The dichotomy in degree correlation of biological networks

Most complex networks from different areas such as biology, sociology or technology, show a correlation on node degree where the possibility of a link between two nodes depends on their connectivity. It is widely believed that complex networks are either disassortative (links between hubs are systematically suppressed) or assortative (links between hubs are enhanced). In this paper, we analyze a variety of biological networks and find that they generally show a dichotomous degree correlation. We find that many properties of biological networks can be explained by this dichotomy in degree correlation, including the neighborhood connectivity, the sickle-shaped clustering coefficient distribution and the modularity structure. This dichotomy distinguishes biological networks from real disassortative networks or assortative networks such as the Internet and social networks. We suggest that the modular structure of networks accounts for the dichotomy in degree correlation and vice versa, shedding light on the source of modularity in biological networks. We further show that a robust and well connected network necessitates the dichotomy of degree correlation, suggestive of an evolutionary motivation for its existence. Finally, we suggest that a dichotomous degree correlation favors a centrally connected modular network, by which the integrity of network and specificity of modules might be reconciled.     

The role of asymmetric interactions on the effect of habitat destruction in mutualistic networks

Plant-pollinator mutualistic networks are asymmetric in their interactions: specialist plants are pollinated by generalist animals, while generalist plants are pollinated by a broad range involving specialists and generalists. It has been suggested that this asymmetric--or disassortative--assemblage could play an important role in determining the observed equal susceptibility of specialist and generalist plants under habitat destruction. At the core of the analysis of the phenomenon lies the observation that specialist plants, otherwise candidates to extinction, could cope with the disruption thanks to their interaction with a few generalist pollinators. We present a theoretical framework that supports this thesis. We analyze a dynamical model of a system of mutualistic plants and pollinators, subject to the destruction of their habitat. We analyze and compare two families of interaction topologies, ranging from highly assortative to highly disassortative ones, as well as real pollination networks. We found that several features observed in natural systems are predicted by the mathematical model. First, there is a tendency to increase the asymmetry of the network as a result of the extinctions. Second, an entropy measure of the differential susceptibility to extinction of specialist and generalist species show that they tend to balance when the network is disassortative. Finally, the disappearance of links in the network, as a result of extinctions, shows that specialist plants preserve more connections than the corresponding plants in an assortative system, enabling them to resist the disruption.     

An evolving model of undirected networks based on microscopic biological interaction systems

With protein or gene interaction systems as the background, this paper proposes an evolving model of biological undirected networks, which are consistent with some plausible mechanisms in biology. Through introducing a rule of preferential duplication of a node inversely proportional to the degree of existing nodes and an attribute of the age of the node (the older, the more influence), by which the probability of a node receiving re-wiring links is chosen, the model networks generated in certain parameter conditions could reproduce series of statistic topological characteristics of real biological graphs, including the scale-free feature, small world effect, hierarchical modularity, limited structural robustness, and disassortativity of degree–degree correlation.     

Organization of excitable dynamics in hierarchical biological networks

This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.     

In vivo protein complex topologies: sights through a cross-linking lens

Proteins are a remarkable class of molecules that exhibit wide diversity of shapes or topological features that underpin protein interactions and give rise to biological function. In addition to quantitation of abundance levels of proteins in biological systems under a variety of conditions, the field of proteome research has as a primary mission the assignment of function for proteins and if possible, illumination of factors that enable function. For many years, chemical cross-linking methods have been used to provide structural data on single purified proteins and purified protein complexes. However, these methods also offer the alluring possibility to extend capabilities to complex biological samples such as cell lysates or intact living cells where proteins may exhibit native topological features that do not exist in purified form. Recent efforts are beginning to provide glimpses of protein complexes and topologies in cells that suggest continued development will yield novel capabilities to view functional topological features of many proteins and complexes as they exist in cells, tissues, or other complex samples. This review will describe rationale, challenges, and a few success stories along the path of development of cross-linking technologies for measurement of in vivo protein interaction topologies.     

