RNA Folding Kinetics Research Articles

Nonequilibrium NMR Methods for Monitoring Protein and RNA Folding

AbstractThe review introduces to time-resolved NMR spectroscopic investigations of the kinetics of protein and RNA folding. The description of the experimental investigations is discussed in the context of possible kinetic folding pathways showing the extent of information that can be gained from the various kinetic experiments. The review introduces to four different methods to initiate folding reactions in connection with time-resolved NMR experiments and discusses examples of refolding of the model proteinα-lactalbumin and of bistable RNAs.

Folding Kinetics for the Conformational Switch Between Alternative RNA Structures

The conformational switching between different conformational states is intrinsic to RNA catalytic and regulatory functions, which oftenly occurs on time-scales of several seconds. In combination with the recent real-time NMR experiments (Wenter et al. Angew. Chem. Int. Ed. (2005). 44, 2600; Wenter et al. ChemBioChem. (2006). 7, 417) for the transitions between bistable RNA conformations, we combine the master equation method with the kinetic cluster method to investigate the detailed kinetic mechanism and the factors that govern the folding kinetics. Based on the computational studies, we propose that heat capacity change upon RNA folding may be important for RNA folding kinetics. In addition, we find that noncanonical (tertiary) intraloop interactions in tetraloop hairpins are important to determine the folding kinetics. Furthermore, through theory-experiment comparisons, we find that the different rate models for the fundamental steps (i.e., formation/disruption of a base pair or stack) can cause contrasting results in the theoretical predictions.

Sequencing of a Tick-Borne Encephalitis Virus fromIxodes ricinusReveals a Thermosensitive RNA Switch Significant for Virus Propagation in Ectothermic Arthropods

Tick-borne encephalitis virus (TBEV) is a flavivirus with major impact on global health. The geographical TBEV distribution is expanding, thus making it pivotal to further characterize the natural virus populations. In this study, we completed the earlier partial sequencing of a TBEV pulled out of a pool of RNA extracted from 115 ticks collected on Torö in the Stockholm archipelago. The total RNA was sufficient for all sequencing of a TBEV genome (Torö-2003), without conventional enrichment procedures such as cell culturing or suckling mice amplification. To our knowledge, this is the first time that the genome of TBEV has been sequenced directly from an arthropod reservoir. The Torö-2003 sequence has been characterized and compared with other TBE viruses. In silico analyses of secondary RNA structures formed by the two untranslated regions revealed a temperature-sensitive structural shift between a closed replicative form and an open AUG accessible form, analogous to a recently described bacterial thermoswitch. Additionally, novel phylogenetic conserved structures were identified in the variable part of the 3'-untranslated region, and their sequence and structure similarity when compared with earlier identified structures suggests an enhancing function on virus replication and translation. We propose that the thermo-switch mechanism may explain the low TBEV prevalence often observed in environmentally sampled ticks. Finally, we were able to detect variations that help in the understanding of virus adaptations to varied environmental temperatures and mammalian hosts through a comparative approach that compares RNA folding dynamics between strains with different mammalian cell passage histories.

Folding kinetics for the conformational switch between alternative RNA structures.

Transitions between different conformational states, so-called conformational switching, are intrinsic to RNA catalytic and regulatory functions. Often, conformational switching occurs on time scales of several seconds. In combination with the recent real-time NMR experiments (Wenter et al. Angew. Chem. Int. Ed. 2005, 44, 2600; Wenter et al. ChemBioChem 2006, 7, 417) for the transitions between bistable RNA conformations, we combine the master equation method with the kinetic cluster method to investigate the detailed kinetic mechanism and the factors that govern the folding kinetics. We propose that heat capacity change (ΔC(p)) upon RNA folding may be important for RNA folding kinetics. In addition, we find that, for tetraloop hairpins, noncanonical (tertiary) intraloop interactions are important to determine the folding kinetics. Furthermore, through theory-experiment comparisons, we find that the different rate models for the fundamental steps (i.e., formation/disruption of a base pair or stack) can cause contrasting results in the theoretical predictions.

A Motion Planning Approach to Studying Molecular Motions

While structurally very different, protein and RNA molecules share an important attribute. The motions they undergo are strongly related to the function they perform. For example, many diseases such as Mad Cow disease or Alzheimer's disease are associated with protein misfolding and aggregation. Similarly, RNA folding velocity may regulate the plasmid copy number, and RNA folding kinetics can regulate gene expression at the translational level. Knowledge of the stability, folding, kinetics and detailed mechanics of the folding process may help provide insight into how proteins and RNAs fold. In this paper, we present an overview of our work with a computational method we have adapted from robotic motion planning to study molecular motions. We have val- idated against experimental data and have demonstrated that our method can capture biological results such as stochastic folding pathways, population kinetics of various conformations, and rela- tive folding rates. Thus, our method provides both a detailed view (e.g., individual pathways) and a global view (e.g., population kinetics, relative folding rates, and reaction coordinates) of energy land- scapes of both proteins and RNAs. We have validated these techniques by showing that we observe the same relative folding rates as shown in experiments for structurally similar protein molecules that exhibit different folding behaviors. Our analysis has also been able to predict the same relative gene expression rate for wild-type MS2 phage RNA and three of its mutants.

