets in the non-mevalonate pathway.

Conclusions

Using elaborated features characterizing network topology, sequence information and microarray data enables to predict essential genes from a bacterial reference organism to a related query organism without any knowledge about the essentiality of genes of the query organism. In general, such a method is beneficial for inferring drug targets when experimental data about genome-wide knockout screens is not available for the investigated organism.

Decoupling Environment-Dependent and Independent Genetic Robustness across Bacterial Species

The evolutionary origins of genetic robustness are still under debate: it may arise as a consequence of requirements imposed by varying environmental conditions, due to intrinsic factors such as metabolic requirements, or directly due to an adaptive selection in favor of genes that allow a species to endure genetic perturbations. Stratifying the individual effects of each origin requires one to study the pertaining evolutionary forces across many species under diverse conditions. Here we conduct the first large-scale computational study charting the level of robustness of metabolic networks of hundreds of bacterial species across many simulated growth environments. We provide evidence that variations among species in their level of robustness reflect ecological adaptations. We decouple metabolic robustness into two components and quantify the extents of each: the first, environmental-dependent, is responsible for at least 20% of the non-essential reactions and its extent is associated with the species' lifestyle (specialized/generalist); the second, environmental-independent, is associated (correlation = approximately 0.6) with the intrinsic metabolic capacities of a species-higher robustness is observed in fast growers or in organisms with an extensive production of secondary metabolites. Finally, we identify reactions that are uniquely susceptible to perturbations in human pathogens, potentially serving as novel drug-targets.

Structural and Functional Analysis of Giant Strong Component of Bacillus thuringiensis Metabolic Network

The purpose of this work was to study the giant strong component (GSC) of B. thuringiensis metabolic network by structural and functional analysis. Based on so-called “bow tie” structure, we extracted and studied GSC with its functional significance. Global structural properties such as degree distribution and average path length were computed and indicated that the GSC is also a small-world and scale-free network. Furthermore, the GSC was decomposed and functional significant for metabolism of these divisions were investigated by comparing to KEGG metabolic pathways.

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.

Cascading failure and robustness in metabolic networks

We investigate the relationship between structure and robustness in the metabolic networks of Escherichia coli, Methanosarcina barkeri, Staphylococcus aureus, and Saccharomyces cerevisiae, using a cascading failure model based on a topological flux balance criterion. We find that, compared to appropriate null models, the metabolic networks are exceptionally robust. Furthermore, by decomposing each network into rigid clusters and branched metabolites, we demonstrate that the enhanced robustness is related to the organization of branched metabolites, as rigid cluster formations in the metabolic networks appear to be consistent with null model behavior. Finally, we show that cascading in the metabolic networks can be described as a percolation process.

Machine learning based analyses on metabolic networks supports high-throughput knockout screens

Background

Computational identification of new drug targets is a major goal of pharmaceutical bioinformatics.

Results

This paper presents a machine learning strategy to study and validate essential enzymes of a metabolic network. Each single enzyme was characterized by its local network topology, gene homologies and co-expression, and flux balance analyses. A machine learning system was trained to distinguish between essential and non-essential reactions. It was validated by a comprehensive experimental dataset, which consists of the phenotypic outcomes from single knockout mutants of Escherichia coli (KEIO collection). We yielded very reliable results with high accuracy (93%) and precision (90%). We show that topologic, genomic and transcriptomic features describing the network are sufficient for defining the essentiality of a reaction. These features do not substantially depend on specific media conditions and enabled us to apply our approach also for less specific media conditions, like the lysogeny broth rich medium.

Conclusion

Our analysis is feasible to validate experimental knockout data of high throughput screens, can be used to improve flux balance analyses and supports experimental knockout screens to define drug targets.

Impacts of yeast metabolic network structure on enzyme evolution

Vitkup et al. recently presented an analysis of the influence of yeast metabolic network structure on enzyme evolution; different conclusions are reached when modularity is properly accounted for.

A comment on D Vitkup, P Kharchenko and A Wagner: Influence of metabolic network structure and function on enzyme evolution. Genome Biol 2006, 7:R39.

Using a logical model to predict the growth of yeast

BACKGROUND

A logical model of the known metabolic processes in S. cerevisiae was constructed from iFF708, an existing Flux Balance Analysis (FBA) model, and augmented with information from the KEGG online pathway database. The use of predicate logic as the knowledge representation for modelling enables an explicit representation of the structure of the metabolic network, and enables logical inference techniques to be used for model identification/improvement.

