The many paths to frameshifting: kinetic modelling and analysis of the effects of different elongation steps on programmed –1 ribosomal frameshifting

Liao, Pei-Yu; Choi, Yong Seok; Dinman, Jonathan D.; Lee, Kelvin H.

All pathways were mathematically described as systems of ordinary differential equations (Supplementary Data). Assuming steady state, the expressions of intermediate Figure 2 . The kinetic framework for programmed -1 ribosomal frameshifting. Top: the procedure from PA to E 0 P 0 represents translocation, which involves r 1 , r -1 (reversible EF-G binding), r TL0 (GTP hydrolysis, unlocking conformation change, tRNA movement and Pi release), and r 45 (re-locking conformation change and EF-G dissociation). The E 0 P 0 complex then undergoes aa-tRNA selection: from E 0 P 0 to P 0 A 0 . The selection of aa-tRNA involves: k 1 , k -1 (reversible EF-Tu binding), k 2 , k -2 (reversible codon recognition), k 345 (GTPase activation, GTP hydrolysis, EF-Tu conformation change and dissociation), and k 6 (aa-tRNA rejection by proofreading), or k 7 (aa-tRNA accommodation). The elongation cycle without a -1 PRF event results in synthesis of non-frameshift proteins (NFS). Pathway I in green suggests that -1 PRF occurs during the relocking step in the first translocation, leading to the formation of FS m . Pathway Ia indicates that the E 02 P 02 complex may interact with a zero frame aa-tRNA and eventually produce FS z . Pathways II suggests that -1 PRF occurs during aa-tRNA selection and accommodation, resulting in FS z . Pathway III suggests that -1 PRF occurs during the second translocation step, resulting in FS z production. concentrations in terms of initial reactant (PA) were solved by Matlab v.R2008a (Mathworks Inc., Natick, MA, USA). By applying the empirically-determined rate constants and assumed ranges of rate constants of incomplete translocation, P-and A-site tRNA slippage (Supplementary Tables S1-S4) , the amount of non-frameshift proteins NFS (p 0 a 0 pt in the kinetic model) and two types of frameshift proteins, FS m (P 02 A 2 pt in the kinetic model) and FS z (P 02 A 02 pt and p 02 a 02 pt in the kinetic model), were identified. The frameshift efficiency (FS%) in the model is defined as the amount of frameshift proteins divided by the amount of total proteins and multiplied by 100% [Equation (1)]. The fraction of FS m is calculated as the amount of FS m divided by the amount of total frameshift proteins and multiplied by 100% [Equation (2)].