A thermodynamic framework for the magnesium-dependent folding of RNA

TPP Riboswitch Populates Holo-Form-like Structure Even in the Absence of Cognate Ligand at High Mg2+ Concentration

Riboswitches are noncoding RNA that regulate gene expression by folding into specific three-dimensional structures (holo-form) upon binding by their cognate ligand in the presence of Mg²⁺. Riboswitch functioning is also hypothesized to be under kinetic control requiring large cognate ligand concentrations. We ask the question under thermodynamic conditions, can the riboswitches populate structures similar to the holo-form only in the presence of Mg²⁺ and absence of cognate ligand binding. We addressed this question using thiamine pyrophosphate (TPP) riboswitch as a model system and computer simulations using a coarse-grained model for RNA. The folding free energy surface (FES) shows that with the initial increase in Mg²⁺ concentration ([Mg²⁺]), the aptamer domain (AD) of TPP riboswitch undergoes a barrierless collapse in its dimensions. On further increase in [Mg²⁺], intermediates separated by barriers appear on the FES, and one of the intermediates has a TPP ligand-binding competent structure. We show that site-specific binding of the Mg²⁺ aids in the formation of tertiary contacts. For [Mg²⁺] greater than physiological concentration, AD folds into a structure similar to the crystal structure of the TPP holo-form even in the absence of the TPP ligand. The folding kinetics shows that TPP AD populates an intermediate due to the misalignment of two arms present in the structure, which acts as a kinetic trap, leading to larger folding timescales. The predictions of the intermediate structures from the simulations are amenable for experimental verification.

Magnesium ions reversibly bind to DNA double stranded helix in thin films

Effects of magnesium (Mg²⁺) ions on the stability and structural properties of double-stranded DNA are vitally important for DNA folding and functional behavior. Complementing our previous study on highly hydrated thin films of DNA with sodium counterions, with no buffer (pH ≈ 6) and surrounded with Mg²⁺ cations, here we use Fourier transform infrared spectroscopy and band shape analysis to explore in detail the vibrational signatures of DNA-magnesium interaction in the case when DNA charges are neutralized solely by Mg²⁺ cations, hereafter called MgDNA. Ion atmosphere has been controlled by the magnesium to phosphate molar concentration ratio r which varied between 0.0067 and 10. For r = 0 we find that spectral features in the base region remain similar as in DNA, whereas changes in the backbone region indicate that the B conformation becomes fully stabilized. With increasing r a pronounced structural reshaping occurs in the phosphate backbone region indicating a blue shift of the asymmetric band, while the symmetric band does not show any displacement in frequency. The band shape analysis of overlapping peaks in the respective phosphate regions demonstrates that the number of constituent modes as well as their positions in frequency do not change, whereas their intensities and bandwidths display disparate changes. The results reflect a variety of local environments at the DNA backbone due to a heterogeneous ion atmosphere with randomly distributed magnesium ions and local patterns of hydrogen bonds which change with increasing r. Remarkably, after crowded r = 10 ion atmosphere is depleted, Mg induced spectral changes vanish and structural features of MgDNA (r ≈ 0) are fully restored. Overall results strongly suggest that in MgDNA on highly hydrated thin films the hydrogen-base pairing remains preserved and that Mg²⁺ ions, similar to sodium ions, retain their mobility and interact with double helix via water-mediated electrostatic forces.

Functional Roles of Chelated Magnesium Ions in RNA Folding and Function

RNA regulates myriad cellular events such as transcription, translation, and splicing. To perform these essential functions, RNA often folds into complex tertiary structures in which its negatively charged ribose-phosphate backbone interacts with metal ions. Magnesium, the most abundant divalent metal ion in cells, neutralizes the backbone, thereby playing essential roles in RNA folding and function. This has been known for more than 50 years, and there are now thousands of in vitro studies, most of which have used ≥10 mM free Mg²⁺ ions to achieve optimal RNA folding and function. In the cell, however, concentrations of free Mg²⁺ ions are much lower, with most Mg²⁺ ions chelated by metabolites. In this Perspective, we curate data from a number of sources to provide extensive summaries of cellular concentrations of metabolites that bind Mg²⁺ and to estimate cellular concentrations of metabolite-chelated Mg²⁺ species, in the representative prokaryotic and eukaryotic systems Escherichia coli, Saccharomyces cerevisiae, and iBMK cells. Recent research from our lab and others has uncovered the fact that such weakly chelated Mg²⁺ ions can enhance RNA function, including its thermodynamic stability, chemical stability, and catalysis. We also discuss how metabolite-chelated Mg²⁺ complexes may have played roles in the origins of life. It is clear from this analysis that bound Mg²⁺ should not be simply considered non-RNA-interacting and that future RNA research, as well as protein research, could benefit from considering chelated magnesium.

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Mg2+ Impacts the Twister Ribozyme through Push-Pull Stabilization of Nonsequential Phosphate Pairs

RNA molecules perform a variety of biological functions for which the correct three-dimensional structure is essential, including as ribozymes where they catalyze chemical reactions. Metal ions, especially Mg2+, neutralize these negatively charged nucleic acids and specifically stabilize RNA tertiary structures as well as impact the folding landscape of RNAs as they assume their tertiary structures. Specific binding sites of Mg2+ in folded conformations of RNA have been studied extensively; however, the full range of interactions of the ion with compact intermediates and unfolded states of RNA is challenging to investigate, and the atomic details of the mechanism by which the ion facilitates tertiary structure formation is not fully known. Here, umbrella sampling combined with oscillating chemical potential Grand Canonical Monte Carlo/molecular dynamics simulations are used to capture the energetics and atomic-level details of Mg2+-RNA interactions that occur along an unfolding pathway of the Twister ribozyme. The free energy profiles reveal stabilization of partially unfolded states by Mg2+, as observed in unfolding experiments, with this stabilization being due to increased sampling of simultaneous interactions of Mg2+ with two or more nonsequential phosphate groups. Notably, these results indicate a push-pull mechanism in which the Mg2+-RNA interactions actually lead to destabilization of specific nonsequential phosphate-phosphate interactions (i.e., pushed apart), whereas other interactions are stabilized (i.e., pulled together), a balance that stabilizes unfolded states and facilitates the folding of Twister, including the formation of hydrogen bonds associated with the tertiary structure. This study establishes a better understanding of how Mg2+-ion interactions contribute to RNA structural properties and stability.

