Emergence of assortative mixing between clusters of cultured neurons

Network Bursts in 3D Neuron Clusters Cultured on Microcontact-Printed Substrates

Microcontact printing (CP) is widely used to guide neurons to form 2D networks for neuroscience research. However, it is still difficult to establish 3D neuronal cultures on the CP substrate even though 3D neuronal structures are able to recapitulate critical aspects of native tissue. Here, we demonstrate that the reduced cell-substrate adhesion caused by the CP substrate could conveniently facilitate the aggregate formation of large-scale 3D neuron cluster networks. Furthermore, based on the quantitative analysis of the calcium activity of the resulting cluster networks, the effect of cell seeding density and local restriction of the CP substrate on network dynamics was investigated in detail. The results revealed that cell aggregation degree, rather than cell number, could take on the main role of the generation of synchronized network-wide calcium oscillation (network bursts) in the 3D neuron cluster networks. This finding may provide new insights for easy and cell-saving construction of in vitro 3D pathological models of epilepsy, and into deciphering the onset and evolution of network bursts in developmental nerve systems.

Modular architecture facilitates noise-driven control of synchrony in neuronal networks

High-level information processing in the mammalian cortex requires both segregated processing in specialized circuits and integration across multiple circuits. One possible way to implement these seemingly opposing demands is by flexibly switching between states with different levels of synchrony. However, the mechanisms behind the control of complex synchronization patterns in neuronal networks remain elusive. Here, we use precision neuroengineering to manipulate and stimulate networks of cortical neurons in vitro, in combination with an in silico model of spiking neurons and a mesoscopic model of stochastically coupled modules to show that (i) a modular architecture enhances the sensitivity of the network to noise delivered as external asynchronous stimulation and that (ii) the persistent depletion of synaptic resources in stimulated neurons is the underlying mechanism for this effect. Together, our results demonstrate that the inherent dynamical state in structured networks of excitable units is determined by both its modular architecture and the properties of the external inputs.

Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks

Numerous studies suggest that biological neuronal networks self-organize toward a critical state with stable recruitment dynamics. Individual neurons would then statistically activate exactly one further neuron during activity cascades termed neuronal avalanches. Yet, it is unclear if and how this can be reconciled with the explosive recruitment dynamics within neocortical minicolumns in vivo and within neuronal clusters in vitro, which indicates that neurons form supercritical local circuits. Theoretical studies propose that modular networks with a mix of regionally subcritical and supercritical dynamics would create apparently critical dynamics, resolving this inconsistency. Here, we provide experimental support by manipulating the structural self-organization process of networks of cultured rat cortical neurons (either sex). Consistent with the prediction, we show that increasing clustering in neuronal networks developing in vitro strongly correlates with avalanche size distributions transitioning from supercritical to subcritical activity dynamics. Avalanche size distributions approximated a power law in moderately clustered networks, indicating overall critical recruitment. We propose that activity-dependent self-organization can tune inherently supercritical networks toward mesoscale criticality by creating a modular structure in neuronal networks.SIGNIFICANCE STATEMENT Critical recruitment dynamics in neuronal networks are considered optimal for information processing in the brain. However, it remains heavily debated how neuronal networks would self-organize criticality by detailed fine-tuning of connectivity, inhibition, and excitability. We provide experimental support for theoretical considerations that modularity tunes critical recruitment dynamics at the mesoscale level of interacting neuron clusters. This reconciles reports of supercritical recruitment dynamics in local neuron clusters with findings on criticality sampled at mesoscopic network scales. Intriguingly, altered mesoscale organization is a prominent aspect of various neuropathological diseases currently investigated in the framework of criticality. We therefore believe that our findings would also be of interest for clinical scientists searching to link the functional and anatomic signatures of such brain disorders.

Neuronal Cultures: Exploring Biophysics, Complex Systems, and Medicine in a Dish

Neuronal cultures are one of the most important experimental models in modern interdisciplinary neuroscience, allowing to investigate in a control environment the emergence of complex behavior from an ensemble of interconnected neurons. Here, I review the research that we have conducted at the neurophysics laboratory at the University of Barcelona over the last 15 years, describing first the neuronal cultures that we prepare and the associated tools to acquire and analyze data, to next delve into the different research projects in which we actively participated to progress in the understanding of open questions, extend neuroscience research on new paradigms, and advance the treatment of neurological disorders. I finish the review by discussing the drawbacks and limitations of neuronal cultures, particularly in the context of brain-like models and biomedicine.

