Development of Large-Scale Functional Brain Networks in Children

The ontogeny of large-scale functional organization of the human brain is not well understood. Here we use network analysis of intrinsic functional connectivity to characterize the organization of brain networks in 23 children (ages 7–9 y) and 22 young-adults (ages 19–22 y). Comparison of network properties, including path-length, clustering-coefficient, hierarchy, and regional connectivity, revealed that although children and young-adults' brains have similar “small-world” organization at the global level, they differ significantly in hierarchical organization and interregional connectivity. We found that subcortical areas were more strongly connected with primary sensory, association, and paralimbic areas in children, whereas young-adults showed stronger cortico-cortical connectivity between paralimbic, limbic, and association areas. Further, combined analysis of functional connectivity with wiring distance measures derived from white-matter fiber tracking revealed that the development of large-scale brain networks is characterized by weakening of short-range functional connectivity and strengthening of long-range functional connectivity. Importantly, our findings show that the dynamic process of over-connectivity followed by pruning, which rewires connectivity at the neuronal level, also operates at the systems level, helping to reconfigure and rebalance subcortical and paralimbic connectivity in the developing brain. Our study demonstrates the usefulness of network analysis of brain connectivity to elucidate key principles underlying functional brain maturation, paving the way for novel studies of disrupted brain connectivity in neurodevelopmental disorders such as autism.     

State-Related Changes in MEG Functional Connectivity Reveal the Task-Positive Sensorimotor Network

Functional connectivity measures applied to magnetoencephalography (MEG) data have the capacity to elucidate neuronal networks. However, the task-related modulation of these measures is essential to identifying the functional relevance of the identified network. In this study, we provide evidence for the efficacy of measuring “state-related” (i.e., task vs. rest) changes in MEG functional connectivity for revealing a sensorimotor network. We investigate changes in functional connectivity, measured as cortico-cortical coherence (CCC), between rest blocks and the performance of a visually directed motor task in a healthy cohort. Task-positive changes in CCC were interpreted in the context of any concomitant modulations in spectral power. Task-related increases in whole-head CCC relative to the resting state were identified between areas established as part of the sensorimotor network as well as frontal eye fields and prefrontal cortices, predominantly in the beta and gamma frequency bands. This study provides evidence for the use of MEG to identify task-specific functionally connected sensorimotor networks in a non-invasive, patient friendly manner.     

Emergence of Assortative Mixing between Clusters of Cultured Neurons

The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous self-sustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters'' activations within the bursts allows the reconstruction of the directed functional connectivity of the network. We propose a method to statistically infer this connectivity and analyze the resulting properties of the associated complex networks. Surprisingly enough, in contrast to what has been reported for many biological networks, the clustered neuronal cultures present assortative mixing connectivity values, meaning that there is a preference for clusters to link to other clusters that share similar functional connectivity, as well as a rich-club core, which shapes a ‘connectivity backbone’ in the network. These results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture.     

The Default Mode Network and the Working Memory Network Are Not Anti-Correlated during All Phases of a Working Memory Task

Introduction

The default mode network and the working memory network are known to be anti-correlated during sustained cognitive processing, in a load-dependent manner. We hypothesized that functional connectivity among nodes of the two networks could be dynamically modulated by task phases across time.

Methods

To address the dynamic links between default mode network and the working memory network, we used a delayed visuo-spatial working memory paradigm, which allowed us to separate three different phases of working memory (encoding, maintenance, and retrieval), and analyzed the functional connectivity during each phase within and between the default mode network and the working memory network networks.

Results

We found that the two networks are anti-correlated only during the maintenance phase of working memory, i.e. when attention is focused on a memorized stimulus in the absence of external input. Conversely, during the encoding and retrieval phases, when the external stimulation is present, the default mode network is positively coupled with the working memory network, suggesting the existence of a dynamically switching of functional connectivity between “task-positive” and “task-negative” brain networks.

