Observed network dynamics from altering the balance between excitatory and inhibitory neurons in cultured networks

Mathematical and Dynamic Modeling of the Anatomical Localization of the Insula in the Brain

The insula, a deeply situated cortical structure beneath the Sylvian sulcus, plays a critical role in sensory integration, emotion regulation, and cognitive control in the brain. Although several studies have described its anatomical and functional characteristics, mathematical models that quantitatively represent the insula's complex structure and connectivity are lacking. This study aimed to develop a mathematical model to represent the anatomical localization and functional organization of the insula, drawing on current neuroimaging findings and established anatomical data. A three-dimensional (3D) ellipsoid model was constructed to mathematically represent the anatomical boundaries of the insula using Montreal Neurological Institute (MNI) coordinate data. This geometric model adapts the ellipsoid equation to reflect the spatial configuration of the insula and is primarily based on cytoarchitectonic mapping and anatomical literature. Relevant findings from prior imaging research, particularly those reporting microstructural variations across insular subdivisions, were reviewed and conceptually integrated to guide the model's structural assumptions and interpretation of potential applications. The ellipsoid-based 3D model accurately represented the anatomical dimensions and spatial localization of the right insula, centered at the MNI coordinates (40, 5, 5 mm), and matched well with the known volumetric data. Functional regions (face, hand, and foot) were successfully plotted within the model, and statistical analysis confirmed significant differences along the anteroposterior and superoinferior axes (p < 0.01 and p < 0.05, respectively). Dynamic simulations revealed oscillatory patterns of excitatory and inhibitory neural activity, consistent with established insular neurophysiology. Additionally, connectivity modeling demonstrated strong bidirectional interactions between the insula and key regions, such as the prefrontal cortex and anterior cingulate cortex (ACC), reflecting its integrative role in brain networks. This study presents a scientifically validated mathematical model that captures the anatomical structure, functional subdivisions, and dynamic connectivity patterns of the insula. By integrating anatomical data with computational simulations, this model provides a foundation for future research in neuroimaging, functional mapping, and clinical applications involving insula-related disorders.

Higher-order interactions induce stepwise explosive phase transitions

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.

Locally repulsive coupling-induced tunable oscillations

The precise amplitude and period of neuronal oscillations are crucial for the functioning of neuronal networks. We propose a chain model featuring a repulsive coupling at the first node, followed by attractive couplings at subsequent nodes. This model allows for the simultaneous regulation of both quantities. The repulsive coupling at the first neuron enables it to act as a pacemaker, generating oscillations whose amplitude and period are correlated with the coupling strength. At the same time, attractive couplings help transmit these oscillations along the chain, leading to collective oscillations of varying scales. Our study demonstrates that a three-node chain with locally repulsive coupling forms the fundamental structure for generating tunable oscillations. By using a simplified neuron model, we investigate how locally repulsive coupling affects the amplitude and period of oscillations and find results that align with numerical observations. These findings indicate that repulsive couplings play a crucial role in regulating oscillatory patterns within neuronal networks.

Emergence of task-related spatiotemporal population dynamics in transplanted neurons

Loss of nervous system tissue after severe brain injury is a main determinant of poor functional recovery. Cell transplantation is a promising method to restore lost tissue and function, yet it remains unclear if transplanted neurons can demonstrate the population level dynamics important for movement control. Here we present a comprehensive approach for long-term single neuron monitoring and manipulation of transplanted embryonic cortical neurons after cortical injury in adult male mice performing a prehension task. The observed patterns of population activity in the transplanted network strongly resembled that of healthy networks. Specifically, the task-related spatiotemporal activity patterns of transplanted neurons could be represented by latent factors that evolve within a low dimensional manifold. We also demonstrate reliable modulation of the transplanted networks using minimally invasive epidural stimulation. Our approach may allow greater insight into how restoration of cell-type specific network dynamics in vivo can restore motor function.

