Small-world Configuration Research Articles

Endothelial signalling operates on a small‐world network to control vascular function

The endothelium is the innermost layer of all blood vessels and it controls a host of cardiovascular functions including vascular contractility, hemostasis, inflammation and the exchange of nutrients and waste products between circulating blood and tissue. The importance of the endothelium is clear since changes in the behaviour of this single layer of cells underlies almost all cardiovascular disease. To control each cardiovascular function, the endothelium processes and responds to endless streams of information that originate from multiple sources (i.e. blood cells, hormones, neighboring endothelial cells or underlying smooth muscle cells). To process so much information, the endothelium utilises distributed sensing on spatially‐distinct populations of cells that are primed to detect specific activators. These spatially‐distinct populations communicate across the endothelial network to coordinate vascular responses. The nature of the endothelial network, and how communication is achieved, is currently not understood. Here, by examining the Ca2+ responses in thousands of endothelial cells in intact arteries, we show how the endothelial network operates.Network organization controls overall system behaviour by determining the signal propagation speed, the robustness of the system to failures and attack, and the degree of synchronizability in the system. To determine the endothelial network structure, we used network (graph) theory. Graph theory has gained much attention due to its ability to quantify social, technological and biological systems, especially the connectivity and synchronisation of the nervous system. However, no studies have examined the network structure employed by the endothelium in the control of cardiovascular function. We analysed muscarinic‐ and histaminergic‐evoked Ca2+ activity from ~1000 endothelial cells from intact resistance arteries. Ca2+ signals were separately analysed in each of the 1000 individual endothelial cells using a custom‐written Python algorithm.Ca2+ activity in active cells was cross‐correlated and compared to a stochastic model to statistically quantify network connections. We show highly‐correlated Ca2+ activities occurred in multiple, separate, cell clusters for each agonist. The network communication links between the clusters exhibited unexpectedly short path‐lengths, i.e. the number of links between active cells was significantly shorter than expected when active cells were randomly positioned. The number of connections between active cells (degree distribution) followed a power‐law relationship, revealing a scale‐free network topology. The path‐length and degree distribution reveal an endothelial network with a ‘small‐world’ configuration. The small‐world configuration confers particularly dynamic endothelial properties including high signal‐propagation speed, stability and a high degree of synchronizability.These findings show that endothelial network design is effective for local and global efficiency in the interaction of cells, and for rapid and robust communication to efficiently control cardiovascular activity. The network organization explains how coordinated cell activity occurs across large regions of endothelium, despite sensing being distributed on spatially‐distinct populations of cells.

Small-world connectivity dictates collective endothelial cell signaling

Every blood vessel is lined by a single layer of highly specialized, yet adaptable and multifunctional endothelial cells. These cells, the endothelium, control vascular contractility, hemostasis, and inflammation and regulate the exchange of oxygen, nutrients, and waste products between circulating blood and tissue. To control each function, the endothelium processes endlessly arriving requests from multiple sources using separate clusters of cells specialized to detect specific stimuli. A well-developed but poorly understood communication system operates between cells to integrate multiple lines of information and coordinate endothelial responses. Here, the nature of the communication network has been addressed using single-cell Ca2+ imaging across thousands of endothelial cells in intact blood vessels. Cell activities were cross-correlated and compared to a stochastic model to determine network connections. Highly correlated Ca2+ activities occurred in scattered cell clusters, and network communication links between them exhibited unexpectedly short path lengths. The number of connections between cells (degree distribution) followed a power-law relationship revealing a scale-free network topology. The path length and degree distribution revealed an endothelial network with a “small-world” configuration. The small-world configuration confers particularly dynamic endothelial properties including high signal-propagation speed, stability, and a high degree of synchronizability. Local activation of small clusters of cells revealed that the short path lengths and rapid signal transmission were achieved by shortcuts via connecting extensions to nonlocal cells. These findings reveal that the endothelial network design is effective for local and global efficiency in the interaction of the cells and rapid and robust communication between endothelial cells in order to efficiently control cardiovascular activity.

