Single-neuron discharge properties and network activity in dissociated cultures of neocortex

Proceedings of the First Pediatric Coma and Disorders of Consciousness Symposium by the Curing Coma Campaign, Pediatric Neurocritical Care Research Group, and NINDS: Gearing for Success in Coma Advancements for Children and Neonates

This proceedings article presents the scope of pediatric coma and disorders of consciousness based on presentations and discussions at the First Pediatric Disorders of Consciousness Care and Research symposium held on September 14th, 2021. Herein we review the current state of pediatric coma care and research opportunities as well as shared experiences from seasoned researchers and clinicians. Salient current challenges and opportunities in pediatric and neonatal coma care and research were identified through the contributions of the presenters, who were Jose I. Suarez, MD, Nina F. Schor, MD, PhD, Beth S. Slomine, PhD Erika Molteni, PhD, and Jan-Marino Ramirez, PhD, and moderated by Varina L. Boerwinkle, MD, with overview by Mark Wainwright, MD, and subsequent audience discussion. The program, executively planned by Varina L. Boerwinkle, MD, Mark Wainwright, MD, and Michelle Elena Schober, MD, drove the identification and development of priorities for the pediatric neurocritical care community.

Multidimensional Functional Profiling of Human Neuropathogenic FOXG1 Alleles in Primary Cultures of Murine Pallial Precursors

FOXG1 is an ancient transcription factor gene mastering telencephalic development. A number of distinct structural FOXG1 mutations lead to the “FOXG1 syndrome”, a complex and heterogeneous neuropathological entity, for which no cure is presently available. Reconstruction of primary neurodevelopmental/physiological anomalies evoked by these mutations is an obvious pre-requisite for future, precision therapy of such syndrome. Here, as a proof-of-principle, we functionally scored three FOXG1 neuropathogenic alleles, FOXG1G224S, FOXG1W308X, and FOXG1N232S, against their healthy counterpart. Specifically, we delivered transgenes encoding for them to dedicated preparations of murine pallial precursors and quantified their impact on selected neurodevelopmental and physiological processes mastered by Foxg1: pallial stem cell fate choice, proliferation of neural committed progenitors, neuronal architecture, neuronal activity, and their molecular correlates. Briefly, we found that FOXG1G224S and FOXG1W308X generally performed as a gain- and a loss-of-function-allele, respectively, while FOXG1N232S acted as a mild loss-of-function-allele or phenocopied FOXG1WT. These results provide valuable hints about processes misregulated in patients heterozygous for these mutations, to be re-addressed more stringently in patient iPSC-derivative neuro-organoids. Moreover, they suggest that murine pallial cultures may be employed for fast multidimensional profiling of novel, human neuropathogenic FOXG1 alleles, namely a step propedeutic to timely delivery of therapeutic precision treatments.

Neuronal circuits overcome imbalance in excitation and inhibition by adjusting connection numbers

The interplay between excitation and inhibition is crucial for neuronal circuitry in the brain. Inhibitory cell fractions in the neocortex and hippocampus are typically maintained at 15 to 30%, which is assumed to be important for stable dynamics. We have studied systematically the role of precisely controlled excitatory/inhibitory (E/I) cellular ratios on network activity using mice hippocampal cultures. Surprisingly, networks with varying E/I ratios maintain stable bursting dynamics. Interburst intervals remain constant for most ratios, except in the extremes of 0 to 10% and 90 to 100% inhibitory cells. Single-cell recordings and modeling suggest that networks adapt to chronic alterations of E/I compositions by balancing E/I connectivity. Gradual blockade of inhibition substantiates the agreement between the model and experiment and defines its limits. Combining measurements of population and single-cell activity with theoretical modeling, we provide a clearer picture of how E/I balance is preserved and where it fails in living neuronal networks.

Single-Cell and Neuronal Network Alterations in an In Vitro Model of Fragile X Syndrome

The Fragile X mental retardation protein (FMRP) is involved in many cellular processes and it regulates synaptic and network development in neurons. Its absence is known to lead to intellectual disability, with a wide range of comorbidities including autism. Over the past decades, FMRP research focused on abnormalities both in glutamatergic and GABAergic signaling, and an altered balance between excitation and inhibition has been hypothesized to underlie the clinical consequences of absence of the protein. Using Fmrp knockout mice, we studied an in vitro model of cortical microcircuitry and observed that the loss of FMRP largely affected the electrophysiological correlates of network development and maturation but caused less alterations in single-cell phenotypes. The loss of FMRP also caused a structural increase in the number of excitatory synaptic terminals. Using a mathematical model, we demonstrated that the combination of an increased excitation and reduced inhibition describes best our experimental observations during the ex vivo formation of the network connections.

Foetal neural progenitors contribute to postnatal circuits formation ex vivo: an electrophysiological investigation

Neuronal progenitor cells (NPC) play an essential role in homeostasis of the central nervous system (CNS). Considering their ability to differentiate into specific lineages, their manipulation and control could have a major therapeutic impact for those CNS injuries or degenerative diseases characterized by neuronal cell loss. In this work, we established an in vitro co-culture and tested the ability of foetal NPC (fNPC) to integrate among post-mitotic hippocampal neurons and contribute to the electrical activity of the resulting networks. We performed extracellular electrophysiological recordings of the activity of neuronal networks and compared the properties of spontaneous spiking in hippocampal control cultures (HCC), fNPC, and mixed circuitries ex vivo. We further employed patch-clamp intracellular recordings to examine single-cell excitability. We report of the capability of fNPC to mature when combined to hippocampal neurons, shaping the profile of network activity, a result suggestive of newly formed connectivity ex vivo.

