Comment on "Network Motifs: Simple Building Blocks of Complex Networks" and "Superfamilies of Evolved and Designed Networks"

Human mobility networks manifest dissimilar resilience characteristics at macroscopic, substructure, and microscopic scales

Human mobility networks can reveal insights into resilience phenomena, such as population response to, impacts on, and recovery from crises. The majority of human mobility network resilience characterizations, however, focus mainly on macroscopic network properties; little is known about variation in measured resilience characteristics (i.e., the extent of impact and recovery duration) across macroscopic, substructure (motif), and microscopic mobility scales. To address this gap, in this study, we examine the human mobility network in eight parishes in Louisiana (USA) impacted by the 2021 Hurricane Ida. We constructed human mobility networks using location-based data and examined three sets of measures: (1) macroscopic measures, such as network density, giant component size, and modularity; (2) substructure measures, such as motif distribution; and (3) microscopic mobility measures, such as the radius of gyration and average travel distance. To determine the extent of impact and duration of recovery, for each measure, we established the baseline values and examined the fluctuation of measures during the perturbation caused by Hurricane Ida. The results reveal the variation of impact extent and recovery duration obtained from different sets of measures at different scales. Macroscopic measures, such as giant components, tend to recover more quickly than substructure and microscopic measures. In fact, microscopic measures tend to recover more slowly than measures in other scales. These findings suggest that resilience characteristics in human mobility networks are scale-variant, and thus, a single measure at a particular scale may not be representative of the perturbation impacts and recovery duration in the network as a whole. These results spotlight the need to use measures at different scales to properly characterize resilience in human mobility networks.

Shortcomings of reusing species interaction networks created by different sets of researchers

Given the requisite cost associated with observing species interactions, ecologists often reuse species interaction networks created by different sets of researchers to test their hypotheses regarding how ecological processes drive network topology. Yet, topological properties identified across these networks may not be sufficiently attributable to ecological processes alone as often assumed. Instead, much of the totality of topological differences between networks-topological heterogeneity-could be due to variations in research designs and approaches that different researchers use to create each species interaction network. To evaluate the degree to which this topological heterogeneity is present in available ecological networks, we first compared the amount of topological heterogeneity across 723 species interaction networks created by different sets of researchers with the amount quantified from non-ecological networks known to be constructed following more consistent approaches. Then, to further test whether the topological heterogeneity was due to differences in study designs, and not only to inherent variation within ecological networks, we compared the amount of topological heterogeneity between species interaction networks created by the same sets of researchers (i.e., networks from the same publication) with the amount quantified between networks that were each from a unique publication source. We found that species interaction networks are highly topologically heterogeneous: while species interaction networks from the same publication are much more topologically similar to each other than interaction networks that are from a unique publication, they still show at least twice as much heterogeneity as any category of non-ecological networks that we tested. Altogether, our findings suggest that extra care is necessary to effectively analyze species interaction networks created by different researchers, perhaps by controlling for the publication source of each network.

Does gender structure social networks across domains of cooperation? An exploration of gendered networks among matrilineal and patrilineal Mosuo

Cooperative networks are essential features of human society. Evolutionary theory hypothesizes that networks are used differently by men and women, yet the bulk of evidence supporting this hypothesis is based on studies conducted in a limited range of contexts and on few domains of cooperation. In this paper, we compare individual-level cooperative networks from two communities in Southwest China that differ systematically in kinship norms and institutions-one matrilineal and one patrilineal-while sharing an ethnic identity. Specifically, we investigate whether network structures differ based on prevailing kinship norms and type of gendered cooperative activity, one woman-centred (preparation of community meals) and one man-centred (farm equipment lending). Our descriptive results show a mixture of 'feminine' and 'masculine' features in all four networks. The matrilineal meals network stands out in terms of high degree skew. Exponential random graph models reveal a stronger role for geographical proximity in patriliny and a limited role of affinal relatedness across all networks. Our results point to the need to consider domains of cooperative activity alongside gender and cultural context to fully understand variation in how women and men leverage social relationships toward different ends. This article is part of the theme issue 'Cooperation among women: evolutionary and cross-cultural perspectives'.

Graph convolutional networks fusing motif-structure information

With the advent of the wave of big data, the generation of more and more graph data brings great pressure to the traditional deep learning model. The birth of graph neural network fill the gap of deep learning in graph data. At present, graph convolutional networks (GCN) have surpassed traditional methods such as network embedding in node classification. However, The existing graph convolutional networks only consider the edge structure information of first-order neighbors as the bridge of information aggregation in a convolution operation, which undoubtedly loses the higher-order structure information in complex networks. In order to capture more abundant information of the graph topology and mine the higher-order information in complex networks, we put forward our own graph convolutional networks model fusing motif-structure information. By identifying the motif-structure in the network, our model fuses the motif-structure information of nodes to study the aggregation feature weights, which enables nodes to aggregate higher-order network information, thus improving the capability of GCN model. Finally, we conduct node classification experiments in several real networks, and the experimental results show that the GCN model fusing motif-structure information can improve the accuracy of node classification.

Local topological features of robust supply networks

The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting upon such a system, even formulating an appropriate research question to address this topic is non-trivial. Here we present an abstraction of a supply and distribution system leading to a minimal model, which only retains stylized facts of the systemic function and, in this way, allows us to investigate the generic properties of robust supply networks. On this level of abstraction, a supply and distribution system is the strategic use of transportation to eliminate mismatches between production patterns (i.e., the amounts of goods produced at each production site of a company) and demand patterns (i.e., the amount of goods consumed at each location). When creating networks based on this paradigm and furthermore requiring the robustness of the system with respect to the loss of transportation routes (edge of the network) we see that robust networks are built from specific sets of subgraphs, while vulnerable networks display a markedly different subgraph composition. Our findings confirm a long-standing hypothesis in the field of network science, namely, that network motifs-statistically over-represented small subgraphs-are informative about the robust functioning of a network. Also, our findings offer a blueprint for enhancing the robustness of real-world supply and distribution systems.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-022-00470-2.

