Internal Signal Stochastic Resonance Research Articles

Internal signal stochastic resonance of a two-component gene regulatory network under Lévy noise

Noises are ubiquitous in nature and can often induce some curious phenomena. In this paper, we investigate the internal signal stochastic resonance (ISSR) phenomenon of a two-component gene regulatory network under the excitation of Levy noise. Our results reveal that the Levy noise can induce the periodic oscillation of the protein concentration when the control parameter is close to its bifurcation points. Furthermore, we consider the noise-induced periodic signal as the periodic excitation and study the ISSR phenomenon under the cooperation of the nonlinear system, noise-induced periodic signal and random noise. And we found that there may be a connection between the ISSR phenomenon and the bifurcation mechanism. Besides, we also investigate the effects of different noise parameters on the ISSR phenomenon. The simulation results indicate that there is an optimal interval of the stability index $$\alpha $$ which can induce the ISSR phenomenon, and the skewness parameter $$\beta $$ has a negative correlation with the ISSR phenomenon. Our results may provide a pathway to uncover the positive functional mechanism of noises in complex gene regulatory networks.

Two types of coherence resonance in an intracellular calcium oscillation system

Two types of noise induced oscillations (NIOs) near Hopf bifurcation and coherence resonance (CR) have been studied analytically in a calcium system. One is NIOs with small amplitude and internal signal stochastic resonance (CR type I) occurs, and the other is noise induced spike and the regularity of which reaches a maximum at an optimal noise level (CR type II). For the first type, stochastic normal form theory is employed to analyze the signal to noise ratio of the NIOs depending on the noise intensity. For the second type, based on the independent assumption, activation time and excursion time have been split, and the sum of which reach a minimum with the variation of noise intensity. The theoretical evidence is also explained in detail. Numerical simulations show good agreements with the theoretical results. It may indicate some kind of transmit mechanism involved in stochastic calcium dynamics.

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system was studied by using a mesoscopic stochastic model. When the stimulus was too weak to fire calcium spikes for the cell, separately, we found that calcium spikes could be induced by the external noise or internal noise, and internal signal stochastic resonance (ISSR) or internal noise stochastic resonance (INSR) occurred, respectively, so that the cell system could detect the weak stimulus through intracellular calcium spikes with the help of external noise or internal noise. When considering both of the noises, we found that internal noise could suppress ISSR, while external noise could enhance INSR in a certain range of external noise intensity. Interestingly, when the INSR occurs, the optimal size matched well with the real cell size, this was of significant biological meaning.

Influences of a periodic signal on a noisy synthetic gene network

The effects of noise and a periodic signal on a synthetic gene network have been investigated. By tuning the distance of a parameter from the Hopf bifurcation point, both implicit internal signal stochastic resonance and explicit internal signal stochastic resonance can be induced by noise. Furthermore, a switch process can also be elicited. When a periodic signal is coupled to the gene network, two interesting phenomena occur with the modulation of the frequency of the signal: the effect of noise amplifying cellular signal can be inhibited or even destroyed, and “locked” coherence resonance occurs.

Signal transduction and amplification in a circadian oscillator: Interaction between two colored noises

The signal transduction and amplification in a Neurospora circadian clock system is studied by using the mechanism of internal signal stochastic resonance (ISSR). Two cases have been investigated: the case of no correlations between multiplicative and additive colored noises and the case of correlations between two noises. The results show that, in both cases, the noise-induced circadian oscillations can be transduced with the phenomenon of internal signal stochastic resonance (ISSR). However, the correlation time and intensity of an additive colored noise play different roles for the ISSR, driven by multiplicative colored noise, while the correlation time and intensity of multiplicative colored noise hardly influence the ISSR driven by additive colored noise. In addition, the ISSR can be amplified or suppressed at an appropriate range of the correlation intensity between two colored noises. The fundamental frequency of noise-induced circadian oscillations is hardly shifted with the increment of the intensity and correlation time of colored noises, which implies that the Neurospora system could be resistant to colored noises, exhibit strong vitality and sustain intrinsic circadian rhythms.

