Engineered internal noise stochastic resonator in gene network: a model study

Based on a genetic bistable switch model coupled with a gene oscillator model, we have constructed a mesoscopic stochastic model for the coupled synthetic gene network, and studied how internal noise would influence the oscillation of such a system. We found that the state-to-state transitions can occur if the internal noise is taken into account, and the performance of resulting oscillation can reach a maximum in a certain internal noise level, which indicates the occurrence of internal noise stochastic resonance (SR) and makes the coupled gene network work as a stochastic resonator. The potential role of such an effect on gene expression systems is also discussed.     

Modeling the emergence of circadian rhythms in a clock neuron network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.     

Temporally incoherent magnetic fields mitigate the response of biological systems to temporally coherent magnetic fields

We have previously demonstrated that a weak, extremely-low-frequency magnetic field must be coherent for some minimum length of time (≈? 10 s) in order to affect the specific activity of ornithine decarboxylase (ODC) in L929 mouse cells. In this study we explore whether or not the superposition of an incoherent (noise) magnetic field can block the bioeffect of a coherent 60 Hz magnetic field, since the sum of the two fields is incoherent. An experimental test of this idea was conducted using as a biological marker the twofold enhancement of ODC activity found in L929 murine cells after exposure to a 60 Hz, 10 μT_rms magnetic field. We superimposed an incoherent magnetic noise field, containing frequencies from 30 to 90 Hz, whose rms amplitude was comparable to that of the 60 Hz field. Under these conditions the ODC activity observed after exposure was equal to control levels. It is concluded that the superposition of incoherent magnetic fields can block the enhancement of ODC activity by a coherent magnetic field if the strength of the incoherent field is equal to or greater than that of the coherent field. When the superimposed, incoherent noise field was reduced in strength, the enhancement of ODC activity by the coherent field increased. Full ODC enhancement was obtained when the rms value of the applied EM noise was less than one-tenth that of the coherent field. These results are discussed in relation to the question of cellular detection of weak EM fields in the presence of endogenous thermal noise fields. © 1994 Wiley-Liss, Inc.     

Weak electric fields detectability in a noisy neural network

We investigate the detectability of weak electric field in a noisy neural network based on Izhikevich neuron model systematically. The neural network is composed of excitatory and inhibitory neurons with similar ratio as that in the mammalian neocortex, and the axonal conduction delays between neurons are also considered. It is found that the noise intensity can modulate the detectability of weak electric field. Stochastic resonance (SR) phenomenon induced by white noise is observed when the weak electric field is added to the network. It is interesting that SR almost disappeared when the connections between neurons are cancelled, suggesting the amplification effects of the neural coupling on the synchronization of neuronal spiking. Furthermore, the network parameters, such as the connection probability, the synaptic coupling strength, the scale of neuron population and the neuron heterogeneity, can also affect the detectability of the weak electric field. Finally, the model sensitivity is studied in detail, and results show that the neural network model has an optimal region for the detectability of weak electric field signal.     

Stochastic resonance modulates neural synchronization within and between cortical sources

Neural synchronization is a mechanism whereby functionally specific brain regions establish transient networks for perception, cognition, and action. Direct addition of weak noise (fast random fluctuations) to various neural systems enhances synchronization through the mechanism of stochastic resonance (SR). Moreover, SR also occurs in human perception, cognition, and action. Perception, cognition, and action are closely correlated with, and may depend upon, synchronized oscillations within specialized brain networks. We tested the hypothesis that SR-mediated neural synchronization occurs within and between functionally relevant brain areas and thus could be responsible for behavioral SR. We measured the 40-Hz transient response of the human auditory cortex to brief pure tones. This response arises when the ongoing, random-phase, 40-Hz activity of a group of tuned neurons in the auditory cortex becomes synchronized in response to the onset of an above-threshold sound at its "preferred" frequency. We presented a stream of near-threshold standard sounds in various levels of added broadband noise and measured subjects' 40-Hz response to the standards in a deviant-detection paradigm using high-density EEG. We used independent component analysis and dipole fitting to locate neural sources of the 40-Hz response in bilateral auditory cortex, left posterior cingulate cortex and left superior frontal gyrus. We found that added noise enhanced the 40-Hz response in all these areas. Moreover, added noise also increased the synchronization between these regions in alpha and gamma frequency bands both during and after the 40-Hz response. Our results demonstrate neural SR in several functionally specific brain regions, including areas not traditionally thought to contribute to the auditory 40-Hz transient response. In addition, we demonstrated SR in the synchronization between these brain regions. Thus, both intra- and inter-regional synchronization of neural activity are facilitated by the addition of moderate amounts of random noise. Because the noise levels in the brain fluctuate with arousal system activity, particularly across sleep-wake cycles, optimal neural noise levels, and thus SR, could be involved in optimizing the formation of task-relevant brain networks at several scales under normal conditions.     

