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.     

Exploring the complex folding kinetics of RNA hairpins: I. General folding kinetics analysis

Depending on the nucleotide sequence, the temperature, and other conditions, RNA hairpin-folding kinetics can be very complex. The complexity with a wide range of cooperative and noncooperative kinetic behaviors arises from the interplay between the formation of the loops, the disruption of the misfolded states, and the formation of the rate-limiting base stacks. With a rate constant model and a kinetic-cluster theory, we explore the broad landscape for RNA hairpin-folding kinetics. The model is validated through direct tests against several experimental measurements. The general kinetic folding mechanisms and the predicted great variety of folding kinetics are directly applicable and quantitatively testable in experiments. The results from this study suggest that 1), previous experimental findings based on the individual hairpins revealed only a small fraction of much broader and more complex RNA hairpin-folding landscapes; 2), even for structures as simple as hairpins, universal folding timescales and pathways do not exist; and 3), to treat the loop size as the sole factor to determine the hairpin-folding rate is an oversimplification.     

B-S transition in short oligonucleotides

Stretching experiments with long double-stranded DNA molecules in physiological ambient revealed a force-induced transition at a force of 65 pN. During this transition between B-DNA and highly overstretched S-DNA the DNA lengthens by a factor of 1.7 of its B-form contour length. Here, we report the occurrence of this so-called B-S transition in short duplexes consisting of 30 basepairs. We employed atomic-force-microscope-based single molecule force spectroscopy to explore the unbinding mechanism of two short duplexes containing 30 or 20 basepairs by pulling at the opposite 5' termini. For a 30-basepair-long DNA duplex the B-S transition is expected to cause a length increase of 6.3 nm and should therefore be detectable. Indeed 30% of the measured force-extension curves exhibit a region of constant force (plateau) at 65 pN, which corresponds to the B-S transition. The observed plateaus show a length between 3 and 7 nm. This plateau length distribution indicates that the dissociation of a 30-basepair duplex mainly occurs during the B-S transition. In contrast, the measured force-extension curves for a 20-basepair DNA duplex exhibited rupture forces below 65 pN and did not show any evidence of a B-S transition.     

Biphasic folding kinetics of RNA pseudoknots and telomerase RNA activity

Using a combined master equation and kinetic cluster approach, we investigate RNA pseudoknot folding and unfolding kinetics. The energetic parameters are computed from a recently developed Vfold model for RNA secondary structure and pseudoknot folding thermodynamics. The folding kinetics theory is based on the complete conformational ensemble, including all the native-like and non-native states. The predicted folding and unfolding pathways, activation barriers, Arrhenius plots, and rate-limiting steps lead to several findings. First, for the PK5 pseudoknot, a misfolded 5' hairpin emerges as a stable kinetic trap in the folding process, and the detrapping from this misfolded state is the rate-limiting step for the overall folding process. The calculated rate constant and activation barrier agree well with the experimental data. Second, as an application of the model, we investigate the kinetic folding pathways for human telomerase RNA (hTR) pseudoknot. The predicted folding and unfolding pathways not only support the proposed role of conformational switch between hairpin and pseudoknot in hTR activity, but also reveal molecular mechanism for the conformational switch. Furthermore, for an experimentally studied hTR mutation, whose hairpin intermediate is destabilized, the model predicts a long-lived transient hairpin structure, and the switch between the transient hairpin intermediate and the native pseudoknot may be responsible for the observed hTR activity. Such finding would help resolve the apparent contradiction between the observed hTR activity and the absence of a stable hairpin.     

Packaging contests between viral RNA molecules and kinetic selectivity

The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.     

Forced-unfolding and force-quench refolding of RNA hairpins

Nanomanipulation of individual RNA molecules, using laser optical tweezers, has made it possible to infer the major features of their energy landscape. Time-dependent mechanical unfolding trajectories, measured at a constant stretching force (f_S) of simple RNA structures (hairpins and three-helix junctions) sandwiched between RNA/DNA hybrid handles show that they unfold in a reversible all-or-none manner. To provide a molecular interpretation of the experiments we use a general coarse-grained off-lattice Gō-like model, in which each nucleotide is represented using three interaction sites. Using the coarse-grained model we have explored forced-unfolding of RNA hairpin as a function of f_S and the loading rate (r_f). The simulations and theoretical analysis have been done both with and without the handles that are explicitly modeled by semiflexible polymer chains. The mechanisms and timescales for denaturation by temperature jump and mechanical unfolding are vastly different. The directed perturbation of the native state by f_S results in a sequential unfolding of the hairpin starting from their ends, whereas thermal denaturation occurs stochastically. From the dependence of the unfolding rates on r_f and f_S we show that the position of the unfolding transition state is not a constant but moves dramatically as either r_f or f_S is changed. The transition-state movements are interpreted by adopting the Hammond postulate for forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to the two ends, show that the value of the unfolding force increases (especially at high pulling speeds) as the length of the handles increases. The pathways for refolding of RNA from stretched initial conformation, upon quenching f_S to the quench force f_Q, are highly heterogeneous. The refolding times, upon force-quench, are at least an order-of-magnitude greater than those obtained by temperature-quench. The long f_Q-dependent refolding times starting from fully stretched states are analyzed using a model that accounts for the microscopic steps in the rate-limiting step, which involves the trans to gauche transitions of the dihedral angles in the GAAA tetraloop. The simulations with explicit molecular model for the handles show that the dynamics of force-quench refolding is strongly dependent on the interplay of their contour length and persistence length and the RNA persistence length. Using the generality of our results, we also make a number of precise experimentally testable predictions.     

