Mg(2+) binding to tRNA revisited: the nonlinear Poisson-Boltzmann model

Understanding the Thermodynamics of Magnesium Binding to RNA Structural Motifs

Divalent magnesium ions (Mg2+) serve a vital role in defining the structural and catalytic chemistry of a wide array of RNA molecules. The body of structural information on RNA motifs continues to expand and, in turn, the functional importance of Mg2+ is revealed. A combination of prior work on the structural characterization of magnesium binding ligands with inner- and outer-sphere coordination modes, with recorded experimental binding energies for inner- and outer-sphere contacts, demonstrates the relative affinity and thermodynamic hierarchy for these sites. In turn, these can be correlated with cellular concentrations of free available magnesium ions, allowing the prioritization of populating important functional sites and a correlation with physiological function. This paper summarizes some of the key results of that analysis and provides predictive rules for the affinity and role of newly identified Mg binding sites on complex RNA structures. The influence of crystal packing on magnesium binding to RNA motifs, relative to their solution form, is addressed and caveats made.

Elucidating the influence of RNA modifications and Magnesium ions on tRNA Phe conformational dynamics in S. cerevisiae : Insights from Replica Exchange Molecular Dynamics simulations

Post-transcriptional modifications in RNA can significantly impact their structure and function. In particular, transfer RNAs (tRNAs) are heavily modified, with around 100 different naturally occurring nucleotide modifications contributing to codon bias and decoding efficiency. Here, we describe our efforts to investigate the impact of RNA modifications on the structure and stability of tRNA Phenylalanine (tRNA Phe ) from S. cerevisiae using molecular dynamics (MD) simulations. Through temperature replica exchange MD (T-REMD) studies, we explored the unfolding pathway to understand how RNA modifications influence the conformational dynamics of tRNA Phe , both in the presence and absence of magnesium ions (Mg 2+ ). We observe that modified nucleotides in key regions of the tRNA establish a complex network of hydrogen bonds and stacking interactions which is essential for tertiary structure stability of the tRNA. Furthermore, our simulations show that modifications facilitate the formation of ion binding sites on the tRNA. However, high concentrations of Mg 2+ ions can stabilize the tRNA tertiary structure in the absence of modifications. Our findings illuminate the intricate interactions between modifications, magnesium ions, and RNA structural stability.

Geometric deep learning for the prediction of magnesium-binding sites in RNA structures

Magnesium ions (Mg2+) are essential for the folding, functional expression, and structural stability of RNA molecules. However, predicting Mg2+-binding sites in RNA molecules based solely on RNA structures is still challenging. The molecular surface, characterized by a continuous shape with geometric and chemical properties, is important for RNA modelling and carries essential information for understanding the interactions between RNAs and Mg2+ ions. Here, we propose an approach named RNA-magnesium ion surface interaction fingerprinting (RMSIF), a geometric deep learning-based conceptual framework to predict magnesium ion binding sites in RNA structures. To evaluate the performance of RMSIF, we systematically enumerated decoy Mg2+ ions across a full-space grid within the range of 2 to 10 Å from the RNA molecule and made predictions accordingly. Visualization techniques were used to validate the prediction results and calculate success rates. Comparative assessments against state-of-the-art methods like MetalionRNA, MgNet, and Metal3DRNA revealed that RMSIF achieved superior success rates and accuracy in predicting Mg2+-binding sites. Additionally, in terms of the spatial distribution of Mg2+ ions within the RNA structures, a majority were situated in the deep grooves, while a minority occupied the shallow grooves. Collectively, the conceptual framework developed in this study holds promise for advancing insights into drug design, RNA co-transcriptional folding, and structure prediction.

Thermodynamics of d(GGGGCCCC) Binding to Neomycin-Class Aminoglycosides

DNA adopts a number of conformations that can affect its binding to other macromolecules. The conformations (A, B, Z) can be sequence- and/or solution-dependent. While AT-rich DNA sequences generally adopt a Canonical B-form structure, GC-rich sequences are more promiscuous. Recognition of GC-rich nucleic acids by small molecules has been much more challenging than the recognition of AT-rich duplexes. Spectrophotometric and calorimetric techniques were used to characterize the binding of neomycin-class aminoglycosides to a GC-rich DNA duplex, G₄C₄, in various ionic and pH conditions. Our results reveal that binding enhances the thermal stability of G₄C₄, with thermal enhancement decreasing with increasing pH and/or Na⁺ concentration. Although G₄C₄ bound to aminoglycosides demonstrated a mixed A- and B-form conformation, circular dichroism studies indicate that binding induces a conformational shift toward A-form DNA. Isothermal titration calorimetry studies reveal that aminoglycoside binding to G₄C₄ is linked to the uptake of protons at pH = 7.0 and that this uptake is pH-dependent. Increased pH and/or Na⁺ concentration results in a decrease in G₄C₄ affinity for the aminoglycosides. The binding affinities of the aminoglycosides follow the expected hierarchy: neomycin > paromomycin > ribostamycin. The salt dependence of DNA binding affinities of aminoglycosides is consistent with at least two drug NH₃⁺ groups participating in electrostatic interactions with G₄C₄. These studies further embellish our understanding of the many factors facilitating recognition of GC-rich DNA structures as guided by their optimum charge and shape complementarity for small-molecule amino sugars.

