Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks

Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3–20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks.     

Cognitive relevance of the community structure of the human brain functional coactivation network

There is growing interest in the complex topology of human brain functional networks, often measured using resting-state functional MRI (fMRI). Here, we used a meta-analysis of the large primary literature that used fMRI or PET to measure task-related activation (>1,600 studies; 1985–2010). We estimated the similarity (Jaccard index) of the activation patterns across experimental tasks between each pair of 638 brain regions. This continuous coactivation matrix was used to build a weighted graph to characterize network topology. The coactivation network was modular, with occipital, central, and default-mode modules predominantly coactivated by specific cognitive domains (perception, action, and emotion, respectively). It also included a rich club of hub nodes, located in parietal and prefrontal cortex and often connected over long distances, which were coactivated by a diverse range of experimental tasks. Investigating the topological role of edges between a deactivated and an activated node, we found that such competitive interactions were most frequent between nodes in different modules or between an activated rich-club node and a deactivated peripheral node. Many aspects of the coactivation network were convergent with a connectivity network derived from resting state fMRI data (n = 27, healthy volunteers); although the connectivity network was more parsimoniously connected and differed in the anatomical locations of some hubs. We conclude that the community structure of human brain networks is relevant to cognitive function. Deactivations may play a role in flexible reconfiguration of the network according to cognitive demand, varying the integration between modules, and between the periphery and a central rich club.     

Cascading failure and robustness in metabolic networks

We investigate the relationship between structure and robustness in the metabolic networks of Escherichia coli, Methanosarcina barkeri, Staphylococcus aureus, and Saccharomyces cerevisiae, using a cascading failure model based on a topological flux balance criterion. We find that, compared to appropriate null models, the metabolic networks are exceptionally robust. Furthermore, by decomposing each network into rigid clusters and branched metabolites, we demonstrate that the enhanced robustness is related to the organization of branched metabolites, as rigid cluster formations in the metabolic networks appear to be consistent with null model behavior. Finally, we show that cascading in the metabolic networks can be described as a percolation process.     

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.     

Topological structure of rat mesenteric microvessel networks

Microvascular lengths, diameters, and flow directions were determined in all vessel segments (n = 1303) between bifurcations in three complete rat mesenteric microvessel networks (25 mm2 each) using intravital video- and photomicroscopy. The classification of vessel segments as arteriolar, venular, or av-segments (all segments connecting the arteriolar to the venular tree) was based on purely topological criteria. The topological structure of the networks was analyzed using the Horton-Strahler technique and a new generation scheme. Generation numbers were assigned to the vessel segments on the basis of the number of upstream (in the arteriolar tree) and downstream (in the venular tree) bifurcations. The mean generation number of the av-segments, a characteristic parameter of the generation scheme, reflects the topological structure of the network more accurately than Horton's branching ratio Rb. Both the arteriolar and venular tree of the mesenteric networks were found to be dichotomous branching structures which were neither strictly symmetric nor strictly asymmetric. The topological information obtained was compared to network models generated by different random branching algorithms. The result of this comparison suggests that the network structure changes at a certain generation level. Distal to this generation level, the mesenteric networks resemble a model network generated by random branching at any segment, while the proximal portion is similar to a model allowing random branching at terminal segments only.     

Metagenomic systems biology of the human gut microbiome reveals topological shifts associated with obesity and inflammatory bowel disease

