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

Sequence-Dependent Melting and Refolding Dynamics of RNA UNCG Tetraloops Using Temperature-Jump/Drop Infrared Spectroscopy

Time-resolved temperature-jump/drop infrared (IR) spectroscopy has been used to measure the impact of stem base sequence on the melting and refolding dynamics of ribonucleic acid (RNA) tetraloops. A series of three 12-nucleotide RNA hairpin sequences were studied, each featuring a UACG tetraloop motif and a double-stranded stem containing four base pairs. In each case, the stem comprised three GC pairs plus a single AU base pair inserted at the closing point of the loop (RNA_loop), in the middle of the stem (RNA_mid), or at the stem terminus (RNA_end). Results from analogous DNA tetraloop (TACG) sequences were also obtained. Inclusion of AU or AT base pairs in the stem leads to faster melting of the stem-loop structure compared to a stem sequence featuring four GC base pairs while refolding times were found to be slower, consistent with a general reduction in stem-loop stability caused by the AU/AT pair. Independent measurement of the dynamic timescales for melting and refolding of ring vibrational modes of guanine (G_R) and adenine (A_R) provided position-specific insight into hairpin dynamics. The G_R-derived data showed that DNA sequences melted more quickly (0.5 ± 0.1 to 0.7 ± 0.1 μs at 70 °C) than analogous RNA sequences (4.3 ± 0.4 to 4.4 ± 0.3 μs at 70 °C). Position-sensitive data from the A_R modes suggests that DNA hairpins begin melting from the terminal end of the stem toward the loop while RNA sequences begin melting from the loop. Refolding timescales for both RNA and DNA hairpins were found to be similar (250 ± 50 μs at 70 °C) except for RNA_end and DNA_loop which refolded much more slowly (746 ± 36 and 430 ± 31 μs, respectively), showing that the refolding pathway is significantly impaired by the placement of AU/AT pairs at different points in the stem. We conclude that conformational changes of analogous pairs of RNA and DNA tetraloops proceed by different mechanisms.

Measuring RNA UNCG Tetraloop Refolding Dynamics Using Temperature-Jump/Drop Infrared Spectroscopy

Determining the structural dynamics of RNA and DNA is essential to understanding their cellular function, but direct measurement of strand association or folding remains experimentally challenging. Here we illustrate a temperature-jump/drop method able to reveal refolding dynamics. Time-resolved temperature-jump/drop infrared spectroscopy is used to measure the melting and refolding dynamics of a 12-nucleotide RNA sequence comprising a UACG tetraloop and a four-base-pair double-stranded GC stem, comparing them to an equivalent DNA (TACG) sequence. Stem-loop melting occurred an order of magnitude more slowly in RNA than DNA (6.0 ± 0.1 μs versus 0.8 ± 0.1 μs at 70 °C). In contrast, the refolding dynamics of both sequences occurred on similar time scales (200 μs). While the melting and refolding dynamics of RNA and DNA hairpins both followed Arrhenius temperature dependences, refolding was characterized by an apparent negative activation energy, consistent with a mechanism involving multiple misfolded intermediates prior to zipping of the stem base pairs.

RAFFT: Efficient prediction of RNA folding pathways using the fast Fourier transform

We propose a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. This heuristic is inspired by the kinetic partitioning mechanism, by which molecules follow alternative folding pathways to their native structure, some much faster than others. Similarly, our algorithm RAFFT starts by generating an ensemble of concurrent folding pathways ending in multiple metastable structures, which is in contrast with traditional thermodynamic approaches that find single structures with minimal free energies. When we constrained the algorithm to predict only 50 structures per sequence, near-native structures were found for RNA molecules of length ≤ 200 nucleotides. Our heuristic has been tested on the coronavirus frameshifting stimulation element (CFSE): an ensemble of 68 distinct structures allowed us to produce complete folding kinetic trajectories, whereas known methods require evaluating millions of sub-optimal structures to achieve this result. Thanks to the fast Fourier transform on which RAFFT (RNA folding Algorithm wih Fast Fourier Transform) is based, these computations are efficient, with complexity O ( L 2logL ).

