Predicting secondary structural folding kinetics for nucleic acids

Effect of pausing on the cotranscriptional folding kinetics of RNAs

The pausing event in RNA molecule folding that occurs during the cotranscription process plays a critical role in cellular RNA function. Based on Conformational Resampling through Kinetic Relaxation (CRKR), this paper investigates a method to reveal the specifics of pausing for RNA cotranscriptional folding of 117-nucleotide E. coli SRP RNA and 73-nucleotide HIV-1 TAR RNA. It can be inferred from the results that pausing events generate valid cotranscriptional conformational rearrangement to protect the function structures and influence the folding pathway, which is remarkably consistent with the experimental results. Additionally, different transcription speeds result in different levels of protection capability. The folding pathway or conformational rearrangement can also be affected by a change in transcription speed after pausing site. These findings illuminate that RNAs with functional structures undergo complex rearrangement folding in pausing events, and different RNAs prefer different speeds for specific folding pathways. Moreover, pausing in particular circumstances can be employed to regulate the population of final functional structures. In conclusion, this paper offers fresh perspectives on the pausing event in the cotranscriptional folding of RNAs.

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.

Salt effect on thermodynamics and kinetics of a single RNA base pair

Due to the polyanionic nature of RNAs, the structural folding of RNAs are sensitive to solution salt conditions, while there is still lack of a deep understanding of the salt effect on the thermodynamics and kinetics of RNAs at a single base-pair level. In this work, the thermodynamic and the kinetic parameters for the base-pair AU closing/opening at different salt concentrations were calculated by 3-µsec all-atom molecular dynamics (MD) simulations at different temperatures. It was found that for the base-pair formation, the enthalpy change [Formula: see text] is nearly independent of salt concentration, while the entropy change [Formula: see text] exhibits a linear dependence on the logarithm of salt concentration, verifying the empirical assumption based on thermodynamic experiments. Our analyses revealed that such salt concentration dependence of the entropy change mainly results from the dependence of ion translational entropy change for the base pair closing/opening on salt concentration. Furthermore, the closing rate increases with the increasing of salt concentration, while the opening rate is nearly independent of salt concentration. Additionally, our analyses revealed that the free energy surface for describing the base-pair opening and closing dynamics becomes more rugged with the decrease of salt concentration.

Regulation of the thiamine pyrophosphate (TPP)-sensing riboswitch in NMT1 mRNA from Neurospora crassa

The expression of Neurospora crassa NMT1 involved in thiamine pyrophosphate (TPP) metabolism is regulated at the level of mRNA splicing by a TPP-sensing riboswitch within the precursor NMT1 mRNA. Here, using the systematic helix-based computational method, we investigated the regulation of this riboswitch. We find that the function of the riboswitch does not depend on the transcription process. Whether TPP is present or not, the riboswitch predominately folds into the ON state, while the OFF state aptamer structure does not appear during transcription. Since the transition from the ON state to the aptamer structure is extremely slow, TPP may interact with the RNA before full formation of the aptamer structure, promoting the switch flipping. The potential to fully form helix P0 of the ON state is necessary to restore ligand-dependent gene control by the riboswitch.

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.

Computational approaches for alternative and transient secondary structures of ribonucleic acids

Transient and alternative structures of ribonucleic acids (RNAs) play essential roles in various regulatory processes, such as translation regulation in living cells. Because experimental analyses for RNA structures are difficult and time-consuming, computational approaches based on RNA secondary structures are promising. In this article, we review computational methods for detecting and analyzing transient/alternative secondary structures of RNAs, including static approaches based on probabilistic distributions of RNA secondary structures and dynamic approaches such as kinetic folding and folding pathway predictions.

Stem-Loop RNA Hairpins in Giant Viruses: Invading rRNA-Like Repeats and a Template Free RNA

We examine the hypothesis that de novo template-free RNAs still form spontaneously, as they did at the origins of life, invade modern genomes, contribute new genetic material. Previously, analyses of RNA secondary structures suggested that some RNAs resembling ancestral (t)RNAs formed recently de novo, other parasitic sequences cluster with rRNAs. Here positive control analyses of additional RNA secondary structures confirm ancestral and de novo statuses of RNA grouped according to secondary structure. Viroids with branched stems resemble de novo RNAs, rod-shaped viroids resemble rRNA secondary structures, independently of GC contents. 5' UTR leading regions of West Nile and Dengue flavivirid viruses resemble de novo and rRNA structures, respectively. An RNA homologous with Megavirus, Dengue and West Nile genomes, copperhead snake microsatellites and levant cotton repeats, not templated by Mimivirus' genome, persists throughout Mimivirus' infection. Its secondary structure clusters with candidate de novo RNAs. The saltatory phyletic distribution and secondary structure of Mimivirus' peculiar RNA suggest occasional template-free polymerization of this sequence, rather than noncanonical transcriptions (swinger polymerization, posttranscriptional editing).

Genetic regulation mechanism of the yjdF riboswitch

The yjdF riboswitch resides in potential 5' UTRs of homologues of protein-coding gene yjdF in Firmicutes. Unlike other 30 riboswitch classes previously validated, this riboswitch class, can sense and bind to a broad collection of azaaromatic ligands. Among these compounds, some do activate production of yjdF protein driven by the riboswitch, while others are out of riboswitch-mediated modulation possibly because of the toxicity at high ligand concentrations. By incorporating the structures with pseudoknots and ligand binding kinetics into the co-transcriptional folding theory, we theoretically studied the co-transcriptional folding behaviors of the yjdF riboswitch from Bacillus subtilis at different transcription conditions. Like most riboswitches, the yjdF riboswitch can quickly fold into the aptamer structure without any trapped states during the transcription process. After the aptamer structure is formed, the riboswitch shows two main co-transcriptional folding pathways: aptamer→ON state→OFF state and aptamer → the ligand bound aptamer → the ligand bound ON state. Our results suggested that this translational riboswitch is coupled with the transcription process to exert its biological function and it is kinetically controlled. The threshold concentration for the ligand to activate the riboswitch depends on the transcription rate and the association rate of the ligand binding.

Computational Methods for Modeling Aptamers and Designing Riboswitches

Riboswitches, which are located within certain noncoding RNA region perform functions as genetic "switches", regulating when and where genes are expressed in response to certain ligands. Understanding the numerous functions of riboswitches requires computation models to predict structures and structural changes of the aptamer domains. Although aptamers often form a complex structure, computational approaches, such as RNAComposer and Rosetta, have already been applied to model the tertiary (three-dimensional (3D)) structure for several aptamers. As structural changes in aptamers must be achieved within the certain time window for effective regulation, kinetics is another key point for understanding aptamer function in riboswitch-mediated gene regulation. The coarse-grained self-organized polymer (SOP) model using Langevin dynamics simulation has been successfully developed to investigate folding kinetics of aptamers, while their co-transcriptional folding kinetics can be modeled by the helix-based computational method and BarMap approach. Based on the known aptamers, the web server Riboswitch Calculator and other theoretical methods provide a new tool to design synthetic riboswitches. This review will represent an overview of these computational methods for modeling structure and kinetics of riboswitch aptamers and for designing riboswitches.

Co-Transcriptional Folding and Regulation Mechanisms of Riboswitches

Riboswitches are genetic control elements within non-coding regions of mRNA. These self-regulatory elements have been found to sense a range of small metabolites, ions, and other physical signals to exert regulatory control of transcription, translation, and splicing. To date, more than a dozen riboswitch classes have been characterized that vary widely in size and secondary structure. Extensive experiments and theoretical studies have made great strides in understanding the general structures, genetic mechanisms, and regulatory activities of individual riboswitches. As the ligand-dependent co-transcriptional folding and unfolding dynamics of riboswitches are the key determinant of gene expression, it is important to investigate the thermodynamics and kinetics of riboswitches both in the presence and absence of metabolites under the transcription. This review will provide a brief summary of the studies about the regulation mechanisms of the pbuE, S_MK, yitJ, and metF riboswitches based on the ligand-dependent co-transcriptional folding of the riboswitches.

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.

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.

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.

RNA folding pathways and kinetics using 2D energy landscapes

RNA folding pathways play an important role in various biological processes, such as (i) the hok/sok (host-killing/suppression of killing) system in E. coli to check for sufficient plasmid copy number, (ii) the conformational switch in spliced leader (SL) RNA from Leptomonas collosoma, which controls trans splicing of a portion of the '5 exon, and (iii) riboswitches--portions of the 5' untranslated region of messenger RNA that regulate genes by allostery. Since RNA folding pathways are determined by the energy landscape, we describe a novel algorithm, FFTbor2D, which computes the 2D projection of the energy landscape for a given RNA sequence. Given two metastable secondary structures A, B for a given RNA sequence, FFTbor2D computes the Boltzmann probability p(x, y) = Z(x,y)/Z that a secondary structure has base pair distance x from A and distance y from B. Using polynomial interpolationwith the fast Fourier transform,we compute p(x, y) in O(n(5)) time and O(n(2)) space, which is an improvement over an earlier method, which runs in O(n(7)) time and O(n(4)) space. FFTbor2D has potential applications in synthetic biology, where one might wish to design bistable switches having target metastable structures A, B with favorable pathway kinetics. By inverting the transition probability matrix determined from FFTbor2D output, we show that L. collosoma spliced leader RNA has larger mean first passage time from A to B on the 2D energy landscape, than 97.145% of 20,000 sequences, each having metastable structures A, B. Source code and binaries are freely available for download at http://bioinformatics.bc.edu/clotelab/FFTbor2D. The program FFTbor2D is implemented in C++, with optional OpenMP parallelization primitives.

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.

Molecular dynamics simulation of RNA pseudoknot unfolding pathway

Many biological functions of RNA molecules are related to their pseudoknot structures. It is significant for predicting the structure and function of RNA that learning about the stability and the process of RNA pseudoknot folding and unfolding. The structural features of mouse mammary tumor virus (MMTV) RNA pseudoknot in different ion concentration, the unfolding process of the RNA pseudoknot, and the two hairpin helices that constitute the RNA pseudoknot were studied with all atom molecule dynamics simulation method in this paper. We found that the higher cation concentration can cause structure of the RNA molecules more stable, and ions played an indispensable role in keeping the structure of RNA molecules stable; the unfolding process of hairpin structure was corresponding to the antiprocess of its folding process. The main pathway of pseudoknot unfolding was that the inner base pair opened first, and then, the two helices, which formed the RNA pseudoknot opened decussately, while the folding pathway of the RNA pseudoknot was a helix folding after formation of the other helix. Therefore, the unfolding process of RNA pseudoknot is different from the antiprocess of its folding process, and the unfolding process of each helix in the RNA pseudoknot is similar to the hairpin structure’s unfolding process, which means that both are the unzipping process.

Abstract folding space analysis based on helices

RNA has many pivotal functions especially in the regulation of gene expression by ncRNAs. Identification of their structure is an important requirement for understanding their function. Structure prediction alone is often insufficient for this task, due to algorithmic problems, parameter inaccuracies, and biological peculiarities. Among the latter, there are base modifications, cotranscriptional folding leading to folding traps, and conformational switching as in the case of riboswitches. All these require more in-depth analysis of the folding space. The major drawback, which all methods have to cope with, is the exponential growth of the folding space. Therefore, methods are often limited in the sequence length they can analyze, or they make use of heuristics, sampling, or abstraction. Our approach adopts the abstraction strategy and remedies some problems of existing methods. We introduce a position-specific abstraction based on helices that we term helix index shapes, or hishapes for short. Utilizing a dynamic programming framework, we have implemented this abstraction in the program RNAHeliCes. Furthermore, we developed two hishape-based methods, one for energy barrier estimation, called HiPath, and one for abstract structure comparison, termed HiTed. We demonstrate the superior performance of HiPath compared to other existing methods and the competitive accuracy of HiTed. RNAHeliCes, together with HiPath and HiTed, are available for download at http://www.cyanolab.de/software/RNAHeliCes.htm.

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.

Predicting folding pathways between RNA conformational structures guided by RNA stacks

BACKGROUND

Accurately predicting low energy barrier folding pathways between conformational secondary structures of an RNA molecule can provide valuable information for understanding its catalytic and regulatory functions. Most existing heuristic algorithms guide the construction of folding pathways by free energies of intermediate structures in the next move during the folding. However due to the size and ruggedness of RNA energy landscape, energy-guided search can become trapped in local optima.

RESULTS

In this paper, we propose an algorithm that guides the construction of folding pathways through the formation and destruction of RNA stacks. Guiding the construction of folding pathways by coarse grained movements of RNA stacks can help reduce the search space and make it easier to jump out of local optima. RNAEAPath is able to find lower energy barrier folding pathways between secondary structures of conformational switches and outperforms the existing heuristic algorithms in most test cases.

CONCLUSIONS

RNAEAPath provides an alternate approach for predicting low-barrier folding pathways between RNA conformational secondary structures. The source code of RNAEAPath and the test data sets are available at http://genome.ucf.edu/RNAEAPath.

Approximating the set of local minima in partial RNA folding landscapes

MOTIVATION

We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

RESULTS

The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n(2)Dνlnν), where n is the sequence length, ν is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

Sequence-structure relationships in yeast mRNAs

It is generally accepted that functionally important RNA structure is more conserved than sequence due to compensatory mutations that may alter the sequence without disrupting the structure. For small RNA molecules sequence–structure relationships are relatively well understood. However, structural bioinformatics of mRNAs is still in its infancy due to a virtual absence of experimental data. This report presents the first quantitative assessment of sequence–structure divergence in the coding regions of mRNA molecules based on recently published transcriptome-wide experimental determination of their base paring patterns. Structural resemblance in paralogous mRNA pairs quickly drops as sequence identity decreases from 100% to 85–90%. Structures of mRNAs sharing sequence identity below roughly 85% are essentially uncorrelated. This outcome is in dramatic contrast to small functional non-coding RNAs where sequence and structure divergence are correlated at very low levels of sequence similarity. The fact that very similar mRNA sequences can have vastly different secondary structures may imply that the particular global shape of base paired elements in coding regions does not play a major role in modulating gene expression and translation efficiency. Apparently, the need to maintain stable three-dimensional structures of encoded proteins places a much higher evolutionary pressure on mRNA sequences than on their RNA structures.

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.