Table 1

Macro- and mesoscopic fluxes and their stationary distributions (Eq. A3)

	Standard	Michaelis–Menten elimination	Auto-catalysis	Standard modification	Zero-order modification	Gene expression
J₊[s]	k′_s	k′_s	k′_s + k[s]	k_s(C−[s])	k′_s	k′_sρ/(1−ρ)
J₋[s]	k_d[s]		k_d[s]	k_d[s]	k′_d	k_d[s]
J₊(n)	k_s	k_s	k_s + kn	k_s(N − n)	k_s	k_s (burst)
J₋(n)	k_dn		k_dn	k_dn	k_d	k_dn
Distribution	Poisson	NB	NB	Binomial	Trunc. Geo.	NB

Primed and unprimed constants are related as k_s = vk_s′ and the reaction volume v goes to infinity in the macroscopic limit but is time constant. Standard, autocatalysis, standard modification, and gene expression are linear and the rate equation for the average number of molecules take the same form as the macroscopic equation. For Michaelis–Menten elimination and zero-order modification the average behaves in a more complicated way.