Structural Properties of Small Single-Stranded Circular Nucleic Acids

One strategy to avoid rapid degradation of small nucleic acids in biomedical applications is to covalently link their 3'- and 5'-ends, turning them into circular nucleic acids (circNAs). Here, we examine structural properties of flexible non-base-paired circNAs, containing 6-48 nucleotides, in aqueous solution, using microsecond long molecular dynamics simulations. Analyses of conformational ensembles of circular DNA (circDNA) and RNA (circRNA) molecules of different lengths and sequences reveal how their structures and dynamics are affected by the constraints of their geometries. The circDNAs are more bent and flexible than circRNAs, with distinctly different arrangements of phosphate backbones and bases. Small circNAs can sequester counterions in conformations that resemble crown ethers for the smallest (6-8 nucleotide long) molecules examined, in contrast to their linear counterparts. At millimolar concentrations (7.9 mM), circNA molecules were observed to aggregate, adopting linear chain shapes at physiological ionic strengths.

Ion counting demonstrates a high electrostatic field generated by the nucleosome

In eukaryotes, a first step towards the nuclear DNA compaction process is the formation of a nucleosome, which is comprised of negatively charged DNA wrapped around a positively charged histone protein octamer. Often, it is assumed that the complexation of the DNA into the nucleosome completely attenuates the DNA charge and hence the electrostatic field generated by the molecule. In contrast, theoretical and computational studies suggest that the nucleosome retains a strong, negative electrostatic field. Despite their fundamental implications for chromatin organization and function, these opposing views of nucleosome electrostatics have not been experimentally tested. Herein, we directly measure nucleosome electrostatics and find that while nucleosome formation reduces the complex charge by half, the nucleosome nevertheless maintains a strong negative electrostatic field. Our studies highlight the importance of considering the polyelectrolyte nature of the nucleosome and its impact on processes ranging from factor binding to DNA compaction.

Interactions between cyclic nucleotides and common cations: an ab initio molecular dynamics study

We present the first, to the best of our knowledge, ab initio molecular dynamics (AIMD) investigation on three aqueous solutions where an abasic cyclic nucleotide model is solvated in the presence of distinct cations (i.e., Na⁺, K⁺ and Mg²⁺). We elucidate the typical modalities of interaction between those ionic species and the nucleotide moiety by first-principles numerical simulations, starting from an inner-shell binding configuration on a time scale of 100 ps (total simulation time of ∼600 ps). Whereas the strong "structure-maker" Mg²⁺ is permanently bound to one of the two oxygen atoms of the phosphate group of the nucleotide model, Na⁺ and K⁺ show binding times τ_b of 65 ps and 10-15 ps, respectively, thus reflecting their chemical nature in aqueous solutions. Furthermore, we qualitatively relate these findings to approximate free-energy barriers of the cations' unbinding obtained by means of exploratory well-tempered metadynamics. With the aim of shedding light on the features of commonly employed force-fields (FFs), classical MD simulations (almost 200 trajectories with a total simulation time of ∼18 μs) using the biomolecular AMBER FF are also reported. By choosing several combinations of the parametrization for the water environment (i.e., TIP3P, SPC/E and OPC) and cations (i.e., Joung-Cheatham, Li-Merz 12-6 and Li-Merz 12-6-4), we found significant differences in the radial distribution functions and residence times compared to the ab initio results. The Na⁺ and K⁺ ions wrongly show quasi-identical radial distribution functions and the Li & Merz 12-6-4 Lennard-Jones parameters for Mg²⁺ were found to be essential in quickly reaching the binding state consistent with AIMD.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Tetracycline determines the conformation of its aptamer at physiological magnesium concentrations

Synthetic riboswitches are versatile tools for the study and manipulation of biological systems. Yet, the underlying mechanisms governing its structural properties and regulation under physiological conditions are poorly studied. We performed spectroscopic and calorimetric experiments to explore the folding kinetics and thermodynamics of the tetracycline-binding aptamer, which can be employed as synthetic riboswitch, in the range of physiological magnesium concentrations. The dissociation constant of the ligand-aptamer complex was found to strongly depend on the magnesium concentration. At physiological magnesium concentrations, tetracycline induces a significant conformational shift from a compact, but heterogeneous intermediate state toward the completely formed set of tertiary interactions defining the regulation-competent structure. Thus, the switching functionality of the tetracycline-binding aptamer appears to include both a conformational rearrangement toward the regulation-competent structure and its thermodynamic stabilization.

Structure, dynamics, and mechanism of the lead-dependent ribozyme

Leadzyme is a small catalytic RNA that was identified by in vitro selection for Pb2+-dependent cleavage from a tRNA library. Leadzyme employs a unique two-step Pb2+-specific mechanism to cleave within its active site. NMR and crystal structures of the active site revealed different folding patterns, but neither features the in-line alignment for attack by the 2'-OH nucleophilic group. These experimentally determined structures most likely represent ground states and are catalytically inactive. There are significant dynamics of the active site and the motif samples multiple conformations at the ground states. Various metal ion binding sites have been identified, including one that may be occupied by a catalytic Pb2+. Based on functional group analysis, a computational model of the transition state has been proposed. This model features a unique base triple that is consistent with sequence and functional group requirements for catalysis. This structure is likely only populated transiently, but imposing appropriate conformational constraints may significantly stabilize this state thereby promoting catalysis. Other ions may inhibit the cleavage by competing for the Pb2+ binding site, or by stabilizing the ground state thereby suppressing its transition to the catalytically active conformation. Some rare earth ions can enhance the reaction via an unknown mechanism. Because of its unique chemistry and dynamic behavior, leadzyme can continue to serve as an excellent model system for teaching us RNA biology and chemistry.