Mechanism of Mss116 ATPase reveals functional diversity of DEAD-Box proteins

Mss116 is a Saccharomyces cerevisiae mitochondrial DEAD-box RNA helicase protein that is essential for efficient in vivo splicing of all group I and group II introns and for activation of mRNA translation. Catalysis of intron splicing by Mss116 is coupled to its ATPase activity. Knowledge of the kinetic pathway(s) and biochemical intermediates populated during RNA-stimulated Mss116 ATPase is fundamental for defining how Mss116 ATP utilization is linked to in vivo function. We therefore measured the rate and equilibrium constants underlying Mss116 ATP utilization and nucleotide-linked RNA binding. RNA accelerates the Mss116 steady-state ATPase ∼ 7-fold by promoting rate-limiting ATP hydrolysis such that inorganic phosphate (P_i) release becomes (partially) rate-limiting. RNA binding displays strong thermodynamic coupling to the chemical states of the Mss116-bound nucleotide such that Mss116 with bound ADP-P_i binds RNA more strongly than Mss116 with bound ADP or in the absence of nucleotide. The predominant biochemical intermediate populated during in vivo steady-state cycling is the strong RNA-binding Mss116-ADP-P_i state. Strong RNA binding allows Mss116 to fulfill its biological role in the stabilization of group II intron folding intermediates. ATPase cycling allows for transient population of the weak RNA-binding ADP state of Mss116 and linked dissociation from RNA, which is required for the final stages of intron folding. In cases where Mss116 functions as a helicase, the data collectively favor a model in which ATP hydrolysis promotes a weak-to-strong RNA binding transition that disrupts stable RNA duplexes. The subsequent strong-to-weak RNA binding transition associated with P_i release dissociates Mss116-RNA complexes, regenerating free Mss116.     

Low spring constant regulates P-selectin-PSGL-1 bond rupture

Forced dissociation of selectin-ligand bonds is crucial to such biological processes as leukocyte recruitment, thrombosis formation, and tumor metastasis. Although the bond rupture has been well known at high loading rate r_f (≥10² pN/s), defined as the product of spring constant k and retract velocity v, how the low r_f (<10² pN/s) or the low k regulates the bond dissociation remains unclear. Here an optical trap assay was used to quantify the bond rupture at r_f ≤ 20 pN/s with low k (∼10⁻³-10⁻² pN/nm) when P-selectin and P-selectin glycoprotein ligand 1 (PSGL-1) were respectively coupled onto two glass microbeads. Our data indicated that the bond rupture force f retained the similar values when r_f increased up to 20 pN/s. It was also found that f varied with different combinations of k and v even at the same r_f. The most probable force, f*, was enhanced with the spring constant when k < 47.0 × 10⁻³ pN/nm, indicating that the bond dissociation at low r_f was spring constant dependent and that bond rupture force depended on both the loading rate and the mechanical compliance of force transducer. These results provide new insights into understanding the P-selectin glycoprotein ligand 1 bond dissociation at low r_f or k.     

Helix Capping in RNA Structure

Helices are an essential element in defining the three-dimensional architecture of structured RNAs. While internal basepairs in a canonical helix stack on both sides, the ends of the helix stack on only one side and are exposed to the loop side, thus susceptible to fraying unless they are protected. While coaxial stacking has long been known to stabilize helix ends by directly stacking two canonical helices coaxially, based on analysis of helix-loop junctions in RNA crystal structures, herein we describe helix capping, topological stacking of a helix end with a basepair or an unpaired nucleotide from the loop side, which in turn protects helix ends. Beyond the topological protection of helix ends against fraying, helix capping should confer greater stability onto the resulting composite helices. Our analysis also reveals that this general motif is associated with the formation of tertiary structure interactions. Greater knowledge about the dynamics at the helix-junctions in the secondary structure should enhance the prediction of RNA secondary structure with a richer set of energetic rules and help better understand the folding of a secondary structure into its three-dimensional structure. These together suggest that helix capping likely play a fundamental role in driving RNA folding.     