The human microbiome plays a key role in a wide range of host-related processes and has a profound effect on human health. Comparative analyses of the human microbiome have revealed substantial variation in species and gene composition associated with a variety of disease states but may fall short of providing a comprehensive understanding of the impact of this variation on the community and on the host. Here, we introduce a metagenomic systems biology computational framework, integrating metagenomic data with an in silico systems-level analysis of metabolic networks. Focusing on the gut microbiome, we analyze fecal metagenomic data from 124 unrelated individuals, as well as six monozygotic twin pairs and their mothers, and generate community-level metabolic networks of the microbiome. Placing variations in gene abundance in the context of these networks, we identify both gene-level and network-level topological differences associated with obesity and inflammatory bowel disease (IBD). We show that genes associated with either of these host states tend to be located at the periphery of the metabolic network and are enriched for topologically derived metabolic "inputs." These findings may indicate that lean and obese microbiomes differ primarily in their interface with the host and in the way they interact with host metabolism. We further demonstrate that obese microbiomes are less modular, a hallmark of adaptation to low-diversity environments. We additionally link these topological variations to community species composition. The system-level approach presented here lays the foundation for a unique framework for studying the human microbiome, its organization, and its impact on human health.     

Scaling theory of transport in complex biological networks

Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well understood in these systems, probably because of the lack of a general theoretical framework. Here, based on the finding that renormalization can be applied to bionetworks, we develop a scaling theory of transport in self-similar networks. We demonstrate the networks invariance under length scale renormalization, and we show that the problem of transport can be characterized in terms of a set of critical exponents. The scaling theory allows us to determine the influence of the modular structure on transport in metabolic and protein-interaction networks. We also generalize our theory by presenting and verifying scaling arguments for the dependence of transport on microscopic features, such as the degree of the nodes and the distance between them. Using transport concepts such as diffusion and resistance, we exploit this invariance, and we are able to explain, based on the topology of the network, recent experimental results on the broad flow distribution in metabolic networks.     

Predicting errors from reconfiguration patterns in human brain networks

Task preparation is a complex cognitive process that implements anticipatory adjustments to facilitate future task performance. Little is known about quantitative network parameters governing this process in humans. Using functional magnetic resonance imaging (fMRI) and functional connectivity measurements, we show that the large-scale topology of the brain network involved in task preparation shows a pattern of dynamic reconfigurations that guides optimal behavior. This network could be decomposed into two distinct topological structures, an error-resilient core acting as a major hub that integrates most of the network’s communication and a predominantly sensory periphery showing more flexible network adaptations. During task preparation, core–periphery interactions were dynamically adjusted. Task-relevant visual areas showed a higher topological proximity to the network core and an enhancement in their local centrality and interconnectivity. Failure to reconfigure the network topology was predictive for errors, indicating that anticipatory network reconfigurations are crucial for successful task performance. On the basis of a unique network decoding approach, we also develop a general framework for the identification of characteristic patterns in complex networks, which is applicable to other fields in neuroscience that relate dynamic network properties to behavior.     

Hubs of brain functional networks are radically reorganized in comatose patients

Human brain networks have topological properties in common with many other complex systems, prompting the following question: what aspects of brain network organization are critical for distinctive functional properties of the brain, such as consciousness? To address this question, we used graph theoretical methods to explore brain network topology in resting state functional MRI data acquired from 17 patients with severely impaired consciousness and 20 healthy volunteers. We found that many global network properties were conserved in comatose patients. Specifically, there was no significant abnormality of global efficiency, clustering, small-worldness, modularity, or degree distribution in the patient group. However, in every patient, we found evidence for a radical reorganization of high degree or highly efficient “hub” nodes. Cortical regions that were hubs of healthy brain networks had typically become nonhubs of comatose brain networks and vice versa. These results indicate that global topological properties of complex brain networks may be homeostatically conserved under extremely different clinical conditions and that consciousness likely depends on the anatomical location of hub nodes in human brain networks.     

Simple models of human brain functional networks

Human brain functional networks are embedded in anatomical space and have topological properties--small-worldness, modularity, fat-tailed degree distributions--that are comparable to many other complex networks. Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown. Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.     