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.

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg2+) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg2+ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg2+ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg2+-excess concentrations and comparison with fluorescence titration measurements shows that on average 20-30% of the Mg2+ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.

The mutual interactions of RNA, counterions and water - quantifying the electrostatics at the phosphate-water interface

The structure and dynamics of polyanionic biomolecules, like RNA, are decisively determined by their electric interactions with the water molecules and the counterions in the environment. The solvation dynamics of the biomolecules involves a subtle balance of non-covalent and many-body interactions with structural fluctuations due to thermal motion occurring in a femto- to subnanosecond time range. This complex fluctuating many particle scenario is crucial in defining the properties of biological interfaces with far reaching significance for the folding of RNA structures and for facilitating RNA-protein interactions. Given the inherent complexity, suited model systems, carefully calibrated and benchmarked by experiments, are required to quantify the relevant interactions of RNA with the aqueous environment. In this feature article we summarize our recent progress in the understanding of the electrostatics at the biological interface of double stranded RNA (dsRNA) and transfer RNA (tRNA). Dimethyl phosphate (DMP) is introduced as a viable and rigorously accessible model system allowing the interaction strength with water molecules and counterions, their relevant fluctuation timescales and the spatial reach of interactions to be established. We find strong (up to ≈90 MV cm-1) interfacial electric fields with fluctuations extending up to ≈20 THz and demonstrate how the asymmetric stretching vibration νAS(PO2)- of the polarizable phosphate group can serve as the most sensitive probe for interfacial interactions, establishing a rigorous link between simulations and experiment. The approach allows for the direct interfacial observation of interactions of biologically relevant Mg2+ counterions with phosphate groups in contact pair geometries via the rise of a new absorption band imposed by exchange repulsion interactions at short interatomic distances. The systematic extension to RNA provides microscopic insights into the changes of the hydration structure that accompany the temperature induced melting of the dsRNA double helix and quantify the ionic interactions in the folded tRNA. The results show that pairs of negatively charged phosphate groups and Mg2+ ions represent a key structural feature of RNA embedded in water. They highlight the importance of binding motifs made of contact pairs in the electrostatic stabilization of RNA structures that have a strong impact on the surface potential and enable the fine tuning of the local electrostatic properties which are expected to be relevant for mediating the interactions between biomolecules.

Magnesium Contact Ions Stabilize the Tertiary Structure of Transfer RNA: Electrostatics Mapped by Two-Dimensional Infrared Spectra and Theoretical Simulations

Ions interacting with hydrated RNA play a central role in defining its secondary and tertiary structure. While spatial arrangements of ions, water molecules, and phosphate groups have been inferred from X-ray studies, the role of electrostatic and other noncovalent interactions in stabilizing compact folded RNA structures is not fully understood at the molecular level. Here, we demonstrate that contact ion pairs of magnesium (Mg²⁺) and phosphate groups embedded in local water shells stabilize the tertiary equilibrium structure of transfer RNA (tRNA). Employing dialyzed tRNA^Phe from yeast and tRNA from Escherichia coli, we follow the population of Mg²⁺ sites close to phosphate groups of the ribose-phosphodiester backbone step by step, combining linear and nonlinear infrared spectroscopy of phosphate vibrations with molecular dynamics simulations and ab initio vibrational frequency calculations. The formation of up to six Mg²⁺/phosphate contact pairs per tRNA and local field-induced reorientations of water molecules balance the phosphate–phosphate repulsion in nonhelical parts of tRNA, thus stabilizing the folded structure electrostatically. Such geometries display limited sub-picosecond fluctuations in the arrangement of water molecules and ion residence times longer than 1 μs. At higher Mg²⁺ excess, the number of contact ion pairs per tRNA saturates around 6 and weakly interacting ions prevail. Our results suggest a predominance of contact ion pairs over long-range coupling of the ion atmosphere and the biomolecule in defining and stabilizing the tertiary structure of tRNA.

Role of Wybutosine and Mg2+ Ions in Modulating the Structure and Function of tRNAPhe: A Molecular Dynamics Study

Transfer RNA remains to be a mysterious molecule of the cell repertoire. With its modified bases and selectivity of codon recognition, it remains to be flexible inside the ribosomal machinery for smooth and hassle-free protein biosynthesis. Structural changes occurring in tRNA due to the presence or absence of wybutosine, with and without Mg²⁺ ions, have remained a point of interest for structural biologists. Very few studies have come to a conclusion correlating the changes either with the structure and flexibility or with the codon recognition. Considering the above facts, we have implemented molecular modeling methods to address these problems using multiple molecular dynamics (MD) simulations of tRNA^Phe along with codons. Our results highlight some of the earlier findings and also shed light on some novel structural and functional aspects. Changes in the stability of tRNA^Phe in native or codon-bound states result from the conformations of constituent nucleotides with respect to each other. A smaller change in their conformations leads to structural distortions in the base-pairing geometry and eventually in the ribose-phosphate backbone. MD simulation studies highlight the preference of UUC codons over UUU by tRNA^Phe in the presence of wybutosine and Mg²⁺ ions. This study also suggests that magnesium ions are required by tRNA^Phe for proper recognition of UUC/UUU codons during ribosomal interactions with tRNA.

Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting

RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg²⁺, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg²⁺-DNA and Mg²⁺-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.

Dynamics of metal ions around an RNA molecule

Noncoding RNA molecules take part in many biological processes, while metal ions play crucial roles in helping RNAs to perform their functions. However, the statics and dynamics of these metal ions around RNA molecules are still not well understood. In this work, we report a detailed molecular dynamics study of the type-I preQ_{1}-bound riboswitch aptamer domain (PRAD) at different ionic conditions (K^{+}, Na^{+}, and Mg^{2+}). The results show that the structural properties and flexibility of the PRAD molecule greatly influence the distributions and dynamics of metal ions around it. Simultaneously, Na^{+} ions show a stronger competitiveness with Mg^{2+} ions than K^{+} ions, and the three types of metal ions have different modes of interaction with the RNA molecule. Furthermore, we have also investigated specific binding sites of metal ions on the PRAD molecule and found that the dynamics and hydration structures of metal ions located at the ion-binding sites were obviously affected by the RNA structure near these ion-binding sites. These results may be useful to understand the role of the metal ions in noncoding RNA functions.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding

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

Counting the ions surrounding nucleic acids

Nucleic acids are strongly negatively charged, and thus electrostatic interactions—screened by ions in solution—play an important role in governing their ability to fold and participate in biomolecular interactions. The negative charge creates a region, known as the ion atmosphere, in which cation and anion concentrations are perturbed from their bulk values. Ion counting experiments quantify the ion atmosphere by measuring the preferential ion interaction coefficient: the net total number of excess ions above, or below, the number expected due to the bulk concentration. The results of such studies provide important constraints on theories, which typically predict the full three-dimensional distribution of the screening cloud. This article reviews the state of nucleic acid ion counting measurements and critically analyzes their ability to test both analytical and simulation-based models.

Divalent ion competition reveals reorganization of an RNA ion atmosphere upon folding

Although RNA interactions with K+ and Mg2+ have been studied extensively, much less is known about the third most abundant cation in bacterial cells, putrescine2+, and how RNA folding might be influenced by the three ions in combination. In a new approach, we have observed the competition between Mg2+ and putrescine2+ (in a background of K+) with native, partially unfolded and highly extended conformations of an adenine riboswitch aptamer. With the native state, putrescine2+ is a weak competitor when the ratio of the excess Mg2+ (which neutralizes phosphate charge) to RNA is very low, but becomes much more effective at replacing Mg2+ as the excess Mg2+ in the RNA ion atmosphere increases. Putrescine2+ is even more effective in competing Mg2+ from the extended conformation, independent of the Mg2+ excess. To account for these and other results, we propose that both ions closely approach the surface of RNA secondary structure, but the completely folded RNA tertiary structure develops small pockets of very negative electrostatic potential that are more accessible to the compact charge of Mg2+. The sensitivity of RNA folding to the combination of Mg2+ and putrescine2+ found in vivo depends on the architectures of both the unfolded and native conformations.

All-atom MD indicates ion-dependent behavior of therapeutic DNA polymer

Understanding the efficacy of and creating delivery mechanisms for therapeutic nucleic acids requires understanding structural and kinetic properties which allow these polymers to promote the death of cancerous cells. One molecule of interest is a 10 mer of FdUMP (5-fluoro-2'-deoxyuridine-5'-O-monophosphate) - also called F10. Here we investigate the structural and kinetic behavior of F10 in intracellular and extracellular solvent conditions along with non-biological conditions that may be efficacious in in vitro preparations of F10 delivery systems. From our all-atom molecular dynamics simulations totaling 80 microseconds, we predict that F10's phosphate groups form close-range interactions with calcium and zinc ions, with calcium having the highest affinity of the five ions investigated. We also predict that F10's interactions with magnesium, potassium and sodium are almost exclusively long-range interactions. In terms of intramolecular interactions, we find that F10 is least structured (in terms of hydrogen bonds among bases) in the 150 mM NaCl (extracellular-like solvent conditions) and most structured in 150 mM ZnCl2. Kinetically, we see that F10 is unstable in the presence of magnesium, sodium or potassium, finding stable kinetic traps in the presence of calcium or zinc.

