The binding of Mg++ ions to polyadenylate, polyuridylate, and their complexes

Mutual effects between single-stranded DNA conformation and Na+-Mg2+ ion competition in mixed salt solutions

The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na⁺/Mg²⁺ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na⁺-Mg²⁺ competition; this in turn reveals their mutual impact in the ion atmosphere.

Direct Measurement of Interhelical DNA Repulsion and Attraction by Quantitative Cross-Linking

To better understand the forces that mediate nucleic acid compaction in biology, we developed the disulfide cross-linking approach xHEED (X-linking of Helices to measure Electrostatic Effects at Distance) to measure the distance-dependent encounter frequency of two DNA helices in solution. Using xHEED, we determined the distance that the electrostatic potential extends from DNA helices, the dependence of this distance on ionic conditions, and the magnitude of repulsion when two helices approach one another. Across all conditions tested, the potential falls to that of the bulk solution within 15 Å of the major groove surface. For separations of ∼30 Å, we measured a repulsion of 1.8 kcal/mol in low monovalent ion concentration (30 mM Na+), with higher Na+ concentrations ameliorating this repulsion, and 2 M Na+ or 100 mM Mg2+ eliminating it. Strikingly, we found full screening at very low Co3+ concentrations and net attraction at higher concentrations, without the higher-order DNA condensation that typically complicates studies of helical attraction. Our measurements define the relevant distances for electrostatic interactions of nucleic-acid helices in biology and introduce a new method to propel further understanding of how these forces impact biological processes.

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.

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.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

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.

Predicting ion-nucleic acid interactions by energy landscape-guided sampling

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Folding of the hammerhead ribozyme: pyrrolo-cytosine fluorescence separates core folding from global folding and reveals a pH-dependent conformational change

The catalytic activity of the hammerhead ribozyme is limited by its ability to fold into the native tertiary structure. Analysis of folding has been hampered by a lack of assays that can independently monitor the environment of nucleobases throughout the ribozyme-substrate complex in real time. Here, we report the development and application of a new folding assay in which we use pyrrolo-cytosine (pyC) fluorescence to (1) probe active-site formation, (2) examine the ability of peripheral ribozyme domains to support native folding, (3) identify a pH-dependent conformational change within the ribozyme, and (4) explore its influence on the equilibrium between the folded and unfolded core of the hammerhead ribozyme. We conclude that the natural ribozyme folds in two distinct noncooperative steps and the pH-dependent correlation between core folding and activity is linked to formation of the G8-C3 base pair.

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.

Full-length Dengue virus RNA-dependent RNA polymerase-RNA/DNA complexes: stoichiometries, intrinsic affinities, cooperativities, base, and conformational specificities

Fundamental aspects of interactions of the Dengue virus type 3 full-length polymerase with the single-stranded and double-stranded RNA and DNA have been quantitatively addressed. The polymerase exists as a monomer with an elongated shape in solution. In the absence of magnesium, the total site size of the polymerase-ssRNA complex is 26 ± 2 nucleotides. In the presence of Mg(2+), the site size increases to 29 ± 2 nucleotides, indicating that magnesium affects the enzyme global conformation. The enzyme shows a preference for the homopyrimidine ssRNAs. Positive cooperativity in the binding to homopurine ssRNAs indicates that the type of nucleic acid base dramatically affects the enzyme orientation in the complex. Both the intrinsic affinity and the cooperative interactions are accompanied by a net ion release. The polymerase binds the dsDNA with an affinity comparable with the ssRNAs affinity, indicating that the binding site has an open conformation in solution. The lack of detectable dsRNA or dsRNA-DNA hybrid affinities indicates that the entry to the binding site is specific for the sugar-phosphate backbone and/or conformation of the duplex.

