Mesoscale Architecture Shapes Initiation and Richness of Spontaneous Network Activity

From pixels to connections: exploring in vitro neuron reconstruction software for network graph generation

Digital reconstruction has been instrumental in deciphering how in vitro neuron architecture shapes information flow. Emerging approaches reconstruct neural systems as networks with the aim of understanding their organization through graph theory. Computational tools dedicated to this objective build models of nodes and edges based on key cellular features such as somata, axons, and dendrites. Fully automatic implementations of these tools are readily available, but they may also be purpose-built from specialized algorithms in the form of multi-step pipelines. Here we review software tools informing the construction of network models, spanning from noise reduction and segmentation to full network reconstruction. The scope and core specifications of each tool are explicitly defined to assist bench scientists in selecting the most suitable option for their microscopy dataset. Existing tools provide a foundation for complete network reconstruction, however more progress is needed in establishing morphological bases for directed/weighted connectivity and in software validation.

Connectivity and network burst properties of in-vitro neuronal networks induced by a clustered structure with alginate hydrogel patterning

Modularity is one of the important structural properties that affect information processing and other functionalities of neuronal networks. Researchers have developed in-vitro clustered network models for reproducing the modularity, but it is still challenging to control the segregation and integration of several sub-populations of them. We cultured clustered networks with alginate patterning and collected the electrophysiological signals to investigate the changes in functional properties during the development. We built inter-connected neuronal clusters using alginate micro-patterning with a circular shape on the surface of the micro-electrode array. The neuronal clusters were enabled to be connected at 3 or 10 days-in-vitro (DIV) by removing the barrier. The neuronal signals from different types of networks were collected from 16 to 34 DIV, and functional characteristics were examined. Connectivity and burst motif analysis were carried out to find out the relation between the structure and function of the networks. Neuronal networks with clustered structure showed different activity properties from the random networks along the development. The clustered networks had more short-range connections compared to the random networks. In the network burst motif analysis, the clustered networks showed more various patterns and a slower propagation of the activation patterns. In this study, we successfully cultured neuronal networks with clustered structure, and the structure affected the functional properties. The network model suggested in this study will be a good solution for observing the effect of structure on function during their development.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13534-023-00289-5.

A computational model to uncover the biophysical underpinnings of neural firing heterogeneity in dissociated hippocampal cultures

Calcium (Ca2+ ) imaging reveals a variety of correlated firing in cultures of dissociated hippocampal neurons, pinpointing the non-synaptic paracrine release of glutamate as a possible mediator for such firing patterns, although the biophysical underpinnings remain unknown. An intriguing possibility is that extracellular glutamate could bind metabotropic receptors linked with inositol trisphosphate (IP3 ) mediated release of Ca2+ from the endoplasmic reticulum of individual neurons, thereby modulating neural activity in combination with sarco/endoplasmic reticulum Ca2+ transport ATPase (SERCA) and voltage-gated Ca2+ channels (VGCC). However, the possibility that such release may occur in different neuronal compartments and can be inherently stochastic poses challenges in the characterization of such interplay between various Ca2+ channels. Here we deploy biophysical modeling in association with Monte Carlo parameter sampling to characterize such interplay and successfully predict experimentally observed Ca2+ patterns. The results show that the neurotransmitter level at the plasma membrane is the extrinsic source of heterogeneity in somatic Ca2+ transients. Our analysis, in particular, identifies the origin of such heterogeneity to an intrinsic differentiation of hippocampal neurons in terms of multiple cellular properties pertaining to intracellular Ca2+ signaling, such as VGCC, IP3 receptor, and SERCA expression. In the future, the biophysical model and parameter estimation approach used in this study can be upgraded to predict the response of a system of interconnected neurons.

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.

Selective inhibition of excitatory synaptic transmission alters the emergent bursting dynamics of in vitro neural networks

Neurons in vitro connect to each other and form neural networks that display emergent electrophysiological activity. This activity begins as spontaneous uncorrelated firing in the early phase of development, and as functional excitatory and inhibitory synapses mature, the activity typically emerges as spontaneous network bursts. Network bursts are events of coordinated global activation among many neurons interspersed with periods of silencing and are important for synaptic plasticity, neural information processing, and network computation. While bursting is the consequence of balanced excitatory-inhibitory (E/I) interactions, the functional mechanisms underlying their evolution from physiological to potentially pathophysiological states, such as decreasing or increasing in synchrony, are still poorly understood. Synaptic activity, especially that related to maturity of E/I synaptic transmission, is known to strongly influence these processes. In this study, we used selective chemogenetic inhibition to target and disrupt excitatory synaptic transmission in in vitro neural networks to study functional response and recovery of spontaneous network bursts over time. We found that over time, inhibition resulted in increases in both network burstiness and synchrony. Our results indicate that the disruption in excitatory synaptic transmission during early network development likely affected inhibitory synaptic maturity which resulted in an overall decrease in network inhibition at later stages. These findings lend support to the importance of E/I balance in maintaining physiological bursting dynamics and, conceivably, information processing capacity in neural networks.