Long-term morphological and functional dynamics of human stem cell-derived neuronal networks on high-density micro-electrode arrays

Comprehensive electrophysiological characterizations of human induced pluripotent stem cell (hiPSC)-derived neuronal networks are essential to determine to what extent these in vitro models recapitulate the functional features of in vivo neuronal circuits. High-density micro-electrode arrays (HD-MEAs) offer non-invasive recording with the best spatial and temporal resolution possible to date. For 3 months, we tracked the morphology and activity features of developing networks derived from a transgenic hiPSC line in which neurogenesis is inducible by neurogenic transcription factor overexpression. Our morphological data revealed large-scale structural changes from homogeneously distributed neurons in the first month to the formation of neuronal clusters over time. This led to a constant shift in position of neuronal cells and clusters on HD-MEAs and corresponding changes in spatial distribution of the network activity maps. Network activity appeared as scarce action potentials (APs), evolved as local bursts with longer duration and changed to network-wide synchronized bursts with higher frequencies but shorter duration over time, resembling the emerging burst features found in the developing human brain. Instantaneous firing rate data indicated that the fraction of fast spiking neurons (150–600 Hz) increases sharply after 63 days post induction (dpi). Inhibition of glutamatergic synapses erased burst features from network activity profiles and confirmed the presence of mature excitatory neurotransmission. The application of GABAergic receptor antagonists profoundly changed the bursting profile of the network at 120 dpi. This indicated a GABAergic switch from excitatory to inhibitory neurotransmission during circuit development and maturation. Our results suggested that an emerging GABAergic system at older culture ages is involved in regulating spontaneous network bursts. In conclusion, our data showed that long-term and continuous microscopy and electrophysiology readouts are crucial for a meaningful characterization of morphological and functional maturation in stem cell-derived human networks. Most importantly, assessing the level and duration of functional maturation is key to subject these human neuronal circuits on HD-MEAs for basic and biomedical applications.

Diversity-induced resonance in a globally coupled bistable system with diversely distributed heterogeneity

A moderate degree of diversity, in form of quenched noise or intrinsic heterogeneity, can significantly strengthen the collective response of coupled extended systems. As yet, related discoveries on diversity-induced resonance are mainly concentrated on symmetrically distributed heterogeneity, e.g., the Gaussian or uniform distributions with zero-mean. The necessary conditions that guarantee the arise of resonance phenomenon in heterogeneous oscillators remain largely unknown. In this work, we show that the standard deviation and the ratio of negative entities of a given distribution jointly modulate diversity-induced resonance and the concomitance of negative and positive entities is the prerequisite for this resonant behavior emerging in diverse symmetrical and asymmetrical distributions. Particularly, for a proper degree of diversity of a given distribution, the collective signal response behaves like a bell-shaped curve as the ratio of negative oscillator increases, which can be termed negative-oscillator-ratio induced resonance. Furthermore, we analytically reveal that the ratio of negative oscillators plays a gating role in the resonance phenomenon on the basis of a reduced equation. Finally, we examine the robustness of these results in globally coupled bistable elements with asymmetrical potential functions. Our results suggest that the phenomenon of diversity-induced resonance can arise in arbitrarily distributed heterogeneous bistable oscillators by regulating the ratio of negative entities appropriately.

Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration–a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration–determined from partial information decomposition–varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow.

Networks compute information. That is, they modify inputs to generate distinct outputs. These computations are an important component of network information processing. Knowing how the routing of information in a network influences computation is therefore crucial. Here we asked how a key form of computation—synergistic integration—is related to the direction of local information flow in networks of spiking cortical neurons. Specifically, we asked how information flow between input neurons (i.e., recurrent information flow) and information flow from output neurons to input neurons (i.e., feedback information flow) was related to the amount of synergistic integration performed by output neurons. We found that greater synergistic integration occurred where there was more recurrent information flow. And, lesser synergistic integration occurred where there was more feedback information flow relative to feedforward information flow. These results show that computation, in the form of synergistic integration, is distinctly influenced by the directionality of local information flow. Such work is valuable for predicting where and how network computation occurs and for designing networks with desired computational abilities.