Mechanical Folding Kinetics of RNA Hairpins: a New Computational Approach

From the distribution of the low-lying states on the energy landscape, we recently developed a new computational method for the prediction of RNA folding kinetics [1]. The method can treat long sequences because it is based on a small ensemble of seed states. Additionally, the method is based on an analytic formalism and thus enables predictions for long-time folding kinetics. Applications of the new kinetic model to mechanical folding of RNA hairpins reveal distinct kinetic behaviors for a wide range of different force regimes, from zero force to forces much stronger than the critical force for the folding-unfolding transition.

A pH-responsive riboregulator

The locus alx, which encodes a putative transporter, was discovered previously in a screen for genes induced under extreme alkaline conditions. Here we show that the RNA region preceding the alx ORF acts as a pH-responsive element, which, in response to high pH, leads to an increase in alx expression. Under normal growth conditions this RNA region forms a translationally inactive structure, but when exposed to high pH, a translationally active structure is formed to produce Alx. Formation of the active structure occurs while transcription is in progress under alkaline conditions and involves pausing of RNA polymerase at two distinct sites. Alkali increases the longevity of pausing at these sites and thereby interferes with formation of the inactive structure and promotes folding of the active one. The alx locus represents the first example of a pH-responsive riboregulator of gene expression, introducing a novel regulatory mechanism that involves RNA folding dynamics driven by pH.

Protein Roles in Group I Intron RNA Folding: The Tyrosyl-tRNA Synthetase CYT-18 Stabilizes the Native State Relative to a Long-Lived Misfolded Structure without Compromising Folding Kinetics

The Neurospora crassa CYT-18 protein is a mitochondrial tyrosyl-tRNA synthetase that also promotes self-splicing of group I intron RNAs by stabilizing the functional structure in the conserved core. CYT-18 binds the core along the same surface as a common peripheral element, P5abc, suggesting that CYT-18 can replace P5abc functionally. In addition to stabilizing structure generally, P5abc stabilizes the native conformation of the Tetrahymena group I intron relative to a globally similar misfolded conformation that has only local differences within the core and is populated significantly at equilibrium by a ribozyme variant lacking P5abc (E ΔP5abc). Here, we show that CYT-18 specifically promotes formation of the native group I intron core from this misfolded conformation. Catalytic activity assays demonstrate that CYT-18 shifts the equilibrium of E ΔP5abc toward the native state by at least 35-fold, and binding assays suggest an even larger effect. Thus, similar to P5abc, CYT-18 preferentially recognizes the native core, despite the global similarity of the misfolded core and despite forming crudely similar complexes, as revealed by dimethyl sulfate footprinting. Interestingly, the effects of CYT-18 and P5abc on folding kinetics differ. Whereas P5abc inhibits refolding of the misfolded conformation by forming peripheral contacts that must break during refolding, CYT-18 does not display analogous inhibition, most likely because it relies to a greater extent on direct interactions with the core. Although CYT-18 does not encounter this RNA in vivo, our results suggest that it stabilizes its cognate group I introns relative to analogous misfolded intermediates. By specifically recognizing native structural features, CYT-18 may also interact with earlier folding intermediates to avoid RNA misfolding or to trap native contacts as they form. More generally, our results highlight the ability of a protein cofactor to stabilize a functional RNA structure specifically without incurring associated costs in RNA folding kinetics.

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.

