RNA Folding Kinetics Research Articles

3’ Terminal end‐labeling of structured RNA by Klenow DNA polymerase

RNA labeling is a key step in studying RNA localization, folding, and structural dynamics using fluorescence based assays. Current methods of fluorophore attachment to long (>100 nucleotides) and structured RNAs are hampered by low labeling yields and limitations in attachment position. These challenges have led to an interest in developing alternative methods that would enable the site‐specific labeling of long and structured RNAs. To this end, we have developed a site‐specific, chemo‐enzymatic method of fluorophore incorporation to RNAs. This novel method uses Klenow enzyme, a DNA polymerase, to add modified nucleotides to RNAs 3’ end in a templated manner. To facilitate this modified nucleotide addition in structured RNAs, we designed helper DNA oligonucleotides to disrupt any pre‐existing RNA intramolecular structure. Using this method, we have achieved efficient 3’ terminal end‐labeling of chemically synthesized and in‐vitro transcribed RNAs of different lengths with cyanine dyes.This method will be routinely used in fluorescence‐based assays that investigate the structure‐function relationships of RNAs involved in cancer and HIV progression.

Single-Molecule FRET Assay for Studying Cotranscriptional RNA Folding.

Cotranscriptional RNA folding plays important roles in gene regulation steps such as splicing, transcription termination, and translation initiation. Progression of our understanding of cotranscriptional RNA folding mechanisms is still retarded by the lacking of experimental tools to study the kinetics of cotranscriptional RNA folding properly. In this chapter, we describe fluorescence resonance energy transfer (FRET) assay that enables the study of RNA cotranscriptional folding at the single-molecule level.

Base-pair ambiguity and the kinetics of RNA folding

BackgroundA folding RNA molecule encounters multiple opportunities to form non-native yet energetically favorable pairings of nucleotide sequences. Given this forbidding free-energy landscape, mechanisms have evolved that contribute to a directed and efficient folding process, including catalytic proteins and error-detecting chaperones. Among structural RNA molecules we make a distinction between “bound” molecules, which are active as part of ribonucleoprotein (RNP) complexes, and “unbound,” with physiological functions performed without necessarily being bound in RNP complexes. We hypothesized that unbound molecules, lacking the partnering structure of a protein, would be more vulnerable than bound molecules to kinetic traps that compete with native stem structures. We defined an “ambiguity index”—a normalized function of the primary and secondary structure of an individual molecule that measures the number of kinetic traps available to nucleotide sequences that are paired in the native structure, presuming that unbound molecules would have lower indexes. The ambiguity index depends on the purported secondary structure, and was computed under both the comparative (“gold standard”) and an equilibrium-based prediction which approximates the minimum free energy (MFE) structure. Arguing that kinetically accessible metastable structures might be more biologically relevant than thermodynamic equilibrium structures, we also hypothesized that MFE-derived ambiguities would be less effective in separating bound and unbound molecules.ResultsWe have introduced an intuitive and easily computed function of primary and secondary structures that measures the availability of complementary sequences that could disrupt the formation of native stems on a given molecule—an ambiguity index. Using comparative secondary structures, the ambiguity index is systematically smaller among unbound than bound molecules, as expected. Furthermore, the effect is lost when the presumably more accurate comparative structure is replaced instead by the MFE structure.ConclusionsA statistical analysis of the relationship between the primary and secondary structures of non-coding RNA molecules suggests that stem-disrupting kinetic traps are substantially less prevalent in molecules not participating in RNP complexes. In that this distinction is apparent under the comparative but not the MFE secondary structure, the results highlight a possible deficiency in structure predictions when based upon assumptions of thermodynamic equilibrium.

Ant colony optimization for predicting RNA folding pathways

RNA folding dynamics plays important roles in various functions of RNAs. To date, coarse-grained modeling has been successfully employed to simulate RNA folding dynamics on the energy landscape composed of secondary structures. In such a modeling, the energy barrier height between metastable structures is a key parameter that crucially affects the simulation results. Although a number of approaches ranging from the exact method to heuristic ones are available to predict the barrier heights, developing an efficient heuristic for this purpose is still an algorithmic challenge.We developed a novel RNA folding pathway prediction method, ACOfoldpath, based on Ant Colony Optimization (ACO). ACO is a widely used powerful combinatorial optimization algorithm inspired from the food-seeking behavior of ants. In ACOfoldpath, to accelerate the folding pathway prediction, we reduce the search space by utilizing originally devised structure generation rules. To evaluate the performance of the proposed method, we benchmarked ACOfoldpath on the known nineteen conformational RNA switches. As a result, ACOfoldpath successfully predicted folding pathways better than or comparable to the previous heuristics. The results of RNA folding dynamics simulations and pseudoknotted pathway predictions are also presented.