Understanding the Impact of Neural Variations and Random Connections on Inference

Recent research suggests that in vitro neural networks created from dissociated neurons may be used for computing and performing machine learning tasks. To develop a better artificial intelligent system, a hybrid bio-silicon computer is worth exploring, but its performance is still inferior to that of a silicon-based computer. One reason may be that a living neural network has many intrinsic properties, such as random network connectivity, high network sparsity, and large neural and synaptic variability. These properties may lead to new design considerations, and existing algorithms need to be adjusted for living neural network implementation. This work investigates the impact of neural variations and random connections on inference with learning algorithms. A two-layer hybrid bio-silicon platform is constructed and a five-step design method is proposed for the fast development of living neural network algorithms. Neural variations and dynamics are verified by fitting model parameters with biological experimental results. Random connections are generated under different connection probabilities to vary network sparsity. A multi-layer perceptron algorithm is tested with biological constraints on the MNIST dataset. The results show that a reasonable inference accuracy can be achieved despite the presence of neural variations and random network connections. A new adaptive pre-processing technique is proposed to ensure good learning accuracy with different living neural network sparsity.

In silico hippocampal modeling for multi-target pharmacotherapy in schizophrenia

Treatment of schizophrenia has had limited success in treating core cognitive symptoms. The evidence of multi-gene involvement suggests that multi-target therapy may be needed. Meanwhile, the complexity of schizophrenia pathophysiology and psychopathology, coupled with the species-specificity of much of the symptomatology, places limits on analysis via animal models, in vitro assays, and patient assessment. Multiscale computer modeling complements these traditional modes of study. Using a hippocampal CA3 computer model with 1200 neurons, we examined the effects of alterations in NMDAR, HCN (Ih current), and GABAAR on information flow (measured with normalized transfer entropy), and in gamma activity in local field potential (LFP). We found that altering NMDARs, GABAAR, Ih, individually or in combination, modified information flow in an inverted-U shape manner, with information flow reduced at low and high levels of these parameters. Theta-gamma phase-amplitude coupling also had an inverted-U shape relationship with NMDAR augmentation. The strong information flow was associated with an intermediate level of synchrony, seen as an intermediate level of gamma activity in the LFP, and an intermediate level of pyramidal cell excitability. Our results are consistent with the idea that overly low or high gamma power is associated with pathological information flow and information processing. These data suggest the need for careful titration of schizophrenia pharmacotherapy to avoid extremes that alter information flow in different ways. These results also identify gamma power as a potential biomarker for monitoring pathology and multi-target pharmacotherapy.

Exploring the mechanisms underlying excitation/inhibition imbalance in human iPSC-derived models of ASD

Autism spectrum disorder (ASD) is a range of neurodevelopmental disorders characterized by impaired social interaction and communication, and repetitive or restricted behaviors. ASD subjects exhibit complex genetic and clinical heterogeneity, thus hindering the discovery of pathophysiological mechanisms. Considering that several ASD-risk genes encode proteins involved in the regulation of synaptic plasticity, neuronal excitability, and neuronal connectivity, one hypothesis that has emerged is that ASD arises from a disruption of the neuronal network activity due to perturbation of the synaptic excitation and inhibition (E/I) balance. The development of induced pluripotent stem cell (iPSC) technology and recent advances in neuronal differentiation techniques provide a unique opportunity to model complex neuronal connectivity and to test the E/I hypothesis of ASD in human-based models. Here, we aim to review the latest advances in studying the different cellular and molecular mechanisms contributing to E/I balance using iPSC-based in vitro models of ASD.

Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators

We investigate a system of globally coupled bistable oscillators subjected to a common weak signal, where the couplings are oscillator dependent with random signs: positive or negative. We find that neither purely positive nor purely negative couplings are optimal for signal amplification of the system; a mixture of both positive and negative couplings is more beneficial for the signal amplification. Our numerical results further show that different from the fully synchronous state caused by purely positive couplings or asynchronous state caused by purely negative couplings, the mixed positive and negative couplings can generate a clustering synchronous state, which allows the system to generate a resonancelike response to the weak signal, and thus, amplifies the signal. We finally propose a reduced model to analyze the mechanism underlying this resonancelike behavior, and find a complementary effect of these two types of couplings in signal amplification.

