Thinking inside the box: designing, implementing, and interpreting thermodynamic cycles to dissect cooperativity in RNA and DNA folding

DNA Structure Design Is Improved Using an Artificially Expanded Alphabet of Base Pairs Including Loop and Mismatch Thermodynamic Parameters

We show that in silico design of DNA secondary structures is improved by extending the base pairing alphabet beyond A-T and G-C to include the pair between 2-amino-8-(1'-β-d-2'-deoxyribofuranosyl)-imidazo-[1,2-a]-1,3,5-triazin-(8H)-4-one and 6-amino-3-(1'-β-d-2'-deoxyribofuranosyl)-5-nitro-(1H)-pyridin-2-one, abbreviated as P and Z. To obtain the thermodynamic parameters needed to include P-Z pairs in the designs, we performed 47 optical melting experiments and combined the results with previous work to fit free energy and enthalpy nearest neighbor folding parameters for P-Z pairs and G-Z wobble pairs. We find G-Z pairs have stability comparable to that of A-T pairs and should therefore be included as base pairs in structure prediction and design algorithms. Additionally, we extrapolated the set of loop, terminal mismatch, and dangling end parameters to include the P and Z nucleotides. These parameters were incorporated into the RNAstructure software package for secondary structure prediction and analysis. Using the RNAstructure Design program, we solved 99 of the 100 design problems posed by Eterna using the ACGT alphabet or supplementing it with P-Z pairs. Extending the alphabet reduced the propensity of sequences to fold into off-target structures, as evaluated by the normalized ensemble defect (NED). The NED values were improved relative to those from the Eterna example solutions in 91 of 99 cases in which Eterna-player solutions were provided. P-Z-containing designs had average NED values of 0.040, significantly below the 0.074 of standard-DNA-only designs, and inclusion of the P-Z pairs decreased the time needed to converge on a design. This work provides a sample pipeline for inclusion of any expanded alphabet nucleotides into prediction and design workflows.

Cooperativity and Allostery in RNA Systems

Allostery is among the most basic biological principles employed by biological macromolecules to achieve a biologically active state in response to chemical cues. Although initially used to describe the impact of small molecules on the conformation and activity of protein enzymes, the definition of this term has been significantly broadened to describe long-range conformational change of macromolecules in response to small or large effectors. Such a broad definition could be applied to RNA molecules, which do not typically serve as protein-free cellular enzymes but fold and form macromolecular assemblies with the help of various ligand molecules, including ions and proteins. Ligand-induced allosteric changes in RNA molecules are often accompanied by cooperative interactions between RNA and its ligand, thus streamlining the folding and assembly pathways. This chapter provides an overview of the interplay between cooperativity and allostery in RNA systems and outlines methods to study these two biological principles.

Stability of the pH-Dependent Parallel-Stranded d(CGA) Motif

Noncanonical DNA structures that retain programmability and structural predictability are increasingly being used in DNA nanotechnology applications, in which they offer versatility beyond traditional Watson-Crick interactions. The d(CGA) triplet repeat motif is structurally dynamic and can transition between parallel-stranded homo-base paired duplex and antiparallel unimolecular hairpin in a pH-dependent manner. Here, we evaluate the thermodynamic stability and nuclease sensitivity of oligonucleotides composed of the d(CGA) motif and several structurally related sequence variants. These results show that the structural transition resulting from decreasing the pH is accompanied by both a significant energetic stabilization and decreased nuclease sensitivity as unimolecular hairpin structures are converted to parallel-stranded homo-base paired duplexes. Furthermore, the stability of the parallel-stranded duplex form can be altered by changing the 5'-nucleobase of the d(CGA) triplet and the frequency and position of the altered triplets within long stretches of d(CGA) triplets. This work offers insight into the stability and versatility of the d(CGA) triplet repeat motif and provides constraints for using this pH-adaptive structural motif for creating DNA-based nanomaterials.

Double-mutant cycles: new directions and applications

Double-mutant cycle (DMC) analysis is a powerful approach for detecting and quantifying the energetics of both direct and long-range interactions in proteins and other chemical systems. It can also be used to unravel higher-order interactions (e.g. three-body effects) that lead to cooperativity in protein folding and function. In this review, we describe new applications of DMC analysis based on advances in native mass spectrometry and high-throughput methods such as next generation sequencing and protein complementation assays. These developments have facilitated carrying out high-throughput DMC analysis, which can be used to characterize increasingly higher-order interactions and very large interaction networks in proteins. Such studies have provided insights into the extent of cooperativity (epistasis) in protein structures. High-throughput DMC studies have also been used to validate correlated mutation analysis and can provide restraints for protein docking.