Temporal motifs in patent opposition and collaboration networks

Patents are intellectual properties that reflect innovative activities of companies and organizations. The literature is rich with the studies that analyze the citations among the patents and the collaboration relations among companies that own the patents. However, the adversarial relations between the patent owners are not as well investigated. One proxy to model such relations is the patent opposition, which is a legal activity in which a company challenges the validity of a patent. Characterizing the patent oppositions, collaborations, and the interplay between them can help better understand the companies’ business strategies. Temporality matters in this context as the order and frequency of oppositions and collaborations characterize their interplay. In this study, we construct a two-layer temporal network to model the patent oppositions and collaborations among the companies. We utilize temporal motifs to analyze the oppositions and collaborations from structural and temporal perspectives. We first characterize the frequent motifs in patent oppositions and investigate how often the companies of different sizes attack other companies. We show that large companies tend to engage in opposition with multiple companies. Then we analyze the temporal interplay between collaborations and oppositions. We find that two adversarial companies are more likely to collaborate in the future than two collaborating companies oppose each other in the future.

The small world coefficient 4.8 ± 1 optimizes information processing in 2D neuronal networks

Small world networks have recently attracted much attention because of their unique properties. Mounting evidence suggests that communication is optimized in networks with a small world topology. However, despite the relevance of the argument, little is known about the effective enhancement of information in similar graphs. Here, we provide a quantitative estimate of the efficiency of small world networks. We used a model of the brain in which neurons are described as agents that integrate the signals from other neurons and generate an output that spreads in the system. We then used the Shannon Information Entropy to decode those signals and compute the information transported in the grid as a function of its small-world-ness (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{SW}}$$\end{document}SW), of the length (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\triangle t$$\end{document}∆t) and frequency (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document}f) of the originating stimulus. 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Moreover, we found that the information processing capacity of a system steadily increases with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{SW}}$$\end{document}SW until the value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{SW}}=4.8\pm 1$$\end{document}SW=4.8±1, independently on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\triangle t$$\end{document}∆t and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document}f. After this threshold, the performance degrades with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{SW}}$$\end{document}SW and there is no convenience in increasing indefinitely the number of active links in the system. Supported by the findings of the work and in analogy with the exergy in thermodynamics, we introduce the concept of exordic systems: a system is exordic if it is topologically biased to transmit information efficiently.

Learning network embeddings using small graphlets

Techniques for learning vectorial representations of graphs (graph embeddings) have recently emerged as an effective approach to facilitate machine learning on graphs. Some of the most popular methods involve sophisticated features such as graph kernels or convolutional networks. In this work, we introduce two straightforward supervised learning algorithms based on small-size graphlet counts, combined with a dimension reduction step. The first relies on a classic feature extraction method powered by principal component analysis (PCA). The second is a feature selection procedure also based on PCA. Despite their conceptual simplicity, these embeddings are arguably more meaningful than some popular alternatives and at the same time are competitive with state-of-the-art methods. We illustrate this second point on a downstream classification task. We then use our algorithms in a novel setting, namely to conduct an analysis of author relationships in Wikipedia articles, for which we present an original dataset. Finally, we provide empirical evidence suggesting that our methods could also be adapted to unsupervised learning algorithms.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Differences in evolutionary accessibility determine which equally effective regulatory motif evolves to generate pulses

Transcriptional regulatory networks (TRNs) are enriched for certain "motifs." Motif usage is commonly interpreted in adaptationist terms, i.e., that the optimal motif evolves. But certain motifs can also evolve more easily than others. Here, we computationally evolved TRNs to produce a pulse of an effector protein. Two well-known motifs, type 1 incoherent feed-forward loops (I1FFLs) and negative feedback loops (NFBLs), evolved as the primary solutions. The relative rates at which these two motifs evolve depend on selection conditions, but under all conditions, either motif achieves similar performance. I1FFLs generally evolve more often than NFBLs. Selection for a tall pulse favors NFBLs, while selection for a fast response favors I1FFLs. I1FFLs are more evolutionarily accessible early on, before the effector protein evolves high expression; when NFBLs subsequently evolve, they tend to do so from a conjugated I1FFL-NFBL genotype. In the empirical S. cerevisiae TRN, output genes of NFBLs had higher expression levels than those of I1FFLs. These results suggest that evolutionary accessibility, and not relative functionality, shapes which motifs evolve in TRNs, and does so as a function of the expression levels of particular genes.

Exploiting graphlet decomposition to explain the structure of complex networks: the GHuST framework

The characterization of topology is crucial in understanding network evolution and behavior. This paper presents an innovative approach, the GHuST framework to describe complex-network topology from graphlet decomposition. This new framework exploits the local information provided by graphlets to give a global explanation of network topology. The GHuST framework is comprised of 12 metrics that analyze how 2- and 3-node graphlets shape the structure of networks. The main strengths of the GHuST framework are enhanced topological description, size independence, and computational simplicity. It allows for straight comparison among different networks disregarding their size. It also reduces the complexity of graphlet counting, since it does not use 4- and 5-node graphlets. The application of the novel framework to a large set of networks shows that it can classify networks of distinct nature based on their topological properties. To ease network classification and enhance the graphical representation of them, we reduce the 12 dimensions to their main principal components. Furthermore, the 12 dimensions are easily interpretable. This enables the connection between complex-network analyses and diverse real applications.