SAXS studies of ion-nucleic acid interactions

Positively charged ions, atoms, or molecules compensate the high negative charge of the nucleic acid backbone. Their presence is critical to the biological function of DNA and RNA. This review focuses on experimental studies probing (a) interactions between small ions and nucleic acids and (b) ion-mediated interactions between nucleic acid duplexes. Experimental results on these simple model systems can be compared with specific theoretical models to validate their predictions. Small angle X-ray scattering (SAXS) provides unique insight into these interactions. Anomalous SAXS reports the spatial correlations of condensed (e.g., locally concentrated) counterions to individual DNA or RNA duplexes. SAXS very effectively reports interactions between nucleic acid helices, which range from strongly repulsive to strongly attractive depending on the ionic species present. The sign and strength of interparticle interactions are easily deduced from dramatic changes in the scattering profiles of interacting duplexes.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

Both helix topology and counterion distribution contribute to the more effective charge screening in dsRNA compared with dsDNA

The recent discovery of the RNA interference mechanism emphasizes the biological importance of short, isolated, double-stranded (ds) RNA helices and calls for a complete understanding of the biophysical properties of dsRNA. However, most previous studies of the electrostatics of nucleic acid duplexes have focused on DNA. Here, we present a comparative investigation of electrostatic effects in RNA and DNA. Using resonant (anomalous) and non-resonant small-angle X-ray scattering, we characterized the charge screening efficiency and counterion distribution around short (25 bp) dsDNA and RNA molecules of comparable sequence. Consistent with theoretical predictions, we find counterion mediated screening to be more efficient for dsRNA than dsDNA. Furthermore, the topology of the RNA A-form helix alters the spatial distribution of counterions relative to B-form DNA. The experimental results reported here agree well with ion-size-corrected non-linear Poisson-Boltzmann calculations. We propose that differences in electrostatic properties aid in selective recognition of different types of short nucleic acid helices by target binding partners.

Enzyme enhanced quantitative determination of multiple DNA targets based on capillary electrophoresis

In the current paper, enzyme enhanced simultaneous quantitative determination of multiple DNA targets based on capillary electrophoresis (CE) was described. We used three biotin-modified DNA probes, which reacted with avidin-conjugated horseradish peroxidase (avidin-HRP) conjugate to obtain the HRP labeled probes, to hybridize with three corresponding targets. The resulting mixture containing double-strand DNA (dsDNA)-HRP, excess single-strand DNA (ssDNA)-HRP and remaining avidin-HRP was separated by capillary electrophoresis, and then the system of HRP catalyzing H(2)O(2)/o-aminophenol (OAP) reaction was adopted. The catalytic product was detected with electrochemical detection. With this protocol, the limits of quantification for the hybridization assay of 21-, 39- and 80-mer DNA fragments were of 1.2 x 10(-11), 2.4 x 10(-11) and 3.0 x 10(-11)M, respectively. The multiplex assay also provided good specificity without any cross-reaction.

Predicting electrostatic forces in RNA folding

Metal ion-mediated electrostatic interactions are critical to RNA folding. Although considerable progress has been made in mechanistic studies, the problem of accurate predictions for the ion effects in RNA folding remains unsolved, mainly due to the complexity of several potentially important issues such as ion correlation and dehydration effects. In this chapter, after giving a brief overview of the experimental findings and theoretical approaches, we focus on a recently developed new model, the tightly bound ion (TBI) model, for ion electrostatics in RNA folding. The model is unique because it can treat ion correlation and fluctuation effects for realistic RNA 3D structures. For monovalent ion (such as Na(+)) solutions, where ion correlation is weak, TBI and the Poisson-Boltzmann (PB) theory give the same results and the results agree with the experimental data. For multivalent ion (such as Mg(2+)) solutions, where ion correlation can be strong, however, TBI gives much improved predictions than the PB. Moreover, the model suggests an ion correlation-induced mechanism for the unusual efficiency of Mg(2+) ions in the stabilization of RNA tertiary folds. In this chapter, after introducing the theoretical framework of the TBI model, we will describe how to apply the model to predict ion-binding properties and ion-dependent folding stabilities.

Probing nucleic acid-ion interactions with buffer exchange-atomic emission spectroscopy

The ion atmosphere of nucleic acids directly affects measured biochemical and biophysical properties. However, study of the ion atmosphere is difficult due to its diffuse and dynamic nature. Standard techniques available have significant limitations in sensitivity, specificity, and directness of the assays. Buffer exchange-atomic emission spectroscopy (BE-AES) was developed to overcome many of the limitations of previously available techniques. This technique can provide a complete accounting of all ions constituting the ionic atmosphere of a nucleic acid at thermodynamic equilibrium. Although initially developed for the study of the ion atmosphere of nucleic acids, BE-AES has also been applied to study site-bound ions in RNA and protein.

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.

