Self-sustained irregular activity in 2-D small-world networks of excitatory and inhibitory neurons

Desynchronization of neuronal firing in multiparameter ultrasound stimulation

Low-intensity transcranial ultrasound stimulation, a novel neuromodulation technique, that possesses the advantages of non-invasiveness, high penetration depth, and high spatial resolution, has achieved positive neuromodulation effects in animal studies. But the regulatory mechanism remains controversial. The intramembrane cavitation effect is considered one of the mechanisms for ultrasound neuromodulation. In this study, the modified equations of ultrasonic cavitation bubble dynamics were coupled with the dual-coupled neuron Hindmarsh-Rose model, small-world neural network model, and the Jansen-Rit neural mass model, which simulate simple coupled neurons, complex neuronal networks, and discharge signals in epileptic disorders respectively. The results demonstrated that ultrasound stimulation has an appreciable modulatory effect on neuronal firing desynchronization in Hindmarsh-Rose model and small-world neural network model. The desynchronization effect is related to the stimulation frequency and intensity. Furthermore, ultrasound stimulation has an inhibitory effect on epileptic seizures, and the effect is enhanced by increasing ultrasound frequency from 0.1-1.0 MHz. This is the first combination of ultrasonic intramembrane cavitation effect theory with neurons and neural network firing desynchronization, which can provide guidance of parametric and theories support for the studies of neurological diseases such as epilepsy and Parkinson's disease.

Memristive Izhikevich Spiking Neuron Model and Its Application in Oscillatory Associative Memory

The Izhikevich (IZH) spiking neuron model can display spiking and bursting behaviors of neurons. Based on the switching property and bio-plausibility of the memristor, the memristive Izhikevich (MIZH) spiking neuron model is built. Firstly, the MIZH spiking model is introduced and used to generate 23 spiking patterns. We compare the 23 spiking patterns produced by the IZH and MIZH spiking models. Secondly, the MIZH spiking model actively reproduces various neuronal behaviors, including the excitatory cortical neurons, the inhibitory cortical neurons, and other cortical neurons. Finally, the collective dynamic activities of the MIZH neuronal network are performed, and the MIZH oscillatory network is constructed. Experimental results illustrate that the constructed MIZH spiking neuron model performs high firing frequency and good frequency adaptation. The model can easily simulate various spiking and bursting patterns of distinct neurons in the brain. The MIZH neuronal network realizes the synchronous and asynchronous collective behaviors. The MIZH oscillatory network can memorize and retrieve the information patterns correctly and efficiently with high retrieval accuracy.

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

Less is more: Wiring-economical modular networks support self-sustained firing-economical neural avalanches for efficient processing

The brain network is notably cost-efficient, while the fundamental physical and dynamic mechanisms underlying its economical optimization in network structure and activity have not been determined. In this study, we investigate the intricate cost-efficient interplay between structure and dynamics in biologically plausible spatial modular neuronal network models. We observe that critical avalanche states from excitation-inhibition balance under modular network topology with less wiring cost can also achieve lower costs in firing but with strongly enhanced response sensitivity to stimuli. We derive mean-field equations that govern the macroscopic network dynamics through a novel approximate theory. The mechanism of low firing cost and stronger response in the form of critical avalanches is explained as a proximity to a Hopf bifurcation of the modules when increasing their connection density. Our work reveals the generic mechanism underlying the cost-efficient modular organization and critical dynamics widely observed in neural systems, providing insights into brain-inspired efficient computational designs.

Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights

Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain's dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure

Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.

Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.