Rich dynamics and functional organization on topographically designed neuronal networks in vitro

Neuronal cultures are a prominent experimental tool to understand complex functional organization in neuronal assemblies. However, neurons grown on flat surfaces exhibit a strongly coherent bursting behavior with limited functionality. To approach the functional richness of naturally formed neuronal circuits, here we studied neuronal networks grown on polydimethylsiloxane (PDMS) topographical patterns shaped as either parallel tracks or square valleys. We followed the evolution of spontaneous activity in these cultures along 20 days in vitro using fluorescence calcium imaging. The networks were characterized by rich spatiotemporal activity patterns that comprised from small regions of the culture to its whole extent. Effective connectivity analysis revealed the emergence of spatially compact functional modules that were associated with both the underpinned topographical features and predominant spatiotemporal activity fronts. Our results show the capacity of spatial constraints to mold activity and functional organization, bringing new opportunities to comprehend the structure-function relationship in living neuronal circuits.

Learning populations with hubs govern the initiation and propagation of spontaneous bursts in neuronal networks after learning

Spontaneous bursts in neuronal networks with propagation involving a large number of synchronously firing neurons are considered to be a crucial feature of these networks both in vivo and in vitro. Recently, learning has been shown to improve the association and synchronization of spontaneous events in neuronal networks by promoting the firing of spontaneous bursts. However, little is known about the relationship between the learning phase and spontaneous bursts. By combining high-resolution measurement with a 4,096-channel complementary metal-oxide-semiconductor (CMOS) microelectrode array (MEA) and graph theory, we studied how the learning phase influenced the initiation of spontaneous bursts in cultured networks of rat cortical neurons in vitro. We found that a small number of selected populations carried most of the stimulus information and contributed to learning. Moreover, several new burst propagation patterns appeared in spontaneous firing after learning. Importantly, these "learning populations" had more hubs in the functional network that governed the initiation of spontaneous burst activity. These results suggest that changes in the functional structure of learning populations may be the key mechanism underlying increased bursts after learning. Our findings could increase understanding of the important role that synaptic plasticity plays in the regulation of spontaneous activity.

Spontaneous Activity Predicts Survival of Developing Cortical Neurons

Spontaneous activity plays a crucial role in brain development by coordinating the integration of immature neurons into emerging cortical networks. High levels and complex patterns of spontaneous activity are generally associated with low rates of apoptosis in the cortex. However, whether spontaneous activity patterns directly encode for survival of individual cortical neurons during development remains an open question. Here, we longitudinally investigated spontaneous activity and apoptosis in developing cortical cultures, combining extracellular electrophysiology with calcium imaging. These experiments demonstrated that the early occurrence of calcium transients was strongly linked to neuronal survival. Silent neurons exhibited a higher probability of cell death, whereas high frequency spiking and burst behavior were almost exclusively detected in surviving neurons. In local neuronal clusters, activity of neighboring neurons exerted a pro-survival effect, whereas on the functional level, networks with a high modular topology were associated with lower cell death rates. Using machine learning algorithms, cell fate of individual neurons was predictable through the integration of spontaneous activity features. Our results indicate that high frequency spiking activity constrains apoptosis in single neurons through sustained calcium rises and thereby consolidates networks in which a high modular topology is reached during early development.

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.

Neurons-on-a-Chip: In Vitro NeuroTools

Neurons-on-a-Chip technology has been developed to provide diverse in vitro neuro-tools to study neuritogenesis, synaptogensis, axon guidance, and network dynamics. The two core enabling technologies are soft-lithography and microelectrode array technology. Soft lithography technology made it possible to fabricate microstamps and microfluidic channel devices with a simple replica molding method in a biological laboratory and innovatively reduced the turn-around time from assay design to chip fabrication, facilitating various experimental designs. To control nerve cell behaviors at the single cell level via chemical cues, surface biofunctionalization methods and micropatterning techniques were developed. Microelectrode chip technology, which provides a functional readout by measuring the electrophysiological signals from individual neurons, has become a popular platform to investigate neural information processing in networks. Due to these key advances, it is possible to study the relationship between the network structure and functions, and they have opened a new era of neurobiology and will become standard tools in the near future.