Activation of nicotinic acetylcholine receptors induces potentiation and synchronization within in vitro hippocampal networks

Nicotinic acetylcholine receptors (nAChRs) are known to play a role in cognitive functions of the hippocampus, such as memory consolidation. Given that they conduct Ca²⁺ and are capable of regulating the release of glutamate and γ-aminobutyric acid (GABA) within the hippocampus, thereby shifting the excitatory-inhibitory ratio, we hypothesized that the activation of nAChRs will result in the potentiation of hippocampal networks and alter synchronization. We used nicotine as a tool to investigate the impact of activation of nAChRs on neuronal network dynamics in primary embryonic rat hippocampal cultures prepared from timed-pregnant Sprague-Dawley rats. We perturbed cultured hippocampal networks with increasing concentrations of bath-applied nicotine and performed network extracellular recordings of action potentials using a microelectrode array. We found that nicotine modulated network dynamics in a concentration-dependent manner; it enhanced firing of action potentials as well as facilitated bursting activity. In addition, we used pharmacological agents to determine the contributions of discrete nAChR subtypes to the observed network dynamics. We found that β4-containing nAChRs are necessary for the observed increases in spiking, bursting, and synchrony, while the activation of α7 nAChRs augments nicotine-mediated network potentiation but is not necessary for its manifestation. We also observed that antagonists of N-methyl-D-aspartate receptors (NMDARs) and group I metabotropic glutamate receptors (mGluRs) partially blocked the effects of nicotine. Furthermore, nicotine exposure promoted autophosphorylation of Ca²⁺ /calmodulin-dependent kinase II (CaMKII) and serine 831 phosphorylation of the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) subunit GluA1. These results suggest that nicotinic receptors induce potentiation and synchronization of hippocampal networks and glutamatergic synaptic transmission. Findings from this work highlight the impact of cholinergic signaling in generating network-wide potentiation in the form of enhanced spiking and bursting dynamics that coincide with molecular correlates of memory such as increased phosphorylation of CaMKII and GluA1. OPEN SCIENCE BADGES: This article has received a badge for *Open Materials* because it provided all relevant information to reproduce the study in the manuscript. More information about the Open Practices badges can be found at https://cos.io/our-services/open-science-badges/.

Resonance induced by coupling diversity in globally coupled bistable oscillators

We investigate the collective response of an ensemble of bistable oscillators to an external periodic signal, where the coupling strength between oscillators is diverse. We find that there exists an optimal level of coupling diversity, at which the collective response of the system can be largely improved, i.e., resonance induced by coupling diversity. We also observe that the system splits into three oscillation clusters when this resonance happens. We finally propose a reduced model based on the three oscillation clusters, which can well predict the collective response of the system.

Jensen's force and the statistical mechanics of cortical asynchronous states

Cortical networks are shaped by the combined action of excitatory and inhibitory interactions. Among other important functions, inhibition solves the problem of the all-or-none type of response that comes about in purely excitatory networks, allowing the network to operate in regimes of moderate or low activity, between quiescent and saturated regimes. Here, we elucidate a noise-induced effect that we call “Jensen’s force” –stemming from the combined effect of excitation/inhibition balance and network sparsity– which is responsible for generating a phase of self-sustained low activity in excitation-inhibition networks. The uncovered phase reproduces the main empirically-observed features of cortical networks in the so-called asynchronous state, characterized by low, un-correlated and highly-irregular activity. The parsimonious model analyzed here allows us to resolve a number of long-standing issues, such as proving that activity can be self-sustained even in the complete absence of external stimuli or driving. The simplicity of our approach allows for a deep understanding of asynchronous states and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronous-state and critical-state hypotheses, putting them within a unified framework. We argue that Jensen’s forces are measurable experimentally and might be relevant in contexts beyond neuroscience.

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.

Connectomics of Morphogenetically Engineered Neurons as a Predictor of Functional Integration in the Ischemic Brain

Recent advances in cell reprogramming technologies enable the in vitro generation of theoretically unlimited numbers of cells, including cells of neural lineage and specific neuronal subtypes from human, including patient-specific, somatic cells. Similarly, as demonstrated in recent animal studies, by applying morphogenetic neuroengineering principles in situ, it is possible to reprogram resident brain cells to the desired phenotype. These developments open new exciting possibilities for cell replacement therapy in stroke, albeit not without caveats. Main challenges include the successful integration of engineered cells in the ischemic brain to promote functional restoration as well as the fact that the underlying mechanisms of action are not fully understood. In this review, we aim to provide new insights to the above in the context of connectomics of morphogenetically engineered neural networks. Specifically, we discuss the relevance of combining advanced interdisciplinary approaches to: validate the functionality of engineered neurons by studying their self-organizing behavior into neural networks as well as responses to stroke-related pathology in vitro; derive structural and functional connectomes from these networks in healthy and perturbed conditions; and identify and extract key elements regulating neural network dynamics, which might predict the behavior of grafted engineered neurons post-transplantation in the stroke-injured brain.

