Self-organization of a neural network with heterogeneous neurons enhances coherence and stochastic resonance

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing P (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing F (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay [Formula: see text], the average degree [Formula: see text], and the rewiring probability [Formula: see text] have some appropriate values. When [Formula: see text], [Formula: see text], and [Formula: see text] are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when F increases, depending on the network topology. It is also found that the time delay [Formula: see text] can induce intermittent CS and PS whose occurrence is independent F. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Avalanche size distribution of an integrate-and-fire neural model on complex networks

We considered the neural avalanche dynamics of a modified integrate-and-fire model on complex networks, as well as the neural dynamics in a fully connected network, random network, small-world network, and scale-free network. We observed the self-organized criticality of the neural model on complex networks. The probability distribution of the avalanche size and lifetime follow the power law at the critical synaptic strength. Neuronal dynamics on a complex network are not universal. The critical exponents of the avalanche dynamics depend on the structure of the complex network. We observed that the critical exponents deviate from the mean-field value.

Effects of network topologies on stochastic resonance in feedforward neural network

The effects of network topologies on signal propagation are studied in noisy feedforward neural network in detail, where the network topologies are modulated by changing both the in-degree and out-degree distributions of FFNs as identical, uniform and exponential respectively. Stochastic resonance appeared in three FFNs when the same external stimuli and noise are applied to the three different network topologies. It is found that optimal noise intensity decreases with the increase of network's layer index. Meanwhile, the Q index of FFN with identical distribution is higher than that of the other two FFNs, indicating that the synchronization between the neuronal firing activities and the external stimuli is more obvious in FFN with identical distribution. The optimal parameter regions for the time cycle of external stimuli and the noise intensity are found for three FFNs, in which the resonance is more easily induced when the parameters of stimuli are set in this region. Furthermore, the relationship between the in-degree, the average membrane potential and the resonance performance is studied at the neuronal level, where it is found that both the average membrane potentials and the Q indexes of neurons in FFN with identical degree distribution is more consistent with each other than that of the other two FFNs due to their network topologies. In summary, the simulations here indicate that the network topologies play essential roles in affecting the signal propagation of FFNs.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

Developed through evolution, brain neural system self-organizes into an economical and dynamic network structure with the modulation of repetitive neuronal firing activities through synaptic plasticity. These highly variable electric activities inevitably produce a spontaneous magnetic field, which also significantly modulates the dynamic neuronal behaviors in the brain. However, how this spontaneous electromagnetic induction affects the self-organization process and what is its role in the formation of an economical neuronal network still have not been reported. Here, we investigate the effects of spontaneous electromagnetic induction on the self-organization process and the topological properties of the self-organized neuronal network. We first find that spontaneous electromagnetic induction slows down the self-organization process of the neuronal network by decreasing the neuronal excitability. In addition, spontaneous electromagnetic induction can result in a more homogeneous directed-weighted network structure with lower causal relationship and less modularity which supports weaker neuronal synchronization. Furthermore, we show that spontaneous electromagnetic induction can reconfigure synaptic connections to optimize the economical connectivity pattern of self-organized neuronal networks, endowing it with enhanced local and global efficiency from the perspective of graph theory. Our results reveal the critical role of spontaneous electromagnetic induction in the formation of an economical self-organized neuronal network and are also helpful for understanding the evolution of the brain neural system.

On distributed coordination in networks of cyber-physical systems

This paper is concerned with the study of the global emerging behavior in complex networks where each node can be modeled as a cyber-physical system. We recast the problem of characterizing the behavior of such systems as a stability problem and give two technical results to assess this property. We then illustrate the effectiveness of our approach by considering two testbed examples arising in applications where networks, arising from Internet of Things applications, need to be designed so as to fulfill a given task.

Biological modelling of a computational spiking neural network with neuronal avalanches

In recent years, an increasing number of studies have demonstrated that networks in the brain can self-organize into a critical state where dynamics exhibit a mixture of ordered and disordered patterns. This critical branching phenomenon is termed neuronal avalanches. It has been hypothesized that the homeostatic level balanced between stability and plasticity of this critical state may be the optimal state for performing diverse neural computational tasks. However, the critical region for high performance is narrow and sensitive for spiking neural networks (SNNs). In this paper, we investigated the role of the critical state in neural computations based on liquid-state machines, a biologically plausible computational neural network model for real-time computing. The computational performance of an SNN when operating at the critical state and, in particular, with spike-timing-dependent plasticity for updating synaptic weights is investigated. The network is found to show the best computational performance when it is subjected to critical dynamic states. Moreover, the active-neuron-dominant structure refined from synaptic learning can remarkably enhance the robustness of the critical state and further improve computational accuracy. These results may have important implications in the modelling of spiking neural networks with optimal computational performance.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Effects of bursting dynamic features on the generation of multi-clustered structure of neural network with symmetric spike-timing-dependent plasticity learning rule