All-Atom MD Predicts Magnesium-Induced Hairpin in Chemically Perturbed RNA Analog of F10 Therapeutic

Given their increasingly frequent usage, understanding the chemical and structural properties which allow therapeutic nucleic acids to promote the death of cancer cells is critical for medical advancement. One molecule of interest is a 10-mer of FdUMP (5-fluoro-2'-deoxyuridine-5'-O-monophosphate) also called F10. To investigate causes of structural stability, we have computationally restored the 2' oxygen on each ribose sugar of the phosphodiester backbone, creating FUMP[10]. Microsecond time-scale, all-atom, simulations of FUMP[10] in the presence of 150 mM MgCl₂ predict that the strand has a 45% probability of folding into a stable hairpin-like secondary structure. Analysis of 16 μs of data reveals phosphate interactions as likely contributors to the stability of this folded state. Comparison with polydT and polyU simulations predicts that FUMP[10]'s lowest order structures last for one to 2 orders of magnitude longer than similar nucleic acid strands. Here we provide a brief structural and conformational analysis of the predicted structures of FUMP[10], and suggest insights into its stability via comparison to F10, polydT, and polyU.

The 2D Structure of the T. brucei Preedited RPS12 mRNA Is Not Affected by Macromolecular Crowding

Mitochondrial transcript maturation in African trypanosomes requires RNA editing to convert sequence-deficient pre-mRNAs into translatable mRNAs. The different pre-mRNAs have been shown to adopt highly stable 2D folds; however, it is not known whether these structures resemble the in vivo folds given the extreme "crowding" conditions within the mitochondrion. Here, we analyze the effects of macromolecular crowding on the structure of the mitochondrial RPS12 pre-mRNA. We use high molecular mass polyethylene glycol as a macromolecular cosolute and monitor the structure of the RNA globally and with nucleotide resolution. We demonstrate that crowding has no impact on the 2D fold and we conclude that the MFE structure in dilute solvent conditions represents a good proxy for the folding of the pre-mRNA in its mitochondrial solvent context.

Nucleic acid polymeric properties and electrostatics: Directly comparing theory and simulation with experiment

Nucleic acids are biopolymers that carry genetic information and are also involved in various gene regulation functions such as gene silencing and protein translation. Because of their negatively charged backbones, nucleic acids are polyelectrolytes. To adequately understand nucleic acid folding and function, we need to properly describe its i) polymer/polyelectrolyte properties and ii) associating ion atmosphere. While various theories and simulation models have been developed to describe nucleic acids and the ions around them, many of these theories/simulations have not been well evaluated due to complexities in comparison with experiment. In this review, I discuss some recent experiments that have been strategically designed for straightforward comparison with theories and simulation models. Such data serve as excellent benchmarks to identify limitations in prevailing theories and simulation parameters.

Folding of RNA tertiary structure: Linkages between backbone phosphates, ions, and water

The functional forms of many RNAs have compact architectures. The placement of phosphates within such structures must be influenced not only by the strong electrostatic repulsion between phosphates, but also by networks of interactions between phosphates, water, and mobile ions. This review first explores what has been learned of the basic thermodynamic constraints on these arrangements from studies of hydration and ions in simple DNA molecules, and then gives an overview of what is known about ion and water interactions with RNA structures. A brief survey of RNA crystal structures identifies several interesting architectures in which closely spaced phosphates share hydration shells or phosphates are buried in environments that provide intramolecular hydrogen bonds or site-bound cations. Formation of these structures must require strong coupling between the uptake of ions and release of water.

Computational modeling of RNA 3D structures and interactions

RNA molecules have key functions in cellular processes beyond being carriers of protein-coding information. These functions are often dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is difficult, which has prompted the development of computational methods for structure prediction from sequence. Recent progress in 3D structure modeling of RNA and emerging approaches for predicting RNA interactions with ions, ligands and proteins have been stimulated by successes in protein 3D structure modeling.

Computational methods for prediction of RNA interactions with metal ions and small organic ligands

In the recent years, it has become clear that a wide range of regulatory functions in bacteria are performed by riboswitches--regions of mRNA that change their structure upon external stimuli. Riboswitches are therefore attractive targets for drug design, molecular engineering, and fundamental research on regulatory circuitry of living cells. Several mechanisms are known for riboswitches controlling gene expression, but most of them perform their roles by ligand binding. As with other macromolecules, knowledge of the 3D structure of riboswitches is crucial for the understanding of their function. The development of experimental methods allowed for investigation of RNA structure and its complexes with ligands (which are either riboswitches' substrates or inhibitors) and metal cations (which stabilize the structure and are also known to be riboswitches' inhibitors). The experimental probing of different states of riboswitches is however time consuming, costly, and difficult to resolve without theoretical support. The natural consequence is the use of computational methods at least for initial research, such as the prediction of putative binding sites of ligands or metal ions. Here, we present a review on such methods, with a special focus on knowledge-based methods developed in our laboratory: LigandRNA--a scoring function for the prediction of RNA-small molecule interactions and MetalionRNA--a predictor of metal ions-binding sites in RNA structures. Both programs are available free of charge as a Web servers, LigandRNA at http://ligandrna.genesilico.pl and MetalionRNA at http://metalionrna.genesilico.pl/.