The cotranscriptional folding landscape for two cyclic di-nucleotide-sensing riboswitches with highly homologous aptamer domains acting either as ON- or OFF-switches

Riboswitches are gene regulatory elements located in untranslated mRNA regions. They bind inducer molecules with high affinity and specificity. Cyclic-di-nucleotide-sensing riboswitches are major regulators of genes for the environment, membranes and motility (GEMM) of bacteria. Up to now, structural probing assays or crystal structures have provided insight into the interaction between cyclic-di-nucleotides and their corresponding riboswitches. ITC analysis, NMR analysis and computational modeling allowed us to gain a detailed understanding of the gene regulation mechanisms for the Cd1 (Clostridium difficile) and for the pilM (Geobacter metallireducens) riboswitches and their respective di-nucleotides c-di-GMP and c-GAMP. Binding capability showed a 25 nucleotide (nt) long window for pilM and a 61 nt window for Cd1. Within this window, binding affinities ranged from 35 μM to 0.25 μM spanning two orders of magnitude for Cd1 and pilM showing a strong dependence on competing riboswitch folds. Experimental results were incorporated into a Markov simulation to further our understanding of the transcriptional folding pathways of riboswitches. Our model showed the ability to predict riboswitch gene regulation and its dependence on transcription speed, pausing and ligand concentration.

Landscape Zooming toward the Prediction of RNA Cotranscriptional Folding

RNA molecules fold as they are transcribed. Cotranscriptional folding of RNA plays a critical role in RNA functions in vivo. Present computational strategies focus on simulations where large structural changes may not be completely sampled. Here, we describe an alternative approach to predicting cotranscriptional RNA folding by zooming in and out of the RNA folding energy landscape. By classifying the RNA structural ensemble into "partitions" based on long, stable helices, we zoom out of the landscape and predict the overall slow folding kinetics from the interpartition kinetic network, and for each interpartition transition, we zoom in on the landscape to simulate the kinetics. Applications of the model to the 117-nucleotide E. coli SRP RNA and the 59-nucleotide HIV-1 TAR RNA show agreements with the experimental data and new structural and kinetic insights into biologically significant conformational switches and pathways for these important systems. This approach, by zooming in/out of an RNA folding landscape at different resolutions, might allow us to treat large RNAs in vivo with transcriptional pause, transcription speed, and other in vivo effects.

Regulation of the ThiM riboswitch is facilitated by the trapped structure formed during transcription of the wild-type sequence

The ThiM riboswitch from Escherichia coli is a typical mRNA device that modulates downstream gene expression by sensing TPP. The helix-based RNA folding theory is used to investigate its detailed regulatory behaviors in cells. This RNA molecule is transcriptionally trapped in a state with the unstructured SD sequence in the absence of TPP, which induces downstream gene expression. As a key step to turn on gene expression, formation of this trapped state (the genetic ON state) highly depends on the co-transcriptional folding of its wild-type sequence. Instead of stabilities of the genetic ON and OFF states, the transcription rate, pause, and ligand levels are combined to affect the ThiM riboswitch-mediated gene regulation, which is consistent with a kinetic control model.

Clusters of hairpins induce intrinsic transcription termination in bacteria

Intrinsic transcription termination (ITT) sites are currently identified by locating single and double-adjacent RNA hairpins downstream of the stop codon. ITTs for a limited number of genes/operons in only a few bacterial genomes are currently known. This lack of coverage is a lacuna in the existing ITT inference methods. We have studied the inter-operon regions of 13 genomes covering all major phyla in bacteria, for which good quality public RNA-seq data exist. We identify ITT sites in 87% of cases by predicting hairpin(s) and validate against 81% of cases for which the RNA-seq derived sites could be calculated. We identify 72% of these sites correctly, with 98% of them located ≤ 80 bases downstream of the stop codon. The predicted hairpins form a cluster (when present < 15 bases) in two-thirds of the cases, the remaining being single hairpins. The largest number of clusters is formed by two hairpins, and the occurrence decreases exponentially with an increasing number of hairpins in the cluster. Our study reveals that hairpins form an effective ITT unit when they act in concert in a cluster. Their pervasiveness along with single hairpin terminators corroborates a wider utilization of ITT mechanisms for transcription control across bacteria.

