RNA Folding Thermodynamics Research Articles

Vfold2D-MC: A Physics-Based Hybrid Model for Predicting RNA Secondary Structure Folding.

Accurate prediction of RNA structure and folding stability has a far-reaching impact on our understanding of RNA functions. Here we develop Vfold2D-MC, a new physics-based model, to predict RNA structure and folding thermodynamics from the sequence. The model employs virtual bond-based coarse-graining of RNA backbone conformation and generates RNA conformations through Monte Carlo sampling of the bond angles and torsional angles of the virtual bonds. Using a coarse-grained statistical potential derived from the known structures, we assign each conformation with a statistical weight. The weighted average over the conformational ensemble gives the entropy and free energy parameters for the hairpin, bulge, and internal loops, and multiway junctions. From the thermodynamic parameters, we predict RNA structures, melting curves, and structural changes from the sequence. Theory-experiment comparisons indicate that Vfold2D-MC not only gives improved structure predictions but also enables the interpretation of thermodynamic results for different RNA structures, including multibranched junctions. This new model sets a promising framework to treat more complicated RNA structures, such as pseudoknotted and intramolecular kissing loops, for which experimental thermodynamic parameters are often unavailable.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding.

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k c ln c + const, where the coefficient k c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln c at all c with k c = 2 kB T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔGalign, the probability of aligning tertiary contact partners, and ΔGtert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔGHJH) or from changes in the electrostatic environment (ΔG+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔGtert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔGtert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

Bridging the gap between in vitro and in vivo RNA folding.

Deciphering the folding pathways and predicting the structures of complex three-dimensional biomolecules is central to elucidating biological function. RNA is single-stranded, which gives it the freedom to fold into complex secondary and tertiary structures. These structures endow RNA with the ability to perform complex chemistries and functions ranging from enzymatic activity to gene regulation. Given that RNA is involved in many essential cellular processes, it is critical to understand how it folds and functions in vivo. Within the last few years, methods have been developed to probe RNA structures in vivo and genome-wide. These studies reveal that RNA often adopts very different structures in vivo and in vitro, and provide profound insights into RNA biology. Nonetheless, both in vitro and in vivo approaches have limitations: studies in the complex and uncontrolled cellular environment make it difficult to obtain insight into RNA folding pathways and thermodynamics, and studies in vitro often lack direct cellular relevance, leaving a gap in our knowledge of RNA folding in vivo. This gap is being bridged by biophysical and mechanistic studies of RNA structure and function under conditions that mimic the cellular environment. To date, most artificial cytoplasms have used various polymers as molecular crowding agents and a series of small molecules as cosolutes. Studies under such in vivo-like conditions are yielding fresh insights, such as cooperative folding of functional RNAs and increased activity of ribozymes. These observations are accounted for in part by molecular crowding effects and interactions with other molecules. In this review, we report milestones in RNA folding in vitro and in vivo and discuss ongoing experimental and computational efforts to bridge the gap between these two conditions in order to understand how RNA folds in the cell.

Probing the kinetic and thermodynamic consequences of the tetraloop/tetraloop receptor monovalent ion-binding site in P4-P6 RNA by smFRET.

Structured RNA molecules play roles in central biological processes and understanding the basic forces and features that govern RNA folding kinetics and thermodynamics can help elucidate principles that underlie biological function. Here we investigate one such feature, the specific interaction of monovalent cations with a structured RNA, the P4-P6 domain of the Tetrahymena ribozyme. We employ single molecule FRET (smFRET) approaches as these allow determination of folding equilibrium and rate constants over a wide range of stabilities and thus allow direct comparisons without the need for extrapolation. These experiments provide additional evidence for specific binding of monovalent cations, Na+ and K+, to the RNA tetraloop-tetraloop receptor (TL-TLR) tertiary motif. These ions facilitate both folding and unfolding, consistent with an ability to help order the TLR for binding and further stabilize the tertiary contact subsequent to attainment of the folding transition state.

Vfold: a web server for RNA structure and folding thermodynamics prediction.

BackgroundThe ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies.ResultsThe Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization.ConclusionsThe Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at “http://rna.physics.missouri.edu”.

Entropic stabilization of the folded states of RNA due to macromolecular crowding.

