Counterion association with native and denatured nucleic acids: an experimental approach

Developing Community Resources for Nucleic Acid Structures

In this review, we describe the creation of the Nucleic Acid Database (NDB) at Rutgers University and how it became a testbed for the current infrastructure of the RCSB Protein Data Bank. We describe some of the special features of the NDB and how it has been used to enable research. Plans for the next phase as the Nucleic Acid Knowledgebase (NAKB) are summarized.

Comparative thermal and thermodynamic study of DNA chemically modified with antitumor drug cisplatin and its inactive analog transplatin

Antitumor activity of cisplatin is exerted by covalent binding to DNA. For comparison, studies of cisplatin-DNA complexes often employ the very similar but inactive transplatin. In this work, thermal and thermodynamic properties of DNA complexes with these compounds were studied using differential scanning calorimetry (DSC) and computer modeling. DSC demonstrates that cisplatin decreases thermal stability (melting temperature, Tm) of long DNA, and transplatin increases it. At the same time, both compounds decrease the enthalpy and entropy of the helix-coil transition, and the impact of transplatin is much higher. From Pt/nucleotide molar ratio rb=0.001, both compounds destroy the fine structure of DSC profile and increase the temperature melting range (ΔT). For cisplatin and transplatin, the dependences δTm vs rb differ in sign, while δΔT vs rb are positive for both compounds. The change in the parameter δΔT vs rb demonstrates the GC specificity in the location of DNA distortions. Our experimental results and calculations show that 1) in contrast to [Pt(dien)Cl]Cl, monofunctional adducts formed by transplatin decrease the thermal stability of long DNA at [Na(+)]>30mM; 2) interstrand crosslinks of cisplatin and transplatin only slightly increase Tm; 3) the difference in thermal stability of DNA complexes with cisplatin vs DNA complexes with transplatin mainly arises from the different thermodynamic properties of their intrastrand crosslinks. This type of crosslink appears to be responsible for the antitumor activity of cisplatin. At any [Na(+)] from interval 10-210mM, cisplatin and transplatin intrastrand crosslinks give rise to destabilization and stabilization, respectively.

Polyelectrolyte effects in G-quadruplexes

The role of counterion condensation as a dominant force governing the stability of DNA duplexes and triplexes is well established. In contrast, the effect of counterion condensation on the stability of G-quadrupex conformations is poorly understood. Unlike other ordered nucleic acid structures, G-quadruplexes exhibit a specific binding of counterions (typically, Na(+) or K(+)) which are buried inside the central cavity and coordinated to the O6 carbonyls of the guanines forming the G-quartets. While it has been known that the G-quadruplex-to-coil transition temperature, TM, increases with an increase in the concentration of the stabilizing ion, the contributions of the specific (coordination in the central cavity) and nonspecific (condensation) ion binding have not been resolved. In this work, we separate the two contributions by studying the change in TM of preformed G-quadruplexes following the addition of nonstabilizing ions Li(+), Cs(+), and TMA(+) (tetramethylammonium). In our studies, we used two G-quadruplexes formed by the human telomeric sequences which are distinct with respect to the folding topology and the identity and the number of sequestered stabilizing ions. Our data suggest that the predominant ionic contribution to G-quadruplex stability comes from the specifically bound Na(+) or K(+) ions and not from counterion condensation. We offer molecular rationalizations to the observed insensitivity of G-quadruplex stability to counterion condensation and emphasize the need to expand such studies to assess the generality of our findings.

Atom transfer radical polymerization preparation and photophysical properties of polypyridylruthenium derivatized polystyrenes

A ruthenium containing polymer featuring a short carbonyl-amino-methylene linker has been prepared by atom transfer radical polymerization (ATRP). The polymer was derived from ATRP of the N-hydroxysuccinimide (NHS) derivative of p-vinylbenzoic acid, followed by an amide coupling reaction of the NHS-polystyrene with Ru(II) complexes derivatized with aminomethyl groups (i.e., [Ru(bpy)2(CH3-bpy-CH2NH2)](2+) where bpy is 2,2'-bipyridine, and CH3-bpy-CH2NH2 is 4-methyl-4'-aminomethyl-2,2'-bipyridine). The Ru-functionalized polymer structure was confirmed by using nuclear magnetic resonance and infrared spectroscopy, and the results suggest that a high loading ratio of polypyridylruthenium chromophores on the polystyrene backbone was achieved. The photophysical properties of the polymer were characterized in solution and in rigid ethylene glycol glasses. In solution, emission quantum yield and lifetime studies reveal that the polymer's metal-to-ligand charge transfer (MLCT) excited states are quenched relative to a model Ru complex chromophore. In rigid media, the MLCT-ground state band gap and lifetime are both increased relative to solution with time-resolved emission measurements revealing fast energy transfer hopping within the polymer. Molecular dynamics studies of the polymer synthesized here as well as similar model systems with various spatial arrangements of the pendant Ru complex chromophores suggest that the carbonyl-amino-methylene linker probed in our target polymer provides shorter Ru-Ru nearest-neighbor distances leading to an increased Ru*-Ru energy hopping rate, compared to those with longer linkers in counterpart polymers.

