Locating monovalent cations in the grooves of B-DNA

Here we demonstrate that monovalent cations can localize around B-DNA in geometrically regular, sequence-specific sites in oligonucleotide crystals. Positions of monovalent ions were determined from high-resolution X-ray diffraction of DNA crystals grown in the presence of thallium(I) cations (Tl(+)). Tl(+) has previously been shown to be a useful K(+) mimic. Tl(+) positions determined by refinement of model to data are consistent with positions determined using isomorphous F(Tl) - F(K) difference Fouriers and anomalous difference Fouriers. None of the observed Tl(+) sites surrounding CGCGAATTCGCG are fully occupied by Tl(+) ions. The most highly occupied sites, located within the G-tract major groove, have estimated occupancies ranging from 20% to 35%. The occupancies of the minor groove sites are estimated to be around 10%. The Tl(+) positions in general are not in direct proximity to phosphate groups. The A-tract major groove appears devoid of localized cations. The majority of the observed Tl(+) ions interact with a single duplex and so are not engaged in lattice interactions or crystal packing. The locations of the cation sites are dictated by coordination geometry, electronegative potential, avoidance of electropositive amino groups, and cation-pi interactions. It appears that partially dehydrated monovalent cations, hydrated divalent cations, and polyamines compete for a common binding region on the floor of the G-tract major groove.     

The contribution of metal ions to the structural stability of the large ribosomal subunit

Both monovalent cations and magnesium ions are well known to be essential for the folding and stability of large RNA molecules that form complex and compact structures. In the atomic structure of the large ribosomal subunit from Haloarcula marismortui, we have identified 116 magnesium ions and 88 monovalent cations bound principally to rRNA. Although the rRNA structures to which these metal ions bind are highly idiosyncratic, a few common principles have emerged from the identities of the specific functional groups that coordinate them. The nonbridging oxygen of a phosphate group is the most common inner shell ligand of Mg++, and Mg++ ions having one or two such inner shell ligands are very common. Nonbridging phosphate oxygens and the heteroatoms of nucleotide bases are common outer shell ligands for Mg++ ions. Monovalent cations usually interact with nucleotide bases and protein groups, although some interactions with nonbridging phosphate oxygens are found. The most common monovalent cation binding site is the major groove side of G-U wobble pairs. Both divalent and monovalent cations stabilize the tertiary structure of 23S rRNA by mediating interactions between its structural domains. Bound metal ions are particularly abundant in the region surrounding the peptidyl transferase center, where stabilizing cationic tails of ribosomal proteins are notably absent. This may point to the importance of metal ions for the stabilization of specific RNA structures in the evolutionary period prior to the appearance of proteins, and hence many of these metal ion binding sites may be conserved across all phylogenetic kingdoms.     

Electrostatic effects on the stability of condensed DNA in the presence of divalent cations.

Cylindrical cell model Poisson-Boltzmann (P-B) calculations are used to evaluate the electrostatic contributions to the relative stability of various DNA conformations (A, B, C, Z, and single-stranded (ss) with charge spacings of 3.38 and 4.2 A) as a function of interhelix distance in a concentrated solution of divalent cations. The divalent ion concentration was set at 100 mM, to compare with our earlier reports of spectroscopic and calorimetric experiments, which demonstrate substantial disruption of B-DNA geometry. Monovalent cations neutralize the DNA phosphates in two ways, corresponding to different experimental situations: 1) There is no significant contribution to the ionic strength from the neutralizing cations, corresponding to DNA condensation from dilute solution and to osmotic stress experiments in which DNA segments are brought into close proximity to each other in the presence of a large excess of buffer. 2) The solution is uniformly concentrated in DNA, so that the neutralizing cations add significantly to those in the buffer at close DNA packing. In case 1), conformations with lower charge density (Z and ssDNA) have markedly lower electrostatic free energies than B-DNA as the DNA molecules approach closely, due largely to ionic entropy. If the divalent cations bind preferentially to single-stranded DNA or a distorted form of B-DNA, as is the case with transition metals, the base pairing and stacking free energies that stabilize the double helix against electrostatic denaturation may be overcome. Strong binding to the bases is favored by the high concentration of divalent cations at the DNA surface arising from the large negative surface potential; the surface concentration increases sharply as the interhelical distance decreases. In case 2), the concentration of neutralizing monovalent cations becomes very large and the electrostatic free energy difference between secondary structures becomes small as the interhelical spacing decreases. Such high ionic concentrations will be expected to modify the stability of DNA by changing water activity as well as by screening electrostatic interactions. This may be the root of the decreased thermal stability of DNA in the presence of high concentrations of magnesium ions.     

