Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems

It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.     

ModuleBlast: identifying activated sub-networks within and across species

Identifying conserved and divergent response patterns in gene networks is becoming increasingly important. A common approach is integrating expression information with gene association networks in order to find groups of connected genes that are activated or repressed. In many cases, researchers are also interested in comparisons across species (or conditions). Finding an active sub-network is a hard problem and applying it across species requires further considerations (e.g. orthology information, expression data and networks from different sources). To address these challenges we devised ModuleBlast, which uses both expression and network topology to search for highly relevant sub-networks. We have applied ModuleBlast to expression and interaction data from mouse, macaque and human to study immune response and aging. The immune response analysis identified several relevant modules, consistent with recent findings on apoptosis and NFκB activation following infection. Temporal analysis of these data revealed cascades of modules that are dynamically activated within and across species. We have experimentally validated some of the novel hypotheses resulting from the analysis of the ModuleBlast results leading to new insights into the mechanisms used by a key mammalian aging protein.     

Rich Club Organization of Macaque Cerebral Cortex and Its Role in Network Communication

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.     

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic,functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether the connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.     

Identifying disease-associated biomarker network features through conditional graphical model

Biomarkers are often organized into networks, in which the strengths of network connections vary across subjects depending on subject-specific covariates (eg, genetic variants). Variation of network connections, as subject-specific feature variables, has been found to predict disease clinical outcome. In this work, we develop a two-stage method to estimate biomarker networks that account for heterogeneity among subjects and evaluate network's association with disease clinical outcome. In the first stage, we propose a conditional Gaussian graphical model with mean and precision matrix depending on covariates to obtain covariate-dependent networks with connection strengths varying across subjects while assuming homogeneous network structure. In the second stage, we evaluate clinical utility of network measures (connection strengths) estimated from the first stage. The second-stage analysis provides the relative predictive power of between-region network measures on clinical impairment in the context of regional biomarkers and existing disease risk factors. We assess the performance of proposed method by extensive simulation studies and application to a Huntington's disease (HD) study to investigate the effect of HD causal gene on the rate of change in motor symptom through affecting brain subcortical and cortical gray matter atrophy connections. We show that cortical network connections and subcortical volumes, but not subcortical connections are identified to be predictive of clinical motor function deterioration. We validate these findings in an independent HD study. Lastly, highly similar patterns seen in the gray matter connections and a previous white matter connectivity study suggest a shared biological mechanism for HD and support the hypothesis that white matter loss is a direct result of neuronal loss as opposed to the loss of myelin or dysmyelination.     

Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays

The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.     

Decreasing-Rate Pruning Optimizes the Construction of Efficient and Robust Distributed Networks

Robust, efficient, and low-cost networks are advantageous in both biological and engineered systems. During neural network development in the brain, synapses are massively over-produced and then pruned-back over time. This strategy is not commonly used when designing engineered networks, since adding connections that will soon be removed is considered wasteful. Here, we show that for large distributed routing networks, network function is markedly enhanced by hyper-connectivity followed by aggressive pruning and that the global rate of pruning, a developmental parameter not previously studied by experimentalists, plays a critical role in optimizing network structure. We first used high-throughput image analysis techniques to quantify the rate of pruning in the mammalian neocortex across a broad developmental time window and found that the rate is decreasing over time. Based on these results, we analyzed a model of computational routing networks and show using both theoretical analysis and simulations that decreasing rates lead to more robust and efficient networks compared to other rates. We also present an application of this strategy to improve the distributed design of airline networks. Thus, inspiration from neural network formation suggests effective ways to design distributed networks across several domains.     

Is My Network Module Preserved and Reproducible?

In many applications, one is interested in determining which of the properties of a network module change across conditions. For example, to validate the existence of a module, it is desirable to show that it is reproducible (or preserved) in an independent test network. Here we study several types of network preservation statistics that do not require a module assignment in the test network. We distinguish network preservation statistics by the type of the underlying network. Some preservation statistics are defined for a general network (defined by an adjacency matrix) while others are only defined for a correlation network (constructed on the basis of pairwise correlations between numeric variables). Our applications show that the correlation structure facilitates the definition of particularly powerful module preservation statistics. We illustrate that evaluating module preservation is in general different from evaluating cluster preservation. We find that it is advantageous to aggregate multiple preservation statistics into summary preservation statistics. We illustrate the use of these methods in six gene co-expression network applications including 1) preservation of cholesterol biosynthesis pathway in mouse tissues, 2) comparison of human and chimpanzee brain networks, 3) preservation of selected KEGG pathways between human and chimpanzee brain networks, 4) sex differences in human cortical networks, 5) sex differences in mouse liver networks. While we find no evidence for sex specific modules in human cortical networks, we find that several human cortical modules are less preserved in chimpanzees. In particular, apoptosis genes are differentially co-expressed between humans and chimpanzees. Our simulation studies and applications show that module preservation statistics are useful for studying differences between the modular structure of networks. Data, R software and accompanying tutorials can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation.     