Ionic microenvironmental effects on triplex DNA stabilization: cationic counterion effects on poly(dT)·poly(dA)·poly(dT)

The structure and conformation of nucleic acids are influenced by metal ions, polyamines, and the microenvironment. In poly(purine) · poly(pyrimidine) sequences, triplex DNA formation is facilitated by metal ions, polyamines and other ligands. We studied the effects of mono- and di-valent metal ions, and ammonium salts on the stability of triple- and double-stranded structures formed from poly(dA) and poly(dT) by measuring their respective melting temperatures. In the presence of metal ions, the absorbance versus temperature profile showed two transitions: Tm1 for triplex to duplex and single stranded DNA, and Tm2 for duplex DNA melting to single stranded DNA. Monovalent cations (Li(+), Na(+), K(+), Rb(+), Cs(+) and [Formula: see text] ) promoted triplex DNA at concentrations ≥150 mM. Tm1 varied from 49.8 °C in the presence of 150 mM Li(+) to 30.6 °C in the presence of 150 mM K(+). [Formula: see text] was very effective in stabilizing triplex DNA and its efficacy decreased with increasing substitution of the hydrogen atoms with methyl, ethyl, propyl and butyl groups. As in the case of monovalent cations, a concentration-dependent increase in Tm1 was observed with divalent ions and triplex DNA stabilization decreased in the order: Mg(2+) > Ca(2+) > Sr(2+) > Ba(2+). All positively charged cations increased the melting temperature of duplex DNA. Values of Δn (number of ions released) on triplex DNA melting were 0.46 ± 0.06 and 0.18 ± 0.02, respectively, for mono- and di-valent cations, as calculated from 1/Tm1 versus ln[M(+,2+)] plots. The corresponding values for duplex DNA were 0.25 ± 0.02 and 0.12 ± 0.02, respectively, for mono- and di-valent cations. Circular dichroism spectroscopic studies showed distinct conformational changes in triplex DNA stabilized by alkali metal and ammonium ions. Our results might be useful in developing triplex forming oligonucleotide based gene silencing techniques.

Energy landscapes of dynamic ensembles of rolling triplet repeat bulge loops: implications for DNA expansion associated with disease states

DNA repeat domains can form ensembles of canonical and noncanonical states, including stable and metastable DNA secondary structures. Such sequence-induced structural diversity creates complex conformational landscapes for DNA processing pathways, including those triplet expansion events that accompany replication, recombination, and/or repair. Here we demonstrate further levels of conformational complexity within repeat domains. Specifically, we show that bulge loop structures within an extended repeat domain can form dynamic ensembles containing a distribution of loop positions, thereby yielding families of positional loop isomers, which we designate as "rollamers". Our fluorescence, absorbance, and calorimetric data are consistent with loop migration/translocation between sites within the repeat domain ("rollamerization"). We demonstrate that such "rollameric" migration of bulge loops within repeat sequences can invade and disrupt previously formed base-paired domains via an isoenthalpic, entropy-driven process. We further demonstrate that destabilizing abasic lesions alter the loop distributions so as to favor "rollamers" with the lesion positioned at the duplex/loop junction, sites where the flexibility of the abasic "universal hinge" relaxes unfavorable interactions and/or facilitates topological accommodation. Another strategic siting of an abasic site induces directed loop migration toward denaturing domains, a phenomenon that merges destabilizing domains. In the aggregate, our data reveal that dynamic ensembles within repeat domains profoundly impact the overall energetics of such DNA constructs as well as the distribution of states by which they denature/renature. These static and dynamic influences within triplet repeat domains expand the conformational space available for selection and targeting by the DNA processing machinery. We propose that such dynamic ensembles and their associated impact on DNA properties influence pathways that lead to DNA expansion.

