Internal Stochastic Resonance Research Articles

Augmenting Global Coherence in EEG Signals with Binaural or Monaural Noises.

Internal stochastic resonance (internal SR) is a phenomenon of non-linear systems in which the addition of a non-zero level of noise produces an enhancement in the coherence between two or more signals. In a previous study, we found that the simultaneous administration of multisensory visual and auditory noise augments global coherence in electroencephalographic (EEG) signals via this phenomenon. Here, we examined whether such global coherence can also be augmented with at least one noisy acoustic source. We performed experiments on healthy subjects and applied the following binaural and monaural noise-stimulation protocols. First, we administered to the left ear Gaussian noise of fixed intensity, while we delivered to the right ear a second Gaussian noise of variable intensity levels (binaural protocol). Second, we applied the Gaussian noise of the same variable intensity levels but only to one ear (monaural protocol). We performed a permutation test analysis, finding that during both noise protocols there was a significant enhancement in the global coherence in EEG signals via the occurrence of internal SR within central pathways of the auditory system.

Augmenting EEG-global-coherence with auditory and visual noise: Multisensory internal stochastic resonance.

The present investigation documents the electrophysiological occurrence of multisensory internal stochastic resonance (MISR) in the human electroencephalographic (EEG) coherence elicited by auditory and visual noise.We define MISR of EEG coherence as the phenomenon for which an intermediate level of input noise of a sensory modality enhances EEG coherence in response to another noisy sensory modality. Here, EEG coherence is computed by the global weighted coherence (GWC), modulated by quasi-Brownian noise. Specifically, we examined whether a particular level of auditory noise together with constant visual noise (experimental condition 1) and a specified level of visual noise together with constant auditory noise (experimental condition 2), improves EEG's GWC. We compared GWC between ongoing EEG basal activity (BA), zero noise (ZN), optimal noise (ON), and high noise (HN).The data disclosed an intermediate level of input noise that enhances the GWC for the majority of the subjects, thus demonstrating for the first time the occurrence of multisensory internal stochastic resonance (SR) in visuoauditory processing within the central nervous system.

P861: The long-range corticomuscular synchronization as the neural correlate of the internal stochastic resonance phenomenon

P861: The long-range corticomuscular synchronization as the neural correlate of the internal stochastic resonance phenomenon

Improved Sensorimotor Performance via Stochastic Resonance

Several studies about noise-enhanced balance control in humans support the hypothesis that stochastic resonance can enhance the detection and transmission in sensorimotor system during a motor task. The purpose of the present study was to extend these findings in a simpler and controlled task. We explored whether a particular level of a mechanical Gaussian noise (0-15 Hz) applied on the index finger can improve the performance during compensation for a static force generated by a manipulandum. The finger position was displayed on a monitor as a small white point in the center of a gray circle. We considered a good performance when the subjects exhibited a low deviation from the center of this circle and when the performance had less variation over time. Several levels of mechanical noise were applied on the manipulandum. We compared the performance between zero noise (ZN), optimal noise (ON), and high noise (HN). In all subjects (8 of 8) the data disclosed an inverted U-like graph between the inverse of the mean variation in position and the input noise level. In other words, the mean variation was significantly smaller during ON than during ZN or HN. The findings suggest that the application of a tactile-proprioceptive noise can improve the stability in sensorimotor performance via stochastic resonance. Possible explanations for this improvement in motor precision are an increase of the peripheral receptors sensitivity and of the internal stochastic resonance, causing a better sensorimotor integration and an increase in corticomuscular synchronization.

Enhancement of internal stochastic resonance in Neurospora circadian clock system：Multiplicative and additive noises effects

The effects of multiplicative noise on additive noise-induced internal signal stochastic resonance（ISR）are studied in a Neurospora circadian clock system driven by external signal or not. Two cases are investigated: multiplicative noise and additive noise are independent or correlated. The results show that in the two cases, there exists a critical intensity of multiplicative noise for the additive noise-induced ISR in the system without the external signal. When a multiplicative noise with intensity smaller than the critical level is introduced，the strength of ISR can be significantly reinforced; while the ISR behaviors cannot be further enhanced when the noise with the intensity larger than the critical level is introduced. The latter implies that the Neurospora system might be robust to environmental noise and sustain the intrinsic circadian rhythms. When the external signal is injected into the system, for the case of without correlation between two noises, there exists an optimal frequency （0003 Hz） of the signal for the ISR information amplification, but for the case of with correlation between the two noises, the ISR is suppressed by the signal with any frequency. In addition, the correlation’s intensity between the two noises can also control the ISR, and there exists a proper range of correlation’s intensity for the ISR amplification.

