Stochastic resonance as an inherent property of rate-modulated random series of events

At the molecular level, processes in physics and biology are intrinsically random. Quite often they can be described as random series of elementary events, Poisson trains, whose event generation rate is a function of an input driving parameter. We analyze the transduction of weak signals by such trains in the presence of additive input noise in terms of transfer coefficient and output signal-to-noise ratio. We show that the noise-facilitated signal transduction, stochastic resonance (SR), is an inherent property of parameter-dependent Poisson trains with a nonlinear relationship between the event generation rate, r(V(t)), and the driving parameter, V(t). We obtain a sufficient condition for the SR onset that shows that for the input noise with a sufficiently broad bandwidth, SR can be observed in a wide variety of such systems. If this relationship is represented by r(V(t)) proportional to 1 + Sigma(1)(3) r(n)V(n)(t), then the system is capable of SR if 6r(3)/r(1) - r(2) > 0 Addition of small noise with a broad bandwidth to the system input increases the output signal quality. To highlight the mechanism of noise-facilitated signal transduction in such systems, we also analyze the "linearizing" effect of the additive noise on signal transduction in rate-modulated Poisson series. (C) 1998 Elsevier Science B.V.