Approaches to integrating genetic data into ecological networks

As molecular tools for assessing trophic interactions become common, research is increasingly focused on the construction of interaction networks. Here, we demonstrate three key methods for incorporating DNA data into network ecology and discuss analytical considerations using a model consisting of plants, insects, bats and their parasites from the Costa Rica dry forest. The simplest method involves the use of Sanger sequencing to acquire long sequences to validate or refine field identifications, for example of bats and their parasites, where one specimen yields one sequence and one identification. This method can be fully quantified and resolved and these data resemble traditional ecological networks. For more complex taxonomic identifications, we target multiple DNA loci, for example from a seed or fruit pulp sample in faeces. These networks are also well resolved but gene targets vary in resolution and quantification is difficult. Finally, for mixed templates such as faecal contents of insectivorous bats, we use DNA metabarcoding targeting two sequence lengths (157 and 407 bp) of one gene region and a MOTU, BLAST and BIN association approach to resolve nodes. This network type is complex to generate and analyse, and we discuss the implications of this type of resolution on network analysis. Using these data, we construct the first molecular‐based network of networks containing 3,304 interactions between 762 nodes of eight trophic functions and involving parasitic, mutualistic and predatory interactions. We provide a comparison of the relative strengths and weaknesses of these data types in network ecology.     

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

Systematic Reverse Engineering of Network Topologies: A Case Study of Resettable Bistable Cellular Responses

A focused theme in systems biology is to uncover design principles of biological networks, that is, how specific network structures yield specific systems properties. For this purpose, we have previously developed a reverse engineering procedure to identify network topologies with high likelihood in generating desired systems properties. Our method searches the continuous parameter space of an assembly of network topologies, without enumerating individual network topologies separately as traditionally done in other reverse engineering procedures. Here we tested this CPSS (continuous parameter space search) method on a previously studied problem: the resettable bistability of an Rb-E2F gene network in regulating the quiescence-to-proliferation transition of mammalian cells. From a simplified Rb-E2F gene network, we identified network topologies responsible for generating resettable bistability. The CPSS-identified topologies are consistent with those reported in the previous study based on individual topology search (ITS), demonstrating the effectiveness of the CPSS approach. Since the CPSS and ITS searches are based on different mathematical formulations and different algorithms, the consistency of the results also helps cross-validate both approaches. A unique advantage of the CPSS approach lies in its applicability to biological networks with large numbers of nodes. To aid the application of the CPSS approach to the study of other biological systems, we have developed a computer package that is available in Information S1.     

Community identity in a temporal network: A taxonomy proposal

Communities of nodes are one of the most important meso structures in a network. In static networks they are essentially characterized by the nodes they hold, how modular they are and how they connect to other communities. Once identified, they do not change. In networks that evolve over time, communities can shed and acquire new nodes. This generates new constructs and raises the question of community identity, and of the characterization of the events that define their lifecycle. Although researchers have devoted efforts to address some of these questions, we believe that a formalized classification and a principled method to identify community events is still lacking. In this paper we propose such a classification in the form of a robust taxonomy, supported by a similarity metric based on the Jaccard index but adjusted to chance, and a set of rules that unequivocally can track a community journey from ”cradle to grave”.     

Do bipartite binary antagonistic and mutualistic networks have different responses to the taxonomic resolution of nodes?

1. Bipartite network analyses are increasingly being used to better understand mutualistic and antagonistic plant–insect interactions at the community level. As a result of taxonomic limitations, it is usually very difficult to identify all nodes of a network down to the species level and many studies leave some specimens identified as lower resolution taxa. Accordingly, we do not know how much a lower resolution taxonomic representation changes the network structure compared with a representation with all nodes at species level. 2. The present study aimed to test whether insect–plant networks built using different combinations of taxonomic levels can still preserve the same basic structure of networks built only with species. 3. In total, 73 bipartite published interaction networks (mutualistic and antagonistic) were selected, which were turned into binary networks and reconstructed using the nodes classified as species, genus, family or order (representing different levels of classification difficulty). The network structures were compared using their binary representations mainly using connectance, NODF (Nestedness metric based on Overlap and Decreasing Fill) and modularity. 4. The mutualistic network structure was strongly linearly related to the original network structures if all nodes were grouped up to genus level. In antagonistic networks, the structure was related to the original network only if nodes were only grouped at the species level. 5. The findings of the present study are especially helpful for comparative network studies, such as those assessing the effects of environmental gradients. For mutualistic networks, Citizen Science programmes can provide useful ecological indicators, even with its taxonomic limitations.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

A framework to find the logic backbone of a biological network

Background

Cellular behaviors are governed by interaction networks among biomolecules, for example gene regulatory and signal transduction networks. An often used dynamic modeling framework for these networks, Boolean modeling, can obtain their attractors (which correspond to cell types and behaviors) and their trajectories from an initial state (e.g. a resting state) to the attractors, for example in response to an external signal. The existing methods however do not elucidate the causal relationships between distant nodes in the network.