Constructive Role of Internal Noise for the Detection of Weak Stimulation in a Coupled Biological Cell System

By constructing a mesoscopic stochastic model for intracellular calcium oscillations in coupled cell system, we investigated the influence of internal noise on the detection of weak stimulation using the chemical Langevin equation (CLE). We found that an optimal cell size V existed for a coupled cell chain length N and an optimal value of N existed for a given cell size V. At these values, the collective calcium oscillations showed the best performance, indicating the occurrence of"system size resonance (SSR)"or"internal noise stochastic resonance (INSR)". And such a phenomenon was robust to the coupling strength. Living cells may have learned to exploit the internal noise to detect weak stimulation via the mechanism of INSR, and then encode information to specifically regulate distinct cellular functions. It is interesting to note that the optimal cell size is always present at V≈103 μm3, which is close to the real living cell size in vivo. Since the internal noise in living systems can not be ignored and the systems may often encounter weak stimulations, our findings might have significance for stimulation detecting processes in living systems.

Optimal Internal Noise for Mammalian Circadian Oscillator

Based on a deterministic mammalian circadian oscillator proposed recently, we have constructed the corresponding mesoscopic stochastic model, and studied the effect of internal noise on the genetic oscillations of such a system. It is found that the stochastic genetic oscillations can show best performance at an optimal internal noise level via a mechanism of internal noise stochastic resonance. Furthermore, it is found that there exists a moderate system size that makes the stochastic model show effective oscillation at more extended region than the deterministic description, which indicates enhanced robustness as the result of internal noise. The potential biological application of such an effect is also discussed.

Enhancement and sustainment of internal stochastic resonance in unidirectional coupled neural system

In this study, the collective dynamical behavior of two unidirectionally, linearly coupled neurons was investigated. Our investigation illustrates that, depending on the coupling strength, the internal stochastic resonance (ISR) effect observed in one of the two neurons could be amplified or sustained by the other. The amplification of ISR is enhanced as the coupling strength is increased from 0. However, when the coupling strength is increased above a certain level, the amplification of ISR is reduced, implicating that there exists an optimal coupling strength for the information flow between two neurons. As the coupling strength is increased further, i.e., above the critical level, synchronization of the two subsystems is achieved, yet the two subsystems exhibit the same magnitude response to the external noise, suggesting that the information transmission among coupled subunits could not be improved by further enhancing their coupling strength. And similar phenomena could also be obtained for the nonidentical case.

The influence of coupling on internal stochastic resonance in neural system

A noisy biological system is applied to investigate the influence of coupling on the internal stochastic resonance. It is found that the internal stochastic resonance could be transferred by coupling, and the enhancement and suppression of the stochastic resonance could be realized by controlling the coupling strength at proper range. The explicit internal signal stochastic resonance without tuning occurs. An appropriate coupling strength is found to enhance the propagation of the internal stochastic resonance most effectively with the increment of the external noise.

Internal noise enhanced detection of hormonal signal through intracellular calcium oscillations

A variety of cell types respond to extracellular hormonal signals by repetitive intracellular calcium spikes. Here, by constructing a mesoscopic stochastic model for intracellular calcium oscillations in hepatocytes, we have investigated the influence of internal noise on the detection of sub-threshold hormonal signals using chemical Langevin equation (CLE) and Poisson approximation. It is found that stochastic calcium spikes appear when the internal noise is considered, and the regularity of the spike train undergoes a maximum with the variation of the internal noise level, indicating the occurrence of internal noise stochastic resonance (INSR). Since the magnitude of the internal noise is changed via the variation of the system size, the INSR also represents itself a kind of system size resonance.

Internal noise stochastic resonance in CO oxidation on nm-sized palladium particles

Based on a stochastic mesoscopic model, the influence of internal noise on the oscillatory kinetics of the catalytic oxidation of CO on nm-sized palladium particles is studied, using the chemical Langevin equations, Poisson approximation algorithm, and exact stochastic simulation algorithm. The reaction rate oscillations are of stochastic nature due to considerable internal noise in such mesoscopic systems. It is found that the performance of the stochastic oscillations undergoes a maximum with the variation of internal noise level for a given CO partial pressure, which demonstrates the occurrence of internal noise stochastic resonance. This phenomenon implies that optimal internal noise would favor the reaction rate oscillation of CO oxidation on nm particles. Such a phenomenon is robust to the change of external parameters, such as CO pressures.

Internal stochastic resonance under two-parameter modulation in intercellular calcium ion oscillations.

