Model validation of simple-graph representations of metabolism

Scarcity of scale-free topology is universal across biochemical networks

Biochemical reactions underlie the functioning of all life. Like many examples of biology or technology, the complex set of interactions among molecules within cells and ecosystems poses a challenge for quantification within simple mathematical objects. A large body of research has indicated many real-world biological and technological systems, including biochemistry, can be described by power-law relationships between the numbers of nodes and edges, often described as "scale-free". Recently, new statistical analyses have revealed true scale-free networks are rare. We provide a first application of these methods to data sampled from across two distinct levels of biological organization: individuals and ecosystems. We analyze a large ensemble of biochemical networks including networks generated from data of 785 metagenomes and 1082 genomes (sampled from the three domains of life). The results confirm no more than a few biochemical networks are any more than super-weakly scale-free. Additionally, we test the distinguishability of individual and ecosystem-level biochemical networks and show there is no sharp transition in the structure of biochemical networks across these levels of organization moving from individuals to ecosystems. This result holds across different network projections. Our results indicate that while biochemical networks are not scale-free, they nonetheless exhibit common structure across different levels of organization, independent of the projection chosen, suggestive of shared organizing principles across all biochemical networks.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

Network-based strategies in metabolomics data analysis and interpretation: from molecular networking to biological interpretation

INTRODUCTION

Metabolomics has become a crucial part of systems biology; however, data analysis is still often undertaken in a reductionist way focusing on changes in individual metabolites. Whilst such approaches indeed provide relevant insights into the metabolic phenotype of an organism, the intricate nature of metabolic relationships may be better explored when considering the whole system.

AREAS COVERED

This review highlights multiple network strategies that can be applied for metabolomics data analysis from different perspectives including: association networks based on quantitative information, mass spectra similarity networks to assist metabolite annotation and biochemical networks for systematic data interpretation. We also highlight some relevant insights into metabolic organization obtained through the exploration of such approaches.

EXPERT OPINION

Network based analysis is an established method that allows the identification of non-intuitive metabolic relationships as well as the identification of unknown compounds in mass spectrometry. Additionally, the representation of data from metabolomics within the context of metabolic networks is intuitive and allows for the use of statistical analysis that can better summarize relevant metabolic changes from a systematic perspective.

MetaboRank: network-based recommendation system to interpret and enrich metabolomics results

Motivation

Metabolomics has shown great potential to improve the understanding of complex diseases, potentially leading to therapeutic target identification. However, no single analytical method allows monitoring all metabolites in a sample, resulting in incomplete metabolic fingerprints. This incompleteness constitutes a stumbling block to interpretation, raising the need for methods that can enrich those fingerprints. We propose MetaboRank, a new solution inspired by social network recommendation systems for the identification of metabolites potentially related to a metabolic fingerprint.

Results

MetaboRank method had been used to enrich metabolomics data obtained on cerebrospinal fluid samples from patients suffering from hepatic encephalopathy (HE). MetaboRank successfully recommended metabolites not present in the original fingerprint. The quality of recommendations was evaluated by using literature automatic search, in order to check that recommended metabolites could be related to the disease. Complementary mass spectrometry experiments and raw data analysis were performed to confirm these suggestions. In particular, MetaboRank recommended the overlooked α-ketoglutaramate as a metabolite which should be added to the metabolic fingerprint of HE, thus suggesting that metabolic fingerprints enhancement can provide new insight on complex diseases.

Availability and implementation

Method is implemented in the MetExplore server and is available at www.metexplore.fr. A tutorial is available at https://metexplore.toulouse.inra.fr/com/tutorials/MetaboRank/2017-MetaboRank.pdf.

Supplementary information

Supplementary data are available at Bioinformatics online.

Multilayer Network Analysis of Nuclear Reactions

The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, (4)He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals that, in the remainder layer, the β-stability has high correlation with node degree difference and overlapping coefficient. Moreover, when reaction rates are considered as node strength, we find that, at lower temperatures, nuclide half-life scales reciprocally with its out-strength. The connection between physical properties and topological characteristics may help to explore the boundary of the nuclide chart.

