Probing the mechanical folding kinetics of TAR RNA by hopping, force-jump, and force-ramp methods

Mechanical unfolding and refolding of single RNA molecules have previously been observed in optical traps as sudden changes in molecular extension. Two methods have been traditionally used: "force-ramp", with the applied force continuously changing, and "hopping". In hopping experiments the force is held constant and the molecule jumps spontaneously between two different states. Unfolding/refolding rates are measured directly, but only over a very narrow range of forces. We have now developed a force-jump method to measure the unfolding and refolding rates independently over a wider range of forces. In this method, the applied force is rapidly stepped to a new value and either the unfolding or refolding event is monitored through changes in the molecular extension. The force-jump technique is compared to the force-ramp and hopping methods by using a 52-nucleotide RNA hairpin with a three-nucleotide bulge, i.e., the transactivation response region RNA from the human immunodeficiency virus. We find the unfolding kinetics and Gibbs free energies obtained from all three methods to be in good agreement. The transactivation response region RNA hairpin unfolds in an all-or-none two-state reaction at any loading rate with the force-ramp method. The unfolding reaction is reversible at small loading rates, but shows hysteresis at higher loading rates. Although the RNA unfolds and refolds without detectable intermediates in constant-force conditions (hopping and force-jump), it shows partially folded intermediates in force-ramp experiments at higher unloading rates. Thus, we find that folding of RNA hairpins can be more complex than a simple single-step reaction, and that application of several methods can improve understanding of reaction mechanisms.     

Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.     

Kinetic Folding Mechanism of Erythropoietin

This report describes what to our knowledge is the first kinetic folding studies of erythropoietin, a glycosylated four-helical bundle cytokine responsible for the regulation of red blood cell production. Kinetic responses for folding and unfolding reactions initiated by manual mixing were monitored by far-ultraviolet circular dichroism and fluorescence spectroscopy, and folding reactions initiated by stopped-flow mixing were monitored by fluorescence. The urea concentration dependence of the observed kinetics were best described by a three-state model with a transiently populated intermediate species that is on-pathway and obligatory. This folding scheme was further supported by the excellent agreement between the free energy of unfolding and m-value calculated from the microscopic rate constants derived from this model and these parameters determined from separate equilibrium unfolding experiments. Compared to the kinetics of other members of the four-helical bundle cytokine family, erythropoietin folding and unfolding reactions were slower and less susceptible to aggregation. We tentatively attribute these slower rates and protection from association events to the large amount of carbohydrate attached to erythropoietin at four sites.     

40 Probing single molecule RNA folding using temperature and force

Nucleic acids can be unfolded either by temperature, such as in UV melting, or by mechanical force using optical tweezers. In UV melting experiments, the folding free energy of nucleic acids at mesophilic temperatures are extrapolated from unfolding occurring at elevated temperatures. Additionally, single molecule unfolding experiments are typically performed only at room temperature, preventing calculation of changes in enthalpy and entropy. Here, we present temperature-controlled optical tweezers suitable for studying folding of single RNA molecules at physiological temperatures. Constant temperatures between 22 and 37?°C are maintained with an accuracy of 0.1?°C, whereas the optical tweezers display a spatial resolution of ～1?nm over the temperature range. Using this instrument, we measured the folding thermodynamics and kinetics of a 20-base-pair RNA hairpin by force-ramp and constant force experiments. Between 22 and 37?°C, the hairpin unfolds and refolds in a single step. Increasing temperature decreases the stability of the hairpin and thus decreases the force required to unfold it. The equilibrium force, at which unfolding and refolding rates are equal, drops ～1?pN as temperature increases every 5?°C. At each temperature, the folding energy can be quantified by reversible work done to unfold the RNA and from the equilibrium constant at constant forces. Over the experimental temperature range, the folding free energy of the hairpin depends linearly on temperature, indicating that ΔH is constant. The measured folding thermodynamics are further compared with the nearest neighbor calculations using Turner’s parameters of nucleic acid folding energetics.     

Slow unfolding and refolding kinetics of the mesophilic Rop wild-type protein in the transition range.

We describe the guanidinium hydrochloride induced folding kinetics of the four-helix-bundle protein Rop wild-type (wt) under equilibrium conditions at three temperatures. The choice of appropriate denaturant conditions inside the transition range permitted, in combination with equilibrium transition curves, the determination of both unfolding and refolding rate constants. The ratio of the rate constants at zero denaturant concentration provided equilibrium constants and standard free energy changes that are in good agreement with values obtained in previous differential scanning calorimetry studies. The DeltaG0D values for 19, 25 and 40 degrees C calculated from the present kinetic studies are, respectively, 66.8, 70.8 and 57.2 kJ.mol-1. The unfolding reactions are extremely slow under these conditions. Equilibrium was reached only after 18, 12 and 6 days at 19, 25 and 40 degrees C. These results demonstrate that for Rop wt high stability correlates with slow folding kinetics.     