Ion Condensation onto Ribozyme Is Site Specific and Fold Dependent

The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions in the absence of ions. For ribozymes, divalent cations are known to be more efficient than monovalent ions in driving them to a compact state, although Mg²⁺ ions are needed for catalytic activities. Therefore, how ions interact with RNA is relevant in understanding RNA folding. It is often thought that most of the ions are territorially and nonspecifically bound to the RNA, as predicted by the counterion condensation theory. Here, we show using simulations of Azoarcus ribozyme, based on an accurate coarse-grained three-site interaction model with explicit divalent and monovalent cations, that ion condensation is highly specific and depends on the nucleotide position. The regions with high coordination between the phosphate groups and the divalent cations are discernible even at very low Mg²⁺ concentrations when the ribozyme does not form tertiary interactions. Surprisingly, these regions also contain the secondary structural elements that nucleate subsequently in the self-assembly of RNA, implying that ion condensation is determined by the architecture of the folded state. These results are in sharp contrast to interactions of ions (monovalent and divalent) with rigid charged rods, in which ion condensation is uniform and position independent. The differences are explained in terms of the dramatic nonmonotonic shape fluctuations in the ribozyme as it folds with increasing Mg²⁺ or Ca²⁺ concentration.     

Structural roles of monovalent cations in the HDV ribozyme

The hepatitis delta virus (HDV) ribozyme catalyzes viral RNA self-cleavage through general acid-base chemistry in which an active-site cytidine and at least one metal ion are involved. Monovalent metal ions support slow catalysis and were proposed to substitute for structural, but not catalytic, divalent metal ions in the RNA. To investigate the role of monovalent cations in ribozyme structure and function, we determined the crystal structure of the precursor HDV ribozyme in the presence of thallium ions (Tl(+)). Two Tl(+) ions can occupy a previously observed divalent metal ion hexahydrate-binding site located near the scissile phosphate, but are easily competed away by cobalt hexammine, a magnesium hexahydrate mimic and potent reaction inhibitor. Intriguingly, a third Tl(+) ion forms direct inner-sphere contacts with the ribose 2'-OH nucleophile and the pro-S(p) scissile phosphate oxygen. We discuss possible structural and catalytic implications of monovalent cation binding for the HDV ribozyme mechanism.     

Study of substrate-enzyme interaction between immobilized pyridoxamine and recombinant porcine pyridoxal kinase using surface plasmon resonance biosensor

Pyridoxal kinase (PK) is an important enzyme involved in bioactivation of vitamin B(6). Binding of PK with its substrate is the prerequisite step for the subsequent catalytic phosphorylation of the substrate. In the present study, a surface plasmon resonance biosensor (BIAcore) was employed to characterize the binding interaction between wild-type porcine PK and an immobilized substrate, pyridoxamine. Pyridoxamine was modified with 11-mercaptoundecanic acid and immobilized on a sensor chip through the formation of a self-assembled monolayer. The binding of PK to the immobilized pyridoxamine was followed in real time and the kinetic parameters were derived from non-linear analysis of the sensorgram. The effects of buffer pH, monovalent cations (Na(+), K(+)) and divalent cations (Mn(2+), Zn(2+), Mg(2+)) on the binding kinetics were determined. Optimal pH for PK-pyridoxamine interaction in the absence of divalent ions is at around 7.4. While K(+) increased and Na(+) decreased the binding affinity (K(A)) of PK to immobilized pyridoxamine, all divalent cations increased the K(A) of PK for pyridoxamine. Solution phase affinity measurement based on a competitive binding assay was used to determine the affinities of PK for different vitamin B(6) analogues. The order of affinity of PK for different analogues is: pyridoxal-oxime>pyridoxine>pyridoxamine>pyridoxal>pyridoxal phosphate. This is the first study to demonstrate that buffer conditions such as pH and concentration of monovalent and/or divalent ions can directly alter the binding of PK for its substrates. The quantitative kinetic and thermodynamic parameters obtained by SPR measurement provide the insight information into the catalytic activity of this enzyme.     

Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamics simulation and a Poisson‐Boltzmann approach

The ion atmosphere created by monovalent (Na⁺) or divalent (Mg²⁺) cations surrounding a B‐form DNA duplex were examined using atomistic molecular dynamics (MD) simulations and the nonlinear Poisson‐Boltzmann (PB) equation. The ion distributions predicted by the two methods were compared using plots of radial and two‐dimensional cation concentrations and by calculating the total number of cations and net solution charge surrounding the DNA. Na⁺ ion distributions near the DNA were more diffuse in PB calculations than in corresponding MD simulations, with PB calculations predicting lower concentrations near DNA groove sites and phosphate groups and a higher concentration in the region between these locations. Other than this difference, the Na⁺ distributions generated by the two methods largely agreed, as both predicted similar locations of high Na⁺ concentration and nearly identical values of the number of cations and the net solution charge at all distances from the DNA. In contrast, there was greater disagreement between the two methods for Mg²⁺ cation concentration profiles, as both the locations and magnitudes of peaks in Mg²⁺ concentration were different. Despite experimental and simulation observations that Mg²⁺ typically maintains its first solvation shell when interacting with nucleic acids, modeling Mg²⁺ as an unsolvated ion during PB calculations improved the agreement of the Mg²⁺ ion atmosphere predicted by the two methods and allowed for values of the number of bound ions and net solution charge surrounding the DNA from PB calculations that approached the values observed in MD simulations. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 834–848, 2014.     

88 Comparison of monovalent and divalent ion distributions around a DNA duplex with molecular dynamic simulation and Poisson–Boltzmann approach

Ion interactions with nucleic acids (both DNA and RNA) are an important and evolving field of investigation. Positively charged cations may interact with highly negatively charged nucleic acids via simple electrostatic interactions to help screen the electrostatic repulsion along the nucleic acids and assist their folding and/or compaction. Cations may also bind at specific sites and become integral parts of the structures, possibly playing important enzymatic roles. Two popular methods for computationally exploring a nucleic acid’s ion atmosphere are atomistic molecular dynamics (MD) simulations and the Poisson–Boltzmann (PB) equation. In general, monovalent ion results obtained from MD simulations and the PB equation agree well with experiment. However, Bai et al. (2007) observed discrepancies between experiment and the PB equation while examining the competitive binding of monovalent and divalent ions, with more significant discrepancies for divalent ions. The goal of this project was to thoroughly investigate monovalent (Na⁺) and divalent (Mg²⁺) ion distributions formed around a DNA duplex with MD simulations and the PB equation. We simulated three different cation concentrations, and matched the equilibrated bulk ion concentration for our theoretical calculations with the PB equation. Based on previous work, our Mg²⁺ ions were fully solvated, the expected state of Mg²⁺ ions when interacting with a duplex, when the production simulations began and remained throughout the simulations (Kirmizialtin, 2010; Robbins, 2012). Na⁺ ion distributions and number of Na⁺ ions within 10?Å of the DNA obtained from our two methods agreed well. However, results differed for Mg²⁺ ions, with a lower number of ions within the cut-off distance obtained from the PB equation when compared to MD simulations. The Mg²⁺ ion distributions around the DNA obtained via the two methods also differed. Based on our results, we conclude that the PB equation will systematically underestimate Mg²⁺ ions bound to DNA, and much of this deviation is attributed to dielectric saturation associated with high valency ions.     

Absence of minor groove monovalent cations in the crosslinked dodecamer C-G-C-G-A-A-T-T-C-G-C-G.

The structure of a crosslinked B -DNA dodecamer of sequence C-G-C-G-A-A-T-T-C-G-C-G has been solved to a resolution of 1.43 A. The dithiobis-propane crosslink, -CH2-CH2-CH2-S-S-CH2-CH2-CH2-, bridges N7 atoms of adenine bases 6 and 18 in the two central base-pairs within the major groove. The crosslink is sufficiently long that no bending is induced in the helix, which is essentially isostructural with the native unlinked dodecamer at 1.9 A. A constellation of solvent peaks tentatively fitted as a spermine molecule in that earlier analysis is now seen at higher resolution to be a well-defined octahedral magnesium hexahydrate complex in the major groove. One end of the duplex curves around that complex to produce a roll-bend near base-pairs 3-5, and an overall bend in helix axis, as has long been noted. Two other magnesium complexes connect the helices and help to knit the crystal lattice together. No evidence exists for partial sodium or potassium ion substitution for solvent water molecules within the minor groove spine of hydration, as had been suggested previously: not coordination geometry and environment, nor B values, nor calculated valence values, nor difference map analyses. Indeed, the very numbers that have been claimed in support of partial substitution by sodium or potassium ions are reproduced with the present crystals, which by chemical analysis contains only one trace sodium ion per 160 bp, and one potassium ion per 41 bp. In contrast, our crystals contain one Mg2+ per base-pair, meaning that phosphate group charge neutrality is accomplished by divalent cations, not monovalent ions. Three of these magnesium cations per duplex are localized and visible in the X-ray analysis, and nine are disordered and invisible. Hence although binding of monovalent cations within the minor groove of A -tracts on occasion may be a consequence of groove narrowing, it cannot be the cause of that narrowing. Cations, contrary to what has been claimed, are not in charge.     

