Thermodynamic control of -1 programmed ribosomal frameshifting

Abstract

mRNA contexts containing a 'slippery' sequence and a downstream secondary structure element stall the progression of the ribosome along the mRNA and induce its movement into the -1 reading frame. In this study we build a thermodynamic model based on Bayesian statistics to explain how -1 programmed ribosome frameshifting can work. As training sets for the model, we measured frameshifting efficiencies on 64 dnaX mRNA sequence variants in vitro and also used 21 published in vivo efficiencies. With the obtained free-energy difference between mRNA-tRNA base pairs in the 0 and -1 frames, the frameshifting efficiency of a given sequence can be reproduced and predicted from the tRNA-mRNA base pairing in the two frames. Our results further explain how modifications in the tRNA anticodon modulate frameshifting and show how the ribosome tunes the strength of the base-pair interactions.

Fig. 1

Variants of the dnaX slippery sequence. a Mutations of the slippery sequence coding for Lys–Lys, Phe–Phe, Lys–Phe, and Phe–Lys. For each tRNA pair (upper row), the mRNA sequence (lower row) is shown for the 0-frame (left) and the −1-frame (right) together with mutations (light green) that do not change the codon identity in the 0-frame, but affect frameshifting. The resulting codon–anticodon interactions at the slippery site codons are highlighted by colors, with Watson–Crick interactions highlighted in light and dark cyan; G·S and A·S pairs, where S denotes the modified nucleotide mnm⁵s²U (Supplementary Fig. 4), in dark purple and brown, respectively; the U·G wobble pair in purple; and A·A and U·U mismatches in different shades of blue. b FS (gray bars) for the indicated slippery sequence variants. Error bars denote the standard deviation from at least three independent experiments (dots, N ≥ 3, Supplementary Table 1)

Fig. 2

Inferred mRNA–tRNA base-pair free-energy differences on the ribosome during frameshifting. a Probability densities (colored histograms) of the free-energy differences ΔG_bp for the P-site base pairs obtained from the model based on the full FS data set (64 FS values, blue), and a set of the FS values measured in vivo by Tsuchihashi et al. (21 FS values, green). b Probability densities for changing A-site base pairs. c Probability densities for changing P-site and A-site base pairs simultaneously. d FS from experiment compared to that calculated from the free-energy model. Each panel shows FS values for a tRNA pair (rmsd 2.5%). e For cross-validation of the model, iteratively, each FS value was predicted using free-energy differences obtained from all other FS values (rmsd 4.1%). For each mRNA sequence, one square is centered at the mean value and the width and height correspond to two times the standard deviation

Fig. 3

Kinetic contribution to the frameshifting efficiency. a FS as a function of the free-energy difference ΔG between 0-frame and −1-frame for different kinetic factors κ, where κ = 0% corresponds to frameshifting in equilibrium. b Probability density for the mean kinetic factor, obtained from a modified free-energy model that takes into account kinetic barrier crossing between 0-frame and −1-frame

Fig. 4

mRNA–tRNA base-pair free-energy differences obtained from published FS values measured in vivo. a–c Probability densities of the free-energy differences ΔG_bp upon changing base pairs in the P site, the A site, as well as in the P and A sites simultaneously, obtained from the free-energy model applied to the Tsuchihashi FS set. d FS values from the Tsuchihashi set compared to those calculated from the model (rmsd 2.6%). For each mRNA sequence, one square is centered at the mean value and the width and height correspond to two times the standard deviation

Fig. 5

Comparison of P-site and A-site base pairs. Free-energy differences for the A and the P sites shown as the mean (points) and standard deviations (error bars)

Fig. 6

Base pairs in solution and on the ribosome. a In the A site. Free energy of base pairs in solution, ΔG_sol, was estimated from MD simulations. For ΔG_bp values, the mean (circle) and standard deviation (bar) of the probability densities is shown (from Fig. 2a). Gray lines (at ΔG = 0) indicate whether a given base pair change is favorable or unfavorable. Blue line separates the regions where the interaction is more favorable on the ribosome (above the line) or in solution (below). b In the P site. c Upper row, base-pair conformations in the A site from X-ray structures^,. Lower row, the minimum free-energy conformation for the same base pairs in solution (adapted from Vendeix et al. )