Beyond Dyads and Triads: A Comparison of Tetrads in Twenty Social Networks

Social psychologists focus on the microlevel features that define interaction, often attending to dyads and triads. We argue that there also is utility in studying how configurations of four actors, or tetrads, pattern our social world. The current project considers the prevalence of directed tetrads across twenty social networks representing five relationship types (friendship, legislative co-sponsorship, Twitter, advice seeking, and email). By comparing these observed networks to randomly generated conditional networks, we identify tetrads that occur more frequently than expected, or network motifs. In all twenty networks, we find evidence for six tetrad motifs that collectively highlight tendencies toward hierarchy, clustering, and bridging in social interaction. Variations across network genres also emerge, suggesting that unique tetrad structural signatures could define different types of interaction.

Treating Different Diseases With the Same Method-A Traditional Chinese Medicine Concept Analyzed for Its Biological Basis

Introduction

The fundamental theory of traditional Chinese medicine (TCM) implies that when different diseases have the same pathogen, the syndromes of these individual diseases will be the same. “Treating different diseases with the same method” is a TCM principle suggesting that when different diseases have similar pathological changes during different stages of their development, the same method of treatment can be applied. Our study aims to analyze the concept “treating different diseases with the same method” from a molecular perspective, in order to clarify its biological basis and to objectively standardize future TCM syndrome research.

Objective

The TCM syndromes Qi deficiency and blood stasis have similar pathogenesis in relation to coronary heart disease (CHD) and stroke. We aim to use big data technology and complex network theory to mine the genes specifically relevant to these TCM syndromes. This study aims to explore the correlation between the biological indicators of CHD and stroke from a scientific perspective.

Methods

Mining the relevant neuroendocrine-immune (NEI) genes by means of gene entity recognition, complex network construction, network integration, and decomposition to categorize relevant syndrome terms and establish a digital dictionary of gene specifically related to individual diseases. We analyzed the biological basis of “treating different diseases with the same method” from a molecular level using the TCMIP v2.0 platform in order to categorize the TCM syndromes most relevant to CHD and stroke.

Results

We found 46 genes were involved in the TCM syndromes of Qi deficiency and blood stasis of CHD and stroke. The same genes and their molecular mechanism also appeared to be in close relation to inflammatory response, apoptosis, and proliferation.

Conclusion

By using information extraction and complex network technology, we discovered the biological indicators of the TCM syndromes Qi deficiency and blood stasis of CHD and stroke. In the era of big data, our results can provide a new method for the researchers of TCM syndrome differentiation, as well as an effective and specific methodology for standardization of TCM.

The stability of mutualism

Positive interactions are observed at high frequencies in nearly all living systems, ranging from human and animal societies down to the scale of microbial organisms. However, historically, detailed ecological studies of mutualism have been relatively unrepresented. Moreover, while ecologists have long portrayed competition as a stabilizing process, mutualism is often deemed destabilizing. Recently, several key modelling studies have applied random matrix methods, and have further corroborated the instability of mutualism. Here, I reassess these findings by factoring in species densities into the “community matrix,” a practice which has almost always been ignored in random matrix analyses. With this modification, mutualistic interactions are found to boost equilibrium population densities and stabilize communities by increasing their resilience. By taking into account transient dynamics after a strong population perturbation, it is found that mutualists have the ability to pull up communities by their bootstraps when species are dangerously depressed in numbers.

Mutualism is typically portrayed as a destabilizing process in community ecology. Here, via a random matrix model that considers species density, the author shows that mutualistic interactions can, in fact, enhance population density at equilibrium and increase community resilience to perturbation.

Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

In transcriptional regulatory networks (TRNs), a canonical 3-node feed-forward loop (FFL) is hypothesized to evolve to filter out short spurious signals. We test this adaptive hypothesis against a novel null evolutionary model. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function but not in negative controls. Interestingly, a 4-node “diamond” motif also emerges as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no idealized external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves. While our results support the adaptive hypothesis, we also show that non-adaptive factors, including the intrinsic expression dynamics, matter.

Feed‐forward loops (FFLs) can filter out noise, but whether their overrepresentation in GRNs reflects adaptive evolution for this function is debated. Here, the authors develop a null model of regulatory evolution and find that FFLs evolve readily under selection for the noise filtering function.

Unmasking structural patterns in incidence matrices: an application to ecological data

Null models have become a crucial tool for understanding structure within incidence matrices across multiple biological contexts. For example, they have been widely used for the study of ecological and biogeographic questions, testing hypotheses regarding patterns of community assembly, species co-occurrence and biodiversity. However, to our knowledge we remain without a general and flexible approach to study the mechanisms explaining such structures. Here, we provide a method for generating 'correlation-informed' null models, which combine the classic concept of null models and tools from community ecology, like joint statistical modelling. Generally, this model allows us to assess whether the information encoded within any given correlation matrix is predictive for explaining structural patterns observed within an incidence matrix. To demonstrate its utility, we apply our approach to two different case studies that represent examples of common scenarios encountered in community ecology. First, we use a phylogenetically informed null model to detect a strong evolutionary fingerprint within empirically observed food webs, reflecting key differences in the impact of shared evolutionary history when shaping the interactions of predators or prey. Second, we use multiple informed null models to identify which factors determine structural patterns of species assemblages, focusing in on the study of nestedness and the influence of site size, isolation, species range and species richness. In addition to offering a versatile way to study the mechanisms shaping the structure of any incidence matrix, including those describing ecological communities, our approach can also be adapted further to test even more sophisticated hypotheses.

Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models

Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous time switching systems provide a computationally accessible way to translate the structure of the network to predictions about the dynamics. Recent work has shown that the parameterized dynamics of switching systems can be captured by a combinatorial object, called a Dynamic Signatures Generated by Regulatory Networks (DSGRN) database, that consists of a parameter graph characterizing a finite parameter space decomposition, whose nodes are assigned a Morse graph that captures global dynamics for all corresponding parameters. We show that for a given network there is a way to associate the same type of object by considering a continuous time ODE system with a continuous right-hand side, which we call an L-system. The main goal of this paper is to compare the two DSGRN databases for the same network. Since the L-systems can be thought of as perturbations (not necessarily small) of the switching systems, our results address the correspondence between global parameterized dynamics of switching systems and their perturbations. We show that, at corresponding parameters, there is an order preserving map from the Morse graph of the switching system to that of the L-system that is surjective on the set of attractors and bijective on the set of fixed-point attractors. We provide important examples showing why this correspondence cannot be strengthened.

Dysfunctional Mechanism of Liver Cancer Mediated by Transcription Factor and Non-coding RNA

Background:

There have been numerous experiments and studies on liver cancer by biomedical scientists, while no comprehensive and systematic exploration has yet been conducted. Therefore, this study aimed to systematically dissect the transcriptional and non-coding RNAmediated mechanisms of liver cancer dysfunction.

Method:

At first, we collected 974 liver cancer associated genes from the Online Mendelian Inheritance in Man (OMIM). Afterwards, their interactors were recruited from STRING database so as to identify 18 co-expression modules in liver cancer patient expression profile. Crosstalk analysis showed the interactive relationship between these modules. In addition, core drivers for modules were identified, including 111 transcription factors (STAT3, JUN and NFKB1, etc.) and 1492 ncRNAs (FENDRR and miR-340-5p, etc.).

Results:

In view of the results of enrichment, we found that these core drivers were significantly involved in Notch signaling, Wnt / β-catenin pathways, cell proliferation, apoptosis-related functions and pathways, suggesting they can affect the development of liver cancer. Furthermore, a global effect on bio-network associated with liver cancer has been integrated from the ncRNA and TF pivot network, module crosstalk network, module-function/pathways network. It involves various development and progression of cancer.

Conclusion:

Overall, our analysis further suggests that comprehensive network analysis will help us to not only understand in depth the molecular mechanisms, but also reveal the influence of related gene dysfunctional modules on the occurrence and progression of liver cancer. It provides a valuable reference for the design of liver cancer diagnosis and treatment.

Fast Maximum Likelihood Estimation via Equilibrium Expectation for Large Network Data

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach becomes increasingly problematic as network size increases. In the context of current research on efficient estimation of models for large network data sets, we propose a fast algorithm for maximum likelihood estimation (MLE) that affords a significant increase in the size of networks amenable to direct empirical analysis. The algorithm we propose in this paper relies on properties of Markov chains at equilibrium, and for this reason it is called equilibrium expectation (EE). We demonstrate the performance of the EE algorithm in the context of exponential random graph models (ERGMs) a family of statistical models commonly used in empirical research based on network data observed at a single period in time. Thus far, the lack of efficient computational strategies has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The approach we propose allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes.

Towards a Dynamic Interaction Network of Life to unify and expand the evolutionary theory

The classic Darwinian theory and the Synthetic evolutionary theory and their linear models, while invaluable to study the origins and evolution of species, are not primarily designed to model the evolution of organisations, typically that of ecosystems, nor that of processes. How could evolutionary theory better explain the evolution of biological complexity and diversity? Inclusive network-based analyses of dynamic systems could retrace interactions between (related or unrelated) components. This theoretical shift from a Tree of Life to a Dynamic Interaction Network of Life, which is supported by diverse molecular, cellular, microbiological, organismal, ecological and evolutionary studies, would further unify evolutionary biology.

Identifying robust hysteresis in networks

We present a new modeling and computational tool that computes rigorous summaries of network dynamics over large sets of parameter values. These summaries, organized in a database, can be searched for observed dynamics, e.g., bistability and hysteresis, to discover parameter regimes over which they are supported. We illustrate our approach on several networks underlying the restriction point of the cell cycle in humans and yeast. We rank networks by how robustly they support hysteresis, which is the observed phenotype. We find that the best 6-node human network and the yeast network share similar topology and robustness of hysteresis, in spite of having no homology between the corresponding nodes of the network. Our approach provides a new tool linking network structure and dynamics.

To summarize our understanding of how genes, their products and other cellular actors interact with each other, we often employ networks to describe their interactions. However, networks do not fully specify how the underlying biological system behaves in different conditions, nor how such response evolves in time. We present a new modeling and computational approach that allows us to compute and collect summaries of network dynamics for large sets of parameter values. We can then search these summaries for all observed behavior. We illustrate our approach on networks that govern entry to the cell cycle in humans and yeast. We rank networks based on how robustly they exhibit the experimentally observed behavior of hysteresis. We find similarities in network structure of the best ranked networks in yeast and humans, which are not explained by a common ancestry. Our approach provides a tool linking network structure and the behavior of the underlying system.

Applications of Microfluidics in Quantitative Biology

Quantitative biology is dedicated to taking advantage of quantitative reasoning and advanced engineering technologies to make biology more predictable. Microfluidics, as an emerging technique, provides new approaches to precisely control fluidic conditions on small scales and collect data in high-throughput and quantitative manners. In this review, the authors present the relevant applications of microfluidics to quantitative biology based on two major categories (channel-based microfluidics and droplet-based microfluidics), and their typical features. We also envision some other microfluidic techniques that may not be employed in quantitative biology right now, but have great potential in the near future.