Long-term calcium imaging reveals functional development in hiPSC-derived cultures comparable to human but not rat primary cultures

Models for human brain-oriented research are often established on primary cultures from rodents, which fails to recapitulate cellular specificity and molecular cues of the human brain. Here we investigated whether neuronal cultures derived from human induced pluripotent stem cells (hiPSCs) feature key advantages compared with rodent primary cultures. Using calcium fluorescence imaging, we tracked spontaneous neuronal activity in hiPSC-derived, human, and rat primary cultures and compared their dynamic and functional behavior as they matured. We observed that hiPSC-derived cultures progressively changed upon development, exhibiting gradually richer activity patterns and functional traits. By contrast, rat primary cultures were locked in the same dynamic state since activity onset. Human primary cultures exhibited features in between hiPSC-derived and rat primary cultures, although traits from the former predominated. Our study demonstrates that hiPSC-derived cultures are excellent models to investigate development in neuronal assemblies, a hallmark for applications that monitor alterations caused by damage or neurodegeneration.

Dynamic and Functional Alterations of Neuronal Networks In Vitro upon Physical Damage: A Proof of Concept

There is a growing technological interest in combining biological neuronal networks with electronic ones, specifically for biological computation, human-machine interfacing and robotic implants. A major challenge for the development of these technologies is the resilience of the biological networks to physical damage, for instance, when used in harsh environments. To tackle this question, here, we investigated the dynamic and functional alterations of rodent cortical networks grown in vitro that were physically damaged, either by sequentially removing groups of neurons that were central for information flow or by applying an incision that cut the network in half. In both cases, we observed a remarkable capacity of the neuronal cultures to cope with damage, maintaining their activity and even reestablishing lost communication pathways. We also observed-particularly for the cultures cut in half-that a reservoir of healthy neurons surrounding the damaged region could boost resilience by providing stimulation and a communication bridge across disconnected areas. Our results show the remarkable capacity of neuronal cultures to sustain and recover from damage, and may be inspirational for the development of future hybrid biological-electronic systems.

Flexibility of in vitro cortical circuits influences resilience from microtrauma

Background

Small clusters comprising hundreds to thousands of neurons are an important level of brain architecture that correlates single neuronal properties to fulfill brain function, but the specific mechanisms through which this scaling occurs are not well understood. In this study, we developed an in vitro experimental platform of small neuronal circuits (islands) to probe the importance of structural properties for their development, physiology, and response to microtrauma.

Methods

Primary cortical neurons were plated on a substrate patterned to promote attachment in clusters of hundreds of cells (islands), transduced with GCaMP6f, allowed to mature until 10-13 days in vitro (DIV), and monitored with Ca²⁺ as a non-invasive proxy for electrical activity. We adjusted two structural factors-island size and cellular density-to evaluate their role in guiding spontaneous activity and network formation in neuronal islands.

Results

We found cellular density, but not island size, regulates of circuit activity and network function in this system. Low cellular density islands can achieve many states of activity, while high cellular density biases islands towards a limited regime characterized by low rates of activity and high synchronization, a property we summarized as "flexibility." The injury severity required for an island to lose activity in 50% of its population was significantly higher in low-density, high flexibility islands.

Conclusion

Together, these studies demonstrate flexible living cortical circuits are more resilient to microtrauma, providing the first evidence that initial circuit state may be a key factor to consider when evaluating the consequences of trauma to the cortex.

Self-organization of in vitro neuronal assemblies drives to complex network topology

Activity-dependent self-organization plays an important role in the formation of specific and stereotyped connectivity patterns in neural circuits. By combining neuronal cultures, and tools with approaches from network neuroscience and information theory, we can study how complex network topology emerges from local neuronal interactions. We constructed effective connectivity networks using a transfer entropy analysis of spike trains recorded from rat embryo dissociated hippocampal neuron cultures between 6 and 35 days in vitro to investigate how the topology evolves during maturation. The methodology for constructing the networks considered the synapse delay and addressed the influence of firing rate and population bursts as well as spurious effects on the inference of connections. We found that the number of links in the networks grew over the course of development, shifting from a segregated to a more integrated architecture. As part of this progression, three significant aspects of complex network topology emerged. In agreement with previous in silico and in vitro studies, a small-world architecture was detected, largely due to strong clustering among neurons. Additionally, the networks developed in a modular topology, with most modules comprising nearby neurons. Finally, highly active neurons acquired topological characteristics that made them important nodes to the network and integrators of modules. These findings leverage new insights into how neuronal effective network topology relates to neuronal assembly self-organization mechanisms.

Generation of Interconnected Neural Clusters in Multiscale Scaffolds from Human-Induced Pluripotent Stem Cells

The development of in vitro neural networks depends to a large extent on the scaffold properties, including the scaffold stiffness, porosity, and dimensionality. Herein, we developed a method to generate interconnected neural clusters in a multiscale scaffold consisting of a honeycomb microframe covered on both sides with a monolayer of cross-linked gelatin nanofibers. Cortical neural precursor cells were first produced from human-induced pluripotent stem cells and then loaded into the scaffold for a long period of differentiation toward cortical neural cells. As a result, neurons and astrocytes self-organized in the scaffold to form clusters in each of the honeycomb compartments with remarkable inter-cluster connections. These cells highly expressed neuron- and astrocyte-specific proteins, including NF200, tau, synapsin I, and glial fibrillary acidic protein, and showed spatially correlated neural activities. Two types of neural clusters, that is, spheroid-like and hourglass-like clusters, were found, indicating the complexity of neural-scaffold interaction and the variability of three-dimensional neural organization. Furthermore, we incorporated a reconstituted basement membrane into the scaffold and performed co-culture of the neural network with brain microvascular endothelial cells. As a proof of concept, an improved neurovascular unit model was tested, showing large astrocytic end-feet on the back side of the endothelium.

