Fig. 2

Subordinated process. On the top graph, the amount of molecules for the complex MEK + ERK in function of the time t is shown. This curve represents the subordinated signal x(t). The trend of the signal, derived by time average, and the envelope, derived by Hilbert transform, are used to detect the critical events. In the bottom graph, the signal interim period (SIP) τ_i between two consecutive critical events are shown in function of the physical time t_i^* = i. The curve t(t_i^*), given by the sum of all the SIP τ up to the i^th event, is a realization of the directing process. In the same graph, the curve x(t_i^*), given by the sum of all the steps ∆x up to the i^th event, is a realization of the principal process. For convenience, in the bottom graph, the fluctuations around the trend are shown. In the curve x(t_i^*), regions with high number of events resemble a stretched form of the subordinated signal while regions with few events manifest shrunk portions of the subordinated signal