A fluctuating environment as a source of periodic modulation

We study the intermittent fluorescence of a single molecule, jumping from the ''light on'' to the ''light off'' state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic environmental fluctuations make the distribution of the times of sojourn in the ''light off'' state depart from the exponential form, and that their succession in time mirrors environmental dynamics. As an illustration, we discuss some recent experimental results, where the environmental fluctuations depend on enzymatic activity.