Conservation of Species- and Trait-Based Modeling Network Interactions in Extremely Acidic Microbial Community Assembly

Understanding microbial interactions is essential to decipher the mechanisms of community assembly and their effects on ecosystem functioning, however, the conservation of species- and trait-based network interactions along environmental gradient remains largely unknown. Here, by using the network-based analyses with three paralleled data sets derived from 16S rRNA gene pyrosequencing, functional microarray, and predicted metagenome, we test our hypothesis that the network interactions of traits are more conserved than those of taxonomic measures, with significantly lower variation of network characteristics along the environmental gradient in acid mine drainage. The results showed that although the overall network characteristics remained similar, the structural variation was significantly lower at trait levels. The higher conserved individual node topological properties at trait level rather than at species level indicated that the responses of diverse traits remained relatively consistent even though different species played key roles under different environmental conditions. Additionally, the randomization tests revealed that it could not reject the null hypothesis that species-based correlations were random, while the tests suggested that correlation patterns of traits were non-random. Furthermore, relationships between trait-based network characteristics and environmental properties implied that trait-based networks might be more useful in reflecting the variation of ecosystem function. Taken together, our results suggest that deterministic trait-based community assembly results in greater conservation of network interaction, which may ensure ecosystem function across environmental regimes, emphasizing the potential importance of measuring the complexity and conservation of network interaction in evaluating the ecosystem stability and functioning.

LoTo: a graphlet based method for the comparison of local topology between gene regulatory networks

One of the main challenges of the post-genomic era is the understanding of how gene expression is controlled. Changes in gene expression lay behind diverse biological phenomena such as development, disease and the adaptation to different environmental conditions. Despite the availability of well-established methods to identify these changes, tools to discern how gene regulation is orchestrated are still required. The regulation of gene expression is usually depicted as a Gene Regulatory Network (GRN) where changes in the network structure (i.e., network topology) represent adjustments of gene regulation. Like other networks, GRNs are composed of basic building blocks; small induced subgraphs called graphlets. Here we present LoTo, a novel method that using Graphlet Based Metrics (GBMs) identifies topological variations between different states of a GRN. Under our approach, different states of a GRN are analyzed to determine the types of graphlet formed by all triplets of nodes in the network. Subsequently, graphlets occurring in a state of the network are compared to those formed by the same three nodes in another version of the network. Once the comparisons are performed, LoTo applies metrics from binary classification problems calculated on the existence and absence of graphlets to assess the topological similarity between both network states. Experiments performed on randomized networks demonstrate that GBMs are more sensitive to topological variation than the same metrics calculated on single edges. Additional comparisons with other common metrics demonstrate that our GBMs are capable to identify nodes whose local topology changes between different states of the network. Notably, due to the explicit use of graphlets, LoTo captures topological variations that are disregarded by other approaches. LoTo is freely available as an online web server at http://dlab.cl/loto.

CMIP: a software package capable of reconstructing genome-wide regulatory networks using gene expression data

BACKGROUND

A gene regulatory network (GRN) represents interactions of genes inside a cell or tissue, in which vertexes and edges stand for genes and their regulatory interactions respectively. Reconstruction of gene regulatory networks, in particular, genome-scale networks, is essential for comparative exploration of different species and mechanistic investigation of biological processes. Currently, most of network inference methods are computationally intensive, which are usually effective for small-scale tasks (e.g., networks with a few hundred genes), but are difficult to construct GRNs at genome-scale.

RESULTS

Here, we present a software package for gene regulatory network reconstruction at a genomic level, in which gene interaction is measured by the conditional mutual information measurement using a parallel computing framework (so the package is named CMIP). The package is a greatly improved implementation of our previous PCA-CMI algorithm. In CMIP, we provide not only an automatic threshold determination method but also an effective parallel computing framework for network inference. Performance tests on benchmark datasets show that the accuracy of CMIP is comparable to most current network inference methods. Moreover, running tests on synthetic datasets demonstrate that CMIP can handle large datasets especially genome-wide datasets within an acceptable time period. In addition, successful application on a real genomic dataset confirms its practical applicability of the package.

CONCLUSIONS

This new software package provides a powerful tool for genomic network reconstruction to biological community. The software can be accessed at http://www.picb.ac.cn/CMIP/ .

Graphlet-based Characterization of Directed Networks

We are flooded with large-scale, dynamic, directed, networked data. Analyses requiring exact comparisons between networks are computationally intractable, so new methodologies are sought. To analyse directed networks, we extend graphlets (small induced sub-graphs) and their degrees to directed data. Using these directed graphlets, we generalise state-of-the-art network distance measures (RGF, GDDA and GCD) to directed networks and show their superiority for comparing directed networks. Also, we extend the canonical correlation analysis framework that enables uncovering the relationships between the wiring patterns around nodes in a directed network and their expert annotations. On directed World Trade Networks (WTNs), our methodology allows uncovering the core-broker-periphery structure of the WTN, predicting the economic attributes of a country, such as its gross domestic product, from its wiring patterns in the WTN for up-to ten years in the future. It does so by enabling us to track the dynamics of a country's positioning in the WTN over years. On directed metabolic networks, our framework yields insights into preservation of enzyme function from the network wiring patterns rather than from sequence data. Overall, our methodology enables advanced analyses of directed networked data from any area of science, allowing domain-specific interpretation of a directed network's topology.