BmK NT1-induced neurotoxicity is mediated by PKC/CaMKⅡ-dependent ERK1/2 and p38 activation in primary cultured cerebellar granule cells

Voltage-gated sodium channels (VGSCs) represent molecular targets for a number of potent neurotoxins that affect the ion permeation or gating kinetics. BmK NT1, an α-scorpion toxin purified from Buthus martensii Karch (BMK), induces excitatory neurotoxicity by activation of VGSCs with subsequent overloading of intracellular Ca²⁺ in cerebellar granule cells (CGCs). In the current study, we further investigated signaling pathways responsible for BmK NT1-induced neurotoxicity in CGCs. BmK NT1 exposure induced neuronal death in different development stages of CGCs with similar potencies ranging from 0.21-0.48 μM. The maximal neuronal death induced by BmK NT1 gradually increased from 25.6% at 7 days in vitro (DIVs) to 42.1%, 47.8%, and 67.2% at 10, 13, and 16 DIVs, respectively, suggesting that mature CGCs are more vulnerable to BmK NT1 exposure. Application of Ca²⁺/calmodulin-dependent protein kinase Ⅱ (CaMKⅡ) inhibitors, KN-62 or KN-93, but not Ca²⁺/calmodulin-dependent protein kinase kinase (CaMKK) inhibitor, STO-609, completely abolished BmK NT1-induced neuronal death. Moreover, BmK NT1 exposure stimulated CaMKⅡ phosphorylation. BmK NT1 also stimulated extracellular regulated protein kinases 1/2 (ERK1/2) and p38 phosphorylation which was abolished by tetrodotoxin demonstrating the role of VGSCs on BmK NT1-induced ERK1/2 and p38 phosphorylation. However, BmK NT1 didn't affect c-Jun N-terminal kinase (JNK) phosphorylation. In addition, both ERK1/2 inhibitor, U0126 and p38 inhibitor, SB203580 attenuated BmK NT1-induced neuronal death. Both PKC inhibitor, Gö 6983 and CaMKⅡ inhibitor, KN-62 abolished BmK NT1-induced ERK1/2 and p38 phosphorylation. Considered together, these data demonstrate that BmK NT1-induced neurotoxicity is through PKC/CaMKⅡ mediated ERK1/2 and p38 activation.

Robust entropy requires strong and balanced excitatory and inhibitory synapses

It is widely appreciated that balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, balance could be achieved by many possible configurations of excitatory and inhibitory synaptic strengths and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses or a few inhibitory neurons with strong synapses. Among the continuum of different but balanced configurations, why should any particular configuration be favored? Here, we address this question in the context of the entropy of network dynamics by studying an analytically tractable network of binary neurons. We find that entropy is highest at the boundary between excitation-dominant and inhibition-dominant regimes. Entropy also varies along this boundary with a trade-off between high and robust entropy: weak synapse strengths yield high network entropy which is fragile to parameter variations, while strong synapse strengths yield a lower, but more robust, network entropy. In the case where inhibitory and excitatory synapses are constrained to have similar strength, we find that a small, but non-zero fraction of inhibitory neurons, like that seen in mammalian cortex, results in robust and relatively high entropy.

