Double inverse stochastic resonance with dynamic synapses

Inverse stochastic resonance in adaptive small-world neural networks

Inverse stochastic resonance (ISR) is a counterintuitive phenomenon where noise reduces the oscillation frequency of an oscillator to a minimum occurring at an intermediate noise intensity, and sometimes even to the complete absence of oscillations. In neuroscience, ISR was first experimentally verified with cerebellar Purkinje neurons [Buchin et al., PLOS Comput. Biol. 12, e1005000 (2016)]. These experiments showed that ISR enables a locally optimal information transfer between the input and output spike train of neurons. Subsequent studies have further demonstrated the efficiency of information processing and transfer in neural networks with small-world network topology. We have conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bi-metastable regime consisting of a metastable fixed point and a metastable limit cycle. Our results show that the degree of ISR is highly dependent on the value of the FHN model's timescale separation parameter ε. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter P or homeostatic structural plasticity (HSP) with rewiring frequency F. We demonstrate that both STDP and HSP amplify the effect of ISR when ε lies within the bi-stability region of FHN neurons. Specifically, at larger values of ε within the bi-stability regime, higher rewiring frequencies F are observed to enhance ISR at intermediate (weak) synaptic noise intensities, while values of P consistent with depression-domination (potentiation-domination) consistently enhance (deteriorate) ISR. Moreover, although STDP and HSP control parameters may jointly enhance ISR, P has a greater impact on improving ISR compared to F. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize local information transfer between input and output spike trains in neuromorphic systems and prompt venues for experiments in neural networks.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

Dynamics and Information Import in Recurrent Neural Networks

Recurrent neural networks (RNNs) are complex dynamical systems, capable of ongoing activity without any driving input. The long-term behavior of free-running RNNs, described by periodic, chaotic and fixed point attractors, is controlled by the statistics of the neural connection weights, such as the density d of non-zero connections, or the balance b between excitatory and inhibitory connections. However, for information processing purposes, RNNs need to receive external input signals, and it is not clear which of the dynamical regimes is optimal for this information import. We use both the average correlations C and the mutual information I between the momentary input vector and the next system state vector as quantitative measures of information import and analyze their dependence on the balance and density of the network. Remarkably, both resulting phase diagrams C(b, d) and I(b, d) are highly consistent, pointing to a link between the dynamical systems and the information-processing approach to complex systems. Information import is maximal not at the "edge of chaos," which is optimally suited for computation, but surprisingly in the low-density chaotic regime and at the border between the chaotic and fixed point regime. Moreover, we find a completely new type of resonance phenomenon, which we call "Import Resonance" (IR), where the information import shows a maximum, i.e., a peak-like dependence on the coupling strength between the RNN and its external input. IR complements previously found Recurrence Resonance (RR), where correlation and mutual information of successive system states peak for a certain amplitude of noise added to the system. Both IR and RR can be exploited to optimize information processing in artificial neural networks and might also play a crucial role in biological neural systems.

Stochastic and vibrational resonance in complex networks of neurons

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Collective firing patterns of neuronal networks with short-term synaptic plasticity

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity

Transient, task related synchronous activity within neural populations has been recognized as the substrate of temporal coding in the brain. The mechanisms underlying inducing and propagation of transient synchronous activity are still unknown, and we propose that short-term plasticity (STP) of neural circuits may serve as a supplemental mechanism therein. By computational modeling, we showed that short-term facilitation greatly increases the reactivation rate of population spikes and decreases the latency of response to reactivation stimuli in local recurrent neural networks. Meanwhile, the timing of population spike reactivation is controlled by the memory effect of STP, and it is mediated primarily by the facilitation time constant. Furthermore, we demonstrated that synaptic facilitation dramatically enhances synchrony propagation in feedforward neural networks and that response timing mediated by synaptic facilitation offers a scheme for information routing. In addition, we verified that synaptic strengthening of intralayer or interlayer coupling enhances synchrony propagation, and we verified that other factors such as the delay of synaptic transmission and the mode of synaptic connectivity are also involved in regulating synchronous activity propagation. Overall, our results highlight the functional role of STP in regulating the inducing and propagation of transient synchronous activity, and they may inspire testable hypotheses for future experimental studies.

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.

Two paradigmatic scenarios for inverse stochastic resonance

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold. In the first scenario, shown for the two rotators in the excitable regime, inverse stochastic resonance emerges due to a biased switching between the oscillatory and the quasi-stationary metastable states derived from the attractors of the noiseless system. In the second scenario, illustrated for the rotators in the oscillatory regime, inverse stochastic resonance arises due to a trapping effect associated with a noise-enhanced stability of an unstable fixed point. The details of the mechanisms behind the resonant effect are explained in terms of slow-fast analysis of the corresponding noiseless systems.