Dopamine Transporter Is a Master Regulator of Dopaminergic Neural Network Connectivity

Dopaminergic neurons of the substantia nigra pars compacta (SNC) and ventral tegmental area (VTA) exhibit spontaneous firing activity. The dopaminergic neurons in these regions have been shown to exhibit differential sensitivity to neuronal loss and psychostimulants targeting dopamine transporter. However, it remains unclear whether these regional differences scale beyond individual neuronal activity to regional neuronal networks. Here, we used live-cell calcium imaging to show that network connectivity greatly differs between SNC and VTA regions with higher incidence of hub-like neurons in the VTA. Specifically, the frequency of hub-like neurons was significantly lower in SNC than in the adjacent VTA, consistent with the interpretation of a lower network resilience to SNC neuronal loss. We tested this hypothesis, in DAT-cre/loxP-GCaMP6f mice of either sex, when activity of an individual dopaminergic neuron is suppressed, through whole-cell patch clamp electrophysiology, in either SNC or VTA networks. Neuronal loss in the SNC increased network clustering, whereas the larger number of hub-neurons in the VTA overcompensated by decreasing network clustering in the VTA. We further show that network properties are regulatable via a dopamine transporter but not a D2 receptor dependent mechanism. Our results demonstrate novel regulatory mechanisms of functional network topology in dopaminergic brain regions.SIGNIFICANCE STATEMENT In this work, we begin to untangle the differences in complex network properties between the substantia nigra pars compacta (SNC) and VTA, that may underlie differential sensitivity between regions. The methods and analysis employed provide a springboard for investigations of network topology in multiple deep brain structures and disorders.

Dynamics of Structured Networks of Winfree Oscillators

Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.

Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures

An elusive phenomenon in network neuroscience is the extent of neuronal activity remodeling upon damage. Here, we investigate the action of gradual synaptic blockade on the effective connectivity in cortical networks in vitro. We use two neuronal cultures configurations-one formed by about 130 neuronal aggregates and another one formed by about 600 individual neurons-and monitor their spontaneous activity upon progressive weakening of excitatory connectivity. We report that the effective connectivity in all cultures exhibits a first phase of transient strengthening followed by a second phase of steady deterioration. We quantify these phases by measuring GEFF, the global efficiency in processing network information. We term hyperefficiency the sudden strengthening of GEFF upon network deterioration, which increases by 20-50% depending on culture type. Relying on numerical simulations we reveal the role of synaptic scaling, an activity-dependent mechanism for synaptic plasticity, in counteracting the perturbative action, neatly reproducing the observed hyperefficiency. Our results demonstrate the importance of synaptic scaling as resilience mechanism.

Impact of Physical Obstacles on the Structural and Effective Connectivity of in silico Neuronal Circuits

Scaffolds and patterned substrates are among the most successful strategies to dictate the connectivity between neurons in culture. Here, we used numerical simulations to investigate the capacity of physical obstacles placed on a flat substrate to shape structural connectivity, and in turn collective dynamics and effective connectivity, in biologically-realistic neuronal networks. We considered μ-sized obstacles placed in mm-sized networks. Three main obstacle shapes were explored, namely crosses, circles and triangles of isosceles profile. They occupied either a small area fraction of the substrate or populated it entirely in a periodic manner. From the point of view of structure, all obstacles promoted short length-scale connections, shifted the in- and out-degree distributions toward lower values, and increased the modularity of the networks. The capacity of obstacles to shape distinct structural traits depended on their density and the ratio between axonal length and substrate diameter. For high densities, different features were triggered depending on obstacle shape, with crosses trapping axons in their vicinity and triangles funneling axons along the reverse direction of their tip. From the point of view of dynamics, obstacles reduced the capacity of networks to spontaneously activate, with triangles in turn strongly dictating the direction of activity propagation. Effective connectivity networks, inferred using transfer entropy, exhibited distinct modular traits, indicating that the presence of obstacles facilitated the formation of local effective microcircuits. Our study illustrates the potential of physical constraints to shape structural blueprints and remodel collective activity, and may guide investigations aimed at mimicking organizational traits of biological neuronal circuits.