A coarse-grained model of DNA with explicit solvation by water and ions

Solvation by water and ions has been shown to be vitally important for biological molecules, yet fully atomistic simulations of large biomolecules remain a challenge due to their high computational cost. The effect of solvation is the most pronounced in polyelectrolytes, of which DNA is a paradigmatic example. Coarse-grained (CG) representations have been developed to model the essential physics of the DNA molecule, yet almost without exception, these models replace the water and ions by implicit solvation in order to significantly reduce the computational expense. This work introduces the first coarse-grained model of DNA solvated explicitly with water and ions. To this end, we combined two established CG models; the recently developed mW-ion model [DeMille, R. C.; Molinero, V. J. Chem. Phys. 2009, 131, 034107], which reproduces the structure of aqueous ionic solutions without electrostatic interactions, was coupled to the three-sites-per-nucleotide (3SPN) CG model of DNA [Knotts, T. A., IV; et al. J. Chem. Phys. 2007, 126, 084901]. Using atomistic simulations of d(CGCGAATTCGCG)(2) as a reference, we optimized the coarse-grained interactions between DNA and solvent to reproduce the solvation structure of water and ions around CG DNA. The resulting coarse-grained model of DNA explicitly solvated by ions and water (mW/3SPN-DNA) exhibits base-pair specificity and ion-condensation effects and it is 2 orders of magnitude computationally more efficient than atomistic models. We describe the parametrization strategy and offer insight into how other CG models may be combined with a coarse-grained solvent model such as mW-ion.

Counterion condensation and shape within Poisson-Boltzmann theory

An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined "condensation distance" although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte.

Compatible solute influence on nucleic acids: many questions but few answers

Compatible solutes are small organic osmolytes including but not limited to sugars, polyols, amino acids, and their derivatives. They are compatible with cell metabolism even at molar concentrations. A variety of organisms synthesize or take up compatible solutes for adaptation to extreme environments. In addition to their protective action on whole cells, compatible solutes display significant effects on biomolecules in vitro. These include stabilization of native protein and nucleic acid structures. They are used as additives in polymerase chain reactions to increase product yield and specificity, but also in other nucleic acid and protein applications.

Interactions of compatible solutes with nucleic acids and protein-nucleic acid complexes are much less understood than the corresponding interactions of compatible solutes with proteins. Although we may begin to understand solute/nucleic acid interactions there are only few answers to the many questions we have. I summarize here the current state of knowledge and discuss possible molecular mechanisms and thermodynamics.

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.

Continuum molecular electrostatics, salt effects, and counterion binding--a review of the Poisson-Boltzmann theory and its modifications

This work is a review of the Poisson-Boltzmann (PB) continuum electrostatics theory and its modifications, with a focus on salt effects and counterion binding. The PB model is one of the mesoscopic theories that describes the electrostatic potential and equilibrium distribution of mobile ions around molecules in solution. It serves as a tool to characterize electrostatic properties of molecules, counterion association, electrostatic contributions to solvation, and molecular binding free energies. We focus on general formulations which can be applied to large molecules of arbitrary shape in all-atomic representation, including highly charged biomolecules such as nucleic acids. These molecules present a challenge for theoretical description, because the conventional PB model may become insufficient in those cases. We discuss the conventional PB equation, the corresponding functionals of the electrostatic free energy, including a connection to DFT, simple empirical extensions to this model accounting for finite size of ions, the modified PB theory including ionic correlations and fluctuations, the cell model, and supplementary methods allowing to incorporate site-bound ions in the PB calculations.

Polymer brush-stabilized polyplex for a siRNA carrier with long circulatory half-life

Delivery systems of small interfering RNA (siRNA) are the key to siRNA therapeutic application. In this study, we prepared and evaluated a series of cationic comb-type copolymers (CCCs) possessing a polycationic backbone (less than 30 weight (wt) %) and abundant water-soluble side chains (more than 70 wt.%) as a siRNA carrier with prolonged blood circulation time. Markedly, the CCC with the higher side chain content (10 wt.% PLL and 90 wt.% PEG) showed stronger interaction with siRNA than that with the lower content (30 wt.% PLL and 70 wt.% PEG), suggesting that highly dense PEG brush reinforces interpolyelectrolyte complex between the PLL backbone and siRNA. The siRNA complexed with the CCC was resistant to nucleases in 90% plasma for 24 h in vitro. The CCC having the higher side chain content increased circulation time of siRNA in mouse bloodstream by 100-fold. Surprisingly, even when the CCC and siRNA were separately injected into mouse at 20 min interval, blood circulation of post-injected siRNA was significantly increased. These results imply that the CCC has higher selectivity in its ionic interaction with siRNA than other anionic substances in blood stream. To our knowledge, this is the first example of a polyplex carrier that prolongs blood circulation time of unmodified siRNA without resource-consuming preparation process.