Effect of Colored Noise on Circadian Oscillation and Internal Signal Stochastic Resonance in Biological Clock System*

The effect of colored noise on circadian oscillation and internal signal stochastic resonance(ISSR) has been studied in a Neurospora circadian clock system. The result shows that the correlation time of colored noise can affect strongly the strength of ISSR. For the case of no external signal(ES), the correlation time of colored noise plays a suppressive role for ISSR, and the suppressive role is increased with the increment of correlation time of colored noise. When the ES is injected to the system, with the increasing of the correlation time of colored noise, not only its suppressive role for ISSR is increased, but also the single peak ISSR can be transformed as internal single stochastic bi-resonance (ISSBR). There exists an optimal frequency of ES for the ISSR information amplification, while the ISSR is suppressed for another frequency of ES. In contrast to external colored noise, internal colored noise is more efficient to sustain and amplify the ISSR information. Furthermore, there exists a critical noise intensity for destroying the difference between white and colored noises.

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.

Sustainment and Controlment of Noise-Induced Circadian Oscillations in Neurospora: Noise and External Signal Effects

The effect of light noise on a Neurospora circadian clock system in the steady states is investigated. It is found that the circadian oscillations could be induced by light noise, leading to various resonance phenomena including internal signal stochastic resonance (ISSR) and ISSR without tuning in the system. The strength of ISSR could be significantly reinforced with the decrease of the distance of the control parameter to the Hopf bifurcation point of the system. The fundamental frequency of noise-induced circadian oscillations almost does not change with the increment of light noise intensity, which implies that the Neurospora system could sustain intrinsic circadian rhythms. In addition, the ISSR and ISSR without tuning could be both amplified, suppressed or destroyed by tuning the frequency or amplitude of external signal.

Signal transduction in a coupled hormone system: Selective explicit internal signal stochastic resonance and its control

Cooperative interactions of signal transduction and environmental noise are investigated with a coupled hormone system, in which selective explicit internal signal stochastic resonance (EISSR) is observed. More specifically, the large peak of a period-2 oscillation (i.e., a strong signal) is greatly amplified by the environmental noise while the small peak (i.e., a weak signal) does not exhibit cooperative interactions with noise. The EISSR phenomenon could be controlled by adjusting the frequency or amplitude of an external signal and a critical amplitude for external signal is found. Significantly, the maximal signal-to-noise ratio increases almost linearly with the increment of control parameter, despite that the magnitude of the large peak is decreased. In addition, the noise does not alter the fundamental frequencies of the strong signal and the weak signal, which implicates that the system can keep its intrinsic oscillatory state and resist the effect of environmental fluctuations.

Implicit and explicit internal signal stochastic resonance in calcium ion oscillations

Responses of Ca 2+ oscillations to random perturbation are investigated at the conditions where the system stays at a steady state (before bifurcation point) or an oscillatory state (after bifurcation point). It is found that noise can induce both implicit and explicit internal signal stochastic resonance (IISSR and EISSR). In particular, the internal signal stochastic bi-resonance is also observed. When an external signal is added to the system, no IISSR or EISSR phenomenon occurs, implying an external signal destroys cooperation of Ca 2+ signal and environment noise.

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.

Explicit internal signal stochastic resonance and mechanic of noise-resistance in a chemical oscillator

The explicit internal signal stochastic resonance (EISSR) that happened in the Willamowski–Rössler reaction model was investigated. The z-variable's output signal-to-noise ratio (SNR) as a function of the noise intensity shows non-monotonic behavior, indicating the occurrence of EISSR. It is first found that EISSR happened in the periodic-2 oscillations state. A worthy noting point is that the fundamental frequency of the intrinsic period signal of the system is shifted little with the change of noise intensity. EISSR is a cooperative effect of the intrinsic period signal and external noise or fluctuations. Our studies have shown that EISSR can lead to noise-resistance of the chemical oscillator.

Explicit internal signal stochastic resonance in a chemical oscillator

Explicit internal signal stochastic resonance (EISSR) is first found in the periodic-2 oscillations state of Willamowski-Rossler reaction model.

Noise enhanced the preponderant oscillation

Explicit internal signal stochastic resonance (EISSR) is investigated in the Willamowski-Rossler reaction model located in the dynamical region of periodic-2 oscillations, which subjects to Gaussian white noise. The z-variable's output signal-to-noise ratio (SNR) as a function of the noise intensity shows non-monotonic behavior, indicating the occurrence of EISSR. It is first found that EISSR happened in the periodic-2 oscillations state. When the system exist two intrinsic signals, noise can enhance the preponderant oscillation signal.