Development of a motif‐based topology‐independent structure comparison method to identify evolutionarily related folds

Structure conservation, functional similarities, and homologous relationships that exist across diverse protein topologies suggest that some regions of the protein fold universe are continuous. However, the current structure classification systems are based on hierarchical organizations, which cannot accommodate structural relationships that span fold definitions. Here, we describe a novel, super‐secondary‐structure motif‐based, topology‐independent structure comparison method (SmotifCOMP) that is able to quantitatively identify structural relationships between disparate topologies. The basis of SmotifCOMP is a systematically defined super‐secondary‐structure motif library whose representative geometries are shown to be saturated in the Protein Data Bank and exhibit a unique distribution within the known folds. SmotifCOMP offers a robust and quantitative technique to compare domains that adopt different topologies since the method does not rely on a global superposition. SmotifCOMP is used to perform an exhaustive comparison of the known folds and the identified relationships are used to produce a nonhierarchical representation of the fold space that reflects the notion of a continuous and connected fold universe. The current work offers insight into previously hypothesized evolutionary relationships between disparate folds and provides a resource for exploring novel ones. Proteins 2016; 84:1859–1874. © 2016 Wiley Periodicals, Inc.     

Evolving Robust Gene Regulatory Networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.     

Structural efficiency of percolated landscapes in flow networks

The large-scale structure of complex systems is intimately related to their functionality and evolution. In particular, global transport processes in flow networks rely on the presence of directed pathways from input to output nodes and edges, which organize in macroscopic connected components. However, the precise relation between such structures and functional or evolutionary aspects remains to be understood. Here, we investigate which are the constraints that the global structure of directed networks imposes on transport phenomena. We define quantitatively under minimal assumptions the structural efficiency of networks to determine how robust communication between the core and the peripheral components through interface edges could be. Furthermore, we assess that optimal topologies in terms of access to the core should look like "hairy balls" so to minimize bottleneck effects and the sensitivity to failures. We illustrate our investigation with the analysis of three real networks with very different purposes and shaped by very different dynamics and time-scales-the Internet customer-provider set of relationships, the nervous system of the worm Caenorhabditis elegans, and the metabolism of the bacterium Escherichia coli. Our findings prove that different global connectivity structures result in different levels of structural efficiency. In particular, biological networks seem to be close to the optimal layout.     

Interaction and domain networks of yeast

Data of currently available protein-protein interaction sets and protein domain sets of yeast are used to set up protein and domain interaction and domain sequence networks. All of them are far from being random or regular networks. In fact, they turn out to be sparse and locally well clustered indicating so-called scale-free and partially small-world topology. These subtle topologies display considerable indirect properties which are measured with a newly introduced transitivity coefficient. Fairly small sets of highly connected proteins and domains shape the topologies of the underlying networks, emphasizing a kind of backbone the nets are based on. The biological nature of these particular nodes is further investigated. Since highly connected proteins and domains accumulated a significant higher number of links by their important involvement in certain cellular aspects, their mutational effect on the cell is considered by a perturbation analysis. In comparison to domains of yeast, what factors force domains to accumulate links to other domains in protein sequences of higher eukaryotes are investigated.     

Interactome Mapping: Using Protein Microarray Technology to Reconstruct Diverse Protein Networks

A major focus of systems biology is to characterize interactions between cellular components, in order to develop an accurate picture of the intricate networks within biological systems. Over the past decade, protein microarrays have greatly contributed to advances in proteomics and are becoming an important platform for systems biology. Protein microarrays are highly flexible, ranging from large-scale proteome microarrays to smaller customizable microarrays, making the technology amenable for detection of a broad spectrum of biochemical properties of proteins. In this article, we will focus on the numerous studies that have utilized protein microarrays to reconstruct biological networks including protein-DNA interactions, posttranslational protein modifications (PTMs), lectin-glycan recognition, pathogen-host interactions and hierarchical signaling cascades. The diversity in applications allows for integration of interaction data from numerous molecular classes and cellular states, providing insight into the structure of complex biological systems. We will also discuss emerging applications and future directions of protein microarray technology in the global frontier.     

Robustness of Oscillatory Behavior in Correlated Networks

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.     

When do host–parasite interactions drive the evolution of non‐random mating?