Graphlet Based Metrics for the Comparison of Gene Regulatory Networks

Understanding the control of gene expression remains one of the main challenges in the post-genomic era. Accordingly, a plethora of methods exists to identify variations in gene expression levels. These variations underlay almost all relevant biological phenomena, including disease and adaptation to environmental conditions. However, computational tools to identify how regulation changes are scarce. Regulation of gene expression is usually depicted in the form of a gene regulatory network (GRN). Structural changes in a GRN over time and conditions represent variations in the regulation of gene expression. Like other biological networks, GRNs are composed of basic building blocks called graphlets. As a consequence, two new metrics based on graphlets are proposed in this work: REConstruction Rate (REC) and REC Graphlet Degree (RGD). REC determines the rate of graphlet similarity between different states of a network and RGD identifies the subset of nodes with the highest topological variation. In other words, RGD discerns how th GRN was rewired. REC and RGD were used to compare the local structure of nodes in condition-specific GRNs obtained from gene expression data of Escherichia coli, forming biofilms and cultured in suspension. According to our results, most of the network local structure remains unaltered in the two compared conditions. Nevertheless, changes reported by RGD necessarily imply that a different cohort of regulators (i.e. transcription factors (TFs)) appear on the scene, shedding light on how the regulation of gene expression occurs when E. coli transits from suspension to biofilm. Consequently, we propose that both metrics REC and RGD should be adopted as a quantitative approach to conduct differential analyses of GRNs. A tool that implements both metrics is available as an on-line web server (http://dlab.cl/loto).

Spatial Embedding and Wiring Cost Constrain the Functional Layout of the Cortical Network of Rodents and Primates

Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing interareal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Using tract tracing data from macaque and mouse, we show the existence of a general organizational principle based on an exponential distance rule (EDR) and cortical geometry, enabling network comparisons within the same model framework. These comparisons reveal the existence of network invariants between mouse and macaque, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer disease and schizophrenia. Finally, our data from tracer experiments involving only gray matter connections in the primary visual areas of both species show that an EDR holds at local scales as well (within 1.5 mm), supporting the hypothesis that it is a universally valid property across all scales and, possibly, across the mammalian class.

Small-World Propensity and Weighted Brain Networks

Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.

Exploring the topological sources of robustness against invasion in biological and technological networks

For a network, the accomplishment of its functions despite perturbations is called robustness. Although this property has been extensively studied, in most cases, the network is modified by removing nodes. In our approach, it is no longer perturbed by site percolation, but evolves after site invasion. The process transforming resident/healthy nodes into invader/mutant/diseased nodes is described by the Moran model. We explore the sources of robustness (or its counterpart, the propensity to spread favourable innovations) of the US high-voltage power grid network, the Internet2 academic network, and the C. elegans connectome. We compare them to three modular and non-modular benchmark networks, and samples of one thousand random networks with the same degree distribution. It is found that, contrary to what happens with networks of small order, fixation probability and robustness are poorly correlated with most of standard statistics, but they depend strongly on the degree distribution. While community detection techniques are able to detect the existence of a central core in Internet2, they are not effective in detecting hierarchical structures whose topological complexity arises from the repetition of a few rules. Box counting dimension and Rent’s rule are applied to show a subtle trade-off between topological and wiring complexity.

Habitat variability does not generally promote metabolic network modularity in flies and mammals

The evolution of species habitat range is an important topic over a wide range of research fields. In higher organisms, habitat range evolution is generally associated with genetic events such as gene duplication. However, the specific factors that determine habitat variability remain unclear at higher levels of biological organization (e.g., biochemical networks). One widely accepted hypothesis developed from both theoretical and empirical analyses is that habitat variability promotes network modularity; however, this relationship has not yet been directly tested in higher organisms. Therefore, I investigated the relationship between habitat variability and metabolic network modularity using compound and enzymatic networks in flies and mammals. Contrary to expectation, there was no clear positive correlation between habitat variability and network modularity. As an exception, the network modularity increased with habitat variability in the enzymatic networks of flies. However, the observed association was likely an artifact, and the frequency of gene duplication appears to be the main factor contributing to network modularity. These findings raise the question of whether or not there is a general mechanism for habitat range expansion at a higher level (i.e., above the gene scale). This study suggests that the currently widely accepted hypothesis for habitat variability should be reconsidered.

Event Networks and the Identification of Crime Pattern Motifs

In this paper we demonstrate the use of network analysis to characterise patterns of clustering in spatio-temporal events. Such clustering is of both theoretical and practical importance in the study of crime, and forms the basis for a number of preventative strategies. However, existing analytical methods show only that clustering is present in data, while offering little insight into the nature of the patterns present. Here, we show how the classification of pairs of events as close in space and time can be used to define a network, thereby generalising previous approaches. The application of graph-theoretic techniques to these networks can then offer significantly deeper insight into the structure of the data than previously possible. In particular, we focus on the identification of network motifs, which have clear interpretation in terms of spatio-temporal behaviour. Statistical analysis is complicated by the nature of the underlying data, and we provide a method by which appropriate randomised graphs can be generated. Two datasets are used as case studies: maritime piracy at the global scale, and residential burglary in an urban area. In both cases, the same significant 3-vertex motif is found; this result suggests that incidents tend to occur not just in pairs, but in fact in larger groups within a restricted spatio-temporal domain. In the 4-vertex case, different motifs are found to be significant in each case, suggesting that this technique is capable of discriminating between clustering patterns at a finer granularity than previously possible.

The network motif architecture of dominance hierarchies

The widespread existence of dominance hierarchies has been a central puzzle in social evolution, yet we lack a framework for synthesizing the vast empirical data on hierarchy structure in animal groups. We applied network motif analysis to compare the structures of dominance networks from data published over the past 80 years. Overall patterns of dominance relations, including some aspects of non-interactions, were strikingly similar across disparate group types. For example, nearly all groups exhibited high frequencies of transitive triads, whereas cycles were very rare. Moreover, pass-along triads were rare, and double-dominant triads were common in most groups. These patterns did not vary in any systematic way across taxa, study settings (captive or wild) or group size. Two factors significantly affected network motif structure: the proportion of dyads that were observed to interact and the interaction rates of the top-ranked individuals. Thus, study design (i.e. how many interactions were observed) and the behaviour of key individuals in the group could explain much of the variations we see in social hierarchies across animals. Our findings confirm the ubiquity of dominance hierarchies across all animal systems, and demonstrate that network analysis provides new avenues for comparative analyses of social hierarchies.

