Manifestation of function-follow-form in cultured neuronal networks

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.

Recurrently connected and localized neuronal communities initiate coordinated spontaneous activity in neuronal networks

Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs), interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities) that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity.

Coordinated spontaneous spiking activity is fundamental for the normal formation of brain circuits during development. However, how ensembles of neurons generate these events remains unclear. To address this question, in the present study, we investigated the network properties that might be required to a neuronal system for the generation of these spontaneous waves of spikes. We performed our study on spontaneously active neuronal cell cultures using high-resolution electrical recordings and a computational network model developed to reproduce our experimental data both quantitatively and qualitatively. Through the analysis of both experimental and simulated data, we found that network bursts are initiated in regions of the network, or “functional communities”, characterized by particular local connectivity properties. We also found that these regions can amplify the background asynchronous spiking activity preceding a network burst and, in this way, can give rise to coordinated spiking events.

As a whole, our results suggest the presence of functional communities of neurons in a developing neuronal system that might naturally emerge by following simple constraints on distance-based connectivity. These regions are most likely required for the generation of the spontaneous coordinated activity that can drive activity-dependent circuit formation.

Collective behavior of large-scale neural networks with GPU acceleration

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.

Narrow microtunnel technology for the isolation and precise identification of axonal communication among distinct hippocampal subregion networks

Communication between different sub regions of the hippocampus is fundamental to learning and memory. However accurate knowledge about information transfer between sub regions from access to the activity in individual axons is lacking. MEMS devices with microtunnels connecting two sub networks have begun to approach this problem but the commonly used 10 μm wide tunnels frequently measure signals from multiple axons. To reduce this complexity, we compared polydimethylsiloxane (PDMS) microtunnel devices each with a separate tunnel width of 2.5, 5 or 10 μm bridging two wells aligned over a multi electrode array (MEA). Primary rat neurons were grown in the chambers with neurons from the dentate gyrus on one side and hippocampal CA3 on the other. After 2–3 weeks of culture, spontaneous activity in the axons inside the tunnels was recorded. We report electrophysiological, exploratory data analysis for feature clustering and visual evidence to support the expectation that 2.5 μm wide tunnels have fewer axons per tunnel and therefore more clearly delineated signals than 10 or 5 μm wide tunnels. Several measures indicated that fewer axons per electrode enabled more accurate detection of spikes. A clustering analysis comparing the variations of spike height and width for different tunnel widths revealed tighter clusters representing unique spikes with less height and width variation when measured in narrow tunnels. Wider tunnels tended toward more diffuse clusters from a continuum of spike heights and widths. Standard deviations for multiple cluster measures, such as Average Dissimilarity, Silhouette Value (S) and Separation Factor (average dissimilarity/S value), support a conclusion that 2.5 μm wide tunnels containing fewer axons enable more precise determination of individual action potential peaks, their propagation direction, timing, and information transfer between sub networks.

Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity

We investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous mean-field approximation to encode the role of network structure and we tune the fraction of inhibitory neurons f_{I} and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on f_{I}, highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through dynamical transitions from synchronous to asynchronous regimes. Furthermore, a metastable regime with long memory of external inputs emerges for a specific fraction of hub inhibitory neurons, underlining the role of inhibition and connectivity also for input processing in neural networks.

Repeating Spatial-Temporal Motifs of CA3 Activity Dependent on Engineered Inputs from Dentate Gyrus Neurons in Live Hippocampal Networks