Interactions with parasites may promote the evolution of disassortative mating in host populations as a mechanism through which genetically diverse offspring can be produced. This possibility has been confirmed through simulation studies and suggested for some empirical systems in which disassortative mating by disease resistance genotype has been documented. The generality of this phenomenon is unclear, however, because existing theory has considered only a subset of possible genetic and mating scenarios. Here we present results from analytical models that consider a broader range of genetic and mating scenarios and allow the evolution of non-random mating in the parasite as well. Our results confirm results of previous simulation studies, demonstrating that coevolutionary interactions with parasites can indeed lead to the evolution of host disassortative mating. However, our results also show that the conditions under which this occurs are significantly more fickle than previously thought, requiring specific forms of infection genetics and modes of non-random mating that do not generate substantial sexual selection. In cases where such conditions are not met, hosts may evolve random or assortative mating. Our analyses also reveal that coevolutionary interactions with hosts cause the evolution of non-random mating in parasites as well. In some cases, particularly those where mating occurs within groups, we find that assortative mating evolves sufficiently to catalyze sympatric speciation in the interacting species.     

Controllability in Cancer Metabolic Networks According to Drug Targets as Driver Nodes

Networks are employed to represent many nonlinear complex systems in the real world. The topological aspects and relationships between the structure and function of biological networks have been widely studied in the past few decades. However dynamic and control features of complex networks have not been widely researched, in comparison to topological network features. In this study, we explore the relationship between network controllability, topological parameters, and network medicine (metabolic drug targets). Considering the assumption that targets of approved anticancer metabolic drugs are driver nodes (which control cancer metabolic networks), we have applied topological analysis to genome-scale metabolic models of 15 normal and corresponding cancer cell types. The results show that besides primary network parameters, more complex network metrics such as motifs and clusters may also be appropriate for controlling the systems providing the controllability relationship between topological parameters and drug targets. Consequently, this study reveals the possibilities of following a set of driver nodes in network clusters instead of considering them individually according to their centralities. This outcome suggests considering distributed control systems instead of nodal control for cancer metabolic networks, leading to a new strategy in the field of network medicine.     

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.     

Plant multiscale networks: charting plant connectivity by multi-level analysis and imaging techniques

In multicellular and even single-celled organisms, individual components are interconnected at multiscale levels to produce enormously complex biological networks that help these systems maintain homeostasis for development and environmental adaptation. Systems biology studies initially adopted network analysis to explore how relationships between individual components give rise to complex biological processes. Network analysis has been applied to dissect the complex connectivity of mammalian brains across different scales in time and space in The Human Brain Project. In plant science, network analysis has similarly been applied to study the connectivity of plant components at the molecular, subcellular, cellular, organic, and organism levels. Analysis of these multiscale networks contributes to our understanding of how genotype determines phenotype. In this review, we summarized the theoretical framework of plant multiscale networks and introduced studies investigating plant networks by various experimental and computational modalities. We next discussed the currently available analytic methodologies and multi-level imaging techniques used to map multiscale networks in plants. Finally, we highlighted some of the technical challenges and key questions remaining to be addressed in this emerging field.     

Hydrophobic, hydrophilic, and charged amino acid networks within protein

The native three-dimensional structure of a single protein is determined by the physicochemical nature of its constituent amino acids. The 20 different types of amino acids, depending on their physicochemical properties, can be grouped into three major classes: hydrophobic, hydrophilic, and charged. The anatomy of the weighted and unweighted networks of hydrophobic, hydrophilic, and charged residues separately for a large number of proteins were studied. Results showed that the average degree of the hydrophobic networks has a significantly larger value than that of hydrophilic and charged networks. The average degree of the hydrophilic networks is slightly higher than that of the charged networks. The average strength of the nodes of hydrophobic networks is nearly equal to that of the charged network, whereas that of hydrophilic networks has a smaller value than that of hydrophobic and charged networks. The average strength for each of the three types of networks varies with its degree. The average strength of a node in a charged network increases more sharply than that of the hydrophobic and hydrophilic networks. Each of the three types of networks exhibits the "small-world" property. Our results further indicate that the all-amino-acids networks and hydrophobic networks are of assortative type. Although most of the hydrophilic and charged networks are of the assortative type, few others have the characteristics of disassortative mixing of the nodes. We have further observed that all-amino-acids networks and hydrophobic networks bear the signature of hierarchy, whereas the hydrophilic and charged networks do not have any hierarchical signature.     