Effects of RNA structure and salt concentration on the affinity and kinetics of interactions between pentatricopeptide repeat proteins and their RNA ligands

Pentatricopeptide repeat (PPR) proteins are helical repeat proteins that bind specific RNA sequences via modular 1-repeat:1-nucleotide interactions. Binding specificity is dictated, in part, by hydrogen bonds between the amino acids at two positions in each PPR motif and the Watson-Crick face of the aligned nucleobase. There is evidence that PPR-RNA interactions can compete with RNA-RNA interactions in vivo, and that this competition underlies some effects of PPR proteins on gene expression. Conversely, RNA secondary structure can inhibit the binding of a PPR protein to its specific binding site. The parameters that influence whether PPR-RNA or RNA-RNA interactions prevail are unknown. Understanding these parameters will be important for understanding the functions of natural PPR proteins and for the design of engineered PPR proteins for synthetic biology purposes. We addressed this question by analyzing the effects of RNA structures of varying stability and position on the binding of the model protein PPR10 to its atpH RNA ligand. Our results show that even very weak RNA structures (ΔG° ~ 0 kcal/mol) involving only one nucleotide at either end of the minimal binding site impede PPR10 binding. Analysis of binding kinetics using Surface Plasmon Resonance showed that RNA structures reduce PPR10’s on-rate and increase its off-rate. Complexes between the PPR proteins PPR10 and HCF152 and their respective RNA ligands have long half-lives (one hour or more), correlating with their functions as barriers to exonucleolytic RNA decay in vivo. The effects of salt concentration on PPR10-RNA binding kinetics showed that electrostatic interactions play an important role in establishing PPR10-RNA interactions but play a relatively small role in maintaining specific interactions once established.

Molecular Mechanism for Folding Cooperativity of Functional RNAs in Living Organisms

A diverse set of organisms has adapted to live under extreme conditions. The molecular origin of the stability is unclear, however. It is not known whether the adaptation of functional RNAs, which have intricate tertiary structures, arises from strengthening of tertiary or secondary structure. Herein we evaluate effects of sequence changes on the thermostability of tRNAphe using experimental and computational approaches. To separate out effects of secondary and tertiary structure on thermostability, we modify base pairing strength in the acceptor stem, which does not participate in tertiary structure. In dilute solution conditions, strengthening secondary structure leads to non-two-state thermal denaturation curves and has small effects on thermostability, or the temperature at which tertiary structure and function are lost. In contrast, under cellular conditions with crowding and Mg2+-chelated amino acids, where two-state cooperative unfolding is maintained, strengthening secondary structure enhances thermostability. Investigation of stabilities of each tRNA stem across 44 organisms with a range of optimal growing temperatures revealed that organisms that grow in warmer environments have more stable stems. We also used Shannon entropies to identify positions of higher and lower information content, or sequence conservation, in tRNAphe and found that secondary structures have modest information content allowing them to drive thermal adaptation, while tertiary structures have maximal information content hindering them from participating in thermal adaptation. Base-paired regions with no tertiary structure and modest information content thus offer a facile evolutionary route to enhancing the thermostability of functional RNA by the simple molecular rules of base pairing.

SHAPE analysis of the htrA RNA thermometer from Salmonella enterica

RNA thermometers regulate expression of some genes involved in virulence of pathogenic bacteria such as Yersinia, Neisseria, and Salmonella They often function through temperature-dependent conformational changes that alter accessibility of the ribosome-binding site. The 5'-untranslated region (UTR) of the htrA mRNA from Salmonella enterica contains a very short RNA thermometer. We have systematically characterized the structure and dynamics of this thermometer at single-nucleotide resolution using SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension) assays. Our results confirm that the htrA thermometer adopts the predicted hairpin conformation at low temperatures, with conformational change occurring over a physiological temperature regime. Detailed SHAPE melting curves for individual nucleotides suggest that the thermometer unfolds in a cooperative fashion, with nucleotides from both upper and lower portions of the stem gaining flexibility at a common transition temperature. Intriguingly, analysis of an extended htrA 5' UTR sequence revealed not only the presence of the RNA thermometer, but also an additional, stable upstream structure. We generated and analyzed point mutants of the htrA thermometer, revealing elements that modulate its stability, allowing the hairpin to melt under the slightly elevated temperatures experienced during the infection of a warm-blooded host. This work sheds light on structure-function relationships in htrA and related thermometers, and it also illustrates the utility of SHAPE assays for detailed study of RNA thermometer systems.