Practical synthesis of N-(di-n-butylamino)methylene-protected 2-aminopurine riboside phosphoramidite for RNA solid-phase synthesis

2-Aminopurine (Ap) is a fluorescent nucleobase analog that is frequently used as structure-sensitive reporter to study the chemical and biophysical properties of nucleic acids. In particular, thermodynamics and kinetics of RNA folding and RNA–ligand binding, as well as RNA catalytic activity are addressable by pursuing the Ap fluorescence signal in response to external stimuli. Site-specific incorporation of Ap into RNA is usually achieved by RNA solid-phase synthesis and requires appropriately functionalized Ap riboside building blocks. Here, we introduce a robust synthetic path toward a 2-aminopurine riboside phosphoramidite whose N2 functionality is masked with the N-(di-n-butylamino)methylene group. This protection is considered advantageous over previously described N-(dimethylamino)methylene or acyl protection patterns needed for the fine-tuned deprotection conditions to achieve large synthetic RNAs.Graphic abstract

Conformation and mechanical property of rpoS mRNA inhibitory stem studied by optical tweezers and X-ray scattering.

3′ downstream inhibitory stem plays a crucial role in locking rpoS mRNA 5' untranslated region in a self-inhibitory state. Here, we used optical tweezers to study the unfolding/refolding of rpoS inhibitory stem in the absence and presence of Mg2+. We found adding Mg2+ decreased the free energy of the RNA junction without re-arranging its secondary structure, through confirming that this RNA formed a canonical RNA three-way junction. We suspected increased free energy might change the relative orientation of different stems of rpoS and confirmed this by small angle X-ray scattering. Such changed conformation may improve Hfq-bridged annealing between sRNA and rpoS RNA inhibitory stem. We established a convenient route to analyze the changes of RNA conformation and folding dynamics by combining optical tweezers with X-ray scattering methods. This route can be easily applied in the studies of other RNA structure and ligand-RNA.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding.

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k c ln c + const, where the coefficient k c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln c at all c with k c = 2 kB T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

Conformational switch in the ribosomal protein S1 guides unfolding of structured RNAs for translation initiation.

Initiation of bacterial translation requires that the ribosome-binding site in mRNAs adopts single-stranded conformations. In Gram-negative bacteria the ribosomal protein S1 (rS1) is a key player in resolving of structured elements in mRNAs. However, the exact mechanism of how rS1 unfolds persistent secondary structures in the translation initiation region (TIR) is still unknown. Here, we show by NMR spectroscopy that Vibrio vulnificus rS1 displays a unique architecture of its mRNA-binding domains, where domains D3 and D4 provide the mRNA-binding platform and cover the nucleotide binding length of the full-length rS1. D5 significantly increases rS1’s chaperone activity, although it displays structural heterogeneity both in isolation and in presence of the other domains, albeit to varying degrees. The heterogeneity is induced by the switch between the two equilibrium conformations and is triggered by an order-to-order transition of two mutually exclusive secondary structures (β-strand-to-α-helix) of the ‘AERERI’ sequence. The conformational switching is exploited for melting of structured 5′-UTR’s, as the conformational heterogeneity of D5 can compensate the entropic penalty of complex formation. Our data thus provides a detailed understanding of the intricate coupling of protein and RNA folding dynamics enabling translation initiation of structured mRNAs.