Single-subject gray matter networks in temporal lobe epilepsy patients with hippocampal sclerosis

ObjectivePrevious studies have demonstrated structural brain network abnormalities in patients with temporal lobe epilepsy (TLE) using cortical thickness or gray matter (GM) volume. However, no studies have applied single-subject GM network analysis. Here, we first applied an analysis of similarity-based single-subject GM networks to individual patients with TLE. Materials and methodsWe recruited 51 patients with TLE and unilateral hippocampal sclerosis (22 left, 29 right TLE) and 51 age- and gender- matched healthy controls. Single-subject structural networks were extracted from three-dimensional T1-weighted magnetic resonance images for each subject. In this method, nodes were defined as small cortical regions and edges representing connecting regions that have high statistical similarity. The constructed graphs were analyzed using the graph theoretical approach. The following global and local network properties were calculated: betweenness centrality, clustering coefficient, and characteristic path length. In addition, small world properties (normalized path length λ, normalized clustering coefficient γ, and small-world network value σ) were obtained and compared with those for the controls. ResultsAlthough the small-world configurations were retained, impaired global clustering coefficient was observed in left and right TLE. At a regional level, patients with left TLE showed a widespread decrease of the clustering coefficient beyond the ipsilateral temporal lobe and a decreased characteristic path length in the ipsilateral temporal pole. On the other hand, patients with right TLE showed a localized decrease of the clustering coefficient in the ipsilateral temporal lobe. ConclusionsOur findings suggest that global and local network properties disrupted and moved toward randomized networks in TLE patients in comparison to controls. This network alteration was more extensive in left TLE than in right TLE patients. Single-subject GM networks may contribute to a better understanding of the pathophysiology of TLE.

White matter structural network disturbances in first-episode, drug-naïve adolescents with generalized anxiety disorder

BackgroundPrevious studies have suggested that individuals with generalized anxiety disorder (GAD) would show inefficient whole-brain communication and dysconnectivity in the fronto-parietal-subcortical sub-networks in the white matter (WM) structural network. However, these hypotheses have yet to be tested. MethodsIndividual WM structural networks were constructed based on diffusion MRI data and deterministic tractography in 34 first-episode, medication-naïve adolescents with GAD and 27 healthy controls (HCs). Graph theory was applied to investigate the topological organization alterations of the structural network. ResultsGAD patients showed disrupted small-world configurations (i.e., increased path length and decreased clustering coefficient) and hub organization (i.e., less connection strength in the feeder and local connections). A decreased connection strength was found in a GAD-related sub-network (mainly involving the frontal-subcortical circuits), which was able to distinguish GAD patients from HCs with higher accuracy (area under the curve of 0.96, sensitivity of 94%, specificity of 89%) than clinical scores and other topological alternations. LimitationsThe current study just compared GAD patients with HCs based on a small sample, leaving whether the alternations found here are specific to GAD still an open question. Future studies are recommended to recruit patients with other anxiety disorders (e.g., social anxiety disorder) and/or comorbid mood disorders to identify the GAD-specific WM alterations using a larger sample. ConclusionsOur findings highlight the disruption of the topological organization of the whole-brain WM structural network (especially the frontal-subcortical circuits) in GAD, and suggest the potential of using structural connectivity of the GAD-related sub-network as a biomarker for GAD patients.

Altered effective connectivity network in patients with insular epilepsy: A high-frequency oscillations magnetoencephalography study

ObjectiveThe project aimed to determine the alterations in the effective connectivity (EC) neural network in patients with insular epilepsy based on interictal high-frequency oscillations (HFOs) from magnetoencephalography (MEG) data. MethodsWe studied MEG data from 22 insular epilepsy patients and 20 normal subjects. Alterations in spatial pattern and connection properties of the patients with insular epilepsy were investigated in the entire brain network and insula-based network. ResultsAnalyses of the parameters of graph theory revealed the over-connectivity and small-world configuration of the global connectivity patterns observed in the patients. In the insula-based network, the insular cortex ipsilateral to the seizure onset displayed increased efferent and afferentEC. Left insular epilepsy featured strong connectivity with the bilateral hemispheres, whereas right insular epilepsy featured increased connectivity with only the ipsilateral hemisphere. ConclusionsPatients with insular epilepsy display alterations in the EC network in terms of both whole-brain connectivity and the insula-based network during interictal HFOs. SignificanceAlterations of interictal HFO-based networks provide evidence that epilepsy networks, instead of epileptic foci, play a key role in the complex pathophysiological mechanisms of insular epilepsy. The dysfunction of HFO networks may prove to be a novel promising biomarker and the cause of interictal brain dysfunctions in insular epilepsy.

