Two-dimensional Neuronal Network Research Articles

The vitals for steady nucleation maps of spontaneous spiking coherence in autonomous two-dimensional neuronal networks

Thin pancake-like neuronal networks cultured on top of a planar microelectrode array have been extensively tried out in neuroengineering, as a substrate for the mobile robot’s control unit, i.e., as a cyborg’s brain. Most of these attempts failed due to intricate self-organizing dynamics in the neuronal systems. In particular, the networks may exhibit an emergent spatial map of steady nucleation sites (“n-sites”) of spontaneous population spikes. Being unpredictable and independent of the surface electrode locations, the n-sites drastically change local ability of the network to generate spikes. Here, using a spiking neuronal network model with generative spatially-embedded connectome, we systematically show in simulations that the number, location, and relative activity of spontaneously formed n-sites (“the vitals”) crucially depend on the samplings of three distributions: (1) the network distribution of neuronal excitability, (2) the distribution of connections between neurons of the network, and (3) the distribution of maximal amplitudes of a single synaptic current pulse. Moreover, blocking the dynamics of a small fraction (about 4%) of non-pacemaker neurons having the highest excitability was enough to completely suppress the occurrence of population spikes and their n-sites. This key result is explained theoretically. Remarkably, the n-sites occur taking into account only short-term synaptic plasticity, i.e., without a Hebbian-type plasticity. As the spiking network model used in this study is strictly deterministic, all simulation results can be accurately reproduced. The model, which has already demonstrated a very high richness-to-complexity ratio, can also be directly extended into the three-dimensional case, e.g., for targeting peculiarities of spiking dynamics in cerebral (or brain) organoids. We recommend the model as an excellent illustrative tool for teaching network-level computational neuroscience, complementing a few benchmark models.

A micropatterned thermoplasmonic substrate for neuromodulation of in vitro neuronal networks.

Understanding how the spatial organization of a neural network affects its activity represents a leading issue in neuroscience. Thanks to their accessibility and easy handling, in vitro studies remain an essential tool to investigate the relationship between the structure and function of a neuronal network. Among all the patterning techniques, ink-jet printing acquired great interest thanks to its direct-write approach, which allows the patterned substrate realization without mold, leading to a considerable saving of both cost and time. However, the inks commonly used give the possibility to control only the structure of a neuronal network, leaving aside the functional aspect. In this work, we synthesize a photosensitive ink combining the rheological and bioadhesive properties of chitosan with the plasmonic properties of gold nanorods, obtaining an ink able to control both the spatial organization of a two-dimensional neuronal network and its activity through photothermal effect. After the ink characterization, we demonstrate that it is possible to print, with high precision, different geometries on a microelectrode array. In this way, it is possible obtaining a patterned device to control the structure of a neuronal network, to record its activity and to modulate it via photothermal effect. Finally, to our knowledge, we report the first evidence of photothermal inhibition of human neurons activity. STATEMENT OF SIGNIFICANCE: Patterned cell cultures remain the most efficient and simple tool for linking structural and functional studies, especially in the neuronal field. Ink-jet printing is the technique with which it is possible to realize patterned structures in the fastest, simple, versatile and low-cost way. However, the inks currently used permit the control only of the neuronal network structure but do not allow the control-modulation of the network activity. In this study, we realize and characterize a photosensitive bioink with which it is possible to drive both the structure and the activity of a neuronal network. Moreover, we report the first evidence of activity inhibition by the photothermal effect on human neurons as far as we know.

Rapid generation of functional engineered 3D human neuronal assemblies: network dynamics evaluated by micro-electrodes arrays

Objective. In this work we adapted a protocol for the fast generation of human neurons to build 3D neuronal networks with controlled structure and cell composition suitable for systematic electrophysiological investigations. Approach. We used biocompatible chitosan microbeads as scaffold to build 3D networks and to ensure nutrients-medium exchange from the core of the structure to the external environment. We used excitatory neurons derived from human-induced pluripotent stem cells (hiPSCs) co-cultured with astrocytes. By adapting the well-established NgN2 differentiation protocol, we obtained 3D engineered networks with good control over cell density, volume and cell composition. We coupled the 3D neuronal networks to 60-channel micro electrode arrays (MEAs) to monitor and characterize their electrophysiological development. In parallel, we generated two-dimensional neuronal networks cultured on chitosan to compare the results of the two models. Main results. We sustained samples until 60 d in vitro (DIV) and 3D cultures were healthy and functional. From the structural point of view, the hiPSC derived neurons were able to adhere to chitosan microbeads and to form a stable 3D assembly thanks to the connections among cells. From a functional point of view, neuronal networks showed spontaneous activity after a couple of weeks. Significance. We presented a particular method to generate 3D engineered cultures for the first time with human-derived neurons coupled to MEAs, overcoming some of the limitations related to 2D and 3D neuronal networks and thus increasing the therapeutic target potential of these models for biomedical applications.