An introduction to recurrent nucleotide interactions in RNA

RNA secondary structure diagrams familiar to molecular biologists summarize at a glance the folding of RNA chains to form Watson–Crick paired double helices. However, they can be misleading: First of all, they imply that the nucleotides in loops and linker segments, which can amount to 35% to 50% of a structured RNA, do not significantly interact with other nucleotides. Secondly, they give the impression that RNA molecules are loosely organized in three-dimensional (3D) space. In fact, structured RNAs are compactly folded as a result of numerous long-range, sequence-specific interactions, many of which involve loop or linker nucleotides. Here, we provide an introduction for students and researchers of RNA on the types, prevalence, and sequence variations of inter-nucleotide interactions that structure and stabilize RNA 3D motifs and architectures, using Escherichia coli (E. coli) 16S ribosomal RNA as a concrete example. The picture that emerges is that almost all nucleotides in structured RNA molecules, including those in nominally single-stranded loop or linker regions, form specific interactions that stabilize functional structures or mediate interactions with other molecules. The small number of noninteracting, ‘looped-out’ nucleotides make it possible for the RNA chain to form sharp turns. Base-pairing is the most specific interaction in RNA as it involves edge-to-edge hydrogen bonding (H-bonding) of the bases. Non-Watson–Crick base pairs are a significant fraction (30% or more) of base pairs in structured RNAs.

Structural features of a 3' splice site in influenza a

Influenza A is an RNA virus with a genome of eight negative sense segments. Segment 7 mRNA contains a 3′ splice site for alternative splicing to encode the essential M2 protein. On the basis of sequence alignment and chemical mapping experiments, the secondary structure surrounding the 3′ splice site has an internal loop, adenine bulge, and hairpin loop when it is in the hairpin conformation that exposes the 3′ splice site. We report structural features of a three-dimensional model of the hairpin derived from nuclear magnetic resonance spectra and simulated annealing with restrained molecular dynamics. Additional insight was provided by modeling based on ¹H chemical shifts. The internal loop containing the 3′ splice site has a dynamic guanosine and a stable imino (cis Watson–Crick/Watson–Crick) GA pair. The adenine bulge also appears to be dynamic with the A either stacked in the stem or forming a base triple with a Watson–Crick GC pair. The hairpin loop is a GAAA tetraloop closed by an AC pair.

TBI server: a web server for predicting ion effects in RNA folding

Background

Metal ions play a critical role in the stabilization of RNA structures. Therefore, accurate prediction of the ion effects in RNA folding can have a far-reaching impact on our understanding of RNA structure and function. Multivalent ions, especially Mg²⁺, are essential for RNA tertiary structure formation. These ions can possibly become strongly correlated in the close vicinity of RNA surface. Most of the currently available software packages, which have widespread success in predicting ion effects in biomolecular systems, however, do not explicitly account for the ion correlation effect. Therefore, it is important to develop a software package/web server for the prediction of ion electrostatics in RNA folding by including ion correlation effects.

Results

The TBI web server http://rna.physics.missouri.edu/tbi_index.html provides predictions for the total electrostatic free energy, the different free energy components, and the mean number and the most probable distributions of the bound ions. A novel feature of the TBI server is its ability to account for ion correlation and ion distribution fluctuation effects.

Conclusions

By accounting for the ion correlation and fluctuation effects, the TBI server is a unique online tool for computing ion-mediated electrostatic properties for given RNA structures. The results can provide important data for in-depth analysis for ion effects in RNA folding including the ion-dependence of folding stability, ion uptake in the folding process, and the interplay between the different energetic components.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Many-body effect in ion binding to RNA

Ion-mediated electrostatic interactions play an important role in RNA folding stability. For a RNA in a solution with higher Mg(2+) ion concentration, more counterions in the solution can bind to the RNA, causing a strong many-body coupling between the bound ions. The many-body effect can change the effective potential of mean force between the tightly bound ions. This effect tends to dampen ion binding and lower RNA folding stability. Neglecting the many-body effect leads to a systematic error (over-estimation) of RNA folding stability at high Mg(2+) ion concentrations. Using the tightly bound ion model combined with a conformational ensemble model, we investigate the influence of the many-body effect on the ion-dependent RNA folding stability. Comparisons with the experimental data indicate that including the many-body effect led to much improved predictions for RNA folding stability at high Mg(2+) ion concentrations. The results suggest that the many-body effect can be important for RNA folding in high concentrations of multivalent ions. Further investigation showed that the many-body effect can influence the spatial distribution of the tightly bound ions and the effect is more pronounced for compact RNA structures and structures prone to the formation of local clustering of ions.

Dynamics of riboswitches: Molecular simulations

Riboswitch RNAs play key roles in bacterial metabolism and represent a promising new class of antibiotic targets for treatment of infectious disease. While many studies of riboswitches have been performed, the exact mechanism of riboswitch operation is still not fully understood at the atomistic level of detail. Molecular dynamics simulations are useful for interpreting existing experimental data and producing predictions for new experiments. Here, a wide range of computational studies on riboswitches is reviewed. By elucidating the key principles of riboswitch operation, computation may aid in the effort to design more specific antibiotics with affinities greater than those of the native ligand. Such a detailed understanding may be required to improve efficacy and reduce side effects. These studies are laying the groundwork for understanding the action mechanism of new compounds that inhibit riboswitch activity. Future directions such as magnesium effects, large-scale conformational changes, expression platforms and co-transcriptional folding are also discussed. This article is part of a Special Issue entitled: Riboswitches.

Single-molecule studies of riboswitch folding

The folding dynamics of riboswitches are central to their ability to modulate gene expression in response to environmental cues. In most cases, a structural competition between the formation of a ligand-binding aptamer and an expression platform (or some other competing off-state) determines the regulatory outcome. Here, we review single-molecule studies of riboswitch folding and function, predominantly carried out using single-molecule FRET or optical trapping approaches. Recent results have supplied new insights into riboswitch folding energy landscapes, the mechanisms of ligand binding, the roles played by divalent ions, the applicability of hierarchical folding models, and kinetic vs. thermodynamic control schemes. We anticipate that future work, based on improved data sets and potentially combining multiple experimental techniques, will enable the development of more complete models for complex RNA folding processes. This article is part of a Special Issue entitled: Riboswitches.