Conclusions

Our results demonstrate that the well-established dichotomy of the human brain (anti-correlated networks during rest and balanced activation-deactivation during cognition) has a more nuanced organization than previously thought and engages in different patterns of correlation and anti-correlation during specific sub-phases of a cognitive task. This nuanced organization reinforces the hypothesis of a direct involvement of the default mode network in cognitive functions, as represented by a dynamic rather than static interaction with specific task-positive networks, such as the working memory network.     

Stochastic Blockmodeling of the Modules and Core of the Caenorhabditis elegans Connectome

Recently, there has been much interest in the community structure or mesoscale organization of complex networks. This structure is characterised either as a set of sparsely inter-connected modules or as a highly connected core with a sparsely connected periphery. However, it is often difficult to disambiguate these two types of mesoscale structure or, indeed, to summarise the full network in terms of the relationships between its mesoscale constituents. Here, we estimate a community structure with a stochastic blockmodel approach, the Erdős-Rényi Mixture Model, and compare it to the much more widely used deterministic methods, such as the Louvain and Spectral algorithms. We used the Caenorhabditis elegans (C. elegans) nervous system (connectome) as a model system in which biological knowledge about each node or neuron can be used to validate the functional relevance of the communities obtained. The deterministic algorithms derived communities with 4–5 modules, defined by sparse inter-connectivity between all modules. In contrast, the stochastic Erdős-Rényi Mixture Model estimated a community with 9 blocks or groups which comprised a similar set of modules but also included a clearly defined core, made of 2 small groups. We show that the “core-in-modules” decomposition of the worm brain network, estimated by the Erdős-Rényi Mixture Model, is more compatible with prior biological knowledge about the C. elegans nervous system than the purely modular decomposition defined deterministically. We also show that the blockmodel can be used both to generate stochastic realisations (simulations) of the biological connectome, and to compress network into a small number of super-nodes and their connectivity. We expect that the Erdős-Rényi Mixture Model may be useful for investigating the complex community structures in other (nervous) systems.     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network

The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.     

Efficiency and cost of economical brain functional networks

Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old (N = 11; mean age = 66.5 years) and healthy young (N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or “resting” state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06–0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties—supporting efficient parallel information transfer at relatively low cost—which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.     

A Family of Algorithms for Computing Consensus about Node State from Network Data

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node''s state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node''s direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms'' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.     

Evidence for Anomalous Network Connectivity during Working Memory Encoding in Schizophrenia: An ICA Based Analysis

Background

Numerous neuroimaging studies report abnormal regional brain activity during working memory performance in schizophrenia, but few have examined brain network integration as determined by “functional connectivity” analyses.

Methodology/Principal Findings

We used independent component analysis (ICA) to identify and characterize dysfunctional spatiotemporal networks in schizophrenia engaged during the different stages (encoding and recognition) of a Sternberg working memory fMRI paradigm. 37 chronic schizophrenia and 54 healthy age/gender-matched participants performed a modified Sternberg Item Recognition fMRI task. Time series images preprocessed with SPM2 were analyzed using ICA. Schizophrenia patients showed relatively less engagement of several distinct “normal” encoding-related working memory networks compared to controls. These encoding networks comprised 1) left posterior parietal-left dorsal/ventrolateral prefrontal cortex, cingulate, basal ganglia, 2) right posterior parietal, right dorsolateral prefrontal cortex and 3) default mode network. In addition, the left fronto-parietal network demonstrated a load-dependent functional response during encoding. Network engagement that differed between groups during recognition comprised the posterior cingulate, cuneus and hippocampus/parahippocampus. As expected, working memory task accuracy differed between groups (p<0.0001) and was associated with degree of network engagement. Functional connectivity within all three encoding-associated functional networks correlated significantly with task accuracy, which further underscores the relevance of abnormal network integration to well-described schizophrenia working memory impairment. No network was significantly associated with task accuracy during the recognition phase.