Common network effect-patterns after monoamine reuptake inhibition in dissociated hippocampus cultures

The pharmacological treatment of major depressive disorder with currently available antidepressant drugs is still unsatisfying as response to medication is delayed and in some patients even non-existent. To understand complex psychiatric diseases such as major depressive disorder and their treatment, research focus is shifting from investigating single neurons towards a view of the entire functional and effective neuronal network, because alterations on single synapses through antidepressant drugs may translate to alterations in the entire network. Here, we examined the effects of monoamine reuptake inhibitors on in vitro hippocampal network dynamics using calcium fluorescence imaging and analyzing the data with means of graph theoretical parameters. Hypothesizing that monoamine reuptake inhibitors operate through changes of effective connectivity on micro-scale neuronal networks, we measured the effects of the selective monoamine reuptake inhibitors GBR-12783, Sertraline, Venlafaxine, and Amitriptyline on neuronal networks. We identified a common pattern of effects of the different tested monoamine reuptake inhibitors. After treatment with GBR-12783, Sertraline, and Venlafaxine, the connectivity degree, measuring the number of existing connections in the network, was significantly decreased. All tested substances led to networks with more submodules and a reduced global efficiency. No monoamine reuptake inhibitor did affect network-wide firing rate, the characteristic path length, or the network strength. In our study, we found that monoamine reuptake inhibition in neuronal networks in vitro results in a sharpening of the network structure. These alterations could be the basis for the reorganization of a large-scale miswired network in major depressive disorder.

Thermoplasmonic neural chip platform for in situ manipulation of neuronal connections in vitro

Cultured neuronal networks with a controlled structure have been widely studied as an in vitro model system to investigate the relationship between network structure and function. However, most cell culture techniques lack the ability to control network structures during cell cultivation, making it difficult to assess functional changes induced by specific structural changes. In this study, we present an in situ manipulation platform based on gold-nanorod-mediated thermoplasmonics to interrogate an in vitro network model. We find that it is possible to induce new neurite outgrowths, eliminate interconnecting neurites, and estimate functional relationships in matured neuronal networks. This method is expected to be useful for studying functional dynamics of neural networks under controlled structural changes.

Cultured neuron networks provide insight into network structure and function, but the ability to control network topology is a challenge. Here the authors develop a nanorod-mediated thermoplasmonics platform that enables the formation of new connections, the abolishment of existing connections, and the modulation of network activity during cultivation.

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.

Emergence of informative higher scales in biological systems: a computational toolkit for optimal prediction and control

The biological sciences span many spatial and temporal scales in attempts to understand the function and evolution of complex systems-level processes, such as embryogenesis. It is generally assumed that the most effective description of these processes is in terms of molecular interactions. However, recent developments in information theory and causal analysis now allow for the quantitative resolution of this question. In some cases, macro-scale models can minimize noise and increase the amount of information an experimenter or modeler has about "what does what." This result has numerous implications for evolution, pattern regulation, and biomedical strategies. Here, we provide an introduction to these quantitative techniques, and use them to show how informative macro-scales are common across biology. Our goal is to give biologists the tools to identify the maximally-informative scale at which to model, experiment on, predict, control, and understand complex biological systems.

Functional characterization of human pluripotent stem cell-derived cortical networks differentiated on laminin-521 substrate: comparison to rat cortical cultures

Human pluripotent stem cell (hPSC)-derived neurons provide exciting opportunities for in vitro modeling of neurological diseases and for advancing drug development and neurotoxicological studies. However, generating electrophysiologically mature neuronal networks from hPSCs has been challenging. Here, we report the differentiation of functionally active hPSC-derived cortical networks on defined laminin-521 substrate. We apply microelectrode array (MEA) measurements to assess network events and compare the activity development of hPSC-derived networks to that of widely used rat embryonic cortical cultures. In both of these networks, activity developed through a similar sequence of stages and time frames; however, the hPSC-derived networks showed unique patterns of bursting activity. The hPSC-derived networks developed synchronous activity, which involved glutamatergic and GABAergic inputs, recapitulating the classical cortical activity also observed in rodent counterparts. Principal component analysis (PCA) based on spike rates, network synchronization and burst features revealed the segregation of hPSC-derived and rat network recordings into different clusters, reflecting the species-specific and maturation state differences between the two networks. Overall, hPSC-derived neural cultures produced with a defined protocol generate cortical type network activity, which validates their applicability as a human-specific model for pharmacological studies and modeling network dysfunctions.

