Fig. 5

The deterministic QSSA can inform the validity of the stochastic QSSA with composite reduction. a The diagram of the full model (Eqs. 19) and the reduced model (Eqs. 20). b The three different types of reduced models (ER, DR and EDR) (Additional file 1: Figure S6) accurately approximate the deterministic simulations of full model with an initial condition, which will be used for stochastic simulation: M(0)=R(0)=E _R (0)=G(0)=G _R (0)=0. However, only ER model accurately approximates the full model if R(0)=100. c–e The stochastic simulation of only ER model is accurate for an initial condition with which all three types of reduced model are deterministically accurate (Fig. 5b). The colored ranges and histograms represent a standard deviation of R from its mean and the distribution of R at the steady state. The parameters of the model are adopted from [27]: α _M =50s ⁻¹, β _M =k _R =k ₄=1s ⁻¹, k ₋₁=k ₋₂=k ₋₃=10s ⁻¹, k ₁=10⁻⁵ s ⁻¹, k ₂=10² s ⁻¹, K _M =110, D _T =0.01