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.

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

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

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 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.

Crowders perturb the entropy of RNA energy landscapes to favor folding

Biological macromolecules have evolved to fold and operate in the crowded environment of the cell. We have shown previously that molecular crowding stabilizes folded RNA structures. Here we report SAXS measurements on a 64 kDa bacterial group I ribozyme in the presence of mono- and divalent ions and PEG crowders of different molecular weight. These experiments show that crowders always stabilize the folded RNA, but this stabilization is weaker in NaCl solutions than MgCl2 solutions. Additionally, we find that RNAs with the same global structure, parametrized by Rg, have different scattering functions depending upon the ratio of electrostatic and entropic stabilization by ions and crowders, respectively. We quantify this difference using the scattering length per scattering volume and find that this ratio is larger for RNAs that fold in lower ionic strength solutions due to the higher crowder content. We conclude that lower RNA flexibility, or reduced configurational entropy, widens the free energy gap between the unfolded and folded RNA in crowded MgCl2 solutions.

Identification of the catalytic Mg²⁺ ion in the hepatitis delta virus ribozyme

The hepatitis delta virus ribozyme catalyzes an RNA cleavage reaction using a catalytic nucleobase and a divalent metal ion. The catalytic base, C75, serves as a general acid and has a pK(a) shifted toward neutrality. Less is known about the role of metal ions in the mechanism. A recent crystal structure of the precleavage ribozyme identified a Mg²⁺ ion that interacts through its partial hydration sphere with the G25·U20 reverse wobble. In addition, this Mg²⁺ ion is in position to directly coordinate the nucleophile, the 2'-hydroxyl of U(-1), suggesting it can serve as a Lewis acid to facilitate deprotonation of the 2'-hydroxyl. To test the role of the active site Mg²⁺ ion, we replaced the G25·U20 reverse wobble with an isosteric A25·C20 reverse wobble. This change was found to significantly reduce the negative potential at the active site, as supported by electrostatics calculations, suggesting that active site Mg²⁺ binding could be adversely affected by the mutation. The kinetic analysis and molecular dynamics of the A25·C20 double mutant suggest that this variant stably folds into an active structure. However, pH-rate profiles of the double mutant in the presence of Mg²⁺ are inverted relative to the profiles for the wild-type ribozyme, suggesting that the A25·C20 double mutant has lost the active site metal ion. Overall, these studies support a model in which the partially hydrated Mg²⁺ positioned at the G25·U20 reverse wobble is catalytic and could serve as a Lewis acid, a Brønsted base, or both to facilitate deprotonation of the nucleophile.

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.

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

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

Formulation of a new and simple nonuniform size-modified Poisson-Boltzmann description

The nonlinear Poisson-Boltzmann equation (PBE) governing biomolecular electrostatics neglects ion size and ion correlation effects, and recent research activity has focused on accounting for these effects to achieve better physical modeling realism. Here, attention is focused on the comparatively simpler challenge of addressing ion size effects within a continuum-based solvent modeling framework. Prior works by Borukhov et al. (Phys. Rev. Lett. 1997, 79, 435; Electrochim. Acta 2000, 46, 221) have examined the case of uniform ion size in considerable detail. Generalizations to accommodate different species ion sizes have been performed by Li (Nonlinearity 2009, 22, 811; SIAM J. Math. Anal. 2009, 40, 2536) and Zhou et al. (Phys. Rev. E 2011, 84, 021901) using a variational principle, Chu et al. (Biophys. J. 2007, 93, 3202) using a lattice gas model, and Tresset (Phys. Rev. E 2008, 78, 061506) using a generalized Poisson-Fermi distribution. The current work provides an alternative derivation using simple statistical mechanics principles that place the ion size effects and energy distributions on a consistent statistical footing. The resulting expressions differ from the prior nonuniform ion-size developments. However, all treatments reduce to the same form in the cases of uniform ion-size and zero ion size (the PBE). Because of their importance to molecular modeling and salt-dependent behavior, expressions for the salt sensitivities and ionic forces are also derived using the nonuniform ion size description. Emphasis in this article is on formulation and numerically robust evaluation; results are presented for a simple sphere and a previously considered DNA structure for comparison and validation. More extensive application to biomolecular systems is deferred to a subsequent article.

RNA and its ionic cloud: solution scattering experiments and atomically detailed simulations

RNA molecules play critical roles in many cellular processes. Traditionally viewed as genetic messengers, RNA molecules were recently discovered to have diverse functions related to gene regulation and expression. RNA also has great potential as a therapeutic and a tool for further investigation of gene regulation. Metal ions are an integral part of RNA structure and should be considered in any experimental or theoretical study of RNA. Here, we report a multidisciplinary approach that combines anomalous small-angle x-ray scattering and molecular-dynamics (MD) simulations with explicit solvent and ions around RNA. From experiment and simulation results, we find excellent agreement in the number and distribution of excess monovalent and divalent ions around a short RNA duplex. Although similar agreement can be obtained from a continuum description of the solvent and mobile ions (by solving the Poisson-Boltzmann equation and accounting for finite ion size), the use of MD is easily extended to flexible RNA systems with thermal fluctuations. Therefore, we also model a short RNA pseudoknot and find good agreement between the MD results and the experimentally derived solution structures. Surprisingly, both deviate from crystal structure predictions. These favorable comparisons of experiment and simulations encourage work on RNA in all-atom dynamic models.

