Slow folding kinetics of RNase P RNA.

Understanding the folding mechanisms of large, highly structured RNAs is important for understanding how these molecules carry out their function. Although models for the three-dimensional architecture of several large RNAs have been constructed, the process by which these structures are formed is only now beginning to be explored. The kinetic folding pathway of the Tetrahymena ribozyme involves multiple intermediates and both Mg2+-dependent and Mg2+-independent steps. To determine whether this general mechanism is representative of folding of other large RNAs, a study of RNase P RNA folding was undertaken. We show, using a kinetic oligonucleotide hybridization assay, that there is at least one slow step on the folding pathway of RNase P RNA, resulting in conformational changes in the P7 helix region on the minute timescale. Although this folding event requires the presence of Mg2+, the slow step itself does not involve Mg2+ binding. The P7 and P2 helix regions exhibit distinctly different folding behavior and ion dependence, implying that RNase P folding is likely to be a complex process. Furthermore, there are distinct similarities in the folding of RNase P RNA from both Bacillus subtilis and Escherichia coli, indicating that the folding pathway may also be conserved along with the final structure. The slow folding kinetics, Mg2+-independence of the rate, and existence of intermediates are basic features of the folding mechanism of the Tetrahymena group I intron that are also found in RNase P RNA, suggesting these may be general features of the folding of large RNAs.     

A New Computational Approach for Mechanical Folding Kinetics of RNA Hairpins

Based on an ensemble of kinetically accessible conformations, we propose a new analytical model for RNA folding kinetics. The model gives populational kinetics, kinetic rates, transition states, and pathways from the rate matrix. Applications of the new kinetic model to mechanical folding of RNA hairpins such as trans-activation-responsive RNA reveal distinct kinetic behaviors in different force regimes, from zero force to forces much stronger than the critical force for the folding-unfolding transition. In the absence of force or a low force, folding can be initiated (nucleated) at any position by forming the first base stack and there exist many pathways for the folding process. In contrast, for a higher force, the folding/unfolding would predominantly proceed along a single zipping/unzipping pathway. Studies for different hairpin-forming sequences indicate that depending on the nucleotide sequence, a kinetic intermediate can emerge in the low force regime but disappear in high force regime, and a new kinetic intermediate, which is absent in the low and high force regimes, can emerge in the medium force range. Variations of the force lead to changes in folding cooperativity and rate-limiting steps. The predicted network of pathways for trans-activation-responsive RNA suggests two parallel dominant pathways. The rate-limiting folding steps (at f = 8 pN) are the formation of specific basepairs that are 2-4 basepairs away from the loop. At a higher force (f = 11 pN), the folding rate is controlled by the formation of the bulge loop. The predicted rates and transition states are in good agreement with the experimental data for a broad force regime.     

Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape

An acid-destabilized form of apomyoglobin, the so-called E state, consists of a set of heterogeneous structures that are all characterized by a stable hydrophobic core composed of 30-40 residues at the intersection of the A, G, and H helices of the protein, with little other secondary structure and no other tertiary structure. Relaxation kinetics studies were carried out to characterize the dynamics of core melting and formation in this protein. The unfolding and/or refolding response is induced by a laser-induced temperature jump between the folded and unfolded forms of E, and structural changes are monitored using the infrared amide I' absorbance at 1648-1651 cm(-1) that reports on the formation of solvent-protected, native-like helix in the core and by fluorescence emission changes from apomyoglobin's Trp14, a measure of burial of the indole group of this residue. The fluorescence kinetics data are monoexponential with a relaxation time of 14 micros. However, infrared kinetics data are best fit to a biexponential function with relaxation times of 14 and 59 micros. These relaxation times are very fast, close to the limits placed on folding reactions by diffusion. The 14 micros relaxation time is weakly temperature dependent and thus represents a pathway that is energetically downhill. The appearance of this relaxation time in both the fluorescence and infrared measurements indicates that this folding event proceeds by a concomitant formation of compact secondary and tertiary structures. The 59 micros relaxation time is much more strongly temperature dependent and has no fluorescence counterpart, indicating an activated process with a large energy barrier wherein nonspecific hydrophobic interactions between helix A and the G and H helices cause some helix burial but Trp14 remains solvent exposed. These results are best fit by a multiple-pathway kinetic model when U collapses to form the various folded core structures of E. Thus, the results suggest very robust dynamics for core formation involving multiple folding pathways and provide significant insight into the primary processes of protein folding.     