Low ionic strength reduces cytosine photoreactivity in UVC-irradiated isolated DNA

Exposure of DNA to far-UV radiation leads to the formation of several types of dimeric lesions, including cyclobutane dimers and (6-4) photoproducts. In order to gain insights into the main parameters driving DNA photochemistry, the effect of ionic strength on the yield of formation of these photoproducts was investigated in UVC-irradiated samples of isolated genomic DNA. The main consequence of lowering the ionic strength was a decrease in the UVC-induced formation of thymine-cytosine and cytosine-cytosine photoproducts. The reactivity of thymine-thymine and cytosine-thymine doublets was hardly affected. Evidence was obtained against a major role played by duplex denaturation in these observations. A more likely explanation is a change in the DNA structure as the result of a larger extent of protonation at low counter-ions concentration.

Influence of dT20 and [d(AT)10]2 on cisplatin hydrolysis studied by two-dimensional [1H,15N] HMQC NMR spectroscopy

The influence of the presence of DNA on the kinetics of cisplatin (cis-[PtCl2(NH3)2]) aquation (replacement of Cl- by H2O) and anation (replacement of H2O by Cl-) involved in the hydrolysis of cisplatin have been determined by two-dimensional [1H,15N] HMQC NMR spectroscopy. Single-stranded dT20 and double-stranded [d(AT)10]2 oligonucleotides were used as DNA models, avoiding guanines which are known to react rapidly with aquated cisplatin forms. Reactions starting from cis-[PtCl2(15NH3)2], or from a stoichiometric mixture of cis-[Pt(15NH3)2(H2O)2]2+ and Cl- (all 0.5 mM Pt(II); in ionic strength, adjusted to 0.095 M or 0.011 M with NaClO4, pH between 3.0 and 4.0) were followed in an NMR tube in both the absence and presence of 0.7 mM dT20 or [d(AT)10]2. In the presence of dT20, we observed a slight and ionic-strength-independent decrease (15-20 %) of the first aquation rate constant, and a more significant decrease of the second anation rate constant. The latter was more important at low ionic strength, and can be explained by efficient condensation of cis-[Pt(15NH3)2(H2O)2]2+ on the surface of single-stranded DNA, in a region depleted of chloride anions. At low ionic strength, we observed an additional set of [1H,15N] HMQC spectral signals indicative of an asymmetric species of PtN2O2 coordination, and we assigned them to phosphate-bound monoadducts of cis-[Pt(15NH3)2(H2O)2]2+. Double-stranded [d(AT)10]2 slowed down the first aquation step also by approximately 15 %; however, we could not determine the influence on the second hydrolysis step because of a significant background reaction with cis-[Pt(NH3)2(H2O)2]2+.

Intercalation into the DNA double helix and in vivo biological activity of water-soluble planar [Pt(diimine)(N,N-dihydroxyethyl-N'-benzoylthioureato)]+Cl- complexes: a study of their thermal stability, their CD spectra and their gel mobility

The interaction of newly synthesised water-soluble planar complexes of general structure [Pt(diimine)(N,N-dihydroxyethyl-N'-benzoylthioureato)]+Cl- with DNA was investigated by means of DNA melting studies, CD spectroscopy, and DNA gel mobility studies. Addition of stoichometric amounts of [Pt(diimine)H2L-S,O]Cl complexes to polynucleotides caused a significant increase in the melting temperature of poly(dA-dT) and calf-thymus DNA, respectively, indicating that these complexes interacted with DNA and stabilised the double helical structure. The CD spectra confirmed the relatively strong binding of three related Pt(II) complexes ([Pt(2,2'-bipyridine)H2L-S,O]Cl, [Pt(4,4'-dimethyl-2,2'-bipyridine)H2L-S,O]Cl, and [Pt(1,10-phenanthroline)H2L-S,O]Cl), to DNA. Comparison with the published CD spectra of ethidium bromide/DNA complex suggests a similar intercalation mode of binding. cis-[(4,4'-di-tert-butyl-2,2'-bipyridyl)N,N-di(2-hydroxyethyl)-N'-benzoylthioureatoplatinum(II)] chloride, with its very bulky tert-butyl groups, did not intercalate into the polynucleotide double helix. In DNA mobility studies in the presence of the four [Pt(diimine)H2L-S,O]Cl complexes, only [Pt(2,2'-bipyridine)H2L-S,O]Cl affected the DNA mobility to any detectable extent. Finally, in vivo studies on the biological activity of the complexes, using an Escherichia coli DNA excision repair deficient uvrA mutant strain, indicated that only the [Pt(2,2'-bipyridine)H2L-S,O]Cl complex showed significant cellular toxicity and that this was, in part, linked to DNA damage.