Understanding nucleic acid-ion interactions

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Molecular crowding favors reactivity of a human ribozyme under physiological ionic conditions

In an effort to relate RNA folding to function under cellular-like conditions, we monitored the self-cleavage reaction of the human hepatitis delta virus-like CPEB3 ribozyme in the background of physiological ionic concentrations and various crowding and cosolute agents. We found that at physiological free Mg(2+) concentrations (∼0.1-0.5 mM), both crowders and cosolutes stimulate the rate of self-cleavage, up to ∼6-fold, but that in 10 mM Mg(2+) (conditions widely used for in vitro ribozyme studies) these same additives have virtually no effect on the self-cleavage rate. We further observe a dependence of the self-cleavage rate on crowder size, wherein the level of rate stimulation is diminished for crowders larger than the size of the unfolded RNA. Monitoring effects of crowding and cosolute agents on rates in biological amounts of urea revealed additive-promoted increases at both low and high Mg(2+) concentrations, with a maximal stimulation of more than 10-fold and a rescue of the rate to its urea-free values. Small-angle X-ray scattering experiments reveal a structural basis for this stimulation in that higher-molecular weight crowding agents favor a more compact form of the ribozyme in 0.5 mM Mg(2+) that is essentially equivalent to the form under standard ribozyme conditions of 10 mM Mg(2+) without a crowder. This finding suggests that at least a portion of the rate enhancement arises from favoring the native RNA tertiary structure. We conclude that cellular-like crowding supports ribozyme reactivity by favoring a compact form of the ribozyme, but only under physiological ionic and cosolute conditions.

An RNA folding motif: GNRA tetraloop-receptor interactions

Nearly two decades after Westhof and Michel first proposed that RNA tetraloops may interact with distal helices, tetraloop–receptor interactions have been recognized as ubiquitous elements of RNA tertiary structure. The unique architecture of GNRA tetraloops (N=any nucleotide, R=purine) enables interaction with a variety of receptors, e.g., helical minor grooves and asymmetric internal loops. The most common example of the latter is the GAAA tetraloop–11 nt tetraloop receptor motif. Biophysical characterization of this motif provided evidence for the modularity of RNA structure, with applications spanning improved crystallization methods to RNA tectonics. In this review, we identify and compare types of GNRA tetraloop–receptor interactions. Then we explore the abundance of structural, kinetic, and thermodynamic information on the frequently occurring and most widely studied GAAA tetraloop–11 nt receptor motif. Studies of this interaction have revealed powerful paradigms for structural assembly of RNA, as well as providing new insights into the roles of cations, transition states and protein chaperones in RNA folding pathways. However, further research will clearly be necessary to characterize other tetraloop–receptor and long-range tertiary binding interactions in detail – an important milestone in the quantitative prediction of free energy landscapes for RNA folding.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Magnesium fluctuations modulate RNA dynamics in the SAM-I riboswitch

Experiments demonstrate that Mg(2+) is crucial for structure and function of RNA systems, yet the detailed molecular mechanism of Mg(2+) action on RNA is not well understood. We investigate the interplay between RNA and Mg(2+) at atomic resolution through ten 2-μs explicit solvent molecular dynamics simulations of the SAM-I riboswitch with varying ion concentrations. The structure, including three stemloops, is very stable on this time scale. Simulations reveal that outer-sphere coordinated Mg(2+) ions fluctuate on the same time scale as the RNA, and that their dynamics couple. Locally, Mg(2+) association affects RNA conformation through tertiary bridging interactions; globally, increasing Mg(2+) concentration slows RNA fluctuations. Outer-sphere Mg(2+) ions responsible for these effects account for 80% of Mg(2+) in our simulations. These ions are transiently bound to the RNA, maintaining interactions, but shuttled from site to site. Outer-sphere Mg(2+) are separated from the RNA by a single hydration shell, occupying a thin layer 3-5 Å from the RNA. Distribution functions reveal that outer-sphere Mg(2+) are positioned by electronegative atoms, hydration layers, and a preference for the major groove. Diffusion analysis suggests transient outer-sphere Mg(2+) dynamics are glassy. Since outer-sphere Mg(2+) ions account for most of the Mg(2+) in our simulations, these ions may change the paradigm of Mg(2+)-RNA interactions. Rather than a few inner-sphere ions anchoring the RNA structure surrounded by a continuum of diffuse ions, we observe a layer of outer-sphere coordinated Mg(2+) that is transiently bound but strongly coupled to the RNA.

The role of counterion valence and size in GAAA tetraloop-receptor docking/undocking kinetics

For RNA to fold into compact, ordered structures, it must overcome electrostatic repulsion between negatively charged phosphate groups by counterion recruitment. A physical understanding of the counterion-assisted folding process requires addressing how cations kinetically and thermodynamically control the folding equilibrium for each tertiary interaction in a full-length RNA. In this work, single-molecule FRET (fluorescence resonance energy transfer) techniques are exploited to isolate and explore the cation-concentration-dependent kinetics for formation of a ubiquitous RNA tertiary interaction, that is, the docking/undocking of a GAAA tetraloop with its 11-nt receptor. Rate constants for docking (k(dock)) and undocking (k(undock)) are obtained as a function of cation concentration, size, and valence, specifically for the series Na(+), K(+), Mg(2+), Ca(2+), Co(NH(3))(6)(3+), and spermidine(3+). Increasing cation concentration acceleratesk(dock)dramatically but achieves only a slight decrease in k(undock). These results can be kinetically modeled using parallel cation-dependent and cation-independent docking pathways, which allows for isolation of the folding kinetics from the interaction energetics of the cations with the undocked and docked states, respectively. This analysis reveals a preferential interaction of the cations with the transition state and docked state as compared to the undocked RNA, with the ion-RNA interaction strength growing with cation valence. However, the corresponding number of cations that are taken up by the RNA upon folding decreases with charge density of the cation. The only exception to these behaviors is spermidine(3+), whose weaker influence on the docking equilibria with respect to Co(NH(3))(6)(3+) can be ascribed to steric effects preventing complete neutralization of the RNA phosphate groups.

