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.

Revealing voxel correlation cliques by functional holography analysis of fMRI.

Data acquired by functional brain imaging are of a multivariate and complex nature. Selecting relevant topographically specific information for system-level analysis is a highly non-trivial task. This challenge has traditionally been addressed by hypothesis-driven approaches. Recently, data-driven methods making no a priori assumptions about the signal were developed. Here, we present a hybrid approach, selecting data-driven voxels in paradigm-driven measurements in order to identify functional connectivity motifs in the voxel correlations. Our tool is the functional holography (FH) method, originally developed for analyzing electrophysiological recordings and based on analyzing the voxel-voxel correlation matrices. The algorithm selects the relevant voxels using a dendrogram clustering method combined with a unique standard deviation (STD) filter, identifying the voxels with high STD correlations. Functional connectivity motifs are revealed through a dimension-reduction procedure by principal component analysis (PCA) allowing for a reduced three-dimensional holographic presentation space. Information loss due to PCA is retrieved by connecting voxels in the reduced space with lines that are color-coded according to the correlations. Our results show that the FH analysis performed for a single trial reveals interesting motifs, even in a simple motor task: unilateral hand movements yielded two clusters, one in the contralateral M1 region showing neuronal activation and one in the ipsilateral homologues region showing deactivation. Thus, according to a single trial level analysis, of 12-time points alone, we can determine which hand the subject moved. Moreover, using cluster quantification based on eigenvalue entropy calculation, we obtained good separation between right- and left-handed subjects.

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.

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.

Study of hypothermia on cultured neuronal networks using multi-electrode arrays.

Efficient and safe use of hypothermia during various neuro-medical procedures requires sound understanding of low temperature effects on the neuronal network's activity. In this report, we introduce the use of cultivated dissociated neuronal networks on temperature controlled multi-electrode arrays (MEAs) as a simple methodology for studying the long-term effects of hypothermia. The networks exhibit spontaneous activity in the form of synchronized bursting events (SBEs), followed by long intervals of sporadic firing. Through the use of our correlation method, these SBEs can be clustered into sub-groups of similar spatio-temporal patterns. Application of hypothermia to the network resulted in a reduction in the SBE rate, the spike intensity and an increase in inter-neuronal correlations. Within 2h following the cessation of hypothermia, the cultured network returned to its initial spatio-temporal SBE structure. These results suggest that the network survived cold exposure and demonstrate the feasibility of long-term continuous neural network recording during hypothermic conditions.

Time-invariant person-specific frequency templates in human brain activity.

The various human brain tasks are performed at different locations and time scales. Yet, we discovered the existence of time-invariant (above an essential time scale) partitioning of the brain activity into personal state-specific frequency bands. For that, we perform temporal and ensemble averaging of best wavelet packet bases from multielectrode electroencephalogram recordings. These personal frequency bands provide new templates for quantitative analyses of brain function, e.g., normal versus epileptic activity.

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.

Manifestation of function-follow-form in cultured neuronal networks.

We expose hidden function-follow-form schemata in the recorded activity of cultured neuronal networks by comparing the activity with simulation results of a new modeling approach. Cultured networks grown from an arbitrary mixture of neuron and glia cells in the absence of external stimulations and chemical cues spontaneously form networks of different sizes (from 50 to several millions of neurons) that exhibit non-arbitrary complex spatio-temporal patterns of activity. The latter is marked by formation of a sequence of synchronized bursting events (SBEs)--short time windows (approximately 200 ms) of rapid neuron firing, separated by longer time intervals (seconds) of sporadic neuron firing. The new dynamical synapse and soma (DSS) model, used here, has been successful in generating sequences of SBEs with the same statistical scaling properties (over six time decades) as those of the small networks. Large networks generate statistically distinct sub-groups of SBEs, each with its own characteristic pattern of neuronal firing ('fingerprint'). This special function (activity) motif has been proposed to emanate from a structural (form) motif--self-organization of the large networks into a fabric of overlapping sub-networks of about 1 mm in size. Here we test this function-follow-form idea by investigating the influence of the connectivity architecture of a model network (form) on the structure of its spontaneous activity (function). We show that a repertoire of possible activity states similar to the observed ones can be generated by networks with proper underlying architecture. For example, networks composed of two overlapping sub-networks exhibit distinct types of SBEs, each with its own characteristic pattern of neuron activity that starts at a specific sub-network. We further show that it is possible to regulate the temporal appearance of the different sub-groups of SBEs by an additional non-synaptic current fed into the soma of the modeled neurons. The ability to regulate the relative temporal ordering of different SBEs might endow the networks with higher plasticity and complexity. These findings call for additional mechanisms yet to be discovered. Recent experimental observations indicate that glia cells coupled to neuronal soma might generate such non-synaptic regulating currents.

Functional holography of recorded neuronal networks activity.

We present a new approach for analyzing multi-channel recordings, such as ECoG (electrocorticograph) recordings of cortical brain activity and of individual neuron dynamics, in cultured networks. The latter are used here to illustrate the method and its ability to discover hidden functional connectivity motifs in the recorded activity. The cultured networks are formed from dissociated mixtures of cortical neurons and glia-cells that are homogeneously spread over multi-electrode array for recording of the neuronal activity. Rich, spontaneous dynamical behavior is detected, marked by the formation of temporal sequences of synchronized bursting events (SBEs), partitioned into statistically distinguishable subgroups, each with its own characteristic spatio-temporal pattern of activity.In analogy with coherence connectivity networks for multi-location cortical recordings, we evaluated the inter-neuron correlation-matrix for each subgroup. Ordinarily such matrices are mapped onto a connectivity network between neuron positions in real space. In our functional holography, the correlations are normalized by the correlation distances Euclidian distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of the normalized correlations, or correlation affinities, onto a corresponding 3D manifold (3D Cartesian space constructed by the three leading principal vectors of the principal component algorithm). The neurons are located by their principal eigenvalues and linked by their original (not normalized) correlations. By looking at these holograms, hidden causal motifs are revealed: each SBEs subgroup generates its characteristic connectivity diagram (network) in the 3D manifold, where the neuron locations and their links form simple structures. Moreover, the computed temporal ordering of neuron activity, when projected onto the connectivity diagrams, also exhibits simple patterns of causal propagation. We show that the method can expose functional connectivity motifs like the co-existence of subneuronal functional networks in the space of affinities. The method can be directly utilized to construct similar causal holograms for recorded brain activity. We expect that by doing so, hidden functional connectivity motifs with relevance to the understanding of brain activity might be discovered.

Self-regulated complexity in cultured neuronal networks.

New quantified observables of complexity are identified and utilized to study sequences (time series) recorded during the spontaneous activity of different size cultured networks. The sequence is mapped into a tiled time-frequency domain that maximizes the information about local time-frequency resolutions. The sequence regularity is associated with the domain homogeneity and its complexity with its local and global variations. Shuffling the recorded sequence lowers its complexity down to artificially constructed ones. The new observables are utilized to identify self-regulation motifs in observed complex network activity.

Hidden neuronal correlations in cultured networks.

Utilization of a clustering algorithm on neuronal spatiotemporal correlation matrices recorded during a spontaneous activity of in vitro networks revealed the existence of hidden correlations: the sequence of synchronized bursting events (SBEs) is composed of statistically distinguishable subgroups each with its own distinct pattern of interneuron spatiotemporal correlations. These findings hint that each of the SBE subgroups can serve as a template for coding, storage, and retrieval of a specific information.