Network science characteristics of brain-derived neuronal cultures deciphered from quantitative phase imaging data

Understanding the mechanisms by which neurons create or suppress connections to enable communication in brain-derived neuronal cultures can inform how learning, cognition and creative behavior emerge. While prior studies have shown that neuronal cultures possess self-organizing criticality properties, we further demonstrate that in vitro brain-derived neuronal cultures exhibit a self-optimization phenomenon. More precisely, we analyze the multiscale neural growth data obtained from label-free quantitative microscopic imaging experiments and reconstruct the in vitro neuronal culture networks (microscale) and neuronal culture cluster networks (mesoscale). We investigate the structure and evolution of neuronal culture networks and neuronal culture cluster networks by estimating the importance of each network node and their information flow. By analyzing the degree-, closeness-, and betweenness-centrality, the node-to-node degree distribution (informing on neuronal interconnection phenomena), the clustering coefficient/transitivity (assessing the “small-world” properties), and the multifractal spectrum, we demonstrate that murine neurons exhibit self-optimizing behavior over time with topological characteristics distinct from existing complex network models. The time-evolving interconnection among murine neurons optimizes the network information flow, network robustness, and self-organization degree. These findings have complex implications for modeling neuronal cultures and potentially on how to design biological inspired artificial intelligence.

Spontaneous Functional Recovery after Focal Damage in Neuronal Cultures

Damage in biological neuronal networks triggers a complex functional reorganization whose mechanisms are still poorly understood. To delineate this reorganization process, here we investigate the functional alterations of in vitro rat cortical circuits following localized laser ablation. The analysis of the functional network configuration before and after ablation allowed us to quantify the extent of functional alterations and the characteristic spatial and temporal scales along recovery. We observed that damage precipitated a fast rerouting of information flow that restored network’s communicability in about 15 min. Functional restoration was led by the immediate neighbors around trauma but was orchestrated by the entire network. Our in vitro setup exposes the ability of neuronal circuits to articulate fast responses to acute damage, and may serve as a proxy to devise recovery strategies in actual brain circuits. Moreover, this biological setup can become a benchmark to empirically test network theories about the spontaneous recovery in dynamical networks.

Methamphetamine regulation of activity and topology of ventral midbrain networks

The ventral midbrain supports a variety of functions through the heterogeneity of neurons. Dopaminergic and GABA neurons within this region are particularly susceptible targets of amphetamine-class psychostimulants such as methamphetamine. While this has been evidenced through single-neuron methods, it remains unclear whether and to what extent the local neuronal network is affected and if so, by which mechanisms. Both GABAergic and dopaminergic neurons were heavily featured within the primary ventral midbrain network model system. Using spontaneous calcium activity, our data suggest methamphetamine decreased total network output via a D2 receptor-dependent manner. Over culture duration, functional connectivity between neurons decreased significantly but was unaffected by methamphetamine. However, across culture duration, exposure to methamphetamine significantly altered changes in network assortativity. Here we have established primary ventral midbrain networks culture as a viable model system that reveals specific changes in network activity, connectivity, and topology modulation by methamphetamine. This network culture system enables control over the type and number of neurons that comprise a network and facilitates detection of emergent properties that arise from the specific organization. Thus, the multidimensional properties of methamphetamine can be unraveled, leading to a better understanding of its impact on the local network structure and function.

Self-organization of modular network architecture by activity-dependent neuronal migration and outgrowth

The spatial distribution of neurons and activity-dependent neurite outgrowth shape long-range interaction, recurrent local connectivity and the modularity in neuronal networks. We investigated how this mesoscale architecture develops by interaction of neurite outgrowth, cell migration and activity in cultured networks of rat cortical neurons and show that simple rules can explain variations of network modularity. In contrast to theoretical studies on activity-dependent outgrowth but consistent with predictions for modular networks, spontaneous activity and the rate of synchronized bursts increased with clustering, whereas peak firing rates in bursts increased in highly interconnected homogeneous networks. As Ca²⁺ influx increased exponentially with increasing network recruitment during bursts, its modulation was highly correlated to peak firing rates. During network maturation, long-term estimates of Ca²⁺ influx showed convergence, even for highly different mesoscale architectures, neurite extent, connectivity, modularity and average activity levels, indicating homeostatic regulation towards a common set-point of Ca²⁺ influx.

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience.

Impact of modular organization on dynamical richness in cortical networks

As in many naturally formed networks, the brain exhibits an inherent modular architecture that is the basis of its rich operability, robustness, and integration-segregation capacity. However, the mechanisms that allow spatially segregated neuronal assemblies to swiftly change from localized to global activity remain unclear. Here, we integrate microfabrication technology with in vitro cortical networks to investigate the dynamical repertoire and functional traits of four interconnected neuronal modules. We show that the coupling among modules is central. The highest dynamical richness of the network emerges at a critical connectivity at the verge of physical disconnection. Stronger coupling leads to a persistently coherent activity among the modules, while weaker coupling precipitates the activity to be localized solely within the modules. An in silico modeling of the experiments reveals that the advent of coherence is mediated by a trade-off between connectivity and subquorum firing, a mechanism flexible enough to allow for the coexistence of both segregated and integrated activities. Our results unveil a new functional advantage of modular organization in complex networks of nonlinear units.