BioMe: biologically relevant metals

In this article, we introduce BioMe (biologically relevant metals), a web-based platform for calculation of various statistical properties of metal-binding sites. Users can obtain the following statistical properties: presence of selected ligands in metal coordination sphere, distribution of coordination numbers, percentage of metal ions coordinated by the combination of selected ligands, distribution of monodentate and bidentate metal-carboxyl, bindings for ASP and GLU, percentage of particular binuclear metal centers, distribution of coordination geometry, descriptive statistics for a metal ion–donor distance and percentage of the selected metal ions coordinated by each of the selected ligands. Statistics is presented in numerical and graphical forms. The underlying database contains information about all contacts within the range of 3 Å from a metal ion found in the asymmetric crystal unit. The stored information for each metal ion includes Protein Data Bank code, structure determination method, types of metal-binding chains [protein, ribonucleic acid (RNA), deoxyribonucleic acid (DNA), water and other] and names of the bounded ligands (amino acid residue, RNA nucleotide, DNA nucleotide, water and other) and the coordination number, the coordination geometry and, if applicable, another metal(s). BioMe is on a regular weekly update schedule. It is accessible at http://metals.zesoi.fer.hr.

Electrostatics of nucleic acid folding under conformational constraint

RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.

Characterization of metal ion-nucleic acid interactions in solution

Metal ions are inextricably involved with nucleic acids due to their polyanionic nature. In order to understand the structure and function of RNAs and DNAs, one needs to have detailed pictures on the structural, thermodynamic, and kinetic properties of metal ion interactions with these biomacromolecules. In this review we first compile the physicochemical properties of metal ions found and used in combination with nucleic acids in solution. The main part then describes the various methods developed over the past decades to investigate metal ion binding by nucleic acids in solution. This includes for example hydrolytic and radical cleavage experiments, mutational approaches, as well as kinetic isotope effects. In addition, spectroscopic techniques like EPR, lanthanide(III) luminescence, IR and Raman as well as various NMR methods are summarized. Aside from gaining knowledge about the thermodynamic properties on the metal ion-nucleic acid interactions, especially NMR can be used to extract information on the kinetics of ligand exchange rates of the metal ions applied. The final section deals with the influence of anions, buffers, and the solvent permittivity on the binding equilibria between metal ions and nucleic acids. Little is known on some of these aspects, but it is clear that these three factors have a large influence on the interaction between metal ions and nucleic acids.

EXPLORING THE FOLDING FREE ENERGY LANDSCAPE OF SMALL RNA MOLECULES BY SINGLE-PAIR FÖRSTER RESONANCE ENERGY TRANSFER

Proteins and RNA are biological macromolecules built from linear polymers. The process by which they fold into compact, well-defined, three-dimensional architectures to perform their functional tasks is still not well understood. It can be visualized by Brownian motion of an ensemble of molecules through a rugged energy landscape in search of an energy minimum corresponding to the native state. To explore the conformational energy landscape of small RNAs, single pair Förster resonance energy transfer (spFRET) experiments on solutions as well as on surface-immobilized samples have provided new insights. In this review, we focus on our recent work on two FRET-labeled small RNAs, the Diels-Alderase (DAse) ribozyme and the human mitochondrial tRNA Lys . For both RNAs, three different conformational states can be distinguished, and the associated mean FRET efficiencies provide clues about their structural properties. The systematic variation of their free energies with the concentration of Mg 2+ counterions was analyzed quantitatively by using a thermodynamic model that separates conformational changes from Mg 2+ binding. Furthermore, time-resolved spFRET studies on immobilized DAse reveal slow interconversions between intermediate and folded states on the time scale of ~ 100 ms. The quantitative data obtained from spFRET experiments may likely assist in the further development of theories and models addressing the folding dynamics and (counterion-dependent) energetics of RNA molecules.

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na(+) and Mg(2+)) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na(+) and Mg(2+) concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.

Arginine cofactors on the polymerase ribozyme

The RNA world hypothesis states that the early evolution of life went through a stage in which RNA served both as genome and as catalyst. The central catalyst in an RNA world organism would have been a ribozyme that catalyzed RNA polymerization to facilitate self-replication. An RNA polymerase ribozyme was developed previously in the lab but it is not efficient enough for self-replication. The factor that limits its polymerization efficiency is its weak sequence-independent binding of the primer/template substrate. Here we tested whether RNA polymerization could be improved by a cationic arginine cofactor, to improve the interaction with the substrate. In an RNA world, amino acid-nucleic acid conjugates could have facilitated the emergence of the translation apparatus and the transition to an RNP world. We chose the amino acid arginine for our study because this is the amino acid most adept to interact with RNA. An arginine cofactor was positioned at ten different sites on the ribozyme, using conjugates of arginine with short DNA or RNA oligonucleotides. However, polymerization efficiency was not increased in any of the ten positions. In five of the ten positions the arginine reduced or modulated polymerization efficiency, which gives insight into the substrate-binding site on the ribozyme. These results suggest that the existing polymerase ribozyme is not well suited to using an arginine cofactor.

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.

Linkage of cation binding and folding in human telomeric quadruplex DNA

Formation of DNA quadruplexes requires monovalent cation binding. To characterize the cation binding stoichiometry and linkage between binding and folding, we carried out KCl titrations of Tel22 (d[A(GGGTTA)(3)]), a model of the human telomere sequence, using a fluorescent indicator to determine [K(+)](free) and circular dichroism to assess the extent of folding. At [K(+)](free)=5 mM (sufficient for >95% folding), the apparent binding stoichiometry is 3K(+)/Tel22; at [K(+)](free)=20 mM, it increased to 8-10K(+)/Tel22. Thermodynamic analysis shows that at [K(+)](free)=5 mM, K(+) binding contributes approximately -4.9 kcal/mol for folding Tel22. The overall folding free energy is -2.4 kcal/mol, indicating that there are energetically unfavorable contributions to folding. Thus, quadruplex folding is driven almost entirely by the energy of cation binding with little or no contribution from other weak molecular interactions.

