Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length

Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (especially multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive experimental data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helices. We quantitatively evaluate the effects of ion concentration, ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful analytical formulas for the thermodynamic parameters as functions of finite helix length, ion type, and ion concentration. We find that the helix stability is additive for high ion concentration and long helix and nonadditive for low ion concentration and short helix. All these results are tested against and supported by extensive experimental data.     

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na⁺ and Mg²⁺ play distinctive roles in helix–helix assembly. High [Na⁺] (>0.3 M) causes a reduced helix–helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg²⁺ of concentration >1 mM is predicted to induce helix–helix attraction and results in a more compact and ordered helix–helix packing. Mg²⁺ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.     

Quantitative analysis of the ion-dependent folding stability of DNA triplexes

A DNA triplex is formed through binding of a third strand to the major groove of a duplex. Due to the high charge density of a DNA triplex, metal ions are critical for its stability. We recently developed the tightly bound ion (TBI) model for ion-nucleic acids interactions. The model accounts for the potential correlation and fluctuations of the ion distribution. We now apply the TBI model to analyze the ion dependence of the thermodynamic stability for DNA triplexes. We focus on two experimentally studied systems: a 24-base DNA triplex and a pair of interacting 14-base triplexes. Our theoretical calculations for the number of bound ions indicate that the TBI model provides improved predictions for the number of bound ions than the classical Poisson-Boltzmann (PB) equation. The improvement is more significant for a triplex, which has a higher charge density than a duplex. This is possibly due to the higher ion concentration around the triplex and hence a stronger ion correlation effect for a triplex. In addition, our analysis for the free energy landscape for a pair of 14-mer triplexes immersed in an ionic solution shows that divalent ions could induce an attractive force between the triplexes. Furthermore, we investigate how the protonated cytosines in the triplexes affect the stability of the triplex helices.     

Electrostatic free energy landscapes for DNA helix bending

Nucleic acids are highly charged polyanionic molecules; thus, the ionic conditions are crucial for nucleic acid structural changes such as bending. We use the tightly bound ion theory, which explicitly accounts for the correlation and ensemble effects for counterions, to calculate the electrostatic free energy landscapes for DNA helix bending. The electrostatic free energy landscapes show that DNA bending energy is strongly dependent on ion concentration, valency, and size. In a Na⁺ solution, DNA bending is electrostatically unfavorable because of the strong charge repulsion on backbone. With the increase of the Na⁺ concentration, the electrostatic bending repulsion is reduced and thus the bending becomes less unfavorable. In contrast, in an Mg²⁺ solution, ion correlation induces a possible attractive force between the different parts of the helical strands, resulting in bending. The electrostatically most favorable and unfavorable bending directions are toward the major and minor grooves, respectively. Decreasing the size of the divalent ions enhances the electrostatic bending attraction, causing an increased bending angle, and shifts the most favorable bending to the direction toward the minor groove. The microscopic analysis on ion-binding distribution reveals that the divalent ion-induced helix bending attraction may come from the correlated distribution of the ions across the grooves in the bending direction.     

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.     

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.     

Effect of the number of nucleic acid oligomer charges on the salt dependence of stability (DeltaG 37degrees) and melting temperature (Tm): NLPB analysis of experimental data

For nucleic acid oligomers with variable chain lengths, the salt concentration ([salt]) dependences of the denaturation temperature (T(m)) and of the free energy of helix formation at 37 degrees C (Delta) are predicted using nonlinear Poisson-Boltzmann (NLPB) calculations. Analysis of experimental data reveals that the ratio of the [salt] derivative of melting temperature (ST(m) = dT(m)/d log[salt]) to the value for a polymer with the same base composition (ST(m)/ST(m, infinity)) is independent of base composition but strongly dependent on the number of DNA charges (/Z/) below approximately 8 bp for two-strand helices (formed from association of two complementary strands) and below approximately 18 bp for hairpin helices (formed from folding of one self-complementary strand). We interpret these ST(m)/ST(m, infinity) ratios in terms of the ratio of thermodynamic ion release from the oligomer (Deltan(u), per charge) to that from the same oligomer embedded in polymeric DNA (Deltan(u, infinity), per charge). Experimental values of ST(m)/ST(m, infinity) and its dependence on /Z/ are in good agreement with NLPB predictions for a preaveraged (essential structural) model of DNA. In particular, the NLPB calculations describe the stronger /Z/ dependence of ST(m) observed for melting of oligomeric hairpin helices than for melting of two-strand helices. These calculations predict an experimentally detectable (>or=10%) difference between ST(m) and ST(m, infinity) which increases strongly with decreasing length for two-strand helix lengths of <15 bp and for hairpin helix lengths of <30 bp. From NLPB values of Deltan(u)/Deltan(u, infinity), we predict Delta as a function of [salt] and /Z/. Predictions of thermodynamic and thermal stabilities of oligomeric helices as functions of length and [salt] are consistent with and represent a significant refinement of the average oligomer salt effect currently in use in nearest neighbor stability predictions.     

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.     

Salt contribution to the flexibility of single‐stranded nucleic acid of finite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single‐stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse‐grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual‐bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion‐exclusion‐volume effect to ion Coulomb correlations. In addition, the predicted Na⁺ and Mg²⁺‐dependent persistence length l_p’s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l_p as a function of [Na⁺], [Mg²⁺] and chain length. © 2012 Wiley Periodicals, Inc. Biopolymers 99: 370–381, 2013.     