The binding of divalent metal ions to polyelectrolytes in mixed counterion systems. II. Dextransulfate-Mg2+ and dextransulfate-Ca2+ in solutions containing added NaCl or KCl

Measurements of magnesium and calcium ion activities in solutions of the polyelectrolyte dextransulfate, with added sodium chloride or potassium chloride are presented. A two wavelength dye spectrophotometric method is used. Dextransulfate concentrations Cp (expressed as moles sulfate ion/litre) vary between 0.001 and 0.007, total ionic strengths between 0.005 and 0.08 mole/XXX. Divalent metal ion concentrations are varied between 0 and 1.2 Cp. The results for the metal ion activities are expressed in the form of parameters theta2 = C2/Cp (C(2bp) = bound divalent metal ion concentration) and K2 = theta2/(C2-C2b). For each divalent/univalent counterion pair the values obtained for theta2 and K2 as a function of C2,Cp, and ionic strength are compared to predictions of the "two variable theory" developed for these mixed counterion systems by Manning. This comparison shows that the observed decrease in theta2 with increasing ionic strength at fixed C2 and Cp is generally well predicted by the two variable theory. The extent of divalent ion binding at a given C2, Cp, and ionic strength is largest for the Ca/Na counterion combination, and lowest for the Mg/K combination.

Predicting stability of DNA duplexes in solutions containing magnesium and monovalent cations

Accurate predictions of DNA stability in physiological and enzyme buffers are important for the design of many biological and biochemical assays. We therefore investigated the effects of magnesium, potassium, sodium, Tris ions, and deoxynucleoside triphosphates on melting profiles of duplex DNA oligomers and collected large melting data sets. An empirical correction function was developed that predicts melting temperatures, transition enthalpies, entropies, and free energies in buffers containing magnesium and monovalent cations. The new correction function significantly improves the accuracy of predictions and accounts for ion concentration, G-C base pair content, and length of the oligonucleotides. The competitive effects of potassium and magnesium ions were characterized. If the concentration ratio of [Mg (2+)] (0.5)/[Mon (+)] is less than 0.22 M (-1/2), monovalent ions (K (+), Na (+)) are dominant. Effects of magnesium ions dominate and determine duplex stability at higher ratios. Typical reaction conditions for PCR and DNA sequencing (1.5-5 mM magnesium and 20-100 mM monovalent cations) fall within this range. Conditions were identified where monovalent and divalent cations compete and their stability effects are more complex. When duplexes denature, some of the Mg (2+) ions associated with the DNA are released. The number of released magnesium ions per phosphate charge is sequence dependent and decreases surprisingly with increasing oligonucleotide length.

Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids

The ion atmosphere around nucleic acids critically affects biological and physical processes such as chromosome packing, RNA folding, and molecular recognition. However, the dynamic nature of the ion atmosphere renders it difficult to characterize. The basic thermodynamic description of this atmosphere, a full accounting of the type and number of associated ions, has remained elusive. Here we provide the first complete accounting of the ion atmosphere, using buffer equilibration and atomic emission spectroscopy (BE-AES) to accurately quantitate the cation association and anion depletion. We have examined the influence of ion size and charge on ion occupancy around simple, well-defined DNA molecules. The relative affinity of monovalent and divalent cations correlates inversely with their size. Divalent cations associate preferentially over monovalent cations; e.g., with Na+ in 4-fold excess of Mg2+ (20 vs 5 mM), the ion atmosphere nevertheless has 3-fold more Mg2+ than Na+. Further, the dicationic polyamine putrescine2+ does not compete effectively for association relative to divalent metal ions, presumably because of its lower charge density. These and other BE-AES results can be used to evaluate and guide the improvement of electrostatic treatments. As a first step, we compare the BE-AES results to predictions from the widely used nonlinear Poisson Boltzmann (NLPB) theory and assess the applicability and precision of this theory. In the future, BE-AES in conjunction with improved theoretical models, can be applied to complex binding and folding equilibria of nucleic acids and their complexes, to parse the electrostatic contribution from the overall thermodynamics of important biological processes.

RNA helix stability in mixed Na+/Mg2+ solution

A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solutions, which are physiologically relevant and biologically significant, and the model was based on B-DNA helices and thus cannot directly treat RNA helices. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodynamic stability of finite length RNA helices immersed in a mixed solution of monovalent and divalent ions. Experimental comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helices. The tightly bound ion model makes quantitative predictions on how the Na+-Mg2+ competition determines helix stability and its helix length-dependence. In addition, the model gives empirical formulas for the thermodynamic parameters as functions of Na+/Mg2+ concentrations and helix length. Such formulas can be quite useful for practical applications.

