Entropy-driven folding of an RNA helical junction: an isothermal titration calorimetric analysis of the hammerhead ribozyme

Improving RNA nearest neighbor parameters for helices by going beyond the two-state model

RNA folding free energy change nearest neighbor parameters are widely used to predict folding stabilities of secondary structures. They were determined by linear regression to datasets of optical melting experiments on small model systems. Traditionally, the optical melting experiments are analyzed assuming a two-state model, i.e. a structure is either complete or denatured. Experimental evidence, however, shows that structures exist in an ensemble of conformations. Partition functions calculated with existing nearest neighbor parameters predict that secondary structures can be partially denatured, which also directly conflicts with the two-state model. Here, a new approach for determining RNA nearest neighbor parameters is presented. Available optical melting data for 34 Watson–Crick helices were fit directly to a partition function model that allows an ensemble of conformations. Fitting parameters were the enthalpy and entropy changes for helix initiation, terminal AU pairs, stacks of Watson–Crick pairs and disordered internal loops. The resulting set of nearest neighbor parameters shows a 38.5% improvement in the sum of residuals in fitting the experimental melting curves compared to the current literature set.

Why Does RNA Collapse? The Importance of Water in a Simulation Study of Helix-Junction-Helix Systems

Using computer simulations, we consider the balance of thermodynamic forces that collapse RNA. A model helix-junction-helix (HJH) construct is used to investigate the transition from an extended to a collapsed conformation. Conventional Molecular Dynamics and Milestoning Simulations are used to study the free energy profile of the process for two ion concentrations. We illustrate that HJH folds to a collapsed state with two types of counterions (Mg²⁺ and K⁺). By dissecting the free energy landscape into energetic and entropic contributions, we illustrate that the electrostatic forces between the RNA and the mobile ions do not drive the RNA to a collapsed state. Instead, entropy gains from water expulsion near the neighborhood of the RNA provide the stabilization free energy that tilt HJH into more compact structures. Further simulations of a three-helix hammerhead ribozyme show a similar behavior and support the idea of collapse due to increased gain in water entropy.

Thermodynamics and kinetics of RNA tertiary structure formation in the junctionless hairpin ribozyme

The hairpin ribozyme consists of two RNA internal loops that interact to form the catalytically active structure. This docking transition is a rare example of intermolecular formation of RNA tertiary structure without coupling to helix annealing. We have used temperature-dependent surface plasmon resonance (SPR) to characterize the thermodynamics and kinetics of RNA tertiary structure formation for the junctionless form of the ribozyme, in which loops A and B reside on separate molecules. We find docking to be strongly enthalpy-driven and to be accompanied by substantial activation barriers for association and dissociation, consistent with the structural reorganization of both internal loops upon complex formation. Comparisons with the parallel analysis of a ribozyme variant carrying a 2'-O-methyl modification at the self-cleavage site and with published data in other systems reveal a surprising diversity of thermodynamic signatures, emphasizing the delicate balance of contributions to the free energy of formation of RNA tertiary structure.

Single-molecule kinetics reveal cation-promoted DNA duplex formation through ordering of single-stranded helices

In this work, the kinetics of short, fully complementary oligonucleotides are investigated at the single-molecule level. Constructs 6-9 bp in length exhibit single exponential kinetics over 2 orders of magnitude time for both forward (kon, association) and reverse (koff, dissociation) processes. Bimolecular rate constants for association are weakly sensitive to the number of basepairs in the duplex, with a 2.5-fold increase between 9 bp (k'on = 2.1(1) × 10(6) M(-1) s(-1)) and 6 bp (k'on = 5.0(1) × 10(6) M(-1) s(-1)) sequences. In sharp contrast, however, dissociation rate constants prove to be exponentially sensitive to sequence length, varying by nearly 600-fold over the same 9 bp (koff = 0.024 s(-1)) to 6 bp (koff = 14 s(-1)) range. The 8 bp sequence is explored in more detail, and the NaCl dependence of kon and koff is measured. Interestingly, kon increases by >40-fold (kon = 0.10(1) s(-1) to 4.0(4) s(-1) between [NaCl] = 25 mM and 1 M), whereas in contrast, koff decreases by fourfold (0.72(3) s(-1) to 0.17(7) s(-1)) over the same range of conditions. Thus, the equilibrium constant (Keq) increases by ≈160, largely due to changes in the association rate, kon. Finally, temperature-dependent measurements reveal that increased [NaCl] reduces the overall exothermicity (ΔΔH° > 0) of duplex formation, albeit by an amount smaller than the reduction in entropic penalty (-TΔΔS° < 0). This reduced entropic cost is attributed to a cation-facilitated preordering of the two single-stranded species, which lowers the association free-energy barrier and in turn accelerates the rate of duplex formation.