Thermodynamic and kinetic properties of a single base pair in A-DNA and B-DNA

Double stranded DNA can adopt different forms, the so-called A-, B-, and Z-DNA, which play different biological roles. In this work, the thermodynamic and the kinetic parameters for the base-pair closing and opening in A-DNA and B-DNA were calculated by all-atom molecular dynamics simulations at different temperatures. The thermodynamic parameters of the base pair in B-DNA were in good agreement with the experimental results. The free energy barrier of breaking a single base stack results from the enthalpy increase ΔH caused by the disruption of hydrogen bonding and base-stacking interactions, as well as water and base interactions. The free energy barrier of base pair closing comes from the unfavorable entropy loss ΔS caused by the restriction of torsional angles and hydration. It was found that the enthalpy change ΔH and the entropy change ΔS for the base pair in A-DNA are much larger than those in B-DNA, and the transition rates between the opening and the closing state for the base pair in A-DNA are much slower than those in B-DNA. The large difference of the enthalpy and entropy change for forming the base pair in A-DNA and B-DNA results from different hydration in A-DNA and B-DNA. The hydration pattern observed around DNA is an accompanying process for forming the base pair, rather than a follow-up of the conformation.

Ligand-dependent tRNA processing by a rationally designed RNase P riboswitch

We describe a synthetic riboswitch element that implements a regulatory principle which directly addresses an essential tRNA maturation step. Constructed using a rational in silico design approach, this riboswitch regulates RNase P-catalyzed tRNA 5′-processing by either sequestering or exposing the single-stranded 5′-leader region of the tRNA precursor in response to a ligand. A single base pair in the 5′-leader defines the regulatory potential of the riboswitch both in vitro and in vivo. Our data provide proof for prior postulates on the importance of the structure of the leader region for tRNA maturation. We demonstrate that computational predictions of ligand-dependent structural rearrangements can address individual maturation steps of stable non-coding RNAs, thus making them amenable as promising target for regulatory devices that can be used as functional building blocks in synthetic biology.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Effects of flanking regions on HDV cotranscriptional folding kinetics

Hepatitis delta virus (HDV) ribozyme performs the self-cleavage activity through folding to a double pseudoknot structure. The folding of functional RNA structures is often coupled with the transcription process. In this work, we developed a new approach for predicting the cotranscriptional folding kinetics of RNA secondary structures with pseudoknots. We theoretically studied the cotranscriptional folding behavior of the 99-nucleotide (nt) HDV sequence, two upstream flanking sequences, and one downstream flanking sequence. During transcription, the 99-nt HDV can effectively avoid the trap intermediates and quickly fold to the cleavage-active state. It is different from its refolding kinetics, which folds into an intermediate trap state. For all the sequences, the ribozyme regions (from 1 to 73) all fold to the same structure during transcription. However, the existence of the 30-nt upstream flanking sequence can inhibit the ribozyme region folding into the active native state through forming an alternative helix Alt1 with the segments 70-90. The longer upstream flanking sequence of 54 nt itself forms a stable hairpin structure, which sequesters the formation of the Alt1 helix and leads to rapid formation of the cleavage-active structure. Although the 55-nt downstream flanking sequence could invade the already folded active structure during transcription by forming a more stable helix with the ribozyme region, the slow transition rate could keep the structure in the cleavage-active structure to perform the activity.

Predicting Cotranscriptional Folding Kinetics For Riboswitch

On the basis of a helix-based transition rate model, we developed a new method for sampling cotranscriptional RNA conformational ensemble and the prediction of cotranscriptional folding kinetics. Applications to E. coli. SRP RNA and pbuE riboswitch indicate that the model may provide reliable predictions for the cotranscriptional folding pathways and population kinetics. For E. coli. SRP RNA, the predicted population kinetics and the folding pathway are consistent with the SHAPE profiles in the recent cotranscriptional SHAPE-seq experiments. For the pbuE riboswitch, the model predicts the transcriptional termination efficiency as a function of the force. The theoretical results show (a) a force-induced transition from the aptamer (antiterminator) to the terminator structure and (b) the different folding pathways for the riboswitch with and without the ligand (adenine). More specifically, without adenine, the aptamer structure emerges as a short-lived kinetic transient state instead of a thermodynamically stable intermediate state. Furthermore, from the predicted extension-time curves, the model identifies a series of conformational switches in the pulling process, where the predicted relative residence times for the different structures are in accordance with the experimental data. The model may provide a new tool for quantitative predictions of cotranscriptional folding kinetics, and results can offer useful insights into cotranscriptional folding-related RNA functions such as regulation of gene expression with riboswitches.