Theta rhythm-like bidirectional cycling dynamics of living neuronal networks in vitro

The phenomena of synchronization, rhythmogenesis and coherence observed in brain networks are believed to be a dynamic substrate for cognitive functions such as learning and memory. However, researchers are still debating whether the rhythmic activity emerges from the network morphology that developed during neurogenesis or as a result of neuronal dynamics achieved under certain conditions. In the present study, we observed self-organized spiking activity that converged to long, complex and rhythmically repeated superbursts in neural networks formed by mature hippocampal cultures with a high cellular density. The superburst lasted for tens of seconds and consisted of hundreds of short (50-100 ms) small bursts with a high spiking rate of 139.0 ± 78.6 Hz that is associated with high-frequency oscillations in the hippocampus. In turn, the bursting frequency represents a theta rhythm (11.2 ± 1.5 Hz). The distribution of spikes within the bursts was non-random, representing a set of well-defined spatio-temporal base patterns or motifs. The long superburst was classified into two types. Each type was associated with a unique direction of spike propagation and, hence, was encoded by a binary sequence with random switching between the two "functional" states. The precisely structured bidirectional rhythmic activity that developed in self-organizing cultured networks was quite similar to the activity observed in the in vivo experiments.

Simultaneous multi-patch-clamp and extracellular-array recordings: Single neuron reflects network activity

The increasing number of recording electrodes enhances the capability of capturing the network’s cooperative activity, however, using too many monitors might alter the properties of the measured neural network and induce noise. Using a technique that merges simultaneous multi-patch-clamp and multi-electrode array recordings of neural networks in-vitro, we show that the membrane potential of a single neuron is a reliable and super-sensitive probe for monitoring such cooperative activities and their detailed rhythms. Specifically, the membrane potential and the spiking activity of a single neuron are either highly correlated or highly anti-correlated with the time-dependent macroscopic activity of the entire network. This surprising observation also sheds light on the cooperative origin of neuronal burst in cultured networks. Our findings present an alternative flexible approach to the technique based on a massive tiling of networks by large-scale arrays of electrodes to monitor their activity.

Vitality of Neural Networks under Reoccurring Catastrophic Failures

Catastrophic failures are complete and sudden collapses in the activity of large networks such as economics, electrical power grids and computer networks, which typically require a manual recovery process. Here we experimentally show that excitatory neural networks are governed by a non-Poissonian reoccurrence of catastrophic failures, where their repetition time follows a multimodal distribution characterized by a few tenths of a second and tens of seconds timescales. The mechanism underlying the termination and reappearance of network activity is quantitatively shown here to be associated with nodal time-dependent features, neuronal plasticity, where hyperactive nodes damage the response capability of their neighbors. It presents a complementary mechanism for the emergence of Poissonian catastrophic failures from damage conductivity. The effect that hyperactive nodes degenerate their neighbors represents a type of local competition which is a common feature in the dynamics of real-world complex networks, whereas their spontaneous recoveries represent a vitality which enhances reliable functionality.

Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons

Chimera states occur when identically coupled groups of nonlinear oscillators exhibit radically different dynamics, with one group exhibiting synchronized oscillations and the other desynchronized behavior. This dynamical phenomenon has recently been studied in computational models and demonstrated experimentally in mechanical, optical, and chemical systems. The theoretical basis of these states is currently under active investigation. Chimera behavior is of particular relevance in the context of neural synchronization, given the phenomenon of unihemispheric sleep and the recent observation of asymmetric sleep in human patients with sleep apnea. The similarity of neural chimera states to neural "bump" states, which have been suggested as a model for working memory and visual orientation tuning in the cortex, adds to their interest as objects of study. Chimera states have been demonstrated in the FitzHugh-Nagumo model of excitable cells and in the Hindmarsh-Rose neural model. Here, we demonstrate chimera states and chimera-like behaviors in a Hodgkin-Huxley-type model of thermally sensitive neurons both in a system with Abrams-Strogatz (mean field) coupling and in a system with Kuramoto (distance-dependent) coupling. We map the regions of parameter space for which chimera behavior occurs in each of the two coupling schemes.