Characterization of the kinetic and thermodynamic landscape of RNA folding using a novel application of isothermal titration calorimetry

A novel isothermal titration calorimetry (ITC) method was applied to investigate RNA helical packing driven by the GAAA tetraloop-receptor interaction in magnesium and potassium solutions. Both the kinetics and thermodynamics were obtained in individual ITC experiments, and analysis of the kinetic data over a range of temperatures provided Arrhenius activation energies (ΔH(‡)) and Eyring transition state entropies (ΔS(‡)). The resulting rich dataset reveals strongly contrasting kinetic and thermodynamic profiles for this RNA folding system when stabilized by potassium versus magnesium. In potassium, association is highly exothermic (ΔH(25°C) = -41.6 ± 1.2 kcal/mol in 150 mM KCl) and the transition state is enthalpically barrierless (ΔH(‡) = -0.6 ± 0.5). These parameters are significantly positively shifted in magnesium (ΔH(25°C) = -20.5 ± 2.1 kcal/mol, ΔH(‡) = 7.3 ± 2.2 kcal/mol in 0.5 mM MgCl(2)). Mixed salt solutions approximating physiological conditions exhibit an intermediate thermodynamic character. The cation-dependent thermodynamic landscape may reflect either a salt-dependent unbound receptor conformation, or alternatively and more generally, it may reflect a small per-cation enthalpic penalty associated with folding-coupled magnesium uptake.

Visualizing large RNA molecules in solution

Single-stranded RNAs (ssRNAs) longer than a few hundred nucleotides do not have a unique structure in solution. Their equilibrium properties therefore reflect the average of an ensemble of structures. We use cryo-electron microscopy to image projections of individual long ssRNA molecules and characterize the anisotropy of their ensembles in solution. A flattened prolate volume is found to best represent the shapes of these ensembles. The measured sizes and anisotropies are in good agreement with complementary determinations using small-angle X-ray scattering and coarse-grained molecular dynamics simulations. A long viral ssRNA is compared with shorter noncoding transcripts to demonstrate that prolate geometry and flatness are generic properties independent of sequence length and origin. The anisotropy persists under physiological as well as low-ionic-strength conditions, revealing a direct correlation between secondary structure asymmetry and 3D shape and size. We discuss the physical origin of the generic anisotropy and its biological implications.

Analysis of RNA folding and ligand binding by conventional and high-throughput calorimetry

Noncoding RNAs serve myriad functions in the cell, but their biophysical properties are not well understood. Calorimetry offers direct and label-free means for characterizing the ligand-binding and thermostability properties of these RNA. We apply two main types of calorimetry--isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC)--to the characterization of these functional RNA molecules. ITC can describe ligand binding in terms of stoichiometry, affinity, and heat (enthalpy), while DSC can provide RNA stability in terms of heat capacity, melting temperature, and folding enthalpy. Here, we offer detailed experimental protocols for studying such RNA systems with commercially available conventional and high-throughput ITC and DSC instruments.

Fluorescence competition and optical melting measurements of RNA three-way multibranch loops provide a revised model for thermodynamic parameters

Three-way multibranch loops (junctions) are common in RNA secondary structures. Computer algorithms such as RNAstructure and MFOLD do not consider the identity of unpaired nucleotides in multibranch loops when predicting secondary structure. There is limited experimental data, however, to parametrize this aspect of these algorithms. In this study, UV optical melting and a fluorescence competition assay are used to measure stabilities of multibranch loops containing up to five unpaired adenosines or uridines or a loop E motif. These results provide a test of our understanding of the factors affecting multibranch loop stability and provide revised parameters for predicting stability. The results should help to improve predictions of RNA secondary structure.

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.

Monitoring of an RNA multistep folding pathway by isothermal titration calorimetry

Isothermal titration calorimetry was used to monitor the energetic landscape of a catalytic RNA, specifically that of the hepatitis delta virus ribozyme. Using mutants that isolated various tertiary interactions, the thermodynamic parameters of several ribozyme-substrate intermediates were determined. The results shed light on the impact of several tertiary interactions on the global structure of the ribozyme. In addition, the data indicate that the formation of the P1.1 pseudoknot is the limiting step of the molecular mechanism. Last, as illustrated here, isothermal titration calorimetry appears to be a method of choice for the elucidation of an RNA's folding pathway.