A Computational Model of Interactions Between Neuronal and Astrocytic Networks: The Role of Astrocytes in the Stability of the Neuronal Firing Rate

Recent research in neuroscience indicates the importance of tripartite synapses and gliotransmission mediated by astrocytes in neuronal system modulation. Although the astrocyte and neuronal network functions are interrelated, they are fundamentally different in their signaling patterns and, possibly, the time scales at which they operate. However, the exact nature of gliotransmission and the effect of the tripartite synapse function at the network level are currently elusive. In this paper, we propose a computational model of interactions between an astrocyte network and a neuron network, starting from tripartite synapses and spanning to a joint network level. Our model focuses on a two-dimensional setup emulating a mixed in vitro neuron-astrocyte cell culture. The model depicts astrocyte-released gliotransmitters exerting opposing effects on the neurons: increasing the release probability of the presynaptic neuron while hyperpolarizing the post-synaptic one at a longer time scale. We simulated the joint networks with various levels of astrocyte contributions and neuronal activity levels. Our results indicate that astrocytes prolong the burst duration of neurons, while restricting hyperactivity. Thus, in our model, the effect of astrocytes is homeostatic; the firing rate of the network stabilizes to an intermediate level independently of neuronal base activity. Our computational model highlights the plausible roles of astrocytes in interconnected astrocytic and neuronal networks. Our simulations support recent findings in neurons and astrocytes in vivo and in vitro suggesting that astrocytic networks provide a modulatory role in the bursting of the neuronal network.

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.

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.

The effect of pharmacological inhibition of Serine Proteases on neuronal networks in vitro

Neurons are embedded in an extracellular matrix (ECM), which functions both as a scaffold and as a regulator of neuronal function. The ECM is in turn dynamically altered through the action of serine proteases, which break down its constituents. This pathway has been implicated in the regulation of synaptic plasticity and of neuronal intrinsic excitability. In this study, we determined the short-term effects of interfering with proteolytic processes in the ECM, with a newly developed serine protease inhibitor. We monitored the spontaneous electrophysiological activity of in vitro primary rat cortical cultures, using microelectrode arrays. While pharmacological inhibition at a low dosage had no significant effect, at elevated concentrations it altered significantly network synchronization and functional connectivity but left unaltered single-cell electrical properties. These results suggest that serine protease inhibition affects synaptic properties, likely through its actions on the ECM.

Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

Inference methods are widely used to recover effective models from observed data. However, few studies attempted to investigate the dynamics of inferred models in neuroscience, and none, to our knowledge, at the network level. We introduce a principled modification of a widely used generalized linear model (GLM), and learn its structural and dynamic parameters from in-vitro spike data. The spontaneous activity of the new model captures prominent features of the non-stationary and non-linear dynamics displayed by the biological network, where the reference GLM largely fails, and also reflects fine-grained spatio-temporal dynamical features. Two ingredients were key for success. The first is a saturating transfer function: beyond its biological plausibility, it limits the neuron's information transfer, improving robustness against endogenous and external noise. The second is a super-Poisson spikes generative mechanism; it accounts for the undersampling of the network, and allows the model neuron to flexibly incorporate the observed activity fluctuations.

Challenges in Reproducibility, Replicability, and Comparability of Computational Models and Tools for Neuronal and Glial Networks, Cells, and Subcellular Structures

The possibility to replicate and reproduce published research results is one of the biggest challenges in all areas of science. In computational neuroscience, there are thousands of models available. However, it is rarely possible to reimplement the models based on the information in the original publication, let alone rerun the models just because the model implementations have not been made publicly available. We evaluate and discuss the comparability of a versatile choice of simulation tools: tools for biochemical reactions and spiking neuronal networks, and relatively new tools for growth in cell cultures. The replicability and reproducibility issues are considered for computational models that are equally diverse, including the models for intracellular signal transduction of neurons and glial cells, in addition to single glial cells, neuron-glia interactions, and selected examples of spiking neuronal networks. We also address the comparability of the simulation results with one another to comprehend if the studied models can be used to answer similar research questions. In addition to presenting the challenges in reproducibility and replicability of published results in computational neuroscience, we highlight the need for developing recommendations and good practices for publishing simulation tools and computational models. Model validation and flexible model description must be an integral part of the tool used to simulate and develop computational models. Constant improvement on experimental techniques and recording protocols leads to increasing knowledge about the biophysical mechanisms in neural systems. This poses new challenges for computational neuroscience: extended or completely new computational methods and models may be required. Careful evaluation and categorization of the existing models and tools provide a foundation for these future needs, for constructing multiscale models or extending the models to incorporate additional or more detailed biophysical mechanisms. Improving the quality of publications in computational neuroscience, enabling progressive building of advanced computational models and tools, can be achieved only through adopting publishing standards which underline replicability and reproducibility of research results.

Shaping the Default Activity Pattern of the Cortical Network

Slow oscillations have been suggested as the default emergent activity of the cortical network. This is a low complexity state that integrates neuronal, synaptic, and connectivity properties of the cortex. Shaped by variations of physiological parameters, slow oscillations provide information about the underlying healthy or pathological network. We review how this default activity is shaped, how it acts as a powerful attractor, and how getting out of it is necessary for the brain to recover the levels of complexity associated with conscious states. We propose that slow oscillations provide a robust unifying paradigm for the study of cortical function.

Cortical Dynamics in Presence of Assemblies of Densely Connected Weight-Hub Neurons

Experimental measurements of pairwise connection probability of pyramidal neurons together with the distribution of synaptic weights have been used to construct randomly connected model networks. However, several experimental studies suggest that both wiring and synaptic weight structure between neurons show statistics that differ from random networks. Here we study a network containing a subset of neurons which we call weight-hub neurons, that are characterized by strong inward synapses. We propose a connectivity structure for excitatory neurons that contain assemblies of densely connected weight-hub neurons, while the pairwise connection probability and synaptic weight distribution remain consistent with experimental data. Simulations of such a network with generalized integrate-and-fire neurons display regular and irregular slow oscillations akin to experimentally observed up/down state transitions in the activity of cortical neurons with a broad distribution of pairwise spike correlations. Moreover, stimulation of a model network in the presence or absence of assembly structure exhibits responses similar to light-evoked responses of cortical layers in optogenetically modified animals. We conclude that a high connection probability into and within assemblies of excitatory weight-hub neurons, as it likely is present in some but not all cortical layers, changes the dynamics of a layer of cortical microcircuitry significantly.