Cooperative RNA Folding under Cellular Conditions Arises From Both Tertiary Structure Stabilization and Secondary Structure Destabilization

RNA folding has been studied extensively in vitro, typically under dilute solution conditions and abiologically high salt concentrations of 1 M Na⁺ or 10 mM Mg²⁺. The cellular environment is very different, with 20-40% crowding and only 10-40 mM Na⁺, 140 mM K⁺, and 0.5-2.0 mM Mg²⁺. As such, RNA structures and functions can be radically altered under cellular conditions. We previously reported that tRNA^phe secondary and tertiary structures unfold together in a cooperative two-state fashion under crowded in vivo-like ionic conditions, but in a noncooperative multistate fashion under dilute in vitro ionic conditions unless in nonphysiologically high concentrations of Mg²⁺. The mechanistic basis behind these effects remains unclear, however. To address the mechanism that drives RNA folding cooperativity, we probe effects of cellular conditions on structures and stabilities of individual secondary structure fragments comprising the full-length RNA. We elucidate effects of a diverse set of crowders on tRNA secondary structural fragments and full-length tRNA at three levels: at the nucleotide level by temperature-dependent in-line probing, at the tertiary structure level by small-angle X-ray scattering, and at the global level by thermal denaturation. We conclude that cooperative RNA folding is induced by two overlapping mechanisms: increased stability and compaction of tertiary structure through effects of Mg²⁺, and decreased stability of certain secondary structure elements through the effects of molecular crowders. These findings reveal that despite having very different chemical makeups RNA and protein can both have weak secondary structures in vivo leading to cooperative folding.

Stabilization of the i-motif structure by the intra-strand cross-link formation

The i-motif structures are formed by oligonucleotides containing cytosine tracts under acidic conditions. The folding of the i-motif under physiological conditions is of great interest because of its biological role. In this study, we investigated the effect of the intra-strand cross-link on the stability of the i-motif structure. The 4-vinyl-substituted analog of thymidine (T-vinyl) was incorporated into the 5'-end of the human telomere complementary strand, which formed the intra-strand cross-link with the internal adenine. The intra-strand cross-linked i-motif displayed CD spectra similar to that of the natural i-motif at acidic pH, which was transformed into a random coil with the increasing pH. The pH midpoint for the transition from the i-motif to random coil increased from pH 6.1 for the natural one to pH 6.8 for the cross-linked one. The thermodynamic parameters were obtained by measuring the thermal melting behaviors by CD and UV, and it was determined that the intra-strand cross-linked i-motif is stabilized due to a favorable entropy effect. Thus, this study has clearly indicated the validity of the intra-strand cross-linking for stabilization of the i-motif structure.

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg(2+) ion concentrations are low, K(+) concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo-like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg(2+) (0.5-2 mM) and K(+) (140 mM) if the solution is supplemented with physiological amounts (∼ 20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution.

The determination of RNA folding nearest neighbor parameters

The stability of RNA secondary structure can be predicted using a set of nearest neighbor parameters. These parameters are widely used by algorithms that predict secondary structure. This contribution introduces the UV optical melting experiments that are used to determine the folding stability of short RNA strands. It explains how the nearest neighbor parameters are chosen and how the values are fit to the data. A sample nearest neighbor calculation is provided. The contribution concludes with new methods that use the database of sequences with known structures to determine parameter values.

pKa shifting in double-stranded RNA is highly dependent upon nearest neighbors and bulge positioning

