FIGURE 6.

Absolute relative errors in the steady-state concentrations of P and Q associated with the quadratic autocatalator, given by Eq. 12, as a function of the input substrate concentration. (Solid lines) Second-order SCKEs with respect to the exact SCKEs; (dotted lines) CKEs with respect to the exact SCKEs; and (dashed lines) CKEs with respect to the second-order SCKEs. The steady-state values obtained by the exact and second-order SCKEs have been respectively computed by Monte Carlo simulation using the Gillespie algorithm and numerically, whereas the values obtained by the CKEs have been computed analytically from Eq. 44. The system is initialized with two molecules D (the number of DNA copies of a particular gene per eukaryotic cell), and zero molecules P and Q. Parameters used are c₁ = 0.002 s⁻¹, c₂ = 0.001 s⁻¹, c₃ = 0.005 s⁻¹, c₄ = 0.004 s⁻¹, c₆ = 0.05 s⁻¹, V = 2 pL, and K = 8000 cells. Moreover, c₅ = 0.002 s⁻¹ in panel A, and c₅ = 0.006 s⁻¹ in panel B.