A DEAD-box RNA helicase promotes thermodynamic equilibration of kinetically trapped RNA structures in vivo

RNAs must assemble into specific structures in order to carry out their biological functions, but in vitro RNA folding reactions produce multiple misfolded structures that fail to exchange with functional structures on biological time scales. We used carefully designed self-cleaving mRNAs that assemble through well-defined folding pathways to identify factors that differentiate intracellular and in vitro folding reactions. Our previous work showed that simple base-paired RNA helices form and dissociate with the same rate and equilibrium constants in vivo and in vitro. However, exchange between adjacent secondary structures occurs much faster in vivo, enabling RNAs to quickly adopt structures with the lowest free energy. We have now used this approach to probe the effects of an extensively characterized DEAD-box RNA helicase, Mss116p, on a series of well-defined RNA folding steps in yeast. Mss116p overexpression had no detectable effect on helix formation or dissociation kinetics or on the stability of interdomain tertiary interactions, consistent with previous evidence that intracellular factors do not affect these folding parameters. However, Mss116p overexpression did accelerate exchange between adjacent helices. The nonprocessive nature of RNA duplex unwinding by DEAD-box RNA helicases is consistent with a branch migration mechanism in which Mss116p lowers barriers to exchange between otherwise stable helices by the melting and annealing of one or two base pairs at interhelical junctions. These results suggest that the helicase activity of DEAD-box proteins like Mss116p distinguish intracellular RNA folding pathways from nonproductive RNA folding reactions in vitro and allow RNA structures to overcome kinetic barriers to thermodynamic equilibration in vivo.     

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.     

Explicit-chain model of native-state hydrogen exchange: implications for event ordering and cooperativity in protein folding

Native-state hydrogen exchange experiments on several proteins have revealed partially unfolded conformations with diverse stabilities. These equilibrium observations have been used to support kinetic arguments that folding proceeds via a sequential "pathway." This interpretative logic is evaluated here by analyzing the relationship between thermodynamic behavior and folding kinetics in a class of simplified lattice protein models. The chain models studied have varying degrees of cooperative interplay (coupling) between local helical conformational preference and favorable nonlocal interactions. When model cooperativity is high, as native conditions are weakened, "isotherms" of free energy of exchange for residues belonging to the same helix merge together before global unfolding. The point of merger depends on the model energetic favorability of the helix. This trend is similar to the corresponding experimental observations. Kinetically, we find that the ordering of helix formation in the very last stage of native core assembly tends to follow the stabilities of their converged isotherms. In a majority (but not all) of folding trajectories, the final assembly of helices that are thermodynamically more stable against exchange precedes that of helices that are less stable against exchange. These model features are in partial agreement with common experimental interpretations. However, the model results also underscore the ensemble nature of the folding process: the kinetics of helix formation is not a discrete, strictly "all-or-none" process as that envisioned by certain non-explicit-chain models. Helices generally undergo many cycles of partial formation and dissolution before their conformations are fixed in the final assembly stage of folding, a kinetic stage that takes up only approximately 2% of the average folding time in the present model; and the ordering of the helices' final assembly in some trajectories can be different from the dominant ordering stipulated by the exchange isotherms.     