Sampling Motif-Constrained Ensembles of Networks

The statistical significance of network properties is conditioned on null models which satisfy specified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this Letter we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, networks with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60% of the variation of motif profiles.

Mechanisms of mutational robustness in transcriptional regulation

Robustness is the invariance of a phenotype in the face of environmental or genetic change. The phenotypes produced by transcriptional regulatory circuits are gene expression patterns that are to some extent robust to mutations. Here we review several causes of this robustness. They include robustness of individual transcription factor binding sites, homotypic clusters of such sites, redundant enhancers, transcription factors, redundant transcription factors, and the wiring of transcriptional regulatory circuits. Such robustness can either be an adaptation by itself, a byproduct of other adaptations, or the result of biophysical principles and non-adaptive forces of genome evolution. The potential consequences of such robustness include complex regulatory network topologies that arise through neutral evolution, as well as cryptic variation, i.e., genotypic divergence without phenotypic divergence. On the longest evolutionary timescales, the robustness of transcriptional regulation has helped shape life as we know it, by facilitating evolutionary innovations that helped organisms such as flowering plants and vertebrates diversify.

Function does not follow form in gene regulatory circuits

Gene regulatory circuits are to the cell what arithmetic logic units are to the chip: fundamental components of information processing that map an input onto an output. Gene regulatory circuits come in many different forms, distinct structural configurations that determine who regulates whom. Studies that have focused on the gene expression patterns (functions) of circuits with a given structure (form) have examined just a few structures or gene expression patterns. Here, we use a computational model to exhaustively characterize the gene expression patterns of nearly 17 million three-gene circuits in order to systematically explore the relationship between circuit form and function. Three main conclusions emerge. First, function does not follow form. A circuit of any one structure can have between twelve and nearly thirty thousand distinct gene expression patterns. Second, and conversely, form does not follow function. Most gene expression patterns can be realized by more than one circuit structure. And third, multifunctionality severely constrains circuit form. The number of circuit structures able to drive multiple gene expression patterns decreases rapidly with the number of these patterns. These results indicate that it is generally not possible to infer circuit function from circuit form, or vice versa.

Exploring the structure and function of temporal networks with dynamic graphlets

MOTIVATION

With increasing availability of temporal real-world networks, how to efficiently study these data? One can model a temporal network as a single aggregate static network, or as a series of time-specific snapshots, each being an aggregate static network over the corresponding time window. Then, one can use established methods for static analysis on the resulting aggregate network(s), but losing in the process valuable temporal information either completely, or at the interface between different snapshots, respectively. Here, we develop a novel approach for studying a temporal network more explicitly, by capturing inter-snapshot relationships.

RESULTS

We base our methodology on well-established graphlets (subgraphs), which have been proven in numerous contexts in static network research. We develop new theory to allow for graphlet-based analyses of temporal networks. Our new notion of dynamic graphlets is different from existing dynamic network approaches that are based on temporal motifs (statistically significant subgraphs). The latter have limitations: their results depend on the choice of a null network model that is required to evaluate the significance of a subgraph, and choosing a good null model is non-trivial. Our dynamic graphlets overcome the limitations of the temporal motifs. Also, when we aim to characterize the structure and function of an entire temporal network or of individual nodes, our dynamic graphlets outperform the static graphlets. Clearly, accounting for temporal information helps. We apply dynamic graphlets to temporal age-specific molecular network data to deepen our limited knowledge about human aging.

AVAILABILITY AND IMPLEMENTATION

http://www.nd.edu/∼cone/DG.

Proper evaluation of alignment-free network comparison methods

Motivation: Network comparison is a computationally intractable problem with important applications in systems biology and other domains. A key challenge is to properly quantify similarity between wiring patterns of two networks in an alignment-free fashion. Also, alignment-based methods exist that aim to identify an actual node mapping between networks and as such serve a different purpose. Various alignment-free methods that use different global network properties (e.g. degree distribution) have been proposed. Methods based on small local subgraphs called graphlets perform the best in the alignment-free network comparison task, due to high level of topological detail that graphlets can capture. Among different graphlet-based methods, Graphlet Correlation Distance (GCD) was shown to be the most accurate for comparing networks. Recently, a new graphlet-based method called NetDis was proposed, which was claimed to be superior. We argue against this, as the performance of NetDis was not properly evaluated to position it correctly among the other alignment-free methods.

Results: We evaluate the performance of available alignment-free network comparison methods, including GCD and NetDis. We do this by measuring accuracy of each method (in a systematic precision-recall framework) in terms of how well the method can group (cluster) topologically similar networks. By testing this on both synthetic and real-world networks from different domains, we show that GCD remains the most accurate, noise-tolerant and computationally efficient alignment-free method. That is, we show that NetDis does not outperform the other methods, as originally claimed, while it is also computationally more expensive. Furthermore, since NetDis is dependent on the choice of a network null model (unlike the other graphlet-based methods), we show that its performance is highly sensitive to the choice of this parameter. Finally, we find that its performance is not independent on network sizes and densities, as originally claimed.