Network burst activity in hippocampal neuronal cultures: the role of synaptic and intrinsic currents

The goal of this work was to define the contributions of intrinsic and synaptic mechanisms toward spontaneous network-wide bursting activity, observed in dissociated rat hippocampal cell cultures. This network behavior is typically characterized by short-duration bursts, separated by order of magnitude longer interburst intervals. We hypothesize that while short-timescale synaptic processes modulate spectro-temporal intraburst properties and network-wide burst propagation, much longer timescales of intrinsic membrane properties such as persistent sodium (Nap) currents govern burst onset during interburst intervals. To test this, we used synaptic receptor antagonists picrotoxin, 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), and 3-(2-carboxypiperazine-4-yl)propyl-1-phosphonate (CPP) to selectively block GABAA, AMPA, and NMDA receptors and riluzole to selectively block Nap channels. We systematically compared intracellular activity (recorded with patch clamp) and network activity (recorded with multielectrode arrays) in eight different synaptic connectivity conditions: GABAA + NMDA + AMPA, NMDA + AMPA, GABAA + AMPA, GABAA + NMDA, AMPA, NMDA, GABAA, and all receptors blocked. Furthermore, we used mixed-effects modeling to quantify the aforementioned independent and interactive synaptic receptor contributions toward spectro-temporal burst properties including intraburst spike rate, burst activity index, burst duration, power in the local field potential, network connectivity, and transmission delays. We found that blocking intrinsic Nap currents completely abolished bursting activity, demonstrating their critical role in burst onset within the network. On the other hand, blocking different combinations of synaptic receptors revealed that spectro-temporal burst properties are uniquely associated with synaptic functionality and that excitatory connectivity is necessary for the presence of network-wide bursting. In addition to confirming the critical contribution of direct excitatory effects, mixed-effects modeling also revealed distinct combined (nonlinear) contributions of excitatory and inhibitory synaptic activity to network bursting properties.

Micro-electrode array recordings reveal reductions in both excitation and inhibition in cultured cortical neuron networks lacking Shank3

Numerous risk genes have recently been implicated in susceptibility to autism and schizophrenia. Translating such genetic findings into disease-relevant neurobiological mechanisms is challenging due to the lack of throughput assays that can be used to assess their functions on an appropriate scale. To address this issue, we explored the feasibility of using a micro-electrode array (MEA) as a potentially scalable assay to identify the electrical network phenotypes associated with risk genes. We first characterized local and global network firing in cortical neurons with MEAs, and then developed methods to analyze the alternation between the network active period (NAP) and the network inactive period (NIP), each of which lasts tens of seconds. We then evaluated the electric phenotypes of neurons derived from Shank3 knockout (KO) mice. Cortical neurons cultured on MEAs displayed a rich repertoire of spontaneous firing, and Shank3 deletion led to reduced firing activity. Enhancing excitation with CX546 rescued the deficit in the spike rate in the Shank3 KO network. In addition, the Shank3 KO network produced a shorter NIP, and this altered network firing pattern was normalized by clonazepam, a positive modulator of the GABAA receptor. MEA recordings revealed electric phenotypes that displayed altered excitation and inhibition in the network lacking Shank3. Thus, our study highlights MEAs as an experimental framework for measuring multiple robust neurobiological end points in dynamic networks and as an assay system that could be used to identify electric phenotypes in cultured neuronal networks and to analyze additional risk genes identified in psychiatric genetics.

Perchance to dream? Primordial motor activity patterns in vertebrates from fish to mammals: their prenatal origin, postnatal persistence during sleep, and pathological reemergence during REM sleep behavior disorder

An overview is presented of the literature dealing with sleep-like motility and concomitant neuronal activity patterns throughout the life cycle in vertebrates, ectothermic as well as endothermic. Spontaneous, periodically modulated, neurogenic bursts of non-purposive movements are a universal feature of larval and prenatal behavior, which in endothermic animals (i.e. birds and mammals) continue to occur periodically throughout life. Since the entire body musculature is involved in ever-shifting combinations, it is proposed that these spontaneously active periods be designated as 'rapid-BODY-movement' (RBM) sleep. The term 'rapid-EYE-movement (REM) sleep', characterized by attenuated muscle contractions and reduced tonus, can then be reserved for sleep at later stages of development. Mature stages of development in which sustained muscle atonia is combined with 'paradoxical arousal' of cortical neuronal firing patterns indisputably represent the evolutionarily most recent aspect of REM sleep, but more research with ectothermic vertebrates, such as fish, amphibians and reptiles, is needed before it can be concluded (as many prematurely have) that RBM is absent in these species. Evidence suggests a link between RBM sleep in early development and the clinical condition known as 'REM sleep behavior disorder (RBD)', which is characterized by the resurgence of periodic bouts of quasi-fetal motility that closely resemble RBM sleep. Early developmental neuromotor risk factors for RBD in humans also point to a relationship between RBM sleep and RBD.

