Comparing ODE, TASEP and Petri net models. The relationship between the initiation rate and a) the translation rate; b) the codon density of the first codon; c) the codon density of the middle codon; and d) the codon density of the last codon, as obtained from the various models: TASEP with the random-sequential update rule (Algorithm 1), the Heinrich model , and the deterministic Petri net model . The parameters are set as β=γ
=0.5,i=r,…,n−1 (all parameters dimensionless). The waiting times in the Petri net model are determined by the mean of Γ, i.e., the inverse of the event rates, as discussed in . The codon density is the average occupancy of the codons by the ribosome on the mRNA at the steady state.