Communication Between Noncontacting Macromolecules

Molecular interactions are the language that molecules use to communicate recognition, binding, and regulation, events central to biological control mechanisms. Traditionally, such interactions involve direct, atom-to-atom, noncovalent contacts, or indirect contacts bridged by relatively fixed solvent molecules. Here we discuss a third class of molecular communication that, to date, has received less experimental attention, namely solvent-mediated communication between noncontacting macromolecules. This form of communication can be understood in terms of fundamental, well-established principles (coupled equilibria and linkage thermodynamics) that govern interactions between individual polymers and their solutions. In contrast to simple solutions used in laboratory studies, biological systems contain a multitude of nominally noninteracting biopolymers within the same solution environment. The exquisite control of biological function requires some form of communication between many of these solution components, even in the absence of direct and/or indirect contacts. Such communication must be considered when describing potential mechanisms of biological regulation.

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

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

Effects of Sodium Ions on DNA Duplex Oligomers: Improved Predictions of Melting Temperatures

Melting temperatures, T(m), were systematically studied for a set of 92 DNA duplex oligomers in a variety of sodium ion concentrations ranging from 69 mM to 1.02 M. The relationship between T(m) and ln [Na(+)] was nonlinear over this range of sodium ion concentrations, and the observed melting temperatures were poorly predicted by existing algorithms. A new empirical relationship was derived from UV melting data that employs a quadratic function, which better models the melting temperatures of DNA duplex oligomers as sodium ion concentration is varied. Statistical analysis shows that this improved salt correction is significantly more accurate than previously suggested algorithms and predicts salt-corrected melting temperatures with an average error of only 1.6 degrees C when tested against an independent validation set of T(m) measurements obtained from the literature. Differential scanning calorimetry studies demonstrate that this T(m) salt correction is insensitive to DNA concentration. The T(m) salt correction function was found to be sequence-dependent and varied with the fraction of G.C base pairs, in agreement with previous studies of genomic and polymeric DNAs. The salt correction function is independent of oligomer length, suggesting that end-fraying and other end effects have little influence on the amount of sodium counterions released during duplex melting. The results are discussed in the context of counterion condensation theory.

Application of the Poisson Boltzmann polyelectrolyte model for analysis of equilibria between single-, double-, and triple-stranded polynucleotides in the presence of K(+), Na(+), and Mg(2+) ions

The Poisson Boltzmann (PB) cell model of polyelectrolyte solution has been used for numerical calculations of the change in electrostatic free energy, DeltaG(el), for transformations between different structural forms (tri-, double-, and single-stranded) of the polyribonucleotides poly(rA).poly(rU)2, poly(rA).poly(rU), poly(rA), and poly(rU). In particular, the dependence on monovalent salt concentration, MCl (M = Na or K) in the absence and in the presence of MgCl(2) has been calculated. The results were obtained for conditions relevant to available experimental values of structural transition ("melting") temperatures (T(m)) and other thermodynamic quantities. Using the experimental T(m) values and theoretical electrostatic DeltaG(el), DeltaH(el), and DeltaS(el) functions, non-electrostatic contributions to the corresponding thermodynamic parameters of the poly(rA)/poly(rU) melting transitions were determined in MCl solutions in the absence of Mg(2+). Qualitative and to a large extent quantitative reproduction of the experimental calorimetry enthalpy, entropy and heat capacity values was found from the results of the PB theory. Furthermore, dependencies of T(m) on MCl concentration in the presence of MgCl(2) for the poly(rA)/poly(rU) transitions were also calculated. Compared to a model considering Mg(2+) as a fully-hydrated ion, much better agreement between experimental and PB theory was achieved by assuming the ion size of Mg(2+) to be given by that of a bare non-hydrated ion smaller than that of hydrated Na(+) or K(+). In agreement with data of experimental studies reported in literature, this result indicates that magnesium(II) can bind to RNA as a bare ion in a way that is different from that of DNA. Generally, we can conclude that the PB polyelectrolyte theory can provide an adequate description of thermally induced structural transitions in polydeoxy- and polyribonucleotides in different salt solutions in spite of the rather simplified model treating the solvent as dielectric continuum, the polyion as a uniformly charged cylinder, and the mobile ions as hard spheres in the absence of excluded volume effects.