Traveling chimera patterns in a two-dimensional neuronal network

We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, i.e. the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of the instantaneous local order parameter in two dimensions. Finally we extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of patterns' propagation in two dimensions.

Various effects induced by local synchronization in neural networks

In the cerebral cortex, the large-scale synchronous firing of neurons can cause epilepsy, during which spiral waves can spontaneously occur. The relationship between the synchronous firing of a large number of neurons and the spontaneous generation of spiral waves is still unclear. In this paper, a two-dimensional neuronal network with the long-range coupling regions generated by adding long-range horizontal connections is constructed. The Morris-Lecar neuron model is used to study the propagation of waves in the two-dimensional neuronal network with the rectangular long-range coupling regions. Numerical simulation results show that the plan and target waves whose propagation directions are both parallel to that of the long-range coupling can lead the neurons to be excited synchronously in the long-range coupling region. This synchronous firing is accompanied by delayed firing of some neurons and premature firing of others. When the width of the long-range coupling region exceeds the critical width, all the neurons in the long-range coupling region delay firing. When the width of the long-range coupling region exceeds a maximum conduction width, the waves will not pass through the long-range coupling region. When the size of the rectangular region of the long-range coupling is selected appropriately, the synchronous excitation of neurons can cause network to present the backfiring effect and to have the selectivity of wave propagation direction. Furthermore, the selectivity of wave propagation direction is very sensitive to whether the neuron is in the stationary state and also to the change of coupling strength, so that the high frequency plane wave train can partially pass through the long-range coupling region whose width exceeds the maximum conduction width. So we can control whether the wave can pass through the long-range coupling region of a certain width by giving the neurons in the long-range coupling region a tiny perturbation. When one or two long-range coupling regions are constructed in the neural network and the size of the long-range coupling regions is selected appropriately, the self-sustaining plane wave, spiral wave and target wave can appear spontaneously in the network when the wave passes through the long-range coupling regions. The physical mechanisms behind those phenomena are also analyzed.

Spiral wave chimera states in regular and fractal neuronal networks

Chimera states are spatial patterns in which coherent and incoherent patterns coexist. It was reported that small populations of coupled oscillators can exhibit chimera with transient nature. This spatial coexistence has been observed in various network topologies of coupled systems, such as coupled pendula, coupled chemical oscillators, and neuronal networks. In this work, we build two-dimensional neuronal networks with regular and fractal topologies to study chimera states. In the regular network, we consider a coupling between the nearest neighbours neurons, while the fractal network is constructed according to the square Cantor set. Our networks are composed of coupled adaptive exponential integrate-and-fire neurons, that can exhibit spike or burst activities. Depending on the parameters, we find spiral wave chimeras in both regular and fractal networks. The spiral wave chimeras arise for different values of the intensity of the excitatory synaptic conductance. In our simulations, we verify the existence of multicore chimera states. The cores are made up of neurons with desynchronous behaviour and the spiral waves rotates around them. The cores can be related to bumps or spatially localised pulses of neuronal activities. We also show that the initial value of the adaptation current plays an important role in the existence of spiral wave chimera states.

From mini-brains to neural networks

Cells dissociated from cerebral organoids self-organize into two-dimensional neuronal networks with relatively advanced functionality.

Spatial patterns in a network composed of neurons with different excitabilities induced by autapse

It has been identified that autapse can modulate dynamics of single neurons and spatial patterns of neuronal networks. In the present paper, based on the results that autapse can induce type II excitability changed to type I excitability, spatial pattern transitions are simulated in a two-dimensional neuronal network composed of excitatory coupled neurons with autapse which can induce excitability transition. Different spatial patterns including random-like pattern, irregular wave, regular wave, and nearly synchronous behavior are simulated with increasing the percentage (σ) of neurons with type I excitability. When noise is introduced, spiral waves are induced. By calculating signal-to-noise ratio from the spatial structure function and the mean firing probability of neurons, regular waves and spiral waves exhibit optimal spatial correlation, implying the occurrence of spatial coherence resonance phenomenon. The changes of mean firing probability of neurons show that different firing frequency between type I excitability and type II excitability may be an important factor to modulate the spatial patterns. The results are helpful to understand the spatial patterns including spiral waves observed in the biological experiment on the rat cortex perfused with drugs which can induce single neurons changed from type II excitability to type I excitability and block the inhibitory couplings between neurons. The excitability transition, absence of inhibitory coupling, noise as well as the autapse are important factors to modulate the spatial patterns including spiral waves.