Anatomical and behavioral studies, and in vivo and slice electrophysiology of the hippocampus suggest specific functions of the dentate gyrus (DG) and the CA3 subregions, but the underlying activity dynamics and repeatability of information processing remains poorly understood. To approach this problem, we engineered separate living networks of the DG and CA3 neurons that develop connections through 51 tunnels for axonal communication. Growing these networks on top of an electrode array enabled us to determine whether the subregion dynamics were separable and repeatable. We found spontaneous development of polarized propagation of 80% of the activity in the native direction from DG to CA3 and different spike and burst dynamics for these subregions. Spatial-temporal differences emerged when the relationships of target CA3 activity were categorized with to the number and timing of inputs from the apposing network. Compared to times of CA3 activity when there was no recorded tunnel input, DG input led to CA3 activity bursts that were 7× more frequent, increased in amplitude and extended in temporal envelope. Logistic regression indicated that a high number of tunnel inputs predict CA3 activity with 90% sensitivity and 70% specificity. Compared to no tunnel input, patterns of >80% tunnel inputs from DG specified different patterns of first-to-fire neurons in the CA3 target well. Clustering dendrograms revealed repeating motifs of three or more patterns at up to 17 sites in CA3 that were importantly associated with specific spatial-temporal patterns of tunnel activity. The number of these motifs recorded in 3 min was significantly higher than shuffled spike activity and not seen above chance in control networks in which CA3 was apposed to CA3 or DG to DG. Together, these results demonstrate spontaneous input-dependent repeatable coding of distributed activity in CA3 networks driven by engineered inputs from DG networks. These functional configurations at measured times of activation (motifs) emerge from anatomically accurate feed-forward connections from DG through tunnels to CA3.

Extrasynaptic glutamate NMDA receptors: key players in striatal function

N-methyl-D-aspartate receptors (NMDAR) are crucial for the function of excitatory neurotransmission and are present at the synapse and on the extrasynaptic membrane. The major nucleus of the basal ganglia, striatum, receives a large glutamatergic excitatory input carrying information about movements and associated sensory stimulation for its proper function. Such bombardment of glutamate synaptic release results in a large extracellular concentration of glutamate that can overcome the neuronal and glial uptake homeostatic systems therefore allowing the stimulation of extrasynaptic glutamate receptors. Here we have studied the participation of their extrasynaptic type in cortically evoked responses or in the presence of NMDARs stimulation. We report that extrasynaptic NMDAR blocker memantine, reduced in a dose-dependent manner cortically induced NMDA excitatory currents in striatal neurons (recorded in zero-Mg(++) plus DNQX 10 μM). Moreover, memantine (2-4 μM) significantly reduced the NMDAR-dependent membrane potential oscillations called up and down states. Recordings of neuronal striatal networks with a fluorescent calcium indicator or with multielectrode arrays (MEA) also showed that memantine reduced in a dose-dependent manner, NMDA-induced excitatory currents and network behavior. We used multielectrode arrays (MEA) to grow segregated cortical and striatal neurons. Once synaptic contacts were developed (>21DIV) recordings of extracellular activity confirmed the cortical drive of spontaneous synchronous discharges in both compartments. After severing connections between compartments, active striatal neurons in the presence of memantine (1 μM) and CNQX (10 μM) were predominantly fast spiking interneurons (FSI). The significance of extrasynaptic receptors in the regulation of striatal function and neuronal network activity is evident.

Identification of neuronal network properties from the spectral analysis of calcium imaging signals in neuronal cultures

Neuronal networks in vitro are prominent systems to study the development of connections in living neuronal networks and the interplay between connectivity, activity and function. These cultured networks show a rich spontaneous activity that evolves concurrently with the connectivity of the underlying network. In this work we monitor the development of neuronal cultures, and record their activity using calcium fluorescence imaging. We use spectral analysis to characterize global dynamical and structural traits of the neuronal cultures. We first observe that the power spectrum can be used as a signature of the state of the network, for instance when inhibition is active or silent, as well as a measure of the network's connectivity strength. Second, the power spectrum identifies prominent developmental changes in the network such as GABA_A switch. And third, the analysis of the spatial distribution of the spectral density, in experiments with a controlled disintegration of the network through CNQX, an AMPA-glutamate receptor antagonist in excitatory neurons, reveals the existence of communities of strongly connected, highly active neurons that display synchronous oscillations. Our work illustrates the interest of spectral analysis for the study of in vitro networks, and its potential use as a network-state indicator, for instance to compare healthy and diseased neuronal networks.

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.