A Model for Viral Assembly around an Explicit RNA Sequence Generates an Implicit Fitness Landscape

Previously, a stochastic model of single-stranded RNA virus assembly was created to model the cooperative effects between capsid proteins and genomic RNA that would occur in a packaging signal-mediated assembly process. In such an assembly scenario, multiple secondary structural elements from within the RNA, termed "packaging signals" (PS), contact coat proteins and facilitate efficient capsid assembly. In this work, the assembly model is extended to incorporate explicit nucleotide sequence information as well as simple aspects of RNA folding that would be occurring during the RNA/capsid coassembly process. Applying this paradigm to a dodecahedral viral capsid, a computer-derived nucleotide sequence is evolved de novo that is optimal for packaging the RNA into capsids, while also containing capacity for coding for a viral protein. Analysis of the effects of mutations on the ability of the RNA sequence to successfully package into a viral capsid reveals a complex fitness landscape where the majority of mutations are neutral with respect to packaging efficiency with a small number of mutations resulting in a near-complete loss of RNA packaging. Moreover, the model shows how attempts to ablate PSs in the viral RNA sequence may result in redundant PSs already present in the genome fulfilling their packaging role. This explains why recent experiments that attempt to ablate putative PSs may not see an effect on packaging. This modeling framework presents an example of how an implicit mapping can be made from genotype to a fitness parameter important for viral biology, i.e., viral capsid yield, with potential applications to theoretical models of viral evolution.

Reversible-Switch Mechanism of the SAM-III Riboswitch

Riboswitches are self-regulatory elements located at the 5' untranslated region of certain mRNAs. The Enterococcus faecalis SAM-III (S_MK) riboswitch regulates downstream gene expression through conformational change by sensing S-adenosylmethionine (SAM) at the translation level. Using the recently developed systematic helix-based computational method, we studied the co-transcriptional folding behavior of the S_MK riboswitch and its shortened construct lacking the first six nucleotides. We find that there are no obvious misfolded structures formed during the transcription and refolding processes for this riboswitch. The full-length riboswitch quickly folds into the ON-state in the absence of SAM, and the coupling between transcription and translation is not required for the riboswitch to function. The potential to form helix P0 is necessary for the riboswitch to function as a switch. For this thermodynamically controlled reversible riboswitch, the fast helix-exchanging transition pathway between the two functional structures guaranteed that this riboswitch can act as a reversible riboswitch.

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.

Design criteria for synthetic riboswitches acting on transcription

Riboswitches are RNA-based regulators of gene expression composed of a ligand-sensing aptamer domain followed by an overlapping expression platform. The regulation occurs at either the level of transcription (by formation of terminator or antiterminator structures) or translation (by presentation or sequestering of the ribosomal binding site). Due to a modular composition, these elements can be manipulated by combining different aptamers and expression platforms and therefore represent useful tools to regulate gene expression in synthetic biology. Using computationally designed theophylline-dependent riboswitches we show that 2 parameters, terminator hairpin stability and folding traps, have a major impact on the functionality of the designed constructs. These have to be considered very carefully during design phase. Furthermore, a combination of several copies of individual riboswitches leads to a much improved activation ratio between induced and uninduced gene activity and to a linear dose-dependent increase in reporter gene expression. Such serial arrangements of synthetic riboswitches closely resemble their natural counterparts and may form the basis for simple quantitative read out systems for the detection of specific target molecules in the cell.

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.

