Entropic origin of Mg ²⁺ -facilitated RNA folding

Abstract

Mg 2þ is essential for the proper folding and function of RNA, though the effect of Mg 2þ 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 2þ ]. 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 2þ ]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg 2þ ] promotes tetraloop-receptor interaction by reducing the entropic barrier (−T ΔS ‡ dock ) and the overall entropic penalty (−T ΔS°d ock ) for docking, with essentially negligible effects on both the activation enthalpy (ΔH ‡ dock ) and overall exothermicity (ΔH°d ock ). These observations contrast with the conventional notion that increasing [Mg 2þ ] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH ‡ dock and ΔH°d ock with [Mg 2þ ]. Instead we propose that higher [Mg 2þ ] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.T he folding of RNA proceeds hierarchically, whereby secondary structure is formed rapidly and subsequent slow helical packing is mediated by tertiary interactions (1, 2). RNA secondary structure prediction from the known thermodynamics is quite reliable (3), though correspondingly accurate prediction of tertiary structure remains a major challenge (1). Static tertiary structure data alone are also not enough to predict RNA functionality, as time-dependent conformational dynamics occur during biochemical processes (4, 5). As a result, one needs the full free energy, enthalpy, and entropy landscapes for folding. A major road block in achieving a predictive understanding of RNA folding landscapes is that they are often "rugged,", i.e., with alternative conformations acting as kinetic traps (6, 7). Moreover, the electrostatic challenge of folding a charged biopolymer highlights the particularly critical role of Mg 2þ and other counterions in the folding process.Characterization of folding transition states-and the role of Mg 2þ in stabilizing transition states-remains a crucial bottleneck for reconciling the kinetics and thermodynamics of RNA folding (8-13). Some insight into the free energy landscapes for RNA folding can be obtained from temperature-dependent stopped-flow kinetic studies, which offer the ability to deconstruct free energy barriers (ΔG ‡ ) into enthalpic (ΔH ‡ ) and entropic (−TΔS ‡ ) components. However, with such methods, only the net rate constant (i.e., k total ¼ k fold þ k unfold ) for approach to equilibrium can be observed, which requires strong assumptions (e.g., that k fold ≫ k unfol...

Molecular-crowding effects on single-molecule RNA folding/unfolding thermodynamics and kinetics

“…3 A and B and 5A, the unfolded state is characterized by the largest effective radius [r unfold ∼ 27 (2) Å], which decreases substantially at the transition state [r tst ∼ 16 (1) Å], followed by an additional, but more modest decrease to the final folded state (r fold ∼ 12.5 Å). The kinetic data therefore confirm that the greater decrease in free volume for the tetraloop-receptor occurs between the unfolded and transition states, supporting previous claims that the transition state for RNA folding may be relatively compact for similar constructs (22,23).…”

“…where ΔG ‡ represents the free-energy barrier and ν is the attempt frequency along the reaction coordinate to surmount this barrier (22,23,28). By scaling the rate constants to the values at zero PEG 8000 concentrations, we can extract Δ[ln(k(T)/ν)] and therefore ΔΔG ‡ /RT for the tetraloop-receptor folding/unfolding directions as a function of excluded volume fraction φ.…”

The Role of Counterion Valence and Size in GAAA Tetraloop–Receptor Docking/Undocking Kinetics

“…This is consistent with prior expectation that the A 7 linker, which is slightly more rigid than U 7 due to base-stacking interactions, can weakly interfere with achieving the correct transition-state configuration. 65 …”

“…1a) with a U 7 alternative has essentially no effect on K M , K′ M , or n (Table 1). 65 This suggests that cation uptake is intrinsic to the tetraloop-receptor docking interaction, rather than the specific linker in the construct design. By way of contrast, however, the docking rate constants (i.e., k 1 and k 2 ) are nearly 2-fold faster for the U 7 linker construct.…”

“…In contrast, single-molecule FRET studies of this construct have permitted the underlying kinetics to be studied, which reveal that both undocking and docking rate constants are affected by [Mg 2 + ]. 64 Moreover, recent calorimetric and single-molecule studies have elucidated fundamental differences in the underlying thermodynamics of the tetraloop-receptor interaction in monovalent versus divalent cationic environments, [65][66][67] highlighting the need to further understand the role of cation identity in RNA-ion interactions.…”