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.

Unique Features of Network Bursts Emerge From the Complex Interplay of Excitatory and Inhibitory Receptors in Rat Neocortical Networks

Spontaneous network activity plays a fundamental role in the formation of functional networks during early development. The landmark of this activity is the recurrent emergence of intensive time-limited network bursts (NBs) rapidly spreading across the entire dissociated culture in vitro. The main excitatory mediators of NBs are glutamatergic alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) and N-Methyl-D-aspartic-acid receptors (NMDARs) that express fast and slow ion channel kinetics, respectively. The fast inhibition of the activity is mediated through gamma-aminobutyric acid type A receptors (GABA_ARs). Although the AMPAR, NMDAR and GABA_AR kinetics have been biophysically characterized in detail at the monosynaptic level in a variety of brain areas, the unique features of NBs emerging from the kinetics and the complex interplay of these receptors are not well understood. The goal of this study is to analyze the contribution of fast GABA_ARs on AMPAR- and NMDAR- mediated spontaneous NB activity in dissociated neonatal rat cortical cultures at 3 weeks in vitro. The networks were probed by both acute and gradual application of each excitatory receptor antagonist and combinations of acute excitatory and inhibitory receptor antagonists. At the same time, the extracellular network-wide activity was recorded with microelectrode arrays (MEAs). We analyzed the characteristic NB measures extracted from NB rate profiles and the distributions of interspike intervals, interburst intervals, and electrode recruitment time as well as the similarity of spatio-temporal patterns of network activity under different receptor antagonists. We show that NBs were rapidly initiated and recruited as well as diversely propagated by AMPARs and temporally and spatially maintained by NMDARs. GABA_ARs reduced the spiking frequency in AMPAR-mediated networks and dampened the termination of NBs in NMDAR-mediated networks as well as slowed down the recruitment of activity in all networks. Finally, we show characteristic super bursts composed of slow NBs with highly repetitive spatio-temporal patterns in gradually AMPAR blocked networks. To the best of our knowledge, this study is the first to unravel in detail how the three main mediators of synaptic transmission uniquely shape the NB characteristics, such as the initiation, maintenance, recruitment and termination of NBs in cortical cell cultures in vitro.

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.

Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.

Inhomogeneities in Network Structure and Excitability Govern Initiation and Propagation of Spontaneous Burst Activity

The mesoscale architecture of neuronal networks strongly influences the initiation of spontaneous activity and its pathways of propagation. Spontaneous activity has been studied extensively in networks of cultured cortical neurons that generate complex yet reproducible patterns of synchronous bursting events that resemble the activity dynamics in developing neuronal networks in vivo. Synchronous bursts are mostly thought to be triggered at burst initiation sites due to build-up of noise or by highly active neurons, or to reflect reverberating activity that circulates within larger networks, although neither of these has been observed directly. Inferring such collective dynamics in neuronal populations from electrophysiological recordings crucially depends on the spatial resolution and sampling ratio relative to the size of the networks assessed. Using large-scale microelectrode arrays with 1024 electrodes at 0.3 mm pitch that covered the full extent of in vitro networks on about 1 cm², we investigated where bursts of spontaneous activity arise and how their propagation patterns relate to the regions of origin, the network's structure, and to the overall distribution of activity. A set of alternating burst initiation zones (BIZ) dominated the initiation of distinct bursting events and triggered specific propagation patterns. Moreover, BIZs were typically located in areas with moderate activity levels, i.e., at transitions between hot and cold spots. The activity-dependent alternation between these zones suggests that the local networks forming the dominating BIZ enter a transient depressed state after several cycles (similar to Eytan et al., 2003), allowing other BIZs to take over temporarily. We propose that inhomogeneities in the network structure define such BIZs and that the depletion of local synaptic resources limit repetitive burst initiation.

Distinct dynamical behavior in Erdős-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdős-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. While ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely, ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

To integrate essential anatomical and physiological properties of local cortical circuits and to elucidate mechanistic links between them, we develop a novel circuit model capturing key synaptic connectivity features. We show that the model explains the emergence of a range of connectivity patterns such as rich-club connectivity, and gives rise to a rich repertoire of cortical states. We identify both the anatomical and physiological mechanisms underlying the transition of these cortical states, and show that our model reconciles an otherwise disparate set of key physiological findings on neural activity dynamics. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to diverse neural population correlations as observed recently. Our model thus provides a framework for integrating and explaining a variety of neural connectivity properties and spatiotemporal activity dynamics observed in experimental studies, and provides novel experimentally testable predictions.