Reduced contact order and RNA folding rates

We investigated the relationship between RNA structure and folding rates accounting for hierarchical structural formation. Folding rates of two-state folding proteins correlate well with relative contact order, a quantitative measure of the number and sequence distance between tertiary contacts. These proteins do not form stable structures prior to the rate-limiting step. In contrast, most secondary structures are stably formed prior to the rate-limiting step in RNA folding. Accordingly, we introduce "reduced contact order", a metric that reflects only the number of residues available to participate in the conformational search after the formation of secondary structure. Plotting the folding rates and the reduced contact order from ten different RNAs suggests that RNA folding can be divided into two classes. To examine this division, folding rates of circularly permutated isomers are compared for two RNAs, one from each class. Folding rates vary by tenfold for circularly permuted Bacillus subtilis RNase P RNA isomers, whereas folding rates vary by only 1.2-fold for circularly permuted catalytic domains. This difference is likely related to the dissimilar natures of their rate-limiting steps.     

Folding path of P5abc RNA involves direct coupling of secondary and tertiary structures

Folding mechanisms in which secondary structures are stabilized through the formation of tertiary interactions are well documented in protein folding but challenge the folding hierarchy normally assumed for RNA. However, it is increasingly clear that RNA could fold by a similar mechanism. P5abc, a small independently folding tertiary domain of the Tetrahymena thermophila group I ribozyme, is known to fold by a secondary structure rearrangement involving helix P5c. However, the extent of this rearrangement and the precise stage of folding that triggers it are unknown. We use experiments and simulations to show that the P5c helix switches to the native secondary structure late in the folding pathway and is directly coupled to the formation of tertiary interactions in the A-rich bulge. P5c mutations show that the switch in P5c is not rate-determining and suggest that non-native interactions in P5c aid folding rather than impede it. Our study illustrates that despite significant differences in the building blocks of proteins and RNA, there may be common ways in which they self-assemble.     

An implementation of the Gillespie algorithm for RNA kinetics with logarithmic time update

In this paper I outline a fast method called KFOLD for implementing the Gillepie algorithm to stochastically sample the folding kinetics of an RNA molecule at single base-pair resolution. In the same fashion as the KINFOLD algorithm, which also uses the Gillespie algorithm to predict folding kinetics, KFOLD stochastically chooses a new RNA secondary structure state that is accessible from the current state by a single base-pair addition/deletion following the Gillespie procedure. However, unlike KINFOLD, the KFOLD algorithm utilizes the fact that many of the base-pair addition/deletion reactions and their corresponding rates do not change between each step in the algorithm. This allows KFOLD to achieve a substantial speed-up in the time required to compute a prediction of the folding pathway and, for a fixed number of base-pair moves, performs logarithmically with sequence size. This increase in speed opens up the possibility of studying the kinetics of much longer RNA sequences at single base-pair resolution while also allowing for the RNA folding statistics of smaller RNA sequences to be computed much more quickly.     

Consequences of stabilizing the natively disordered f helix for the folding pathway of apomyoglobin

The F helix region of sperm whale apomyoglobin is disordered, undergoing conformational fluctuations between a folded helical conformation and one or more locally unfolded states. To examine the effects of F helix stabilization on the folding pathway of apomyoglobin, we have introduced mutations to augment intrinsic helical structure in the F helix of the kinetic folding intermediate and to increase its propensity to fold early in the pathway, using predictions based on plots of the average area buried upon folding (AABUF) derived from the primary sequence. Two mutant proteins were prepared: a double mutant, P88K/S92K (F2), and a quadruple mutant, P88K/A90L/S92K/A94L (F4). Whereas the AABUF for F2 predicts that the F helix will not fold early in the pathway, the F helix in F4 shows a significantly increased AABUF and is therefore predicted to fold early. Protection of amide protons by formation of hydrogen-bonded helical structure during the early folding events has been analyzed by pH-pulse labeling. Consistent with the AABUF prediction, many of the F helix residues for F4 are significantly protected in the kinetic intermediate but are not protected in the F2 mutant. F4 folds via a kinetically trapped burst-phase intermediate that contains stabilized secondary structure in the A, B, F, G, and H helix regions. Rapid folding of the F helix stabilizes the central core of the misfolded intermediate and inhibits translocation of the H helix back to its native position, thereby decreasing the overall folding rate.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