Results

In this work, we propose a simple logic framework, based on categorizing causal relationships as sufficient or necessary, as a complement to Boolean networks. We identify and explore the properties of complex subnetworks that are distillable into a single logic relationship. We also identify cyclic subnetworks that ensure the stabilization of the state of participating nodes regardless of the rest of the network. We identify the logic backbone of biomolecular networks, consisting of external signals, self-sustaining cyclic subnetworks (stable motifs), and output nodes. Furthermore, we use the logic framework to identify crucial nodes whose override can drive the system from one steady state to another. We apply these techniques to two biological networks: the epithelial-to-mesenchymal transition network corresponding to a developmental process exploited in tumor invasion, and the network of abscisic acid induced stomatal closure in plants. We find interesting subnetworks with logical implications in these networks. Using these subgraphs and motifs, we efficiently reduce both networks to succinct backbone structures.

Conclusions

The logic representation identifies the causal relationships between distant nodes and subnetworks. This knowledge can form the basis of network control or used in the reverse engineering of networks.

     

Detecting network communities: an application to phylogenetic analysis

This paper proposes a new method to identify communities in generally weighted complex networks and apply it to phylogenetic analysis. In this case, weights correspond to the similarity indexes among protein sequences, which can be used for network construction so that the network structure can be analyzed to recover phylogenetically useful information from its properties. The analyses discussed here are mainly based on the modular character of protein similarity networks, explored through the Newman-Girvan algorithm, with the help of the neighborhood matrix . The most relevant networks are found when the network topology changes abruptly revealing distinct modules related to the sets of organisms to which the proteins belong. Sound biological information can be retrieved by the computational routines used in the network approach, without using biological assumptions other than those incorporated by BLAST. Usually, all the main bacterial phyla and, in some cases, also some bacterial classes corresponded totally (100%) or to a great extent (>70%) to the modules. We checked for internal consistency in the obtained results, and we scored close to 84% of matches for community pertinence when comparisons between the results were performed. To illustrate how to use the network-based method, we employed data for enzymes involved in the chitin metabolic pathway that are present in more than 100 organisms from an original data set containing 1,695 organisms, downloaded from GenBank on May 19, 2007. A preliminary comparison between the outcomes of the network-based method and the results of methods based on Bayesian, distance, likelihood, and parsimony criteria suggests that the former is as reliable as these commonly used methods. We conclude that the network-based method can be used as a powerful tool for retrieving modularity information from weighted networks, which is useful for phylogenetic analysis.     

Critical Cooperation Range to Improve Spatial Network Robustness

A robust worldwide air-transportation network (WAN) is one that minimizes the number of stranded passengers under a sequence of airport closures. Building on top of this realistic example, here we address how spatial network robustness can profit from cooperation between local actors. We swap a series of links within a certain distance, a cooperation range, while following typical constraints of spatially embedded networks. We find that the network robustness is only improved above a critical cooperation range. Such improvement can be described in the framework of a continuum transition, where the critical exponents depend on the spatial correlation of connected nodes. For the WAN we show that, except for Australia, all continental networks fall into the same universality class. Practical implications of this result are also discussed.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

A thermodynamic view of networks

Networks can be described by the frequency distribution of the number of links associated with each node (the degree of the node). Of particular interest are the power law distributions, which give rise to the so-called scale-free networks, and the distributions of the form of the simplified canonical law (SCL) introduced by Mandelbrot, which give what we shall call the Mandelbrot networks. Many dynamical methods have been obtained for the construction of scale-free networks, but no dynamical construction of Mandelbrot networks has been demonstrated. Here we develop a systematic technique to obtain networks with any given distribution of the degrees of the nodes. This is done using a thermodynamic approach in which we maximise the entropy associated with degree distribution of the nodes of the network subject to certain constraints. These constraints can be chosen systematically to produce the desired network architecture. For large networks we therefore replace a dynamical approach to the stationary state by a thermodynamical viewpoint. We use the method to generate scale-free and Mandelbrot networks with arbitrarily chosen parameters. We emphasise that this approach opens the possibility of insights into a thermodynamics of networks by suggesting thermodynamic relations between macroscopic variables for networks.     

Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.     

Control of Neuronal Network in Caenorhabditis elegans

Caenorhabditis elegans, a soil dwelling nematode, is evolutionarily rudimentary and contains only ∼ 300 neurons which are connected to each other via chemical synapses and gap junctions. This structural connectivity can be perceived as nodes and edges of a graph. Controlling complex networked systems (such as nervous system) has been an area of excitement for mankind. Various methods have been developed to identify specific brain regions, which when controlled by external input can lead to achievement of control over the state of the system. But in case of neuronal connectivity network the properties of neurons identified as driver nodes is of much importance because nervous system can produce a variety of states (behaviour of the animal). Hence to gain insight on the type of control achieved in nervous system we implemented the notion of structural control from graph theory to C. elegans neuronal network. We identified ‘driver neurons’ which can provide full control over the network. We studied phenotypic properties of these neurons which are referred to as ‘phenoframe’ as well as the ‘genoframe’ which represents their genetic correlates. We find that the driver neurons are primarily motor neurons located in the ventral nerve cord and contribute to biological reproduction of the animal. Identification of driver neurons and its characterization adds a new dimension in controllability of C. elegans neuronal network. This study suggests the importance of driver neurons and their utility to control the behaviour of the organism.