Kinetics and Mechanism of RNA Folding studied by SAXS

RNAs fold into unique native structures to perform specific biological functions. Detailed identification of the kinetics of RNA-folding should provide insight to the nucleation and collapse mechanisms. The Azoarcus ribozyme exhibits two thermodynamic transitions: 1) U to Ic at low Mg2+ concentrations (U: unfolded state, Ic: compact intermediate state), ascribed to the assembly of double helices in the center of the RNA and 2) Ic to N at high Mg2+ concentration (N: native state), which involves further secondary-structural rearrangements to form the final folded structure including tertiary interactions. We have studied the rate of the folding transitions and the role of cooperative tertiary interactions in stabilizing the Ic and N states in order to understand the folding mechanism. The real-time dependence of folding of the wild type and mutant Azoarcus ribozyme as a function of cation concentration (Mg2+ or Ba2+) was monitored using time-resolved small angle X-ray scattering (SAXS) coupled with a stopped-flow sample system. At high Mg2+ concentrations the Azoarcus ribozyme collapses through multiple pathways, with a majority (∼ 90 %) following a fast folding route within t ∼ 10 ms and the rest collapsing at t > 3 min. The folding rate at short time scales decreases with decreasing cation concentration. The rate changes significantly in the range of the first transition, suggesting that initial cation charge screening of the repulsion of the negatively charged RNA chains plays an important role in determining the formation of tertiary interactions. Interestingly, Ba2+ and single-site mutations in the Azoarcus ribozyme lead to faster collapse of the RNAs on short timescales, suggesting that folding of the wild type in Mg2+ requires more time to stabilize the correct folded tertiary structure through the rearrangement of secondary structures.

Force-induced misfolding in RNA

RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite its importance in modern biophysics, the current understanding of RNA folding kinetics is limited by the complex interplay between the weak base pair interactions that stabilize the native structure and the disordering effect of thermal forces. The possibility of mechanically pulling individual molecules offers a new perspective to understand the folding of nucleic acids. Here we investigate the folding and misfolding mechanism in RNA secondary structures pulled by mechanical forces. We introduce a model based on the identification of the minimal set of structures that reproduce the patterns of force-extension curves obtained in single molecule experiments. The model requires only two fitting parameters: the attempt frequency at the level of individual base pairs and a parameter associated to a free-energy correction that accounts for the configurational entropy of an exponentially large number of neglected secondary structures. We apply the model to interpret results recently obtained in pulling experiments in the three-helix junction S15 RNA molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where force favors the formation of a stable non-native hairpin. The model reproduces the pattern of unfolding and refolding force-extension curves, the distribution of breakage forces, and the misfolding probability obtained in the experiments.

Unifying evolutionary and thermodynamic information for RNA folding of multiple alignments

Computational methods for determining the secondary structure of RNA sequences from given alignments are currently either based on thermodynamic folding, compensatory base pair substitutions or both. However, there is currently no approach that combines both sources of information in a single optimization problem. Here, we present a model that formally integrates both the energy-based and evolution-based approaches to predict the folding of multiple aligned RNA sequences. We have implemented an extended version of Pfold that identifies base pairs that have high probabilities of being conserved and of being energetically favorable. The consensus structure is predicted using a maximum expected accuracy scoring scheme to smoothen the effect of incorrectly predicted base pairs. Parameter tuning revealed that the probability of base pairing has a higher impact on the RNA structure prediction than the corresponding probability of being single stranded. Furthermore, we found that structurally conserved RNA motifs are mostly supported by folding energies. Other problems (e.g. RNA-folding kinetics) may also benefit from employing the principles of the model we introduce. Our implementation, PETfold, was tested on a set of 46 well-curated Rfam families and its performance compared favorably to that of Pfold and RNAalifold.

RNA Folding: Conformational Statistics, Folding Kinetics, and Ion Electrostatics

RNA folding is a remarkably complex problem that involves ion-mediated electrostatic interaction, conformational entropy, base pairing and stacking, and noncanonical interactions. During the past decade, results from a variety of experimental and theoretical studies pointed to (a) the potential ion correlation effect in Mg2+-RNA interactions, (b) the rugged energy landscapes and multistate RNA folding kinetics even for small RNA systems such as hairpins and pseudoknots, (c) the intraloop interactions and sequence-dependent loop free energy, and (d) the strong nonadditivity of chain entropy in RNA pseudoknot and other tertiary folds. Several related issues, which have not been thoroughly resolved, require combined approaches with thermodynamic and kinetic experiments, statistical mechanical modeling, and all-atom computer simulations.

Ab initio RNA folding by discrete molecular dynamics: From structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.

Beyond energy minimization: approaches to the kinetic folding of RNA

The term RNA folding is often used synonymously with the prediction of equilibrium structures. Yet many RNAs function thanks to their ability to undergo structural changes. In this contribution we present a systematic overview of existing approaches to the prediction of RNA folding kinetics, and in particular discuss the strengths and limitations of each method.

Simulating RNA Folding Kinetics on Approximated Energy Landscapes

We present a general computational approach to simulate RNA folding kinetics that can be used to extract population kinetics, folding rates and the formation of particular substructures that might be intermediates in the folding process. Simulating RNA folding kinetics can provide unique insight into RNA whose functions are dictated by folding kinetics and not always by nucleotide sequence or the structure of the lowest free-energy state. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the master equation on the map. We present results obtained using an analysis technique, map-based Monte Carlo simulation, which stochastically extracts folding pathways from the map. Our method compares favorably with other computational methods that begin with a comprehensive free-energy landscape, illustrating that the smaller, approximate map captures the major features of the complete energy landscape. As a result, our method scales to larger RNAs. For example, here we validate kinetics of RNA of more than 200 nucleotides. Our method accurately computes the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.