Mg2+-RNA interaction free energies and their relationship to the folding of RNA tertiary structures

Mg2+ ions are very effective at stabilizing tertiary structures in RNAs. In most cases, folding of an RNA is so strongly coupled to its interactions with Mg2+ that it is difficult to separate free energies of Mg2+-RNA interactions from the intrinsic free energy of RNA folding. To devise quantitative models accounting for this phenomenon of Mg2+-induced RNA folding, it is necessary to independently determine Mg2+-RNA interaction free energies for folded and unfolded RNA forms. In this work, the energetics of Mg2+-RNA interactions are derived from an assay that measures the effective concentration of Mg2+ in the presence of RNA. These measurements are used with other measures of RNA stability to develop an overall picture of the energetics of Mg2+-induced RNA folding. Two different RNAs are discussed, a pseudoknot and an rRNA fragment. Both RNAs interact strongly with Mg2+ when partially unfolded, but the two folded RNAs differ dramatically in their inherent stability in the absence of Mg2+ and in the free energy of their interactions with Mg2+. From these results, it appears that any comprehensive framework for understanding Mg2+-induced stabilization of RNA will have to (i) take into account the interactions of ions with the partially unfolded RNAs and (ii) identify factors responsible for the widely different strengths with which folded tertiary structures interact with Mg2+.

Affinity capillary electrophoresis with a DNA-nanoparticle conjugate as a new tool for genotyping

We have developed a novel method for genotyping based on free solution affinity capillary electrophoresis. We prepared DNA-nanoparticle conjugates by mixing biotin-modified DNA and NeutrAvidin-modified polystyrene nanoparticles; this mixture was then injected into a capillary. Subsequently, we injected the fluorescent-labeled sample DNAs into the capillary, applied the voltage, increased its temperature after 7 min, and detected the fluorescence at its anodic end. This novel method was applied for genotyping human c-K-ras, and the three genotypes were definitely distinguishable with high reproducibility. This method can be easily automated, and it is useful for high-throughput gene mutation analysis.

Capillary electrophoretic discrimination of single nucleotide polymorphisms using an oligodeoxyribonucleotidepolyacrylamide conjugate as a pseudo-immobilized affinity ligand: optimum ligand length predicted by the melting temperature values

We developed a weak-affinity separation system for single-nucleotide polymorphisms (SNPs) based on capillary electrophoresis. In this approach, single-stranded DNA (ssDNA)-polyacrylamide (polyAAm) conjugate was used as a pseudo-immobilized affinity ligand to separate the target DNA, cytochrome P450 2C9 (CYP2C9), and its point mutant. The ligand DNA was designed to be complementary to the normal DNA, and the target DNA was electrophoretically separated by the difference in the affinity with the pseudo-immobilized ligand in the capillary. We showed that the separation efficiency was closely associated with the Tm value of double-stranded DNA (dsDNA) consisting of the target and ligand DNA, which depends on the measurement conditions, such as the base number of the ligand DNA and the concentration of Mg2+ in the buffer solution.

Binding of Mg2+ to single-stranded polynucleotides: hydration and optical studies

The binding of Mg(2+) to single-stranded ribo- and deoxy-polynucleotides, poly(rA), poly(rU), poly(dA) and poly(dT), has been investigated in dilute aqueous solutions at pH 7.5 and 20 degrees C. A combination of ultrasound velocimetry, density, UV and CD spectroscopy have been employed to study hydration and spectral effects of Mg(2+) binding to the polynucleotides. Volume and compressibility effects of Mg(2+) binding to random-coiled poly(rU) and poly(dT) correspond to two coordination bonds probably between the adjacent phosphate groups. The same parameters for poly(rA)+Mg(2+) correspond to an inner-sphere complex with three-four direct contacts. However, almost no hydration effects are arising in binding to its deoxy analog, poly(dA), indicating mostly a delocalized binding mode. In agreement with hydration studies, optical investigations revealed almost no influence of Mg(2+) on poly(dA) properties, while it stabilizes and aggregates poly(rA) single-helix. The evidence presented here indicates that Mg(2+) are able to bind specifically to single-stranded polynucleotides, and recognize their composition and backbone conformation.