De novo design of heat-repressible RNA thermosensors in E. coli

RNA-based temperature sensing is common in bacteria that live in fluctuating environments. Most naturally-occurring RNA thermosensors are heat-inducible, have long sequences, and function by sequestering the ribosome binding site in a hairpin structure at lower temperatures. Here, we demonstrate the de novo design of short, heat-repressible RNA thermosensors. These thermosensors contain a cleavage site for RNase E, an enzyme native to Escherichia coli and many other organisms, in the 5′ untranslated region of the target gene. At low temperatures, the cleavage site is sequestered in a stem–loop, and gene expression is unobstructed. At high temperatures, the stem–loop unfolds, allowing for mRNA degradation and turning off expression. We demonstrated that these thermosensors respond specifically to temperature and provided experimental support for the central role of RNase E in the mechanism. We also demonstrated the modularity of these RNA thermosensors by constructing a three-input composite circuit that utilizes transcriptional, post-transcriptional, and post-translational regulation. A thorough analysis of the 24 thermosensors allowed for the development of design guidelines for systematic construction of similar thermosensors in future applications. These short, modular RNA thermosensors can be applied to the construction of complex genetic circuits, facilitating rational reprogramming of cellular processes for synthetic biology applications.

Effect of loop composition on the stability and folding kinetics of RNA hairpins with large loops

RNA hairpins are ubiquitous structural elements in biological RNAs, where they have the potential to regulate RNA folding and interactions with other molecules. There are established methods for predicting the thermodynamic stability of an RNA hairpin, but there are still relatively few detailed examinations of the kinetics of folding. Nonetheless, several recent studies indicate that hairpin folding does not proceed via a simple two-state model. Here, we monitor fluorescence from hairpins constructed as molecular beacons in ensemble, fluorescence correlation spectroscopy, and stopped-flow experiments to describe the folding of RNA hairpins with long (15 nucleotide) loops. Our results show that folding of these hairpins occurs through more than two states and that the mechanism of folding includes a fast intermediate phase observed on the tens of microseconds time scale and a slow phase, attributed to formation of the native folded hairpin loop and stem, observed on the milliseconds time scale. The composition of the RNA loop determines the time scale of intermediate and native folded states. Hairpins with a polyuracil loop sequence exhibit slower relaxation of the intermediate state and faster relaxation of the native folded state when compared to that of hairpins with cytosine or adenine in the loop. We hypothesize this composition dependence could be attributed to nucleobase stacking in cytosine and adenine containing regions of the loop, which would be absent in hairpins containing polyuracil loops. Such base stacking could destabilize the intermediate folds, thereby speeding the relaxation of the intermediate relative to similar sized hairpins with no base stacking in the loop. Likewise, the lower intermediate stability could prolong the relaxation of the native folded state.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Counterion and polythymidine loop-length-dependent folding and thermodynamic stability of DNA hairpins reveal the unusual counterion-dependent stability of tetraloop hairpins

Stem-loop DNA hairpins containing a 5-base-pair (bp) stem and single-stranded polythymidine loop were investigated using thermodynamic melting analysis and stopped-flow kinetics. These studies revealed the thermodynamic stability and folding kinetics as a function of loop length and counterion concentration. Our results show the unusually high thermodynamic stability for tetraloop or 4 poly(dT) loop hairpin as compared with longer loop length hairpins. Furthermore, this exceptional stability is highly counterion-dependent. For example, in the higher counterion concentration regime of 50 mM NaCl and above, the tetraloop hairpin displays enhanced stability as compared with longer loop length hairpins. However, at lower counterion concentration of 25 mM NaCl and below, the thermal stability of tetraloop hairpin is consistent with the longer loop hairpins. The enhanced stability of tetraloop hairpins at higher counterion concentration can be explained on the basis of the combined entropic effect of loop closure as well as base stacking in the loop regions. The stability of longer loop length hairpins at all counterion concentrations as well as tetraloop hairpin at lower counterion concentration can be explained on the basis of entropic effect of loop closure alone. The thermodynamic parameters at lower and higher counterion concentrations were determined to quantify the enhanced stability of base-stacking effects occurring at higher counterion concentrations. For example, for 100 mM NaCl, excess Gibbs energy and enthalpy due to base stacking within the tetraloops were measured to be -1.2 ± 0.14 and -3.28 ± 0.32 kcal/mol, respectively, whereas, no excess of Gibbs energy and enthalpy was observed for 0, 5, 10, and 25 mM NaCl. These findings suggest significant base-stacking interactions occurring in the loop region of the tetraloop hairpins at higher counterion concentration and less significant base-stacking interactions in the lower counterion concentration regime. We suggest that at higher counterion concentrations, hydrophobic collapse of the nucleotides in the loop may be enhanced due to the increased polarity of the solvent, thereby enhancing base-stacking interactions that contribute to unusually high stability.