Landscape, flux, correlation, resonance, coherence, stability, and key network wirings of stochastic circadian oscillation

Circadian rhythms with a period of ∼24 h, are natural timing machines. They are broadly distributed in living organisms, such as Neurospora, Drosophila, and mammals. The underlying natures of the rhythmic behavior have been explored by experimental and theoretical approaches. However, the global and physical natures of the oscillation under fluctuations are still not very clear. We developed a landscape and flux framework to explore the global stability and robustness of a circadian oscillation system. The potential landscape of the network is uncovered and has a global Mexican-hat shape. The height of the Mexican-hat provides a quantitative measure to evaluate the robustness and coherence of the oscillation. We found that in nonequilibrium dynamic systems, not only the potential landscape but also the probability flux are important to the dynamics of the system under intrinsic noise. Landscape attracts the systems down to the oscillation ring while flux drives the coherent oscillation on the ring. We also investigated the phase coherence and the entropy production rate of the system at different fluctuations and found that dissipations are less and the coherence is higher for larger number of molecules. We also found that the power spectrum of autocorrelation functions show resonance peak at the frequency of coherent oscillations. The peak is less prominent for smaller number of molecules and less barrier height and therefore can be used as another measure of stability of oscillations. As a consequence of nonzero probability flux, we show that the three-point correlations from the time traces show irreversibility, providing a possible way to explore the flux from the observations. Furthermore, we explored the escape time from the oscillation ring to outside at different molecular number. We found that when barrier height is higher, escape time is longer and phase coherence of oscillation is higher. Finally, we performed the global sensitivity analysis of the underlying parameters to find the key network wirings responsible for the stability of the oscillation system.     

Modeling of Nonlinear Chemical Reaction Systems and Two-Parameter Stochastic Resonance

The idea of stochastic resonance (SR) is extended to two-parameter dynamical systems based on the Oregonator model of the Belousov-Zhabotinsky (BZ) reaction. The first case presents the photosensitivity of the reaction, and light flux and a flow rate are the two control parameters. The second case presents the effect of temperature on the oscillatory behaviors, and temperature and a flow rate are the control parameters. Stochastic resonance is demonstrated in the first case in which a signal and noise are applied to the different inputs, respectively. The scenario and novel aspects of SR in two-parameter systems are discussed, and the possibility of the analogous SR in biological systems is also pointed out.     

White-noise stimulation of the Hodgkin–Huxley model

 We studied the combined influence of noise and constant current stimulations on the Hodgkin–Huxley neuron model through time and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of the linearized Hodgkin–Huxley system. Conversely, nonlinearities due to firing dominate at large noise or current stimulations. The transition between the two regimes is abrupt, and takes place in the same range of noise and current intensities as the noise-induced transition characterized by the qualitative change in the stationary distribution of the membrane potential (Tanabe and Pakdaman 2001a). The implications of these results are discussed. Received: 27 July 2001 / Accepted in revised form: 18 December 2001     