Investigating the impact of electrical stimulation temporal distribution on cortical network responses

Background

The brain is continuously targeted by a wealth of stimuli with complex spatio-temporal patterns and has presumably evolved in order to cope with those inputs in an optimal way. Previous studies investigating the response capabilities of either single neurons or intact sensory systems to external stimulation demonstrated that stimuli temporal distribution is an important, if often overlooked, parameter.

Results

In this study we investigated how cortical networks plated over micro-electrode arrays respond to different stimulation sequences in which inter-pulse intervals followed a 1/f^β distribution, for different values of β ranging from 0 to ∞. Cross-correlation analysis revealed that network activity preferentially synchronizes with external input sequences featuring β closer to 1 and, in any case, never for regular (i.e. fixed-frequency) stimulation sequences. We then tested the interplay between different average stimulation frequencies (based on the intrinsic firing/bursting frequency of the network) for two selected values of β, i.e. 1 (scale free) and ∞ (regular). In general, we observed no preference for stimulation frequencies matching the endogenous rhythms of the network. Moreover, we found that in case of regular stimulation the capability of the network to follow the stimulation sequence was negatively correlated to the absolute stimulation frequency, whereas using scale-free stimulation cross-correlation between input and output sequences was independent from average input frequency.

Conclusions

Our results point out that the preference for a scale-free distribution of the stimuli is observed also at network level and should be taken into account in designing more efficient protocols for neuromodulation purposes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12868-017-0366-z) contains supplementary material, which is available to authorized users.

Analysis and Modeling of Subthreshold Neural Multi-Electrode Array Data by Statistical Field Theory

Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous neuronal network activity. The recorded signals comprise several distinct components: Apart from artifacts without biological significance, one can distinguish between spikes (action potentials) and subthreshold fluctuations (local fields potentials). Here we aim to develop a theoretical model that allows for a compact and robust characterization of subthreshold fluctuations in terms of a Gaussian statistical field theory in two spatial and one temporal dimension. What is usually referred to as the driving noise in the context of statistical physics is here interpreted as a representation of the neural activity. Spatial and temporal correlations of this activity give valuable information about the connectivity in the neural tissue. We apply our methods on a dataset obtained from MEA-measurements in an acute hippocampal brain slice from a rat. Our main finding is that the empirical correlation functions indeed obey the logarithmic behavior that is a general feature of theoretical models of this kind. We also find a clear correlation between the activity and the occurrence of spikes. Another important insight is the importance of correctly separating out certain artifacts from the data before proceeding with the analysis.

Mesoscale Architecture Shapes Initiation and Richness of Spontaneous Network Activity

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

Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity

Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.

Brief wide-field photostimuli evoke and modulate oscillatory reverberating activity in cortical networks

Cell assemblies manipulation by optogenetics is pivotal to advance neuroscience and neuroengineering. In in vivo applications, photostimulation often broadly addresses a population of cells simultaneously, leading to feed-forward and to reverberating responses in recurrent microcircuits. The former arise from direct activation of targets downstream, and are straightforward to interpret. The latter are consequence of feedback connectivity and may reflect a variety of time-scales and complex dynamical properties. We investigated wide-field photostimulation in cortical networks in vitro, employing substrate-integrated microelectrode arrays and long-term cultured neuronal networks. We characterized the effect of brief light pulses, while restricting the expression of channelrhodopsin to principal neurons. We evoked robust reverberating responses, oscillating in the physiological gamma frequency range, and found that such a frequency could be reliably manipulated varying the light pulse duration, not its intensity. By pharmacology, mathematical modelling, and intracellular recordings, we conclude that gamma oscillations likely emerge as in vivo from the excitatory-inhibitory interplay and that, unexpectedly, the light stimuli transiently facilitate excitatory synaptic transmission. Of relevance for in vitro models of (dys)functional cortical microcircuitry and in vivo manipulations of cell assemblies, we give for the first time evidence of network-level consequences of the alteration of synaptic physiology by optogenetics.

Stimuli Reduce the Dimensionality of Cortical Activity

The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively localized on smaller subspaces. The dimensionality of the neural space is an important determinant of the computational tasks supported by the neural activity. Here, we investigate the dimensionality of neural ensembles from the sensory cortex of alert rats during periods of ongoing (inter-trial) and stimulus-evoked activity. We find that dimensionality grows linearly with ensemble size, and grows significantly faster during ongoing activity compared to evoked activity. We explain these results using a spiking network model based on a clustered architecture. The model captures the difference in growth rate between ongoing and evoked activity and predicts a characteristic scaling with ensemble size that could be tested in high-density multi-electrode recordings. Moreover, we present a simple theory that predicts the existence of an upper bound on dimensionality. This upper bound is inversely proportional to the amount of pair-wise correlations and, compared to a homogeneous network without clusters, it is larger by a factor equal to the number of clusters. The empirical estimation of such bounds depends on the number and duration of trials and is well predicted by the theory. Together, these results provide a framework to analyze neural dimensionality in alert animals, its behavior under stimulus presentation, and its theoretical dependence on ensemble size, number of clusters, and correlations in spiking network models.

Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model

Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them has been variously recognized in previous works as expression of the excitability of the cortical tissue and the associated nonlinear dynamics, a unified picture of the determinant factors (dynamical and architectural) is desirable and not yet available. Progress has also been partially hindered by the use of a variety of statistical measures to define the network events of interest. We propose here a common probabilistic definition of network events that, applied to the firing activity of cultured neural networks, highlights the co-occurrence of network spikes, power-law distributed avalanches, and exponentially distributed 'quasi-orbits', which offer a third type of collective behavior. A rate model, including synaptic excitation and inhibition with no imposed topology, synaptic short-term depression, and finite-size noise, accounts for all these different, coexisting phenomena. We find that their emergence is largely regulated by the proximity to an oscillatory instability of the dynamics, where the non-linear excitable behavior leads to a self-amplification of activity fluctuations over a wide range of scales in space and time. In this sense, the cultured network dynamics is compatible with an excitation-inhibition balance corresponding to a slightly sub-critical regime. Finally, we propose and test a method to infer the characteristic time of the fatigue process, from the observed time course of the network's firing rate. Unlike the model, possessing a single fatigue mechanism, the cultured network appears to show multiple time scales, signalling the possible coexistence of different fatigue mechanisms.