Conclusions/Significance

This study extends the results of numerous previous schizophrenia studies that identified isolated dysfunctional brain regions by providing evidence of disrupted schizophrenia functional connectivity using ICA within widely-distributed neural networks engaged for working memory cognition.     

Structural Synaptic Plasticity Has High Memory Capacity and Can Explain Graded Amnesia,Catastrophic Forgetting,and the Spacing Effect

Although already William James and, more explicitly, Donald Hebb''s theory of cell assemblies have suggested that activity-dependent rewiring of neuronal networks is the substrate of learning and memory, over the last six decades most theoretical work on memory has focused on plasticity of existing synapses in prewired networks. Research in the last decade has emphasized that structural modification of synaptic connectivity is common in the adult brain and tightly correlated with learning and memory. Here we present a parsimonious computational model for learning by structural plasticity. The basic modeling units are “potential synapses” defined as locations in the network where synapses can potentially grow to connect two neurons. This model generalizes well-known previous models for associative learning based on weight plasticity. Therefore, existing theory can be applied to analyze how many memories and how much information structural plasticity can store in a synapse. Surprisingly, we find that structural plasticity largely outperforms weight plasticity and can achieve a much higher storage capacity per synapse. The effect of structural plasticity on the structure of sparsely connected networks is quite intuitive: Structural plasticity increases the “effectual network connectivity”, that is, the network wiring that specifically supports storage and recall of the memories. Further, this model of structural plasticity produces gradients of effectual connectivity in the course of learning, thereby explaining various cognitive phenomena including graded amnesia, catastrophic forgetting, and the spacing effect.     

Widespread Disruption of Functional Brain Organization in Early-Onset Alzheimer’s Disease

Early-onset Alzheimer’s disease (AD) patients present a different clinical profile than late-onset AD patients. This can be partially explained by cortical atrophy, although brain organization might provide more insight. The aim of this study was to examine functional connectivity in early-onset and late-onset AD patients. Resting-state fMRI scans of 20 early-onset (<65 years old), 28 late-onset (≥65 years old) AD patients and 15 “young” (<65 years old) and 31 “old” (≥65 years old) age-matched controls were available. Resting-state network-masks were used to create subject-specific maps. Group differences were examined using a non-parametric permutation test, accounting for gray-matter. Performance on five cognitive domains were used in a correlation analysis with functional connectivity in AD patients. Functional connectivity was not different in any of the RSNs when comparing the two control groups (young vs. old controls), which implies that there is no general effect of aging on functional connectivity. Functional connectivity in early-onset AD was lower in all networks compared to age-matched controls, where late-onset AD showed lower functional connectivity in the default-mode network. Functional connectivity was lower in early-onset compared to late-onset AD in auditory-, sensory-motor, dorsal-visual systems and the default mode network. Across patients, an association of functional connectivity of the default mode network was found with visuoconstruction. Functional connectivity of the right dorsal visual system was associated with attention across patients. In late-onset AD patients alone, higher functional connectivity of the sensory-motor system was associated with poorer memory performance. Functional brain organization was more widely disrupted in early-onset AD when compared to late-onset AD. This could possibly explain different clinical profiles, although more research into the relationship of functional connectivity and cognitive performance is needed.     

Efficient "Shotgun" Inference of Neural Connectivity from Highly Sub-sampled Activity Data

Inferring connectivity in neuronal networks remains a key challenge in statistical neuroscience. The “common input” problem presents a major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons versus correlations induced by common input from unobserved neurons. Available techniques allow us to simultaneously record, with sufficient temporal resolution, only a small fraction of the network. Consequently, naive connectivity estimators that neglect these common input effects are highly biased. This work proposes a “shotgun” experimental design, in which we observe multiple sub-networks briefly, in a serial manner. Thus, while the full network cannot be observed simultaneously at any given time, we may be able to observe much larger subsets of the network over the course of the entire experiment, thus ameliorating the common input problem. Using a generalized linear model for a spiking recurrent neural network, we develop a scalable approximate expected loglikelihood-based Bayesian method to perform network inference given this type of data, in which only a small fraction of the network is observed in each time bin. We demonstrate in simulation that the shotgun experimental design can eliminate the biases induced by common input effects. Networks with thousands of neurons, in which only a small fraction of the neurons is observed in each time bin, can be quickly and accurately estimated, achieving orders of magnitude speed up over previous approaches.     