Phase-sensitive excitability of a limit cycle

The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e., the excitability happens to be phase-sensitive. As a paradigmatic example of this concept, we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase-sensitive nonlinear threshold-like response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase-sensitive excitability of the relaxation oscillations by noise, we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response.

Short-Term Dosage Regimen for Stimulation-Induced Long-Lasting Desynchronization

In this paper, we computationally generate hypotheses for dose-finding studies in the context of desynchronizing neuromodulation techniques. Abnormally strong neuronal synchronization is a hallmark of several brain disorders. Coordinated Reset (CR) stimulation is a spatio-temporally patterned stimulation technique that specifically aims at disrupting abnormal neuronal synchrony. In networks with spike-timing-dependent plasticity CR stimulation may ultimately cause an anti-kindling, i.e., an unlearning of abnormal synaptic connectivity and neuronal synchrony. This long-lasting desynchronization was theoretically predicted and verified in several pre-clinical and clinical studies. We have shown that CR stimulation with rapidly varying sequences (RVS) robustly induces an anti-kindling at low intensities e.g., if the CR stimulation frequency (i.e., stimulus pattern repetition rate) is in the range of the frequency of the neuronal oscillation. In contrast, CR stimulation with slowly varying sequences (SVS) turned out to induce an anti-kindling more strongly, but less robustly with respect to variations of the CR stimulation frequency. Motivated by clinical constraints and inspired by the spacing principle of learning theory, in this computational study we propose a short-term dosage regimen that enables a robust anti-kindling effect of both RVS and SVS CR stimulation, also for those parameter values where RVS and SVS CR stimulation previously turned out to be ineffective. Intriguingly, for the vast majority of parameter values tested, spaced multishot CR stimulation with demand-controlled variation of stimulation frequency and intensity caused a robust and pronounced anti-kindling. In contrast, spaced CR stimulation with fixed stimulation parameters as well as singleshot CR stimulation of equal integral duration failed to improve the stimulation outcome. In the model network under consideration, our short-term dosage regimen enables to robustly induce long-term desynchronization at comparably short stimulation duration and low integral stimulation duration. Currently, clinical proof of concept is available for deep brain CR stimulation for Parkinson's therapy and acoustic CR stimulation for tinnitus therapy. Promising first in human data is available for vibrotactile CR stimulation for Parkinson's treatment. For the clinical development of these treatments it is mandatory to perform dose-finding studies to reveal optimal stimulation parameters and dosage regimens. Our findings can straightforwardly be tested in human dose-finding studies.

Effects of topologies on signal propagation in feedforward networks

We systematically investigate the effects of topologies on signal propagation in feedforward networks (FFNs) based on the FitzHugh-Nagumo neuron model. FFNs with different topological structures are constructed with same number of both in-degrees and out-degrees in each layer and given the same input signal. The propagation of firing patterns and firing rates are found to be affected by the distribution of neuron connections in the FFNs. Synchronous firing patterns emerge in the later layers of FFNs with identical, uniform, and exponential degree distributions, but the number of synchronous spike trains in the output layers of the three topologies obviously differs from one another. The firing rates in the output layers of the three FFNs can be ordered from high to low according to their topological structures as exponential, uniform, and identical distributions, respectively. Interestingly, the sequence of spiking regularity in the output layers of the three FFNs is consistent with the firing rates, but their firing synchronization is in the opposite order. In summary, the node degree is an important factor that can dramatically influence the neuronal network activity.

Frequency-difference-dependent stochastic resonance in neural systems

Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural systems to the weak envelope modulation signal, which is superimposed by two periodic signals with different frequencies. We show that stochastic resonance occurs at the beat frequency in neural systems at the single-neuron as well as the population level. The performance of this frequency-difference-dependent stochastic resonance is influenced by both the beat frequency and the two forcing frequencies. Compared to a single neuron, a population of neurons is more efficient in detecting the information carried by the weak envelope modulation signal at the beat frequency. Furthermore, an appropriate fine-tuning of the excitation-inhibition balance can further optimize the response of a neural ensemble to the superimposed signal. Our results thus introduce and provide insights into the generation and modulation mechanism of the frequency-difference-dependent stochastic resonance in neural systems.

Inverse stochastic resonance in networks of spiking neurons

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.