Dynamic graph metrics: Tutorial, toolbox, and tale

The central nervous system is composed of many individual units - from cells to areas - that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and parsimonious representation of such a system is a graph in which nodes (units) are connected by edges (interactions). While applicable across spatiotemporal scales, species, and cohorts, the traditional graph approach is unable to address the complexity of time-varying connectivity patterns that may be critically important for an understanding of emotional and cognitive state, task-switching, adaptation and development, or aging and disease progression. Here we survey a set of tools from applied mathematics that offer measures to characterize dynamic graphs. Along with this survey, we offer suggestions for visualization and a publicly-available MATLAB toolbox to facilitate the application of these metrics to existing or yet-to-be acquired neuroimaging data. We illustrate the toolbox by applying it to a previously published data set of time-varying functional graphs, but note that the tools can also be applied to time-varying structural graphs or to other sorts of relational data entirely. Our aim is to provide the neuroimaging community with a useful set of tools, and an intuition regarding how to use them, for addressing emerging questions that hinge on accurate and creative analyses of dynamic graphs.

Dynamic graph metrics: Tutorial, toolbox, and tale

The central nervous system is composed of many individual units - from cells to areas - that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and parsimonious representation of such a system is a graph in which nodes (units) are connected by edges (interactions). While applicable across spatiotemporal scales, species, and cohorts, the traditional graph approach is unable to address the complexity of time-varying connectivity patterns that may be critically important for an understanding of emotional and cognitive state, task-switching, adaptation and development, or aging and disease progression. Here we survey a set of tools from applied mathematics that offer measures to characterize dynamic graphs. Along with this survey, we offer suggestions for visualization and a publicly-available MATLAB toolbox to facilitate the application of these metrics to existing or yet-to-be acquired neuroimaging data. We illustrate the toolbox by applying it to a previously published data set of time-varying functional graphs, but note that the tools can also be applied to time-varying structural graphs or to other sorts of relational data entirely. Our aim is to provide the neuroimaging community with a useful set of tools, and an intuition regarding how to use them, for addressing emerging questions that hinge on accurate and creative analyses of dynamic graphs.

Assortative mixing in spatially-extended networks

We focus on spatially-extended networks during their transition from short-range connectivities to a scale-free structure expressed by heavy-tailed degree-distribution. In particular, a model is introduced for the generation of such graphs, which combines spatial growth and preferential attachment. In this model the transition to heterogeneous structures is always accompanied by a change in the graph's degree-degree correlation properties: while high assortativity levels characterize the dominance of short distance couplings, long-range connectivity structures are associated with small amounts of disassortativity. Our results allow to infer that a disassortative mixing is essential for establishing long-range links. We discuss also how our findings are consistent with recent experimental studies of 2-dimensional neuronal cultures.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Dominance of Metric Correlations in Two-Dimensional Neuronal Cultures Described through a Random Field Ising Model

We introduce a novel random field Ising model, grounded on experimental observations, to assess the importance of metric correlations in cortical circuits in vitro. Metric correlations arise from both the finite axonal length and the heterogeneity in the spatial arrangement of neurons. The experiments consider the response of neuronal cultures to an external electric stimulation for a gradually weaker connectivity strength between neurons, and in cultures with different spatial configurations. The model can be analytically solved in the metric-free, mean-field scenario. The presence of metric correlations precipitates a strong deviation from the mean field. Null models of the same networks that preserve the distribution of connections recover the mean field. Our results show that metric-inherited correlations in spatial networks dominate the connectivity blueprint, mask the actual distribution of connections, and may emerge as the asset that shapes network dynamics.

Small-world human brain networks: Perspectives and challenges

Modelling the human brain as a complex network has provided a powerful mathematical framework to characterize the structural and functional architectures of the brain. In the past decade, the combination of non-invasive neuroimaging techniques and graph theoretical approaches enable us to map human structural and functional connectivity patterns (i.e., connectome) at the macroscopic level. One of the most influential findings is that human brain networks exhibit prominent small-world organization. Such a network architecture in the human brain facilitates efficient information segregation and integration at low wiring and energy costs, which presumably results from natural selection under the pressure of a cost-efficiency balance. Moreover, the small-world organization undergoes continuous changes during normal development and ageing and exhibits dramatic alterations in neurological and psychiatric disorders. In this review, we survey recent advances regarding the small-world architecture in human brain networks and highlight the potential implications and applications in multidisciplinary fields, including cognitive neuroscience, medicine and engineering. Finally, we highlight several challenging issues and areas for future research in this rapidly growing field.