Metal-induced specific and nonspecific oligonucleotide folding studied by FRET and related biophysical and bioanalytical implications

Metal induced nucleic acid folding has been extensively studied with ribozymes, DNAzymes, tRNA and riboswitches. These RNA/DNA molecules usually have a high content of double-stranded regions to support a rigid scaffold. On the other hand, such rigid structural features are not available for many in vitro selected or rationally designed DNA aptamers; they adopt flexible random coil structures in the absence of target molecules. Upon target binding, these aptamers adaptively fold into a compact structure with a reduced end-to-end distance, making fluorescence resonance energy transfer (FRET) a popular signaling mechanism. However, nonspecific folding induced by mono- or divalent metal ions can also reduce the end-to-end distance and thus lead to false positive results. In this study we used a FRET pair labeled Hg(II) binding DNA and monitored metal-induced folding in the presence of various cations. While nonspecific electrostatically mediated folding can be very significant, at each tested salt condition, Hg(II) induced folding was still observed with a similar sensitivity. We also studied the biophysical meaning of the acceptor/donor fluorescence ratio that allowed us to explain the experimental observations. Potential solutions for this ionic strength problem have been discussed. For example, probes designed to signal the formation of double-stranded DNA showed a lower dependency on ionic strength.

MetalionRNA: computational predictor of metal-binding sites in RNA structures

Motivation: Metal ions are essential for the folding of RNA molecules into stable tertiary structures and are often involved in the catalytic activity of ribozymes. However, the positions of metal ions in RNA 3D structures are difficult to determine experimentally. This motivated us to develop a computational predictor of metal ion sites for RNA structures.

Results: We developed a statistical potential for predicting positions of metal ions (magnesium, sodium and potassium), based on the analysis of binding sites in experimentally solved RNA structures. The MetalionRNA program is available as a web server that predicts metal ions for RNA structures submitted by the user.

Availability: The MetalionRNA web server is accessible at http://metalionrna.genesilico.pl/.

Contact:iamb@genesilico.pl

Supplementary information:Supplementary data are available at Bioinformatics online.

Evidence for a thermodynamically distinct Mg2+ ion associated with formation of an RNA tertiary structure

A folding strategy adopted by some RNAs is to chelate cations in pockets or cavities, where the ions neutralize charge from solvent-inaccessible phosphate. Although such buried Mg(2+)-RNA chelates could be responsible for a significant fraction of the Mg(2+)-dependent stabilization free energy of some RNA tertiary structures, direct measurements have not been feasible because of the difficulty of finding conditions under which the free energy of Mg(2+) chelation is uncoupled from RNA folding and from unfavorable interactions with Mg(2+) ions in other environments. In a 58mer rRNA fragment, we have used a high-affinity thermophilic ribosomal protein to trap the RNA in a structure nearly identical to native; Mg(2+)- and protein-stabilized structures differ in the solvent exposure of a single nucleotide located at the chelation site. Under these conditions, titration of a high affinity chelation site takes place in a micromolar range of Mg(2+) concentration, and is partially resolved from the accumulation of Mg(2+) in the ion atmosphere. From these experiments, we estimate the total and site-specific Mg(2+)-RNA interaction free energies over the range of accessed Mg(2+) concentrations. At 0.1 mM Mg(2+) and 60 mM K(+), specific site binding contributes ∼-3 kcal/mol of the total Mg(2+) interaction free energy of ∼-13 kcal/mol from all sources; at higher Mg(2+) concentrations the site-binding contribution becomes a smaller proportion of the total (-4.5 vs -33 kcal/mol). Under approximately physiological ionic conditions, the specific binding site will be saturated but will provide only a fraction of the total free energy of Mg(2+)-RNA interactions.

Mechanical unfolding of the beet western yellow virus -1 frameshift signal

Using mechanical unfolding by optical tweezers (OT) and steered molecular dynamics (SMD) simulations, we have demonstrated the critical role of Mg(2+) ions for the resistance of the Beet Western Yellow Virus (BWYV) pseudoknot (PK) to unfolding. The two techniques were found to be complementary, providing information at different levels of molecular scale. Findings from the OT experiments indicated a critical role of stem 1 for unfolding of the PK, which was confirmed in the SMD simulations. The unfolding pathways of wild type and mutant appeared to depend upon pH and nucleotide sequence. SMD simulations support the notion that the stability of stem 1 is critical for -1 frameshifting. The all-atom scale nature of the SMD enabled clarification of the precise role of two Mg(2+) ions, Mg45 and Mg52, as identified in the BWYV X-ray crystallography structure, in -1 frameshifting. On the basis of simulations with "partially" and "fully" hydrated Mg(2+) ions, two possible mechanisms of stabilizing stem 1 are proposed. In both these cases Mg(2+) ions play a critical role in stabilizing stem 1, either by directly forming a salt bridge between the strands of stem 1 or by stabilizing parallel orientation of the strands in stem 1, respectively. These findings explain the unexpected drop in frameshifting efficiency to null levels of the C8U mutant in a manner consistent with experimental observations.