Discovery of the ammonium substrate site on glutamine synthetase, a third cation binding site.

Glutamine synthetase (GS) catalyzes the ATP-dependent condensation of ammonia and glutamate to yield glutamine, ADP, and inorganic phosphate in the presence of divalent cations. Bacterial GS is an enzyme of 12 identical subunits, arranged in two rings of 6, with the active site between each pair of subunits in a ring. In earlier work, we have reported the locations within the funnel-shaped active site of the substrates glutamate and ATP and of the two divalent cations, but the site for ammonia (or ammonium) has remained elusive. Here we report the discovery by X-ray crystallography of a binding site on GS for monovalent cations, Tl+ and Cs+, which is probably the binding site for the substrate ammonium ion. Fourier difference maps show the following. (1) Tl+ and Cs+ bind at essentially the same site, with ligands being Glu 212, Tyr 179, Asp 50', Ser 53' of the adjacent subunit, and the substrate glutamate. From its position adjacent to the substrate glutamate and the cofactor ADP, we propose that this monovalent cation site is the substrate ammonium ion binding site. This proposal is supported by enzyme kinetics. Our kinetic measurements show that Tl+, Cs+, and NH4+ are competitive inhibitors to NH2OH in the gamma-glutamyl transfer reaction. (2) GS is a trimetallic enzyme containing two divalent cation sites (n1, n2) and one monovalent cation site per subunit. These three closely spaced ions are all at the active site: the distance between n1 and n2 is 6 A, between n1 and Tl+ is 4 A, and between n2 and Tl+ is 7 A. Glu 212 and the substrate glutamate are bridging ligands for the n1 ion and Tl+. (3) The presence of a monovalent cation in this site may enhance the structural stability of GS, because of its effect of balancing the negative charges of the substrate glutamate and its ligands and because of strengthening the "side-to-side" intersubunit interaction through the cation-protein bonding. (4) The presence of the cofactor ADP increases the Tl+ binding to GS because ADP binding induces movement of Asp 50' toward this monovalent cation site, essentially forming the site. This observation supports a two-step mechanism with ordered substrate binding: ATP first binds to GS, then Glu binds and attacks ATP to form gamma-glutamyl phosphate and ADP, which complete the ammonium binding site. The third substrate, an ammonium ion, then binds to GS, and then loses a proton to form the more active species ammonia, which attacks the gamma-glutamyl phosphate to yield Gln. (5) Because the products (Glu or Gln) of the reactions catalyzed by GS are determined by the molecule (water or ammonium) attacking the intermediate gamma-glutamyl phosphate, this negatively charged ammonium binding pocket has been designed naturally for high affinity of ammonium to GS, permitting glutamine synthesis to proceed in aqueous solution.     

Solution conformation of various uridine diphosphoglucose salts as probed by NMR spectroscopy

The solution conformations of uridine diphosphoglucose (UDP-Glc) under a variety of conditions (solvent, ionic strength, various mono- and divalent cations) have been studied by NMR spectroscopy (1H, 13C, 31P, and 25Mg). In the case of divalent cations (Ca2+, Mg2+, Mn2+) the phosphate oxygens are the preferred coordination sites and analysis of the 25Mg linewidths of solutions with various [Mg2+]/[UDP-Glc] ratios, indicates that the 1:1 Mg2+ UDP-Glc complex is the major species. From 13C relaxation data and hydrodynamic theory, it has been demonstrated that under all conditions UDP-Glc adopts a fairly extended overall shape and that magnesium ions lead to a significant increase in the average length of the UDP-Glc molecule as compared to monovalent cations. Thus, one of the roles of the metal ion in enzymic reactions involving nucleotide sugars may be to preorganize the nucleotide sugar.     