RESULTS

Compared to the FBA model, the logical model has information on an additional 263 putative genes and 247 additional reactions. The correctness of this model was evaluated by comparison with iND750 (an updated FBA model closely related to iFF708) by evaluating the performance of both models on predicting empirical minimal medium growth data/essential gene listings.

CONCLUSION

ROC analysis and other statistical studies revealed that use of the simpler logical form and larger coverage results in no significant degradation of performance compared to iND750.

Estimating novel potential drug targets of Plasmodium falciparum by analysing the metabolic network of knock-out strains in silico

Malaria is one of the world's most common and serious diseases causing death of about 3 million people each year. Its most severe occurrence is caused by the protozoan Plasmodium falciparum. Biomedical research could enable treating the disease by effectively and specifically targeting essential enzymes of this parasite. However, the parasite has developed resistance to existing drugs making it indispensable to discover new drugs. We have established a simple computational tool which analyses the topology of the metabolic network of P. falciparum to identify essential enzymes as possible drug targets. We investigated the essentiality of a reaction in the metabolic network by deleting (knocking-out) such a reaction in silico. The algorithm selected neighbouring compounds of the investigated reaction that had to be produced by alternative biochemical pathways. Using breadth first searches, we tested qualitatively if these products could be generated by reactions that serve as potential deviations of the metabolic flux. With this we identified 70 essential reactions. Our results were compared with a comprehensive list of 38 targets of approved malaria drugs. When combining our approach with an in silico analysis performed recently [Yeh, I., Hanekamp, T., Tsoka, S., Karp, P.D., Altman, R.B., 2004. Computational analysis of Plasmodium falciparum metabolism: organizing genomic information to facilitate drug discovery. Genome Res. 14, 917-924] we could improve the precision of the prediction results. Finally we present a refined list of 22 new potential candidate targets for P. falciparum, half of which have reasonable evidence to be valid targets against micro-organisms and cancer.

Structural analyses of a hypothetical minimal metabolism

By integrating data from comparative genomics and large-scale deletion studies, we previously proposed a minimal gene set comprising 206 protein-coding genes. To evaluate the consistency of the metabolism encoded by such a minimal genome, we have carried out a series of computational analyses. Firstly, the topology of the minimal metabolism was compared with that of the reconstructed networks from natural bacterial genomes. Secondly, the robustness of the metabolic network was evaluated by simulated mutagenesis and, finally, the stoichiometric consistency was assessed by automatically deriving the steady-state solutions from the reaction set. The results indicated that the proposed minimal metabolism presents stoichiometric consistency and that it is organized as a complex power-law network with topological parameters falling within the expected range for a natural metabolism of its size. The robustness analyses revealed that most random mutations do not alter the topology of the network significantly, but do cause significant damage by preventing the synthesis of several compounds or compromising the stoichiometric consistency of the metabolism. The implications that these results have on the origins of metabolic complexity and the theoretical design of an artificial minimal cell are discussed.

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.

Modular decomposition of metabolic systems via null-space analysis

We describe a method by which the reactions in a metabolic system may be grouped hierarchically into sets of modules to form a metabolic reaction tree. In contrast to previous approaches, the method described here takes into account the fact that, in a viable network, reactions must be capable of sustaining a steady-state flux. In order to achieve this decomposition we introduce a new concept--the reaction correlation coefficient, phi, and show that this is a logical extension of the concept of enzyme (or reaction) subsets. In addition to their application to modular decomposition, reaction correlation coefficients have a number of other interesting properties, including a convenient means for identifying disconnected subnetworks in a system and potential applications to metabolic engineering. The method computes reaction correlation coefficients from an orthonormal basis of the null-space of the stoichiometry matrix. We show that reaction correlation coefficients are uniquely defined, even though the basis of the null-space is not. Once a complete set of reaction correlation coefficients is calculated, a metabolic reaction tree can be determined through the application of standard programming techniques. Computation of the reaction correlation coefficients, and the subsequent construction of the metabolic reaction tree is readily achievable for genome-scale models using a commodity desk-top PC.

Computational approaches to the topology, stability and dynamics of metabolic networks

Cellular metabolism is characterized by an intricate network of interactions between biochemical fluxes, metabolic compounds and regulatory interactions. To investigate and eventually understand the emergent global behavior arising from such networks of interaction is not possible by intuitive reasoning alone. This contribution seeks to describe recent computational approaches that aim to asses the topological and functional properties of metabolic networks. In particular, based on a recently proposed method, it is shown that it is possible to acquire a quantitative picture of the possible dynamics of metabolic systems, without assuming detailed knowledge of the underlying enzyme-kinetic rate equations and parameters. Rather, the method builds upon a statistical exploration of the comprehensive parameter space to evaluate the dynamic capabilities of a metabolic system, thus providing a first step towards the transition from topology to function of metabolic pathways. Utilizing this approach, the role of feedback mechanisms in the maintenance of stability is discussed using minimal models of cellular pathways.