Life times of metastable states guide regulatory signaling in transcriptional riboswitches

Transcriptional riboswitches modulate downstream gene expression by a tight coupling of ligand-dependent RNA folding kinetics with the rate of transcription. RNA folding pathways leading to functional ON and OFF regulation involve the formation of metastable states within well-defined sequence intervals during transcription. The kinetic requirements for the formation and preservation of these metastable states in the context of transcription remain unresolved. Here, we reversibly trap the previously defined regulatory relevant metastable intermediate of the Mesoplasma florum 2′-deoxyguanosine (2′dG)-sensing riboswitch using a photocaging-ligation approach, and monitor folding to its native state by real-time NMR in both presence and absence of ligand. We further determine transcription rates for two different bacterial RNA polymerases. Our results reveal that the riboswitch functions only at transcription rates typical for bacterial polymerases (10–50 nt s−1) and that gene expression is modulated by 40–50% only, while subtle differences in folding rates guide population ratios within the structural ensemble to a specific regulatory outcome.

Generating Two-Dimensional Repertoire of siRNA Linc-ROR and siRNA mRNA ARF6 from the lincRNA-RoR/miR-145/ARF6 expression Pathway that involved in the progression of Triple Negative Breast Cancer

The research for finding the cure for breast cancer is currently entering the interesting phase of the transcriptomics based method. With the application of Next Generation Sequencing (NGS), molecular information on breast cancer could be gathered. Thus, both in silico and wet lab research has determined that the role of lincRNA-RoR/miR-145/ARF6 expression Pathway could not be ignored as one of the cardinal starting points for Triple-Negative Breast Cancer (TNBC). As the most hazardous type of breast cancer, TNBC should be treated with the most advanced approach that available in the scientific community. Bioinformatics approach has found the possible siRNA-based drug candidates for TNBC. It was found that siRNA that interfere with lincRNA-ROR and mRNA ARF6 could be a feasible opportunity as the drug candidate for TNBC. However, this claim should be validated with more thorough thermodynamics and kinetics computational approach as the comprehensive way to comprehend their molecular repertoire. In this respect, the claim was validated using various tools such as the RNAfold server to determine the 2D structure, Barriers server to comprehend the RNA folding kinetics, RNAeval server to validate the siRNA-target interaction. It was found that the thermodynamics and kinetics repertoire of the siRNA are indeed rational and feasible. In this end, our computation approach has proven that our designed siRNA could interact with lincRNA-RoR/miR-145/ARF6 expression Pathway.

Tractable RNA\u2013ligand interaction kinetics

BackgroundThe binding of small ligands to RNA elements can cause substantial changes in the RNA structure. This constitutes an important, fast-acting mechanism of ligand-controlled transcriptional and translational gene regulation implemented by a wide variety of riboswitches. The associated refolding processes often cannot be explained by thermodynamic effects alone. Instead, they are governed by the kinetics of RNA folding. While the computational analysis of RNA folding can make use of well-established models of the thermodynamics of RNA structures formation, RNA–RNA interaction, and RNA–ligand interaction, kinetic effects pose fundamentally more challenging problems due to the enormous size of the conformation space. The analysis of the combined process of ligand binding and structure formation even for small RNAs is plagued by intractably large state spaces. Moreover, the interaction is concentration-dependent and thus is intrinsically non-linear. This precludes the direct transfer of the strategies previously used for the analysis of RNA folding kinetics.ResultsIn our novel, computationally tractable approach to RNA–ligand kinetics, we overcome the two main difficulties by applying a gradient-based coarse graining to RNA–ligand systems and solving the process in a pseudo-first order approximation. The latter is well-justified for the most common case of ligand excess in RNA–ligand systems. We present the approach rigorously and discuss the parametrization of the model based on empirical data. The method supports the kinetic study of RNA–ligand systems, in particular at different ligand concentrations. As an example, we apply our approach to analyze the concentration dependence of the ligand response of the rationally designed, artificial theophylline riboswitch RS3.ConclusionThis work demonstrates the tractability of the computational analysis of RNA–ligand interaction. Naturally, the model will profit as more accurate measurements of folding and binding parameters become available. Due to this work, computational analysis is available to support tasks like the design of riboswitches; our analysis of RS3 suggests strong co-transcriptional effects for this riboswitch.The method used in this study is available online, cf. Section “Availability of data and materials”.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔGalign, the probability of aligning tertiary contact partners, and ΔGtert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔGHJH) or from changes in the electrostatic environment (ΔG+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔGtert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔGtert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

RNA folding kinetics using Monte Carlo and Gillespie algorithms.