Computational methods to identify metabolic sub-networks based on metabolomic profiles

Untargeted metabolomics makes it possible to identify compounds that undergo significant changes in concentration in different experimental conditions. The resulting metabolomic profile characterizes the perturbation concerned, but does not explain the underlying biochemical mechanisms. Bioinformatics methods make it possible to interpret results in light of the whole metabolism. This knowledge is modelled into a network, which can be mined using algorithms that originate in graph theory. These algorithms can extract sub-networks related to the compounds identified. Several attempts have been made to adapt them to obtain more biologically meaningful results. However, there is still no consensus on this kind of analysis of metabolic networks. This review presents the main graph approaches used to interpret metabolomic data using metabolic networks. Their advantages and drawbacks are discussed, and the impacts of their parameters are emphasized. We also provide some guidelines for relevant sub-network extraction and also suggest a range of applications for most methods.

Network motif frequency vectors reveal evolving metabolic network organisation

At the systems level many organisms of interest may be described by their patterns of interaction, and as such, are perhaps best characterised via network or graph models. Metabolic networks, in particular, are fundamental to the proper functioning of many important biological processes, and thus, have been widely studied over the past decade or so. Such investigations have revealed a number of shared topological features, such as a short characteristic path-length, large clustering coefficient and hierarchical modular structure. However, the extent to which evolutionary and functional properties of metabolism manifest via this underlying network architecture remains unclear. In this paper, we employ a novel graph embedding technique, based upon low-order network motifs, to compare metabolic network structure for 383 bacterial species categorised according to a number of biological features. In particular, we introduce a new global significance score which enables us to quantify important evolutionary relationships that exist between organisms and their physical environments. Using this new approach, we demonstrate a number of significant correlations between environmental factors, such as growth conditions and habitat variability, and network motif structure, providing evidence that organism adaptability leads to increased complexities in the resultant metabolic networks.

The network organization of cancer-associated protein complexes in human tissues

Differential gene expression profiles for detecting disease genes have been studied intensively in systems biology. However, it is known that various biological functions achieved by proteins follow from the ability of the protein to form complexes by physically binding to each other. In other words, the functional units are often protein complexes rather than individual proteins. Thus, we seek to replace the perspective of disease-related genes by disease-related complexes, exemplifying with data on 39 human solid tissue cancers and their original normal tissues. To obtain the differential abundance levels of protein complexes, we apply an optimization algorithm to genome-wide differential expression data. From the differential abundance of complexes, we extract tissue- and cancer-selective complexes, and investigate their relevance to cancer. The method is supported by a clustering tendency of bipartite cancer-complex relationships, as well as a more concrete and realistic approach to disease-related proteomics.

The use of weighted graphs for large-scale genome analysis

There is an acute need for better tools to extract knowledge from the growing flood of sequence data. For example, thousands of complete genomes have been sequenced, and their metabolic networks inferred. Such data should enable a better understanding of evolution. However, most existing network analysis methods are based on pair-wise comparisons, and these do not scale to thousands of genomes. Here we propose the use of weighted graphs as a data structure to enable large-scale phylogenetic analysis of networks. We have developed three types of weighted graph for enzymes: taxonomic (these summarize phylogenetic importance), isoenzymatic (these summarize enzymatic variety/redundancy), and sequence-similarity (these summarize sequence conservation); and we applied these types of weighted graph to survey prokaryotic metabolism. To demonstrate the utility of this approach we have compared and contrasted the large-scale evolution of metabolism in Archaea and Eubacteria. Our results provide evidence for limits to the contingency of evolution.

Current understanding of the formation and adaptation of metabolic systems based on network theory

Formation and adaptation of metabolic networks has been a long-standing question in biology. With recent developments in biotechnology and bioinformatics, the understanding of metabolism is progressively becoming clearer from a network perspective. This review introduces the comprehensive metabolic world that has been revealed by a wide range of data analyses and theoretical studies; in particular, it illustrates the role of evolutionary events, such as gene duplication and horizontal gene transfer, and environmental factors, such as nutrient availability and growth conditions, in evolution of the metabolic network. Furthermore, the mathematical models for the formation and adaptation of metabolic networks have also been described, according to the current understanding from a perspective of metabolic networks. These recent findings are helpful in not only understanding the formation of metabolic networks and their adaptation, but also metabolic engineering.