Impact of sub and supra-threshold adaptation currents in networks of spiking neurons

Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulation of the activity and gain control. The effects of adaptation have already been studied at the single-cell level, resulting from either voltage or calcium gated channels both activated by the spiking activity and modulating the dynamical responses of the neurons. In this study, by disentangling those effects into a linear (sub-threshold) and a non-linear (supra-threshold) part, we focus on the the functional role of those two distinct components of adaptation onto the neuronal activity at various scales, starting from single-cell responses up to recurrent networks dynamics, and under stationary or non-stationary stimulations. The effects of slow currents on collective dynamics, like modulation of population oscillation and reliability of spike patterns, is quantified for various types of adaptation in sparse recurrent networks.

Dynamics of multistable states during ongoing and evoked cortical activity

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the model's ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/f scaling. 1/f scaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

Network bursting dynamics in excitatory cortical neuron cultures results from the combination of different adaptive mechanisms

In the brain, synchronization among cells of an assembly is a common phenomenon, and thought to be functionally relevant. Here we used an in vitro experimental model of cell assemblies, cortical cultures, combined with numerical simulations of a spiking neural network (SNN) to investigate how and why spontaneous synchronization occurs. In order to deal with excitation only, we pharmacologically blocked GABA_Aergic transmission using bicuculline. Synchronous events in cortical cultures tend to involve almost every cell and to display relatively constant durations. We have thus named these “network spikes” (NS). The inter-NS-intervals (INSIs) proved to be a more interesting phenomenon. In most cortical cultures NSs typically come in series or bursts (“bursts of NSs”, BNS), with short (∼1 s) INSIs and separated by long silent intervals (tens of s), which leads to bimodal INSI distributions. This suggests that a facilitating mechanism is at work, presumably short-term synaptic facilitation, as well as two fatigue mechanisms: one with a short timescale, presumably short-term synaptic depression, and another one with a longer timescale, presumably cellular adaptation. We thus incorporated these three mechanisms into the SNN, which, indeed, produced realistic BNSs. Next, we systematically varied the recurrent excitation for various adaptation timescales. Strong excitability led to frequent, quasi-periodic BNSs (CV∼0), and weak excitability led to rare BNSs, approaching a Poisson process (CV∼1). Experimental cultures appear to operate within an intermediate weakly-synchronized regime (CV∼0.5), with an adaptation timescale in the 2–8 s range, and well described by a Poisson-with-refractory-period model. Taken together, our results demonstrate that the INSI statistics are indeed informative: they allowed us to infer the mechanisms at work, and many parameters that we cannot access experimentally.

Quantitative examination of stimulus-response relations in cortical networks in vitro

Variable responses of neuronal networks to repeated sensory or electrical stimuli reflect the interaction of the stimulus' response with ongoing activity in the brain and its modulation by adaptive mechanisms, such as cognitive context, network state, or cellular excitability and synaptic transmission capability. Here, we focus on reliability, length, delays, and variability of evoked responses with respect to their spatial distribution, interaction with spontaneous activity in the networks, and the contribution of GABAergic inhibition. We identified network-intrinsic principles that underlie the formation and modulation of spontaneous activity and stimulus-response relations with the use of state-dependent stimulation in generic neuronal networks in vitro. The duration of spontaneously recurring network-wide bursts of spikes was best predicted by the length of the preceding interval. Length, delay, and structure of responses to identical stimuli systematically depended on stimulus timing and distance to the stimulation site, which were described by a set of simple functions of spontaneous activity. Response length at proximal recording sites increased with the duration of prestimulus inactivity and was best described by a saturation function y( t) = A( 1 − e−α t). Concomitantly, the delays of polysynaptic late responses at distant sites followed an exponential decay y( t) = Be−β t + C. In addition, the speed of propagation was determined by the overall state of the network at the moment of stimulation. Disinhibition increased the number of spikes/network burst and interburst interval length at unchanged gross firing rate, whereas the response modulation by the duration of prestimulus inactivity was preserved. Our data suggest a process of network depression during bursts and subsequent recovery that limit evoked responses following distinct rules. We discuss short-term synaptic depression due to depletion of neurotransmitter vesicles as an underlying mechanism. The seemingly unreliable patterns of spontaneous activity and stimulus-response relations thus follow a predictable structure determined by the interdependencies of network structures and activity states.

Interactions between network synchrony and the dynamics of neuronal threshold

Synchronous activity impacts on a range of functional brain capacities in health and disease. To address the interrelations between cellular level activity and network-wide synchronous events, we implemented in vitro a recently introduced technique, the response clamp, which enables online monitoring of single neuron threshold dynamics while ongoing network synchronous activity continues uninterrupted. We show that the occurrence of a synchronous network event causes a significant biphasic change in the single neuron threshold. These threshold dynamics are correlated across the neurons constituting the network and are entailed by the input to the neurons rather than by their own spiking (i.e., output) activity. The magnitude of network activity during a synchronous event is correlated with the threshold state of individual neurons at the event's onset. Recovery from the impact of a given synchronous event on the neuronal threshold lasts several seconds and seems to be a key determinant of the time to the next spontaneously occurring synchronous event. Moreover, the neuronal threshold is shown to be correlated with the excitability dynamics of the entire network. We conclude that the relations between the two levels (network activity and the single neuron threshold) should be thought of in terms that emphasize their interactive nature.

