Topographic Hub Maps of the Human Structural Neocortical Network

Hubs within the neocortical structural network determined by graph theoretical analysis play a crucial role in brain function. We mapped neocortical hubs topographically, using a sample population of 63 young adults. Subjects were imaged with high resolution structural and diffusion weighted magnetic resonance imaging techniques. Multiple network configurations were then constructed per subject, using random parcellations to define the nodes and using fibre tractography to determine the connectivity between the nodes. The networks were analysed with graph theoretical measures. Our results give reference maps of hub distribution measured with betweenness centrality and node degree. The loci of the hubs correspond with key areas from known overlapping cognitive networks. Several hubs were asymmetrically organized across hemispheres. Furthermore, females have hubs with higher betweenness centrality and males have hubs with higher node degree. Female networks have higher small-world indices.     

Structural Controllability and Controlling Centrality of Temporal Networks

Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it''s urgent and significant to focus on its structural controllability as well as the corresponding characteristics, which nowadays is still an untouched topic. We develop graphic tools to study the structural controllability as well as its characteristics, identifying the intrinsic mechanism of the ability of individuals in controlling a dynamic and large-scale temporal network. Classifying temporal trees of a temporal network into different types, we give (both upper and lower) analytical bounds of the controlling centrality, which are verified by numerical simulations of both artificial and empirical temporal networks. We find that the positive relationship between aggregated degree and controlling centrality as well as the scale-free distribution of node''s controlling centrality are virtually independent of the time scale and types of datasets, meaning the inherent robustness and heterogeneity of the controlling centrality of nodes within temporal networks.     

Controllability of Deterministic Networks with the Identical Degree Sequence

Controlling complex network is an essential problem in network science and engineering. Recent advances indicate that the controllability of complex network is dependent on the network''s topology. Liu and Barabási, et.al speculated that the degree distribution was one of the most important factors affecting controllability for arbitrary complex directed network with random link weights. In this paper, we analysed the effect of degree distribution to the controllability for the deterministic networks with unweighted and undirected. We introduce a class of deterministic networks with identical degree sequence, called (x,y)-flower. We analysed controllability of the two deterministic networks ((1, 3)-flower and (2, 2)-flower) by exact controllability theory in detail and give accurate results of the minimum number of driver nodes for the two networks. In simulation, we compare the controllability of (x,y)-flower networks. Our results show that the family of (x,y)-flower networks have the same degree sequence, but their controllability is totally different. So the degree distribution itself is not sufficient to characterize the controllability of deterministic networks with unweighted and undirected.     

Functional Cortical Hubs in the Eyes-Closed Resting Human Brain from an Electrophysiological Perspective Using Magnetoencephalography

It is not clear whether specific brain areas act as hubs in the eyes-closed (EC) resting state, which is an unconstrained state free from any passive or active tasks. Here, we used electrophysiological magnetoencephalography (MEG) signals to study functional cortical hubs in 88 participants. We identified several multispectral cortical hubs. Although cortical hubs vary slightly with different applied measures and frequency bands, the most consistent hubs were observed in the medial and posterior cingulate cortex, the left dorsolateral superior frontal cortex, and the left pole of the middle temporal cortex. Hubs were characterized as connector nodes integrating EC resting state functional networks. Hubs in the gamma band were more likely to include midline structures. Our results confirm the existence of multispectral cortical cores in EC resting state functional networks based on MEG and imply the existence of optimized functional networks in the resting brain.     

Structural Controllability of Complex Networks Based on Preferential Matching

Minimum driver node sets (MDSs) play an important role in studying the structural controllability of complex networks. Recent research has shown that MDSs tend to avoid high-degree nodes. However, this observation is based on the analysis of a small number of MDSs, because enumerating all of the MDSs of a network is a #P problem. Therefore, past research has not been sufficient to arrive at a convincing conclusion. In this paper, first, we propose a preferential matching algorithm to find MDSs that have a specific degree property. Then, we show that the MDSs obtained by preferential matching can be composed of high- and medium-degree nodes. Moreover, the experimental results also show that the average degree of the MDSs of some networks tends to be greater than that of the overall network, even when the MDSs are obtained using previous research method. Further analysis shows that whether the driver nodes tend to be high-degree nodes or not is closely related to the edge direction of the network.     