Active-Site Monovalent Cations Revealed in a 1.55-Å-Resolution Hammerhead Ribozyme Structure

We have obtained a 1.55-Å crystal structure of a hammerhead ribozyme derived from Schistosoma mansoni under conditions that permit detailed observations of Na⁺ ion binding in the ribozyme's active site. At least two such Na⁺ ions are observed. The first Na⁺ ion binds to the N7 of G10.1 and the adjacent A9 phosphate in a manner identical with that previously observed for divalent cations. A second Na⁺ ion binds to the Hoogsteen face of G12, the general base in the hammerhead cleavage reaction, thereby potentially dissipating the negative charge of the catalytically active enolate form of the nucleotide base. A potential but more ambiguous third site bridges the A9 and scissile phosphates in a manner consistent with that of previous predictions. Hammerhead ribozymes have been observed to be active in the presence of high concentrations of monovalent cations, including Na⁺, but the mechanism by which monovalent cations substitute for divalent cations in hammerhead catalysis remains unclear. Our results enable us to suggest that Na⁺ directly and specifically substitutes for divalent cations in the hammerhead active site. The detailed geometry of the pre-catalytic active-site complex is also revealed with a new level of precision, thanks to the quality of the electron density maps obtained from what is currently the highest-resolution ribozyme structure in the Protein Data Bank.     

Effect of finite ionic size on the solution of the Poisson-Boltzmann equation: Application to the binding of divalent metal ions to DNA

The nonlinear Poisson-Boltzmann equation is solved for a cylindrical polyelectrolyte solution containing mono- and divalent counterions and monovalent coions. The finite size of the ions is taken into account by the introduction of the distances of closest approach between the ionic charges and the surface of the polyelectrolyte. The choice of these distances is based on the physicochemical properties of the polyelectrolyte and ions in solution. The effects of the finite ionic size on the distribution of the counterions around the polyelectrolyte and on the local ion concentration and the integrated charge fraction of the divalent cations in the vicinity of the polyelectrolyte are discussed. Theoretical predictions regarding the overall extent of binding and the extent of inner-sphere binding of divalent counterions to rodlike polyions are compared with the results of nmr studies of the binding of divalent metal ions to DNA.     

1 A crystal structures of B-DNA reveal sequence-specific binding and groove-specific bending of DNA by magnesium and calcium

The 1 A resolution X-ray crystal structures of Mg(2+) and Ca(2+) salts of the B-DNA decamers CCAACGTTGG and CCAGCGCTGG reveal sequence-specific binding of Mg(2+) and Ca(2+) to the major and minor grooves of DNA, as well as non-specific binding to backbone phosphate oxygen atoms. Minor groove binding involves H-bond interactions between cross-strand DNA base atoms of adjacent base-pairs and the cations' water ligands. In the major groove the cations' water ligands can interact through H-bonds with O and N atoms from either one base or adjacent bases, and in addition the softer Ca(2+) can form polar covalent bonds bridging adjacent N7 and O6 atoms at GG bases. For reasons outlined earlier, localized monovalent cations are neither expected nor found.Ultra-high atomic resolution gives an unprecedented view of hydration in both grooves of DNA, permits an analysis of individual anisotropic displacement parameters, and reveals up to 22 divalent cations per DNA duplex. Each DNA helix is quite anisotropic, and alternate conformations, with motion in the direction of opening and closing the minor groove, are observed for the sugar-phosphate backbone. Taking into consideration the variability of experimental parameters and crystal packing environments among these four helices, and 24 other Mg(2+) and Ca(2+) bound B-DNA structures, we conclude that sequence-specific and strand-specific binding of Mg(2+) and Ca(2+) to the major groove causes DNA bending by base-roll compression towards the major groove, while sequence-specific binding of Mg(2+) and Ca(2+) in the minor groove has a negligible effect on helix curvature. The minor groove opens and closes to accommodate Mg(2+) and Ca(2+) without the necessity for significant bending of the overall helix.The program Shelxdna was written to facilitate refinement and analysis of X-ray crystal structures by Shelxl-97 and to plot and analyze one or more Curves and Freehelix output files.     

An energy dependent divalent cation-hydrogen ion binding in the outer membranes of rat liver mitochondria and its dependence on monovalent cation-hydrogen ion binding

Intact mitochondria are able to bind monovalent and divalent metal cations and to release protons in an energy-independent exchange process. Directly accessible binding sites exist in the outer membrane. They seem to be identical for monovalent and divalent metal ions. The inner membrane-matrix-fraction possesses exchange sites after ultrasonic disruption only for monovalent cations, but not for divalent cations.     