Protonation of base pairs in RNA: context analysis and quantum chemical investigations of their geometries and stabilities

Base pairs involving protonated nucleobases play important roles in mediating global macromolecular conformational changes and in facilitation of catalysis in a variety of functional RNA molecules. Here we present our attempts at understanding the role of such base pairs by detecting possible protonated base pairs in the available RNA crystal structures using BPFind software, in their specific structural contexts, and by the characterization of their geometries, interaction energies, and stabilities using advanced quantum chemical computations. We report occurrences of 18 distinct protonated base pair combinations from a representative data set of RNA crystal structures and propose a theoretical model for one putative base pair combination. Optimization of base pair geometries was carried out at the B3LYP/cc-pVTZ level, and the BSSE corrected interaction energies were calculated at the MP2/aug-cc-pVDZ level of theory. The geometries for each of the base pairs were characterized in terms of H-bonding patterns observed, rmsd values observed on optimization, and base pair geometrical parameters. In addition, the intermolecular interaction in these complexes was also analyzed using Morokuma energy decomposition. The gas phase interaction energies of the base pairs range from -24 to -49 kcal/mol and reveal the dominance of Hartree-Fock component of interaction energy constituting 73% to 98% of the total interaction energy values. On the basis of our combined bioinformatics and quantum chemical analysis of different protonated base pairs, we suggest resolution of structural ambiguities and correlate their geometric and energetic features with their structural and functional roles. In addition, we also examine the suitability of specific base pairs as key elements in molecular switches and as nucleators for higher order structures such as base triplets and quartets.

Unexpected dissociation energetics of the Na(+) counterion from GC motifs in DNA hole-migration

We present here a theoretical investigation of the electronic and energetic properties of Na(+)GC, a DNA motif bound to a sodium ion (Na(+)) at the N(7) and O(6) sites of guanine (G), and its hole-trapped derivative [Na(+)GC](+) using density functional theory calculations. Normally, Na(+)GC has positive dissociation energies along various dissociation channels. However, hole-trapping of the Na(+)GC motif can lead to an unusual energetic phenomenon. Hole-trapping can reduce not only the dissociation barrier by destabilizing the Na(+)GC motif to a metastable state, but also the dissociation energy of the Na(+)N(7)/O(6) bond with an unexpected change from a positive to a negative value (61.51 versus-16.18 kcal mol(-1)). This unexpected negative dissociation energy phenomenon implies that this motif can store energy (∼16 kcal mol(-1)) in the Na(+)N(7)/O(6) bond zone due to hole-trapping. The topological properties of electron densities and the Laplacian values at the bond critical points indicate that this energetic phenomenon mainly originates from additional electrostatic repulsions between two moieties linked via a high-energy bond (Na(+)N(7)/O(6)). Proton transfer from G induced by hole-trapping can expand the negative dissociation energy zone to both Na(+)N(7)/O(6) and Watson-Crick (WC) H-bond zones. Similar phenomena can be observed for the Na(+) binding at the minor groove. Solvation of the hole-trapped Na(+)GC motif can change the negative dissociation energies by varying degrees, depending on the solvent-binding sites and the polarity of the solvents.

Prediction of RNA multiloop and pseudoknot conformations from a lattice-based, coarse-grain tertiary structure model

We present a semiquantitative lattice model of RNA folding, which is able to reproduce complex folded structures such as multiloops and pseudoknots without relying on the frequently employed ad hoc generalization of the Jacobson-Stockmayer loop entropy. We derive the model parameters from the Turner description of simple secondary structural elements and pay particular attention to the unification of mismatch and coaxial stacking parameters as well as of border and nonlocal loop parameters, resulting in a reduced, unified parameter set for simple loops of arbitrary type and size. For elementary structures, the predictive power of the model is comparable to the standard secondary structure approaches, from which its parameters are derived. For complex structures, our approach offers a systematic treatment of generic effects of chain connectivity as well as of excluded volume or attractive interactions between and within all elements of the secondary structure. We reproduce the native structures of tRNA multiloops and of viral frameshift signal pseudoknots.

Nucleophile activation in PD...(D/E)xK metallonucleases: an experimental and computational pK(a) study

Metallonucleases conduct metal-dependent nucleic acid hydrolysis. While metal ions serve in multiple mechanistic capacities in these enzymes, precisely how the attacking water is activated remains unclear for those lacking an obvious general base. All arguments hinge on appropriate pK(a)s for active site moieties very close to this species, and measurement of the pK(a) of a specific water molecule is difficult to access experimentally. Here we describe a computational approach for exploring the local electrostatic influences on the water-derived nucleophile in metallonucleases featuring the common PD...(D/E)xK motif. We utilized UHBD to predict the pK(a)s of active site groups, including that of a water molecule positioned to act as a nucleophile. The pK(a) of a Mg(II)-ligated water molecule hydrogen bonded to the conserved Lys70 in a Mg(II)-PvuII enzyme complex was calculated to be 6.5. The metal and the charge on the Lys group were removed in separate experiments; both resulted in the elevation of the pK(a) of this water molecule, consistent with contributions from both moieties to lowering this pK(a). This behavior is preserved among other PD...(D/E)xK metallonucleases. pK(a)s extracted from the pH dependence of the single turnover rate constant are compared to previous experimental data and the above predicted pK(a)s.

A quantitative Raman spectroscopic signal for metal-phosphodiester interactions in solution

Accurate identification and quantification of metal ion-phosphodiester interactions are essential for understanding the role of metal ions as determinants of three-dimensional folding of large RNAs and as cofactors in the active sites of both RNA and protein phosphodiesterases. Accomplishing this goal is difficult due to the dynamic and complex mixture of direct and indirect interactions formed with nucleic acids and other phosphodiesters in solution. To address this issue, Raman spectroscopy has been used to measure changes in bond vibrational energies due to metal interactions. However, the contributions of inner-sphere, H-bonding, and electrostatic interactions to the Raman spectrum of phosphoryl oxygens have not been analyzed quantitatively. Here, we report that all three forms of metal ion interaction result in attenuation of the Raman signal for the symmetric vibration of the nonbridging phosphate oxygens (nu(s)PO(2)(-)), while only inner-sphere coordination gives rise to an apparent shift of nu(s)PO(2)(-) to higher wavenumbers (nu(s)PO(2)(-)M) in solution. Formation of nu(s)PO(2)(-)M is shown to be both dependent on metal ion identity and an accurate measure of site-specific metal ion binding. In addition, the spectroscopic parameter reflecting the energetic difference between nu(s)PO(2)(-) and nu(s)PO(2)(-)M (DeltanuM) is largely insensitive to changes in phosphodiester structure but strongly dependent on the absolute electronegativity and hardness of the interacting metal ion. Together, these studies provide strong experimental support for the use of nu(s)PO(2)(-)M and DeltanuM as general spectroscopic features for the quantitative analysis of metal binding affinity and the identification of metal ions associated with phosphodiesters in solution.