Network activity and spike discharge oscillations in cortical slice cultures from neonatal rat

Network bursts and oscillations are forms of spontaneous activity in cortical circuits that have been described in vivo and in vitro. Searching for mechanisms involved in their generation, we investigated the collective network activity and spike discharge oscillations in cortical slice cultures of neonatal rats, combining multielectrode arrays with patch clamp recordings from individual neurons. The majority of these cultures showed spontaneous collective network activity [population bursts (PBs)] that could be described as neuronal avalanches. The largest of these PBs were followed by fast spike discharge oscillations in the beta to theta range, and sometimes additional repetitive PBs, together forming seizure-like episodes. During such episodes, all neurons showed sustained depolarization with increased spike rates. However, whereas regular-spiking (RS) and fast-spiking (FS) neurons fired during the PBs, only the FS neurons fired during the fast oscillations. Blockade of N-methyl-d-aspartate receptors reduced the depolarization and suppressed both the increased FS neuron firing and the oscillations. To investigate the generation of PBs, we studied the network responses to electrical stimulation. For most of the stimulation sites, the relationship between the stimulated inputs and the evoked PBs was linear. From a few stimulation sites, however, large PBs could be evoked with small inputs, indicating the activation of hub circuits. Taken together, our findings suggests that the oscillations originate from recurrent inhibition in local networks of depolarized inhibitory FS interneurons, whereas the PBs originate from recurrent excitation in networks of RS and FS neurons that is initiated in hub circuits.

Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity

Rhythms at slow (<1 Hz) frequency of alternating Up and Down states occur during slow-wave sleep states, under deep anaesthesia and in cortical slices of mammals maintained in vitro. Such spontaneous oscillations result from the interplay between network reverberations nonlinearly sustained by a strong synaptic coupling and a fatigue mechanism inhibiting the neurons firing in an activity-dependent manner. Varying pharmacologically the excitability level of brain slices we exploit the network dynamics underlying slow rhythms, uncovering an intrinsic anticorrelation between Up and Down state durations. Besides, a non-monotonic change of Down state duration is also observed, which shrinks the distribution of the accessible frequencies of the slow rhythms. Attractor dynamics with activity-dependent self-inhibition predicts a similar trend even when the system excitability is reduced, because of a stability loss of Up and Down states. Hence, such cortical rhythms tend to display a maximal size of the distribution of Up/Down frequencies, envisaging the location of the system dynamics on a critical boundary of the parameter space. This would be an optimal solution for the system in order to display a wide spectrum of dynamical regimes and timescales.

Inferring network dynamics and neuron properties from population recordings

Understanding the computational capabilities of the nervous system means to “identify” its emergent multiscale dynamics. For this purpose, we propose a novel model-driven identification procedure and apply it to sparsely connected populations of excitatory integrate-and-fire neurons with spike frequency adaptation (SFA). Our method does not characterize the system from its microscopic elements in a bottom-up fashion, and does not resort to any linearization. We investigate networks as a whole, inferring their properties from the response dynamics of the instantaneous discharge rate to brief and aspecific supra-threshold stimulations. While several available methods assume generic expressions for the system as a black box, we adopt a mean-field theory for the evolution of the network transparently parameterized by identified elements (such as dynamic timescales), which are in turn non-trivially related to single-neuron properties. In particular, from the elicited transient responses, the input–output gain function of the neurons in the network is extracted and direct links to the microscopic level are made available: indeed, we show how to extract the decay time constant of the SFA, the absolute refractory period and the average synaptic efficacy. In addition and contrary to previous attempts, our method captures the system dynamics across bifurcations separating qualitatively different dynamical regimes. The robustness and the generality of the methodology is tested on controlled simulations, reporting a good agreement between theoretically expected and identified values. The assumptions behind the underlying theoretical framework make the method readily applicable to biological preparations like cultured neuron networks and in vitro brain slices.

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

Rhythmic bursting is the most striking behavior of cultured cortical networks and may start in the second week after plating. In this study, we focus on the intervals between spontaneously occurring bursts, and compare experimentally recorded values with model simulations. In the models, we use standard neurons and synapses, with physiologically plausible parameters taken from literature. All networks had a random recurrent architecture with sparsely connected neurons. The number of neurons varied between 500 and 5,000. We find that network models with homogeneous synaptic strengths produce asynchronous spiking or stable regular bursts. The latter, however, are in a range not seen in recordings. By increasing the synaptic strength in a (randomly chosen) subset of neurons, our simulations show interburst intervals (IBIs) that agree better with in vitro experiments. In this regime, called weakly synchronized, the models produce irregular network bursts, which are initiated by neurons with relatively stronger synapses. In some noise-driven networks, a subthreshold, deterministic, input is applied to neurons with strong synapses, to mimic pacemaker network drive. We show that models with such "intrinsically active neurons" (pacemaker-driven models) tend to generate IBIs that are determined by the frequency of the fastest pacemaker and do not resemble experimental data. Alternatively, noise-driven models yield realistic IBIs. Generally, we found that large-scale noise-driven neuronal network models required synaptic strengths with a bimodal distribution to reproduce the experimentally observed IBI range. Our results imply that the results obtained from small network models cannot simply be extrapolated to models of more realistic size. Synaptic strengths in large-scale neuronal network simulations need readjustment to a bimodal distribution, whereas small networks do not require such changes.

The dynamics of integrate-and-fire: mean versus variance modulations and dependence on baseline parameters

The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low and moderate frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. However, the cutoff shows a rapid, supralinear increase with firing rate, with a steeper increase in the case of lower noise. For modulations of the input variance, the gain at high frequency remains finite. Here, we show that the low-frequency responses depend strongly on baseline parameters and derive an analytic condition specifying the parameters at which responses switch from being dominated by low versus high frequencies. Additionally, we show that the resonant responses for variance modulations have properties not expected for common oscillatory resonances: they peak at frequencies higher than the baseline firing rate and persist when oscillatory spiking is disrupted by high noise. Finally, the responses to mean and variance modulations are shown to have a complementary dependence on baseline parameters at higher frequencies, resulting in responses to modulations of Poisson input rates that are independent of baseline input statistics.

