Conformational Shannon Entropy of mRNA Structures from Force Spectroscopy Measurements Predicts the Efficiency of $\ensuremath{-}1$ Programmed Ribosomal Frameshift Stimulation

Conformational Shannon Entropy of mRNA Structures from Force Spectroscopy Measurements Predicts the Efficiency of $- 1$ Programmed Ribosomal Frameshift Stimulation

Matthew T. J. Halma, Dustin B. Ritchie, and Michael T. Woodside

Phys. Rev. Lett. 126, 038102 – Published 21 January 2021

Abstract

$- 1$ programmed ribosomal frameshifting ( $- 1 PRF$ ) is stimulated by structures in messenger RNA (mRNA), but the factors determining $- 1 PRF$ efficiency are unclear. We show that $- 1 PRF$ efficiency varies directly with the conformational heterogeneity of the stimulatory structure, quantified as the Shannon entropy of the state occupancy, for a panel of stimulatory structures with efficiencies from 2% to 80%. The correlation is force dependent and vanishes at forces above those applied by the ribosome. These results support the hypothesis that heterogeneous conformational dynamics are a key factor in stimulating $- 1 PRF$ .

Received 17 May 2020
Accepted 15 December 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.038102

Physics Subject Headings (PhySH)

Gene expression RNA folding

RNA

Optical tweezers

Physics of Living Systems

Authors & Affiliations

Matthew T. J. Halma , Dustin B. Ritchie, and Michael T. Woodside

Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada

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Vol. 126, Iss. 3 — 22 January 2021

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Figure 1
$- 1 PRF$ and conformational Shannon entropy. (a) $- 1 PRF$ is stimulated by a structure in the mRNA (here, a pseudoknot) just downstream of a slippery sequence, leading to a shift in the ribosome reading frame. (b) The Shannon entropy of the stimulatory structure as a function of force on the mRNA is illustrated notionally for a simple case where a pseudoknot unfolds via an intermediate (left) and a more complex case where multiple structures can be formed (right).
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Figure 2
Force spectroscopy measurements of frameshift-stimulatory structures. (a) Sample force-extension curves of the stimulatory structures from PLRV (left) and WNV (right). For PLRV, three different states are seen (as numbered), whereas for WNV, eight different states are seen. Sets of curves containing different states are offset for clarity. The states seen in stimulatory structures from different viruses are generally unrelated. Inset: schematic of measurement showing RNA connected by double-stranded handles to beads held in optical traps. (b) Fractional occupancy of each state as a function of force (bottom) and force-dependent conformational Shannon entropy (top) for PLRV (left) and WNV (right).
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Figure 3
Correlation between Shannon entropy and $- 1 PRF$ efficiency for wild-type stimulatory structures. (a)–(c) Shannon entropy and $- 1 PRF$ efficiency vary linearly at low force [(a) 0, (b) 13 pN], but are poorly correlated at high force [(c) 30 pN] for the whole panel of wild-type stimulatory structures. (d) The Pearson correlation coefficient is strongly force dependent, with the correlation vanishing above $\sim 20 pN$ , which is higher than the maximum force applied by the ribosome during translation ( $\sim 13 pN$ ). Dashed lines show critical $r^{2}$ value (cyan, 99% confidence level; orange, 95% confidence level); shaded region shows standard error in $r^{2}$ .
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Figure 4
Correlation for mutant pseudoknots. (a) Shannon entropy and $- 1 PRF$ efficiency vary linearly at 13 pN for mutants of the human telomerase pseudoknot. (b) The Pearson correlation again vanishes above the maximum biologically relevant force. Dashed lines show critical $r^{2}$ values at 99% (cyan) and 95% (orange) confidence levels; shaded region shows standard error in $r^{2}$ .
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Figure 5
Correlation for pseudoknot bound with antiframeshifting ligand. (a) Shannon entropy at 13 pN varies linearly with the fraction of SARS-CoV pseudoknot bound by a $- 1 PRF$ -inhibiting ligand. (b) The Pearson correlation vanishes above the maximum biologically relevant force. Dashed lines show critical $r^{2}$ values at 99% (cyan) and 95% (orange) confidence levels; shaded region shows standard error in $r^{2}$ .
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Physical Review Letters

Conformational Shannon Entropy of mRNA Structures from Force Spectroscopy Measurements Predicts the Efficiency of −1 Programmed Ribosomal Frameshift Stimulation

Matthew T. J. Halma, Dustin B. Ritchie, and Michael T. Woodside

Phys. Rev. Lett. 126, 038102 – Published 21 January 2021

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Conformational Shannon Entropy of mRNA Structures from Force Spectroscopy Measurements Predicts the Efficiency of $- 1$ Programmed Ribosomal Frameshift Stimulation