The Snakelike Chain Character of Unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.     

The Mechanical Properties of RNA-DNA Hybrid Duplex Stretched by Magnetic Tweezers

RNA can anneal to its DNA template to generate an RNA-DNA hybrid (RDH) duplex and a displaced DNA strand, termed R-loop. RDH duplex occupies up to 5% of the mammalian genome and plays important roles in many biological processes. The functions of RDH duplex are affected by its mechanical properties, including the elasticity and the conformation transitions. The mechanical properties of RDH duplex, however, are still unclear. In this work, we studied the mechanical properties of RDH duplex using magnetic tweezers in comparison with those of DNA and RNA duplexes with the same sequences. We report that the contour length of RDH duplex is ～0.30 nm/bp, and the stretching modulus of RDH duplex is ～660 pN, neither of which is sensitive to NaCl concentration. The persistence length of RDH duplex depends on NaCl concentration, decreasing from ～63 nm at 1 mM NaCl to ～49 nm at 500 mM NaCl. Under high tension of ～60 pN, the end-opened RDH duplex undergoes two distinct overstretching transitions; at high salt in which the basepairs are stable, it undergoes the nonhysteretic transition, leading to a basepaired elongated structure, whereas at low salt, it undergoes a hysteretic peeling transition, leading to the single-stranded DNA strand under force and the single-stranded RNA strand coils. The peeled RDH is difficult to reanneal back to the duplex conformation, which may be due to the secondary structures formed in the coiled single-stranded RNA strand. These results help us understand the full picture of the structures and mechanical properties of nucleic acid duplexes in solution and provide a baseline for studying the interaction of RDH with proteins at the single-molecule level.     

The Snakelike Chain Character of Unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.     

Connecting Thermal and Mechanical Protein (Un)folding Landscapes

Molecular dynamics simulations supplement single-molecule pulling experiments by providing the possibility of examining the full free energy landscape using many coordinates. Here, we use an all-atom structure-based model to study the force and temperature dependence of the unfolding of the protein filamin by applying force at both termini. The unfolding time-force relation τ(F) indicates that the force-induced unfolding behavior of filamin can be characterized into three regimes: barrier-limited low- and intermediate-force regimes, and a barrierless high-force regime. Slope changes of τ(F) separate the three regimes. We show that the behavior of τ(F) can be understood from a two-dimensional free energy landscape projected onto the extension X and the fraction of native contacts Q. In the low-force regime, the unfolding rate is roughly force-independent due to the small (even negative) separation in X between the native ensemble and transition state ensemble (TSE). In the intermediate-force regime, force sufficiently separates the TSE from the native ensemble such that τ(F) roughly follows an exponential relation. This regime is typically explored by pulling experiments. While X may fail to resolve the TSE due to overlap with the unfolded ensemble just below the folding temperature, the overlap is minimal at lower temperatures where experiments are likely to be conducted. The TSE becomes increasingly structured with force, whereas the average order of structural events during unfolding remains roughly unchanged. The high-force regime is characterized by barrierless unfolding, and the unfolding time approaches a limit of ∼10 μs for the highest forces we studied. Finally, a combination of X and Q is shown to be a good reaction coordinate for almost the entire force range.     

An early transition state for folding of the P4-P6 RNA domain

Tertiary folding of the 160-nt P4-P6 domain of the Tetrahymena group I intron RNA involves burying of substantial surface area, providing a model for the folding of other large RNA domains involved in catalysis. Stopped-flow fluorescence was used to monitor the Mg2+-induced tertiary folding of pyrene-labeled P4-P6. At 35 degrees C with [Mg2+] approximately 10 mM, P4-P6 folds on the tens of milliseconds timescale with k(obs) = 15-31 s(-1). From these values, an activation free energy deltaG(double dagger) of approximately 8-16 kcal/mol is calculated, where the large range for deltaG(double dagger) arises from uncertainty in the pre-exponential factor relating k(obs) and delta G(double dagger). The folding rates of six mutant P4-P6 RNAs were measured and found to be similar to that of the wild-type RNA, in spite of significant thermodynamic destabilization or stabilization. The ratios of the kinetic and thermodynamic free energy changes phi = delta deltaG(double dagger)/delta deltaG(o') are approximately 0, implying a folding transition state in which most of the native-state tertiary contacts are not yet formed (an early folding transition state). The k(obs) depends on the Mg2+ concentration, and the initial slope of k(obs) versus [Mg2+] suggests that only approximately 1 Mg2+ ion is bound in the rate-limiting folding step. This is consistent with an early folding transition state, because folded P4-P6 binds many Mg2+ ions. The observation of a substantial deltaG(double dagger) despite an early folding transition state suggests that a simple two-state folding diagram for Mg2+-induced P4-P6 folding is incomplete. Our kinetic data are some of the first to provide quantitative values for an activation barrier and location of a transition state for tertiary folding of an RNA domain.     