Studying RNA-RNA and RNA-protein interactions by isothermal titration calorimetry

Isothermal Titration Calorimetry (ITC) provides a sensitive and accurate means by which to study the thermodynamics of RNA folding, RNA binding to small molecules, and RNA-protein interactions. The advent of extremely sensitive instrumentation and the increasing availability of ITC in shared facilities have made it increasingly valuable as a tool for RNA biochemistry. As an isothermal measurement, it allows analysis at a defined temperature, distinguishing it from thermal melting approaches (UV melting and differential scanning calorimetry, for instance) that provide thermodynamic information specific to the melting temperature. Residual structures at low temperature in the unfolded state and heat capacity changes lead to potential differences between thermodynamic values measured by ITC and those derived from melting studies. This article describes how ITC can be put to use in the study of RNA biochemistry.

Monitoring RNA-ligand interactions using isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a biophysical technique that measures the heat evolved or absorbed during a reaction to report the enthalpy, entropy, stoichiometry of binding, and equilibrium association constant. A significant advantage of ITC over other methods is that it can be readily applied to almost any RNA-ligand complex without having to label either molecule and can be performed under a broad range of pH, temperature, and ionic concentrations. During our application of ITC to investigate the thermodynamic details of the interaction of a variety of compounds with the purine riboswitch, we have explored and optimized experimental parameters that yield the most useful and reproducible results for RNAs. In this chapter, we detail this method using the titration of an adenine-binding RNA with 2,6-diaminopurine (DAP) as a practical example. Our insights should be generally applicable to observing the interactions of a broad range of molecules with structured RNAs.

Isothermal titration calorimetry of RNA

Isothermal titration calorimetry (ITC) is a fast and robust method to study the physical basis of molecular interactions. A single well-designed experiment can provide complete thermodynamic characterization of a binding reaction, including K(a), DeltaG, DeltaH, DeltaS and reaction stoichiometry (n). Repeating the experiment at different temperatures allows determination of the heat capacity change (DeltaC(P)) of the interaction. Modern calorimeters are sensitive enough to probe even weak biological interactions making ITC a very popular method among biochemists. Although ITC has been applied to protein studies for many years, it is becoming widely applicable in RNA biochemistry as well, especially in studies which involve RNA folding and RNA interactions with small molecules, proteins and with other RNAs. This review focuses on best practices for planning, designing and executing effective ITC experiments when one or more of the reactants is an RNA.

Thermodynamics and folding pathway of tetraloop receptor-mediated RNA helical packing

Little is known about the thermodynamic forces that drive the folding pathways of higher-order RNA structure. In this study, we employ calorimetric [isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC)] and spectroscopic (NMR and UV) methods to characterize the thermodynamics of the GAAA tetraloop-receptor interaction, utilizing a previously described bivalent construct. ITC studies indicate that the bivalent interaction is enthalpy driven and highly stable, with a binding constant (K(obs)) of 5.5x10(6) M(-1) and enthalpy (DeltaH(obs)(o)) of -33.8 kcal/mol at 45 degrees C in 20 mM KCl and 2 mM MgCl(2). Thus, we derive the DeltaH(obs)(o) for a single tetraloop-receptor interaction to be -16.9 kcal/mol at these conditions. UV absorbance data indicate that an increase in base stacking quality contributes to the enthalpy of complex formation. These highly favorable thermodynamics are consistent with the known critical role for the tetraloop-receptor motif in the folding of large RNAs. Additionally, a significant heat capacity change (DeltaC(p,obs)(o)) of -0.24 kcal mol(-1) K(-1) was determined by ITC. DSC and UV-monitored thermal denaturation experiments indicate that the bivalent tetraloop-receptor construct follows a minimally five-state unfolding pathway and suggest the observed DeltaC(p,obs)(o) for the interaction results from a temperature-dependent unbound receptor RNA structure.

Discrete state model and accurate estimation of loop entropy of RNA secondary structures

Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson-Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson-Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.

Applications of isothermal titration calorimetry in RNA biochemistry and biophysics

Isothermal titration calorimetry (ITC) has been applied to the study of proteins for many years. Its use in the biophysical analysis of RNAs has lagged significantly behind its use in protein biochemistry, however, in part because of the relatively large samples required. As the instrumentation has become more sensitive, the ability to obtain high quality data on RNA folding and RNA ligand interactions has improved dramatically. This review provides an overview of the ITC experiment and describes recent work on RNA systems that have taken advantage of its versatility for the study of small molecule binding, protein binding, and the analysis of RNA folding.

