(A) Steady-state value of X as a function of input cyclin, Xe, for different values of (n, k) as indicated on the plot, revealing different classes of behaviors: monostability, bistability, and irreversibility. The red line segments indicate possible stable states, whereas black line segments show unstable regions. The amplitude, A, of the bistability region is indicated. (B) Map of the different possible behaviors as a function of the parameters n, k. The dashed region indicates the subsection of the map where the experimental system is thought to function. (Please note that the n = 1 or k = 0 cases yield limit monostable behaviors.) (C) Left panel: simulation of the temporal response of X as a function of a transient pulse of Xe in the presence of positive feedback. Right panel: SBF transcription (assumed to be proportional to the first term in the right-hand side of Equation 2) as a function of Xe. Arrows indicate the direction of the trajectory. (D) Same as [C]), except that the positive feedback is removed (X = 0). (E) Stochastic simulation (following Gillespie's method [44]) of X activation in the absence of any input (Xe = 0) but after adding a basal transcription term l (0<l<1) to the right-hand term of Equation 2. The value of n used was 4.8, the values of other parameters are indicated. To control the amplitude of statistical fluctuations in protein number, the value of alpha was adjusted such that the maximum number of proteins is on average 20. Left, middle, and right panels show sample temporal traces for different values of l. Each trace represents a single cell.