Slow intrinsic oscillations in thick neocortical slices of hypoxia tolerant deep diving seals

Direct evidence that the mammalian neocortex is an important generator of intrinsic activity comes from isolated neocortical slices that spontaneously generate multiple rhythms including those in the beta, delta and gamma range. These oscillations are also seen in intact animals where they interact with other areas including the hippocampus, thalamus and basal ganglia. Here we show that thick isolated neocortical slices from hooded seals intrinsically generate persistent spontaneous activities, both repetitive non-rhythmic activity with activity states lasting for several minutes, and oscillating activity with rhythms that are much slower (<0.1 Hz) than the rhythms previously described in vitro. These intrinsic activities were very robust and persisted for up to 1 h even in severely hypoxic conditions. We hypothesize that the remarkable hypoxia tolerance of the hooded seal nervous system made it possible to maintain functional integrity in slices thick enough to preserve intact neuronal networks capable of generating these slow oscillations. The observed activities in seal neocortical slices support the notion that mammalian cortical networks intrinsically generate multiple states of activity that include oscillatory activity all the way down to <0.1 Hz. This intrinsic neocortical excitability is an important contributor not only to sleep but also to the default awake state of the neocortex.

Tracking burst patterns in hippocampal cultures with high-density CMOS-MEAs

In this work, we investigate the spontaneous bursting behaviour expressed by in vitro hippocampal networks by using a high-resolution CMOS-based microelectrode array (MEA), featuring 4096 electrodes, inter-electrode spacing of 21 µm and temporal resolution of 130 µs. In particular, we report an original development of an adapted analysis method enabling us to investigate spatial and temporal patterns of activity and the interplay between successive network bursts (NBs). We first defined and detected NBs, and then, we analysed the spatial and temporal behaviour of these events with an algorithm based on the centre of activity trajectory. We further refined the analysis by using a technique derived from statistical mechanics, capable of distinguishing the two main phases of NBs, i.e. (i) a propagating and (ii) a reverberating phase, and by classifying the trajectory patterns. Finally, this methodology was applied to signal representations based on spike detection, i.e. the instantaneous firing rate, and directly based on voltage-coded raw data, i.e. activity movies. Results highlight the potentialities of this approach to investigate fundamental issues on spontaneous neuronal dynamics and suggest the hypothesis that neurons operate in a sort of 'team' to the perpetuation of the transmission of the same information.

Fractals in the nervous system: conceptual implications for theoretical neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.

Contribution of GABAergic interneurons to the development of spontaneous activity patterns in cultured neocortical networks

Periodic synchronized events are a hallmark feature of developing neuronal networks and are assumed to be crucial for the maturation of the neuronal circuitry. In the developing neocortex, the early network oscillations coincide with an excitatory action of the neurotransmitter gamma-aminobutyric acid (GABA). A relationship between the emerging inhibitory action of GABA and the gradual disappearance of early synchronized network activity has been previously suggested. Therefore we investigate the interplay between the action of GABA and spontaneous activity in cultured networks of the lateral or dorsal embryonic rat neocortex, which show considerable difference in the content of GABAergic neurons. Here we present the results of long-term monitoring of spontaneous electrical activity of cultured networks growing on microelectrode arrays and the time course of changes in GABA action using calcium imaging. All cultures studied displayed stereotyped synchronized burst events at the end of the first week in vitro. As the GABA_A depolarizing action decreases, naturally or after bumetanide treatment, network activity in lateral cortex cultures changed from stereotypic bursting to more clustered and asynchronous activity patterns. Dorsal cortex cultures and cultures lacking GABA_A-receptor mediated synaptic transmission, retained an immature synchronous firing pattern, but developed prominent intraburst oscillations (∼3–10 Hz). Large, mostly parvalbumin positive, GABAergic neurons dominate the GABAergic population in lateral cortex cultures. These large interneurons were virtually absent in dorsal cortex cultures. Based on these results, we suggest that the richly interconnected large GABAergic neurons contribute to desynchronize and temporally differentiate the spontaneous activity of cultured cortical networks.

Directional neurite growth using carbon nanotube patterned substrates as a biomimetic cue

Researchers have made extensive efforts to mimic or reverse-engineer in vivo neural circuits using micropatterning technology. Various surface chemical cues or topographical structures have been proposed to design neuronal networks in vitro. In this paper, we propose a carbon nanotube (CNT)-based network engineering method which naturally mimics the structure of extracellular matrix (ECM). On CNT patterned substrates, poly-L-lysine (PLL) was coated, and E18 rat hippocampal neurons were cultured. In the early developmental stage, soma adhesion and neurite extension occurred in disregard of the surface CNT patterns. However, later the majority of neurites selectively grew along CNT patterns and extended further than other neurites that originally did not follow the patterns. Long-term cultured neuronal networks had a strong resemblance to the in vivo neural circuit structures. The selective guidance is possibly attributed to higher PLL adsorption on CNT patterns and the nanomesh structure of the CNT patterns. The results showed that CNT patterned substrates can be used as novel neuronal patterning substrates for in vitro neural engineering.

Orchestration of "presto" and "largo" synchrony in up-down activity of cortical networks

It has been demonstrated using single-cell and multiunit electrophysiology in layer III entorhinal cortex and disinhibited hippocampal CA3 slices that the balancing of the up-down activity is characterized by both GABA_A and GABA_B mechanisms. Here we report novel results obtained using multi-electrode array (60 electrodes) simultaneous recordings from reverberating postnatal neocortical networks containing 19.2 ± 1.4% GABAergic neurons, typical of intact tissue. We observed that in each spontaneous active-state the total number of spikes in identified clusters of excitatory and inhibitory neurons is almost equal, thus suggesting a balanced average activity. Interestingly, in the active-state, the early phase is sustained by only 10% of the total spikes and the firing rate follows a sigmoidal regenerative mode up to peak at 35 ms with the number of excitatory spikes greater than inhibitory, therefore indicating an early unbalance. Concentration-response pharmacology of up- and down-state lifetimes in clusters of excitatory (n = 1067) and inhibitory (n = 305) cells suggests that, besides the GABA_A and GABA_B mechanisms, others such as GAT-1-mediated uptake, I_h, I_NaP and I_M ion channel activity, robustly govern both up- and down-activity. Some drugs resulted to affect up- and/or down-states with different IC₅₀s, providing evidence that various mechanisms are involved. These results should reinforce not only the role of synchrony in CNS networks, but also the recognized analogies between the Hodgkin–Huxley action potential and the population bursts as basic mechanisms for originating membrane excitability and CNS network synchronization, respectively.

