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

How noise can generate calcium spike-type oscillations in deterministic equilibrium modes

Stochastic excitability of spiking oscillatory regimes in the calcium kinetics is studied on the basis of the Li-Rinzel conceptual model. The probabilistic mechanisms of the noise-induced generation of large-amplitude oscillations in parametric zones, where the original deterministic model has only stable equilibria, are investigated numerically and analytically. A parametric statistical description of interspike intervals is curried out and the phenomenon of coherence resonance is discussed. For the analytical study of the stochastic excitement, the confidence domain method using a stochastic sensitivity technique is applied. In this analysis, a key role of mutual arrangement of the confidence ellipses and separatrices detaching the sub- and supercritical regions is demonstrated. It is shown that in the Li-Rinzel model such separatrices are the stable manifolds of the saddle equilibria and the transient semiattractors.

Enhanced corticomuscular coherence by external stochastic noise

Noise can have beneficial effects as shown by the stochastic resonance (SR) phenomenon which is characterized by performance improvement when an optimal noise is added. Modern attempts to improve human performance utilize this phenomenon. The purpose of the present study was to investigate whether performance improvement by addition of optimum noise (ON) is related to increased cortical motor spectral power (SP) and increased corticomuscular coherence. Eight subjects performed a visuomotor task requiring to compensate with the right index finger a static force (SF) generated by a manipulandum on which Gaussian noise was applied. The finger position was displayed on-line on a monitor as a small white dot which the subjects had to maintain in the center of a green bigger circle. Electroencephalogram from the contralateral motor area, electromyogram from active muscles and finger position were recorded. The performance was measured by the mean absolute deviation (MAD) of the white dot from the zero position. ON compared to the zero noise condition induced an improvement in motor accuracy together with an enhancement of cortical motor SP and corticomuscular coherence in beta-range. These data suggest that the improved sensorimotor performance via SR is consistent with an increase in the cortical motor SP and in the corticomuscular coherence.

Chemical oscillator as a generalized Rayleigh oscillator

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

Noise-induced effective oscillation in oil-water membrane oscillator

Noise-induced oscillation (NIO) was investigated in a model of an oil-water membrane oscillator. First, we analyzed an unexcitable region and an excitable region of the system by proposing a critical threshold of NIO appearance and found a linearlike relation between the critical threshold and noise intensity. Then the phenomenon of noise-induced coherence resonance was investigated by calculating the signal-to-noise ratio. Furthermore, it was found that an optimal noise intensity range could most improve the appearance of effective oscillation (EO). The presence of EO regions made the stochastic model show EO at a more extended region than the deterministic description.

Roles of external noise correlation in optimal intracellular calcium signaling

The dynamics of a minimal calcium model, which is subjected to white noise or colored noise, was investigated. For white noise, coherence of noise-induced calcium oscillations reached a maximum at an optimal noise intensity, characterizing coherence resonance. Higher resonance peaks could be observed at lower noise intensity when a control parameter is tuned to approach a bifurcation point. For colored noise, a maximal coherence of the oscillations was found for suitable values of both the intensity and the correlation time. Moreover, the coherence of the oscillations exhibited two maxima at two values of noise intensity (correlation time) for appropriate noise correlation time (intensity). In addition, a quantitative description of the effects of noise correlation time on the resonance behavior was presented. The resonance behavior, which is induced either by white noise or colored noise, was interpreted by terms of height and relative width of a spectral peak.

Enhancement of internal-noise coherence resonance by modulation of external noise in a circadian oscillator

A circadian oscillator driven by external noise and internal noise has been studied by use of the chemical Langevin equation method. When the system is near a Hopf bifurcation and driven by internal noise only, it is found that the coherence resonance phenomenon can be induced by the internal noise. When the system is simultaneously driven by internal and external noise, it is found that external-noise coherence resonance can be suppressed by internal noise, while internal-noise coherence resonance can be enhanced by modulation of the external noise intensity in a certain range of noise intensity. Another interesting result is that the external noise can regulate the optimal system size when the internal-noise coherence resonance occurs.