Portrait of the regulatory structure dynamics and its transmission to RNA and protein levels. (A1) The power spectrum S
(ω) of the transcriptional efficiency process X(t) (red curve) is the sum of simple components (dashed curves). (A2) These fluctuations of transcriptional efficiency are transmitted to RNA and protein levels undergoing at each step (cf Eq. 6) the addition of a shot noise due to finite synthesis/degradation events (horizontal gray dashed lines: noise levels) and a low pass filtering due to time averaging (vertical gray dashed lines: cutoff frequencies). Dashed red and green curves are intermediate spectra 2γ⟨R⟩+S
(ω) and illustrating the effect of the shot noise. (B) Each eigenvalue λ
of matrix -M (or pair of conjugates) corresponds to an elementary component (or mode) in (A1) and determines its characteristics (eg. frequency and thinness of the peak). For instance, the arrows correspond to a 40 min oscillation period and a 10 s relaxation time. Colored crosses identify the components displayed in (A1). Many observables on the promoter can be described by the spectrum of -M (cf text), making it an accurate representation of the whole regulatory structure dynamics.