Mechanical unfolding of RNA: from hairpins to structures with internal multiloops

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force (f), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. For simple hairpins, such as P5GA, application of constant force or constant loading rate results in bistable cooperative transitions between folded and unfolded states without populating any intermediates. The transition state location (DeltaxFTS) changes dramatically as the loading rate is varied. At loading rates comparable to those used in laser optical tweezer experiments, the hairpin is plastic, with DeltaxFTS being midway between folded and unfolded states; whereas at high loading rates, DeltaxFTS moves close to the folded state, i.e., RNA is brittle. For the 29-nucleotide TAR RNA with the three-nucleotide bulge, unfolding occurs in a nearly two-state manner with an occasional pause in a high free energy metastable state. Forced unfolding of the 55 nucleotides of the Hepatitis IRES domain IIa, which has a distorted L-shaped structure, results in well-populated stable intermediates. The most stable force-stabilized intermediate represents straightening of the L-shaped structure. For these structures, the unfolding pathways can be predicted using the contact map of the native structures. Unfolding of a RNA motif with internal multiloop, namely, the 109-nucleotide prohead RNA that is part of the 29 DNA packaging motor, at constant value of rf occurs with three distinct rips that represent unraveling of the paired helices. The rips represent kinetic barriers to unfolding. Our work shows 1), the response of RNA to force is largely determined by the native structure; and 2), only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.     

Stability and cooperativity of individual tertiary contacts in RNA revealed through chemical denaturation

For proteins, understanding tertiary interactions involved in local versus global unfolding has become increasingly important for understanding the nature of the native state ensemble, the mechanisms of unfolding, and the stability of both the native and intermediate states in folding. In this work we have addressed related questions with respect to RNA structure by combining chemical denaturation and hydroxyl radical footprinting methods. We have determined unfolding isotherms for each of 26 discrete sites of protection located throughout the Tetrahymena thermophila group I ribozyme. The cooperativity of folding, m-value, and the free energy, DeltaG degrees N-U, associated with formation of each tertiary contact was determined by analysis of the isotherms. The DeltaG degrees N-U values measured in this study vary from 1.7 +/- 0.2 to 7. 6 +/- 1.2 kcal mol-1. Thus, the stability of these discrete tertiary contacts vary by almost 104. In addition, an intradomain contact and three interdomain contacts show high cooperativity (m-values of 1.1 +/- 0.2 to 1.7 +/- 0.3 kcal mol-1 M-1) indicating that these contacts exhibit global cooperatively in their folding behavior. This new approach to examining RNA stability provides an exciting comparison to our understanding of protein structure and folding mechanisms.     

Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA

RNA unfolding and folding reactions in physiological conditions can be facilitated by mechanical force one molecule at a time. By using force-measuring optical tweezers, we studied the mechanical unfolding and folding of a hairpin-type pseudoknot in human telomerase RNA in a near-physiological solution, and at room temperature. Discrete two-state folding transitions of the pseudoknot are seen at approximately 10 and approximately 5 piconewtons (pN), with ensemble rate constants of approximately 0.1 sec(-1), by stepwise force-drop experiments. Folding studies of the isolated 5'-hairpin construct suggested that the 5'-hairpin within the pseudoknot forms first, followed by formation of the 3'-stem. Stepwise formation of the pseudoknot structure at low forces are in contrast with the one-step unfolding at high forces of approximately 46 pN, at an average rate of approximately 0.05 sec(-1). In the constant-force folding trajectories at approximately 10 pN and approximately 5 pN, transient formation of nonnative structures were observed, which is direct experimental evidence that folding of both the hairpin and pseudoknot takes complex pathways. Possible nonnative structures and folding pathways are discussed.     

Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.     

