Entropic origin of Mg2+-facilitated RNA folding

Abstract

Mg(2+) is essential for the proper folding and function of RNA, though the effect of Mg(2+) concentration on the free energy, enthalpy, and entropy landscapes of RNA folding is unknown. This work exploits temperature-controlled single-molecule FRET methods to address the thermodynamics of RNA folding pathways by probing the intramolecular docking/undocking kinetics of the ubiquitous GAAA tetraloop-receptor tertiary interaction as a function of [Mg(2+)]. These measurements yield the barrier and standard state enthalpies, entropies, and free energies for an RNA tertiary transition, in particular, revealing the thermodynamic origin of [Mg(2+)]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg(2+)] promotes tetraloop-receptor interaction by reducing the entropic barrier (-TΔS(++)(dock)) and the overall entropic penalty (-TΔS(+) (dock)) for docking, with essentially negligible effects on both the activation enthalpy (ΔH(++)(dock)) and overall exothermicity (ΔH(+)(dock)). These observations contrast with the conventional notion that increasing [Mg(2+)] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH(++)(dock)) and ΔH(+)(dock)) with [Mg(2+)]. Instead we propose that higher [Mg(2+)] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.

Fig. 1.

Single-molecule observation of GAAA tetraloop and receptor docking/undocking via a U₇ linker. (A) TL-R construct, in which docking and undocking rate constants (k_dock and k_undock) are monitored by FRET between the donor (Cy3) and acceptor (Cy5). (B and C) Temperature-dependent E_FRET trajectories and probability histograms at 0 mM and 1 mM MgCl₂, respectively, with corresponding dwell time (τ) probability densities (D–E) from many molecules, which yield k_dock and k_undock from single exponential fits of the undocked (circles) and docked (triangles) dwell times, respectively.

Fig. 2.

[Mg²⁺]-dependence of TL-R RNA docking at 20 ± 1 °C: (A) k_dock, k_undock and (B) K_dock = k_dock/k_undock described by a four-state model allowing for [Mg²⁺]-dependent and independent docking pathways (U = undocked, D = docked) and Mg²⁺ binding is not resolved by FRET. From this model, k_dock = {k₁(K_d)ⁿ + k₂[Mg²⁺]ⁿ}/{(K_d)ⁿ + [Mg²⁺)} and . Fits of the k_dock and k_undock titrations with the detailed balance constraint that , yield n = 1.8 ± 0.2, k₁ = 12.6 ± 0.9 s^-1, k₂ = 156 ± 23 s^-1, k_-1 = 8.6 ± 0.7 s^-1, k_-2 = 5.4 ± 0.2 s^-1, K_d = 1.3 ± 0.3 mM, and .

Fig. 3.

Temperature dependence of equilibrium constant (K_dock) for TL-R docking as a function of [Mg²⁺] yields the standard state enthalpy () and entropy () of docking from Eq. 1 (Table 1, top, 100 mM NaCl).

Fig. 4.

Temperature dependence of k_dock and k_undock as function of [Mg²⁺]. Transition-state analysis yields the activation enthalpy (ΔH^‡) and entropy (ΔS^‡) for docking and undocking from Eq. 2 (Table 2, top, 100 mM NaCl).

Fig. 5.

Scheme for Mg²⁺-facilitated TL-R folding. (A) The entropic and enthalpic reaction coordinate for TL-R docking at 1 mM Mg²⁺, where U, ‡, and D indicate the undocked, transition, and docked states. (B) The proposed transition state is early and compact, i.e., the tertiary interaction (red lines in docked state) is largely unformed, whereas the tetraloop and receptor are in close proximity, requiring localization of counterions (e.g., Mg²⁺, blue circles).