Modeling stopped-flow data for nucleic acid duplex formation reactions: the importance of off-path intermediates

Evidence for unexpected off-path intermediates to DNA duplex formation is presented. These off-path intermediates are shown to involve unimolecular and, in one case, bimolecular structure in one of the single strands of complementary DNA. Three models are developed to account for the observed single-stranded structures that are formed in parallel with duplex formation. These models are applied to the analysis of stopped-flow data for eight different nonself-complementary duplex formation reactions in order to extract the elementary rate constant for formation of the duplex from the complementary random coil single-stranded DNA. The free energy of activation (at 25 °C) for the denaturation of each duplex is calculated from these data and is shown to have a linear correlation to the overall standard free energy for duplex formation (also at 25 °C). Duplexes that contain mismatches obey a parallel linear free-energy (LFE) relationship with a y-intercept that is greater than that of duplexes without mismatches. Slopes near unity for the LFE relationships indicate that all duplexes go through an early, unstructured transition state.

The impact of a ligand binding on strand migration in the SAM-I riboswitch

Riboswitches sense cellular concentrations of small molecules and use this information to adjust synthesis rates of related metabolites. Riboswitches include an aptamer domain to detect the ligand and an expression platform to control gene expression. Previous structural studies of riboswitches largely focused on aptamers, truncating the expression domain to suppress conformational switching. To link ligand/aptamer binding to conformational switching, we constructed models of an S-adenosyl methionine (SAM)-I riboswitch RNA segment incorporating elements of the expression platform, allowing formation of an antiterminator (AT) helix. Using Anton, a computer specially developed for long timescale Molecular Dynamics (MD), we simulated an extended (three microseconds) MD trajectory with SAM bound to a modeled riboswitch RNA segment. Remarkably, we observed a strand migration, converting three base pairs from an antiterminator (AT) helix, characteristic of the transcription ON state, to a P1 helix, characteristic of the OFF state. This conformational switching towards the OFF state is observed only in the presence of SAM. Among seven extended trajectories with three starting structures, the presence of SAM enhances the trend towards the OFF state for two out of three starting structures tested. Our simulation provides a visual demonstration of how a small molecule (<500 MW) binding to a limited surface can trigger a large scale conformational rearrangement in a 40 kDa RNA by perturbing the Free Energy Landscape. Such a mechanism can explain minimal requirements for SAM binding and transcription termination for SAM-I riboswitches previously reported experimentally.

Kinetics and thermodynamics of DNA, RNA, and hybrid duplex formation

The rates of duplex formation for two octamers of DNA (5' d-CACGGCTC/5' d-GAGCCGTG and 5' d-CACAGCAC/5' d-GTGCTGTG), the homologous RNA, and both sets of hybrids in 1 M NaCl buffer have been measured using stopped-flow spectroscopy. In addition, the thermodynamic parameters, ΔH° and ΔS°, have been determined for the same sequences under the same buffer conditions using optical melting techniques. These data reveal a linear free energy relationship between the free energy of activation for denaturation and the change in free energy for formation of the duplexes. This relationship indicates that these duplex formation reactions occur through a common unstructured transition state that is more similar to the single strands in solution than to the ensuing duplex. In addition, these data confirm that the greater stability of RNA duplexes relative to that of homologous DNA and hybrid duplexes is controlled by the denaturation rate and not the duplex formation rate.

Kinetic mechanism of conformational switch between bistable RNA hairpins

Transitions between the different conformational states play a critical role in many RNA catalytic and regulatory functions. In this study, we use the Kinetic Monte Carlo method to investigate the kinetic mechanism for the conformational switches between bistable RNA hairpins. We find three types of conformational switch pathways for RNA hairpins: refolding after complete unfolding, folding through basepair-exchange pathways and through pseudoknot-assisted pathways, respectively. The result of the competition between the three types of pathways depends mainly on the location of the rate-limiting base stacks (such as the GC base stacks) in the structures. Depending on the structural relationships between the two bistable hairpins, the conformational switch can follow single or multiple dominant pathways. The predicted folding pathways are supported by the activation energy results derived from the Arrhenius plot as well as the NMR spectroscopy data.