Metal binding motif in the active site of the HDV ribozyme binds divalent and monovalent ions

The hepatitis delta virus (HDV) ribozyme uses both metal ion and nucleobase catalysis in its cleavage mechanism. A reverse G·U wobble was observed in a recent crystal structure of the precleaved state. This unusual base pair positions a Mg(2+) ion to participate in catalysis. Herein, we used molecular dynamics (MD) and X-ray crystallography to characterize the conformation and metal binding characteristics of this base pair in product and precleaved forms. Beginning with a crystal structure of the product form, we observed formation of the reverse G·U wobble during MD trajectories. We also demonstrated that this base pair is compatible with the diffraction data for the product-bound state. During MD trajectories of the product form, Na(+) ions interacted with the reverse G·U wobble in the RNA active site, and a Mg(2+) ion, introduced in certain trajectories, remained bound at this site. Beginning with a crystal structure of the precleaved form, the reverse G·U wobble with bound Mg(2+) remained intact during MD simulations. When we removed Mg(2+) from the starting precleaved structure, Na(+) ions interacted with the reverse G·U wobble. In support of the computational results, we observed competition between Na(+) and Mg(2+) in the precleaved ribozyme crystallographically. Nonlinear Poisson-Boltzmann calculations revealed a negatively charged patch near the reverse G·U wobble. This anionic pocket likely serves to bind metal ions and to help shift the pK(a) of the catalytic nucleobase, C75. Thus, the reverse G·U wobble motif serves to organize two catalytic elements, a metal ion and catalytic nucleobase, within the active site of the HDV ribozyme.

Effects of Mg2+ on the free energy landscape for folding a purine riboswitch RNA

There are potentially several ways Mg2+ might promote formation of an RNA tertiary structure: by causing a general "collapse" of the unfolded ensemble to more compact conformations, by favoring a reorganization of structure within a domain to a form with specific tertiary contacts, and by enhancing cooperative linkages between different sets of tertiary contacts. To distinguish these different modes of action, we have studied Mg2+ interactions with the adenine riboswitch, in which a set of tertiary interactions that forms around a purine-binding pocket is thermodynamically linked to the tertiary "docking" of two hairpin loops in another part of the molecule. Each of four RNA forms with different extents of tertiary structure were characterized by small-angle X-ray scattering. The free energy of interconversion between different conformations in the absence of Mg2+ and the free energy of Mg2+ interaction with each form have been estimated, yielding a complete picture of the folding energy landscape as a function of Mg2+ concentration. At 1 mM Mg2+ (50 mM K+), the overall free energy of stabilization by Mg2+ is large, -9.8 kcal/mol, and about equally divided between its effect on RNA collapse to a partially folded structure and on organization of the binding pocket. A strong cooperative linkage between the two sets of tertiary contacts is intrinsic to the RNA. This quantitation of the effects of Mg2+ on an RNA with two distinct sets of tertiary interactions suggests ways that Mg2+ may work to stabilize larger and more complex RNA structures.

Deciphering the role of glucosamine-6-phosphate in the riboswitch action of glmS ribozyme

The GlmS ribozyme is believed to exploit a general acid-base catalytic mechanism in the presence of glucosamine-6-phosphate (GlcN6P) to accelerate self-cleavage by approximately six orders of magnitude. The general acid and general base are not known, and the role of the GlcN6P cofactor is even less well understood. The amine group of GlcN6P has the ability to either accept or donate a proton and could therefore potentially act as an acid or a base. In order to decipher the role of GlcN6P in the self-cleavage of glmS, we have determined the preferred protonation state of the amine group in the wild-type and an inactive G40A mutant using molecular dynamics simulations and free energy calculations. Here we show that, upon binding of GlcN6P to wild-type glmS, the pK(a) of the amine moiety is altered by the active site environment, decreasing by about 2.2 from a solution pK(a) of about 8.2. On the other hand, we show that the pK(a) of the amine group slightly increases to about 8.4 upon binding to the G40A inactive mutant of glmS. These results suggest that GlcN6P acts as a general acid in the self-cleavage of glmS. Upon binding to glmS, GlcN6P can easily release a proton to the 5'-oxygen of G1 during self-cleavage of the backbone phosphodiester bond. However, in the G40A inactive mutant of glmS, the results suggest that the ability of GlcN6P to easily release its proton is diminished, in addition to the possible lack of G40 as an effective base.