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to [Formula: see text] times that of the Gillespie algorithm, where [Formula: see text] denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by [Formula: see text]; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gillespie algorithms is publicly available, as is our software to compute the expected degree of the network of secondary structures of a given RNA sequence-see http://bioinformatics.bc.edu/clote/RNAexpNumNbors .

Amino Acid Specific Effects on RNA Tertiary Interactions: Single-Molecule Kinetic and Thermodynamic Studies.

In light of the current models for an early RNA-based universe, the potential influence of simple amino acids on tertiary folding of ribozymal RNA into biochemically competent structures is speculated to be of significant evolutionary importance. In the present work, the folding-unfolding kinetics of a ubiquitous tertiary interaction motif, the GAAA tetraloop-tetraloop receptor (TL-TLR), is investigated by single-molecule fluorescence resonance energy transfer spectroscopy in the presence of natural amino acids both with (e.g., lysine, arginine) and without (e.g., glycine) protonated side chain residues. By way of control, we also investigate the effects of a special amino acid (e.g., proline) and amino acid mimetic (e.g., betaine) that contain secondary or quaternary amine groups rather than a primary amine group. This combination permits systematic study of amino acid induced (or amino acid like) RNA folding dynamics as a function of side chain complexity, pKa, charge state, and amine group content. Most importantly, each of the naturally occurring amino acids is found to destabilize the TL-TLR tertiary folding equilibrium, the kinetic origin of which is dominated by a decrease in the folding rate constant (kdock), also affected by a strongly amino acid selective increase in the unfolding rate constant (kundock). To further elucidate the underlying thermodynamics, single-molecule equilibrium constants (Keq) for TL-TLR folding have been probed as a function of temperature, which reveal an amino acid dependent decrease in both overall exothermicity (ΔΔH° > 0) and entropic cost (-TΔΔS° < 0) for the overall folding process. Temperature-dependent studies on the folding/unfolding kinetic rate constants reveal analogous amino acid specific changes in both enthalpy (ΔΔH⧧) and entropy (ΔΔS⧧) for accessing the transition state barrier. The maximum destabilization of the TL-TLR tertiary interaction is observed for arginine, which is consistent with early studies of arginine and guanidine ion-inhibited self-splicing kinetics for the full Tetrahymena ribozyme [ Yarus , M. ; Christian , E. L. Nature 1989 , 342 , 349 - 350 ; Yarus , M. Science 1988 , 240 , 1751 - 1758 ].

Translation Initiation is Controlled by RNA Folding Kinetics via a Ribosome Drafting Mechanism.

RNA folding plays an important role in controlling protein synthesis as well as other cellular processes. Existing models have focused on how RNA folding energetics control translation initiation rate under equilibrium conditions but have largely ignored the effects of nonequilibrium RNA folding. We introduce a new mechanism, called "ribosome drafting", that explains how a mRNA's folding kinetics and the ribosome's binding rate collectively control its translation initiation rate. During cycles of translation, ribosome drafting emerges whenever successive ribosomes bind to a mRNA faster than the mRNA can refold, maintaining it in a nonequilibrium state with an acceleration of protein synthesis. Using computational design, time-correlated single photon counting, and expression measurements, we demonstrate that slow-folding and fast-folding RNA structures with equivalent folding energetics can vary protein synthesis rates by 1000-fold. We determine the necessary conditions for ribosome drafting by characterizing mRNAs with rationally designed ribosome binding rates, folding kinetics, and folding energetics, confirming the predictions of a nonequilibrium Markov model of translation. Our results have widespread implications, illustrating how competitive folding and assembly kinetics can shape the gene expression machinery's sequence-structure-function relationship inside cells.

Measurement and modeling of intrinsic transcription terminators

The reliable forward engineering of genetic systems remains limited by the ad hoc reuse of many types of basic genetic elements. Although a few intrinsic prokaryotic transcription terminators are used routinely, termination efficiencies have not been studied systematically. Here, we developed and validated a genetic architecture that enables reliable measurement of termination efficiencies. We then assembled a collection of 61 natural and synthetic terminators that collectively encode termination efficiencies across an ∼800-fold dynamic range within Escherichia coli. We simulated co-transcriptional RNA folding dynamics to identify competing secondary structures that might interfere with terminator folding kinetics or impact termination activity. We found that structures extending beyond the core terminator stem are likely to increase terminator activity. By excluding terminators encoding such context-confounding elements, we were able to develop a linear sequence-function model that can be used to estimate termination efficiencies (r = 0.9, n = 31) better than models trained on all terminators (r = 0.67, n = 54). The resulting systematically measured collection of terminators should improve the engineering of synthetic genetic systems and also advance quantitative modeling of transcription termination.