Do conformational biases of simple helical junctions influence RNA folding stability and specificity?

Structured RNAs must fold into their native structures and discriminate against a large number of alternative ones, an especially difficult task given the limited information content of RNA's nucleotide alphabet. The simplest motifs within structured RNAs are two helices joined by nonhelical junctions. To uncover the fundamental behavior of these motifs and to elucidate the underlying physical forces and challenges faced by structured RNAs, we computationally and experimentally studied a tethered duplex model system composed of two helices joined by flexible single- or double-stranded polyethylene glycol tethers, whose lengths correspond to those typically observed in junctions from structured RNAs. To dissect the thermodynamic properties of these simple motifs, we computationally probed how junction topology, electrostatics, and tertiary contact location influenced folding stability. Small-angle X-ray scattering was used to assess our predictions. Single- or double-stranded junctions, independent of sequence, greatly reduce the space of allowed helical conformations and influencing the preferred location and orientation of their adjoining helices. A double-stranded junction guides the helices along a hinge-like pathway. In contrast, a single-stranded junction samples a broader set of conformations and has different preferences than the double-stranded junction. In turn, these preferences determine the stability and distinct specificities of tertiary structure formation. These sequence-independent effects suggest that properties as simple as a junction's topology can generally define the accessible conformational space, thereby stabilizing desired structures and assisting in discriminating against misfolded structures. Thus, junction topology provides a fundamental strategy for transcending the limitations imposed by the low information content of RNA primary sequence.

Using analytical ultracentrifugation (AUC) to measure global conformational changes accompanying equilibrium tertiary folding of RNA molecules

Analytical ultracentrifugation (AUC) is a powerful technique to determine the global conformational changes in RNA molecules mediated by cations or small molecule ligands. Although most of the developments in the field of AUC have been centered on studies involving protein molecules, the experimental methods as well as the analytical approaches have been successfully adapted and applied to the study of a variety of RNA molecules ranging from small riboswitches to large ribozymes. Most often AUC studies are performed in conjunction with other structural probing techniques that provide complementary information on local changes in the solvent accessibilities at specific regions within RNA molecules. This chapter provides a brief theoretical background, working knowledge of instrumentation, practical considerations for experimental setup, and guidelines for data analysis procedures to enable the design, execution, and interpretation of sedimentation velocity experiments that detect changes in the global dimensions of an RNA molecule during its equilibrium folding.

EPR methods to study specific metal-ion binding sites in RNA

The properties of metal-ion interactions with RNA can be explored by spectroscopic methods. In this chapter, we describe the use of paramagnetic Mn(2+) ions and electron paramagnetic resonance (EPR)-based techniques to monitor the association of Mn(2+) with RNA and related nucleotides. Solution EPR methods are used to determine the numbers of Mn(2+) ions associating with RNA. For RNA poised with a single-bound Mn(2+), low-temperature EPR characteristics provide information about the asymmetry of the Mn(2+) coordination site. To identify the RNA groups coordinating to the Mn(2+) ion, ENDOR (electron nuclear double resonance) and ESEEM (electron spin echo envelope modulation) methods are applied. Both continuous-wave (CW) and electron spin echo (ESE)-detected ENDOR methods are described. This chapter includes practical details for RNA sample preparation, including isotope substitution and cryoprotection, and an overview of data acquisition and analysis methods used in these techniques, as well as examples from the current literature.

RNA matrix models with external interactions and their asymptotic behavior

We study a matrix model of RNA in which an external perturbation on n nucleotides is introduced in the action of the partition function of the polymer chain. The effect of the perturbation appears in the exponential generating function of the partition function as a factor exp(1-nalpha/L) (where alpha is the ratio of strengths of the original to the perturbed term and L is the length of the chain). The asymptotic behavior of the genus distribution functions as a function of length for the matrix model with interaction is analyzed numerically for all n<or=L. It is found that as nalpha/L is increased from 0 to 1, the term 3L in the number of diagrams a'L,g,alpha at a fixed length L, genus g and alpha, goes to 2L [(3-nalpha/L)L for any nalpha/L] and the total number of diagrams Nalpha' at a fixed length L and alpha but independent of genus g, undergoes a change in the factor exp(sqrt[L]) to 1 (exp[(1-nalpha/L)sqrt[L]] for any nalpha/L). However the exponent L of the dominant length dependent term in a'L,g,alpha stays unchanged. Hence the universality is robust to changes in the interaction (alpha). The distribution functions also exhibit unusual behavior at small lengths.

Tailoring RNA modular units on a common scaffold: a modular ribozyme with a catalytic unit for beta-nicotinamide mononucleotide-activated RNA ligation

A novel ribozyme that accelerates the ligation of beta-nicotinamide mononucleotide (beta-NMN)-activated RNA fragments was isolated and characterized. This artificial ligase ribozyme (YFL ribozyme) was isolated by a "design and selection" strategy, in which a modular catalytic unit was generated on a rationally designed modular scaffold RNA. Biochemical analyses of the YFL ribozyme revealed that it catalyzes RNA ligation in a template-dependent manner, and its activity is highly dependent on its architecture, which consists of a modular scaffold and a catalytic unit. As the design and selection strategy was used for generation of DSL ribozyme, isolation of the YFL ribozyme indicated the versatility of this strategy for generation of functional RNAs with modular architectures. The catalytic unit of the YFL ribozyme accepts not only beta-NMN but also inorganic pyrophosphate and adenosine monophosphate as leaving groups for RNA ligation. This versatility of the YFL ribozyme provides novel insight into the possible roles of beta-NMN (or NADH) in the RNA world.