Taking control of initiated propagating wave in a neuronal network using magnetic radiation

The effect of magnetic radiation is essential to be studied due to its favorable or unfavorable influences especially when it comes to biological systems. In this study, some effects of an external time-varying magnetic induction on the formation of spatiotemporal patterns in a model of excitable tissue are investigated. We have designed a two-dimensional neuronal network, in which the local dynamics of the neurons are governed by the four-variable magnetic Hindmarsh–Rose (HR) neuronal model. Besides, each neuron is set to be in chaotic regime. We have examined some values of the bifurcation parameters, namely the frequency and the amplitude of the external magnetic radiation. The resulting evolutionary spatiotemporal patterns have showed that an extremely low frequency provides the tissue more opportunity to support propagation process, while low frequency confines the evolution of the wave fronts. Moreover, higher amplitude of the sinusoidal radiation caused the wave propagation be impeded by an inherent obstacle that could limit the ultimate radius of the propagated wave. The resulting collective response of the designed neuronal network is represented in snapshots and the time series of a sampled neuron are plotted, as well.

Spatial coherence resonance and spatial pattern transition induced by the decrease of inhibitory effect in a neuronal network

Spiral waves were observed in the biological experiment on rat brain cortex with the application of carbachol and bicuculline which can block inhibitory coupling from interneurons to pyramidal neurons. To simulate the experimental spiral waves, a two-dimensional neuronal network composed of pyramidal neurons and inhibitory interneurons was built. By decreasing the percentage of active inhibitory interneurons, the random-like spatial patterns change to spiral waves and to random-like spatial patterns or nearly synchronous behaviors. The spiral waves appear at a low percentage of inhibitory interneurons, which matches the experimental condition that inhibitory couplings of the interneurons were blocked. The spiral waves exhibit a higher order or signal-to-noise ratio (SNR) characterized by spatial structure function than both random-like spatial patterns and nearly synchronous behaviors, which shows that changes of the percentage of active inhibitory interneurons can induce spatial coherence resonance-like behaviors. In addition, the relationship between the coherence degree and the spatial structures of the spiral waves is identified. The results not only present a possible and reasonable interpretation to the spiral waves observed in the biological experiment on the brain cortex with disinhibition, but also reveal that the spiral waves exhibit more ordered degree in spatial patterns.

Prediction for breakup of spiral wave in a regular neuronal network

Target wave and spiral wave can regulate the collective behaviors of electrical activities in neuronal systems as a powerful ‘pacemaker’. Disordered states occur when normal signal propagation among neurons is disturbed and neuronal disease could be induced. In this paper, a stable rotating spiral wave is developed as initial state that the two-dimensional neuronal network of Hindmarsh–Rose neuron shows distinct periodicity and regularity in space, and then, some parameters are changed sharply to model the destruction effect induced by external large forcing or internal collapse, and the destructed areas will be expanded to occupy a larger area by expanding the damaged boundary in random way. The collapse and instability of spiral wave, ordered states could be predicated by monitoring and analyzing the time series of some nodes. It could be useful to detect the emergence of disaster in some biological or ecological systems.

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.

Effects of correlated Gaussian noise on the mean firing rate and correlations of an electrically coupled neuronal network

In this paper, we examine the effects of correlated Gaussian noise on a two-dimensional neuronal network that is locally modeled by the Rulkov map. More precisely, we study the effects of the noise correlation on the variations of the mean firing rate and the correlations among neurons versus the noise intensity. Via numerical simulations, we show that the mean firing rate can always be optimized at an intermediate noise intensity, irrespective of the noise correlation. On the other hand, variations of the population coherence with respect to the noise intensity are strongly influenced by the ratio between local and global Gaussian noisy inputs. Biological implications of our findings are also discussed.

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.

NEURONAL NETWORK GROWTH: MODEL AND EXPERIMENT

The growth of connections in a quasi two-dimensional neuronal network in vitro is probed by the synchronized bursting frequency of the system. A model of an early stage of active search growth followed by a later stage of diffusive search mode is proposed. Our model can explain quantitatively the variation of the critical age(for synchronized firing) of the culture as a function of cell density. The later stage of growth implies a probability of connection that is exponentially decay in the mean connectivity. The biological significance of the model is discussed in the light of homeostatic feedback and plasticity.

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.

Dendrite classification in rat hippocampal neurons according to signal propagation properties. Observation by multichannel optical recording in cultured neuronal networks.

Two-dimensional neuronal networks were formed using a dissociated culture of rat hippocampal neurons on glass plates. Neural activity in response to pulse stimuli applied to the neurons by whole-cell clamp electrodes was observed with a 128-channel optical recording apparatus using a voltage-sensitive dye, RH482. Dendrites emerging from the somata of single neurons were classified according to two signal-transmission properties, those with lower conduction velocities (0.12+/-0.034 m/s, n=24) and those with very fast conduction velocity (faster than 1.0 m/s), by evaluating the conduction velocities of pulse responses. The distinction between these two properties seemed to be related to the morphological differences in input connectivity with the axons of neighboring neurons.