Characterization of the mechanical unfolding of RNA pseudoknots

The pseudoknot is an important RNA structural element that provides an excellent model system for studying the contributions of tertiary interactions to RNA stability and to folding kinetics. RNA pseudoknots are also of interest because of their key role in the control of ribosomal frameshifting by viral RNAs. Their mechanical properties are directly relevant to their unfolding by ribosomes during translation. We have used optical tweezers to study the kinetics and thermodynamics of mechanical unfolding and refolding of single RNA molecules. Here we describe the unfolding of the frameshifting pseudoknot from infectious bronchitis virus (IBV), three constituent hairpins, and three mutants of the IBV pseudoknot. All four pseudoknots cause −1 programmed ribosomal frameshifting. We have measured the free energies and rates of mechanical unfolding and refolding of the four frameshifting pseudoknots. Our results show that the IBV pseudoknot requires a higher force than its corresponding hairpins to unfold. Furthermore, its rate of unfolding changes little with increasing force, in contrast with the rate of hairpin unfolding. The presence of Mg²⁺ significantly increases the kinetic barriers to unfolding the IBV pseudoknot, but has only a minor effect on the hairpin unfolding. The greater mechanical stability of pseudoknots compared to hairpins, and their kinetic insensitivity to force supports the hypothesis that −1 frameshifting depends on the difficulty of unfolding the mRNA.     

RNA folding and unfolding

Single-molecule studies of RNA folding and unfolding are providing impressive details of the intermediates that occur and their rates of interconversion. The folding and unfolding of RNA are controlled by varying the concentration of magnesium ions and measuring fluorescence energy transfer, or by applying force to the RNA and measuring the end-to-end distance. The hierarchical nature of RNA folding - first secondary structure, then tertiary structure - makes the process susceptible to analysis and prediction.     

Detection of a hidden folding intermediate of the third domain of PDZ

The folding pathway of the third domain of PDZ from the synaptic protein PSD-95 was characterized using kinetic and equilibrium methods by monitoring the fluorescence signal from a Trp residue that is incorporated at a near-surface position. Kinetic folding of this domain showed multiple exponential phases, whereas unfolding showed a single exponential phase. The slow kinetic phases were attributed to isomerization of proline residues, since there are five proline residues in this domain. We found that the logarithms of the rate constants for the fast phase of folding and unfolding are linearly dependent on the concentrations of denaturant. The unfolding free energy derived from these rate constants at zero denaturant was close to the value measured using the equilibrium method, suggesting the absence of detectable sub-millisecond folding intermediates. However, native-state hydrogen exchange experiments detected a partially unfolded intermediate under native conditions. It was further confirmed by a protein engineering study. These data suggest that a hidden intermediate exists after the rate-limiting step in the folding of the third domain of PDZ.     

(Un)Folding Mechanisms of the FBP28 WW Domain in Explicit Solvent Revealed by Multiple Rare Event Simulation Methods

We report a numerical study of the (un)folding routes of the truncated FBP28 WW domain at ambient conditions using a combination of four advanced rare event molecular simulation techniques. We explore the free energy landscape of the native state, the unfolded state, and possible intermediates, with replica exchange molecular dynamics. Subsequent application of bias-exchange metadynamics yields three tentative unfolding pathways at room temperature. Using these paths to initiate a transition path sampling simulation reveals the existence of two major folding routes, differing in the formation order of the two main hairpins, and in hydrophobic side-chain interactions. Having established that the hairpin strand separation distances can act as reasonable reaction coordinates, we employ metadynamics to compute the unfolding barriers and find that the barrier with the lowest free energy corresponds with the most likely pathway found by transition path sampling. The unfolding barrier at 300 K is ∼17 k_BT ≈ 42 kJ/mol, in agreement with the experimental unfolding rate constant. This work shows that combining several powerful simulation techniques provides a more complete understanding of the kinetic mechanism of protein folding.     

Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results

Experimental variables of optical tweezers instrumentation that affect RNA folding/unfolding kinetics were investigated. A model RNA hairpin, P5ab, was attached to two micron-sized beads through hybrid RNA/DNA handles; one bead was trapped by dual-beam lasers and the other was held by a micropipette. Several experimental variables were changed while measuring the unfolding/refolding kinetics, including handle lengths, trap stiffness, and modes of force applied to the molecule. In constant-force mode where the tension applied to the RNA was maintained through feedback control, the measured rate coefficients varied within 40% when the handle lengths were changed by 10-fold (1.1-10.2 Kbp); they increased by two- to threefold when the trap stiffness was lowered to one-third (from 0.1 to 0.035 pN/nm). In the passive mode, without feedback control and where the force applied to the RNA varied in response to the end-to-end distance change of the tether, the RNA hopped between a high-force folded-state and a low-force unfolded-state. In this mode, the rates increased up to twofold with longer handles or softer traps. Overall, the measured rates remained with the same order-of-magnitude over the wide range of conditions studied. In the companion article on pages 3010-3021, we analyze how the measured kinetics parameters differ from the intrinsic molecular rates of the RNA, and thus how to obtain the molecular rates.     