Coulombic free energy of polymeric nucleic acid: low- and high-salt analytical approximations for the cylindrical Poisson-Boltzmann model

An accurate analytical expression for the Coulombic free energy of DNA as a function of salt concentration ([salt]) is essential in applications to nucleic acid (NA) processes. The cylindrical model of DNA and the nonlinear Poisson-Boltzmann (NLPB) equation for ions in solution are among the simplest approaches capable of describing Coulombic interactions of NA and salt ions and of providing analytical expressions for thermodynamic quantities. Three approximations for Coulombic free energy G(u,infinity)(coul) of a polymeric nucleic acid are derived and compared with the numerical solution in a wide experimental range of 1:1 [salt] from 0.01 to 2 M. Two are obtained from the two asymptotic solutions of the cylindrical NLPB equation in the high-[salt] and low-[salt] limits: these are sufficient to determine G(u,infinity)(coul) of double-stranded (ds) DNA with 1% and of single-stranded (ss) DNA with 3% accuracy at any [salt]. The third approximation is experimentally motivated Taylor series up to the quadratic term in ln[salt] in the vicinity of the reference [salt] 0.15 M. This expression with three numerical coefficients (Coulombic free energy and its first and second derivatives at 0.15 M) predicts dependence of G(u,infinity)(coul) on [salt] within 2% of the numerical solution from 0.01 to 1 M for ss (a = 7 A, b = 3.4 A) and ds (a = 10 A, b = 1.7 A) DNA. Comparison of cylindrical free energy with that calculated for the all-atom structural model of linear B-DNA shows that the cylindrical model is completely sufficient above 0.01 M of 1:1 [salt]. The choice of two cylindrical parameters, the distance of closest approach of ion to cylinder axis (radius) a and the average axial charge separation b, is discussed in application to all-atom numerical calculations and analysis of experiment. Further development of analytical expression for Coulombic free energy with thermodynamic approaches accounting for ionic correlations and specific effects is suggested.

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.

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.

Dissecting electrostatic screening, specific ion binding, and ligand binding in an energetic model for glycine riboswitch folding

Riboswitches are gene-regulating RNAs that are usually found in the 5'-untranslated regions of messenger RNA. As the sugar-phosphate backbone of RNA is highly negatively charged, the folding and ligand-binding interactions of riboswitches are strongly dependent on the presence of cations. Using small angle X-ray scattering (SAXS) and hydroxyl radical footprinting, we examined the cation dependence of the different folding stages of the glycine-binding riboswitch from Vibrio cholerae. We found that the partial folding of the tandem aptamer of this riboswitch in the absence of glycine is supported by all tested mono- and divalent ions, suggesting that this transition is mediated by nonspecific electrostatic screening. Poisson-Boltzmann calculations using SAXS-derived low-resolution structural models allowed us to perform an energetic dissection of this process. The results showed that a model with a constant favorable contribution to folding that is opposed by an unfavorable electrostatic term that varies with ion concentration and valency provides a reasonable quantitative description of the observed folding behavior. Glycine binding, on the other hand, requires specific divalent ions binding based on the observation that Mg(2+), Ca(2+), and Mn(2+) facilitated glycine binding, whereas other divalent cations did not. The results provide a case study of how ion-dependent electrostatic relaxation, specific ion binding, and ligand binding can be coupled to shape the energetic landscape of a riboswitch and can begin to be quantitatively dissected.

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.

Contribution of the closing base pair to exceptional stability in RNA tetraloops: roles for molecular mimicry and electrostatic factors

Hairpins are common RNA secondary structures that play multiple roles in nature. Tetraloops are the most frequent RNA hairpin loops and are often phylogenetically conserved. For both the UNCG and GNRA families, CG closing base pairs (cbps) confer exceptional thermodynamic stability but the molecular basis for this has remained unclear. We propose that, despite having very different overall folds, these two tetraloop families achieve stability by presenting the same functionalities to the major groove edge of the CG cbp. Thermodynamic contributions of this molecular mimicry were investigated using substitutions at the nucleobase and functional group levels. By either interrupting or deleting loop-cbp electrostatic interactions, which were identified by solving the nonlinear Poisson-Boltzmann (NLPB) equation, stability changed in a manner consistent with molecular mimicry. We also observed a linear relationship between DeltaG(o)(37) and log[Na(+)] for both families, and loops with a CG cbp had a decreased dependence of stability on salt. NLPB calculations revealed that, for both UUCG and GAAA tetraloops, the GC cbp form has a higher surface charge density, although it arises from changes in loop compaction for UUCG and changes in loop configuration for GAAA. Higher surface charge density leads to stronger interactions of GC cbp loops with solvent and salt, which explains the correlation between experimental and calculated trends of free energy with salt. Molecular mimicry as evidenced in these two stable but otherwise unrelated tetraloops may underlie common functional roles in other RNA and DNA motifs.