Distinct reaction pathway promoted by non-divalent-metal cations in a tertiary stabilized hammerhead ribozyme

Divalent ion sensitivity of hammerhead ribozymes is significantly reduced when the RNA structure includes appropriate tertiary stabilization. Therefore, we investigated the activity of the tertiary stabilized "RzB" hammerhead ribozyme in several nondivalent ions. Ribozyme RzB is active in spermidine and Na(+) alone, although the cleavage rates are reduced by more than 1,000-fold relative to the rates observed in Mg(2+) and in transition metal ions. The trivalent cobalt hexammine (CoHex) ion is often used as an exchange-inert analog of hydrated magnesium ion. Trans-cleavage rates exceeded 8 min(-1) in 20 mM CoHex, which promoted cleavage through outersphere interactions. The stimulation of catalysis afforded by the tertiary structural interactions within RzB does not require Mg(2+), unlike other extended hammerhead ribozymes. Site-specific interaction with at least one Mg(2+) ion is suggested by CoHex competition experiments. In the presence of a constant, low concentration of Mg(2+), low concentrations of CoHex decreased the rate by two to three orders of magnitude relative to the rate in Mg(2+) alone. Cleavage rates increased as CoHex concentrations were raised further, but the final fraction cleaved was lower than what was observed in CoHex or Mg(2+) alone. These observations suggest that Mg(2+) and CoHex compete for binding and that they cause misfolded structures when they are together. The results of this study support the existence of an alternate catalytic mechanism used by nondivalent ions (especially CoHex) that is distinct from the one promoted by divalent metal ions, and they imply that divalent metals influence catalysis through a specific nonstructural role.

A set of nearest neighbor parameters for predicting the enthalpy change of RNA secondary structure formation

A complete set of nearest neighbor parameters to predict the enthalpy change of RNA secondary structure formation was derived. These parameters can be used with available free energy nearest neighbor parameters to extend the secondary structure prediction of RNA sequences to temperatures other than 37°C. The parameters were tested by predicting the secondary structures of sequences with known secondary structure that are from organisms with known optimal growth temperatures. Compared with the previous set of enthalpy nearest neighbor parameters, the sensitivity of base pair prediction improved from 65.2 to 68.9% at optimal growth temperatures ranging from 10 to 60°C. Base pair probabilities were predicted with a partition function and the positive predictive value of structure prediction is 90.4% when considering the base pairs in the lowest free energy structure with pairing probability of 0.99 or above. Moreover, a strong correlation is found between the predicted melting temperatures of RNA sequences and the optimal growth temperatures of the host organism. This indicates that organisms that live at higher temperatures have evolved RNA sequences with higher melting temperatures.

Heat capacity changes associated with nucleic acid folding

Whereas heat capacity changes (DeltaCPs) associated with folding transitions are commonplace in the literature of protein folding, they have long been considered a minor energetic contributor in nucleic acid folding. Recent advances in the understanding of nucleic acid folding and improved technology for measuring the energetics of folding transitions have allowed a greater experimental window for measuring these effects. We present in this review a survey of current literature that confronts the issue of DeltaCPs associated with nucleic acid folding transitions. This work helps to gather the molecular insights that can be gleaned from analysis of DeltaCPs and points toward the challenges that will need to be overcome if the energetic contribution of DeltaCP terms are to be put to use in improving free energy calculations for nucleic acid structure prediction.

Prediction of RNA secondary structure by free energy minimization

RNA secondary structure is often predicted from sequence by free energy minimization. Over the past two years, advances have been made in the estimation of folding free energy change, the mapping of secondary structure and the implementation of computer programs for structure prediction. The trends in computer program development are: efficient use of experimental mapping of structures to constrain structure prediction; use of statistical mechanics to improve the fidelity of structure prediction; inclusion of pseudoknots in secondary structure prediction; and use of two or more homologous sequences to find a common structure.

Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length

Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (especially multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive experimental data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helices. We quantitatively evaluate the effects of ion concentration, ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful analytical formulas for the thermodynamic parameters as functions of finite helix length, ion type, and ion concentration. We find that the helix stability is additive for high ion concentration and long helix and nonadditive for low ion concentration and short helix. All these results are tested against and supported by extensive experimental data.

