Evaluation of the Performance of Information Theory-Based Methods and Cross-Correlation to Estimate the Functional Connectivity in Cortical Networks

Functional connectivity of in vitro neuronal networks was estimated by applying different statistical algorithms on data collected by Micro-Electrode Arrays (MEAs). First we tested these “connectivity methods” on neuronal network models at an increasing level of complexity and evaluated the performance in terms of ROC (Receiver Operating Characteristic) and PPC (Positive Precision Curve), a new defined complementary method specifically developed for functional links identification. Then, the algorithms better estimated the actual connectivity of the network models, were used to extract functional connectivity from cultured cortical networks coupled to MEAs. Among the proposed approaches, Transfer Entropy and Joint-Entropy showed the best results suggesting those methods as good candidates to extract functional links in actual neuronal networks from multi-site recordings.     

Emergence of a small-world functional network in cultured neurons

The functional networks of cultured neurons exhibit complex network properties similar to those found in vivo. Starting from random seeding, cultures undergo significant reorganization during the initial period in vitro, yet despite providing an ideal platform for observing developmental changes in neuronal connectivity, little is known about how a complex functional network evolves from isolated neurons. In the present study, evolution of functional connectivity was estimated from correlations of spontaneous activity. Network properties were quantified using complex measures from graph theory and used to compare cultures at different stages of development during the first 5 weeks in vitro. Networks obtained from young cultures (14 days in vitro) exhibited a random topology, which evolved to a small-world topology during maturation. The topology change was accompanied by an increased presence of highly connected areas (hubs) and network efficiency increased with age. The small-world topology balances integration of network areas with segregation of specialized processing units. The emergence of such network structure in cultured neurons, despite a lack of external input, points to complex intrinsic biological mechanisms. Moreover, the functional network of cultures at mature ages is efficient and highly suited to complex processing tasks.     

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.     

Time-Dependent Increase in Network Response to Stimulation

In vitro neuronal cultures have become a popular method with which to probe network-level neuronal dynamics and phenomena in controlled laboratory settings. One of the key dynamics of interest in these in vitro studies has been the extent to which cultured networks display properties indicative of learning. Here we demonstrate the effects of a high frequency electrical stimulation signal in training cultured networks of cortical neurons. Networks receiving this training signal displayed a time-dependent increase in the response to a low frequency probing stimulation, particularly in the time window of 20–50 ms after stimulation. This increase was found to be statistically significant as compared to control networks that did not receive training. The timing of this increase suggests potentiation of synaptic mechanisms. To further investigate this possibility, we leveraged the powerful Cox statistical connectivity method as previously investigated by our group. This method was used to identify and track changes in network connectivity strength.     

Innate synchronous oscillations in freely-organized small neuronal circuits

Background

Information processing in neuronal networks relies on the network''s ability to generate temporal patterns of action potentials. Although the nature of neuronal network activity has been intensively investigated in the past several decades at the individual neuron level, the underlying principles of the collective network activity, such as the synchronization and coordination between neurons, are largely unknown. Here we focus on isolated neuronal clusters in culture and address the following simple, yet fundamental questions: What is the minimal number of cells needed to exhibit collective dynamics? What are the internal temporal characteristics of such dynamics and how do the temporal features of network activity alternate upon crossover from minimal networks to large networks?

Methodology/Principal Findings

We used network engineering techniques to induce self-organization of cultured networks into neuronal clusters of different sizes. We found that small clusters made of as few as 40 cells already exhibit spontaneous collective events characterized by innate synchronous network oscillations in the range of 25 to 100 Hz. The oscillation frequency of each network appeared to be independent of cluster size. The duration and rate of the network events scale with cluster size but converge to that of large uniform networks. Finally, the investigation of two coupled clusters revealed clear activity propagation with master/slave asymmetry.

Conclusions/Significance

The nature of the activity patterns observed in small networks, namely the consistent emergence of similar activity across networks of different size and morphology, suggests that neuronal clusters self-regulate their activity to sustain network bursts with internal oscillatory features. We therefore suggest that clusters of as few as tens of cells can serve as a minimal but sufficient functional network, capable of sustaining oscillatory activity. Interestingly, the frequencies of these oscillations are similar those observed in vivo.     

