Figure 2.

Simulation results for frequency modulation of the Goldbeter CDC model. Frequencies are normalized to the natural frequency (f_n) of the CDC oscillator, i.e., the frequency when no inhibitor is present (f_n = 0.0518 min⁻¹). The rate of inhibitor binding is quantified as the sum of the inhibitor rate constants, a₁ and a₂. The dissociation constant for the inhibitor is K_d = a₂/a₁ = 1.0. Parameter values for the Goldbeter model are: v_i = 0.1 min⁻¹, k₁ = 0.5 min⁻¹, k_d = 0.02 min⁻¹, K₁ = K₂ = 0.06, K₃ = K₄ = 0.1, K₅ = 0.02, K₆ = 0.3, V_1′ = 0.75 min⁻¹, V₂ = 0.25 min⁻¹, V_3′ = 0.3 min⁻¹, V₄ = 0.1 min⁻¹, d₁ = 0.05 min⁻¹, α = 0.1. (A) Effect of v_s, the rate of inhibitor synthesis, on CDC frequency for two inhibitor binding rates: (a₁ + a₂) = 1.4 min⁻¹ (curve a) and (a₁ + a₂) = 0.06 min⁻¹ (curve b). (B) Contour plot showing the effects of ^v_s and the inhibitor binding rate on the CDC frequency. Oscillations at the natural frequency (f_n) are marked by the thick black contour line. Above the f_n contour, the frequency of oscillations is reduced; below the contour, the frequency is increased.