3-D geometry and irregular connectivity dictate neuronal firing in frequency domain and synchronization

The replication of the complex structure and three dimensional (3-D) interconnectivity of neurons in the brain is a great challenge. A few 3-D neuronal patterning approaches have been developed to mimic the cell distribution in the brain but none have demonstrated the relationship between 3-D neuron patterning and network connectivity. Here, we used photolithographic crosslinking to fabricate in vitro 3-D neuronal structures with distinct sizes, shapes or interconnectivities, i.e., milli-blocks, micro-stripes, separated micro-blocks and connected micro-blocks, which have spatial confinement from "Z" dimension to "XYZ" dimension. During a 4-week culture period, the 3-D neuronal system has shown high cell viability, axonal, dendritic, synaptic growth and neural network activity of cortical neurons. We further studied the calcium oscillation of neurons in different 3-D patterns and used signal processing both in Fast Fourier Transform (FFT) and time domain (TD) to model the fluorescent signal variation. We observed that the firing frequency decreased as the spatial confinement in 3-D system increased. Besides, the neuronal synchronization significantly decreased by irregularly connecting micro-blocks, indicating that network connectivity can be adjusted by changing the linking conditions of 3-D gels. Earlier works showed the importance of 3-D culture over 2-D in terms of cell growth. Here, we showed that not only 3-D geometry over 2-D culture matters, but also the spatial organization of cells in 3-D dictates the neuronal firing frequency and synchronicity.

Long-Term Activity Dynamics of Single Neurons and Networks

The firing rate of neuronal spiking in vitro and in vivo significantly varies over extended timescales, characterized by long-memory processes and complex statistics, and appears in spontaneous as well as evoked activity upon repeated stimulus presentation. These variations in response features and their statistics, in face of repeated instances of a given physical input, are ubiquitous in all levels of brain-behavior organization. They are expressed in single neuron and network response variability but even appear in variations of subjective percepts or psychophysical choices and have been described as stemming from history-dependent, stochastic, or rate-determined processes.But what are the sources underlying these temporally rich variations in firing rate? Are they determined by interactions of the nervous system as a whole, or do isolated, single neurons or neuronal networks already express these fluctuations independent of higher levels? These questions motivated the application of a method that allows for controlled and specific long-term activation of a single neuron or neuronal network, isolated from higher levels of cortical organization.This chapter highlights the research done in cultured cortical networks to study (1) the inherent non-stationarity of neuronal network activity, (2) single neuron response fluctuations and underlying processes, and (3) the interface layer between network and single cell, the non-stationary efficacy of the ensemble of synapses impinging onto the observed neuron.

Machine Learning of Spatiotemporal Bursting Behavior in Developing Neural Networks

As with other modern sciences (and their computational counterparts), neuroscience experiments can now produce data that, in terms of both quantity and complexity, challenge our interpretative abilities. It is relatively common to be faced with datasets containing many millions of neural spikes collected from tens of thousands of neurons. Traditional data analysis methods can, in a relatively straightforward manner, identify large-scale features in such data (e.g., on the scale of entire networks). What these approaches often cannot do is to connect macroscopic activity to the relevant small-scale behaviors of individual cells, especially in the face of ongoing background activity that is not relevant. This communication presents an application of machine learning techniques to bridge the gap between microscopic and macroscopic behaviors and identify the small-scale activity that leads to large-scale behavior, reducing data complexity to a level that can be amenable to further analysis. A small number of spatiotemporal spikes (among many millions) were found to provide reliable information about if and where a burst will occur.

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.

Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Understanding the origin, nature, and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in neuroscience. Such patterns include collective oscillations emerging out of neural synchronization as well as highly heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches." Much debate has been generated about the possible scale invariance or criticality of such avalanches and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but crucially, includes stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-state, synchronous, asynchronous, and up-state phases and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition as usually assumed in theoretical approaches but to a synchronization phase transition, at which incipient oscillations and scale-free avalanches coexist. Furthermore, our model also accounts for up and down states as they occur (e.g., during deep sleep). This approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping to shed light on basic aspects of brain functioning from a very broad perspective.

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.