FluxAnalyzer: exploring structure,pathways, and flux distributions in metabolic networks on interactive flux maps

MOTIVATION: The analysis of structure, pathways and flux distributions in metabolic networks has become an important approach for understanding the functionality of metabolic systems. The need of a user-friendly platform for stoichiometric modeling of metabolic networks in silico is evident. RESULTS: The FluxAnalyzer is a package for MATLAB and facilitates integrated pathway and flux analysis for metabolic networks within a graphical user interface. Arbitrary metabolic network models can be composed by instances of four types of network elements. The abstract network model is linked with network graphics leading to interactive flux maps which allow for user input and display of calculation results within a network visualization. Therein, a large and powerful collection of tools and algorithms can be applied interactively including metabolic flux analysis, flux optimization, detection of topological features and pathway analysis by elementary flux modes or extreme pathways. The FluxAnalyzer has been applied and tested for complex networks with more than 500,000 elementary modes. Some aspects of the combinatorial complexity of pathway analysis in metabolic networks are discussed. AVAILABILITY: Upon request from the corresponding author. Free for academic users (license agreement). Special contracts are available for industrial corporations. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer.     

Statecharts for Gene Network Modeling

State diagrams (stategraphs) are suitable for describing the behavior of dynamic systems. However, when they are used to model large and complex systems, determining the states and transitions among them can be overwhelming, due to their flat, unstratified structure. In this article, we present the use of statecharts as a novel way of modeling complex gene networks. Statecharts extend conventional state diagrams with features such as nested hierarchy, recursion, and concurrency. These features are commonly utilized in engineering for designing complex systems and can enable us to model complex gene networks in an efficient and systematic way. We modeled five key gene network motifs, simple regulation, autoregulation, feed-forward loop, single-input module, and dense overlapping regulon, using statecharts. Specifically, utilizing nested hierarchy and recursion, we were able to model a complex interlocked feed-forward loop network in a highly structured way, demonstrating the potential of our approach for modeling large and complex gene networks.     

Inferring general relations between network characteristics from specific network ensembles

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their ability to generate networks with large structural variability. In particular, we consider the statistical constraints which the respective construction scheme imposes on the generated networks. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This makes it possible to infer global features from local ones using regression models trained on networks with high generalization power. Our results confirm and extend previous findings regarding the synchronization properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks in good approximation. Finally, we demonstrate on three different data sets (C. elegans neuronal network, R. prowazekii metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models.     

The evolutionary potential of the Drosophila sex determination gene network

The evolution of sex determination mechanisms is known to be relatively rapid, though recent evidence indicates that certain parts of the mechanism may be more highly conserved. These characteristics establish the sex determination mechanism as a good candidate for the theoretical study of gene network evolution, particularly of networks involved in development. We investigate the short-term evolutionary potential of the sex determination mechanism in Drosophila melanogaster with the aid of a synchronous logical model. We introduce general theoretical concepts such as a network-specific form of mutation, and a notion of functional equivalence between networks. We apply this theoretical framework to the sex determination mechanism and compare it to a population of random networks, enabling us to find features both general to sex determination networks, and particular to the Drosophila network. In general, sex determination networks exist within large sets of functionally equivalent networks all of which satisfy the sex determination task. These large sets are in turn composed of subsets which are mutationally related, suggesting a high degree of flexibility is available without compromising the core functionality. Two particular characteristics of the Drosophila network are found: (a) a parsimonious use of gene interactions, and (b) the network structure can produce a relatively large number of dynamical pattern variations through single network mutations.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Subnetwork hierarchies of biochemical pathways

MOTIVATION: The vastness and complexity of the biochemical networks that have been mapped out by modern genomics calls for decomposition into subnetworks. Such networks can have inherent non-local features that require the global structure to be taken into account in the decomposition procedure. Furthermore, basic questions such as to what extent the network (graph theoretically) can be said to be built by distinct subnetworks are little studied. RESULTS: We present a method to decompose biochemical networks into subnetworks based on the global geometry of the network. This method enables us to analyze the full hierarchical organization of biochemical networks and is applied to 43 organisms from the WIT database. Two types of biochemical networks are considered: metabolic networks and whole-cellular networks (also including for example information processes). Conceptual and quantitative ways of describing the hierarchical ordering are discussed. The general picture of the metabolic networks arising from our study is that of a few core-clusters centred around the most highly connected substances enclosed by other substances in outer shells, and a few other well-defined subnetworks. AVAILABILITY: An implementation of our algorithm and other programs for analyzing the data is available from http://www.tp.umu.se/forskning/networks/meta/ SUPPLEMENTARY INFORMATION: Supplementary material is available at http://www.tp.umu.se/forskning/networks/meta/     