A thermodynamic framework for the magnesium-dependent folding of RNA

The goal of this review is to present a unified picture of the relationship between ion binding and RNA folding based on recent theoretical and computational advances. In particular, we present a model describing how the association of magnesium ions is coupled to the tertiary structure folding of several well-characterized RNA molecules. This model is developed in terms of the nonlinear Poisson-Boltzmann (NLPB) equation, which provides a rigorous electrostatic description of the interaction between Mg(2+) and specific RNA structures. In our description, most of the ions surrounding an RNA behave as a thermally fluctuating ensemble distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. In some cases, however, individual ions near the RNA may shed some of their surrounding waters to optimize their Coulombic interactions with the negatively charged ligands on the RNA. These chelated ions are energetically distinct from the surrounding ensemble and must be treated explicitly. This model is used to explore several different RNA systems that interact differently with Mg(2+). In each case, the NLPB equation accurately describes the stoichiometric and energetic linkage between Mg(2+) binding and RNA folding without requiring any fitted parameters in the calculation. Based on this model, we present a physical description of how Mg(2+) binds and stabilizes specific RNA structures to promote the folding reaction.

The linkage between magnesium binding and RNA folding

Understanding the linkage between Mg(2+) binding and RNA folding requires a proper theoretical model describing the energetics of Mg(2+) binding to the folded and unfolded states of RNA. Our current understanding of Mg(2+) binding to these different RNA states derives from empirical thermodynamic models that depend on a number of unjustified assumptions. We present a rigorous theoretical model describing the linkage between RNA folding and magnesium ion binding. In this model, based on the non-linear Poisson-Boltzmann (NLPB) equation, the stabilization of RNA by Mg(2+) arises from two distinct binding modes, diffuse binding and site binding. Diffusely bound Mg(2+) are described as an ensemble of hydrated ions that are attracted to the negative charge of the RNA. Site-bound Mg(2+) are partially desolvated ions that are attracted to electronegative pockets on the RNA surface. We explore two systems, yeast tRNA(Phe) and a 58-nucleotide rRNA fragment, with different Mg(2+) binding properties. The NLPB equation accurately describes both the stoichiometric and energetic linkage between Mg(2+) binding and RNA folding for both of these systems without requiring any fitted parameters in the calculation. Moreover, the NLPB model presents a well-defined physical description of how Mg(2+) binding helps fold an RNA. For both of the molecules studied here, the relevant unfolded state is a disordered intermediate state (I) that contains stable helical secondary structure without any tertiary contacts. Diffusely bound Mg(2+) interact with these secondary structure elements to stabilize the I state. The secondary structural elements of the I state fold into a compact, native tertiary structure (the N state). Diffuse binding plays a dominant role in stabilizing the N state for both RNAs studied. However, for the rRNA fragment, site-binding to a location with extraordinarily high electrostatic potential is also coupled to folding. Our results suggest that much experimental data measuring the linkage between Mg(2+) binding and RNA folding must be reinterpreted.

On the role of magnesium ions in RNA stability

Divalent cations, like magnesium, are crucial for the structural integrity and biological activity of RNA. In this article, we present a picture of how magnesium stabilizes a particular folded form of RNA. The overall stabilization of RNA by Mg2+ is given by the free energy of transferring RNA from a reference univalent salt solution to a mixed salt solution. This term has favorable energetic contributions from two distinct modes of binding: diffuse binding and site binding. In diffuse binding, fully hydrated Mg ions interact with the RNA via nonspecific long-range electrostatic interactions. In site binding, dehydrated Mg2+ interacts with anionic ligands specifically arranged by the RNA fold to act as coordinating ligands for the mental ion. Each of these modes has a strong coulombic contribution to binding; however, site binding is also characterized by substantial changes in ion solvation and other nonelectrostatic contributions. We will show how these energetic differences can be exploited to experimentally distinguish between these two classes of ions using analyses of binding polynomials. We survey a number of specific systems in which Mg(2+)-RNA interactions have been studied. In well-characterized systems such as certain tRNAs and some rRNA fragments these studies show that site-bound ions can play an important role in RNA stability. However, the crucial role of diffusely bound ions is also evident. We emphasize that diffuse binding can only be described rigorously by a model that accounts for long-range electrostatic forces. To fully understand the role of magnesium ions in RNA stability, theoretical models describing electrostatic forces in systems with complicated structures must be developed.

