Diffusion can be included by renormalization of second-order rate constants.

(A) Histograms of monomer frequency for different B values from simulations with Smoldyn software [38] (first row) and Gillespie simulations of the generalized Schlögl model with (second row) and without (third row) renormalized rate constants of second-order reactions. Standard parameters were used with volume V = 10. The Kullback-Leiber divergence (D_KL) shows the closer correspondence of the renormalized reactions than the normal reactions with Smoldyn (forth row). For details on renormalization and calculation of D_KL, see Materials and Methods. (B) Corresponding macroscopic bifurcation diagram of deterministic ordinary-differential equation model using renormalized rate constants k_±2 to illustrate effect of diffusion. This shows that diffusion delays entry into bistable regime for increasing B.