Control of Neuronal Network in Caenorhabditis elegans

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

Altered Network Communication Following a Neuroprotective Drug Treatment

Preconditioning is defined as a range of stimuli that allow cells to withstand subsequent anaerobic and other deleterious conditions. While cell protection under preconditioning is well established, this paper investigates the influence of neuroprotective preconditioning drugs, 4-aminopyridine and bicuculline (4-AP/bic), on synaptic communication across a broad network of in vitro rat cortical neurons. Using a permutation test, we evaluated cross-correlations of extracellular spiking activity across all pairs of recording electrodes on a 64-channel multielectrode array. The resulting functional connectivity maps were analyzed in terms of their graph-theoretic properties. A small-world effect was found, characterized by a functional network with high clustering coefficient and short average path length. Twenty-four hours after exposure to 4-AP/bic, small-world properties were comparable to control cultures that were not treated with the drug. Four hours following drug washout, however, the density of functional connections increased, while path length decreased and clustering coefficient increased. These alterations in functional connectivity were maintained at four days post-washout, suggesting that 4-AP/bic preconditioning leads to long-term effects on functional networks of cortical neurons. Because of their influence on communication efficiency in neuronal networks, alterations in small-world properties hold implications for information processing in brain systems. The observed relationship between density, path length, and clustering coefficient is captured by a phenomenological model where connections are added randomly within a spatially-embedded network. Taken together, results provide information regarding functional consequences of drug therapies that are overlooked in traditional viability studies and present the first investigation of functional networks under neuroprotective preconditioning.     

Towards Neuronal Organoids: A Method for Long-Term Culturing of High-Density Hippocampal Neurons

One of the goals in neuroscience is to obtain tractable laboratory cultures that closely recapitulate in vivo systems while still providing ease of use in the lab. Because neurons can exist in the body over a lifetime, long-term culture systems are necessary so as to closely mimic the physiological conditions under laboratory culture conditions. Ideally, such a neuronal organoid culture would contain multiple cell types, be highly differentiated, and have a high density of interconnected cells. However, before these types of cultures can be created, certain problems associated with long-term neuronal culturing must be addressed. We sought to develop a new protocol which may further prolong the duration and integrity of E18 rat hippocampal cultures. We have developed a protocol that allows for culturing of E18 hippocampal neurons at high densities for more than 120 days. These cultured hippocampal neurons are (i) well differentiated with high numbers of synapses, (ii) anchored securely to their substrate, (iii) have high levels of functional connectivity, and (iv) form dense multi-layered cellular networks. We propose that our culture methodology is likely to be effective for multiple neuronal subtypes–particularly those that can be grown in Neurobasal/B27 media. This methodology presents new avenues for long-term functional studies in neurons.     

Altered Cortico-Striatal Connectivity in Offspring of Schizophrenia Patients Relative to Offspring of Bipolar Patients and Controls

Schizophrenia (SZ) and bipolar disorder (BD) share clinical features, genetic risk factors and neuroimaging abnormalities. There is evidence of disrupted connectivity in resting state networks in patients with SZ and BD and their unaffected relatives. Resting state networks are known to undergo reorganization during youth coinciding with the period of increased incidence for both disorders. We therefore focused on characterizing resting state network connectivity in youth at familial risk for SZ or BD to identify alterations arising during this period. We measured resting-state functional connectivity in a sample of 106 youth, aged 7–19 years, comprising offspring of patients with SZ (N = 27), offspring of patients with BD (N = 39) and offspring of community control parents (N = 40). We used Independent Component Analysis to assess functional connectivity within the default mode, executive control, salience and basal ganglia networks and define their relationship to grey matter volume, clinical and cognitive measures. There was no difference in connectivity within any of the networks examined between offspring of patients with BD and offspring of community controls. In contrast, offspring of patients with SZ showed reduced connectivity within the left basal ganglia network compared to control offspring, and they showed a positive correlation between connectivity in this network and grey matter volume in the left caudate. Our findings suggest that dysconnectivity in the basal ganglia network is a robust correlate of familial risk for SZ and can be detected during childhood and adolescence.     

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.     

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.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

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.     

Emergent functional properties of neuronal networks with controlled topology

The interplay between anatomical connectivity and dynamics in neural networks plays a key role in the functional properties of the brain and in the associated connectivity changes induced by neural diseases. However, a detailed experimental investigation of this interplay at both cellular and population scales in the living brain is limited by accessibility. Alternatively, to investigate the basic operational principles with morphological, electrophysiological and computational methods, the activity emerging from large in vitro networks of primary neurons organized with imposed topologies can be studied. Here, we validated the use of a new bio-printing approach, which effectively maintains the topology of hippocampal cultures in vitro and investigated, by patch-clamp and MEA electrophysiology, the emerging functional properties of these grid-confined networks. In spite of differences in the organization of physical connectivity, our bio-patterned grid networks retained the key properties of synaptic transmission, short-term plasticity and overall network activity with respect to random networks. Interestingly, the imposed grid topology resulted in a reinforcement of functional connections along orthogonal directions, shorter connectivity links and a greatly increased spiking probability in response to focal stimulation. These results clearly demonstrate that reliable functional studies can nowadays be performed on large neuronal networks in the presence of sustained changes in the physical network connectivity.     

