Large-Scale,High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures

Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30–80 Hz) and beta (12–30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100–1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.     

Cooperation prevails when individuals adjust their social ties

Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.     

Bursting Reverberation as a Multiscale Neuronal Network Process Driven by Synaptic Depression-Facilitation

Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5–30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation: in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2–5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.     

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.     

Homeostatic control of synaptic rewiring in recurrent networks induces the formation of stable memory engrams

Brain networks store new memories using functional and structural synaptic plasticity. Memory formation is generally attributed to Hebbian plasticity, while homeostatic plasticity is thought to have an ancillary role in stabilizing network dynamics. Here we report that homeostatic plasticity alone can also lead to the formation of stable memories. We analyze this phenomenon using a new theory of network remodeling, combined with numerical simulations of recurrent spiking neural networks that exhibit structural plasticity based on firing rate homeostasis. These networks are able to store repeatedly presented patterns and recall them upon the presentation of incomplete cues. Storage is fast, governed by the homeostatic drift. In contrast, forgetting is slow, driven by a diffusion process. Joint stimulation of neurons induces the growth of associative connections between them, leading to the formation of memory engrams. These memories are stored in a distributed fashion throughout connectivity matrix, and individual synaptic connections have only a small influence. Although memory-specific connections are increased in number, the total number of inputs and outputs of neurons undergo only small changes during stimulation. We find that homeostatic structural plasticity induces a specific type of “silent memories”, different from conventional attractor states.     

Modeling the Impact of Lesions in the Human Brain

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous (“resting-state”) neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions.     

Changes in Task-Related Functional Connectivity across Multiple Spatial Scales Are Related to Reading Performance

Reading requires the interaction of a distributed set of cortical areas whose distinct patterns give rise to a wide range of individual skill. However, the nature of these neural interactions and their relation to reading performance are still poorly understood. Functional connectivity analyses of fMRI data can be used to characterize the nature of interactivity of distributed brain networks, yet most previous studies have focused on connectivity during task-free (i.e., “resting state”) conditions. Here, we report new methods for assessing task-related functional connectivity using data-driven graph theoretical methods and describe how large-scale patterns of connectivity relate to individual variability in reading performance among children. We found that connectivity patterns of subjects performing a reading task could be decomposed hierarchically into multiple sub-networks, and we observed stronger long-range interaction between sub-networks in subjects with higher task accuracy. Additionally, we found a network of hub regions known to be critical to reading that displays increased short-range synchronization in higher accuracy subjects. These individual differences in task-related functional connectivity reveal that increased interaction between distant regions, coupled with selective local integration within key regions, is associated with better reading performance. Importantly, we show that task-related neuroimaging data contains far more information than usually extracted via standard univariate analyses – information that can meaningfully relate neural connectivity patterns to cognition and task.     

Deciphering clock cell network morphology within the biological master clock,suprachiasmatic nucleus: From the perspective of circadian wave dynamics

The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained ‘indegree distribution’ as well as a ‘physical range distribution of afferent clock cells.’ Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced “phase-singularities.” The successful, realistic networks have several common features: 1) “indegree” and “outdegree” should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN.     

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.     

Revisiting Date and Party Hubs: Novel Approaches to Role Assignment in Protein Interaction Networks

The idea of “date” and “party” hubs has been influential in the study of protein–protein interaction networks. Date hubs display low co-expression with their partners, whilst party hubs have high co-expression. It was proposed that party hubs are local coordinators whereas date hubs are global connectors. Here, we show that the reported importance of date hubs to network connectivity can in fact be attributed to a tiny subset of them. Crucially, these few, extremely central, hubs do not display particularly low expression correlation, undermining the idea of a link between this quantity and hub function. The date/party distinction was originally motivated by an approximately bimodal distribution of hub co-expression; we show that this feature is not always robust to methodological changes. Additionally, topological properties of hubs do not in general correlate with co-expression. However, we find significant correlations between interaction centrality and the functional similarity of the interacting proteins. We suggest that thinking in terms of a date/party dichotomy for hubs in protein interaction networks is not meaningful, and it might be more useful to conceive of roles for protein-protein interactions rather than for individual proteins.     

Is the Excessive Use of Microblogs an Internet Addiction? Developing a Scale for Assessing the Excessive Use of Microblogs in Chinese College Students

More and more college students are using microblogs, with some excessive users demonstrating addiction-like symptoms. However, there is currently no published scale available for use in assessing excessive use of these microblogs, a significant impediment to advancing this area of research. We collected data from 3,047 college students in China and developed a Microblog Excessive Use Scale (MEUS) for Chinese college students, comparing it with criteria used for assessing Internet addiction. Our diagnostic scale featured three factors, two of which–“withdrawal and health problem” and “time management and performance”–are already included in Internet addiction assessment scales. The third factor, “social comfort,” does not appear in Internet addiction assessment scales. Our study found that females have significantly higher MEUS scores than males, and that total MEUS scores positively correlated with scores from “self-disclosure” and “real social interaction” scales. These findings differ from results obtained in previous investigations into Internet addiction. Our results indicate that some characteristics of the excessive use of microblogs are different to those of Internet addiction, suggesting that microblog overuse may not correspond exactly to the state of Internet addiction.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Extracting Multiscale Pattern Information of fMRI Based Functional Brain Connectivity with Application on Classification of Autism Spectrum Disorders

We employed a multi-scale clustering methodology known as “data cloud geometry” to extract functional connectivity patterns derived from functional magnetic resonance imaging (fMRI) protocol. The method was applied to correlation matrices of 106 regions of interest (ROIs) in 29 individuals with autism spectrum disorders (ASD), and 29 individuals with typical development (TD) while they completed a cognitive control task. Connectivity clustering geometry was examined at both “fine” and “coarse” scales. At the coarse scale, the connectivity clustering geometry produced 10 valid clusters with a coherent relationship to neural anatomy. A supervised learning algorithm employed fine scale information about clustering motif configurations and prevalence, and coarse scale information about intra- and inter-regional connectivity; the algorithm correctly classified ASD and TD participants with sensitivity of and specificity of . Most of the predictive power of the logistic regression model resided at the level of the fine-scale clustering geometry, suggesting that cellular versus systems level disturbances are more prominent in individuals with ASD. This article provides validation for this multi-scale geometric approach to extracting brain functional connectivity pattern information and for its use in classification of ASD.     