A simple model of cortical culture growth: burst property dependence on network composition and activity

This paper describes large-scale simulations of growth, network formation, and behavior in cultures of dissociated cortical cells. A neuron model that incorporates synaptic facilitation/depression and neurite outgrowth/retraction was used to construct virtual cultures of 10,000 cells whose spiking behavior and evolution were investigated in closed-loop simulations. This approach allows us to perform detailed analysis of the effects of model parameters on burst shape and timing, their changes, and the interrelationship among these behaviors, gross network structure, and model parameters. We examined the effects of two parameters--network composition (fraction of excitatory cells) and neuron excitability (activity level corresponding to neurite outgrowth equilibrium)--on network structure and behavior. Our results suggest that much of the burst shape and timing observed in vitro can be explained by a model that includes only closed-loop neurite outgrowth and dynamic synapses; features such as LTP/LTD, random connectivity, long-distance connections, and detailed neurite topology are not necessary.

Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons

We design and analyze the dynamics of a large network of theta neurons, which are idealized type I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulselike synapses of adjustable sharpness. Using recently developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends toward the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition among these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.

Synaptic potentiation facilitates memory-like attractor dynamics in cultured in vitro hippocampal networks

Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based computational models have been successfully implemented as a theoretical framework for memory storage in networks of neurons. Additionally, activity-dependent modification of synaptic transmission is thought to be the physiological basis of learning and memory. The goal of this study is to demonstrate that using a pharmacological treatment that has been shown to increase synaptic strength within in vitro networks of hippocampal neurons follows the dynamical postulates theorized by attractor models. We use a grid of extracellular electrodes to study changes in network activity after this perturbation and show that there is a persistent increase in overall spiking and bursting activity after treatment. This increase in activity appears to recruit more “errant” spikes into bursts. Phase plots indicate a conserved activity pattern suggesting that a synaptic potentiation perturbation to the attractor leaves it unchanged. Lastly, we construct a computational model to demonstrate that these synaptic perturbations can account for the dynamical changes seen within the network.

MMPs and soluble ICAM-5 increase neuronal excitability within in vitro networks of hippocampal neurons

Matrix metalloproteinases (MMPs) are zinc-dependent endopeptidases that are released from neurons in an activity dependent manner. Published studies suggest their activity is important to varied forms of learning and memory. At least one MMP can stimulate an increase in the size of dendritic spines, structures which represent the post synaptic component for a large number of glutamatergic synapses. This change may be associated with increased synaptic glutamate receptor incorporation, and an increased amplitude and/or frequency of α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) mini excitatory post-synaptic currents (EPSCs). An associated increase in the probability of action potential occurrence would be expected. While the mechanism(s) by which MMPs may influence synaptic structure and function are not completely understood, MMP dependent shedding of specific cell adhesion molecules (CAMs) could play an important role. CAMs are ideally positioned to be cleaved by synaptically released MMPs, and shed N terminal domains could potentially interact with previously unengaged integrins to stimulate dendritic actin polymerization with spine expansion. In the present study, we have used multielectrode arrays (MEAs) to investigate MMP and soluble CAM dependent changes in neuronal activity recorded from hippocampal cultures. We have focused on intercellular adhesion molecule-5 (ICAM-5) in particular, as this CAM is expressed on glutamatergic dendrites and shed in an MMP dependent manner. We show that chemical long-term potentiation (cLTP) evoked changes in recorded activity, and the dynamics of action potential bursts in particular, are altered by MMP inhibition. A blocking antibody to β₁ integrins has a similar effect. We also show that the ectodomain of ICAM-5 can stimulate β₁ integrin dependent increases in spike counts and burst number. These results support a growing body of literature suggesting that MMPs have important effects on neuronal excitability. They also support the possibility that MMP dependent shedding of specific synaptic CAMs can contribute to these effects.

The Functional Benefits of Criticality in the Cortex

Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.