Cotranscriptional folding kinetics of ribonucleic acid secondary structures

We develop a systematic helix-based computational method to predict RNA folding kinetics during transcription. In our method, the transcription is modeled as stepwise process, where each step is the transcription of a nucleotide. For each step, the kinetics algorithm predicts the population kinetics, transition pathways, folding intermediates, and the transcriptional folding products. The folding pathways, rate constants, and the conformational populations for cotranscription folding show contrastingly different features than the refolding kinetics for a fully transcribed chain. The competition between the transcription speed and rate constants for the transitions between the different nascent structures determines the RNA folding pathway and the end product of folding. For example, fast transcription favors the formation of branch-like structures than rod-like structures and chain elongation in the folding process may reduce the probability of the formation of misfolded structures. Furthermore, good theory-experiment agreements suggest that our method may provide a reliable tool for quantitative prediction for cotranscriptional RNA folding, including the kinetics for the population distribution for the whole conformational ensemble.

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

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

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.

TRANSAT-- method for detecting the conserved helices of functional RNA structures, including transient, pseudo-knotted and alternative structures

The prediction of functional RNA structures has attracted increased interest, as it allows us to study the potential functional roles of many genes. RNA structure prediction methods, however, assume that there is a unique functional RNA structure and also do not predict functional features required for in vivo folding. In order to understand how functional RNA structures form in vivo, we require sophisticated experiments or reliable prediction methods. So far, there exist only a few, experimentally validated transient RNA structures. On the computational side, there exist several computer programs which aim to predict the co-transcriptional folding pathway in vivo, but these make a range of simplifying assumptions and do not capture all features known to influence RNA folding in vivo. We want to investigate if evolutionarily related RNA genes fold in a similar way in vivo. To this end, we have developed a new computational method, Transat, which detects conserved helices of high statistical significance. We introduce the method, present a comprehensive performance evaluation and show that Transat is able to predict the structural features of known reference structures including pseudo-knotted ones as well as those of known alternative structural configurations. Transat can also identify unstructured sub-sequences bound by other molecules and provides evidence for new helices which may define folding pathways, supporting the notion that homologous RNA sequence not only assume a similar reference RNA structure, but also fold similarly. Finally, we show that the structural features predicted by Transat differ from those assuming thermodynamic equilibrium. Unlike the existing methods for predicting folding pathways, our method works in a comparative way. This has the disadvantage of not being able to predict features as function of time, but has the considerable advantage of highlighting conserved features and of not requiring a detailed knowledge of the cellular environment.

Many non-coding genes exert their function via an RNA structure which starts emerging while the RNA sequence is being transcribed from the genome. The resulting folding pathway is known to depend on a variety of features such as the transcription speed, the concentration of various ions and the binding of proteins and other molecules. Not all of these influences can be adequately captured by the existing computational methods which try to replicate what happens in vivo. So far, it has been challenging to experimentally investigate co-transcriptional folding pathways in vivo and only little data from in vitro experiments exists. In order to investigate if functionally similar RNA sequences from different organisms fold in a similar way, we have developed a new computational method, called Transat, which does not require the detailed computational modeling of the cellular environment. We show in a comprehensive analysis that our method is capable of detecting known structural features and provide evidence that structural features of the in vivo folding pathways have been conserved for several biologically interesting classes of RNA sequences.

Predicting secondary structural folding kinetics for nucleic acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.

Predicting loop-helix tertiary structural contacts in RNA pseudoknots

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop-stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop-stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop-stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory-experimental comparisons. These comparisons reveal a contact enthalpy (DeltaH) of -14 kcal/mol and a contact entropy (DeltaS) of -38 cal/mol/K for a protonated C(+)*(G-C) base triple at pH 7.0, and (DeltaH = -7 kcal/mol, DeltaS = -19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory-experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop-stem tertiary contacts from the nucleotide sequence alone.