The interpretation of Mg(2+) binding isotherms for nucleic acids using Poisson-Boltzmann theory

Magnesium ions play a crucial role in the structural integrity and biological activity of nucleic acids. Experimental thermodynamic descriptions of Mg(2+) interactions with nucleic acids in solution have generally relied on the analyses of binding polynomials to estimate the energetic contributions of diffuse and site-bound ions. However, since ion binding is dominated by long-range electrostatic forces, such models provide only a phenomenological description of the experimental Mg(2+) binding data and provide little insight into the actual mechanism of the binding equilibria. Here, we present a rigorous theoretical framework based on the non-linear Poisson-Boltzmann (NLPB) equation for understanding diffuse ion interactions that can be used to interpret experimental Mg(2+) binding isotherms. As intuitively expected, in the NLPB model binding is simply the total accumulation of the ion around the nucleic acid. Comparing the experimental data to the calculated curves shows that the NLPB equation provides a remarkably accurate description of Mg(2+) binding to linear polynucleotides like DNA and poly(A x U) without any fitted parameters. In particular, the NLPB model explains two general features of magnesium binding; the strong dependence on univalent salt concentration, and its substantial anticooperativity. Each of these effects can be explained by changes in the Mg(2+) distribution around the polyion under different solution conditions. In order to more fully understand these different aspects of magnesium binding, the free energy of Mg(2+) binding, DeltaGMg, is calculated and partitioned into several salt-dependent contributions: the change in the electrostatic interaction free energy of the charges, DeltaDeltaGE.D (including Mg(2+)-phosphate, Mg(2+)-Mg(2+), Mg(2+)-Na(+), Na(+)-Na(+), Na(+)-phosphate interactions, and similar contributions for Cl(-)) and the cratic free energies of (re)organizing the MgCl2 and NaCl atmospheres, DeltaG(Mg)org and DeltaDeltaG(Na)org, respectively. For the systems studied here, DeltaGMg is strongly influenced by entropic free energy changes in the distributions of both NaCl and MgCl2, DeltaG(Mg)org and DeltaDeltaG(Na)org. From this analysis, we also raise the possibility that coions added with the magnesium salt might play an important role in the overall stability of nucleic acids under some conditions.

Flexibility of single-stranded DNA: use of gapped duplex helices to determine the persistence lengths of poly(dT) and poly(dA)

The forces responsible for the formation and stabilization of secondary and higher-order nucleic acid structure can be more fully understood once the sequence-dependent properties (e.g. intrinsic rigidity, effective rise) of the component single-stranded species are well-defined. Knowledge of the conformations of the single-stranded polymers is also important for the development of better polyelectrolyte models for various structural or strand-dissociation reactions. However, there is at present little quantitative information regarding the sequence dependence of either rise or rigidity in single-stranded DNA or RNA polymers. To address this issue, we describe a form of transient electric birefringence (TEB) measurement in which the rotational decay times (taugap) of DNA molecules possessing central, single-stranded regions (gaps) are compared with the corresponding times (taudplx) for duplex control molecules of the same length (in nucleotides per strand) as the continuous strand in the "gapped duplex". For magnesium ion concentrations above 1-2 mM, the tau ratios ( identical withtaugap/taudplx) for the gapped duplexes reach plateau values, above which no further change in tau ratio is observed; values for the persistence length (P) and internucleotide spacing (h) of the gap sequences are obtained from the experimental tau ratios. For dTn, the permissible ranges of P and h are 20-30 A and 5-7 A per nucleotide (nt), respectively, with optimal values of 31 A (P) and 5. 2 A/nt (h). For dAn, the persistence length for the low temperature (4 degreesC), stacked form is 78 (+/-8) A for a helix rise of 3.2 A/nt. One significant advantage of the current method over previous approaches is the use of short (80-100 nt) molecules, thus facilitating the production of various gap sequences through synthetic means.

Binding of ionic ligands to polyelectrolytes

Ionic ligands can bind to polyelectrolytes such as DNA or charged polysaccharides. We develop a Poisson-Boltzmann treatment to compute binding constants as a function of ligand charge and salt concentration in the limit of low ligand concentration. For flexible chain ligands, such as oligopeptides, we treat their conformations using lattice statistics. The theory predicts the salt dependence and binding free energies, of Mg(2+) ions to polynucleotides, of hexamine cobalt(III) to calf thymus DNA, of polyamines to T7 DNA, of oligolysines to poly(U) and poly(a), and of tripeptides to heparin, a charged polysaccharide. One parameter is required to obtain absolute binding constants, the distance of closest separation of the ligand to the polyion. Some, but not all, of the binding entropies and enthalpies are also predicted accurately by the model.