Shifting of pKa's in RNA is important for many biological processes; however, the driving forces responsible for shifting are not well understood. Herein, we determine how structural environments surrounding protonated bases affect pKa shifting in double-stranded RNA (dsRNA). Using (31)P NMR, we determined the pKa of the adenine in an A(+)·C base pair in various sequence and structural environments. We found a significant dependence of pKa on the base pairing strength of nearest neighbors and the location of a nearby bulge. Increasing nearest neighbor base pairing strength shifted the pKa of the adenine in an A(+)·C base pair higher by an additional 1.6 pKa units, from 6.5 to 8.1, which is well above neutrality. The addition of a bulge two base pairs away from a protonated A(+)·C base pair shifted the pKa by only ~0.5 units less than a perfectly base paired hairpin; however, positioning the bulge just one base pair away from the A(+)·C base pair prohibited formation of the protonated base pair as well as several flanking base pairs. Comparison of data collected at 25 °C and 100 mM KCl to biological temperature and Mg(2+) concentration revealed only slight pKa changes, suggesting that similar sequence contexts in biological systems have the potential to be protonated at biological pH. We present a general model to aid in the determination of the roles protonated bases may play in various dsRNA-mediated processes including ADAR editing, miRNA processing, programmed ribosomal frameshifting, and general acid-base catalysis in ribozymes.

Thio effects and an unconventional metal ion rescue in the genomic hepatitis delta virus ribozyme

Metal ion and nucleobase catalysis are important for ribozyme mechanism, but the extent to which they cooperate is unclear. A crystal structure of the hepatitis delta virus (HDV) ribozyme suggested that the pro-RP oxygen at the scissile phosphate directly coordinates a catalytic Mg(2+) ion and is within hydrogen bonding distance of the amine of the general acid C75. Prior studies of the genomic HDV ribozyme, however, showed neither a thio effect nor metal ion rescue using Mn(2+). Here, we combine experiment and theory to explore phosphorothioate substitutions at the scissile phosphate. We report significant thio effects at the scissile phosphate and metal ion rescue with Cd(2+). Reaction profiles with an SP-phosphorothioate substitution are indistinguishable from those of the unmodified substrate in the presence of Mg(2+) or Cd(2+), supporting the idea that the pro-SP oxygen does not coordinate metal ions. The RP-phosphorothioate substitution, however, exhibits biphasic kinetics, with the fast-reacting phase displaying a thio effect of up to 5-fold and the slow-reacting phase displaying a thio effect of ~1000-fold. Moreover, the fast- and slow-reacting phases give metal ion rescues in Cd(2+) of up to 10- and 330-fold, respectively. The metal ion rescues are unconventional in that they arise from Cd(2+) inhibiting the oxo substrate but not the RP substrate. This metal ion rescue suggests a direct interaction of the catalytic metal ion with the pro-RP oxygen, in line with experiments with the antigenomic HDV ribozyme. Experiments without divalent ions, with a double mutant that interferes with Mg(2+) binding, or with C75 deleted suggest that the pro-RP oxygen plays at most a redundant role in positioning C75. Quantum mechanical/molecular mechanical (QM/MM) studies indicate that the metal ion contributes to catalysis by interacting with both the pro-RP oxygen and the nucleophilic 2'-hydroxyl, supporting the experimental findings.

The RNA Newton polytope and learnability of energy parameters

Motivation: Computational RNA structure prediction is a mature important problem that has received a new wave of attention with the discovery of regulatory non-coding RNAs and the advent of high-throughput transcriptome sequencing. Despite nearly two score years of research on RNA secondary structure and RNA–RNA interaction prediction, the accuracy of the state-of-the-art algorithms are still far from satisfactory. So far, researchers have proposed increasingly complex energy models and improved parameter estimation methods, experimental and/or computational, in anticipation of endowing their methods with enough power to solve the problem. The output has disappointingly been only modest improvements, not matching the expectations. Even recent massively featured machine learning approaches were not able to break the barrier. Why is that?

Approach: The first step toward high-accuracy structure prediction is to pick an energy model that is inherently capable of predicting each and every one of known structures to date. In this article, we introduce the notion of learnability of the parameters of an energy model as a measure of such an inherent capability. We say that the parameters of an energy model are learnable iff there exists at least one set of such parameters that renders every known RNA structure to date the minimum free energy structure. We derive a necessary condition for the learnability and give a dynamic programming algorithm to assess it. Our algorithm computes the convex hull of the feature vectors of all feasible structures in the ensemble of a given input sequence. Interestingly, that convex hull coincides with the Newton polytope of the partition function as a polynomial in energy parameters. To the best of our knowledge, this is the first approach toward computing the RNA Newton polytope and a systematic assessment of the inherent capabilities of an energy model. The worst case complexity of our algorithm is exponential in the number of features. However, dimensionality reduction techniques can provide approximate solutions to avoid the curse of dimensionality.

