Figure 7.

The autocorrelation function. The autocorrelation function determines the degree of correlation existing in any fluctuating signal (mean m and variance σ 2). The signal S(t) is multiplied for any time t_i with its value at t_i + τ, where τ is a delay time. The autocorrelation function at a given time delay is defined as the average of the overlap between the values of the signal taken at two time points at a fixed delay. This function is used to compare the fluctuating signal at two different times in order to quantify temporal correlations. The autocorrelation function describes the persistence of the signal (for example the promoter state). This persistence is characterized by the relaxation time of the autocorrelation function, which is the time at which the autocorrelation function of the signal decays by 1/e, and which represents the average time scale on which the signal has a similar value to its initial value.