Thermodynamics of RNA unfolding: stabilization of a ribosomal RNA tertiary structure by thiostrepton and ammonium ion

RNAs with interesting secondary and tertiary structures tend to melt in several broad and overlapping transitions over a wide temperature range, and it has been consequently difficult to resolve the thermodynamics of individual unfolding steps. In the case that a ligand selectively binds a single folded state of the RNA, it is possible to obtain reliable thermodynamic parameters for both RNA unfolding and RNA-ligand binding simply from the hyperchromicity of RNA denaturation. The analysis procedure involves fitting a three-dimensional surface to absorbance data collected as a function of both temperature and ligand concentration. Analysis of the unfolding of a fragment of the large subunit ribosomal RNA (Escherichia coli sequence 1051 to 1109) is presented; both an antibiotic (thiostrepton) and ammonium ion specifically stabilize a tertiary structure within this RNA. A consistent set of thermodynamic parameters (delta H and tm) for the first two sequentially linked unfolding transitions is obtained from the experiments, and the binding constants obtained for the two ligands are consistent with other independent measurements. The approach is applicable to a variety of RNAs that specifically bind proteins, antibiotics, ions or other ligands.

Spectrophotometric and kinetic studies of the binding of Ni2+, Co2+, and Mg2+ to poly(dG-dC).poly(dG-dC). Determination of the stoichiometry of the Ni2+-induced B--->Z transition

Data are reported for the binding of Ni2+, Co2+, and Mg2+ to the B-form of double-stranded poly(dG-dC) at ionic strength conditions I = 0.001 M, 0.01 M, and 0.1 M. The apparent binding constants for Ni2+ and Co2+ are about the same and are 2- to 3-fold higher than those for Mg2+. Kinetic studies indicate that Mg2+ binds to the polynucleotide mainly (or solely) as a mobile cloud (electrostatically, outer-sphere), whereas the transition metal ions undergo site binding (inner-sphere coordination) with poly(dG-dC). The kinetic data suggest that an Ni2+ ion coordinates to more than one binding site at the polynucleotide, presumably to G-N7 and a phosphate group. At low ionic strength conditions the addition of Ni2+ induces a B-->Z conformational transition in poly(dG-dC). As demonstrated by UV absorption and DC spectroscopy, the transition occurs at I = 0.001 M already when 3 x 10(-5) - 7 x 10(-5) M of Ni2+ are added to 8 x 10(-5) M (in monomeric units) of poly(dG-dC), and at I = 0.01 M between 2.5 x 10(-4) M and 4.5 x 10(-4) M of Ni2+. Using murexide as an indicator of the concentration of free Ni2+ ions, the amount of Ni2+ which is bound to the polynucleotide could be determined. At I = 0.001 M it was established that the B-->Z transition begins when 1 Ni2+ is bound coordinatively per four base pairs, and the transition is complete when 1 Ni2+ is bound coordinatively per three base pairs. It is this coordinated Ni2+ which induces the B-->Z transition.

RNA pseudoknots. Stability and loop size requirements

The effects of ionic conditions, loop size and loop sequence on the formation of pseudoknots by RNA oligonucleotides have been investigated using biochemical and biophysical methods. An oligonucleotide with the sequence 5' GCGAUUUCUGACCGCUUUUUUGUCAG 3' and oligonucleotides with variations in the sequences of the two loop regions, denoted by bold face type, were studied. Each sequence with the potential to form a pseudoknot can also form two stable hairpins. The pseudoknot structure is stabilized relative to the hairpins by addition of Mg2+. Even in the presence of Mg2+, the pseudoknots formed by the sequences investigated are only marginally more stable (1.5 to 2 kcal mol-1 in free energy at 37 degrees C) than either of the constituent hairpins. The pseudoknot structure is the stable conformation in the presence of Mg2+ when the first loop region is at least three nucleotides and the second is at least four nucleotides. Further deletion of nucleotides from the loop regions stabilizes possible hairpin structures relative to the pseudoknot and equilibria among secondary and tertiary structures result.