Functional Brain Networks: Random, “Small World” or Deterministic?

Lately the problem of connectivity in brain networks is being approached frequently by graph theoretical analysis. In several publications based on bivariate estimators of relations between EEG channels authors reported random or “small world” structure of networks. The results of these works often have no relation to other evidence based on imaging, inverse solutions methods, physiological and anatomical data. Herein we try to find reasons for this discrepancy. We point out that EEG signals are very much interdependent, thus bivariate measures applied to them may produce many spurious connections. In fact, they may outnumber the true connections. Giving all connections equal weights, as it is usual in the framework of graph theoretical analysis, further enhances these spurious links. In effect, close to random and disorganized patterns of connections emerge. On the other hand, multivariate connectivity estimators, which are free of the artificial links, show specific, well determined patterns, which are in a very good agreement with other evidence. The modular structure of brain networks may be identified by multivariate estimators based on Granger causality and formalism of assortative mixing. In this way, the strength of coupling may be evaluated quantitatively. During working memory task, by means of multivariate Directed Transfer Function, it was demonstrated that the modules characterized by strong internal bonds exchange the information by weaker connections.     

Molecular basis for evolving modularity in the yeast protein interaction network

Scale-free networks are generically defined by a power-law distribution of node connectivities. Vastly different graph topologies fit this law, ranging from the assortative, with frequent similar-degree node connections, to a modular structure. Using a metric to determine the extent of modularity, we examined the yeast protein network and found it to be significantly self-dissimilar. By orthologous node categorization, we established the evolutionary trend in the network, from an “emerging” assortative network to a present-day modular topology. The evolving topology fits a generic connectivity distribution but with a progressive enrichment in intramodule hubs that avoid each other. Primeval tolerance to random node failure is shown to evolve toward resilience to hub failure, thus removing the fragility often ascribed to scale-free networks. This trend is algorithmically reproduced by adopting a connectivity accretion law that disfavors like-degree connections for large-degree nodes. The selective advantage of this trend relates to the need to prevent a failed hub from inducing failure in an adjacent hub. The molecular basis for the evolutionary trend is likely rooted in the high-entropy penalty entailed in the association of two intramodular hubs.     

Noise during rest enables the exploration of the brain's dynamic repertoire

Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1–100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space–time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.     

Explicating the Face Perception Network with White Matter Connectivity

A network of multiple brain regions is recruited in face perception. Our understanding of the functional properties of this network can be facilitated by explicating the structural white matter connections that exist between its functional nodes. We accomplished this using functional MRI (fMRI) in combination with fiber tractography on high angular resolution diffusion weighted imaging data. We identified the three nodes of the core face network: the “occipital face area” (OFA), the “fusiform face area” (mid-fusiform gyrus or mFus), and the superior temporal sulcus (STS). Additionally, a region of the anterior temporal lobe (aIT), implicated as being important for face perception was identified. Our data suggest that we can further divide the OFA into multiple anatomically distinct clusters – a partitioning consistent with several recent neuroimaging results. More generally, structural white matter connectivity within this network revealed: 1) Connectivity between aIT and mFus, and between aIT and occipital regions, consistent with studies implicating this posterior to anterior pathway as critical to normal face processing; 2) Strong connectivity between mFus and each of the occipital face-selective regions, suggesting that these three areas may subserve different functional roles; 3) Almost no connectivity between STS and mFus, or between STS and the other face-selective regions. Overall, our findings suggest a re-evaluation of the “core” face network with respect to what functional areas are or are not included in this network.     

How to record a million synaptic weights in a hippocampal slice

A key step toward understanding the function of a brain circuit is to find its wiring diagram. New methods for optical stimulation and optical recording of neurons make it possible to map circuit connectivity on a very large scale. However, single synapses produce small responses that are difficult to measure on a large scale. Here I analyze how single synaptic responses may be detectable using relatively coarse readouts such as optical recording of somatic calcium. I model a network consisting of 10,000 input axons and 100 CA1 pyramidal neurons, each represented using 19 compartments with voltage-gated channels and calcium dynamics. As single synaptic inputs cannot produce a measurable somatic calcium response, I stimulate many inputs as a baseline to elicit somatic action potentials leading to a strong calcium signal. I compare statistics of responses with or without a single axonal input riding on this baseline. Through simulations I show that a single additional input shifts the distribution of the number of output action potentials. Stochastic resonance due to probabilistic synaptic release makes this shift easier to detect. With ~80 stimulus repetitions this approach can resolve up to 35% of individual activated synapses even in the presence of 20% recording noise. While the technique is applicable using conventional electrical stimulation and extracellular recording, optical methods promise much greater scaling, since the number of synapses scales as the product of the number of inputs and outputs. I extrapolate from current high-speed optical stimulation and recording methods, and show that this approach may scale up to the order of a million synapses in a single two-hour slice-recording experiment.