Dielectric properties of polyelectrolytes. II. A theory of dielectric increment due to ion fluctuation by a matrix method

The mean square of dipole moment of a linear macromolecule which is responsible for dielectric increment of aqueous polyelectrolyte solutions is calculated by means of a matrix method in which ion binding at discrete sites and the nearest-neighbor interaction are taken into account. On the basis of the relationship between polarization of poly-ion and fluctuation of bound counterions the present theory indicates that the loosely bound ions result in larger increment and otherwise smaller increment. Also, the theory predicts that the dielectric increment has a maximum at an intermediate monovalent–divalent ion ratio when both species coexist. These results are consistent with experiments on polyacrylic acid neutralized with NaOH and Ca(OH)₂. At large contents of divalent ions the effect of chelation is also discussed.     

Surface potential of phosphatidylserine monolayers. I. Divalent ion binding effect

Surface potentials of phosphatidylserine monolayers have been measured in the presence of different divalent ion concentrations in order to determine the way in which divalent ions bind to the membrane surface. The association constants for divalent ions (Mg²⁺, Ca²⁺ and Mn²⁺) with the phosphatidylserine membrane have been obtained from the experimental data and simple ion binding theory. The order of divalent ion binding to the membrane is Mn²⁺ > Ca²⁺ > Mg²⁺. However, none of the divalent ions used completely neutralized the negative charge of phosphatidylserine even at relatively high concentrations. The amounts of the divalent ions bound depended upon the concentration of the monovalent ions present in the subphase. It is suggested that the amounts of bound ions obtained from the use of radioisotope tracer methods may include a considerable contribution from the excess free ions in the double layer region of the phosphatidylserine membrane.     

Comparison of polyelectrolyte theories of the binding of cations to DNA.

Predictions of the binding of counterions to DNA made using the counterion condensation theory developed by Manning are compared with those made using the Poisson-Boltzmann equation, solved numerically by the Runge-Kutta procedure. Ions are defined as territorially or atmospherically bound if they fall within a given distance, defined by counterion condensation theory, from the DNA surface. Two types of experimental situations are considered. The first is the delocalized binding of a single type of counterion to DNA. In this case the Poisson-Boltzmann treatment predicts somewhat lower extents of binding TO DNA, modeled as a 10-A radius cylinder, than does Manning theory. The two theories converge as the radius decreases. The second type of experiment is the competition of ions of different valence for binding to DNA. The theories are compared with literature values of binding constants of divalent ions in the presence of monovalent ions, and of spermidine 3+ in the presence of Na+ or Mg2+. Both predict with fair accuracy the salt dependence of the equilibrium constants.     

Salt-Dependent Folding Energy Landscape of RNA Three-Way Junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg²⁺ ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na⁺ and Mg²⁺ ion concentrations. For Mg²⁺ solutions, the TBI model, which accounts for the Mg²⁺ ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg²⁺ in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.     

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.     

Water counting: quantitating the hydration level of paramagnetic metal ions bound to nucleotides and nucleic acids

Binding of divalent metal ions plays a key role in the structure and function of ribozymes and other RNAs. In turn, the energetics and kinetics of the specific binding process are dominated by the balance between the cost of dehydrating the aqueous ion and the energy gained from inner-sphere interactions with the macromolecule. In this work, we introduce the use of the pulsed EPR technique of 2H Electron Spin-Echo Envelope Modulation (ESEEM) to determine the hydration level of Mn2+ ions bound to nucleotides and nucleic acids. Mn2+ is an excellent structural and functional mimic for Mg2+, the most common divalent ion of physiological interest. Comparison of data in D2O and H2O, with aqueous Mn2+ as a reference standard, allows a robust and precise determination of the number of bound water molecules, and therefore the number of RNA-derived ligands. Examples of applications to the mononucleotide models MnGMP and MnATP, as well as to the paradigmatic RNA system tRNAPhe, are shown.     

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.     

Enhanced ionic interaction in narrow pores and ion pair formation

The same physical phenomenon that gives rise to the increase in the electrostatic self-energy of an ion within a narrow water-filled pore is shown to result in interionic electrical interactions within the pore that are much stronger and of longer range than those between the same ions in the same solution in bulk. Because of the much enhanced attraction between ions of opposite charge within the pore the formation of ion pairs becomes likely, even for strong electrolytes that are fully dissociated in the same solution when not spatially confined. Some predicted consequences of ion pair formation in narrow pores that may be experimentally detected are discussed. It is shown that, in a simple passive pore, due to ion pair formation, an Ussing unidirectional flux ratio exponent of less than 1 is predicted. This is usually thought to characterize a carrier rather than a pore.     

Stability decrease of RNA double helices by phenylalanine-, tyrosine- and tryptophane-amides. Analysis in terms of site binding and relation to melting proteins.

The amides of L-phenylalanine, L-tyrosine and L-tryptophane decrease the melting temperatures tm of poly(A)*poly(U) and poly(I)*poly(C) double helices at low concentrations (1 mM), whereas high concentrations finally lead to an increase of tm. This dependence of the tm-values upon the ligand concentration can be represented quantitatively by a simple site binding model, providing binding parameters for the interaction between the amides and the nucleic acids both in the double- and the single-stranded conformation. According to these data the affinity to the single strands is higher than that to the double strands and increases in the series Phe less than Tyr less than Trp. The binding constants decrease with increasing salt concentration as expected for an interaction driven by electrostatic attraction. However, part of the interaction is also due to stacking between the aromatic amides and the nucleic acid bases. The present results indicate a direct correlation between the presence of aromatic amino acids at the binding site of helix destabilising proteins and the properties of simple derivatives of these amino acids. Furthermore the results suggest that very simple peptides containing aromatic amino acids served as a starting point for the evolution of helix destabilising proteins.