Mesoscale Architecture Shapes Initiation and Richness of Spontaneous Network Activity

Spontaneous activity in the absence of external input, including propagating waves of activity, is a robust feature of neuronal networks in vivo and in vitro The neurophysiological and anatomical requirements for initiation and persistence of such activity, however, are poorly understood, as is their role in the function of neuronal networks. Computational network studies indicate that clustered connectivity may foster the generation, maintenance, and richness of spontaneous activity. Since this mesoscale architecture cannot be systematically modified in intact tissue, testing these predictions is impracticable in vivo Here, we investigate how the mesoscale structure shapes spontaneous activity in generic networks of rat cortical neurons in vitro In these networks, neurons spontaneously arrange into local clusters with high neurite density and form fasciculating long-range axons. We modified this structure by modulation of protein kinase C, an enzyme regulating neurite growth and cell migration. Inhibition of protein kinase C reduced neuronal aggregation and fasciculation of axons, i.e., promoted uniform architecture. Conversely, activation of protein kinase C promoted aggregation of neurons into clusters, local connectivity, and bundling of long-range axons. Supporting predictions from theory, clustered networks were more spontaneously active and generated diverse activity patterns. Neurons within clusters received stronger synaptic inputs and displayed increased membrane potential fluctuations. Intensified clustering promoted the initiation of synchronous bursting events but entailed incomplete network recruitment. Moderately clustered networks appear optimal for initiation and propagation of diverse patterns of activity. Our findings support a crucial role of the mesoscale architectures in the regulation of spontaneous activity dynamics.SIGNIFICANCE STATEMENT Computational studies predict richer and persisting spatiotemporal patterns of spontaneous activity in neuronal networks with neuron clustering. To test this, we created networks of varying architecture in vitro Supporting these predictions, the generation and spatiotemporal patterns of propagation were most variable in networks with intermediate clustering and lowest in uniform networks. Grid-like clustering, on the other hand, facilitated spontaneous activity but led to degenerating patterns of propagation. Neurons outside clusters had weaker synaptic input than neurons within clusters, in which increased membrane potential fluctuations facilitated the initiation of synchronized spike activity. Our results thus show that the intermediate level organization of neuronal networks strongly influences the dynamics of their activity.

Modeling the network dynamics of pulse-coupled neurons

We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.

A Topological Criterion for Filtering Information in Complex Brain Networks

In many biological systems, the network of interactions between the elements can only be inferred from experimental measurements. In neuroscience, non-invasive imaging tools are extensively used to derive either structural or functional brain networks in-vivo. As a result of the inference process, we obtain a matrix of values corresponding to a fully connected and weighted network. To turn this into a useful sparse network, thresholding is typically adopted to cancel a percentage of the weakest connections. The structural properties of the resulting network depend on how much of the inferred connectivity is eventually retained. However, how to objectively fix this threshold is still an open issue. We introduce a criterion, the efficiency cost optimization (ECO), to select a threshold based on the optimization of the trade-off between the efficiency of a network and its wiring cost. We prove analytically and we confirm through numerical simulations that the connection density maximizing this trade-off emphasizes the intrinsic properties of a given network, while preserving its sparsity. Moreover, this density threshold can be determined a-priori, since the number of connections to filter only depends on the network size according to a power-law. We validate this result on several brain networks, from micro- to macro-scales, obtained with different imaging modalities. Finally, we test the potential of ECO in discriminating brain states with respect to alternative filtering methods. ECO advances our ability to analyze and compare biological networks, inferred from experimental data, in a fast and principled way.

Disruption of rich club organisation in cerebral small vessel disease

Cerebral small vessel disease (SVD) is an important cause of vascular cognitive impairment. Recent studies have demonstrated that structural connectivity of brain networks in SVD is disrupted. However, little is known about the extent and location of the reduced connectivity in SVD. Here they investigate the rich club organisation-a set of highly connected and interconnected regions-and investigate whether there is preferential rich club disruption in SVD. Diffusion tensor imaging (DTI) and cognitive assessment were performed in a discovery sample of SVD patients (n = 115) and healthy control subjects (n = 50). Results were replicated in an independent dataset (49 SVD with confluent WMH cases and 108 SVD controls) with SVD patients having a similar SVD phenotype to that of the discovery cases. Rich club organisation was examined in structural networks derived from DTI followed by deterministic tractography. Structural networks in SVD patients were less dense with lower network strength and efficiency. Reduced connectivity was found in SVD, which was preferentially located in the connectivity between the rich club nodes rather than in the feeder and peripheral connections, a finding confirmed in both datasets. In discovery dataset, lower rich club connectivity was associated with lower scores on psychomotor speed (β = 0.29, P < 0.001) and executive functions (β = 0.20, P = 0.009). These results suggest that SVD is characterized by abnormal connectivity between rich club hubs in SVD and provide evidence that abnormal rich club organisation might contribute to the development of cognitive impairment in SVD. Hum Brain Mapp 38:1751-1766, 2017. © 2017 Wiley Periodicals, Inc.