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

Double and triple mutant thermodynamic cycles provide a means to dissect the cooperativity of RNA and DNA folding at both the secondary and tertiary structural levels through use of the thermodynamic box or cube. In this article, we describe three steps for applying thermodynamic cycles to nucleic acid folding, with considerations of both conceptual and experimental features. The first step is design of an appropriate system and development of hypotheses regarding which residues might interact. Next is implementing this design in terms of a tractable experimental strategy, with an emphasis on UV melting. The final step, and the one we emphasize the most, is interpreting mutant cycles in terms of coupling between specific residues in the RNA or DNA. Coupling free energy in the absence and presence of changes elsewhere in the molecule is discussed in terms of specific folding models, including stepwise folding and concerted changes. Last, we provide a practical section on the use of commercially available software (KaleidaGraph) to fit melting data, along with a consideration of error propagation. Along the way, specific examples are chosen from the literature to illustrate the methods. This article is intended to be accessible to the biochemist or biologist without extensive thermodynamics background.

Probing the ionic atmosphere of single-stranded DNA using continuous flow capillary electrophoresis and fluorescence correlation spectroscopy

Two-beam fluorescence cross-correlation spectroscopy coupled with continuous flow capillary electrophoresis (2bFCCS-CFCE) was used to study the relationship between diffusion and effective charge of a fluorescently labeled 40-base polythymine single-stranded DNA (ssDNA) as a function of Mg2+ concentration. Cross-correlation analysis of the fluorescence monitored from two spatially offset microscopic detection volumes revealed the diffusion and electrophoretic migration of ssDNA at a range of Mg2+ concentrations and electric field strengths. The effective charge of the ssDNA could then be determined using simple calculations. It was found that as the Mg2+ concentration in the buffer solution increased, the diffusion of the ssDNA also increased, while the effective charge of the ssDNA decreased. This was believed to be caused by increased association of the Mg2+ counterions with the negatively charged backbone of the ssDNA, which partially neutralized the negatively charged functional groups and allowed the ssDNA to adopt a more compact structure. To our knowledge, this is the first demonstration of the measurement of effective charge of ssDNA in relation to Mg2+ concentration.

Mapping metal-binding sites in the catalytic domain of bacterial RNase P RNA

Ribonuclease P (RNase P) is a ribonucleoprotein enzyme that contains a universally conserved, catalytically active RNA component. RNase P RNA requires divalent metal ions for folding, substrate binding, and catalysis. Despite recent advances in understanding the structure of RNase P RNA, no comprehensive analysis of metal-binding sites has been reported, in part due to the poor crystallization properties of this large RNA. We have developed an abbreviated yet still catalytic construct, Bst P7Delta RNA, which contains the catalytic domain of the bacterial RNase P RNA and has improved crystallization properties. We use this mutant RNA as well as the native RNA to map metal-binding sites in the catalytic core of the bacterial RNase P RNA, by anomalous scattering in diffraction analysis. The results provide insight into the interplay between RNA structure and focalization of metal ions, and a structural basis for some previous biochemical observations with RNase P. We use electrostatic calculations to extract the potential functional significance of these metal-binding sites with respect to binding Mg(2+). The results suggest that with at least one important exception of specific binding, these sites mainly map areas of diffuse association of magnesium ions.

Direct quantitation of Mg2+-RNA interactions by use of a fluorescent dye

The ionic composition of a solution strongly influences the folding of an RNA into its native structure; of particular importance, the stabilities of RNA tertiary structures are sharply dependent on the concentration of Mg2+. Most measurements of the extent of Mg2+ interaction with an RNA have relied on equilibrium dialysis or indirect measurements. Here we describe an approach, based on titrations in the presence of a fluorescent indicator dye, that accurately measures the excess Mg2+ ion neutralizing the charge of an RNA (the interaction or Donnan coefficient, Gamma2+) and the total free energy of Mg2+-RNA interactions (DeltaG(RNA-2+)). Automated data collection with computer-controlled titrators enables the collection of much larger data sets in a short time, compared to equilibrium dialysis. Gamma2+ and DeltaG(RNA-2+) are thermodynamically rigorous quantities that are directly comparable with the results of theoretical calculations and simulations. In the event that RNA folding is coupled to the addition of MgCl2, the method directly monitors the uptake of Mg2+ associated with the folding transition.

RNA folding during transcription: protocols and studies

RNA folds during transcription in the cell. Compared to most in vitro studies where the focus is generally on Mg(2+)-initiated refolding of fully synthesized transcripts, cotranscriptional RNA folding studies better replicate how RNA folds in a cellular environment. Unique aspects of cotranscriptional folding include the 5'- to 3'-polarity of RNA, the transcriptional speed, pausing properties of the RNA polymerase, the effect of the transcriptional complex and associated factors, and the effect of RNA-binding proteins. Identifying strategic pause sites can reveal insights on the folding pathway of the nascent transcript. Structural mapping of the paused transcription complexes identifies important folding intermediates along these pathways. Oligohybridization assays and the appearance of the catalytic activity of a ribozyme either in trans or in cis can be used to monitor cotranscriptional folding under a wide range of conditions. In our laboratory, these methodologies have been applied to study the folding of three highly conserved RNAs (RNase P, SRP, and tmRNA), several circularly permuted forms of a bacterial RNase P RNA, a riboswitch (thiM), and an aptamer-activated ribozyme (glmS).

A repulsive field: advances in the electrostatics of the ion atmosphere

The large electrostatic repulsion arising from the negatively charged backbone of RNA molecules presents a large barrier to folding. Solution counterions assist in the folding process by screening this electrostatic repulsion. While early research interpreted the effect of these counterions in terms of an empirical ligand-binding model, theories based on physical models have supplanted them and revised our view of the roles that ions play in folding. Instead of specific ion-binding sites, most ions in solution interact inside an 'ion atmosphere'--a fluctuating cloud of nonspecifically associated ions surrounding any charged molecule. Recent advances in experiments have begun the task of characterizing the ion atmosphere, yielding valuable data that have revealed deficiencies in Poisson-Boltzmann theory, the most widely used theory of the ion atmosphere. The continued development of experiments will help guide the development of improved theories, with the ultimate goal of understanding RNA folding and function and nucleic acid/protein interactions from a quantitative perspective.