Network bursts in cortical cultures are best simulated using pacemaker neurons and adaptive synapses

One of the most specific and exhibited features in the electrical activity of dissociated cultured neural networks (NNs) is the phenomenon of synchronized bursts, whose profiles vary widely in shape, width and firing rate. On the way to understanding the organization and behavior of biological NNs, we reproduced those features with random connectivity network models with 5,000 neurons. While the common approach to induce bursting behavior in neuronal network models is noise injection, there is experimental evidence suggesting the existence of pacemaker-like neurons. In our simulations noise did evoke bursts, but with an unrealistically gentle rising slope. We show that a small subset of 'pacemaker' neurons can trigger bursts with a more realistic profile. We found that adding pacemaker-like neurons as well as adaptive synapses yield burst features (shape, width, and height of the main phase) in the same ranges as obtained experimentally. Finally, we demonstrate how changes in network connectivity, transmission delays, and excitatory fraction influence network burst features quantitatively.

Mechanism for the universal pattern of activity in developing neuronal networks

Spontaneous episodic activity is a fundamental mode of operation of developing networks. Surprisingly, the duration of an episode of activity correlates with the length of the silent interval that precedes it, but not with the interval that follows. Here we use a modeling approach to explain this characteristic, but thus far unexplained, feature of developing networks. Because the correlation pattern is observed in networks with different structures and components, a satisfactory model needs to generate the right pattern of activity regardless of the details of network architecture or individual cell properties. We thus developed simple models incorporating excitatory coupling between heterogeneous neurons and activity-dependent synaptic depression. These models robustly generated episodic activity with the correct correlation pattern. The correlation pattern resulted from episodes being triggered at random levels of recovery from depression while they terminated around the same level of depression. To explain this fundamental difference between episode onset and termination, we used a mean field model, where only average activity and average level of recovery from synaptic depression are considered. In this model, episode onset is highly sensitive to inputs. Thus noise resulting from random coincidences in the spike times of individual neurons led to the high variability at episode onset and to the observed correlation pattern. This work further shows that networks with widely different architectures, different cell types, and different functions all operate according to the same general mechanism early in their development.

Niche-dependent development of functional neuronal networks from embryonic stem cell-derived neural populations

BACKGROUND

The present work was performed to investigate the ability of two different embryonic stem (ES) cell-derived neural precursor populations to generate functional neuronal networks in vitro. The first ES cell-derived neural precursor population was cultivated as free-floating neural aggregates which are known to form a developmental niche comprising different types of neural cells, including neural precursor cells (NPCs), progenitor cells and even further matured cells. This niche provides by itself a variety of different growth factors and extracellular matrix proteins that influence the proliferation and differentiation of neural precursor and progenitor cells. The second population was cultivated adherently in monolayer cultures to control most stringently the extracellular environment. This population comprises highly homogeneous NPCs which are supposed to represent an attractive way to provide well-defined neuronal progeny. However, the ability of these different ES cell-derived immature neural cell populations to generate functional neuronal networks has not been assessed so far.

RESULTS

While both precursor populations were shown to differentiate into sufficient quantities of mature NeuN+ neurons that also express GABA or vesicular-glutamate-transporter-2 (vGlut2), only aggregate-derived neuronal populations exhibited a synchronously oscillating network activity 24 weeks after initiating the differentiation as detected by the microelectrode array technology. Neurons derived from homogeneous NPCs within monolayer cultures did merely show uncorrelated spiking activity even when differentiated for up to 12 weeks. We demonstrated that these neurons exhibited sparsely ramified neurites and an embryonic vGlut2 distribution suggesting an inhibited terminal neuronal maturation. In comparison, neurons derived from heterogeneous populations within neural aggregates appeared as fully mature with a dense neurite network and punctuated vGlut2 expression within presynaptic vesicles. Also those NPCs that had migrated away from adherent neural aggregates maintained their ability to generate a synchronously oscillating neuronal network, even if they were separated from adherent aggregates, dissociated and re-plated.

CONCLUSION

These findings suggest that the complex environment within niches and aggregates of heterogeneous neural cell populations support the generation of fully mature neurons and functional neuronal networks from ES cell-derived neural cells. In contrast, homogeneous ES cell-derived NPCs within monolayer cultures exhibited an impaired functional neuronal maturation.

Short-latency cross- and autocorrelation identify clusters of interacting cortical neurons recorded from multi-electrode array

Spontaneous bursting activity is present in vivo during CNS development and in vitro in neocortex slices. A prerequisite for understanding the cooperative behavior in neuronal ensembles is large-scale simultaneous extracellular electrophysiology by using either "tetrodes" (4-wire electrode) in awake animals or multi-electrode arrays (MEA) in long-term cultured networks as we did here. We show that from a single low-noise MEA electrode it is possible to identify up to 3-4 types of waveforms whose time stamps show excitatory and inhibitory short-latency (2-4 ms) cross-correlations, indicative of monosynaptic connections. Moreover, the MEA units autocorrelagrams (AC) resulted to have behaviors similar to those demonstrated in vivo by using tetrodes or shanks. Principal component analysis of AC followed by a K-means classification returned 3-4 different clusters whose firing- and burst-related properties were typical of assemblies of putative excitatory and inhibitory neurons. By manipulating the networks with a GABA(A) antagonist (gabazine), we could detect cell groups selectively responding to blockade of GABA transmission with IC(50)s of 82+/-2 and 770+/-70 nM. These methods, expanded to organotypic co-cultures of CNS regions may be useful to better understand their connecting properties in studies of regenerative medicine.