Internal signal stochastic resonance of a synthetic gene network

The dynamics behavior of a synthetic gene network controlled by random noise is investigated using a model proposed recently. The phenomena of noise induced oscillation (NIO) of the protein concentrations and internal signal stochastic resonance (SR) are studied by computer simulation. We also find that there exists an optimal noise intensity that can most favor the occurrence of effective oscillation (EO). Finally we discuss the potential constructive roles of SR on gene expression systems.

Controlling of explicit internal signal stochastic resonance by external signal.

Explicit internal signal stochastic resonance (EISSR) is investigated in a model of energy transduction of molecular machinery when noise is added to the region of oscillation in the presence of external signal (ES). It is found that EISSR could be controlled, i.e., enhanced or suppressed by adjusting frequency (omega(e)) and amplitude (A) of ES, and that there exits an optimal frequency for ES, which makes EISSR strength reach the maximum. Meanwhile, a critical amplitude (A(c)) is found, which is a threshold of occurrence of EISSR. Finally, the difference and similarity between EISSR and IISSR (implicit internal signal stochastic resonance) are discussed.

MESOSCOPIC DESCRIPTION OF CHEMICAL SUPERCRITICAL HOPF BIFURCATION

The mesoscopic dynamic behavior of the Oregonator model of the Belousov–Zhabotinsky chemical reaction is investigated as the model system experiences a supercritical Hopf bifurcation from focus to limit cycle oscillation. The study is performed by stochastically simulating the corresponding chemical master equation. Comparing the mesoscopic dynamic results with those obtained by the macroscopic dynamics, we find in the mesoscopic description a new type of oscillating state, in which large-amplitude oscillations and small-amplitude oscillations appear randomly alternately. This new state comes out spontaneously within a certain region called Hopf bifurcation range by us. In the mesoscopic description, the Hopf bifurcation point cannot be shown, being replaced by a Hopf bifurcation range. Furthermore, the applications of this new oscillating state to internal signal stochastic resonance are pointed out.

Simulation of explicit internal signal stochastic resonance in a qualitative model for intercellular calcium ion oscillations

Explicit internal signal stochastic resonance (EISSR) is investigated numerically when noise is added to the region of periodic-2 oscillatory state in intercellular calcium ion oscillations. It is found that the signal-to-noise ratio (SNR) of strong signal (SS) has a maximum value at an optimal noise intensity and that of weak signal (WS) increases monotonously with the increment of noise intensity. These results indicate that the EISSR has selectivity to two intrinsic signals of system. Moreover, the frequencies of SS and WS hardly change, which implies that system can resist to the effect of noise and sustain intrinsic period oscillatory states.

Internal signal stochastic resonance induced by colored noise in an intracellular calcium oscillations model

An intracellular calcium oscillations model subject to external colored noise is investigated. Internal signal stochastic resonance (ISSR) can be induced and significantly influenced by colored noise. The signal-to-noise ratio (SNR) exhibits two maxima with the increment of the correlation time as the noise intensity is fixed, indicating the occurrence of stochastic bi-resonance. Additionally, we find ISSR and explicit internal signal stochastic resonance (EISSR) have quite similar responses to colored noise, which implies there are some commonalities in their mechanisms.

Selectivity of explicit internal signal stochastic resonance in a chemical model

The explicit internal signal stochastic resonance (EISSR) that happened in the Willamowski–Rössler model was studied. EISSR is a cooperative effect of the intrinsic signal and external noise or internal fluctuation. Our studies have shown that EISSR can exist in the stable periodic-2 oscillation state. The output signal to noise ratio (SNR) of the strong signal (SS) versus noise intensity exhibits explicitly nonmonotonic character. The output SNR of the weak signal decreases with the increment of noise intensity. It is clear that EISSR can hold selectivity to the preponderant intrinsic signal when there are two intrinsic signals in the system. At the same time, the fundamental frequency of the SS almost does not alter. These properties imply that the system can resist to the effect of noise and sustain preponderant intrinsic oscillation by itself. Our results will be helpful to better understand circadian rhythm and signal detecting in creatures.