On the Delay Margin for Consensus in Directed Networks of Anticipatory Agents

We consider a linear consensus problem involving a time delay that arises from predicting the future states of agents based on their past history. In case the agents are coupled in a connected and undirected network, the exact condition for consensus is that the delay be less than a constant threshold that is independent of the network topology or size. In directed networks, however, the situation is quite different. We show that the allowable maximum delay for consensus depends on the network topology in a nontrivial way. We study this delay margin in several network constellations, including various circulant networks with directed links. We show that the delay margin depends not only on the number of neighbors, but also on the directionality of connections with those neighbors. Furthermore, the delay margin improves as the circulant networks are rewired en route to a small-world configuration.

Evaluating the transport in small-world and scale-free networks

We present a study of some properties of transport in small-world and scale-free networks. Particularly, we compare two types of transport: subject to friction (electrical case) and in the absence of friction (maximum flow). We found that in clustered networks based on the Watts–Strogatz (WS) model, for both transport types the small-world configurations exhibit the best trade-off between local and global levels. For non-clustered WS networks the local transport is independent of the rewiring parameter, while the transport improves globally. Moreover, we analyzed both transport types in scale-free networks considering tendencies in the assortative or disassortative mixing of nodes. We construct the distribution of the conductance G and flow F to evaluate the effects of the assortative (disassortative) mixing, finding that for scale-free networks, as we introduce different levels of the degree–degree correlations, the power-law decay in the conductances is altered, while for the flow, the power-law tail remains unchanged. In addition, we analyze the effect on the conductance and the flow of the minimum degree and the shortest path between the source and destination nodes, finding notable differences between these two types of transport.

Disturbed Small-World Networks and Neurocognitive Function in Frontal Lobe Low-Grade Glioma Patients

BackgroundBrain tumor patients often associated with losses of the small-world configuration and neurocognitive functions before operations. However, few studies were performed on the impairments of frontal lobe low-grade gliomas (LGG) after tumor resection using small-world network features.Methodology/Principal FindingsTo detect differences in the whole brain topology among LGG patients before and after operation, a combined study of neurocognitive assessment and graph theoretical network analysis of fMRI data was performed. We collected resting-state fMRI data of 12 carefully selected frontal lobe LGG patients before and after operation. We calculated the topological properties of brain functional networks in the 12 LGG, and compared with 12 healthy controls (HCs). We also applied Montreal Cognitive Assessment (MoCA) in a subset of patients (n = 12, including before and after operation groups) and HCs (n = 12). The resulting functional connectivity matrices were constructed for all 12 patients, and binary network analysis was performed. In the range of , the functional networks in preoperative LGG and postoperative one both fitted the definition of small-worldness. We proposed as small-world network interval, and the results showed that the topological properties were found to be disrupted in the two LGG groups, meanwhile the global efficiency increased and the local efficiency decreased. in the two LGG groups both were longer than HCs. in the LGG groups were smaller than HCs. Compared with the Hcs, MoCA in the two LGG groups were lower than HCs with significant difference, and the disturbed networks in the LGG were negatively related to worse MoCA scores.ConclusionsDisturbed small-worldness preperty in the two LGG groups was found and widely spread in the strength and spatial organization of brain networks, and the alterated small-world network may be responsible for cognitive dysfunction in frontal lobe LGG patients.