Identification and classification of hubs in brain networks

Brain regions in the mammalian cerebral cortex are linked by a complex network of fiber bundles. These inter-regional networks have previously been analyzed in terms of their node degree, structural motif, path length and clustering coefficient distributions. In this paper we focus on the identification and classification of hub regions, which are thought to play pivotal roles in the coordination of information flow. We identify hubs and characterize their network contributions by examining motif fingerprints and centrality indices for all regions within the cerebral cortices of both the cat and the macaque. Motif fingerprints capture the statistics of local connection patterns, while measures of centrality identify regions that lie on many of the shortest paths between parts of the network. Within both cat and macaque networks, we find that a combination of degree, motif participation, betweenness centrality and closeness centrality allows for reliable identification of hub regions, many of which have previously been functionally classified as polysensory or multimodal. We then classify hubs as either provincial (intra-cluster) hubs or connector (inter-cluster) hubs, and proceed to show that lesioning hubs of each type from the network produces opposite effects on the small-world index. Our study presents an approach to the identification and classification of putative hub regions in brain networks on the basis of multiple network attributes and charts potential links between the structural embedding of such regions and their functional roles.     

Bilaterally propagating waves of spontaneous activity arising from discrete pacemakers in the neonatal mouse cerebral cortex

Spontaneous electrical activity that moves in synchronized waves across large populations of neurons plays widespread and important roles in nervous system development. The propagation patterns of such waves can encode the spatial location of neurons to their downstream targets and strengthen synaptic connections in coherent spatial patterns. Such waves can arise as an emergent property of mutually excitatory neural networks, or can be driven by a discrete pacemaker. In the mouse cerebral cortex, spontaneous synchronized activity occurs for approximately 72 h of development centered on the day of birth. It is not known whether this activity is driven by a discrete pacemaker or occurs as an emergent network property. Here we show that this activity propagates as a wave that is initiated at either of two homologous pacemakers in the temporal region, and then propagates rapidly across both sides of the brain. When these regions of origin are surgically isolated, waves do not occur. Therefore, this cortical spontaneous activity is a bilateral wave that originates from a discrete subset of pacemaker neurons. © 2009 Wiley Periodicals, Inc. Develop Neurobiol, 2009     

Spectral Signatures of Reorganised Brain Networks in Disorders of Consciousness

Theoretical advances in the science of consciousness have proposed that it is concomitant with balanced cortical integration and differentiation, enabled by efficient networks of information transfer across multiple scales. Here, we apply graph theory to compare key signatures of such networks in high-density electroencephalographic data from 32 patients with chronic disorders of consciousness, against normative data from healthy controls. Based on connectivity within canonical frequency bands, we found that patient networks had reduced local and global efficiency, and fewer hubs in the alpha band. We devised a novel topographical metric, termed modular span, which showed that the alpha network modules in patients were also spatially circumscribed, lacking the structured long-distance interactions commonly observed in the healthy controls. Importantly however, these differences between graph-theoretic metrics were partially reversed in delta and theta band networks, which were also significantly more similar to each other in patients than controls. Going further, we found that metrics of alpha network efficiency also correlated with the degree of behavioural awareness. Intriguingly, some patients in behaviourally unresponsive vegetative states who demonstrated evidence of covert awareness with functional neuroimaging stood out from this trend: they had alpha networks that were remarkably well preserved and similar to those observed in the controls. Taken together, our findings inform current understanding of disorders of consciousness by highlighting the distinctive brain networks that characterise them. In the significant minority of vegetative patients who follow commands in neuroimaging tests, they point to putative network mechanisms that could support cognitive function and consciousness despite profound behavioural impairment.     

Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat

The number of different cortical structures in mammalian brains and the number of extrinsic fibres linking these regions are both large. As with any complex system, systematic analysis is required to draw reliable conclusions about the organization of the complex neural networks comprising these numerous elements. One aspect of organization that has long been suspected is that cortical networks are organized into 'streams' or 'systems'. Here we report computational analyses capable of showing whether clusters of strongly interconnected areas are aspects of the global organization of cortical systems in macaque and cat. We used two different approaches to analyse compilations of corticocortical connection data from the macaque and the cat. The first approach, optimal set analysis, employed an explicit definition of a neural 'system' or 'stream', which was based on differential connectivity. We defined a two-component cost function that described the cost of the global cluster arrangement of areas in terms of the areas' connectivity within and between candidate clusters. Optimal cluster arrangements of cortical areas were then selected computationally from the very many possible arrangements, using an evolutionary optimization algorithm. The second approach, non-parametric cluster analysis (NPCA), grouped cortical areas on the basis of their proximity in multidimensional scaling representations. We used non-metric multidimensional scaling to represent the cortical connectivity structures metrically in two and five dimensions. NPCA then analysed these representations to determine the nature of the clusters for a wide range of different cluster shape parameters. The results from both approaches largely agreed. They showed that macaque and cat cortices are organized into densely intra-connected clusters of areas, and identified the constituent members of the clusters. These clusters reflected functionally specialized sets of cortical areas, suggesting that structure and function are closely linked at this gross, systems level.     

Communication Efficiency and Congestion of Signal Traffic in Large-Scale Brain Networks

The complex connectivity of the cerebral cortex suggests that inter-regional communication is a primary function. Using computational modeling, we show that anatomical connectivity may be a major determinant for global information flow in brain networks. A macaque brain network was implemented as a communication network in which signal units flowed between grey matter nodes along white matter paths. Compared to degree-matched surrogate networks, information flow on the macaque brain network was characterized by higher loss rates, faster transit times and lower throughput, suggesting that neural connectivity may be optimized for speed rather than fidelity. Much of global communication was mediated by a “rich club” of hub regions: a sub-graph comprised of high-degree nodes that are more densely interconnected with each other than predicted by chance. First, macaque communication patterns most closely resembled those observed for a synthetic rich club network, but were less similar to those seen in a synthetic small world network, suggesting that the former is a more fundamental feature of brain network topology. Second, rich club regions attracted the most signal traffic and likewise, connections between rich club regions carried more traffic than connections between non-rich club regions. Third, a number of rich club regions were significantly under-congested, suggesting that macaque connectivity actively shapes information flow, funneling traffic towards some nodes and away from others. Together, our results indicate a critical role of the rich club of hub nodes in dynamic aspects of global brain communication.     

Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales

Recent studies have emphasized the importance of multiplex networks – interdependent networks with shared nodes and different types of connections – in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy – an information theoretic quantity that can be used to measure linear and nonlinear interactions – to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons (“hubs”) were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.     

Consensus between Pipelines in Structural Brain Networks

Structural brain networks may be reconstructed from diffusion MRI tractography data and have great potential to further our understanding of the topological organisation of brain structure in health and disease. Network reconstruction is complex and involves a series of processesing methods including anatomical parcellation, registration, fiber orientation estimation and whole-brain fiber tractography. Methodological choices at each stage can affect the anatomical accuracy and graph theoretical properties of the reconstructed networks, meaning applying different combinations in a network reconstruction pipeline may produce substantially different networks. Furthermore, the choice of which connections are considered important is unclear. In this study, we assessed the similarity between structural networks obtained using two independent state-of-the-art reconstruction pipelines. We aimed to quantify network similarity and identify the core connections emerging most robustly in both pipelines. Similarity of network connections was compared between pipelines employing different atlases by merging parcels to a common and equivalent node scale. We found a high agreement between the networks across a range of fiber density thresholds. In addition, we identified a robust core of highly connected regions coinciding with a peak in similarity across network density thresholds, and replicated these results with atlases at different node scales. The binary network properties of these core connections were similar between pipelines but showed some differences in atlases across node scales. This study demonstrates the utility of applying multiple structural network reconstrution pipelines to diffusion data in order to identify the most important connections for further study.     

On the Inference of Functional Circadian Networks Using Granger Causality

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals.     

Oscillatory synchronization in large-scale cortical networks predicts perception

Normal brain function requires the dynamic interaction of functionally specialized but widely distributed cortical regions. Long-range synchronization of oscillatory signals has been suggested to mediate these interactions within large-scale cortical networks, but direct evidence is sparse. Here we show that oscillatory synchronization is organized in such large-scale networks. We implemented an analysis approach that allows for imaging synchronized cortical networks and applied this technique to EEG recordings in humans. We identified two networks: beta-band synchronization (~20 Hz) in a fronto-parieto-occipital network and gamma-band synchronization (~80 Hz) in a centro-temporal network. Strong perceptual correlates support their functional relevance: the strength of synchronization within these networks predicted the subjects' perception of an ambiguous audiovisual stimulus as well as the integration of auditory and visual information. Our results provide evidence that oscillatory neuronal synchronization mediates neuronal communication within frequency-specific, large-scale cortical networks.