Internal stochastic resonance (ISR) in a model of intercellular calcium ion oscillations is investigated under the modulation of two parameters, viz., degree of extracellular stimulation (beta) and leak rate (k(f)). ISR can occur when either beta or k(f) is subjected to a noise. Internal stochastic biresonance (ISBR) can occur when noise is added to the two parameters simultaneously. The distance to the bifurcation point is found to be able to enhance or suppress the ISBR, and to affect the number of peaks of ISR.

Internal stochastic resonance in two coupled liquid membrane oscillators.

Internal stochastic resonance (ISR) is investigated in two coupled liquid membrane oscillators when only one oscillator is subjected to environmental noise in the absence of an external signal. Comparing the responses of both subsystems, it is found that enhancement or suppression of ISR for each oscillator depends on the coupling strength, that synchronization of the two oscillators can occur only at strong coupling strength, and that ISR without tuning can also occur under certain conditions in the above-mentioned models.

The effects of an external signal on internal stochastic resonance in a liquid membrane oscillator

Internal stochastic resonance (ISR) in a liquid membrane oscillator is investigated by varying frequency ( ω s ) and amplitude ( A) of an external signal (ES) in the presence of environment noise. It is found that the enhancement or suppression of ISR depends on frequency and amplitude of ES. In the range of low frequency (0.03–0.12 Hz), ISR appears and noise can transfer energy of ES to IS both for A=0.02 M and for A=0.15 M. In the range of high frequency (0.26–0.32 Hz), there exits an optimal frequency for ES, which is equal to frequency of IS and makes ISR strength reach maximum for A=0.02 M; but ISR disappears for A=0.15 M. At the optimal frequency ω s =0.28 Hz, a critical amplitude A c for ES is found, less than which, ISR appears, and more than which, ISR disappears.

Internal spatiotemporal stochastic resonance in the presence of weak noise.

We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating A+1 / 2B(2) reaction on a square lattice. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises when homogeneous nucleation of the individual lattice site states is considered. This nucleation is modeled as a weak noise process. As a result, synchronization of the kinetic oscillations is obtained. We show that all characteristics known from the research on stochastic resonance are obtained in our model. We also show that the model explains easily several phenomena observed in the experiment. Internal stochastic resonance may thus be an internal regulation mechanism of extreme adaptability.

Internal stochastic resonance in the coherence between spinal and cortical neuronal ensembles in the cat

Internal stochastic resonance is a phenomenon in which the coherence of a non-linear system is enhanced by the presence of a particular, non-zero level of noise generated by internal or external sources without a periodic input signal. The aim of this study was to demonstrate the experimental occurrence of internal stochastic resonance in the coherence between spinal and cortical neuronal ensembles. Simultaneous recordings of spinal and cortical evoked potentials were made in the somatosensory system of the anaesthetized cat. Evoked potentials were produced by input noise introduced in the tactile stimulation of the hindpaw skin. Coherence between the spinal and cortical evoked activity recorded during different levels of input noise was calculated. All animals showed distinct internal stochastic resonance like behavior. We found that the mean coherence was an inverted U-like function of the level of input noise with a mean coherence peak of 0.43. To our knowledge, this is the first documented evidence of such phenomenon in an in vivo preparation of the central nervous system.

Internal stochastic resonance in a model system for intracellular calcium oscillations

A model system for intracellular calcium oscillations was investigated when the control parameter was perturbed by noise near a Hopf bifurcation point. Noise-induced oscillations were observed. Furthermore, the output signal-to-noise ratio (SNR) of the system went through a maximum with the increment of noise intensity indicating the occurrence of internal stochastic resonance (SR), which showed the constructive role of noise at the cellular level.

Internal stochastic resonance in two coupled chemical oscillators

The dynamics of two coupled chemical oscillators was investigated numerically when the first subsystem was subjected to external parametric noise. The signal-to-noise ratio (SNR) of the response of each subsystem to external noise shows internal stochastic resonance (SR). In addition, the SNR also shows resonance behavior with the variation of coupling strength.

Effects of colored noise on internal stochastic resonance in a chemical model system

The phenomenon of internal stochastic resonance (SR) in a chemical model system was studied. The effects of colored noise with finite correlation time were compared with those of white noise without any time correlation. It was shown that the correlation time of noise could affect the peak value of internal SR and the location of the optimal noise intensity for resonance behavior. The application of correlation time in controlling internal SR was discussed.

Noise-induced oscillations and internal stochastic resonance in a model of excitable biomembrane

The dynamics of the oil–water liquid membrane oscillator driven by external noise was investigated near a Hopf bifurcation point. Noise activated the system producing a sequence of oscillations. The coherence of noise-induced oscillations reached a maximum for a certain noise intensity indicating occurrence of internal stochastic resonance (SR). The constructive role of noise in some sensory cells is discussed.