LucidDraw: Efficiently visualizing complex biochemical networks within MATLAB

Background  

Biochemical networks play an essential role in systems biology. Rapidly growing network data and versatile research activities call for convenient visualization tools to aid intuitively perceiving abstract structures of networks and gaining insights into the functional implications of networks. There are various kinds of network visualization software, but they are usually not adequate for visual analysis of complex biological networks mainly because of the two reasons: 1) most existing drawing methods suitable for biochemical networks have high computation loads and can hardly achieve near real-time visualization; 2) available network visualization tools are designed for working in certain network modeling platforms, so they are not convenient for general analyses due to lack of broader range of readily accessible numerical utilities.     

Exploring biological network structure using exponential random graph models

MOTIVATION: The functioning of biological networks depends in large part on their complex underlying structure. When studying their systemic nature many modeling approaches focus on identifying simple, but prominent, structural components, as such components are easier to understand, and, once identified, can be used as building blocks to succinctly describe the network. RESULTS: In recent social network studies, exponential random graph models have been used extensively to model global social network structure as a function of their 'local features'. Starting from those studies, we describe the exponential random graph models and demonstrate their utility in modeling the architecture of biological networks as a function of the prominence of local features. We argue that the flexibility, in terms of the number of available local feature choices, and scalability, in terms of the network sizes, make this approach ideal for statistical modeling of biological networks. We illustrate the modeling on both genetic and metabolic networks and provide a novel way of classifying biological networks based on the prevalence of their local features.     

Binding similarity network of ligand

The protein and ligand interaction takes an important part in protein function. Both ligand and its binding site are essential components for understanding how the protein-ligand complex functions. Until now, there have been many studies about protein function and evolution, but they usually lacked ligand information. Accordingly, in this study, we tried to answer the following questions: how much ligand and binding site are associated with protein function, and how ligands themselves are related to each other in terms of binding site. To answer the questions, we presented binding similarity network of ligand. Through the network analysis, we attempted to reveal systematic relationship between the ligand and binding site. The results showed that ligand binding site and function were closely related (conservation ratio, 81%). We also showed conservative tendency of function in line with ligand structure similarity with some exceptional cases. In addition, the binding similarity network of ligand revealed scale-free property to some degree like other biological networks. Since most nodes formed highly connected cluster, a clustering coefficient was very high compared with random. All the highly connected ligands (hubs) were involved in various functions forming large cluster and tended to act as a bridge between modular clusters in the network.     

Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms

MOTIVATION: Information from fully sequenced genomes makes it possible to reconstruct strain-specific global metabolic network for structural and functional studies. These networks are often very large and complex. To properly understand and analyze the global properties of metabolic networks, methods for rationally representing and quantitatively analyzing their structure are needed. RESULTS: In this work, the metabolic networks of 80 fully sequenced organisms are in silico reconstructed from genome data and an extensively revised bioreaction database. The networks are represented as directed graphs and analyzed by using the 'breadth first searching algorithm to identify the shortest pathway (path length) between any pair of the metabolites. The average path length of the networks are then calculated and compared for all the organisms. Different from previous studies the connections through current metabolites and cofactors are deleted to make the path length analysis physiologically more meaningful. The distribution of the connection degree of these networks is shown to follow the power law, indicating that the overall structure of all the metabolic networks has the characteristics of a small world network. However, clear differences exist in the network structure of the three domains of organisms. Eukaryotes and archaea have a longer average path length than bacteria. AVAILABILITY: The reaction database in excel format and the programs in VBA (Visual Basic for Applications) are available upon request. SUPPLEMENTARY MATERIAL: Bioinformatics Online.     