Impedimetric real-time monitoring of neural pluripotent stem cell differentiation process on microelectrode arrays

In today's neurodevelopment and -disease research, human neural stem/progenitor cell-derived networks represent the sole accessible in vitro model possessing a primary phenotype. However, cultivation and moreover, differentiation as well as maturation of human neural stem/progenitor cells are very complex and time-consuming processes. Therefore, techniques for the sensitive non-invasive, real-time monitoring of neuronal differentiation and maturation are highly demanded. Using impedance spectroscopy, the differentiation of several human neural stem/progenitor cell lines was analyzed in detail. After development of an optimum microelectrode array for reliable and sensitive long-term monitoring, distinct cell-dependent impedimetric parameters that could specifically be associated with the progress and quality of neuronal differentiation were identified. Cellular impedance changes correlated well with the temporal regulation of biomolecular progenitor versus mature neural marker expression as well as cellular structure changes accompanying neuronal differentiation. More strikingly, the capability of the impedimetric differentiation monitoring system for the use as a screening tool was demonstrated by applying compounds that are known to promote neuronal differentiation such as the γ-secretase inhibitor DAPT. The non-invasive impedance spectroscopy-based measurement system can be used for sensitive and quantitative monitoring of neuronal differentiation processes. Therefore, this technique could be a very useful tool for quality control of neuronal differentiation and moreover, for neurogenic compound identification and industrial high-content screening demands in the field of safety assessment as well as drug development.

Modularity Induced Gating and Delays in Neuronal Networks

Neural networks, despite their highly interconnected nature, exhibit distinctly localized and gated activation. Modularity, a distinctive feature of neural networks, has been recently proposed as an important parameter determining the manner by which networks support activity propagation. Here we use an engineered biological model, consisting of engineered rat cortical neurons, to study the role of modular topology in gating the activity between cell populations. We show that pairs of connected modules support conditional propagation (transmitting stronger bursts with higher probability), long delays and propagation asymmetry. Moreover, large modular networks manifest diverse patterns of both local and global activation. Blocking inhibition decreased activity diversity and replaced it with highly consistent transmission patterns. By independently controlling modularity and disinhibition, experimentally and in a model, we pose that modular topology is an important parameter affecting activation localization and is instrumental for population-level gating by disinhibition.

The capacity to transmit information between connected parts of a neuronal network is fundamental to its function. The organization of network connections (the topology of the network) is therefore expected to play an important role in determining network transmission. Since modular topology characterizes many brain circuits on multiple scales, investigating the role of modularity in activity gating is clearly desirable. By engineering such modular networks in vitro, we were able to perform such an investigation. Under these experimental conditions, we can independently control the degree of modularity, as well as inhibition in the network. We show that a combination of these two properties is highly beneficial from a communication perspective. Namely, it equips connected modules and large modular networks with the capacity to gate and temporally coordinate activity between the different parts of the network.

Assortativity and leadership emerge from anti-preferential attachment in heterogeneous networks

Real-world networks have distinct topologies, with marked deviations from purely random networks. Many of them exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Though microscopic mechanisms have been suggested for the emergence of other topological features, assortativity has proven elusive. Assortativity can be artificially implanted in a network via degree-preserving link permutations, however this destroys the graph's hierarchical clustering and does not correspond to any microscopic mechanism. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties in degree and clustering distributions and tunable realistic assortativity. Two distinct populations of nodes are incrementally added to an initial network by selecting a subgraph to connect to at random. One population (the followers) follows preferential attachment, while the other population (the potential leaders) connects via anti-preferential attachment: they link to lower degree nodes when added to the network. By selecting the lower degree nodes, the potential leader nodes maintain high visibility during the growth process, eventually growing into hubs. The evolution of links in Facebook empirically validates the connection between the initial anti-preferential attachment and long term high degree. In this way, our work sheds new light on the structure and evolution of social networks.

Advancing multiscale structural mapping of the brain through fluorescence imaging and analysis across length scales

Brain function emerges from hierarchical neuronal structure that spans orders of magnitude in length scale, from the nanometre-scale organization of synaptic proteins to the macroscopic wiring of neuronal circuits. Because the synaptic electrochemical signal transmission that drives brain function ultimately relies on the organization of neuronal circuits, understanding brain function requires an understanding of the principles that determine hierarchical neuronal structure in living or intact organisms. Recent advances in fluorescence imaging now enable quantitative characterization of neuronal structure across length scales, ranging from single-molecule localization using super-resolution imaging to whole-brain imaging using light-sheet microscopy on cleared samples. These tools, together with correlative electron microscopy and magnetic resonance imaging at the nanoscopic and macroscopic scales, respectively, now facilitate our ability to probe brain structure across its full range of length scales with cellular and molecular specificity. As these imaging datasets become increasingly accessible to researchers, novel statistical and computational frameworks will play an increasing role in efforts to relate hierarchical brain structure to its function. In this perspective, we discuss several prominent experimental advances that are ushering in a new era of quantitative fluorescence-based imaging in neuroscience along with novel computational and statistical strategies that are helping to distil our understanding of complex brain structure.