MODELING CLASSIC ATTENUATION REGULATION OF GENE EXPRESSION IN BACTERIA

A model is proposed primarily for the classical RNA attenuation regulation of gene expression through premature transcription termination. The model is based on the concept of the RNA secondary structure macrostate within the regulatory region between the ribosome and RNA-polymerase, on hypothetical equation describing deceleration of RNA-polymerase by a macrostate and on views of transcription and translation initiation and elongation, under different values of the four basic model parameters which were varied. A special effort was made to select adequate model parameters. We first discuss kinetics of RNA folding and define the concept of the macrostate as a specific parentheses structure used to construct a conventional set of hairpins. The originally developed software that realizes the proposed model offers functionality to fully model RNA secondary folding kinetics. Its performance is compared to that of a public server described in Ref. 1. We then describe the delay in RNA-polymerase shifting to the next base or its premature termination caused by an RNA secondary structure or, herefrom, a macrostate. In this description, essential concepts are the basic and excited states of the polymerase first introduced in Ref. 2: the polymerase shifting to the next base can occur only in the basic state, and its detachment from DNA strand - only in excited state. As to the authors' knowledge, such a model incorporating the above-mentioned attenuation characteristics is not published elsewhere. The model was implemented in an application with command line interface for running in batch mode in Windows and Linux environments, as well as a public web server.(3) The model was tested with a conventional Monte Carlo procedure. In these simulations, the estimate of correlation between the premature transcription termination probability p and concentration c of charged amino acyl-tRNA was obtained as function p(c) for many regulatory regions in many bacterial genomes, as well as for local mutations in these regions.

Concordant Exploration of the Kinetics of RNA Folding from Global and Local Perspectives

Time-resolved small-angle X-ray scattering (SAXS) with millisecond time-resolution reveals two discrete phases of global compaction upon Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. Electrostatic relaxation of the RNA occurs rapidly and dominates the first phase of compaction during which the observed radius of gyration (R(g)) decreases from 75 angstroms to 55 angstroms. A further decrease in R(g) to 45 angstroms occurs in a well-defined second phase. An analysis of mutant ribozymes shows that the latter phase depends upon the formation of long-range tertiary contacts within the P4-P6 domain of the ribozyme; disruption of the three remaining long-range contacts linking the peripheral helices has no effect on the 55-45 angstroms compaction transition. A better understanding of the role of specific tertiary contacts in compaction was obtained by concordant time-resolved hydroxyl radical (OH) analyses that report local changes in the solvent accessibility of the RNA backbone. Comparison of the global and local measures of folding shows that formation of a subset of native tertiary contacts (i.e. those defining the ribozyme core) can occur within a highly compact ensemble whose R(g) is close to that of the fully folded ribozyme. Analyses of additional ribozyme mutants and reaction conditions establish the generality of the rapid formation of a partially collapsed state with little to no detectable tertiary structure. These studies directly link global RNA compaction with formation of tertiary structure as the molecule acquires its biologically active structure, and underscore the strong dependence on salt of both local and global measures of folding kinetics.

Time-Resolved Infrared Spectroscopy of RNA Folding

We introduce time-resolved infrared spectroscopy as a powerful method to study the kinetics of RNA folding and unfolding transitions. A laser-induced temperature jump is used to initiate a perturbation in the RNA structure. A probe laser, tuned to a specific infrared absorption of the RNA, is then used to monitor the subsequent relaxation kinetics. A 10-ns pump pulse permits the investigation of fast, nanosecond events. In this work we probe two vibrational transitions, one at 1620cm−1 and one at 1661cm−1. The former transition reports mainly on the dynamics of A and U interactions, the latter is attributed to mainly G and C interactions. Our results reveal three distinct kinetic phases for each vibrational transition probed. We propose two models to describe the data. In one mechanism, the unfolded state partitions into two separate populations; each is conformationally biased to proceed via one of two distinct pathways. In an alternative model, folding proceeds through a series of sequentially populated intermediates. In both cases, the first step in the proposed folding mechanism is rate limiting (hundreds of microseconds) and involves a collapse into incorrectly folded intermediate populations. Two faster kinetic phases (tens of microseconds and hundreds of nanoseconds) follow in which the intermediate populations undergo localized reorganizational motions in the search for native contacts.

A complex adaptive systems approach to the kinetic folding of RNA

The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence-to-structure mapping are discussed.