Slow motion analysis of protein folding intermediates within wet silica gels

Resolving the complete folding pathway of a protein is a major challenge to conventional experimental methods because of the rapidity and complexity of folding. Here, we show that entrapment of the protein cytochrome c in wet, optically transparent, porous silica gel matrices has enabled a dramatic expansion, to days or weeks, of the folding time, allowing direct observation of the entire folding pathway using a combination of three spectroscopic techniques, far-ultraviolet circular dichroism, tryptophan fluorescence, and Soret absorption spectroscopy. During refolding in silica gels, collapse and helix formation occur in a stepwise manner, as observed in aqueous solution. Analysis of kinetics and transient spectra indeed reveals a sequence of four distinct intermediates with progressively increasing degrees of folding, two of which closely resemble those previously characterized in solution, namely, the early collapsed and the molten globule intermediates. The other two are the precollapsed and pre-molten globule intermediates that may escape detection by conventional kinetic methods. Interestingly, varying the strength of the gel network has a dramatic effect on the folding time, but no significant effect on the structural features of each folding intermediate, indicating that the interaction between the protein and gel matrix has no measurable effect on the folding pathway. These results better define the major pathway of cytochrome c folding. In addition, in this paper we present the results of the application of this method to a simple, apparent two-state folder ubiquitin, helping to interpret the results for cytochrome c.     

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.     

A kinetic model of RNA folding

The RNA folding process is represented as a Markov process with states corresponding to RNA secondary structures and transition probabilities corresponding to transformations of a secondary structure caused by formation or disintegration of a helix. Transition probabilities (kinetic constants) are determined. A notion of a group of structures is introduced, and it allows to reduce the state space. Energetic and kinetic parameters of pseudoknots are estimated. Algorithms for computation of a kinetic ensemble for structures and groups of structures are presented, as well as their modifications that take into account pseudoknots. The described algorithms are implemented as a procedure for prediction of RNA secondary structure that is included in the package DNA-SUN.     

Design of a highly reactive HDV ribozyme sequence uncovers facilitation of RNA folding by alternative pairings and physiological ionic strength

The hepatitis delta virus (HDV) ribozyme is a self-cleaving RNA that resides in the HDV genome and regulates its replication. The native fold of the ribozyme is complex, having two pseudoknots. Earlier work implicated four non-native pairings in slowing pseudoknot formation: Alt 1, Alt 2, Alt 3, and Alt P1. The goal of the present work was design of a kinetically simplified and maximally reactive construct for in vitro mechanistic and structural studies. The initial approach chosen was site-directed mutagenesis in which known alternative pairings were destabilized while leaving the catalytic core intact. Based on prior studies, the G11C/U27Delta double mutant was prepared. However, biphasic kinetics and antisense oligonucleotide response trends opposite those of the well-studied G11C mutant were observed suggesting that new alternative pairings with multiple registers, termed Alt X and Alt Y, had been created. Enzymatic structure mapping of oligonucleotide models supported this notion. This led to a model wherein Alt 2 and the phylogenetically conserved Alt 3 act as "folding guides", facilitating folding of the major population of the RNA molecules by hindering formation of the Alt X and Alt Y registers. Attempts to eliminate the strongest of the Alt X pairings by rational design of a quadruple mutant only resulted in more complex kinetic behavior. In an effort to simultaneously destabilize multiple alternative pairings, studies were carried out on G11C/U27Delta in the presence of urea or increased monovalent ion concentration. Inclusion of physiological ionic strength allowed the goal of monophasic, fast-folding (kobs approximately 60 min(-1)) kinetics to be realized. To account for this, a model is developed wherein Na+, which destabilizes secondary and tertiary structures in the presence of Mg2+, facilitates native folding by destabilizing the multiple alternative secondary structures with a higher-order dependence.     