Can the vector space model be used to identify biological entity activities?

BACKGROUND

Biological systems are commonly described as networks of entity interactions. Some interactions are already known and integrate the current knowledge in life sciences. Others remain unknown for long periods of time and are frequently discovered by chance. In this work we present a model to predict these unknown interactions from a textual collection using the vector space model (VSM), a well known and established information retrieval model. We have extended the VSM ability to retrieve information using a transitive closure approach. Our objective is to use the VSM to identify the known interactions from the literature and construct a network. Based on interactions established in the network our model applies the transitive closure in order to predict and rank new interactions.

RESULTS

We have tested and validated our model using a collection of patent claims issued from 1976 to 2005. From 266,528 possible interactions in our network, the model identified 1,027 known interactions and predicted 3,195 new interactions. Iterating the model according to patent issue dates, interactions found in a given past year were often confirmed by patent claims not in the collection and issued in more recent years. Most confirmation patent claims were found at the top 100 new interactions obtained from each subnetwork. We have also found papers on the Web which confirm new inferred interactions. For instance, the best new interaction inferred by our model relates the interaction between the adrenaline neurotransmitter and the androgen receptor gene. We have found a paper that reports the partial dependence of the antiapoptotic effect of adrenaline on androgen receptor.

CONCLUSIONS

The VSM extended with a transitive closure approach provides a good way to identify biological interactions from textual collections. Specifically for the context of literature-based discovery, the extended VSM contributes to identify and rank relevant new interactions even if these interactions occur in only a few documents in the collection. Consequently, we have developed an efficient method for extracting and restricting the best potential results to consider as new advances in life sciences, even when indications of these results are not easily observed from a mass of documents.

The reconstruction and analysis of tissue specific human metabolic networks

Human tissues have distinct biological functions. Many proteins/enzymes are known to be expressed only in specific tissues and therefore the metabolic networks in various tissues are different. Though high quality global human metabolic networks and metabolic networks for certain tissues such as liver have already been studied, a systematic study of tissue specific metabolic networks for all main tissues is still missing. In this work, we reconstruct the tissue specific metabolic networks for 15 main tissues in human based on the previously reconstructed Edinburgh Human Metabolic Network (EHMN). The tissue information is firstly obtained for enzymes from Human Protein Reference Database (HPRD) and UniprotKB databases and transfers to reactions through the enzyme-reaction relationships in EHMN. As our knowledge of tissue distribution of proteins is still very limited, we replenish the tissue information of the metabolic network based on network connectivity analysis and thorough examination of the literature. Finally, about 80% of proteins and reactions in EHMN are determined to be in at least one of the 15 tissues. To validate the quality of the tissue specific network, the brain specific metabolic network is taken as an example for functional module analysis and the results reveal that the function of the brain metabolic network is closely related with its function as the centre of the human nervous system. The tissue specific human metabolic networks are available at .

Identification of biochemical network modules based on shortest retroactive distances

Modularity analysis offers a route to better understand the organization of cellular biochemical networks as well as to derive practically useful, simplified models of these complex systems. While there is general agreement regarding the qualitative properties of a biochemical module, there is no clear consensus on the quantitative criteria that may be used to systematically derive these modules. In this work, we investigate cyclical interactions as the defining characteristic of a biochemical module. We utilize a round trip distance metric, termed Shortest Retroactive Distance (ShReD), to characterize the retroactive connectivity between any two reactions in a biochemical network and to group together network components that mutually influence each other. We evaluate the metric on two types of networks that feature feedback interactions: (i) epidermal growth factor receptor (EGFR) signaling and (ii) liver metabolism supporting drug transformation. For both networks, the ShReD partitions found hierarchically arranged modules that confirm biological intuition. In addition, the partitions also revealed modules that are less intuitive. In particular, ShReD-based partition of the metabolic network identified a ‘redox’ module that couples reactions of glucose, pyruvate, lipid and drug metabolism through shared production and consumption of NADPH. Our results suggest that retroactive interactions arising from feedback loops and metabolic cycles significantly contribute to the modularity of biochemical networks. For metabolic networks, cofactors play an important role as allosteric effectors that mediate the retroactive interactions.