Perturbation-based Markovian transmission model for probing allosteric dynamics of large macromolecular assembling: a study of GroEL-GroES

Large macromolecular assemblies are often important for biological processes in cells. Allosteric communications between different parts of these molecular machines play critical roles in cellular signaling. Although studies of the topology and fluctuation dynamics of coarse-grained residue networks can yield important insights, they do not provide characterization of the time-dependent dynamic behavior of these macromolecular assemblies. Here we develop a novel approach called Perturbation-based Markovian Transmission (PMT) model to study globally the dynamic responses of the macromolecular assemblies. By monitoring simultaneous responses of all residues (>8,000) across many (>6) decades of time spanning from the initial perturbation until reaching equilibrium using a Krylov subspace projection method, we show that this approach can yield rich information. With criteria based on quantitative measurements of relaxation half-time, flow amplitude change, and oscillation dynamics, this approach can identify pivot residues that are important for macromolecular movement, messenger residues that are key to signal mediating, and anchor residues important for binding interactions. Based on a detailed analysis of the GroEL-GroES chaperone system, we found that our predictions have an accuracy of 71-84% judged by independent experimental studies reported in the literature. This approach is general and can be applied to other large macromolecular machineries such as the virus capsid and ribosomal complex.

Mechanism of RNA double helix-propagation at atomic resolution

The conversion of a nucleic acid from single strands to double strands is thought to involve slow nucleation followed by fast double-strand propagation. Here, for RNA double-strand propagation, we propose an atomic resolution reaction mechanism. This mechanism, called the stack-ratchet, is based on data-mining of three-dimensional structures and on available thermodynamic information. The stack-ratchet mechanism extends and adds detail to the classic zipper model proposed by Porschke (Porschke, D. Biophysical Chemistry 1974, 2, pp. 97-101). Porschke's zipper model describes the addition of a base pair to a nucleated helix in terms of a single type of elementary reaction; a concerted process in which the two bases, one from each strand, participate in the transition state. In the stack-ratchet mechanism proposed here a net base-pairing step consists of two elementary reactions. Motions of only one strand are required to achieve a given transition state. One elementary reaction preorganizes and stacks the 3' single-strand, driven by base--base stacking interactions. A second elementary reaction stacks the 5' strand and pairs it with the preorganized 3' strand. In the stack-ratchet mechanism, a variable length 3' stack leads the single-strand/double-strand junction. The stack-ratchet mechanism is not a two-state process. A base can be (i) unstacked and unpaired, (ii) stacked and paired, or (ii) stacked and unpaired (only on the 3' strand). The data suggests that helices of DNA and of RNA do not propagate by similar mechanisms.

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.

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.

Perturbation-based Markovian Transmission Model for macromolecular machinery in cell

The study of the dynamics of a complex system is an important problem that includes large macromolecular complexes, molecular interaction networks, and cell functional modules. Large macromolecular complexes in cellular machinery can be modeled as a connected network, as in the elastic or Gaussian network models as demonstrated by Bahar and colleagues. Here we propose the Perturbation-based Markovian Transmission Model for studying the dynamics of signal transmission in macromolecular machinery. The initial perturbation is transmitted by a Markovian processes, and the dynamics of the probability flow is analytically solved using the master equation. Due to the large size of macromolecular complexes, it is very difficult to obtain analytical time-dependent Markovian dynamics of all atoms from the first perturbation until stationary state. To overcome it, we decrease the level of complexity of the transition matrix using a Krylov subspace method. This method is equivalent to integrating all eigen modes, and we show it can provide a globally accurate solution to the dynamics problem of signal transmission for very large macromolecular complexes with reasonable computational time. We give results of the dynamics of the GroEL-GroES chaperone system by applying uniform perturbation to all residues. We are able to identify experimentally found important residues and provide a set of predicted pivot, messenger, and effector residues, each with distinct dynamic behavior. Further results of selective perturbation on the surface of ATP binding pocket identifies the path of maximal probability flow of signal.

Salt dependence of nucleic acid hairpin stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na(+) and Mg(2+) in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na(+) and Mg(2+) concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.