We review the effects of macromolecular crowding on the folding of RNA by considering the simplest scenario when excluded volume interactions between crowding particles and RNA dominate. Using human telomerase enzyme as an example, we discuss how crowding can alter the equilibrium between pseudoknot and hairpin states of the same RNA molecule-a key aspect of crowder-RNA interactions. We summarize data showing that the crowding effect is significant only if the size of the spherical crowding particle is smaller than the radius of gyration of the RNA in the absence of crowding particles. The implication for function of the wild type and mutants of human telomerase is outlined by using a relationship between enzyme activity and its conformational equilibrium. In addition, we discuss the interplay between macromolecular crowding and ionic strength of the RNA buffer. Finally, we briefly review recent experiments which illustrate the connection between excluded volume due to macromolecular crowding and the thermodynamics of RNA folding.

Coarse-Grained Model for Predicting RNA Folding Thermodynamics

We present a thermodynamically robust coarse-grained model to simulate folding of RNA in monovalent salt solutions. The model includes stacking, hydrogen bond, and electrostatic interactions as fundamental components in describing the stability of RNA structures. The stacking interactions are parametrized using a set of nucleotide-specific parameters, which were calibrated against the thermodynamic measurements for single-base stacks and base-pair stacks. All hydrogen bonds are assumed to have the same strength, regardless of their context in the RNA structure. The ionic buffer is modeled implicitly, using the concept of counterion condensation and the Debye-Hückel theory. The three adjustable parameters in the model were determined by fitting the experimental data for two RNA hairpins and a pseudoknot. A single set of parameters provides good agreement with thermodynamic data for the three RNA molecules over a wide range of temperatures and salt concentrations. In the process of calibrating the model, we establish the extent of counterion condensation onto the single-stranded RNA backbone. The reduced backbone charge is independent of the ionic strength and is 60% of the RNA bare charge at 37 °C. Our model can be used to predict the folding thermodynamics for any RNA molecule in the presence of monovalent ions.

Polypyrimidine tract binding protein-1 (PTB1) is a determinant of the tissue and host tropism of a human rhinovirus/poliovirus chimera PV1(RIPO).

The internal ribosomal entry site (IRES) of picornavirus genomes serves as the nucleation site of a highly structured ribonucleoprotein complex essential to the binding of the 40S ribosomal subunit and initiation of viral protein translation. The transition from naked RNA to a functional "IRESome" complex are poorly understood, involving the folding of secondary and tertiary RNA structure, facilitated by a tightly concerted binding of various host cell proteins that are commonly referred to as IRES trans-acting factors (ITAFs). Here we have investigated the influence of one ITAF, the polypyrimidine tract-binding protein 1 (PTB1), on the tropism of PV1(RIPO), a chimeric poliovirus in which translation of the poliovirus polyprotein is under the control of a human rhinovirus type 2 (HRV2) IRES element. We show that PV1(RIPO)'s growth defect in restrictive mouse cells is partly due to the inability of its IRES to interact with endogenous murine PTB. Over-expression of human PTB1 stimulated the HRV2 IRES-mediated translation, resulting in increased growth of PV1(RIPO) in murine cells and human neuronal SK-N-MC cells. Mutations within the PV1(RIPO) IRES, selected to grow in restrictive mouse cells, eliminated the human PTB1 supplementation requirement, by restoring the ability of the IRES to interact with endogenous murine PTB. In combination with our previous findings these results give a compelling insight into the thermodynamic behavior of IRES structures. We have uncovered three distinct thermodynamic aspects of IRES formation which may independently contribute to overcome the observed PV1(RIPO) IRES block by lowering the free energy δG of the IRESome formation, and stabilizing the correct and functional structure: 1) lowering the growth temperature, 2) modifying the complement of ITAFs in restricted cells, or 3) selection of adaptive mutations. All three mechanisms can conceivably modulate the thermodynamics of RNA folding, and thus facilitate and stabilize the functional IRES structure.

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.