Kinetic coupling between protein folding and prolyl isomerization. I. Theoretical models.

Kinetic models were developed to describe the influence of prolyl peptide bond isomerization on the kinetics of reversible protein folding for cases in which structural intermediates do not occur. In the simulations, the number of prolyl residues and the relative rates of folding and isomerization were varied. The experimentally observed rate constants were found to be identical with the intrinsic rate constants of folding and isomerization only when folding remains much faster than prolyl isomerization throughout the transition region. When the rate of folding becomes similar to or lower than the rate of isomerization, the observed kinetic parameters are complex functions of all microscopic rate constants. In particular, the observed folding rates in the transition region decrease with the number of prolyl residues. Pseudo two-state kinetics with single folding and unfolding reactions are observed in several cases, although the apparent folding rates depend strongly on prolyl isomerization reactions in the unfolded chain. This virtual simplicity can easily lead to misinterpretation of kinetic data. Additional phases can be resolved when refolding is started from the fast-folding species (UF). The coupling between folding and prolyl peptide bond isomerization also modifies the dependence on denaturant concentration of the apparent rate constants of folding. We suggest several tests to detect and characterize the contributions of folding and isomerization steps to the observed folding kinetics.     

Hopping around an entropic barrier created by force

We use Langevin dynamics to investigate the role played by the recently discovered force-induced entropic energy barrier on the two-state hopping phenomena that has been observed in single RNA, DNA and protein molecules placed under a stretching force. Simple considerations about the free energy of a molecule readily show that the application of force introduces an entropic barrier separating the collapsed state of the molecule, from a force-driven extended conformation. A notable characteristic of the force induced barrier is its long distances to transition state, up to tens of nanometers, which renders the kinetics of crossing this barrier highly sensitive to an applied force. Langevin dynamics across such force induced barriers readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Such hopping is frequently interpreted as a manifestation of two-state folding/unfolding reactions observed in bulk experiments. However, given that such barriers do not exist at zero force these reactions do not take place at all in bulk.     

The kinetic pathway of folding of barnase

To search for folding intermediates, we have examined the folding and unfolding kinetics of wild-type barnase and four representative mutants under a wide range of conditions that span two-state and multi-state kinetics. The choice of mutants and conditions provided in-built controls for artifacts that might distort the interpretation of kinetics, such as the non-linearity of kinetic and equilibrium data with concentration of denaturant. We measured unfolding rate constants over a complete range of denaturant concentration by using by 1H/2H-exchange kinetics under conditions that favour folding, conventional stopped-flow methods at higher denaturant concentrations and continuous flow. Under conditions that favour multi-state kinetics, plots of the rate constants for unfolding against denaturant concentration fitted quantitatively to the equation for three-state kinetics, with a sigmoid component for a change of rate determining step, as did the refolding kinetics. The position of the transition state on the reaction pathway, as measured by solvent exposure (the Tanford beta value) also moved with denaturant concentration, fitting quantitatively to the same equations with a change of rate determining step. The sigmoid behaviour disappeared under conditions that favoured two-state kinetics. Those data combined with direct structural observations and simulation support a minimal reaction pathway for the folding of barnase that involves two detectable folding intermediates. The first intermediate, I(1), is the denatured state under physiological conditions, D(Phys), which has native-like topology, is lower in energy than the random-flight denatured state U and is suggested by molecular dynamics simulation of unfolding to be on-pathway. The second intermediate, I(2), is high energy, and is proven by the change in rate determining step in the unfolding kinetics to be on-pathway. The change in rate determining step in unfolding with structure or environment reflects the change in partitioning of this intermediate to products or starting materials.     

Molecular beacons as probes of RNA unfolding under native conditions

Hybridization of fluorescent molecular beacons provides real-time detection of RNA secondary structure with high specificity. We used molecular beacons to measure folding and unfolding rates of the Tetrahymena group I ribozyme under native conditions. A molecular beacon targeted against 15 nt in the 5′ strand of the P3 helix specifically hybridized with misfolded forms of the ribozyme, without invading the native tertiary structure. The beacon associated with the misfolded ribozyme 300 times more slowly than with an unstructured oligonucleotide containing the same target sequence, suggesting that the misfolded ribozyme core remains structured in the absence of Mg²⁺. The rate of beacon hybridization under native conditions revealed a linear relationship between the free energy of unfolding and Mg²⁺ concentration. A small fraction of the RNA population unfolded very rapidly, suggesting parallel unfolding in one step or through misfolded intermediates.