Trade-off between Multiple Constraints Enables Simultaneous Formation of Modules and Hubs in Neural Systems

The formation of the complex network architecture of neural systems is subject to multiple structural and functional constraints. Two obvious but apparently contradictory constraints are low wiring cost and high processing efficiency, characterized by short overall wiring length and a small average number of processing steps, respectively. Growing evidence shows that neural networks are results from a trade-off between physical cost and functional value of the topology. However, the relationship between these competing constraints and complex topology is not well understood quantitatively. We explored this relationship systematically by reconstructing two known neural networks, Macaque cortical connectivity and C. elegans neuronal connections, from combinatory optimization of wiring cost and processing efficiency constraints, using a control parameter , and comparing the reconstructed networks to the real networks. We found that in both neural systems, the reconstructed networks derived from the two constraints can reveal some important relations between the spatial layout of nodes and the topological connectivity, and match several properties of the real networks. The reconstructed and real networks had a similar modular organization in a broad range of , resulting from spatial clustering of network nodes. Hubs emerged due to the competition of the two constraints, and their positions were close to, and partly coincided, with the real hubs in a range of values. The degree of nodes was correlated with the density of nodes in their spatial neighborhood in both reconstructed and real networks. Generally, the rebuilt network matched a significant portion of real links, especially short-distant ones. These findings provide clear evidence to support the hypothesis of trade-off between multiple constraints on brain networks. The two constraints of wiring cost and processing efficiency, however, cannot explain all salient features in the real networks. The discrepancy suggests that there are further relevant factors that are not yet captured here.     

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

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

The dichotomy in degree correlation of biological networks

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

Control of Neuronal Network in Caenorhabditis elegans

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

Convergence and divergence are mostly reciprocated properties of the connections in the network of cortical areas

Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.     

残基相互作用网络特征与木聚糖酶耐热性的关系

残基相互作用网络是体现蛋白质中残基与残基之间协同和制约关系的重要形式。残基相互作用网络的拓扑性质以及社团结构与蛋白质的功能和性质有密切的关系。本文在构建一系列耐热木聚糖酶和常温木聚糖酶的残基相互作用网络后,通过计算网络的度、聚类系数、连接强度、特征路径长度、接近中心性、介数中心性等拓扑参数来确定网络拓扑结构与木聚糖酶耐热性的关系。识别残基相互作用网络的hub点,分析hub点的亲疏水性、带电性以及各种氨基酸在hub点中所占的比例。进一步使用GA-Net算法对网络进行社团划分,并计算社团的规模、直径和密度。网络的高平均度、高连接强度、以及更短的最短路径等表明耐热木聚糖酶残基相互作用网络的结构更加紧密;耐热木聚糖酶网络中的hub节点比常温木聚糖酶网络hub节点具有更多的疏水性残基,hub点中Phe、Ile、Val的占比更高。社团检测后发现,耐热木聚糖酶网络拥有更大的社团规模、较小的社团直径和较大的社团密度。社团规模越大表明耐热木聚糖酶的氨基酸残基更倾向于形成大的社团,而较小的社团直径和较大的社团密度则表明社团内部氨基酸残基的相互作用比常温木聚糖酶更强。     

Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

残基相互作用网络特征与木聚糖酶耐热性的关系

残基相互作用网络是体现蛋白质中残基与残基之间协同和制约关系的重要形式。残基相互作用网络的拓扑性质以及社团结构与蛋白质的功能和性质有密切的关系。本文在构建一系列耐热木聚糖酶和常温木聚糖酶的残基相互作用网络后,通过计算网络的度、聚类系数、连接强度、特征路径长度、接近中心性、介数中心性等拓扑参数来确定网络拓扑结构与木聚糖酶耐热性的关系。识别残基相互作用网络的hub点,分析hub点的亲疏水性、带电性以及各种氨基酸在hub点中所占的比例。进一步使用GA-Net算法对网络进行社团划分,并计算社团的规模、直径和密度。网络的高平均度、高连接强度、以及更短的最短路径等表明耐热木聚糖酶残基相互作用网络的结构更加紧密;耐热木聚糖酶网络中的hub节点比常温木聚糖酶网络hub节点具有更多的疏水性残基,hub点中Phe、Ile、Val的占比更高。社团检测后发现,耐热木聚糖酶网络拥有更大的社团规模、较小的社团直径和较大的社团密度。社团规模越大表明耐热木聚糖酶的氨基酸残基更倾向于形成大的社团,而较小的社团直径和较大的社团密度则表明社团内部氨基酸残基的相互作用比常温木聚糖酶更强。     

On the relationship between emotion and cognition

The current view of brain organization supports the notion that there is a considerable degree of functional specialization and that many regions can be conceptualized as either 'affective' or 'cognitive'. Popular examples are the amygdala in the domain of emotion and the lateral prefrontal cortex in the case of cognition. This prevalent view is problematic for a number of reasons. Here, I will argue that complex cognitive-emotional behaviours have their basis in dynamic coalitions of networks of brain areas, none of which should be conceptualized as specifically affective or cognitive. Central to cognitive-emotional interactions are brain areas with a high degree of connectivity, called hubs, which are critical for regulating the flow and integration of information between regions.     

An Efficient Immunization Strategy for Community Networks

An efficient algorithm that can properly identify the targets to immunize or quarantine for preventing an epidemic in a population without knowing the global structural information is of obvious importance. Typically, a population is characterized by its community structure and the heterogeneity in the weak ties among nodes bridging over communities. We propose and study an effective algorithm that searches for bridge hubs, which are bridge nodes with a larger number of weak ties, as immunizing targets based on the idea of referencing to an expanding friendship circle as a self-avoiding walk proceeds. Applying the algorithm to simulated networks and empirical networks constructed from social network data of five US universities, we show that the algorithm is more effective than other existing local algorithms for a given immunization coverage, with a reduced final epidemic ratio, lower peak prevalence and fewer nodes that need to be visited before identifying the target nodes. The effectiveness stems from the breaking up of community networks by successful searches on target nodes with more weak ties. The effectiveness remains robust even when errors exist in the structure of the networks.     

The overlapping community structure of structural brain network in young healthy individuals

Community structure is a universal and significant feature of many complex networks in biology, society, and economics. Community structure has also been revealed in human brain structural and functional networks in previous studies. However, communities overlap and share many edges and nodes. Uncovering the overlapping community structure of complex networks remains largely unknown in human brain networks. Here, using regional gray matter volume, we investigated the structural brain network among 90 brain regions (according to a predefined anatomical atlas) in 462 young, healthy individuals. Overlapped nodes between communities were defined by assuming that nodes (brain regions) can belong to more than one community. We demonstrated that 90 brain regions were organized into 5 overlapping communities associated with several well-known brain systems, such as the auditory/language, visuospatial, emotion, decision-making, social, control of action, memory/learning, and visual systems. The overlapped nodes were mostly involved in an inferior-posterior pattern and were primarily related to auditory and visual perception. The overlapped nodes were mainly attributed to brain regions with higher node degrees and nodal efficiency and played a pivotal role in the flow of information through the structural brain network. Our results revealed fuzzy boundaries between communities by identifying overlapped nodes and provided new insights into the understanding of the relationship between the structure and function of the human brain. This study provides the first report of the overlapping community structure of the structural network of the human brain.     

Resolving Structural Variability in Network Models and the Brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known in general about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar graph metrics, but presented here in a more complete statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus specifically on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling—in addition to several summary statistics, including the mean clustering coefficient, the shortest path-length, and the network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property (e.g., assortativity) do not in general simultaneously display a second (e.g., hierarchy). This relative independence of network properties suggests that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.