Noise-induced transition in excitable neuron models

 We studied the influence of noisy stimulation on the Hodgkin-Huxley neuron model. Rather than examining the noise-related variability of the discharge times of the model – as has been done previously – our study focused on the effect of noise on the stationary distributions of the membrane potential and gating variables of the model. We observed that a gradual increase in the noise intensity did not result in a gradual change of the distributions. Instead, we could identify a critical intermediate noise range in which the shapes of the distributions underwent a drastic qualitative change. Namely, they moved from narrow unimodal Gaussian-like shapes associated with low noise intensities to ones that spread widely at large noise intensities. In particular, for the membrane potential and the sodium activation variable, the distributions changed from unimodal to bimodal. Thus, our investigation revealed a noise-induced transition in the Hodgkin-Huxley model. In order to further characterize this phenomenon, we considered a reduced one-dimensional model of an excitable system, namely the active rotator. For this model, our analysis indicated that the noise-induced transition is associated with a deterministic bifurcation of approximate equations governing the dynamics of the mean and variance of the state variable. Finally, we shed light on the possible functional importance of this noise-induced transition in neuronal coding by determining its effect on the spike timing precision in models of neuronal ensembles. Received: 19 September 2000 / Accepted in revised form: 4 March 2001     

Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.     

Noise-induced stress in hospital patients: coping and nonauditory health outcomes

This study found that, for 150 postoperative male patients, degree of objective noise, intrinsic sensitivity of the person to noise, and noise-induced stress were positively related to coping, in the form of exercised control over noise (correlations ranged from r = .207 to r = .468, P less than .01 for all cases). Hierarchical multiple regression confirmed these results. Furthermore, greater sensitivity of the person to noise was positively correlated with ability to cope, regardless of the objective level of noise. Patients who were randomly assigned to an experimental group, where they received instructions for control over noise, showed no difference in coping ability than a control group. There was a lack of support for several hypotheses concerned with the effects of noise-induced stress and coping on health, where stress was measured by self-reports of recovery and average time-out-of-bed in minutes. The meaning of these results is discussed in terms of stress theory.     

Reg3b在大鼠耳蜗的分布及噪声刺激后的表达变化

目的：探讨Reg3b在大鼠耳蜗中的分布情况及在噪声刺激前后的表达变化,为治疗噪声性聋提供新思路。方法：30只健康成年SD大鼠,分为噪声暴露组和正常对照组,利用110dBSPL宽频稳态白噪声对噪声组进行噪声暴露,通过免疫组织荧光技术,观察Reg3b在正常及噪声刺激后成年sD大鼠耳蜗内的分布情况。采用实时定量PCR技术（Realtime-PCR）方法检测大鼠接受噪声刺激前后Reg3b在耳蜗内的表达变化。结果：免疫组织荧光技术提示,Reg3b在噪声暴露后主要表达于大鼠耳蜗的内毛细胞、外毛细胞,以及螺旋神经节处,而正常大鼠耳蜗中Reg3b表达不明显或呈阴性表达。与噪声刺激前相比,噪声刺激后,Reg3b在mRNA水平表达较噪声前明显提高。结论：Reg3b在耳蜗内的分布及在噪声刺激后的表达显著升高提示其在噪声诱导的细胞死亡及对抗噪声损伤方面具有一定作用,可能成为治疗感音神经性聋的新靶点。     

External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System

The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.     

Load dependence of simulated central tremor

Previous studies have argued that tremors of central versus peripheral origin can be distinguished based on their load dependence: the frequency of peripheral tremor decreases when a weight is added to the tremulous limb, while the frequency of central tremors remains unchanged. The present study scrutinizes the latter statement. We simulated central tremor using a simple network of coupled neural oscillators, which receives proprioceptive feedback from the motor periphery. The network produced a self-sustained, stable oscillation. When the gain of proprioceptive feedback was high, oscillation frequency decreased in the presence of an inertial load. When the gain was low, the oscillation frequency was load independent. We conclude that load dependence is not an exclusive property of peripheral tremors but may be found in tremors of central origin as well. Therefore, the load test is not sufficient to reject a central tremor origin. Received: 1 October 1998 / Accepted in revised form: 28 January 1999     

Epidemiology of Noise-Induced Tinnitus and the Attitudes and Beliefs towards Noise and Hearing Protection in Adolescents

Background and objectives

Previous research showed an increase of noise-induced symptoms in adolescents. Permanent tinnitus as a consequence of loud music exposure is usually considered as noise-induced damage. The objective was to perform an epidemiological study in order to obtain prevalence data of permanent noise-induced tinnitus as well as temporary tinnitus following noise exposure in a young population. In addition the attitudes and beliefs towards noise and hearing protection were evaluated in order to explain the use/non-use of hearing protection in a young population.