A new computational method to split large biochemical networks into coherent subnets

Background  

Compared to more general networks, biochemical networks have some special features: while generally sparse, there are a small number of highly connected metabolite nodes; and metabolite nodes can also be divided into two classes: internal nodes with associated mass balance constraints and external ones without. Based on these features, reclassifying selected internal nodes (separators) to external ones can be used to divide a large complex metabolic network into simpler subnetworks. Selection of separators based on node connectivity is commonly used but affords little detailed control and tends to produce excessive fragmentation.     

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.     

A comparison of network and clustering methods to detect biogeographical regions

Bioregions are an important concept in biogeography, and are key to our understanding of biodiversity patterns across the world. The use of networks in biogeography to produce bioregions is a relatively novel approach that has been proposed to improve upon current methods. However, it remains unclear if they may be used in place of current methods and/or offer additional biogeographic insights. We compared two network methods to detect bioregions (modularity and map equation) with the conventional distance‐based clustering method. We also explored the relationship between network and biodiversity metrics. For the analysis we used two datasets of iconic Australian plant groups at a continental scale, Acacia and eucalypts, as example groups. The modularity method detected fewer large bioregions produced the most succinct bioregionalisation for both plant groups corresponding to Australian biomes, while map equation detected many small bioregions including interzones at a natural scale of one. The clustering method was less sensitive than network methods in detecting bioregions. The network metric called participation coefficient from both network partition methods identified interzones or transition zones between bioregions. Furthermore, another network metric (betweenness) was highly correlated to richness and endemism. We conclude that the application of networks to biogeography offers a number of advantages and provides novel insights. More specifically, our study showed that these network partition methods were more efficient than the clustering method for bioregionalisation of continental‐scale data in: 1) the identification of bioregions and 2) the quantification of biogeographic transition zones using the participation coefficient metric. The use of network methods and especially the participation coefficient metric adds to bioregionalisation by identifying transition zones which could be useful for conservation purposes and identifying biodiversity hotspots.     

Metabolic networks of microbial systems

In contrast to bioreactors the metabolites within the microbial cells are converted in an impure atmosphere, yet the productivity seems to be well regulated and not affected by changes in operation variables. These features are attributed to integral metabolic network within the microorganism. With the advent of neo-integrative proteomic approaches the understanding of integration of metabolic and protein-protein interaction networks have began. In this article we review the methods employed to determine the protein-protein interaction and their integration to define metabolite networks. We further present a review of current understanding of network properties, and benefit of studying the networks. The predictions using network structure, for example, in silico experiments help illustrate the importance of studying the network properties. The cells are regarded as complex system but their elements unlike complex systems interact selectively and nonlinearly to produce coherent rather than complex behaviors.     

Transition networks for modeling the kinetics of conformational change in macromolecules

The kinetics and thermodynamics of complex transitions in biomolecules can be modeled in terms of a network of transitions between the relevant conformational substates. Such a transition network, which overcomes the fundamental limitations of reaction-coordinate-based methods, can be constructed either based on the features of the energy landscape, or from molecular dynamics simulations. Energy-landscape-based networks are generated with the aid of automated path-optimization methods, and, using graph-theoretical adaptive methods, can now be constructed for large molecules such as proteins. Dynamics-based networks, also called Markov State Models, can be interpreted and adaptively improved using statistical concepts, such as the mean first passage time, reactive flux and sampling error analysis. This makes transition networks powerful tools for understanding large-scale conformational changes.     

RedeR: R/Bioconductor package for representing modular structures, nested networks and multiple levels of hierarchical associations

Visualization and analysis of molecular networks are both central to systems biology. However, there still exists a large technological gap between them, especially when assessing multiple network levels or hierarchies. Here we present RedeR, an R/Bioconductor package combined with a Java core engine for representing modular networks. The functionality of RedeR is demonstrated in two different scenarios: hierarchical and modular organization in gene co-expression networks and nested structures in time-course gene expression subnetworks. Our results demonstrate RedeR as a new framework to deal with the multiple network levels that are inherent to complex biological systems. RedeR is available from http://bioconductor.org/packages/release/bioc/html/RedeR.html.