Dynamics of single DNA looping and cleavage by Sau3AI and effect of tension applied to the DNA

Looping and cleavage of single DNA molecules by the two-site restriction endonuclease Sau3AI were measured with optical tweezers. A DNA template containing many recognition sites was used, permitting loop sizes from approximately 10 to 10,000 basepairs. At high enzyme concentration, cleavage events were detected within 5 s and nearly all molecules were cleaved within 5 min. Activity decreased approximately 10-fold as the DNA tension was increased from 0.03 to 0.7 pN. Substituting Ca(2+) for Mg(2+) blocked cleavage, permitting measurement of stable loops. At low tension, the initial rates of cleavage and looping were similar (approximately 0.025 s(-1) at 0.1 pN), suggesting that looping is rate limiting. Short loops formed more rapidly than long loops. The optimum size decreased from approximately 250 to 45 basepairs and the average number of loops (in 1 min) from 4.2 to 0.75 as tension was increased from 0.03 to 0.7 pN. No looping was detected at 5 pN. These findings are in qualitative agreement with recent theoretical predictions considering only DNA mechanics, but we observed weaker suppression with tension and smaller loop sizes. Our results suggest that the span and elasticity of the protein complex, nesting of loops, and protein-induced DNA bending and wrapping play an important role.     

Understanding the Role of Three-Dimensional Topology in Determining the?Folding Intermediates of Group I Introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg²⁺-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (⋅OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ⋅OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.     

Interactions of cations with RNA loop-loop complexes

RNA loop-loop interactions are essential in many biological processes, including initiation of RNA folding into complex tertiary shapes, promotion of dimerization, and viral replication. In this article, we examine interactions of metal ions with five RNA loop-loop complexes of unique biological significance using explicit-solvent molecular-dynamics simulations. These simulations revealed the presence of solvent-accessible tunnels through the major groove of loop-loop interactions that attract and retain cations. Ion dynamics inside these loop-loop complexes were distinctly different from the dynamics of the counterion cloud surrounding RNA and depend on the number of basepairs between loops, purine sequence symmetry, and presence of unpaired nucleotides. The cationic uptake by kissing loops depends on the number of basepairs between loops. It is interesting that loop-loop complexes with similar functionality showed similarities in cation dynamics despite differences in sequence and loop size.     

High temperature unfolding simulations of the TRPZ1 peptide

We report high temperature molecular dynamics simulations of the unfolding of the TRPZ1 peptide using an explicit model for the solvent. The system has been simulated for a total of 6 μs with 100-ns minimal continuous stretches of trajectory. The populated states along the simulations are identified by monitoring multiple observables, probing both the structure and the flexibility of the conformations. Several unfolding and refolding transition pathways are sampled and analyzed. The unfolding process of the peptide occurs in two steps because of the accumulation of a metastable on-pathway intermediate state stabilized by two native backbone hydrogen bonds assisted by nonnative hydrophobic interactions between the tryptophan side chains. Analysis of the un/folding kinetics and classical commitment probability calculations on the conformations extracted from the transition pathways show that the rate-limiting step for unfolding is the disruption of the ordered native hydrophobic packing (Trp-zip motif) leading from the native to the intermediate state. But, the speed of the folding process is mainly determined by the transition from the completely unfolded state to the intermediate and specifically by the closure of the hairpin loop driven by formation of two native backbone hydrogen bonds and hydrophobic contacts between tryptophan residues. The temperature dependence of the unfolding time provides an estimate of the unfolding activation enthalpy that is in agreement with experiments. The unfolding time extrapolated to room temperature is in agreement with the experimental data as well, thus providing a further validation to the analysis reported here.     

Kinetic pathways of beta-hairpin (un)folding in explicit solvent

We examine the dynamical (un)folding pathways of the C-terminal beta-hairpin of protein G-B1 at room temperature in explicit solvent, by employing transition path sampling algorithms. The path ensembles contain information on the folding kinetics, including solvent motion. We determine the transition state ensembles for the two main transitions: 1), the hydrophobic collapse; and 2), the backbone hydrogen bond formation. In both cases the transition state ensembles are characterized by a layer (1) or a strip (2) of water molecules in between the two hairpin strands, supporting the hypothesis of the solvent as lubricant in the folding process. The transition state ensembles do not correspond with saddle points in the equilibrium free-energy landscapes. The kinetic pathways are thus not completely determined by the free-energy landscape. This phenomenon can occur if the order parameters obey different timescales. Using the transition interface sampling technique, we calculate the rate constants for (un)folding and find them in reasonable agreement with experiments, thus supporting the validation of using all-atom force fields to study protein folding.