Does Habitat Variability Really Promote Metabolic Network Modularity?

The hypothesis that variability in natural habitats promotes modular organization is widely accepted for cellular networks. However, results of some data analyses and theoretical studies have begun to cast doubt on the impact of habitat variability on modularity in metabolic networks. Therefore, we re-evaluated this hypothesis using statistical data analysis and current metabolic information. We were unable to conclude that an increase in modularity was the result of habitat variability. Although horizontal gene transfer was also considered because it may contribute for survival in a variety of environments, closely related to habitat variability, and is known to be positively correlated with network modularity, such a positive correlation was not concluded in the latest version of metabolic networks. Furthermore, we demonstrated that the previously observed increase in network modularity due to habitat variability and horizontal gene transfer was probably due to a lack of available data on metabolic reactions. Instead, we determined that modularity in metabolic networks is dependent on species growth conditions. These results may not entirely discount the impact of habitat variability and horizontal gene transfer. Rather, they highlight the need for a more suitable definition of habitat variability and a more careful examination of relationships of the network modularity with horizontal gene transfer, habitats, and environments.     

Biomolecular network motif counting and discovery by color coding

Protein-protein interaction (PPI) networks of many organisms share global topological features such as degree distribution, k-hop reachability, betweenness and closeness. Yet, some of these networks can differ significantly from the others in terms of local structures: e.g. the number of specific network motifs can vary significantly among PPI networks. Counting the number of network motifs provides a major challenge to compare biomolecular networks. Recently developed algorithms have been able to count the number of induced occurrences of subgraphs with k < or = 7 vertices. Yet no practical algorithm exists for counting non-induced occurrences, or counting subgraphs with k > or = 8 vertices. Counting non-induced occurrences of network motifs is not only challenging but also quite desirable as available PPI networks include several false interactions and miss many others. In this article, we show how to apply the 'color coding' technique for counting non-induced occurrences of subgraph topologies in the form of trees and bounded treewidth subgraphs. Our algorithm can count all occurrences of motif G' with k vertices in a network G with n vertices in time polynomial with n, provided k = O(log n). We use our algorithm to obtain 'treelet' distributions for k < or = 10 of available PPI networks of unicellular organisms (Saccharomyces cerevisiae Escherichia coli and Helicobacter Pyloris), which are all quite similar, and a multicellular organism (Caenorhabditis elegans) which is significantly different. Furthermore, the treelet distribution of the unicellular organisms are similar to that obtained by the 'duplication model' but are quite different from that of the 'preferential attachment model'. The treelet distribution is robust w.r.t. sparsification with bait/edge coverage of 70% but differences can be observed when bait/edge coverage drops to 50%.     

Stability from Structure: Metabolic Networks Are Unlike Other Biological Networks

In recent work, attempts have been made to link the structure of biochemical networks to their complex dynamics. It was shown that structurally stable network motifs are enriched in such networks. In this work, we investigate to what extent these findings apply to metabolic networks. To this end, we extend a previously proposed method by changing the null model for determining motif enrichment, by using interaction types directly obtained from structural interaction matrices, by generating a distribution of partial derivatives of reaction rates and by simulating enzymatic regulation on metabolic networks. Our findings suggest that the conclusions drawn in previous work cannot be extended to metabolic networks, that is, structurally stable network motifs are not enriched in metabolic networks.     

Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph

MOTIVATION: Metabolic networks are organized in a modular, hierarchical manner. Methods for a rational decomposition of the metabolic network into relatively independent functional subsets are essential to better understand the modularity and organization principle of a large-scale, genome-wide network. Network decomposition is also necessary for functional analysis of metabolism by pathway analysis methods that are often hampered by the problem of combinatorial explosion due to the complexity of metabolic network. Decomposition methods proposed in literature are mainly based on the connection degree of metabolites. To obtain a more reasonable decomposition, the global connectivity structure of metabolic networks should be taken into account. RESULTS: In this work, we use a reaction graph representation of a metabolic network for the identification of its global connectivity structure and for decomposition. A bow-tie connectivity structure similar to that previously discovered for metabolite graph is found also to exist in the reaction graph. Based on this bow-tie structure, a new decomposition method is proposed, which uses a distance definition derived from the path length between two reactions. An hierarchical classification tree is first constructed from the distance matrix among the reactions in the giant strong component of the bow-tie structure. These reactions are then grouped into different subsets based on the hierarchical tree. Reactions in the IN and OUT subsets of the bow-tie structure are subsequently placed in the corresponding subsets according to a 'majority rule'. Compared with the decomposition methods proposed in literature, ours is based on combined properties of the global network structure and local reaction connectivity rather than, primarily, on the connection degree of metabolites. The method is applied to decompose the metabolic network of Escherichia coli. Eleven subsets are obtained. More detailed investigations of the subsets show that reactions in the same subset are really functionally related. The rational decomposition of metabolic networks, and subsequent studies of the subsets, make it more amenable to understand the inherent organization and functionality of metabolic networks at the modular level. SUPPLEMENTARY INFORMATION: http://genome.gbf.de/bioinformatics/     

MAVisto: a tool for the exploration of network motifs

SUMMARY: MAVisto is a tool for the exploration of motifs in biological networks. It provides a flexible motif search algorithm and different views for the analysis and visualization of network motifs. These views help to explore interesting motifs: the frequency of motif occurrences can be compared with randomized networks, a list of motifs along with information about structure and number of occurrences depending on the reuse of network elements shows potentially interesting motifs, a motif fingerprint reveals the overall distribution of motifs of a given size and the distribution of a particular motif in the network can be visualized using an advanced layout algorithm. AVAILABILITY: MAVisto is platform independent and available free of charge as a Java webstart application at http://mavisto.ipk-gatersleben.de/ CONTACT: schwoebb@ipk-gatersleben.de SUPPLEMENTARY INFORMATION: Can be found at http://mavisto.ipk-gatersleben.de/     

Exploring statistical and population aspects of network complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples.     

Atmospheric reaction systems as null-models to identify structural traces of evolution in metabolism

The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same physics that gives molecules their stability and affinity to react. These fundamental factors cannot be captured by standard null-models based on randomization. The unique property of organismal metabolism is that it is controlled, to some extent, by an enzymatic machinery that is subject to evolution. In this paper, we explore the possibility that reaction systems of planetary atmospheres can serve as a null-model against which we can define metabolic structure and trace the influence of evolution. We find that the two types of data can be distinguished by their respective degree distributions. This is especially clear when looking at the degree distribution of the reaction network (of reaction connected to each other if they involve the same molecular species). For the Earth's atmospheric network and the human metabolic network, we look into more detail for an underlying explanation of this deviation. However, we cannot pinpoint a single cause of the difference, rather there are several concurrent factors. By examining quantities relating to the modular-functional organization of the metabolism, we confirm that metabolic networks have a more complex modular organization than the atmospheric networks, but not much more. We interpret the more variegated modular arrangement of metabolism as a trace of evolved functionality. On the other hand, it is quite remarkable how similar the structures of these two types of networks are, which emphasizes that the constraints from the chemical properties of the molecules has a larger influence in shaping the reaction system than does natural selection.     

Protein Networks Reveal Detection Bias and Species Consistency When Analysed by Information-Theoretic Methods

We apply our recently developed information-theoretic measures for the characterisation and comparison of protein–protein interaction networks. These measures are used to quantify topological network features via macroscopic statistical properties. Network differences are assessed based on these macroscopic properties as opposed to microscopic overlap, homology information or motif occurrences. We present the results of a large–scale analysis of protein–protein interaction networks. Precise null models are used in our analyses, allowing for reliable interpretation of the results. By quantifying the methodological biases of the experimental data, we can define an information threshold above which networks may be deemed to comprise consistent macroscopic topological properties, despite their small microscopic overlaps. Based on this rationale, data from yeast–two–hybrid methods are sufficiently consistent to allow for intra–species comparisons (between different experiments) and inter–species comparisons, while data from affinity–purification mass–spectrometry methods show large differences even within intra–species comparisons.     