Magnetite-Amyloid-β deteriorates activity and functional organization in an in vitro model for Alzheimer's disease

The understanding of the key mechanisms behind human brain deterioration in Alzheimer' disease (AD) is a highly active field of research. The most widespread hypothesis considers a cascade of events initiated by amyloid-β peptide fibrils that ultimately lead to the formation of the lethal amyloid plaques. Recent studies have shown that other agents, in particular magnetite, can also play a pivotal role. To shed light on the action of magnetite and amyloid-β in the deterioration of neuronal circuits, we investigated their capacity to alter spontaneous activity patterns in cultured neuronal networks. Using a versatile experimental platform that allows the parallel monitoring of several cultures, the activity in controls was compared with the one in cultures dosed with magnetite, amyloid-β and magnetite-amyloid-β complex. A prominent degradation in spontaneous activity was observed solely when amyloid-β and magnetite acted together. Our work suggests that magnetite nanoparticles have a more prominent role in AD than previously thought, and may bring new insights in the understanding of the damaging action of magnetite-amyloid-β complex. Our experimental system also offers new interesting perspectives to explore key biochemical players in neurological disorders through a controlled, model system manner.

Basin stability for burst synchronization in small-world networks of chaotic slow-fast oscillators

The impact of connectivity and individual dynamics on the basin stability of the burst synchronization regime in small-world networks consisting of chaotic slow-fast oscillators is studied. It is shown that there are rewiring probabilities corresponding to the largest basin stabilities, which uncovers a reason for finding small-world topologies in real neuronal networks. The impact of coupling density and strength as well as the nodal parameters of relaxation or excitability are studied. Dynamic mechanisms are uncovered that most strongly influence basin stability of the burst synchronization regime.

Activity and High-Order Effective Connectivity Alterations in Sanfilippo C Patient-Specific Neuronal Networks

Induced pluripotent stem cell (iPSC) technology has been successfully used to recapitulate phenotypic traits of several human diseases in vitro. Patient-specific iPSC-based disease models are also expected to reveal early functional phenotypes, although this remains to be proved. Here, we generated iPSC lines from two patients with Sanfilippo type C syndrome, a lysosomal storage disorder with inheritable progressive neurodegeneration. Mature neurons obtained from patient-specific iPSC lines recapitulated the main known phenotypes of the disease, not present in genetically corrected patient-specific iPSC-derived cultures. Moreover, neuronal networks organized in vitro from mature patient-derived neurons showed early defects in neuronal activity, network-wide degradation, and altered effective connectivity. Our findings establish the importance of iPSC-based technology to identify early functional phenotypes, which can in turn shed light on the pathological mechanisms occurring in Sanfilippo syndrome. This technology also has the potential to provide valuable readouts to screen compounds, which can prevent the onset of neurodegeneration.

•

Fibroblasts from two Sanfilippo C patients were reprogrammed to obtain iPSCs

•

iPSCs were successfully differentiated to neural cells that mimic the disease

•

Networks of patients’ neurons show altered activity and connectivity

•

Early functional phenotypes are prevented in gene-corrected patients’ neurons

Degree Correlations Optimize Neuronal Network Sensitivity to Sub-Threshold Stimuli

Information processing in the brain crucially depends on the topology of the neuronal connections. We investigate how the topology influences the response of a population of leaky integrate-and-fire neurons to a stimulus. We devise a method to calculate firing rates from a self-consistent system of equations taking into account the degree distribution and degree correlations in the network. We show that assortative degree correlations strongly improve the sensitivity for weak stimuli and propose that such networks possess an advantage in signal processing. We moreover find that there exists an optimum in assortativity at an intermediate level leading to a maximum in input/output mutual information.

Combining microfluidics, optogenetics and calcium imaging to study neuronal communication in vitro

In this paper we report the combination of microfluidics, optogenetics and calcium imaging as a cheap and convenient platform to study synaptic communication between neuronal populations in vitro. We first show that Calcium Orange indicator is compatible in vitro with a commonly used Channelrhodopsine-2 (ChR2) variant, as standard calcium imaging conditions did not alter significantly the activity of transduced cultures of rodent primary neurons. A fast, robust and scalable process for micro-chip fabrication was developed in parallel to build micro-compartmented cultures. Coupling optical fibers to each micro-compartment allowed for the independent control of ChR2 activation in the different populations without crosstalk. By analyzing the post-stimuli activity across the different populations, we finally show how this platform can be used to evaluate quantitatively the effective connectivity between connected neuronal populations.

Degree correlations in directed scale-free networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between 2 and 3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.