Research

Noise and Cell Signalling

M. Perc and M. Marhl

Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscilatory behavior

Physical Review E
71 (2005) art. no. 026229

Abstract: We study the amplification of information transfer in excitable systems. We show that excitable systems residing in a steady state near a bifurcation point to complex oscillatory behavior incorporate several frequencies that can be exploited for a resonant amplification of information transfer. In particular, for excitable neurons that reside in a steady state near a bifurcation point to elliptic bursting oscillations, we show that in addition to the resonant frequency of damped oscillations around the stable focus, another frequency exists that resonantly enhances large amplitude bursts and thus amplifies the information transfer in the system. This additional frequency cannot be found by the local stability analysis and has never been used for amplifying the information transfer in a system. The results obtained for elliptic bursting oscillations can be generalized also to other complex oscillators, such as parabolic or square-wave bursters. Additionally, the biological importance of presented results in the field of neuroscience is outlined.

M. Perc and M. Marhl

Frequency dependent stochastic resonance in a model for intracellular Ca2+ oscillations can be explained by local divergence

Physica A
332 (2004) 123-140

Abstract: The phenomenon of stochastic resonance has recently been found in many systems. Despite the pre-conception of a destructive role of noise, its constructive role has been recognised, in particular in amplification of weak external signals, thereby facilitating signal detection and transduction in complex systems. Although the stochastic resonance has been reported for many systems in various fields of physics, chemistry and biology, the understanding of this phenomenon is still limited. In the present paper, we explain the frequency dependent stochastic resonance with the local divergence. In a model for intracellular Ca2+ oscillations, we calculate the local divergence of noise-induced oscillations and show that areas of attractors with close to zero local divergence are crucial for understanding the stochastic resonance, since they represent the most flexible and susceptible states of the system, which are thus most likely to be altered by weak external stimuli and noise. With a detailed analysis of the temporal evolution of the local divergence, we are able to explain the constructive as well as the destructive role of noise, thereby shedding light on the typical bell-shaped dependency of the signal-to-noise ratio vs. the noise intensity. The applicability of our results to other systems and their biological implications are discussed.

M. Perc and M. Marhl

Noise enhances robustness of intracellular Ca2+ oscillations

Physics Letters A
316 (2003) 304-310

APS	M. Perc and M. Marhl Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscilatory behavior Physical Review E 71 (2005) art. no. 026229	Abstract: We study the amplification of information transfer in excitable systems. We show that excitable systems residing in a steady state near a bifurcation point to complex oscillatory behavior incorporate several frequencies that can be exploited for a resonant amplification of information transfer. In particular, for excitable neurons that reside in a steady state near a bifurcation point to elliptic bursting oscillations, we show that in addition to the resonant frequency of damped oscillations around the stable focus, another frequency exists that resonantly enhances large amplitude bursts and thus amplifies the information transfer in the system. This additional frequency cannot be found by the local stability analysis and has never been used for amplifying the information transfer in a system. The results obtained for elliptic bursting oscillations can be generalized also to other complex oscillators, such as parabolic or square-wave bursters. Additionally, the biological importance of presented results in the field of neuroscience is outlined.

Elsevier	*M. Perc and M. Marhl* Frequency dependent stochastic resonance in a model for intracellular Ca2+ oscillations can be explained by local divergence Physica A 332 (2004) 123-140	Abstract: The phenomenon of stochastic resonance has recently been found in many systems. Despite the pre-conception of a destructive role of noise, its constructive role has been recognised, in particular in amplification of weak external signals, thereby facilitating signal detection and transduction in complex systems. Although the stochastic resonance has been reported for many systems in various fields of physics, chemistry and biology, the understanding of this phenomenon is still limited. In the present paper, we explain the frequency dependent stochastic resonance with the local divergence. In a model for intracellular Ca2+ oscillations, we calculate the local divergence of noise-induced oscillations and show that areas of attractors with close to zero local divergence are crucial for understanding the stochastic resonance, since they represent the most flexible and susceptible states of the system, which are thus most likely to be altered by weak external stimuli and noise. With a detailed analysis of the temporal evolution of the local divergence, we are able to explain the constructive as well as the destructive role of noise, thereby shedding light on the typical bell-shaped dependency of the signal-to-noise ratio vs. the noise intensity. The applicability of our results to other systems and their biological implications are discussed.

Elsevier	*M. Perc and M. Marhl* Noise enhances robustness of intracellular Ca2+ oscillations Physics Letters A 316 (2003) 304-310	Abstract: We investigate responses of a model for intracellular Ca2+ oscillations to external pulsatile forcing in the presence of additive Gaussian noise. Our results show that noise makes the system less susceptible to external forcing and thus enhances robustness of Ca2+ oscillations. The results can be well explained by the local divergence of limit cycles in the phase space.