Free energy cost of stretching mRNA hairpin loops inhibits small RNA binding

Abstract

Small RNA-mRNA binding is an essential step in RNA interference, an important cellular regulatory process. Calculations of binding free energy have been used in binding site prediction, but the cost of stretching the mRNA loop when the small RNA-mRNA duplex forms requires further exploration. Here, using both polymer physics theory and simulations, we estimate the free energy of a stretched mRNA loop. We find loop stretching significantly increases the free energy of 3' supplementary/compensatory miRNA binding and siRNA binding to mRNA hairpin loops. We also make the observation that sites where 3' supplementary binding is available may bind at the seed only, and that loop stretching often favors seed-only binding over seed plus 3' supplementary binding in mRNA hairpins.

Figure 1

An example of siRNA binding. (a) Before binding, there are N₀ = 4 a-segments in the mRNA hairpin loop. K = −6 marks the binding position of the first nucleotide of the siRNA. To calculate loop free energy, the loop is modeled as a chain of three a-segments and one b-segment held at end-to-end separation z₀ = a. (b) After breaking 12 stem basepairs, the loop has just enough contour length to accommodate the binding helix, but is still highly stretched. (c) The minimum free energy is reached after another stem basepair is broken. There are N_bd = 21 a-segments involved in binding. N_bk = 13 basepairs (labeled 0 to $-12$) were broken in the mRNA hairpin stem. N_r = 9 a-segments remain in the hairpin loop, which is modeled as a chain of nine a-segments and one b-segment held at separation z_f = z(21) = 57.5 Å.

Figure 2

The theoretical and simulated free energies of a stretched mRNA chain with N = 4 or 8 and M = 1.

Figure 3

The free energy of small RNA binding in mRNA hairpin loops with initial hairpin sizes N₀ = 4 or 8. In (a) siRNA binding and (c) 3′ supplementary/compensatory miRNA binding, our theory offers an improvement over those of the previous model (13). (b) In seed-only miRNA binding, our theory and the previous model largely agree.

Figure 4

Binding free energies at 3′ supplementary sites in mRNA hairpins with initial hairpin sizes N₀ = 4 and 8. Our model (solid circles) takes the net free energy of seed-only and 3′ supplementary binding modalities, while the previous model (triangles) considers only 3′ supp binding. (Dotted line) Seed-only binding component of our theory. (Dashed line) 3′ supplementary binding.