The effects of metal ions on the structure and stability of the DNA gyrase B protein

The effects of mono- and divalent metal ions on the DNA gyrase B subunit, on its 43 kDa and 47 kDa domains, and on two mutants in the Toprim domain (D498A and D500C) were investigated by means of circular dichroism and protein melting experiments. Both types of metal ion, with the notable exception of Mn2+, did not affect the conformational properties of the enzyme subunit at room temperature, but were able to produce selective and differential effects on protein stability. In particular, monovalent (K+) ions increased the stability of the gyrase B structure, whereas destabilising effects were most prominent using Mn2+ as the metal ion. Ca2+ and Mg2+ produced comparable changes in the gyrase B melting profile. Additionally, we found that monovalent (K+) ions were more effective in the 43 kDa N-terminal domain where ATP binding occurs, whereas divalent ions caused large modifications in the conformational stability of the 47 kDa C-terminal domain. Our results on gyrase B mutants indicate that D498 interacts with Mn2+, whereas it has little effect on the binding of the other ions tested. A D500C mutation, in contrast, effectively impairs Mg2+ affinity, suggesting effective contacts between this ion and D500 in the wild-type enzyme. Hence, the sites of metal ion complexation within the Toprim domain are modulated by the nature of the ion species. These results suggest a double role played by metal ions in the catalytic steps involving DNA gyrase B. One has to do with direct involvement of cations complexed to the Toprim domain in the DNA cutting-rejoining process, the other, until now overlooked, is connected to the dramatic changes in protein flexibility produced by ion binding, which reduces the energy required for the huge conformational changes essential for the catalytic cycle to occur.     

Comparison of the hammerhead cleavage reactions stimulated by monovalent and divalent cations

Although the hammerhead reaction proceeds most efficiently in divalent cations, cleavage in 4 M LiCl is only approximately 10-fold slower than under standard conditions of 10 mM MgCl2 (Murray et al., Chem Biol, 1998, 5:587-595; Curtis & Bartel, RNA, 2001, this issue, pp. 546-552). To determine if the catalytic mechanism with high concentrations of monovalent cations is similar to that with divalent cations, we compared the activities of a series of modified hammerhead ribozymes in the two ionic conditions. Nearly all of the modifications have similar deleterious effects under both reaction conditions, suggesting that the hammerhead adopts the same general catalytic structure with both monovalent and divalent cations. However, modification of three ligands previously implicated in the binding of a functional divalent metal ion have substantially smaller effects on the cleavage rate in Li+ than in Mg2+. This result suggests that an interaction analogous to the interaction made by this divalent metal ion is absent in the monovalent reaction. Although the contribution of this divalent metal ion to the overall reaction rate is relatively modest, its presence is needed to achieve the full catalytic rate. The role of this ion appears to be in facilitating formation of the active structure, and any direct chemical role of metal ions in hammerhead catalysis is small.     

Competitive Binding of Mg2+ and Na+ Ions to Nucleic Acids: From Helices to Tertiary Structures

Nucleic acids generally reside in cellular aqueous solutions with mixed divalent/monovalent ions, and the competitive binding of divalent and monovalent ions is critical to the structures of nucleic acids because of their polyanionic nature. In this work, we first proposed a general and effective method for simulating a nucleic acid in mixed divalent/monovalent ion solutions with desired bulk ion concentrations via molecular dynamics (MD) simulations and investigated the competitive binding of Mg²⁺/Na⁺ ions to various nucleic acids by all-atom MD simulations. The extensive MD-based examinations show that single MD simulations conducted using the proposed method can yield desired bulk divalent/monovalent ion concentrations for various nucleic acids, including RNA tertiary structures. Our comprehensive analyses show that the global binding of Mg²⁺/Na⁺ to a nucleic acid is mainly dependent on its structure compactness, as well as Mg²⁺/Na⁺ concentrations, rather than the specific structure of the nucleic acid. Specifically, the relative global binding of Mg²⁺ over Na⁺ is stronger for a nucleic acid with higher effective surface charge density and higher relative Mg²⁺/Na⁺ concentrations. Furthermore, the local binding of Mg²⁺/Na⁺ to a phosphate of a nucleic acid mainly depends on the local phosphate density in addition to Mg²⁺/Na⁺ concentrations.