NEuronMOrphological analysis tool: open-source software for quantitative morphometrics

Morphometric analysis of neurons and brain tissue is relevant to the study of neuron circuitry development during the first phases of brain growth or for probing the link between microstructural morphology and degenerative diseases. As neural imaging techniques become ever more sophisticated, so does the amount and complexity of data generated. The NEuronMOrphological analysis tool NEMO was purposely developed to handle and process large numbers of optical microscopy image files of neurons in culture or slices in order to automatically run batch routines, store data and apply multivariate classification and feature extraction using 3-way principal component analysis (PCA). Here we describe the software's main features, underlining the differences between NEMO and other commercial and non-commercial image processing tools, and show an example of how NEMO can be used to classify neurons from wild-type mice and from animal models of autism.

Engineered neuronal circuits: a new platform for studying the role of modular topology

Neuron–glia cultures serve as a valuable model system for exploring the bio-molecular activity of single cells. Since neurons in culture can be conveniently recorded with great fidelity from many sites simultaneously, it has long been suggested that uniform cultured neurons may also be used to investigate network-level mechanisms pertinent to information processing, activity propagation, memory, and learning. But how much of the functionality of neural circuits can be retained in vitro remains an open question. Recent studies utilizing patterned networks suggest that they provide a most useful platform to address fundamental questions in neuroscience. Here we review recent efforts in the realm of patterned networks’ activity investigations. We give a brief overview of the patterning methods and experimental approaches commonly employed in the field, and summarize the main results reported in the literature. The general picture that emerges from these reports indicates that patterned networks with uniform connectivity do not exhibit unique activity patterns. Rather, their activity is very similar to that of unpatterned uniform networks. However, by breaking the connectivity homogeneity, using a modular architecture, it is possible to introduce pronounced topology-related gating and delay effects. These findings suggest that patterned cultured networks may serve as a new platform for studying the role of modularity in neuronal circuits.

Influence of time delay and channel blocking on multiple coherence resonance in Hodgkin-Huxley neuron networks

Toxins such as tetraethylammonium (TEA) and tetrodotoxin (TTX) may reduce the number of working potassium and sodium ion channels by poisoning and making them blocked, respectively. In this paper, we study how channel blocking (CB) affects the time delay-induced multiple coherence resonance (MCR), i.e., a phenomenon that the spiking of neuronal networks intermittently reaches the most ordered state, in stochastic Hodgkin-Huxley neuron networks. It is found that potassium and sodium CB have distinct effects. For potassium CB, the MCR occurs more frequently as the CB develops, but for sodium CB the MCR is badly impaired and only the first coherence resonance (CR) holds and, consequently, the MCR evolves into a single CR as sodium CB develops. We found for sodium CB the spiking becomes disordered at larger delay lengths, which may be the reason for the destruction of the MCR. The underlying mechanism is briefly discussed in terms of distinct effects of potassium and sodium CB on the spiking activity. These results show that potassium CB can increase the frequency of MCR with time delay, but sodium CB may suppress and even destroy the delay-induced MCR. These findings may help to understand the joint effects of CB and time delay on the spiking coherence of neuronal networks.

Representation and learning in neuronal networks: a conceptual nervous system approach

The work presented in this review describes the use of large cortical networks developing ex vivo, in a culture dish, to study principles underlying synchronization, adaptation, learning, and representation in neuronal assemblies. The motivation to study neuronal networks ex vivo is outlined together with a short description of recent results in this field. Following a short description of the experimental system, a set of basic results will be presented that concern self-organization of activity, dynamical and functional properties of neurons and networks in response to external stimulation. This short review ends with an outline of future questions and research directions.

Synaptic scaling stabilizes persistent activity driven by asynchronous neurotransmitter release

Small networks of cultured hippocampal neurons respond to transient stimulation with rhythmic network activity (reverberation) that persists for several seconds, constituting an in vitro model of synchrony, working memory, and seizure. This mode of activity has been shown theoretically and experimentally to depend on asynchronous neurotransmitter release (an essential feature of the developing hippocampus) and is supported by a variety of developing neuronal networks despite variability in the size of populations (10-200 neurons) and in patterns of synaptic connectivity. It has previously been reported in computational models that "small-world" connection topology is ideal for the propagation of similar modes of network activity, although this has been shown only for neurons utilizing synchronous (phasic) synaptic transmission. We investigated how topological constraints on synaptic connectivity could shape the stability of reverberations in small networks that also use asynchronous synaptic transmission. We found that reverberation duration in such networks was resistant to changes in topology and scaled poorly with network size. However, normalization of synaptic drive, by reducing the variance of synaptic input across neurons, stabilized reverberation in such networks. Our results thus suggest that the stability of both normal and pathological states in developing networks might be shaped by variance-normalizing constraints on synaptic drive. We offer an experimental prediction for the consequences of such regulation on the behavior of small networks.