Mg2+-dependent folding of a large ribozyme without kinetic traps

The folding kinetics of the catalytic domain of Bacillus subtilis ribonuclease P is analyzed here by fluorescence and catalytic activity. The folding pathway is apparently free of kinetic traps, as indicated by a decrease in folding rates upon the addition of urea. We apply Mg2+ and urea chevron analysis to fully describe the folding and unfolding kinetics of this ribozyme. A folding scheme containing two kinetic intermediates completely accounts for the free energy, the Mg2+ Hill coefficient and the surface buried in the equilibrium transition. At saturating Mg 2+concentrations, folding is limited by a barrier that is independent of Mg2+ and urea. These results describe the first trap-free folding pathway of a large ribozyme and indicate that kinetic traps are not an obligate feature of RNA folding.     

The notch ankyrin domain folds via a discrete, centralized pathway

The Notch ankyrin repeat domain contains seven ankyrin sequence repeats, six of which adopt very similar structures. To determine if folding proceeds along parallel pathways and the order in which repeats become structured during folding, we examined the effect of analogous destabilizing Ala-->Gly substitutions in each repeat on folding kinetics. We find that folding proceeds to an on-pathway kinetic intermediate through a transition state ensemble containing structure in repeats three through five. Repeats two, six, and seven remain largely unstructured in this intermediate, becoming structured in a second kinetic step that leads to the native state. These data suggest that the Notch ankyrin domain folds according to a discrete kinetic pathway despite structural redundancy in the native state and highlight the importance of sequence-specific interactions in controlling pathway selection. This centralized pathway roughly corresponds to a low energy channel through the experimentally determined energy landscape.     

A kinetic approach to the prediction of RNA secondary structures

A new approach to the prediction of secondary RNA structures based on the analysis of the kinetics of molecular self-organisation is proposed herein. The Markov process is used to describe structural reconstructions during secondary structure formation. This process is modelled by a Monte-Carlo method. Examples of the calculation by this method of the secondary structures kinetic ensemble are given. Distribution of time-dependent probabilities within the ensembles is obtained. An effective method for search for the equilibrium ensemble is also suggested. This method is based on the construction of a tree of all possible secondary structures of RNA. By ascribing a probability for each structure (according to its free energy) the Boltzmann equilibrium ensemble can be obtained.     

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.     

Unveiling a hidden folding intermediate in c-type cytochromes by protein engineering

Several investigators have highlighted a correlation between the basic features of the folding process of a protein and its topology, which dictates the folding pathway. Within this conceptual framework we proposed that different members of the cytochrome c (cyt c) family share the same folding mechanism, involving a consensus partially structured state. Pseudomonas aeruginosa cyt c(551) (Pa cyt c(551)) folds via an apparent two-state mechanism through a high energy intermediate. Here we present kinetic evidence demonstrating that it is possible to switch its folding mechanism from two to three state, stabilizing the high energy intermediate by rational mutagenesis. Characterization of the folding kinetics of one single-site mutant of the Pa cyt c(551) (Phe(7) to Ala) indeed reveals an additional refolding phase and a fast unfolding process which are explained by the accumulation of a partially folded species. Further kinetic analysis highlights the presence of two parallel processes both leading to the native state, suggesting that the above mentioned species is a non obligatory on-pathway intermediate. Determination of the crystallographic structure of F7A shows the presence of an extended internal cavity, which hosts three "bound" water molecules and a H-bond in the N-terminal helix, which is shorter than in the wild type protein. These two features allow us to propose a detailed structural interpretation for the stabilization of the native and especially the intermediate states induced by a single crucial mutation. These results show how protein engineering, x-ray crystallography and state-of-the-art kinetics concur to unveil a folding intermediate and the structural determinants of its stability.