Exploring the Morphospace of Communication Efficiency in Complex Networks

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system''s dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.     

Dense Percolation in Large-Scale Mean-Field Random Networks Is Provably “Explosive”

Recent reports suggest that evolving large-scale networks exhibit “explosive percolation”: a large fraction of nodes suddenly becomes connected when sufficiently many links have formed in a network. This phase transition has been shown to be continuous (second-order) for most random network formation processes, including classical mean-field random networks and their modifications. We study a related yet different phenomenon referred to as dense percolation, which occurs when a network is already connected, but a large group of nodes must be dense enough, i.e., have at least a certain minimum required percentage of possible links, to form a “highly connected” cluster. Such clusters have been considered in various contexts, including the recently introduced network modularity principle in biological networks. We prove that, contrary to the traditionally defined percolation transition, dense percolation transition is discontinuous (first-order) under the classical mean-field network formation process (with no modifications); therefore, there is not only quantitative, but also qualitative difference between regular and dense percolation transitions. Moreover, the size of the largest dense (highly connected) cluster in a mean-field random network is explicitly characterized by rigorously proven tight asymptotic bounds, which turn out to naturally extend the previously derived formula for the size of the largest clique (a cluster with all possible links) in such a network. We also briefly discuss possible implications of the obtained mathematical results on studying first-order phase transitions in real-world linked systems.     

Avalanches in a Stochastic Model of Spiking Neurons

Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly to changes in input. Thus, the appearance of avalanches in such functionally feedforward networks indicates that avalanches may be a simple consequence of a widely present network structure, when neuron dynamics are noisy. An important implication is that a network need not be “critical” for the production of avalanches, so experimentally observed power laws in burst size may be a signature of noisy functionally feedforward structure rather than of, for example, self-organized criticality.     

Identifying Corridors among Large Protected Areas in the United States

Conservation scientists emphasize the importance of maintaining a connected network of protected areas to prevent ecosystems and populations from becoming isolated, reduce the risk of extinction, and ultimately sustain biodiversity. Keeping protected areas connected in a network is increasingly recognized as a conservation priority in the current era of rapid climate change. Models that identify suitable linkages between core areas have been used to prioritize potentially important corridors for maintaining functional connectivity. Here, we identify the most “natural” (i.e., least human-modified) corridors between large protected areas in the contiguous Unites States. We aggregated results from multiple connectivity models to develop a composite map of corridors reflecting agreement of models run under different assumptions about how human modification of land may influence connectivity. To identify which land units are most important for sustaining structural connectivity, we used the composite map of corridors to evaluate connectivity priorities in two ways: (1) among land units outside of our pool of large core protected areas and (2) among units administratively protected as Inventoried Roadless (IRAs) or Wilderness Study Areas (WSAs). Corridor values varied substantially among classes of “unprotected” non-core land units, and land units of high connectivity value and priority represent diverse ownerships and existing levels of protections. We provide a ranking of IRAs and WSAs that should be prioritized for additional protection to maintain minimal human modification. Our results provide a coarse-scale assessment of connectivity priorities for maintaining a connected network of protected areas.     

Not all scale-free networks are born equal: the role of the seed graph in PPI network evolution

The (asymptotic) degree distributions of the best-known “scale-free” network models are all similar and are independent of the seed graph used; hence, it has been tempting to assume that networks generated by these models are generally similar. In this paper, we observe that several key topological features of such networks depend heavily on the specific model and the seed graph used. Furthermore, we show that starting with the “right” seed graph (typically a dense subgraph of the protein–protein interaction network analyzed), the duplication model captures many topological features of publicly available protein–protein interaction networks very well.