In this paper, the generation of multi-clustered structure of self-organized neural network with different neuronal firing patterns, i.e., bursting or spiking, has been investigated. The initially all-to-all-connected spiking neural network or bursting neural network can be self-organized into clustered structure through the symmetric spike-timing-dependent plasticity learning for both bursting and spiking neurons. However, the time consumption of this clustering procedure of the burst-based self-organized neural network (BSON) is much shorter than the spike-based self-organized neural network (SSON). Our results show that the BSON network has more obvious small-world properties, i.e., higher clustering coefficient and smaller shortest path length than the SSON network. Also, the results of larger structure entropy and activity entropy of the BSON network demonstrate that this network has higher topological complexity and dynamical diversity, which benefits for enhancing information transmission of neural circuits. Hence, we conclude that the burst firing can significantly enhance the efficiency of clustering procedure and the emergent clustered structure renders the whole network more synchronous and therefore more sensitive to weak input. This result is further confirmed from its improved performance on stochastic resonance. Therefore, we believe that the multi-clustered neural network which self-organized from the bursting dynamics has high efficiency in information processing.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Potentiation decay of synapses and length distributions of synfire chains self-organized in recurrent neural networks

Synfire chains are thought to underlie precisely timed sequences of spikes observed in various brain regions and across species. How they are formed is not understood. Here we analyze self-organization of synfire chains through the spike-timing dependent plasticity (STDP) of the synapses, axon remodeling, and potentiation decay of synaptic weights in networks of neurons driven by noisy external inputs and subject to dominant feedback inhibition. Potentiation decay is the gradual, activity-independent reduction of synaptic weights over time. We show that potentiation decay enables a dynamic and statistically stable network connectivity when neurons spike spontaneously. Periodic stimulation of a subset of neurons leads to formation of synfire chains through a random recruitment process, which terminates when the chain connects to itself and forms a loop. We demonstrate that chain length distributions depend on the potentiation decay. Fast potentiation decay leads to long chains with wide distributions, while slow potentiation decay leads to short chains with narrow distributions. We suggest that the potentiation decay, which corresponds to the decay of early long-term potentiation of synapses, is an important synaptic plasticity rule in regulating formation of neural circuity through STDP.

Neuronal avalanches of a self-organized neural network with active-neuron-dominant structure

Neuronal avalanche is a spontaneous neuronal activity which obeys a power-law distribution of population event sizes with an exponent of -3/2. It has been observed in the superficial layers of cortex both in vivo and in vitro. In this paper, we analyze the information transmission of a novel self-organized neural network with active-neuron-dominant structure. Neuronal avalanches can be observed in this network with appropriate input intensity. We find that the process of network learning via spike-timing dependent plasticity dramatically increases the complexity of network structure, which is finally self-organized to be active-neuron-dominant connectivity. Both the entropy of activity patterns and the complexity of their resulting post-synaptic inputs are maximized when the network dynamics are propagated as neuronal avalanches. This emergent topology is beneficial for information transmission with high efficiency and also could be responsible for the large information capacity of this network compared with alternative archetypal networks with different neural connectivity.

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.

Investigating heterogeneity of intracellular calcium dynamics in anterior pituitary lactotrophs using a combined modelling/experimental approach

Cell responses are commonly heterogeneous, even within a subpopulation. In the present study, we investigate the source of heterogeneity in the Ca(2+) response of anterior pituitary lactotrophs to a Ca(2+) mobilisation agonist, thyrotrophin-releasing hormone. This response is characterised by a sharp increase of cytosolic Ca(2+) concentration as a result of mobilisation of Ca(2+) from intracellular stores, followed by a decrease to an elevated plateau level that results from Ca(2+) influx. We focus on heterogeneity of the evoked Ca(2+) spike under extracellular Ca(2+) free conditions. We introduce a method that uses the information provided by a mathematical model to characterise the source of heterogeneity. This method compares scatter plots of features of the Ca(2+) response obtained experimentally with those made from the mathematical model. The model scatter plots reflect random variation of parameters over different ranges, and matching the experimental and model scatter plots allows us to predict which parameters are most variable. We find that a large degree of variation in Ca(2+) efflux is a likely key contributor to the heterogeneity of Ca(2+) responses to thyrotrophin-releasing hormone in lactotrophs. This technique is applicable to any situation in which the heterogeneous biological response is described by a mathematical model.

Optimal network configuration for maximal coherence resonance in excitable systems

We analyze the coherence resonance phenomenon in an ensemble of noise-driven excitable neurons giving special attention to the role of the interaction topology. The neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale-free-like with dominating long-range connections and a network with mostly adjacent neurons connected. We found that besides an optimal noise intensity, also an optimal network configuration exists at which the largest average coherence of noise-induced spikes is achieved. Furthermore, we show that long- as well as short-range interactions between neurons should exist in order to achieve the optimal response of the neuronal network.