Survey of the year 2004: literature on applications of isothermal titration calorimetry

The market for commercially available isothermal titration calorimeters continues to grow as new applications and methodologies are developed. Concomitantly the number of users (and abusers) increases dramatically, resulting in a steady increase in the number of publications in which isothermal titration calorimetry (ITC) plays a role. In the present review, we will focus on areas where ITC is making a significant contribution and will highlight some interesting applications of the technique. This overview of papers published in 2004 also discusses current issues of interest in the development of ITC as a tool of choice in the determination of the thermodynamics of molecular recognition and interaction.

Artificial tertiary motifs stabilize trans-cleaving hammerhead ribozymes under conditions of submillimolar divalent ions and high temperatures

Tertiary stabilizing motifs (TSMs) between terminal loops or internal bulges facilitate folding of natural hammerhead ribozymes (hRz) under physiological conditions. However, both substrate and enzyme strands contribute nucleotides to the TSMs of trans-cleaving hRz, complicating the design of hRz that exploit TSMs to target specific mRNA. To overcome this limitation, we used SELEX to identify new, artificial TSMs that are less sensitive to sequence context. Nucleotides in loop II or in a bulge within the ribozyme strand of stem I were randomized, while the interaction partner was held constant. All nucleotides of the substrate pair with the ribozyme, minimizing their possible recruitment into the TSM, as such recruitment could constrain choice of candidate target sequences. Six cycles of selection identified cis-acting ribozymes that were active in 100 microM MgCl2. The selected motifs partially recapitulate TSMs found in natural hRz, suggesting that the natural motifs are close to optimal for their respective contexts. Ribozyme "RzB" showed enhanced thermal stability by retaining trans-cleavage activity at 80 degrees C in 10 mM MgCl2 and at 70 degrees C in 2 mM MgCl2. A variant of ribozyme "RzB" with a continuously paired stem 1 rapidly lost activity as temperature was increased. The selected motifs are modular, in that they permit trans-cleavage of several substrates in submillimolar MgCl2, including two substrates derived from the U5 genomic region of HIV-1. The new, artificial tertiary stabilized hRz are thus nearly independent of sequence context and enable for the first time the use of highly active hRz targeting almost any mRNA at physiologically relevant magnesium concentrations.

Escherichia coli Hfq has distinct interaction surfaces for DsrA, rpoS and poly(A) RNAs

The bacterial Sm-like protein Hfq facilitates RNA-RNA interactions involved in post-transcriptional regulation of the stress response. Specifically, Hfq helps pair noncoding RNAs (ncRNAs) with complementary regions of target mRNAs. To probe the mechanism of this pairing, we generated a series of Hfq mutants and measured their affinity for RNAs like those with which Hfq must associate in vivo. We tested the mutants' DsrA-dependent activation of rpoS, and their ability to stabilize DsrA ncRNA against degradation in vivo. Our results suggest that Hfq has two independent RNA-binding surfaces. In addition to a well-known site around the core of the Hfq hexamer, we observe interactions with the distal face of Hfq, a new locus with which mRNAs and poly(A) sequences associate. Our model explains how Hfq can simultaneously bind a ncRNA and its mRNA target to facilitate the strand displacement reaction required for Hfq-dependent translational regulation.

Heat capacity changes in RNA folding: application of perturbation theory to hammerhead ribozyme cold denaturation

In proteins, empirical correlations have shown that changes in heat capacity (DeltaC(P)) scale linearly with the hydrophobic surface area buried upon folding. The influence of DeltaC(P) on RNA folding has been widely overlooked and is poorly understood. In addition to considerations of solvent reorganization, electrostatic effects might contribute to DeltaC(P)s of folding in polyanionic species such as RNAs. Here, we employ a perturbation method based on electrostatic theory to probe the hot and cold denaturation behavior of the hammerhead ribozyme. This treatment avoids much of the error associated with imposing two-state folding models on non-two-state systems. Ribozyme stability is perturbed across a matrix of solvent conditions by varying the concentration of NaCl and methanol co-solvent. Temperature-dependent unfolding is then monitored by circular dichroism spectroscopy. The resulting array of unfolding transitions can be used to calculate a DeltaC(P) of folding that accurately predicts the observed cold denaturation temperature. We confirm the accuracy of the calculated DeltaC(P) by using isothermal titration calorimetry, and also demonstrate a methanol-dependence of the DeltaC(P). We weigh the strengths and limitations of this method for determining DeltaC(P) values. Finally, we discuss the data in light of the physical origins of the DeltaC(P)s for RNA folding and consider their impact on biological function.