RNA folding: conformational statistics, folding kinetics, and ion electrostatics

Abstract

RNA folding is a remarkably complex problem that involves ion-mediated electrostatic interaction, conformational entropy, base pairing and stacking, and noncanonical interactions. During the past decade, results from a variety of experimental and theoretical studies pointed to (a) the potential ion correlation effect in Mg2+-RNA interactions, (b) the rugged energy landscapes and multistate RNA folding kinetics even for small RNA systems such as hairpins and pseudoknots, (c) the intraloop interactions and sequence-dependent loop free energy, and (d) the strong nonadditivity of chain entropy in RNA pseudoknot and other tertiary folds. Several related issues, which have not been thoroughly resolved, require combined approaches with thermodynamic and kinetic experiments, statistical mechanical modeling, and all-atom computer simulations.

Figure 1

(a) Graphical representation for an RNA structure, where vertices (i.e., nucleotide monomers) are connected by straight lines (i.e., backbone covalent bonds) and base pairs are denoted by curved links. (b) Graphical representation for a pseudoknot. (c) The virtual bonds (shown as the red and blue lines) for RNA backbone. (d) The three-dimensional structure and (e) base-pairing structure for a typical pseudoknot (gene 32 mRNA pseudoknot of bacteriophage T2; PDB ID: 2TPK). Loop 1 (L ₁) and loop 2 (L₂) span across the major (narrow, deep) groove of helix 2 (S ₂) and the minor (wide, shallow) groove of helix 1 (S₁), respectively. The structure in (d) is adopted from the PDB (PDB ID: 2TPK) (39).

Figure 2

Predicting pseudoknot stability using the loop entropy parameters in Table 1 (14). For loop 1, length of stem 2 is 7 bp, length of loop 1 is 1 nt, so the entropy is read from Table 1 as ΔS₁(7, 1). Similarly, for loop 2, stem 1 is 5 bp, loop 2 is 4 nt, so the loop entropy is ΔS₂(5, 4). The total free energy of the pseudoknot is ΔG = ΔG₁ + ΔG₂ − T ΔS₁(7, 1) − T ΔS₂(5, 4) + ΔG_assemble = (−6.6) kcal/mol + (−11.2) kcal/mol + (k_B T)(2.3) + (k_B T)(9.8) + 1.3 kcal/mol = −9.0 kcal/mol, where ΔG_assemble = 1.3 kcal/mol accounts for the multiple ways to connect the two loops (14) and k_BT = 0.62 kcal/mol at T = 37°C. See Reference for more examples.

Figure 3

Temperature dependence of the reaction rate k (111). (a) T > T_f > T_g: The relaxation process is predominantly unfolding, with single exponential kinetics along an unzipping pathway. The apparent activation barrier [= − d ln(k)/d (1/T)] is positive, equal to the enthalpic cost of breaking the rate-limiting base stack(s). (b) T_g > T > T_f: The relaxation process is predominantly folding, with single exponential kinetics along a zipping pathway. The activation barrier is negative, equal to the stabilizing enthalpy of the rate-limiting base stack(s). (c) T < T_g: The relaxation process is predominantly folding, with multistate multiple exponential kinetics involving multiple pathways, including the zipping pathway and detrapping-refolding pathways. The activation barrier is positive, equal to the average enthalpic cost to detrap the misfolded states.

Figure 4

Two types of cations surrounding the P4-P6 RNA structure (17): specific binding and diffusive binding. A recent Mg²⁺ ion titration study suggested that two metal ions induce cooperative folding of the P4-P6 metal ion core (25).