Changes in the brain intrinsic organization in both on-task state and post-task resting state

The dynamic and robust characteristics of intrinsic functional connectivity of coherent spontaneous activity are critical for the brain functional stability and flexibility. Studies have demonstrated modulation of intrinsic connectivity within local spatial patterns during or after task performance, such as the default mode network (DMN) and task-specific networks. Moreover, recent studies have compared the global spatial pattern in different tasks or over time. However, it is still unclear how the large-scale intrinsic connectivity varies during and after a task. To better understand this issue, we conducted a functional MRI experiment over three sequential periods: an active semantic-matching task period and two rest periods, before and after the task respectively (namely, on-task state and pre-/post-task resting states), to detect task-driven effect on the dynamic large-scale intrinsic organization in both on-task state and post-task resting state. Three hierarchical levels were investigated, including (a) the whole brain small-world topology, (b) the whole pairwise functional connectivity patterns both within the DMN and between the DMN and other regions (i.e., the global/full DMN topography), and (c) the DMN nodal graph properties. The major findings are: (1) The large-scale small-world configuration of brain functional organization is robust, regardless of the behavioral state changing, while it varies adaptively with significantly higher local efficiency and lower global efficiency during the on-task state (P<0.05, Monte-Carlo corrected); (2) The DMN may be essentially engaged during both task and post-task processes with adaptively varied spatial patterns and nodal graph properties. The present study provides further insights into the robustness and plasticity of the brain intrinsic organization over states, which may be the basis of memory and learning in the brain.

Structure of the cortical networks during successful memory encoding in TV commercials

Objective This work intends to evaluate the functional characteristics of the cerebral network during the successful memory encoding of TV commercials. Methods We estimated the functional networks in the frequency domain from a set of high-resolution EEG data in a group of healthy subjects during the showing of commercial spots within a neutral documentary. We evaluated the differences in the cortical network associated with later remembered and not-remembered commercials by calculating the global- E g and local-efficiency E l indexes. Results Successful encoding of TV spots significantly affects the functional communication among cortical areas irrespectively of the frequency band. During the visualization of the video-clips that will be forgotten (FRG), the cortical network exhibited high values of global- and local-efficiency, reflecting a small-world configuration. During the visualization of the video-clips that will be remembered (RMB), the same indexes appeared significantly lower. This difference was especially evident for E l in the alpha band and for E g in the beta and gamma bands. Conclusions The presence of attentional and semantic processes during the RMB condition leads to a significant reduction of the network communication efficiency. Significance Such a reduction could represent a predictive measure of accurate recalls of TV spots.

On representing network heterogeneities in the incidence rate of simple epidemic models

Mean-field ecological models ignore space and other forms of contact structure. At the opposite extreme, high-dimensional models that are both individual-based and stochastic incorporate the distributed nature of ecological interactions. In between, moment approximations have been proposed that represent the effect of correlations on the dynamics of mean quantities. As an alternative closer to the typical temporal models used in ecology, we present here results on “modified mean-field equations” for infectious disease dynamics, in which only mean quantities are followed and the effect of heterogeneous mixing is incorporated implicitly. We specifically investigate the previously proposed empirical parameterization of heterogeneous mixing in which the bilinear incidence rate SI is replaced by a nonlinear term kS p I q , for the case of stochastic SIRS dynamics on different contact networks, from a regular lattice to a random structure via small-world configurations. We show that, for two distinct dynamical cases involving a stable equilibrium and a noisy endemic steady state, the modified mean-field model approximates successfully the steady state dynamics as well as the respective short and long transients of decaying cycles. This result demonstrates that early on in the transients an approximate power-law relationship is established between global (mean) quantities and the covariance structure in the network. The approach fails in the more complex case of persistent cycles observed within the narrow range of small-world configurations.

FRUSTRATION EFFECTS ON SMALL-WORLD NETWORKS

We investigate the frustration effects on small-world networks by studying antiferromagnetic Ising model in two dimensions. When the rewiring is constrained to those sites such that the interaction still occurs between spins in distinct sublattices and frustration does not take place, we observe that the system behaves as in previous investigations of ferromagnetic Ising model. However, when the rewiring procedure does not only produce interactions between spins in distinct sublattices, small-world configurations can effectively produce geometrical frustration and we attain a different critical behavior. In the frustrated case, the critical temperature decreases with the augment of the rewiring probability and the magnetic ordering presents two different regimes for low and high p.