Complexity of the dynamics. (A) The concentration-dependence of promoter activity for the same system as in figure 2 is described by the trajectories of eigenvalues -λ
on the complex plane, showing how the different periodic and aperiodic components of the dynamics are modified (eg. frequency, coherence). (B) They have a direct impact on the power spectrum of transcriptional activity S
(ω). (C) Energy consumption rate Ė also varies significantly with [A]. (D) As a given system is optimized for a coherent periodic activity (D1-3 are different stages of a given optimization), the trajectories of its eigenvalues tend to stereotype. In between a highly disordered system (D1) and a system close to an homogeneous irreversible cycle (D3), the promoter can demonstrate both a significant coherence and a complex concentration-dependence (D2). The comparison of these three systems in terms of in- and out-degrees of promoter states illustrate the structuring of the transition graph toward a unique path (in- and out-degrees of a given state are taken as the sum over the maximum of its in- and out-transitions respectively).