Innate synchronous oscillations in freely-organized small neuronal circuits

Background

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

Methodology/Principal Findings

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

Conclusions/Significance

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

Wrestling model of the repertoire of activity propagation modes in quadruple neural networks

The spontaneous activity of engineered quadruple cultured neural networks (of four-coupled sub-networks) exhibits a repertoire of different types of mutual synchronization events. Each event corresponds to a specific activity propagation mode (APM) defined by the order of activity propagation between the sub-networks. We statistically characterized the frequency of spontaneous appearance of the different types of APMs. The relative frequencies of the APMs were then examined for their power-law properties. We found that the frequencies of appearance of the leading (most frequent) APMs have close to constant algebraic ratio reminiscent of Zipf's scaling of words. We show that the observations are consistent with a simplified “wrestling” model. This model represents an extension of the “boxing arena” model which was previously proposed to describe the ratio between the two activity modes in two coupled sub-networks. The additional new element in the “wrestling” model presented here is that the firing within each network is modeled by a time interval generator with similar intra-network Lévy distribution. We modeled the different burst-initiation zones’ interaction by competition between the stochastic generators with Gaussian inter-network variability. Estimation of the model parameters revealed similarity across different cultures while the inter-burst-interval of the cultures was similar across different APMs as numerical simulation of the model predicts.

Effect of network topology on neuronal encoding based on spatiotemporal patterns of spikes

Despite significant progress in our understanding of the brain at both microscopic and macroscopic scales, the mechanisms by which low-level neuronal behavior gives rise to high-level mental processes such as memory still remain unknown. In this paper, we assess the plausibility and quantify the performance of polychronization, a newly proposed mechanism of neuronal encoding, which has been suggested to underlie a wide range of cognitive phenomena. We then investigate the effect of network topology on the reliability with which input stimuli can be distinguished based on their encoding in the form of so-called polychronous groups or spatiotemporal patterns of spikes. We find that small-world networks perform an order of magnitude better than random ones, enabling reliable discrimination between inputs even when prompted by increasingly incomplete recall cues. Furthermore, we show that small-world architectures operate at significantly reduced energetic costs and that their memory capacity scales favorably with network size. Finally, we find that small-world topologies introduce biologically realistic constraints on the optimal input stimuli, favoring especially the topographic inputs known to exist in many cortical areas. Our results suggest that mammalian cortical networks, by virtue of being both small-world and topographically organized, seem particularly well-suited to information processing through polychronization. This article addresses the fundamental question of encoding in neuroscience. In particular, evidence is presented in support of an emerging model of neuronal encoding in the neocortex based on spatiotemporal patterns of spikes.

Designing Neural Networks in Culture: Experiments are described for controlled growth, of nerve cells taken from rats, in predesigned geometrical patterns on laboratory culture dishes

Technology has advanced to where it is possible to design and grow-with predefined geometry and surprisingly good fidelity-living networks of neurons in culture dishes. Here we overview the elements of design, emphasizing the lithographic techniques that alter the cell culture surface which in turn influences the attachment and growth of the neural networks. Advanced capability in this area makes it possible to design networks of desired complexity. Other issues addressed include the influence of glial cells and media on activity and the potential for extending the designs into three dimensions. Investigators are advancing the art and science of analyzing and controlling through stimulation the function of the neural networks, including the ability to take advantage of their geometric form in order to influence functional properties.