Hierarchical thinking in network biology: the unbiased modularization of biochemical networks

As reconstructed biochemical reaction networks continue to grow in size and scope, there is a growing need to describe the functional modules within them. Such modules facilitate the study of biological processes by deconstructing complex biological networks into conceptually simple entities. The definition of network modules is often based on intuitive reasoning. As an alternative, methods are being developed for defining biochemical network modules in an unbiased fashion. These unbiased network modules are mathematically derived from the structure of the whole network under consideration.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

Structural distance and evolutionary relationship of networks

Exploring common features and universal qualities shared by a particular class of networks in biological and other domains is one of the important aspects of evolutionary study. In an evolving system, evolutionary mechanism can cause functional changes that forces the system to adapt to new configurations of interaction pattern between the components of that system (e.g. gene duplication and mutation play a vital role for changing the connectivity structure in many biological networks. The evolutionary relation between two systems can be retraced by their structural differences). The eigenvalues of the normalized graph Laplacian not only capture the global properties of a network, but also local structures that are produced by graph evolutions (like motif duplication or joining). The spectrum of this operator carries many qualitative aspects of a graph. Given two networks of different sizes, we propose a method to quantify the topological distance between them based on the contrasting spectrum of normalized graph Laplacian. We find that network architectures are more similar within the same class compared to between classes. We also show that the evolutionary relationships can be retraced by the structural differences using our method. We analyze 43 metabolic networks from different species and mark the prominent separation of three groups: Bacteria, Archaea and Eukarya. This phenomenon is well captured in our findings that support the other cladistic results based on gene content and ribosomal RNA sequences. Our measure to quantify the structural distance between two networks is useful to elucidate evolutionary relationships.     

Identification of functional differences in metabolic networks using comparative genomics and constraint-based models

Genome-scale network reconstructions are useful tools for understanding cellular metabolism, and comparisons of such reconstructions can provide insight into metabolic differences between organisms. Recent efforts toward comparing genome-scale models have focused primarily on aligning metabolic networks at the reaction level and then looking at differences and similarities in reaction and gene content. However, these reaction comparison approaches are time-consuming and do not identify the effect network differences have on the functional states of the network. We have developed a bilevel mixed-integer programming approach, CONGA, to identify functional differences between metabolic networks by comparing network reconstructions aligned at the gene level. We first identify orthologous genes across two reconstructions and then use CONGA to identify conditions under which differences in gene content give rise to differences in metabolic capabilities. By seeking genes whose deletion in one or both models disproportionately changes flux through a selected reaction (e.g., growth or by-product secretion) in one model over another, we are able to identify structural metabolic network differences enabling unique metabolic capabilities. Using CONGA, we explore functional differences between two metabolic reconstructions of Escherichia coli and identify a set of reactions responsible for chemical production differences between the two models. We also use this approach to aid in the development of a genome-scale model of Synechococcus sp. PCC 7002. Finally, we propose potential antimicrobial targets in Mycobacterium tuberculosis and Staphylococcus aureus based on differences in their metabolic capabilities. Through these examples, we demonstrate that a gene-centric approach to comparing metabolic networks allows for a rapid comparison of metabolic models at a functional level. Using CONGA, we can identify differences in reaction and gene content which give rise to different functional predictions. Because CONGA provides a general framework, it can be applied to find functional differences across models and biological systems beyond those presented here.     

Functional Roles of Slow Enzyme Conformational Changes in Network Dynamics

Extensive studies from different fields reveal that many macromolecules, especially enzymes, show slow transitions among different conformations. This phenomenon is named such things as dynamic disorder, heterogeneity, hysteretic or mnemonic enzymes across these different fields, and has been directly demonstrated by single molecule enzymology and NMR studies recently. We analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can filter upstream network noises, and can either resonantly respond to the system stimulus at certain frequencies or respond adaptively for sustained input signals of the network fluctuations. It thus can serve as a basic functional motif with properties that are normally for larger intermolecular networks in the field of systems biology. We further analyzed examples including enzymes functioning against pH fluctuations, metabolic state change of Artemia embryos, and kinetic insulation of fluctuations in metabolic networks. The study also suggests that hysteretic enzymes may be building blocks of synthetic networks with various properties such as narrow-banded filtering. The work fills the missing gap between studies on enzyme biophysics and network level dynamics, and reveals that the coupling between the two is functionally important; it also suggests that the conformational dynamics of some enzymes may be evolutionally selected.     