A genome-scale metabolic reconstruction of Pseudomonas putida KT2440: iJN746 as a cell factory

Background

The study of biological interaction networks is a central theme of systems biology. Here, we investigate the relationships between two distinct types of interaction networks: the metabolic pathway map and the protein-protein interaction network (PIN). It has long been established that successive enzymatic steps are often catalyzed by physically interacting proteins forming permanent or transient multi-enzymes complexes. Inspecting high-throughput PIN data, it was shown recently that, indeed, enzymes involved in successive reactions are generally more likely to interact than other protein pairs. In our study, we expanded this line of research to include comparisons of the underlying respective network topologies as well as to investigate whether the spatial organization of enzyme interactions correlates with metabolic efficiency.

Results

Analyzing yeast data, we detected long-range correlations between shortest paths between proteins in both network types suggesting a mutual correspondence of both network architectures. We discovered that the organizing principles of physical interactions between metabolic enzymes differ from the general PIN of all proteins. While physical interactions between proteins are generally dissortative, enzyme interactions were observed to be assortative. Thus, enzymes frequently interact with other enzymes of similar rather than different degree. Enzymes carrying high flux loads are more likely to physically interact than enzymes with lower metabolic throughput. In particular, enzymes associated with catabolic pathways as well as enzymes involved in the biosynthesis of complex molecules were found to exhibit high degrees of physical clustering. Single proteins were identified that connect major components of the cellular metabolism and may thus be essential for the structural integrity of several biosynthetic systems.

Conclusion

Our results reveal topological equivalences between the protein interaction network and the metabolic pathway network. Evolved protein interactions may contribute significantly towards increasing the efficiency of metabolic processes by permitting higher metabolic fluxes. Thus, our results shed further light on the unifying principles shaping the evolution of both the functional (metabolic) as well as the physical interaction network.     

Host–parasite interactions and the evolution of nonrandom mating

Some species mate nonrandomly with respect to alleles underlying immunity. One hypothesis proposes that this is advantageous because nonrandom mating can lead to offspring with superior parasite resistance. We investigate this hypothesis, generalizing previous models in four ways: First, rather than only examining invasibility of modifiers of nonrandom mating, we identify evolutionarily stable strategies. Second, we study coevolution of both haploid and diploid hosts and parasites. Third, we allow for maternal parasite transmission. Fourth, we allow for many alleles at the interaction locus. We find that evolutionarily stable rates of assortative or disassortative mating are usually near zero or one. However, for one case, in which assumptions most closely match the major histocompatibility complex (MHC) system, intermediate rates of disassortative mating can evolve. Across all cases, with haploid hosts, evolution proceeds toward complete disassortative mating, whereas with diploid hosts either assortative or disassortative mating can evolve. Evolution of nonrandom mating is much less affected by the ploidy of parasites. For the MHC case, maternal transmission of parasites, because it creates an advantage to producing offspring that differ from their parents, leads to higher evolutionarily stable rates of disassortative mating. Lastly, with more alleles at the interaction locus, disassortative mating evolves to higher levels.     

Multifunctionality of biocrusts is positively predicted by network topologies consistent with interspecies facilitation

The potential of biodiversity loss to impair the delivery of ecosystem services has motived ecologists to better understand the relationship between biodiversity and ecosystem functioning. Although increasing evidence underlines the collective contribution of different biodiversity components on the simultaneous performance of multiple functions (multifunctionality), we know little about the trade‐offs between individual diversity effects and the extent to which they determine multifunctionality differentially. Here, at a subcontinental scale of 62 dryland sites, we show in phototrophic microbiota of biological soil crusts (biocrusts) that, whereas richness alone is unable to guarantee the maxima of multifunctional performance, interspecies facilitation and compositional identity are particularly stronger but often neglected predictors. The inconsistent effects of different biodiversity components imply that soil multifunctionality can be lost despite certain species remaining present. Moreover, we reveal a significant empirical association between species functional importance and its topological feature in co‐occurrence networks, indicating a functional signal of species interaction. Nevertheless, abundant species tend to isolate and merely interact within small topological structures, but rare species were tightly connected in complicated network modules. Our findings suggest that abundant and rare species of soil phototrophs exhibit distinct functional relevance. These results give a comprehensive view of how soil constructive species drive multifunctionality in biocrusts and ultimately promote a deeper understanding of the consequences of biodiversity loss in real‐world ecosystems.