Synchronization transitions on scale-free neuronal networks due to finite information transmission delays

We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the underlying model of neuronal dynamics, we use the efficient Rulkov map with additive noise. We show that increasing the coupling strength enhances synchronization monotonously, whereas delay plays a more subtle role. In particular, we found that depending on the inherent oscillation frequency of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions manifest as well-expressed minima in the measure for spatial synchrony, appearing at every multiple of the oscillation frequency. Larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization. These results are robust against variations in system size, intensity of additive noise, and the scaling exponent of the underlying scale-free topology. We argue that fine-tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and, indeed, they should be seen as important as the coupling strength or the overall density of interneuronal connections. We finally discuss some biological implications of the presented results.

The selectivity of noise and coupling for coherence biresonance and array-enhanced coherence biresonance in coupled neural systems

The selectivity of noise and coupling for coherence biresonance (CBR) and array-enhanced coherence biresonance (AECBR) in coupled neural systems has been investigated. It is shown that, depending on the coupling strength and noise intensity, various coherence behaviors and phenomena are exhibited, including CBR, coherence resonance without tuning, AECBR and undamped signal transmission. There exist optimal coupling and noise regions for the occurrence of CBR and AECBR in the transmission of noise-induced oscillations (NIOs).

Delay-induced multiple stochastic resonances on scale-free neuronal networks

We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker, respectively, to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, thus providing evidences for stochastic resonance on the scale-free neuronal networks. Interestingly thereby, if the forcing in form of a periodic pulse train is introduced to all neurons forming the network, the stochastic resonance decreases as compared to the case when only a single neuron is paced. Moreover, we show that finite delays in coupling can significantly affect the stochastic resonance on scale-free neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances independently of the placing of the pacemaker, but they can also altogether destroy stochastic resonance. Delay-induced multiple stochastic resonances manifest as well-expressed maxima of the correlation measure, appearing at every multiple of the pacemaker period. We argue that fine-tuned delays and locally active pacemakers are vital for assuring optimal conditions for stochastic resonance on complex neuronal networks.

The emergence and properties of mutual synchronization in in vitro coupled cortical networks

We have studied the emergence of mutual synchronization and activity propagation in coupled neural networks from rat cortical cells grown on a micro-electrode array for parallel activity recording of dozens of neurons. The activity of each sub-network by itself is marked by the formation of synchronized bursting events (SBE) - short time windows of rapid neuronal firing. The joint activity of two coupled networks is characterized by the formation of mutual synchronization, i.e. the formation of SBE whose activity starts at one sub-network and then propagates to the other. The sub-networks switch roles in initiating the mutual SBE. However, spontaneous propagation (initiation) asymmetry emerges - one of the sub-networks takes on the role of initiating substantially more mutual SBE than the other, despite the fact that the two are engineered to be similar in size and cell density. Analysis of the interneuron correlations in the SBE also reveals the emergence of activity (function) asymmetry - one sub-network develops a more organized structure of correlations. We also show activity propagation and mutual synchronization in four coupled networks. Using computer simulations, we propose that the function asymmetry reflects asymmetry between the internal connectivity of the two networks, whereas the propagation asymmetry reflects asymmetry in the connectivity between the sub-networks. These results agree with the experimental findings that the initiation and function asymmetry can be separately regulated, which implies that information transfer (activity propagation) and information processing (function) can be regulated separately in coupled neural networks.

Stochastic resonance on weakly paced scale-free networks

We study the impact of additive Gaussian noise and weak periodic forcing on the dynamics of a scale-free network of bistable overdamped oscillators. The periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble. We show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal, thus providing evidence for stochastic resonance on weakly paced scale-free networks. Because of the inherent degree inhomogeneity of individual oscillators forming the scale-free network, the placement of the pacemaker within the network is thereby crucial. As two extremes, we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree. In both cases the coupling strength plays a crucial role, since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator. Higher coupling strengths facilitate the global outreach of the pacemaker, but require higher noise intensities for the optimal response. In contrast, lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator. If the pacemaker is introduced to the main hub, the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale-free networks. We corroborate the importance of the inhomogeneous structure of scale-free networks by additionally considering regular networks of oscillators with different degrees of coupling.