Carbon nanotubes might improve neuronal performance by favouring electrical shortcuts

Carbon nanotubes have been applied in several areas of nerve tissue engineering to probe and augment cell behaviour, to label and track subcellular components, and to study the growth and organization of neural networks. Recent reports show that nanotubes can sustain and promote neuronal electrical activity in networks of cultured cells, but the ways in which they affect cellular function are still poorly understood. Here, we show, using single-cell electrophysiology techniques, electron microscopy analysis and theoretical modelling, that nanotubes improve the responsiveness of neurons by forming tight contacts with the cell membranes that might favour electrical shortcuts between the proximal and distal compartments of the neuron. We propose the 'electrotonic hypothesis' to explain the physical interactions between the cell and nanotube, and the mechanisms of how carbon nanotubes might affect the collective electrical activity of cultured neuronal networks. These considerations offer a perspective that would allow us to predict or engineer interactions between neurons and carbon nanotubes.

The response of cortical neurons to in vivo-like input current: theory and experiment : I. Noisy inputs with stationary statistics

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

Spontaneous neuronal burst discharges as dependent and independent variables in the maturation of cerebral cortex tissue cultured in vitro: a review of activity-dependent studies in live 'model' systems for the development of intrinsically generated bioelectric slow-wave sleep patterns

A survey is presented of recent experiments which utilize spontaneous neuronal spike trains as dependent and/or independent variables in developing cerebral cortex cultures when synaptic transmission is interfered with for varying periods of time. Special attention is given to current difficulties in selecting suitable preparations for carrying out biologically relevant developmental studies, and in applying spike-train analysis methods with sufficient resolution to detect activity-dependent age and treatment effects. A hierarchy of synchronized nested burst discharges which approximate early slow-wave sleep patterns in the intact organism is established as a stable basis for isolated cortex function. The complexity of reported long- and short-term homeostatic responses to experimental interference with synaptic transmission is reviewed, and the crucial role played by intrinsically generated bioelectric activity in the maturation of cortical networks is emphasized.

Computational models of epileptic activity: a bridge between observation and pathophysiological interpretation

Epilepsy is a neurological disorder characterized by the recurrence of seizures. It affects 50 million people worldwide. Although a considerable number of new antiepileptic drugs with reduced side effects and toxicity have been introduced since the 1950s, 30% of patients remain pharmacoresistant. Although epilepsy research is making progress, advances in understanding drug resistance have been hampered by the complexity of the underlying neuronal systems responsible for epileptic activity. In such systems where short- or long-term plasticity plays a role, pathophysiological alterations may take place at subcellular (i.e., membrane ion channels and neurotransmitter receptors), cellular (neurons), tissular (networks of neurons) and regional (networks of networks of neurons) scales. In such a context, the demand for integrative approaches is high and neurocomputational models become recognized tools for tackling the complexity of epileptic phenomena. The purpose of this report is to provide an overview on computational modeling as a way of structuring and interpreting multimodal data recorded from the epileptic brain. Some examples are briefly described, which illustrate how computational models closely related with either experimental or clinical data can markedly advance our understanding of essential issues in epilepsy such as the transition from background to seizure activity. A commentary is also made on the potential use of such models in the study of therapeutic strategies such as rational drug design or electrical stimulations.

Analysis of cultured neuronal networks using intraburst firing characteristics

It is an open question whether neuronal networks, cultured on multielectrode arrays, retain any capability to usefully process information (learning and memory). A necessary prerequisite for learning is that stimulation can induce lasting changes in the network. To observe these changes, one needs a method to describe the network in sufficient detail, while stable in normal circumstances. We analyzed the spontaneous bursting activity that is encountered in dissociated cultures of rat neocortical cells. Burst profiles (BPs) were made by estimating the instantaneous array-wide firing frequency. The shape of the BPs was found to be stable on a time scale of hours. Spatiotemporal detail is provided by analyzing the instantaneous firing frequency per electrode. The resulting phase profiles (PPs) were estimated by aligning BPs to their peak spiking rate over a period of 15 min. The PPs reveal a stable spatiotemporal pattern of activity during bursts over a period of several hours, making them useful for plasticity and learning studies. We also show that PPs can be used to estimate conditional firing probabilities. Doing so, yields an approach in which network bursting behavior and functional connectivity can be studied.

The dynamical response properties of neocortical neurons to temporally modulated noisy inputs in vitro

Cortical neurons are often classified by current-frequency relationship. Such a static description is inadequate to interpret neuronal responses to time-varying stimuli. Theoretical studies suggested that single-cell dynamical response properties are necessary to interpret ensemble responses to fast input transients. Further, it was shown that input-noise linearizes and boosts the response bandwidth, and that the interplay between the barrage of noisy synaptic currents and the spike-initiation mechanisms determine the dynamical properties of the firing rate. To test these model predictions, we estimated the linear response properties of layer 5 pyramidal cells by injecting a superposition of a small-amplitude sinusoidal wave and a background noise. We characterized the evoked firing probability across many stimulation trials and a range of oscillation frequencies (1-1000 Hz), quantifying response amplitude and phase-shift while changing noise statistics. We found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz. This cut-off frequency is higher than the limits set by passive membrane properties (approximately 50 Hz) and average firing rate (approximately 20 Hz) and is not affected by the rate of change of the input. Finally, above 200 Hz, the response amplitude decays as a power-law with an exponent that is independent of voltage fluctuations induced by the background noise.

The impact of input fluctuations on the frequency-current relationships of layer 5 pyramidal neurons in the rat medial prefrontal cortex

The role of irregular cortical firing in neuronal computation is still debated, and it is unclear how signals carried by fluctuating synaptic potentials are decoded by downstream neurons. We examined in vitro frequency versus current (f-I) relationships of layer 5 (L5) pyramidal cells of the rat medial prefrontal cortex (mPFC) using fluctuating stimuli. Studies in the somatosensory cortex show that L5 neurons become insensitive to input fluctuations as input mean increases and that their f-I response becomes linear. In contrast, our results show that mPFC L5 pyramidal neurons retain an increased sensitivity to input fluctuations, whereas their sensitivity to the input mean diminishes to near zero. This implies that the discharge properties of L5 mPFC neurons are well suited to encode input fluctuations rather than input mean in their firing rates, with important consequences for information processing and stability of persistent activity at the network level.