Fig. 1.

(a) The general workflow of moment-based modelling in Julia using MomentClosure.jl and related packages. (b) Model of a negative auto-regulative genetic feedback loop. If a gene is active (G), an mRNA molecule (M) is produced with rate k_m which can be subsequently translated into proteins (P) with rate k_p (both degrade with rates d_m and d_p, respectively). The negative feedback is introduced via protein binding to the gene with rate σ_b, switching the promoter OFF ($G^{*}$) and preventing the transcription (in contrast, switching ON occurs with rate σ_u). (c) Fano factor of the steady-state protein number as a function of σ_b where we have truncated the moment hierarchy at the second order using normal, gamma and CDM MAs, and compared the results to the true values predicted by the stochastic simulation algorithm (Gillespie, 1977) (averaged over 10⁵ realizations). The initial condition is zero protein and mRNA molecules (set to 0.001 for MAs to ensure numerical stability) in state G, and the parameters are fixed as ${\sigma }_u=10,k_m=3,k_p=50,d_m=10$ and d_p = 1