Narrow-band oscillations in probabilistic cellular automata

Dynamical properties of neural populations are studied using probabilistic cellular automata. Previous work demonstrated the emergence of critical behavior as the function of system noise and density of long-range axonal connections. Finite-size scaling theory identified critical properties, which were consistent with properties of a weak Ising universality class. The present work extends the studies to neural populations with excitatory and inhibitory interactions. It is shown that the populations can exhibit narrow-band oscillations when confined to a range of inhibition levels, with clear boundaries marking the parameter region of prominent oscillations. Phase diagrams have been constructed to characterize unimodal, bimodal, and quadromodal oscillatory states. The significance of these findings is discussed in the context of large-scale narrow-band oscillations in neural tissues, as observed in electroencephalographic and magnetoencephalographic measurements.

Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.

Stochastic resonance on excitable small-world networks via a pacemaker

We show that the correlation between the frequency of subthreshold pacemaker activity and the response of an excitable array is resonantly dependent on the intensity of additive spatiotemporal noise. Thereby, the effect of the underlying network, defining the interactions among excitable units, largely depends on the coupling strength. Only for intermediate coupling strengths is the small world property able to enhance the stochastic resonance, whereas for smaller and larger couplings the impact of the transition from diffusive to random networks is less profound. Thus, the optimal interplay between a localized source of weak rhythmic activity and the response of the whole array demands a delicate balance between the strength of excitation transfer and the effectiveness of the network structure to support it.

Plasticity of recurring spatiotemporal activity patterns in cortical networks

How do neurons encode and store information for long periods of time? Recurring patterns of activity have been reported in various cortical structures and were suggested to play a role in information processing and memory. To study the potential role of bursts of action potentials in memory mechanisms, we investigated patterns of spontaneous multi-single-unit activity in dissociated rat cortical cultures in vitro. Spontaneous spikes were recorded from networks of approximately 50 000 neurons and glia cultured on a grid of 60 extracellular substrate- embedded electrodes (multi-electrode arrays). These networks expressed spontaneous culture- wide bursting from approximately one week in vitro. During bursts, a large portion of the active electrodes showed elevated levels of firing. Spatiotemporal activity patterns within spontaneous bursts were clustered using a correlation-based clustering algorithm, and the occurrences of these burst clusters were tracked over several hours. This analysis revealed spatiotemporally diverse bursts occurring in well-defined patterns, which remained stable for several hours. Activity evoked by strong local tetanic stimulation resulted in significant changes in the occurrences of spontaneous bursts belonging to different clusters, indicating that the dynamical flow of information in the neuronal network had been altered. The diversity of spatiotemporal structure and long-term stability of spontaneous bursts together with their plastic nature strongly suggests that such network patterns could be used as codes for information transfer and the expression of memories stored in cortical networks.

Dynamics of learning in cultured neuronal networks with antagonists of glutamate receptors

Cognitive dysfunction may result from abnormality of ionotropic glutamate receptors. Although various forms of synaptic plasticity in learning that rely on altering of glutamate receptors have been considered, the evidence is insufficient from an informatics view. Dynamics could reflect neuroinformatics encoding, including temporal pattern encoding, spatial pattern encoding, and energy distribution. Discovering informatics encoding is fundamental and crucial to understanding the working principle of the neural system. In this article, we analyzed the dynamic characteristics of response activities during learning training in cultured hippocampal networks under normal and abnormal conditions of ionotropic glutamate receptors, respectively. The rate, which is one of the temporal configurations, was decreased markedly by inhibition of alpha-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid (AMPA) receptors. Moreover, the energy distribution in different characteristic frequencies was changed markedly by inhibition of AMPA receptors. Spatial configurations, including regularization, correlation, and synchrony, were changed significantly by inhibition of N-methyl-d-aspartate receptors. These results suggest that temporal pattern encoding and energy distribution of response activities in cultured hippocampal neuronal networks during learning training are modulated by AMPA receptors, whereas spatial pattern encoding of response activities is modulated by N-methyl-d-aspartate receptors.