Mathematical models are powerful tools to understand and predict the behavior of complex systems. However, the complexity presents many challenges in developing such models. In the case of a biological cell, a fully detailed and comprehensive model of a major function such as signaling and metabolism remains out of reach, due to the very large number of interdependent biochemical reactions that are required to carry out the function. In this regard, one practical approach is to develop simplified models that nevertheless preserve the essential features of the cell as a complex system by better understanding the chemical organization of the cell, or the layout of the biochemical network. In this work, we describe a computational method to systematically identify closely interacting groups of biochemical reactions by recognizing the modular hierarchy inherent in biochemical networks. We focus on cyclical interactions based on the rationale that reactions that mutually influence each other belong in the same group. We demonstrate our method on a signaling and metabolic network and show that the results confirm biological intuition as well as provide new insights into the coordination of biochemical pathways. Prospectively, our modularization method could be used to systematically derive simplified and practically useful models of complex biological networks.

The strength of chemical linkage as a criterion for pruning metabolic graphs

MOTIVATION

A metabolic graph represents the connectivity patterns of a metabolic system, and provides a powerful framework within which the organization of metabolic reactions can be analyzed and elucidated. A common practice is to prune (i.e. remove nodes and edges) the metabolic graph prior to any analysis in order to eliminate confounding signals from the representation. Currently, this pruning process is carried out in an ad hoc fashion, resulting in discrepancies and ambiguities across studies.

RESULTS

We propose a biochemically informative criterion, the strength of chemical linkage (SCL), for a systematic pruning of metabolic graphs. By analyzing the metabolic graph of Escherichia coli, we show that thresholding SCL is powerful in selecting the conventional pathways' connectivity out of the raw network connectivity when the network is restricted to the reactions collected from these pathways. Further, we argue that the root of ambiguity in pruning metabolic graphs is in the continuity of the amount of chemical content that can be conserved in reaction transformation patterns. Finally, we demonstrate how biochemical pathways can be inferred efficiently if the search procedure is guided by SCL.

Properties of metabolic graphs: biological organization or representation artifacts?

Background

Standard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation.

Results

In this paper, we address this question by reanalyzing topological properties of the metabolic network of Escherichia coli under a hypergraph representation, as well as standard graph abstractions. We find that when clustering is properly defined for hypergraphs and subsequently used to analyze metabolic networks, the scaling of clustering, and thus the hierarchical structure hypothesis in metabolic networks, become unsupported. Moreover, we find that incorporating the distribution of reaction sizes into the null model further weakens the support for the scaling patterns.

Conclusions

These results combined suggest that the reported scaling of the clustering coefficients in the metabolic graphs and its specific power coefficient may be an artifact of the graph representation, and may not be supported when biochemical reactions are atomically treated as hyperedges. This study highlights the implications of the way a biological system is represented and the null model employed on the elucidated properties, along with their support, of the system.

Metabolic robustness and network modularity: a model study

BACKGROUND

Several studies have mentioned network modularity-that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other-as a factor affecting metabolic robustness. In this paper we measure the relation between network modularity and several aspects of robustness directly in a model system of metabolism.

METHODOLOGY/PRINCIPAL FINDINGS

By using a model for generating chemical reaction systems where one can tune the network modularity, we find that robustness increases with modularity for changes in the concentrations of metabolites, whereas it decreases with changes in the expression of enzymes. The same modularity scaling is true for the speed of relaxation after the perturbations.

CONCLUSIONS/SIGNIFICANCE

Modularity is not a general principle for making metabolism either more or less robust; this question needs to be addressed specifically for different types of perturbations of the system.