A network perspective on the topological importance of enzymes and their phylogenetic conservation

Background

A metabolic network is the sum of all chemical transformations or reactions in the cell, with the metabolites being interconnected by enzyme-catalyzed reactions. Many enzymes exist in numerous species while others occur only in a few. We ask if there are relationships between the phylogenetic profile of an enzyme, or the number of different bacterial species that contain it, and its topological importance in the metabolic network. Our null hypothesis is that phylogenetic profile is independent of topological importance. To test our null hypothesis we constructed an enzyme network from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database. We calculated three network indices of topological importance: the degree or the number of connections of a network node; closeness centrality, which measures how close a node is to others; and betweenness centrality measuring how frequently a node appears on all shortest paths between two other nodes.

Results

Enzyme phylogenetic profile correlates best with betweenness centrality and also quite closely with degree, but poorly with closeness centrality. Both betweenness and closeness centralities are non-local measures of topological importance and it is intriguing that they have contrasting power of predicting phylogenetic profile in bacterial species. We speculate that redundancy in an enzyme network may be reflected by betweenness centrality but not by closeness centrality. We also discuss factors influencing the correlation between phylogenetic profile and topological importance.

Conclusion

Our analysis falsifies the hypothesis that phylogenetic profile of enzymes is independent of enzyme network importance. Our results show that phylogenetic profile correlates better with degree and betweenness centrality, but less so with closeness centrality. Enzymes that occur in many bacterial species tend to be those that have high network importance. We speculate that this phenomenon originates in mechanisms driving network evolution. Closeness centrality reflects phylogenetic profile poorly. This is because metabolic networks often consist of distinct functional modules and some are not in the centre of the network. Enzymes in these peripheral parts of a network might be important for cell survival and should therefore occur in many bacterial species. They are, however, distant from other enzymes in the same network.

Bioinformatics analysis of mycoplasma metabolism: Important enzymes, metabolic similarities, and redundancy

In this work we apply a bioinformatics approach to determine the most important enzymes of the metabolic network of mycoplasmas. The genomes of several mycoplasmas shared predicted important enzymes. Our method allows us to determine both enzymes that are isolated from the metabolic network of the organism and those that are redundant. We also compare the similarities of the mycoplasmas metabolic networks with the phylogenetic relationships predicted from their 16s rRNA sequences.

Modelling, property verification and behavioural equivalence of lactose operon regulation

Understanding biochemical pathways is one of the biggest challenges in the field of molecular biology nowadays. Computer science can contribute in this area by providing formalisms and tools to simulate and analyse pathways. One formalism that is suited for modelling concurrent systems is Milner's Calculus of Communicating Systems (CCS). This paper shows the viability of using CCS to model and reason about biochemical networks. As a case study, we describe the regulation of lactose operon. After describing this operon formally using CCS, we validate our model by automatically checking some known properties for lactose regulation. Moreover, since biological systems tend to be very complex, we propose to use multiple descriptions of the same system at different levels of abstraction. The compatibility of these multiple views can be assured via mathematical proofs of observational equivalence.

Scale-free networks in cell biology

A cell's behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an ever-changing environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from whole-cell function require integrated, theoretical descriptions of the relationships between different cellular components. Recent theoretical advances allow us to describe cellular network structure with graph concepts and have revealed organizational features shared with numerous non-biological networks. We now have the opportunity to describe quantitatively a network of hundreds or thousands of interacting components. Moreover, the observed topologies of cellular networks give us clues about their evolution and how their organization influences their function and dynamic responses.

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

Recent genomic analyses on the cellular metabolic network show that reaction flux across enzymes are diverse and exhibit power-law behavior in its distribution. While intuition might suggest that the reactions with larger fluxes are more likely to be lethal under the blockade of its catalysing gene products or gene knockouts, we find, by in silico flux analysis, that the lethality rarely has correlations with the flux level owing to the widespread backup pathways innate in the genome-wide metabolism of Escherichia coli. Lethal reactions, of which the deletion generates cascading failure of following reactions up to the biomass reaction, are identified in terms of the Boolean network scheme as well as the flux balance analysis. The avalanche size of a reaction, defined as the number of subsequently blocked reactions after its removal, turns out to be a useful measure of lethality. As a means to elucidate phenotypic robustness to a single deletion, we investigate synthetic lethality in reaction level, where simultaneous deletion of a pair of nonlethal reactions leads to the failure of the biomass reaction. Synthetic lethals identified via flux balance and Boolean scheme are consistently shown to act in parallel pathways, working in such a way that the backup machinery is compromised.