Methods

A questionnaire was completed by 3892 high school students (mean age: 16.64 years old, SD: 1.29 years). The prevalence of temporary and permanent tinnitus was assessed. In addition the ‘Youth Attitudes to Noise Scale’ and the ‘Beliefs About Hearing Protection and Hearing Loss’ were used in order to assess the attitudes and beliefs towards noise and hearing protection respectively.

Results

The prevalence of temporary noise-induced tinnitus and permanent tinnitus in high school students was respectively 74.9% and 18.3%. An increasing prevalence of temporary tinnitus with age was present. Most students had a ‘neutral attitude’ towards loud music and the use of hearing protection was minimal (4.7%). The limited use of hearing protection is explained by a logistic regression analysis showing the relations between certain parameters and the use of hearing protection.

Conclusions

Despite the very high prevalence of tinnitus in such a young population, the rate of hearing protection use and the knowledge about the risks of loud music is extremely low. Future preventive campaigns should focus more on tinnitus as a warning signal for noise-induced damage and emphasize that also temporary symptoms can result in permanent noise-induced damage.     

Stochastic resonance in the speed of memory retrieval

The stochastic resonance (SR) phenomenon in human cognition (memory retrieval speed for arithmetical multiplication rules) is addressed in a behavioral and neurocomputational study. The results of an experiment in which performance was monitored for various magnitudes of acoustic noise are presented. The average response time was found to be minimal for some optimal noise level. Moreover, it was shown that the optimal noise level and the magnitude of the SR effect depend on the difficulty of the task. A computational framework based on leaky accumulators that integrate noisy information and provide the output upon reaching a threshold criterion is used to illustrate the observed phenomena.     

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Fractal characterisation of the effect of noise on biological oscillations: The biosynthesis of ethanol

Summary Biological reactions which interact with their environment are subject to the influx of noise. Noise introduces randomness and imparts fractal character to the deterministic behavior. A methodology is proposed to compute the fractal dimensions of such reactions. It is applied to the continuous culture of Zymomonas mobilis to produce ethanol. Results show that noise can change the nature of oscillations or induce oscillations in a stationary state. The noise-induced oscillations are aperiodic and fractal in nature. The variation of the fractal dimension with dilution rate and the initial ethanol concentration is presented and discussed in terms of the interaction between process kinetics and the incoming noise.     

Noise-induced divisive gain control in neuron models

A recent computational study of gain control via shunting inhibition has shown that the slope of the frequency-versus-input (f-I) characteristic of a neuron can be decreased by increasing the noise associated with the inhibitory input (Neural Comput. 13, 227-248). This novel noise-induced divisive gain control relies on the concommittant increase of the noise variance with the mean of the total inhibitory conductance. Here we investigate this effect using different neuronal models. The effect is shown to occur in the standard leaky integrate-and-fire (LIF) model with additive Gaussian white noise, and in the LIF with multiplicative noise acting on the inhibitory conductance. The noisy scaling of input currents is also shown to occur in the one-dimensional theta-neuron model, which has firing dynamics, as well as a large scale compartmental model of a pyramidal cell in the electrosensory lateral line lobe of a weakly electric fish. In this latter case, both the inhibition and the excitatory input have Poisson statistics; noise-induced divisive inhibition is thus seen in f-I curves for which the noise increases along with the input I. We discuss how the variation of the noise intensity along with inputs is constrained by the physiological context and the class of model used, and further provide a comparison of the divisive effect across models.