Contact: natasha@imperial.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Spatial embedding of structural similarity in the cerebral cortex

Recent anatomical tracing studies have yielded substantial amounts of data on the areal connectivity underlying distributed processing in cortex, yet the fundamental principles that govern the large-scale organization of cortex remain unknown. Here we show that functional similarity between areas as defined by the pattern of shared inputs or outputs is a key to understanding the areal network of cortex. In particular, we report a systematic relation in the monkey, human, and mouse cortex between the occurrence of connections from one area to another and their similarity distance. This characteristic relation is rooted in the wiring distance dependence of connections in the brain. We introduce a weighted, spatially embedded random network model that robustly gives rise to this structure, as well as many other spatial and topological properties observed in cortex. These include features that were not accounted for in any previous model, such as the wide range of interareal connection weights. Connections in the model emerge from an underlying distribution of spatially embedded axons, thereby integrating the two scales of cortical connectivity--individual axons and interareal pathways--into a common geometric framework. These results provide insights into the origin of large-scale connectivity in cortex and have important implications for theories of cortical organization.

Aspects of randomness in neural graph structures

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions have been reported, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these "historical" graphs, both in their directed (original) and symmetrized (a common preprocessing step) forms, and provide a set of measures that can be consistently applied across graphs (directed or undirected, with or without self-loops). We focus on simple structural characterizations of network connectivity and find that in many measures, the networks studied are captured by simple random graph models. In a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in the networks studied is not well captured by existing abstract graph models in their first- and second-order connectivity.

Identifying emerging motif in growing networks

As function units, network motifs have been detected to reveal evolutionary mechanisms of complex systems, such as biological networks, food webs, engineering networks and social networks. However, emergence of motifs in growing networks may be problematic due to large fluctuation of subgraph frequency in the initial stage. This paper contributes to present a method which can identify the emergence of motif in growing networks. Based on the Erdös-Rényi(E-R) random null model, the variation rate of expected frequency of subgraph at adjacent time points was used to define the suitable detection range for motif identification. Upper and lower boundaries of the range were obtained in analytical form according to a chosen risk level. Then, the statistical metric Z-score was extended to a new one,, which effectively reveals the statistical significance of subgraph in a continuous period of time. In this paper, a novel research framework of motif identification was proposed, defining critical boundaries for the evolutionary process of networks and a significance metric of time scale. Finally, an industrial ecosystem at Kalundborg was adopted as a case study to illustrate the effectiveness and convenience of the proposed methodology.

Revealing the hidden language of complex networks

Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network's structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a country's role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists.

Tetramer formation in Arabidopsis MADS domain proteins: analysis of a protein-protein interaction network

BACKGROUND

MADS domain proteins are transcription factors that coordinate several important developmental processes in plants. These proteins interact with other MADS domain proteins to form dimers, and it has been proposed that they are able to associate as tetrameric complexes that regulate transcription of target genes. Whether the formation of functional tetramers is a widespread property of plant MADS domain proteins, or it is specific to few of these transcriptional regulators remains unclear.

RESULTS

We analyzed the structure of the network of physical interactions among MADS domain proteins in Arabidopsis thaliana. We determined the abundance of subgraphs that represent the connection pattern expected for a MADS domain protein heterotetramer. These subgraphs were significantly more abundant in the MADS domain protein interaction network than in randomized analogous networks. Importantly, these subgraphs are not significantly frequent in a protein interaction network of TCP plant transcription factors, when compared to expectation by chance. In addition, we found that MADS domain proteins in tetramer-like subgraphs are more likely to be expressed jointly than proteins in other subgraphs. This effect is mainly due to proteins in the monophyletic MIKC clade, as there is no association between tetramer-like subgraphs and co-expression for proteins outside this clade.

CONCLUSIONS

Our results support that the tendency to form functional tetramers is widespread in the MADS domain protein-protein interaction network. Our observations also suggest that this trend is prevalent, or perhaps exclusive, for proteins in the MIKC clade. Because it is possible to retrodict several experimental results from our analyses, our work can be an important aid to make new predictions and facilitates experimental research on plant MADS domain proteins.

Temporal motifs reveal homophily, gender-specific patterns, and group talk in call sequences

Recent studies on electronic communication records have shown that human communication has complex temporal structure. We study how communication patterns that involve multiple individuals are affected by attributes such as sex and age. To this end, we represent the communication records as a colored temporal network where node color is used to represent individuals' attributes, and identify patterns known as temporal motifs. We then construct a null model for the occurrence of temporal motifs that takes into account the interaction frequencies and connectivity between nodes of different colors. This null model allows us to detect significant patterns in call sequences that cannot be observed in a static network that uses interaction frequencies as link weights. We find sex-related differences in communication patterns in a large dataset of mobile phone records and show the existence of temporal homophily, the tendency of similar individuals to participate in communication patterns beyond what would be expected on the basis of their average interaction frequencies. We also show that temporal patterns differ between dense and sparse neighborhoods in the network. Because also this result is independent of interaction frequencies, it can be seen as an extension of Granovetter's hypothesis to temporal networks.

Extracting labeled topological patterns from samples of networks

An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable for a direct evaluation and interpretation. The new approach addresses the problem of simplifying topological information and characterizes such a sample of networks by finding its locatable characteristic topological patterns. These patterns, essentially sample-specific network motifs with vertex labeling, might represent the essence of the intricate topological information contained in all sample element networks and provides as well a means of differentiating network samples. Central to the accurateness of this approach is the null model and its properties, which is needed to assign significance to topological patterns. As a proof of principle the proposed approach has been applied to the analysis of networks that represent brain connectivity before and during painful stimulation in patients with major depression and in healthy subjects. The accomplished reduction of topological information enables a cautious functional interpretation of the altered neuronal processing of pain in both groups.