Enthalpy-Driven RNA Folding: Single-Molecule Thermodynamics of Tetraloop−Receptor Tertiary Interaction

RNA folding thermodynamics are crucial for structure prediction, which requires characterization of both enthalpic and entropic contributions of tertiary motifs to conformational stability. We explore the temperature dependence of RNA folding due to the ubiquitous GAAA tetraloop-receptor docking interaction, exploiting immobilized and freely diffusing single-molecule fluorescence resonance energy transfer (smFRET) methods. The equilibrium constant for intramolecular docking is obtained as a function of temperature (T = 21-47 degrees C), from which a van't Hoff analysis yields the enthalpy (DeltaH degrees) and entropy (DeltaS degrees) of docking. Tetraloop-receptor docking is significantly exothermic and entropically unfavorable in 1 mM MgCl(2) and 100 mM NaCl, with excellent agreement between immobilized (DeltaH degrees = -17.4 +/- 1.6 kcal/mol, and DeltaS degrees = -56.2 +/- 5.4 cal mol(-1) K(-1)) and freely diffusing (DeltaH degrees = -17.2 +/- 1.6 kcal/mol, and DeltaS degrees = -55.9 +/- 5.2 cal mol(-1) K(-1)) species. Kinetic heterogeneity in the tetraloop-receptor construct is unaffected over the temperature range investigated, indicating a large energy barrier for interconversion between the actively docking and nondocking subpopulations. Formation of the tetraloop-receptor interaction can account for approximately 60% of the DeltaH degrees and DeltaS degrees of P4-P6 domain folding in the Tetrahymena ribozyme, suggesting that it may act as a thermodynamic clamp for the domain. Comparison of the isolated tetraloop-receptor and other tertiary folding thermodynamics supports a theme that enthalpy- versus entropy-driven folding is determined by the number of hydrogen bonding and base stacking interactions.

Editorial overview: exploring the vast dynamic range of RNA dynamics

This issue presents the field of RNA research from the perspective of dynamics. Over the past 20 years or so, our appreciation of the functions of RNA has grown dramatically. RNA has been shown to catalyze chemical reactions and to regulate gene expression, both by binding to small molecule and undergoing conformational changes as riboswitches, and by binding to specific messages as miRNAs. During this period of explosion in RNA biology, much has been learned about RNA physical chemistry and structural biology. For instance, the thermodynamics of RNA folding are better understood, allowing secondary structures to be predicted with increasing success, and the kinetics and folding pathways of complex RNA molecules are being elucidated. At the same time, many structures of functional RNAs have been reported, including multiple ribosome structures and ribozyme and riboswitch structures. These advances have been nothing short of astonishing. Yet at the same time that new RNA biology has been discovered and analyzed in terms of structure and chemistry, new questions have been framed. Central among these is the nature of the dynamics that allow RNA to switch between conformations, as is demanded by these systems. The issue of RNA dynamics comprises the theme of this special issue. We are very fortunate to present here 10 articles from leaders in this field. Topics range from the ultrafast dynamics of simpler model systems to the dynamics of systems of intermediate complexity including ribozymes, to motions in systems of extreme complexity including the ribosome and other RNA-protein (RNP) complexes.

Impact of Loop Statistics on the Thermodynamics of RNA Folding

Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight approximately l(-c) for loops of length l in the recursion relation for the partition function, we show that the heat capacity depends sensitively on the presence and value of the exponent c, even for a short explicit tRNA sequence. For long homo-RNA, we analytically calculate the critical temperature and critical exponents which exhibit a nonuniversal dependence on c.

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. http://iFoldRNA.dokhlab.org.

Site‐Specific Variations in RNA Folding Thermodynamics

The fluorescent base analogue 2‐aminopurine (2‐AP) is commonly used to study specific conformational and protein binding events involving nucleic acids. Here, combinations of steady‐state and time‐resolved fluorescence spectroscopy of 2‐AP were employed to monitor conformational transitions within a model hairpin RNA from diverse structural perspectives. RNA substrates adopting stable, unambiguous secondary structures were labeled with 2‐AP at an unpaired base, within the loop, or inside the base‐paired stem. Steady‐state fluorescence was monitored as the RNA hairpins made the transitions between folded and unfolded conformations using thermal denaturation, urea titration, and cation‐mediated folding. Unstructured control RNA substrates permitted the effects of higher‐order RNA structures on 2‐AP fluorescence to be distinguished from stimulus‐dependent changes in intrinsic 2‐AP photophysics and/or interactions with adjacent residues. Thermodynamic parameters describing local conformational changes were thus resolved from multiple perspectives within the model RNA hairpin. These data provided energetic bases for construction of folding mechanisms, which varied among different folding‐unfolding stimuli. Time‐resolved fluorescence studies further revealed that 2‐AP exhibits characteristic signatures of component fluorescence lifetimes and respective fractional contributions in different RNA structural contexts. Together, these studies demonstrate localized conformational events contributing to RNA folding and unfolding that could not be observed by approaches monitoring only global structural transitions.

