Suprathreshold stochastic resonance in neural processing tuned by correlation

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Recurrence-mediated suprathreshold stochastic resonance

It has previously been shown that the encoding of time-dependent signals by feedforward networks (FFNs) of processing units exhibits suprathreshold stochastic resonance (SSR), which is an optimal signal transmission for a finite level of independent, individual stochasticity in the single units. In this study, a recurrent spiking network is simulated to demonstrate that SSR can be also caused by network noise in place of intrinsic noise. The level of autonomously generated fluctuations in the network can be controlled by the strength of synapses, and hence the coding fraction (our measure of information transmission) exhibits a maximum as a function of the synaptic coupling strength. The presence of a coding peak at an optimal coupling strength is robust over a wide range of individual, network, and signal parameters, although the optimal strength and peak magnitude depend on the parameter being varied. We also perform control experiments with an FFN illustrating that the optimized coding fraction is due to the change in noise level and not from other effects entailed when changing the coupling strength. These results also indicate that the non-white (temporally correlated) network noise in general provides an extra boost to encoding performance compared to the FFN driven by intrinsic white noise fluctuations.

Stochastic Resonance Based Visual Perception Using Spiking Neural Networks

Our aim is to propose an efficient algorithm for enhancing the contrast of dark images based on the principle of stochastic resonance in a global feedback spiking network of integrate-and-fire neurons. By linear approximation and direct simulation, we disclose the dependence of the peak signal-to-noise ratio on the spiking threshold and the feedback coupling strength. Based on this theoretical analysis, we then develop a dynamical system algorithm for enhancing dark images. In the new algorithm, an explicit formula is given on how to choose a suitable spiking threshold for the images to be enhanced, and a more effective quantifying index, the variance of image, is used to replace the commonly used measure. Numerical tests verify the efficiency of the new algorithm. The investigation provides a good example for the application of stochastic resonance, and it might be useful for explaining the biophysical mechanism behind visual perception.

SIGNAL-TO-NOISE RATIO GAIN VIA CORRELATED NOISE IN AN ENSEMBLE OF NOISY NEURONS

The collective response of an ensemble of leaky integrate-and-fire neurons induced by local correlated noise is investigated theoretically. Based on the linear response theory, we derive the analytic expression of signal-to-noise ratio (SNR). Numerical results show that the amplitude of internal noise can be increased up to an optimal value where the output SNR reaches a maximum value. Interestingly, we find that the correlated noise between the nearest neurons could lead to the obvious SNR gain. We also show that the SNR can reach unity under condition that the correlated noise between the nearest neurons is negative. This nonlinear amplification of SNR gain in an ensemble of noisy neurons can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and amplitude of the weak periodic signal.

Detecting single-cell stimulation in a large network of integrate-and-fire neurons

Several experiments have shown that the stimulation of a single neuron in the cortex can influence the local network activity and even the behavior of an animal. From the theoretical point of view, it is not clear how stimulating a single cell in a cortical network can evoke a statistically significant change in the activity of a large population. Our previous study considered a random network of integrate-and-fire neurons and proposed a way of detecting the stimulation of a single neuron in the activity of a local network: a threshold detector biased toward a specific subset of neurons. Here, we revisit this model and extend it by introducing a second network acting as a readout. In the simplest scenario, the readout consists of a collection of integrate-and-fire neurons with no recurrent connections. In this case, the ability to detect the stimulus does not improve. However, a readout network with both feed-forward and local recurrent inhibition permits detection with a very small bias, if compared to the readout scheme introduced previously. The crucial role of inhibition is to reduce global input cross correlations, the main factor limiting detectability. Finally, we show that this result is robust if recurrent excitatory connections are included or if a different kind of readout bias (in the synaptic amplitudes instead of connection probability) is used.

Improvement of signal-to-noise ratio in parallel neuron arrays with spatially nearest neighbor correlated noise

We theoretically investigate the signal-to-noise ratio (SNR) of a parallel array of leaky integrate-and-fire (LIF) neurons that receives a weak periodic signal and uses spatially nearest neighbor correlated noise. By using linear response theory, we derive the analytic expression of the SNR. The results show that the amplitude of internal noise can be increased up to an optimal value, which corresponds to a maximum SNR. Given the existence of spatially nearest neighbor correlated noise in the neural ensemble, the SNR gain of the collective ensemble response can exceed unity, especially for a negative correlation. This nonlinear collective phenomenon of SNR gain amplification may be related to the array stochastic resonance. In addition, we show that the SNR can be improved by varying the number of neurons, frequency, and amplitude of the weak periodic signal. We expect that this investigation will be useful for both controlling the collective response of neurons and enhancing weak signal transmission.

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H∈(1/2,1) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H∈(1/2,1) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations

We compare the information transmission of a time-dependent signal by two types of uncoupled neuron populations that differ in their sources of variability: i) a homogeneous population whose units receive independent noise and ii) a deterministic heterogeneous population, where each unit exhibits a different baseline firing rate ('disorder'). Our criterion for making both sources of variability quantitatively comparable is that the interspike-interval distributions are identical for both systems. Numerical simulations using leaky integrate-and-fire neurons unveil that a non-zero amount of both noise or disorder maximizes the encoding efficiency of the homogeneous and heterogeneous system, respectively, as a particular case of suprathreshold stochastic resonance. Our findings thus illustrate that heterogeneity can render similarly profitable effects for neuronal populations as dynamic noise. The optimal noise/disorder depends on the system size and the properties of the stimulus such as its intensity or cutoff frequency. We find that weak stimuli are better encoded by a noiseless heterogeneous population, whereas for strong stimuli a homogeneous population outperforms an equivalent heterogeneous system up to a moderate noise level. Furthermore, we derive analytical expressions of the coherence function for the cases of very strong noise and of vanishing intrinsic noise or heterogeneity, which predict the existence of an optimal noise intensity. Our results show that, depending on the type of signal, noise as well as heterogeneity can enhance the encoding performance of neuronal populations.