Spatiotemporal dynamics in excitable homogeneous random networks composed of periodically self-sustained oscillation

The collective behaviors of networks are often dependent on the network connections and bifurcation parameters, also the local kinetics plays an important role in contributing the consensus of coupled oscillators. In this paper, we systematically investigate the influence of network structures and system parameters on the spatiotemporal dynamics in excitable homogeneous random networks (EHRNs) composed of periodically self-sustained oscillation (PSO). By using the dominant phase-advanced driving (DPAD) method, the one-dimensional (1D) Winfree loop is exposed as the oscillation source supporting the PSO, and the accurate wave propagation pathways from the oscillation source to the whole network are uncovered. Then, an order parameter is introduced to quantitatively study the influence of network structures and system parameters on the spatiotemporal dynamics of PSO in EHRNs. Distinct results induced by the network structures and the system parameters are observed. Importantly, the corresponding mechanisms are revealed. PSO influenced by the network structures are induced not only by the change of average path length (APL) of network, but also by the invasion of 1D Winfree loop from the outside linking nodes. Moreover, PSO influenced by the system parameters are determined by the excitation threshold and the minimum 1D Winfree loop. Finally, we confirmed that the excitation threshold and the minimum 1D Winfree loop determined PSO will degenerate as the system size is expanded.

Statistical complexity is maximized in a small-world brain

In this paper, we study a network of Izhikevich neurons to explore what it means for a brain to be at the edge of chaos. To do so, we first constructed the phase diagram of a single Izhikevich excitatory neuron, and identified a small region of the parameter space where we find a large number of phase boundaries to serve as our edge of chaos. We then couple the outputs of these neurons directly to the parameters of other neurons, so that the neuron dynamics can drive transitions from one phase to another on an artificial energy landscape. Finally, we measure the statistical complexity of the parameter time series, while the network is tuned from a regular network to a random network using the Watts-Strogatz rewiring algorithm. We find that the statistical complexity of the parameter dynamics is maximized when the neuron network is most small-world-like. Our results suggest that the small-world architecture of neuron connections in brains is not accidental, but may be related to the information processing that they do.

Euchromatin histone methyltransferase 1 regulates cortical neuronal network development

Heterozygous mutations or deletions in the human Euchromatin histone methyltransferase 1 (EHMT1) gene cause Kleefstra syndrome, a neurodevelopmental disorder that is characterized by autistic-like features and severe intellectual disability (ID). Neurodevelopmental disorders including ID and autism may be related to deficits in activity-dependent wiring of brain circuits during development. Although Kleefstra syndrome has been associated with dendritic and synaptic defects in mice and Drosophila, little is known about the role of EHMT1 in the development of cortical neuronal networks. Here we used micro-electrode arrays and whole-cell patch-clamp recordings to investigate the impact of EHMT1 deficiency at the network and single cell level. We show that EHMT1 deficiency impaired neural network activity during the transition from uncorrelated background action potential firing to synchronized network bursting. Spontaneous bursting and excitatory synaptic currents were transiently reduced, whereas miniature excitatory postsynaptic currents were not affected. Finally, we show that loss of function of EHMT1 ultimately resulted in less regular network bursting patterns later in development. These data suggest that the developmental impairments observed in EHMT1-deficient networks may result in a temporal misalignment between activity-dependent developmental processes thereby contributing to the pathophysiology of Kleefstra syndrome.

Regulation of Irregular Neuronal Firing by Autaptic Transmission

The importance of self-feedback autaptic transmission in modulating spike-time irregularity is still poorly understood. By using a biophysical model that incorporates autaptic coupling, we here show that self-innervation of neurons participates in the modulation of irregular neuronal firing, primarily by regulating the occurrence frequency of burst firing. In particular, we find that both excitatory and electrical autapses increase the occurrence of burst firing, thus reducing neuronal firing regularity. In contrast, inhibitory autapses suppress burst firing and therefore tend to improve the regularity of neuronal firing. Importantly, we show that these findings are independent of the firing properties of individual neurons, and as such can be observed for neurons operating in different modes. Our results provide an insightful mechanistic understanding of how different types of autapses shape irregular firing at the single-neuron level, and they highlight the functional importance of autaptic self-innervation in taming and modulating neurodynamics.

