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

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