Effective Connectivity of Depth-Structure–Selective Patches in the Lateral Bank of the Macaque Intraparietal Sulcus

Extrastriate cortical areas are frequently composed of subpopulations of neurons encoding specific features or stimuli, such as color, disparity, or faces, and patches of neurons encoding similar stimulus properties are typically embedded in interconnected networks, such as the attention or face-processing network. The goal of the current study was to examine the effective connectivity of subsectors of neurons in the same cortical area with highly similar neuronal response properties. We first recorded single- and multi-unit activity to identify two neuronal patches in the anterior part of the macaque intraparietal sulcus (IPS) showing the same depth structure selectivity and then employed electrical microstimulation during functional magnetic resonance imaging in these patches to determine the effective connectivity of these patches. The two IPS subsectors we identified—with the same neuronal response properties and in some cases separated by only 3 mm—were effectively connected to remarkably distinct cortical networks in both dorsal and ventral stream in three macaques. Conversely, the differences in effective connectivity could account for the known visual-to-motor gradient within the anterior IPS. These results clarify the role of the anterior IPS as a pivotal brain region where dorsal and ventral visual stream interact during object analysis. Thus, in addition to the anatomical connectivity of cortical areas and the properties of individual neurons in these areas, the effective connectivity provides novel key insights into the widespread functional networks that support behavior.     

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.     

Neural and social correlates of attitudinal brokerage: using the complete social networks of two entire villages

To avoid polarization and maintain small-worldness in society, people who act as attitudinal brokers are critical. These people maintain social ties with people who have dissimilar and even incompatible attitudes. Based on resting-state functional magnetic resonance imaging (n = 139) and the complete social networks from two Korean villages (n = 1508), we investigated the individual-level neural capacity and social-level structural opportunity for attitudinal brokerage regarding gender role attitudes. First, using a connectome-based predictive model, we successfully identified the brain functional connectivity that predicts attitudinal diversity of respondents'' social network members. Brain regions that contributed most to the prediction included mentalizing regions known to be recruited in reading and understanding others’ belief states. This result was corroborated by leave-one-out cross-validation, fivefold cross-validation and external validation where the brain connectivity identified in one village was used to predict the attitudinal diversity in another independent village. Second, the association between functional connectivity and attitudinal diversity of social network members was contingent on a specific position in a social network, namely, the structural brokerage position where people have ties with two people who are not otherwise connected.     

Preparation of Neuronal Co-cultures with Single Cell Precision

Microfluidic embodiments of the Campenot chamber have attracted great interest from the neuroscience community. These interconnected co-culture platforms can be used to investigate a variety of questions, spanning developmental and functional neurobiology to infection and disease propagation. However, conventional systems require significant cellular inputs (many thousands per compartment), inadequate for studying low abundance cells, such as primary dopaminergic substantia nigra, spiral ganglia, and Drosophilia melanogaster neurons, and impractical for high throughput experimentation. The dense cultures are also highly locally entangled, with few outgrowths (<10%) interconnecting the two cultures. In this paper straightforward microfluidic and patterning protocols are described which address these challenges: (i) a microfluidic single neuron arraying method, and (ii) a water masking method for plasma patterning biomaterial coatings to register neurons and promote outgrowth between compartments. Minimalistic neuronal co-cultures were prepared with high-level (>85%) intercompartment connectivity and can be used for high throughput neurobiology experiments with single cell precision.     

Functional integration of grafted neural stem cell-derived dopaminergic neurons monitored by optogenetics in an in vitro Parkinson model

Intrastriatal grafts of stem cell-derived dopamine (DA) neurons induce behavioral recovery in animal models of Parkinson''s disease (PD), but how they functionally integrate in host neural circuitries is poorly understood. Here, Wnt5a-overexpressing neural stem cells derived from embryonic ventral mesencephalon of tyrosine hydroxylase-GFP transgenic mice were expanded as neurospheres and transplanted into organotypic cultures of wild type mouse striatum. Differentiated GFP-labeled DA neurons in the grafts exhibited mature neuronal properties, including spontaneous firing of action potentials, presence of post-synaptic currents, and functional expression of DA D₂ autoreceptors. These properties resembled those recorded from identical cells in acute slices of intrastriatal grafts in the 6-hydroxy-DA-induced mouse PD model and from DA neurons in intact substantia nigra. Optogenetic activation or inhibition of grafted cells and host neurons using channelrhodopsin-2 (ChR2) and halorhodopsin (NpHR), respectively, revealed complex, bi-directional synaptic interactions between grafted cells and host neurons and extensive synaptic connectivity within the graft. Our data demonstrate for the first time using optogenetics that ectopically grafted stem cell-derived DA neurons become functionally integrated in the DA-denervated striatum. Further optogenetic dissection of the synaptic wiring between grafted and host neurons will be crucial to clarify the cellular and synaptic mechanisms underlying behavioral recovery as well as adverse effects following stem cell-based DA cell replacement strategies in PD.     

Cultured Cortical Neurons Can Perform Blind Source Separation According to the Free-Energy Principle

Blind source separation is the computation underlying the cocktail party effect––a partygoer can distinguish a particular talker’s voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes’ principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico) demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle.