Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA

RNA unfolding and folding reactions in physiological conditions can be facilitated by mechanical force one molecule at a time. By using force-measuring optical tweezers, we studied the mechanical unfolding and folding of a hairpin-type pseudoknot in human telomerase RNA in a near-physiological solution, and at room temperature. Discrete two-state folding transitions of the pseudoknot are seen at approximately 10 and approximately 5 piconewtons (pN), with ensemble rate constants of approximately 0.1 sec(-1), by stepwise force-drop experiments. Folding studies of the isolated 5'-hairpin construct suggested that the 5'-hairpin within the pseudoknot forms first, followed by formation of the 3'-stem. Stepwise formation of the pseudoknot structure at low forces are in contrast with the one-step unfolding at high forces of approximately 46 pN, at an average rate of approximately 0.05 sec(-1). In the constant-force folding trajectories at approximately 10 pN and approximately 5 pN, transient formation of nonnative structures were observed, which is direct experimental evidence that folding of both the hairpin and pseudoknot takes complex pathways. Possible nonnative structures and folding pathways are discussed.     

Revisiting higher-order and large-scale chromatin organization

The past several years has seen increasing appreciation for plasticity of higher-level chromatin folding. Four distinct '30nm' chromatin fiber structures have been identified, while new in situ imaging approaches have questioned the universality of 30nm chromatin fibers as building blocks for chromosome folding in vivo. 3C-based approaches have provided a non-microscopic, genomic approach to investigating chromosome folding while uncovering a plethora of long-distance cis interactions difficult to accommodate in traditional hierarchical chromatin folding models. Recent microscopy based studies have suggested complex topologies co-existing within linear interphase chromosome structures. These results call for a reappraisal of traditional models of higher-level chromatin folding.     

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

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

iFoldRNA: three-dimensional RNA structure prediction and folding

Three-dimensional RNA structure prediction and folding is of significant interest in the biological research community. Here, we present iFoldRNA, a novel web-based methodology for RNA structure prediction with near atomic resolution accuracy and analysis of RNA folding thermodynamics. iFoldRNA rapidly explores RNA conformations using discrete molecular dynamics simulations of input RNA sequences. Starting from simplified linear-chain conformations, RNA molecules (<50 nt) fold to native-like structures within half an hour of simulation, facilitating rapid RNA structure prediction. All-atom reconstruction of energetically stable conformations generates iFoldRNA predicted RNA structures. The predicted RNA structures are within 2-5 A root mean squre deviations (RMSDs) from corresponding experimentally derived structures. RNA folding parameters including specific heat, contact maps, simulation trajectories, gyration radii, RMSDs from native state, fraction of native-like contacts are accessible from iFoldRNA. We expect iFoldRNA will serve as a useful resource for RNA structure prediction and folding thermodynamic analyses. AVAILABILITY: http://iFoldRNA.dokhlab.org.     

Thermodynamics and kinetics of the hairpin ribozyme from atomistic folding/unfolding simulations

We report a set of atomistic folding/unfolding simulations for the hairpin ribozyme using a Monte Carlo algorithm. The hairpin ribozyme folds in solution and catalyzes self-cleavage or ligation via a specific two-domain structure. The minimal active ribozyme has been studied extensively, showing stabilization of the active structure by cations and dynamic motion of the active structure. Here, we introduce a simple model of tertiary-structure formation that leads to a phase diagram for the RNA as a function of temperature and tertiary-structure strength. We then employ this model to capture many folding/unfolding events and to examine the transition-state ensemble (TSE) of the RNA during folding to its active “docked” conformation. The TSE is compact but with few tertiary interactions formed, in agreement with single-molecule dynamics experiments. To compare with experimental kinetic parameters, we introduce a novel method to benchmark Monte Carlo kinetic parameters to docking/undocking rates collected over many single molecular trajectories. We find that topology alone, as encoded in a biased potential that discriminates between secondary and tertiary interactions, is sufficient to predict the thermodynamic behavior and kinetic folding pathway of the hairpin ribozyme. This method should be useful in predicting folding transition states for many natural or man-made RNA tertiary structures.     

Analysis of Four-Way Junctions in RNA Structures

RNA secondary structures can be divided into helical regions composed of canonical Watson-Crick and related base pairs, as well as single-stranded regions such as hairpin loops, internal loops, and junctions. These elements function as building blocks in the design of diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze existing RNA four-way junctions in terms of base-pair interactions and 3D configurations. Specifically, we identify nine broad junction families according to coaxial stacking patterns and helical configurations. We find that helices within junctions tend to arrange in roughly parallel and perpendicular patterns and stabilize their conformations using common tertiary motifs such as coaxial stacking, loop-helix interaction, and helix packing interaction. Our analysis also reveals a number of highly conserved base-pair interaction patterns and novel tertiary motifs such as A-minor-coaxial stacking combinations and sarcin/ricin motif variants. Such analyses of RNA building blocks can ultimately help in the difficult task of RNA 3D structure prediction.     

Prediction of RNA pseudoknots using heuristic modeling with mapping and sequential folding

Predicting RNA secondary structure is often the first step to determining the structure of RNA. Prediction approaches have historically avoided searching for pseudoknots because of the extreme combinatorial and time complexity of the problem. Yet neglecting pseudoknots limits the utility of such approaches. Here, an algorithm utilizing structure mapping and thermodynamics is introduced for RNA pseudoknot prediction that finds the minimum free energy and identifies information about the flexibility of the RNA. The heuristic approach takes advantage of the 5' to 3' folding direction of many biological RNA molecules and is consistent with the hierarchical folding hypothesis and the contact order model. Mapping methods are used to build and analyze the folded structure for pseudoknots and to add important 3D structural considerations. The program can predict some well known pseudoknot structures correctly. The results of this study suggest that many functional RNA sequences are optimized for proper folding. They also suggest directions we can proceed in the future to achieve even better results.     

RNA structure: the long and the short of it

The database of RNA structure has grown tremendously since the crystal structure analyses of ribosomal subunits in 2000-2001. During the past year, the trend toward determining the structure of large, complex biological RNAs has accelerated, with the analysis of three intact group I introns, A- and B-type ribonuclease P RNAs, a riboswitch-substrate complex and other structures. The growing database of RNA structures, coupled with efforts directed at the standardization of nomenclature and classification of motifs, has resulted in the identification and characterization of numerous RNA secondary and tertiary structure motifs. Because a large proportion of RNA structure can now be shown to be composed of these recurring structural motifs, a view of RNA as a modular structure built from a combination of these building blocks and tertiary linkers is beginning to emerge. At the same time, however, more detailed analysis of water, metal, ligand and protein binding to RNA is revealing the effect of these moieties on folding and structure formation. The balance between the views of RNA structure either as strictly a construct of preformed building blocks linked in a limited number of ways or as a flexible polymer assuming a global fold influenced by its environment will be the focus of current and future RNA structural biology.     

Mechanical unfoldons as building blocks of maltose-binding protein

Identifying independently folding cores or substructures is important for understanding and assaying the structure, function and assembly of large proteins. Here, we suggest mechanical stability as a criterion to identify building blocks of the 366 amino acid maltose-binding protein (MBP). We find that MBP, when pulled at its termini, unfolds via three (meta-) stable unfolding intermediates. Consequently, the MBP structure consists of four structural blocks (unfoldons) that detach sequentially from the folded structure upon force application. We used cysteine cross-link mutations to characterize the four unfoldons structurally. We showed that many MBP constructs composed of those building blocks indeed form stably folded structures in solution. Mechanical unfoldons may provide a new tool for a systematic search for stable substructures of large proteins.     

Potential folding-function interrelationship in proteins

The possibility is addressed that protein folding and function may be related via regions that are critical for both folding and function. This approach is based on the building blocks folding model that describes protein folding as binding events of conformationally fluctuating building blocks. Within these, we identify building block fragments that are critical for achieving the native fold. A library of such critical building blocks (CBBs) is constructed. Then, it is asked whether the functionally important residues fall in these CBB fragments. We find that for over two-thirds of the proteins in our library with available functional information, the catalytic or binding site residues lie within the CBB regions. From the evolutionary standpoint, a folding-function relationship is advantageous, since the need to guard against mutations is limited to one region. Furthermore, conformationally similar CBBs are found in globally unrelated proteins with different functions. Hence, substituting CBBs may lead to designed proteins with altered functions. We further find that the CBBs in our library are conformationally unstable.     

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.     

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

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

A systematic study of the vibrational free energies of polypeptides in folded and random states

Molecular vibrations, especially low frequency motions, may be used as an indication of the rigidity or the flatness of the protein folding energy landscape. We have studied the vibrational properties of native folded as well as random coil structures of more than 60 polypeptides. The picture we obtain allows us to perceive how and why the energy landscape progressively rigidifies while still allowing potential flexibility. Compared with random coil structures, both alpha-helices and beta-hairpins are vibrationally more flexible. The vibrational properties of loop structures are similar to those of the corresponding random coil structures. Inclusion of an alpha-helix tends to rigidify peptides and so-called building blocks of the structure, whereas the addition of a beta-structure has less effect. When small building blocks coalesce to form larger domains, the protein rigidifies. However, some folded native conformations are still found to be vibrationally more flexible than random coil structures, for example, beta(2)-microglobulin and the SH3 domain. Vibrational free energy contributes significantly to the thermodynamics of protein folding and affects the distribution of the conformational substates. We found a weak correlation between the vibrational folding energy and the protein size, consistent with both previous experimental estimates and theoretical partition of the heat capacity change in protein folding.     

Extended Structures in RNA Folding Intermediates Are Due to Nonnative Interactions Rather than Electrostatic Repulsion

RNA folding occurs via a series of transitions between metastable intermediate states for Mg²⁺ concentrations below those needed to fold the native structure. In general, these folding intermediates are considerably less compact than their respective native states. Our previous work demonstrates that the major equilibrium intermediate of the 154-residue specificity domain (S-domain) of the Bacillus subtilis RNase P RNA is more extended than its native structure. We now investigate two models with falsifiable predictions regarding the origins of the extended intermediate structures in the S-domains of the B. subtilis and the Escherichia coli RNase P RNA that belong to different classes of P RNA and have distinct native structures. The first model explores the contribution of electrostatic repulsion, while the second model probes specific interactions in the core of the folding intermediate. Using small-angle X-ray scattering and Langevin dynamics simulations, we show that electrostatics plays only a minor role, whereas specific interactions largely account for the extended nature of the intermediate. Structural contacts in the core, including a nonnative base pair, help to stabilize the intermediate conformation. We conclude that RNA folding intermediates adopt extended conformations due to short-range, nonnative interactions rather than generic electrostatic repulsion of helical domains. These principles apply to other ribozymes and riboswitches that undergo functionally relevant conformational changes.     

Building blocks, hinge-bending motions and protein topology.

Here we show that the locations of molecular hinges in protein structures fall between building block elements. Building blocks are fragments of the protein chain which constitute local minima. These elements fold first. In the next step they associate through a combinatorial assembly process. While chain-linked building blocks may be expected to trial-associate first, if unstable, alternate more stable associations will take place. Hence, we would expect that molecular hinges will be at such inter-building block locations, or at the less stable, unassigned regions. On the other hand, hinge-bending motions are well known to be critical for protein function. Hence, protein folding and protein function are evolutionarily related. Further, the pathways through which proteins attain their three dimensional folds are determined by protein topology. However, at the same time the locations of the hinges, and hinge-bending motions are also an outcome of protein topology. Thus, protein folding and function appear coupled, and relate to protein topology. Here we provide some results illustrating such a relationship.     

Use of RNA structure flexibility data in nanostructure modeling

In the emerging field of RNA-based nanotechnology there is a need for automation of the structure design process. Our goal is to develop computer methods for aiding in this process. Towards that end, we created the RNA junction database, which is a repository of RNA junctions, i.e. internal, multi-branch and kissing loops with emanating stem stubs, extracted from the larger RNA structures stored in the PDB database. These junctions can be used as building blocks for nanostructures. Two programs developed in our laboratory, NanoTiler and RNA2D3D, can combine such building blocks with idealized fragments of A-form helices to produce desired 3D nanostructures. Initially, the building blocks are treated as rigid objects and the resulting geometry is tested against the design objectives. Experimental data, however, shows that RNA accommodates its shape to the constraints of larger structural contexts. Therefore we are adding analysis of the flexibility of our building blocks to the full design process. Here we present an example of RNA-based nanostructure design, putting emphasis on the need to characterize the structural flexibility of the building blocks to induce ring closure in the automated exploration. We focus on the use of kissing loops (KL) in nanostructure design, since they have been shown to play an important role in RNA self-assembly. By using an experimentally proven system, the RNA tectosquare, we show that considering the flexibility of the KLs as well as distortions of helical regions may be necessary to achieve a realistic design.     

Computing folding pathways between RNA secondary structures

Given an RNA sequence and two designated secondary structures A, B, we describe a new algorithm that computes a nearly optimal folding pathway from A to B. The algorithm, RNAtabupath, employs a tabu semi-greedy heuristic, known to be an effective search strategy in combinatorial optimization. Folding pathways, sometimes called routes or trajectories, are computed by RNAtabupath in a fraction of the time required by the barriers program of Vienna RNA Package. We benchmark RNAtabupath with other algorithms to compute low energy folding pathways between experimentally known structures of several conformational switches. The RNApathfinder web server, source code for algorithms to compute and analyze pathways and supplementary data are available at http://bioinformatics.bc.edu/clotelab/RNApathfinder.     

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.