Small-world network topology of hippocampal neuronal network is lost, in an in vitro glutamate injury model of epilepsy

Neuronal network topologies and connectivity patterns were explored in control and glutamate-injured hippocampal neuronal networks, cultured on planar multielectrode arrays. Spontaneous activity was characterized by brief episodes of synchronous firing at many sites in the array (network bursts). During such assembly activity, maximum numbers of neurons are known to interact in the network. After brief glutamate exposure followed by recovery, neuronal networks became hypersynchronous and fired network bursts at higher frequency. Connectivity maps were constructed to understand how neurons communicate during a network burst. These maps were obtained by analysing the spike trains using cross-covariance analysis and graph theory methods. Analysis of degree distribution, which is a measure of direct connections between electrodes in a neuronal network, showed exponential and Gaussian distributions in control and glutamate-injured networks, respectively. Although both the networks showed random features, small-world properties in these networks were different. These results suggest that functional two-dimensional neuronal networks in vitro are not scale-free. After brief exposure to glutamate, normal hippocampal neuronal networks became hyperexcitable and fired a larger number of network bursts with altered network topology. The small-world network property was lost and this was accompanied by a change from an exponential to a Gaussian network.

Towards neuro-memory-chip: imprinting multiple memories in cultured neural networks

We show that using local chemical stimulations it is possible to imprint persisting (days) multiple memories (collective modes of neuron firing) in the activity of cultured neural networks. Microdroplets of inhibitory antagonist are injected at a location selected based on real-time analysis of the recorded activity. The neurons at the stimulated locations turn into a focus for initiating synchronized bursting events (the collective modes) each with its own specific spatiotemporal pattern of neuron firing.

Functional holography analysis: simplifying the complexity of dynamical networks

We present a novel functional holography (FH) analysis devised to study the dynamics of task-performing dynamical networks. The latter term refers to networks composed of dynamical systems or elements, like gene networks or neural networks. The new approach is based on the realization that task-performing networks follow some underlying principles that are reflected in their activity. Therefore, the analysis is designed to decipher the existence of simple causal motives that are expected to be embedded in the observed complex activity of the networks under study. First we evaluate the matrix of similarities (correlations) between the activities of the network's components. We then perform collective normalization of the similarities (or affinity transformation) to construct a matrix of functional correlations. Using dimension reduction algorithms on the affinity matrix, the matrix is projected onto a principal three-dimensional space of the leading eigenvectors computed by the algorithm. To retrieve back information that is lost in the dimension reduction, we connect the nodes by colored lines that represent the level of the similarities to construct a holographic network in the principal space. Next we calculate the activity propagation in the network (temporal ordering) using different methods like temporal center of mass and cross correlations. The causal information is superimposed on the holographic network by coloring the nodes locations according to the temporal ordering of their activities. First, we illustrate the analysis for simple, artificially constructed examples. Then we demonstrate that by applying the FH analysis to modeled and real neural networks as well as recorded brain activity, hidden causal manifolds with simple yet characteristic geometrical and topological features are deciphered in the complex activity. The term "functional holography" is used to indicate that the goal of the analysis is to extract the maximum amount of functional information about the dynamical network as a whole unit.

Polychronization: Computation with Spikes

We present a minimal spiking network that can polychronize, that is, exhibit reproducible time-locked but not synchronous firing patterns with millisecond precision, as in synfire braids. The network consists of cortical spiking neurons with axonal conduction delays and spike-timing-dependent plasticity (STDP); a ready-to-use MATLAB code is included. It exhibits sleeplike oscillations, gamma (40 Hz) rhythms, conversion of firing rates to spike timings, and other interesting regimes. Due to the interplay between the delays and STDP, the spiking neurons spontaneously self-organize into groups and generate patterns of stereotypical polychronous activity. To our surprise, the number of coexisting polychronous groups far exceeds the number of neurons in the network, resulting in an unprecedented memory capacity of the system. We speculate on the significance of polychrony to the theory of neuronal group selection (TNGS, neural Darwinism), cognitive neural computations, binding and gamma rhythm, mechanisms of attention, and consciousness as “attention to memories.”