Potential landscape and flux framework of nonequilibrium networks: robustness, dissipation, and coherence of biochemical oscillations

We established a theoretical framework for studying nonequilibrium networks with two distinct natures essential for characterizing the global probabilistic dynamics: the underlying potential landscape and the corresponding curl flux. We applied the idea to a biochemical oscillation network and found that the underlying potential landscape for the oscillation limit cycle has a distinct closed ring valley (Mexican hat-like) shape when the fluctuations are small. This global landscape structure leads to attractions of the system to the ring valley. On the ring, we found that the nonequilibrium flux is the driving force for oscillations. Therefore, both structured landscape and flux are needed to guarantee a robust oscillating network. The barrier height separating the oscillation ring and other areas derived from the landscape topography is shown to be correlated with the escaping time from the limit cycle attractor and provides a quantitative measure of the robustness for the network. The landscape becomes shallower and the closed ring valley shape structure becomes weaker (lower barrier height) with larger fluctuations. We observe that the period and the amplitude of the oscillations are more dispersed and oscillations become less coherent when the fluctuations increase. We also found that the entropy production of the whole network, characterizing the dissipation costs from the combined effects of both landscapes and fluxes, decreases when the fluctuations decrease. Therefore, less dissipation leads to more robust networks. Our approach is quite general and applicable to other networks, dynamical systems, and biological evolution. It can help in designing robust networks.     

Applications of social network analysis to obesity: a systematic review

People's health behaviours and outcomes can be profoundly shaped by the social networks they are embedded in. Based on graph theory, social network analysis is a research framework for the study of social interactions and the structure of these interactions among social actors. A literature search was conducted in PubMed and Web of Science for articles published until August 2017 that applied social network analysis to examine obesity and social networks. Eight studies (three cross‐sectional and five longitudinal) conducted in the US (n = 6) and Australia (n = 2) were identified. Seven focused on adolescents' and one on adults' friendship networks. They examined structural features of these networks that were associated with obesity, including degree distribution, popularity, modularity maximization and K‐clique percolation. All three cross‐sectional studies that used exponential random graph models found individuals with similar body weight status and/or weight‐related behaviour were more likely to share a network tie than individuals with dissimilar traits. Three longitudinal studies using stochastic actor‐based models found friendship network characteristics influenced change in individuals' body weight status and/or weight‐related behaviour over time. Future research should focus on diverse populations and types of social networks and identifying the mechanisms by which social networks influence obesity to inform network‐based interventions.     

Redistribution of red blood cell flow in microcirculatory networks by hemodilution.

The effect of isovolemic hemodilution on red blood cell flow distribution was studied in complete self-contained microvessel networks of the rat mesentery. Hematocrit, diameter, and length of all vessel segments as well as the topological structure were determined in control networks (systemic hematocrit, 0.54) and after hemodilution (systemic hematocrit, 0.30). Hemodilution was performed by exchanging blood with hydroxyethyl starch (MW 450,000; 6%) or homologous plasma. With hemodilution, the decrease of microvessel hematocrit exceeded that of systemic hematocrit. The average discharge hematocrit in capillaries was 79% of systemic hematocrit in the control group and 73% with hemodilution (p less than 0.001). The heterogeneity of capillary hematocrit within the network, expressed by the coefficient of variation, increased from 0.4 to 0.7. By using the morphological and topological data of four networks, the distribution of hematocrits was also calculated using a hydrodynamic flow model. The modeling results were found to be in close agreement with the experimental data. This indicates that the observed changes can be deduced from established rheological phenomena, most of all phase separation at arteriolar bifurcations. The changes in hematocrit distribution after hemodilution are accompanied by a redistribution of red blood cell flow within the network: relative to total red blood cell flow, red blood cell flow in the distal capillaries of the network increases by about 40% at the expense of the proximal capillaries that are close to the feeding arteriole and that exhibit the highest red blood cell flow under control conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks

Node characteristics and behaviors are often correlated with the structure of social networks over time. While evidence of this type of assortative mixing and temporal clustering of behaviors among linked nodes is used to support claims of peer influence and social contagion in networks, homophily may also explain such evidence. Here we develop a dynamic matched sample estimation framework to distinguish influence and homophily effects in dynamic networks, and we apply this framework to a global instant messaging network of 27.4 million users, using data on the day-by-day adoption of a mobile service application and users'' longitudinal behavioral, demographic, and geographic data. We find that previous methods overestimate peer influence in product adoption decisions in this network by 300–700%, and that homophily explains >50% of the perceived behavioral contagion. These findings and methods are essential to both our understanding of the mechanisms that drive contagions in networks and our knowledge of how to propagate or combat them in domains as diverse as epidemiology, marketing, development economics, and public health.     

Social networks, health, and emotional well-being among the oldest old in London

A survey of the health and social circumstances of 662 people aged 85 and over, living at home in inner London, was conducted in 1987. A primary aim was to analyze the structure of social support networks of the sample in relation to respondents' emotional well-being and met and unmet needs for practical help. The conceptual and methodological framework that was applied to the study was derived from the theory of social networks. In confirmation of the common assumption that people aged 85+ are different from younger elderly people, as they are the "survivors," high levels of social support and informal help were given to most respondents. Although associations were found between social network variables and the provision of informal help, multifactorial analysis showed that health status explained more of the variation in emotional well-being.     

Geometric constraints on neuronal connectivity facilitate a concise synaptic adhesive code

The nervous system contains trillions of neurons, each forming thousands of synaptic connections. It has been suggested that this complex connectivity is determined by a synaptic "adhesive code," where connections are dictated by a variable set of cell surface proteins, combinations of which form neuronal addresses. The estimated number of neuronal addresses is orders of magnitude smaller than the number of neurons. Here, we show that the limited number of addresses dictates constraints on the possible neuronal network topologies. We show that to encode arbitrary networks, in which each neuron can potentially connect to any other neuron, the number of neuronal addresses needed scales linearly with network size. In contrast, the number of addresses needed to encode the wiring of geometric networks grows only as the square root of network size. The more efficient encoding in geometric networks is achieved through the reutilization of the same addresses in physically independent portions of the network. We also find that ordered geometric networks, in which the same connectivity patterns are iterated throughout the network, further reduce the required number of addresses. We demonstrate our findings using simulated networks and the C. elegans neuronal network. Geometric neuronal connectivity with recurring connectivity patterns have been suggested to confer an evolutionary advantage by saving biochemical resources on the one hand and reutilizing functionally efficient neuronal circuits. Our study suggests an additional advantage of these prominent topological features--the facilitation of the ability to genetically encode neuronal networks given constraints on the number of addresses.     

Metabolic principles of river basin organization

The metabolism of a river basin is defined as the set of processes through which the basin maintains its structure and responds to its environment. Green (or biotic) metabolism is measured via transpiration and blue (or abiotic) metabolism through runoff. A principle of equal metabolic rate per unit area throughout the basin structure is developed and tested in a river basin characterized by large heterogeneities in precipitation, vegetation, soil, and geomorphology. This principle is suggested to have profound implications for the spatial organization of river basin hydrologic dynamics, including the minimization of energy expenditure known to control the scale-invariant characteristics of river networks over several orders of magnitude. Empirically derived, remarkably constant rates of average transpiration per unit area through the basin structure lead to a power law for the probability distribution of transpiration from a randomly chosen subbasin. The average runoff per unit area, evaluated for subbasins of a wide range of topological magnitudes, is also shown to be remarkably constant independently of size. A similar result is found for the rainfall after accounting for canopy interception. Allometric scaling of metabolic rates with size, variously addressed in the biological literature and network theory under the label of Kleiber's law, is similarly derived. The empirical evidence suggests that river basin metabolic activity is linked with the spatial organization that takes place around the drainage network and therefore with the mechanisms responsible for the fractal geometry of the network, suggesting a new coevolutionary framework for biological, geomorphological, and hydrologic dynamics.