Observing and interpreting correlations in metabolomic networks

MOTIVATION: Metabolite profiling aims at an unbiased identification and quantification of all the metabolites present in a biological sample. Based on their pair-wise correlations, the data obtained from metabolomic experiments are organized into metabolic correlation networks and the key challenge is to deduce unknown pathways based on the observed correlations. However, the data generated is fundamentally different from traditional biological measurements and thus the analysis is often restricted to rather pragmatic approaches, such as data mining tools, to discriminate between different metabolic phenotypes. METHODS AND RESULTS: We investigate to what extent the data generated networks reflect the structure of the underlying biochemical pathways. The purpose of this work is 2-fold: Based on the theory of stochastic systems, we first introduce a framework which shows that the emergent correlations can be interpreted as a 'fingerprint' of the underlying biophysical system. This result leads to a systematic relationship between observed correlation networks and the underlying biochemical pathways. In a second step, we investigate to what extent our result is applicable to the problem of reverse engineering, i.e. to recover the underlying enzymatic reaction network from data. The implications of our findings for other bioinformatics approaches are discussed.     

The interaction graph structure of mass-action reaction networks

Behaviour of chemical networks that are described by systems of ordinary differential equations can be analysed via the associated graph structures. This paper deals with observations based on the interaction graph which is defined by the signs of the Jacobian matrix entries. Some of the important graph structures linked to network dynamics are signed circuits and the nucleus (or Hamiltonian hooping). We use mass-action chemical reaction networks as an example to showcase interesting observations about the aforementioned interaction graph structures. We show that positive circuits and specific nucleus structures (associated to multistationarity) are always present in a great generic class of mass-action chemical and biological networks. The theory of negative circuits remains poorly understood, but there is some evidence that they are indicators of stable periodicity. Here we introduce the concept of non-isolated circuits which indicate the presence of a negative circuit.     

Theory of interface: Category theory,directed networks and evolution of biological networks

Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this paper, first we discuss that these two modes can be associated with the category theoretic duality (adjunction) and derive a natural network structure (a path notion) for each mode by appealing to the category theoretic universality. The path notion corresponding to the static mode is just the usual directed path. The path notion for the dynamic mode is called lateral path which is the alternating path considered on the set of arcs. Their general functionalities in a network are transport and coherence, respectively. Second, we introduce a betweenness centrality of arcs for each mode and see how the two modes are embedded in various real biological network data. We find that there is a trade-off relationship between the two centralities: if the value of one is large then the value of the other is small. This can be seen as a kind of division of labor in a network into transport on the network and coherence of the network. Finally, we propose an optimization model of networks based on a quality function involving intensities of the two modes in order to see how networks with the above trade-off relationship can emerge through evolution. We show that the trade-off relationship can be observed in the evolved networks only when the dynamic mode is dominant in the quality function by numerical simulations. We also show that the evolved networks have features qualitatively similar to real biological networks by standard complex network analysis.     

Exploring mitochondrial evolution and metabolism organization principles by comparative analysis of metabolic networks

The endosymbiotic theory proposed that mitochondrial genomes are derived from an alpha-proteobacterium-like endosymbiont, which was concluded from sequence analysis. We rebuilt the metabolic networks of mitochondria and 22 relative species, and studied the evolution of mitochondrial metabolism at the level of enzyme content and network topology. Our phylogenetic results based on network alignment and motif identification supported the endosymbiotic theory from the point of view of systems biology for the first time. It was found that the mitochondrial metabolic network were much more compact than the relative species, probably related to the higher efficiency of oxidative phosphorylation of the specialized organelle, and the network is highly clustered around the TCA cycle. Moreover, the mitochondrial metabolic network exhibited high functional specificity to the modules. This work provided insight to the understanding of mitochondria evolution, and the organization principle of mitochondrial metabolic network at the network level.