Fig. 3.

Temporal and frequency characteristics of the cycle dynamics. (A) Sample time-evolution courses for the enzymatic cycle signal and response molecular counts, X_t and , obtained by using exact numerical simulation of the reaction mechanism given in Expressions 7 and 8. (Inset) Forward enzyme, E₊(t). (B) Spectral density, S(ω), of the process vs. frequency ω and 〈E₊〉 (arbitrary scale). Cycle reaction parameters (Expression 7) are: E₊(t = 0) = 20; X(t = 0) = 0; X^* (t = 0) = 2,000; C₊(t = 0) = 0; C_-(t = 0) = 0; E_-(t = 0) = 50; k₊₁ = 40; k₊₂ = 10⁴; k₊₃ = 10⁴; k_-1 = 200; k_-2 = 100; and k_-3 = 5·10³ given in terms of the number of molecules. Driver reaction (Expression 8) parameters: N(t = 0) = 10 with k₂₁ = 10, k_-21 = 5, k₂₂ = 10, and k_-22 = 0.2.