Latching chains in K-nearest-neighbor and modular small-world networks

Latching dynamics retrieve pattern sequences successively by neural adaption and pattern correlation. We have previously proposed a modular latching chain model in Song et al. (2014) to better accommodate the structured transitions in the brain. Different cortical areas have different network structures. To explore how structural parameters like rewiring probability, threshold, noise and feedback connections affect the latching dynamics, two different connection schemes, K-nearest-neighbor network and modular network both having modular structure are considered. Latching chains are measured using two proposed measures characterizing length of intra-modular latching chains and sequential inter-modular association transitions. Our main findings include: (1) With decreasing threshold coefficient and rewiring probability, both the K-nearest-neighbor network and the modular network experience quantitatively similar phase change processes. (2) The modular network exhibits selectively enhanced latching in the small-world range of connectivity. (3) The K-nearest-neighbor network is more robust to changes in rewiring probability, while the modular network is more robust to the presence of noise pattern pairs and to changes in the strength of feedback connections. According to our findings, the relationships between latching chains in K-nearest-neighbor and modular networks and different forms of cognition and information processing emerging in the brain are discussed.

A modular latching chain

Many cognitive tasks involve transitions between distinct mental processes, which may range from discrete states to complex strategies. The ability of cortical networks to combine discrete jumps with continuous glides along ever changing trajectories, dubbed latching dynamics, may be essential for the emergence of the unique cognitive capacities of modern humans. Novel trajectories have to be followed in the multidimensional space of cortical activity for novel behaviours to be produced; yet, not everything changes: several lines of evidence point at recurring patterns in the sequence of activation of cortical areas in a variety of behaviours. To extend a mathematical model of latching dynamics beyond the simple unstructured auto-associative Potts network previously analysed, we introduce delayed structured connectivity and hetero-associative connection weights, and we explore their effects on the dynamics. A modular model in the small-world regime is considered, with modules arranged on a ring. The synaptic weights include a standard auto-associative component, stabilizing distinct patterns of activity, and a hetero-associative component, favoring transitions from one pattern, expressed in one module, to the next, in the next module. We then study, through simulations, how structural parameters, like those regulating rewiring probability, noise and feedback connections, determine sequential association dynamics.

Population rate coding in recurrent neuronal networks with unreliable synapses

Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.

Fast and robust image segmentation by small-world neural oscillator networks

Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible.

Synchronization of the small-world neuronal network with unreliable synapses

As is well known, synchronization phenomena are ubiquitous in neuronal systems. Recently a lot of work concerning the synchronization of the neuronal network has been accomplished. In these works, the synapses are usually considered reliable, but experimental results show that, in biological neuronal networks, synapses are usually unreliable. In our previous work, we have studied the synchronization of the neuronal network with unreliable synapses; however, we have not paid attention to the effect of topology on the synchronization of the neuronal network. Several recent studies have found that biological neuronal networks have typical properties of small-world networks, characterized by a short path length and high clustering coefficient. In this work, mainly based on the small-world neuronal network (SWNN) with inhibitory neurons, we study the effect of network topology on the synchronization of the neuronal network with unreliable synapses. Together with the network topology, the effects of the GABAergic reversal potential, time delay and noise are also considered. Interestingly, we found a counter-intuitive phenomenon for the SWNN with specific shortcut adding probability, that is, the less reliable the synapses, the better the synchronization performance of the SWNN. We also consider the effects of both local noise and global noise in this work. It is shown that these two different types of noise have distinct effects on the synchronization: one is negative and the other is positive.

Diverse self-sustained oscillatory patterns and their mechanisms in excitable small-world networks

Diverse self-sustained oscillatory patterns and their mechanisms in small-world networks (SWNs) of excitable nodes are studied. Spatiotemporal patterns of SWNs are sensitive to long-range connection probability P and coupling intensity D . By varying P in wide range with fixed D , we observe totally six types of asymptotic states: pure spiral waves, pure self-sustained target waves, patterns of mixtured spirals and target waves, pseudospiral turbulence, synchronizing oscillations, and rest state. The parameter conditions for all these states are specified, and the mechanisms of these states are heuristically explained. In particular, the mechanism of emergence and annihilation of synchronizing oscillations is explained by using the shortest path length analysis.