FIGURE 8.

Effect of kinetic parameters on the optimal transient signal. Optimal duty ratio γ_tr of a transient Ca²⁺ signal as a function of the dephosphorylation rate constant β_X of the target protein. The ratio α_X/β_X is kept constant. If the target protein is rapidly inactivated (β_X ≫ 1), the optimal Ca²⁺ signal is characterized by a high duty ratio. The optimal duty ratio will also increase by increasing the total duration of the Ca²⁺ spikes (upper line). The solid lines are calculated with the analytical approximation (Eq. 24); the solid squares are obtained after numerically solving the full system (Eqs. 2 and 3). Parameters: n = 1, S₀ = 2 μM, Δ = 0.2 and 0.4 min (lower and upper line, respectively), m = 5 spikes; α_X/β_X/μM, α_Y = 1/(μM min), β_Y = 1/min, Y_T = 1 μM.