NOISE-ENHANCED TRANSMISSION OF TIME-MODULATED NEUROTRANSMITTER RANDOM POINT TRAINS IN A NOISY NEURON

We numerically investigate the transmission of time-modulated random point trains in a conductance-based neuron model by including shot noise described as additive noise trains. The results show that additive noise trains can induce neuron responses exhibiting correlation with the temporally modulated random point trains. In addition, the additive noise power density can be increased up to an optimal value where the output signal-noise ratio (SNR) reaches a maximum value. This property of noise-enhanced transmission of random point trains can be related to the stochastic resonance (SR) phenomenon. More interestingly, we find that the SNR gain can exceed unity and can also be optimized by tuning the average rate of the input random point trains. The present study illustrates the potential to utilize the additive noise and temporally modulated random point trains for optimizing the response of the neuron to inputs, as well as a guidance in the design of information processing devices to random neuron spiking.

Energy-efficient population coding constrains network size of a neuronal array system

We consider the open issue of how the energy efficiency of the neural information transmission process, in a general neuronal array, constrains the network size, and how well this network size ensures the reliable transmission of neural information in a noisy environment. By direct mathematical analysis, we have obtained general solutions proving that there exists an optimal number of neurons in the network, where the average coding energy cost (defined as energy consumption divided by mutual information) per neuron passes through a global minimum for both subthreshold and superthreshold signals. With increases in background noise intensity, the optimal neuronal number decreases for subthreshold signals and increases for suprathreshold signals. The existence of an optimal number of neurons in an array network reveals a general rule for population coding that states that the neuronal number should be large enough to ensure reliable information transmission that is robust to the noisy environment but small enough to minimize energy cost.

A review of methods for identifying stochastic resonance in simulations of single neuron models

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

Stochastic information transfer from cochlear implant electrodes to auditory nerve fibers

Cochlear implants, also called bionic ears, are implanted neural prostheses that can restore lost human hearing function by direct electrical stimulation of auditory nerve fibers. Previously, an information-theoretic framework for numerically estimating the optimal number of electrodes in cochlear implants has been devised. This approach relies on a model of stochastic action potential generation and a discrete memoryless channel model of the interface between the array of electrodes and the auditory nerve fibers. Using these models, the stochastic information transfer from cochlear implant electrodes to auditory nerve fibers is estimated from the mutual information between channel inputs (the locations of electrodes) and channel outputs (the set of electrode-activated nerve fibers). Here we describe a revised model of the channel output in the framework that avoids the side effects caused by an "ambiguity state" in the original model and also makes fewer assumptions about perceptual processing in the brain. A detailed comparison of how different assumptions on fibers and current spread modes impact on the information transfer in the original model and in the revised model is presented. We also mathematically derive an upper bound on the mutual information in the revised model, which becomes tighter as the number of electrodes increases. We found that the revised model leads to a significantly larger maximum mutual information and corresponding number of electrodes compared with the original model and conclude that the assumptions made in this part of the modeling framework are crucial to the model's overall utility.

Patterned Brain Stimulation, What a Framework with Rhythmic and Noisy Components Might Tell Us about Recovery Maximization

Brain stimulation is having remarkable impact on clinical neurology. Brain stimulation can modulate neuronal activity in functionally segregated circumscribed regions of the human brain. Polarity, frequency, and noise specific stimulation can induce specific manipulations on neural activity. In contrast to neocortical stimulation, deep-brain stimulation has become a tool that can dramatically improve the impact clinicians can possibly have on movement disorders. In contrast, neocortical brain stimulation is proving to be remarkably susceptible to intrinsic brain-states. Although evidence is accumulating that brain stimulation can facilitate recovery processes in patients with cerebral stroke, the high variability of results impedes successful clinical implementation. Interestingly, recent data in healthy subjects suggests that brain-state dependent patterned stimulation might help resolve some of the intrinsic variability found in previous studies. In parallel, other studies suggest that noisy “stochastic resonance” (SR)-like processes are a non-negligible component in non-invasive brain stimulation studies. The hypothesis developed in this manuscript is that stimulation patterning with noisy and oscillatory components will help patients recover from stroke related deficits more reliably. To address this hypothesis we focus on two factors common to both neural computation (intrinsic variables) as well as brain stimulation (extrinsic variables): noise and oscillation. We review diverse theoretical and experimental evidence that demonstrates that subject-function specific brain-states are associated with specific oscillatory activity patterns. These states are transient and can be maintained by noisy processes. The resulting control procedures can resemble homeostatic or SR processes. In this context we try to extend awareness for inter-individual differences and the use of individualized stimulation in the recovery maximization of stroke patients.

Vibrational resonance induced by transition of phase-locking modes in excitable systems

We study the occurrence of vibrational resonance as well as the underlying mechanism in excitable systems. The single vibration resonance and vibration bi-resonance are observed when tuning the amplitude and frequency of high-frequency force simultaneously. Furthermore, by virtue of the phase diagram of low-frequency-signal-free FitzHugh-Nagumo model, it is found that each maxima of response measure is located exactly at the transition boundary of phase patterns. Therefore, it is the transition between different phase-locking modes that induces vibrational resonance in the excitable systems. Finally, this mechanism is verified in the Hodgkin-Huxley neural model. Our results provide insights into the transmission of weak signals in nonlinear systems, which are valuable in engineering for potential applications.