Robustness of the avalanche dynamics in data-packet transport on scale-free networks

We study the avalanche dynamics in the data-packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with the proportionality constant 1+a . When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter a as well as which vertex triggers it. We find that there exists a critical value a(c) at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3 and is close in value to that of the distribution of the diameter changes by single vertex removal.

GMAP: a genomic mapping and alignment program for mRNA and EST sequences

MOTIVATION

We introduce GMAP, a standalone program for mapping and aligning cDNA sequences to a genome. The program maps and aligns a single sequence with minimal startup time and memory requirements, and provides fast batch processing of large sequence sets. The program generates accurate gene structures, even in the presence of substantial polymorphisms and sequence errors, without using probabilistic splice site models. Methodology underlying the program includes a minimal sampling strategy for genomic mapping, oligomer chaining for approximate alignment, sandwich DP for splice site detection, and microexon identification with statistical significance testing.

RESULTS

On a set of human messenger RNAs with random mutations at a 1 and 3% rate, GMAP identified all splice sites accurately in over 99.3% of the sequences, which was one-tenth the error rate of existing programs. On a large set of human expressed sequence tags, GMAP provided higher-quality alignments more often than blat did. On a set of Arabidopsis cDNAs, GMAP performed comparably with GeneSeqer. In these experiments, GMAP demonstrated a several-fold increase in speed over existing programs.

AVAILABILITY

Source code for gmap and associated programs is available at http://www.gene.com/share/gmap

SUPPLEMENTARY INFORMATION

http://www.gene.com/share/gmap.

Investigating metabolite essentiality through genome-scale analysis of Escherichia coli production capabilities

MOTIVATION

A phenotype mechanism is classically derived through the study of a set of mutants and comparison of their biochemical capabilities. One method of comparing mutant capabilities is to characterize producible and knocked out metabolites. However such an effect is difficult to manually assess, especially for a large biochemical network and a complex media. Current algorithmic approaches towards analyzing metabolic networks either do not address this specific property or are computationally infeasible on the genome-scale.

RESULTS

We have developed a novel genome-scale computational approach that identifies the full set of biochemical species that are knocked out from the metabolome following a gene deletion. Results from this approach are combined with data from in vivo mutant screens to examine the essentiality of metabolite production for a phenotype. This approach can also be a useful tool for metabolic network annotation validation and refinement in newly sequenced organisms. Combining an in silico genome-scale model of Escherichia coli metabolism with in vivo survival data, we uncover possible essential roles for several cell membranes, cell walls, and quinone species. We also identify specific biomass components whose production appears to be non-essential for survival, contrary to the assumptions of previous models.

AVAILABILITY

Programs are available upon request from the authors in the form of Matlab script files.

SUPPLEMENTARY INFORMATION

http://www.cis.upenn.edu/biocomp/manuscripts/bioinformatics_bti245/supp-info.html.

Concept-based annotation of enzyme classes

MOTIVATION

Given the explosive growth of biomedical data as well as the literature describing results and findings, it is getting increasingly difficult to keep up to date with new information. Keeping databases synchronized with current knowledge is a time-consuming and expensive task-one which can be alleviated by automatically gathering findings from the literature using linguistic approaches. We describe a method to automatically annotate enzyme classes with disease-related information extracted from the biomedical literature for inclusion in such a database.

RESULTS

Enzyme names for the 3901 enzyme classes in the BRENDA database, a repository for quantitative and qualitative enzyme information, were identified in more than 100,000 abstracts retrieved from the PubMed literature database. Phrases in the abstracts were assigned to concepts from the Unified Medical Language System (UMLS) utilizing the MetaMap program, allowing for the identification of disease-related concepts by their semantic fields in the UMLS ontology. Assignments between enzyme classes and diseases were created based on their co-occurrence within a single sentence. False positives could be removed by a variety of filters including minimum number of co-occurrences, removal of sentences containing a negation and the classification of sentences based on their semantic fields by a Support Vector Machine. Verification of the assignments with a manually annotated set of 1500 sentences yielded favorable results of 92% precision at 50% recall, sufficient for inclusion in a high-quality database.

AVAILABILITY

Source code is available from the author upon request.

SUPPLEMENTARY INFORMATION

ftp.uni-koeln.de/institute/biochemie/pub/brenda/info/diseaseSupp.pdf.