Site-Specific Variations in RNA Folding Thermodynamics Visualized by 2-Aminopurine Fluorescence

The fluorescent base analogue 2-aminopurine (2-AP) is commonly used to study specific conformational and protein binding events involving nucleic acids. Here, combinations of steady-state and time-resolved fluorescence spectroscopy of 2-AP were employed to monitor conformational transitions within a model hairpin RNA from diverse structural perspectives. RNA substrates adopting stable, unambiguous secondary structures were labeled with 2-AP at an unpaired base, within the loop, or inside the base-paired stem. Steady-state fluorescence was monitored as the RNA hairpins made the transitions between folded and unfolded conformations using thermal denaturation, urea titration, and cation-mediated folding. Unstructured control RNA substrates permitted the effects of higher-order RNA structures on 2-AP fluorescence to be distinguished from stimulus-dependent changes in intrinsic 2-AP photophysics and/or interactions with adjacent residues. Thermodynamic parameters describing local conformational changes were thus resolved from multiple perspectives within the model RNA hairpin. These data provided energetic bases for construction of folding mechanisms, which varied among different folding-unfolding stimuli. Time-resolved fluorescence studies further revealed that 2-AP exhibits characteristic signatures of component fluorescence lifetimes and respective fractional contributions in different RNA structural contexts. Together, these studies demonstrate localized conformational events contributing to RNA folding and unfolding that could not be observed by approaches monitoring only global structural transitions.

Predicting RNA folding thermodynamics with a reduced chain representation model

Based on the virtual bond representation for the nucleotide backbone, we develop a reduced conformational model for RNA. We use the experimentally measured atomic coordinates to model the helices and use the self-avoiding walks in a diamond lattice to model the loop conformations. The atomic coordinates of the helices and the lattice representation for the loops are matched at the loop-helix junction, where steric viability is accounted for. Unlike the previous simplified lattice-based models, the present virtual bond model can account for the atomic details of realistic three-dimensional RNA structures. Based on the model, we develop a statistical mechanical theory for RNA folding energy landscapes and folding thermodynamics. Tests against experiments show that the theory can give much more improved predictions for the native structures, the thermal denaturation curves, and the equilibrium folding/unfolding pathways than the previous models. The application of the model to the P5abc region of Tetrahymena group I ribozyme reveals the misfolded intermediates as well as the native-like intermediates in the equilibrium folding process. Moreover, based on the free energy landscape analysis for each and every loop mutation, the model predicts five lethal mutations that can completely alter the free energy landscape and the folding stability of the molecule.

RNA Challenges for Computational Chemists

Some experimental results for the thermodynamics of RNA folding cannot be explained by simple pairwise hydrogen-bonding models. Such effects include the stabilities of isoguanosine-isocytidine (iG-iC) base pairs and of various 2 x 2 nucleotide internal loops. Presumably, these results can be explained by base stacking effects, which can be partitioned into Coulombic and overlap effects. We review experimental measurements that provide benchmarks for testing the approximations and theories used for modeling nucleic acids. Quantitative agreement between experiment and theory will indicate understanding of the interactions determining RNA stability and structure.

Thermodynamics of ion-induced RNA folding in the hammerhead ribozyme: an isothermal titration calorimetric study.

The hammerhead ribozyme undergoes a well-defined two-stage conformational folding process, induced by the binding of magnesium ions. In this study, we have used isothermal titration calorimetry to analyze the thermodynamics of magnesium binding and magnesium ion-induced folding of the ribozyme. Binding to the natural sequence ribozyme is strongly exothermic and can be analyzed in terms of sequential interaction at two sites with association constants K(A) = 480 and 2840 M(-1). Sequence variants of the hammerhead RNA give very different isothermal titration curves. An A14G variant that cannot undergo ion-induced folding exhibits endothermic binding. By contrast, a deoxyribose G5 variant that can undergo only the first of the two folding transitions gives a complex titration curve. However, despite these differences the ITC data for all three species can be analyzed in terms of the sequential binding of magnesium ions at two sites. While the binding affinities are all in the region of 10(3) M(-1), corresponding to free energies of Delta G degrees = -3.5 to -4 kcal mol(-1), the enthalpic and entropic contributions show much greater variation. The ITC experiments are in good agreement with earlier conformational studies of the folding of the ion-induced folding of the hammerhead ribozyme.