Results: We demonstrated the application of our theory to a simple energy model consisting of a weighted count of A-U, C-G and G-U base pairs. Our results show that this simple energy model satisfies the necessary condition for more than half of the input unpseudoknotted sequence–structure pairs (55%) chosen from the RNA STRAND v2.0 database and severely violates the condition for ∼13%, which provide a set of hard cases that require further investigation. From 1350 RNA strands, the observed 3D feature vector for 749 strands is on the surface of the computed polytope. For 289 RNA strands, the observed feature vector is not on the boundary of the polytope but its distance from the boundary is not more than one. A distance of one essentially means one base pair difference between the observed structure and the closest point on the boundary of the polytope, which need not be the feature vector of a structure. For 171 sequences, this distance is larger than two, and for only 11 sequences, this distance is larger than five.

Availability: The source code is available on http://compbio.cs.wayne.edu/software/rna-newton-polytope.

Contact:chitsaz@wayne.edu

Cooperative tertiary interaction network guides RNA folding

Noncoding RNAs form unique 3D structures, which perform many regulatory functions. To understand how RNAs fold uniquely despite a small number of tertiary interaction motifs, we mutated the major tertiary interactions in a group I ribozyme by single-base substitutions. The resulting perturbations to the folding energy landscape were measured using SAXS, ribozyme activity, hydroxyl radical footprinting, and native PAGE. Double- and triple-mutant cycles show that most tertiary interactions have a small effect on the stability of the native state. Instead, the formation of core and peripheral structural motifs is cooperatively linked in near-native folding intermediates, and this cooperativity depends on the native helix orientation. The emergence of a cooperative interaction network at an early stage of folding suppresses nonnative structures and guides the search for the native state. We suggest that cooperativity in noncoding RNAs arose from natural selection of architectures conducive to forming a unique, stable fold.

Structural insights into ligand recognition by a sensing domain of the cooperative glycine riboswitch

Glycine riboswitches regulate gene expression by feedback modulation in response to cooperative binding to glycine. Here, we report on crystal structures of the second glycine-sensing domain from the Vibrio cholerae riboswitch in the ligand-bound and unbound states. This domain adopts a three-helical fold that centers on a three-way junction and accommodates glycine within a bulge-containing binding pocket above the junction. Glycine recognition is facilitated by a pair of bound Mg(2+) cations and governed by specific interactions and shape complementarity with the pocket. A conserved adenine extrudes from the binding pocket and intercalates into the junction implying that glycine binding in the context of the complete riboswitch could impact on gene expression by stabilizing the riboswitch junction and regulatory P1 helix. Analysis of riboswitch interactions in the crystal and footprinting experiments indicates that adjacent glycine-sensing modules of the riboswitch could form specific interdomain interactions, thereby potentially contributing to the cooperative response.

Role of unsatisfied hydrogen bond acceptors in RNA energetics and specificity

RNA plays essential roles in much of biology. These functions are dictated by structures mediated by hydrogen bonding, stacking, electrostatics, and steric interactions. Roles of unsatisfied hydrogen bond functionalities in these structures are less well understood. Herein, we evaluated the energetic contributions of unsatisfied hydrogen bonding groups by placing chemically modified substituents in select internal positions in RNA helices and conducting thermodynamic studies. We find that unsatisfied carbonyl groups make exceptional contributions to structure formation (approximately 3 kcal/mol in free energy), most likely due to a combination of strain and dehydration effects. Thus, unsatisfied hydrogen bonding groups are likely key determinants in the folding energetics and specificity of many RNA and DNA molecules and may be especially important in tertiary structure interactions.

Optical melting measurements of nucleic acid thermodynamics

Optical melting experiments provide measurements of thermodynamic parameters for nucleic acids. These thermodynamic parameters are widely used in RNA structure prediction programs and DNA primer design software. This review briefly summarizes the theory and underlying assumptions of the method and provides practical details for instrument calibration, experimental design, and data interpretation.