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.

Network Properties of the Ensemble of RNA Structures

We describe the first dynamic programming algorithm that computes the expected degree for the network, or graph G = (V, E) of all secondary structures of a given RNA sequence a = a 1, …, a n. Here, the nodes V correspond to all secondary structures of a, while an edge exists between nodes s, t if the secondary structure t can be obtained from s by adding, removing or shifting a base pair. Since secondary structure kinetics programs implement the Gillespie algorithm, which simulates a random walk on the network of secondary structures, the expected network degree may provide a better understanding of kinetics of RNA folding when allowing defect diffusion, helix zippering, and related conformation transformations. We determine the correlation between expected network degree, contact order, conformational entropy, and expected number of native contacts for a benchmarking dataset of RNAs. Source code is available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.

Linking aptamer-ligand binding and expression platform folding in riboswitches: prospects for mechanistic modeling and design.

The power of riboswitches in regulation of bacterial metabolism derives from coupling of two characteristics: recognition and folding. Riboswitches contain aptamers, which function as biosensors. Upon detection of the signaling molecule, the riboswitch transduces the signal into a genetic decision. The genetic decision is coupled to refolding of the expression platform, which is distinct from, although overlapping with, the aptamer. Early biophysical studies of riboswitches focused on recognition of the ligand by the aptamer‐an important consideration for drug design. A mechanistic understanding of ligand‐induced riboswitch RNA folding can further enhance riboswitch ligand design, and inform efforts to tune and engineer riboswitches with novel properties. X‐ray structures of aptamer/ligand complexes point to mechanisms through which the ligand brings together distal strand segments to form a P1 helix. Transcriptional riboswitches must detect the ligand and form this P1 helix within the timescale of transcription. Depending on the cell's metabolic state and cellular environmental conditions, the folding and genetic outcome may therefore be affected by kinetics of ligand binding, RNA folding, and transcriptional pausing, among other factors. Although some studies of isolated riboswitch aptamers found homogeneous, prefolded conformations, experimental, and theoretical studies point to functional and structural heterogeneity for nascent transcripts. Recently it has been shown that some riboswitch segments, containing the aptamer and partial expression platforms, can form binding‐competent conformers that incorporate an incomplete aptamer secondary structure. Consideration of the free energy landscape for riboswitch RNA folding suggests models for how these conformers may act as transition states—facilitating rapid, ligand‐mediated aptamer folding. WIREs RNA 2015, 6:631–650. doi: 10.1002/wrna.1300For further resources related to this article, please visit the WIREs website.

A U⋅U Pair‐to‐U⋅C Pair Mutation‐Induced RNA Native Structure Destabilisation and Stretching‐Force‐Induced RNA Misfolding

Little is known about how a non-Watson-Crick pair affects the RNA folding dynamics. We studied the effects of a U⋅U-to-U⋅C pair mutation on the folding of a hairpin in human telomerase RNA. The ensemble thermal melting of the hairpins shows an on-pathway intermediate with the disruption of the internal loop structure containing the U⋅U/U⋅C pairs. By using optical tweezers, we applied a stretching force on the terminal ends of the hairpins to probe directly the non-nearest-neighbour effects upon the mutations. The single U⋅U to U⋅C mutations are observed to 1) lower the mechanical unfolding force by approximately 1 picoNewton (pN) per mutation without affecting the unfolding reaction transition-state position (thus suggesting that removing a single hydrogen bond affects the structural dynamics at least two base pairs away), 2) result in more frequent misfolding into a small hairpin at approximately 10 pN and 3) shift the folding reaction transition-state position towards the native hairpin structure and slightly increase the mechanical folding kinetics (thus suggesting that untrapping from the misfolded state is not the rate-limiting step).