Ion Counting from Explicit-Solvent Simulations and 3D-RISM

The ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl_(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20–25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na⁺ binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability.     

Competitive interaction of monovalent cations with DNA from 3D-RISM

The composition of the ion atmosphere surrounding nucleic acids affects their folding, condensation and binding to other molecules. It is thus of fundamental importance to gain predictive insight into the formation of the ion atmosphere and thermodynamic consequences when varying ionic conditions. An early step toward this goal is to benchmark computational models against quantitative experimental measurements. Herein, we test the ability of the three dimensional reference interaction site model (3D-RISM) to reproduce preferential interaction parameters determined from ion counting (IC) experiments for mixed alkali chlorides and dsDNA. Calculations agree well with experiment with slight deviations for salt concentrations >200 mM and capture the observed trend where the extent of cation accumulation around the DNA varies inversely with its ionic size. Ion distributions indicate that the smaller, more competitive cations accumulate to a greater extent near the phosphoryl groups, penetrating deeper into the grooves. In accord with experiment, calculated IC profiles do not vary with sequence, although the predicted ion distributions in the grooves are sequence and ion size dependent. Calculations on other nucleic acid conformations predict that the variation in linear charge density has a minor effect on the extent of cation competition.     

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.     

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.     

Triplex hydration: nanosecond molecular dynamics simulation of the solvated triplex formed by mixed sequences

A theoretical model for the hydration pattern and motion of ions around the triple helical DNA with mixed sequences d(GACTGGTGAC)d(GTCACCAGTC)*d(GACTGGTGAC) in solution, during MD simulation, using the particle mesh Ewald sum method, is elaborated here. The AMBER 5.0 force field has been used during the simulation in solvent. The simulation studies support a dynamically stable atmosphere around the DNA triplex in solution over the entire length of the trajectory. The results have been compared with Hoogsteen triplexes and examined in the context of the observed behaviour of hydration in crystallographic data of duplexes. The dynamical organization of counterions and water molecules around the triplex formed by mixed sequences is described here. It has been observed that cations prefer to bind between two adjoining purines of the second and the third strands. The idea of localized complexes (mobile counterions in unspecific electronegative pockets around the DNA triplex with water molecules) may have important implications for understanding the specificity of the interactions of nucleic acids with proteins and other ligands.     

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using ⁷Li and ¹³³Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li⁺ and Cs⁺ ions around a 15-bp DNA duplex. Together with our previous data on ²³Na⁺ and ¹⁵NH₄⁺ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (D_b and D_f, respectively). We also analyzed ionic competition with K⁺ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li⁺, Na⁺, NH₄⁺, and Cs⁺) analyzed by diffusion NMR spectroscopy exhibited nearly identical D_b/D_f ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.     

Ion distributions around left- and right-handed DNA and RNA duplexes: a comparative study

The ion atmosphere around nucleic acids is an integral part of their solvated structure. However, detailed aspects of the ionic distribution are difficult to probe experimentally, and comparative studies for different structures of the same sequence are almost non-existent. Here, we have used large-scale molecular dynamics simulations to perform a comparative study of the ion distribution around (5′-CGCGCGCGCGCG-3′)₂ dodecamers in solution in B-DNA, A-RNA, Z-DNA and Z-RNA forms. The CG sequence is very sensitive to ionic strength and it allows the comparison with the rare but important left-handed forms. The ions investigated include Na⁺, K⁺ and Mg^{2 +}, with various concentrations of their chloride salts. Our results quantitatively describe the characteristics of the ionic distributions for different structures at varying ionic strengths, tracing these differences to nucleic acid structure and ion type. Several binding pockets with rather long ion residence times are described, both for the monovalent ions and for the hexahydrated Mg[(H₂O)₆]²⁺ ion. The conformations of these binding pockets include direct binding through desolvated ion bridges in the GpC steps in B-DNA and A-RNA; direct binding to backbone oxygens; binding of Mg[(H₂O)₆]²⁺ to distant phosphates, resulting in acute bending of A-RNA; tight ‘ion traps’ in Z-RNA between C-O2 and the C-O2′ atoms in GpC steps; and others.     

Electric dichroism of DNA. Influence of the ionic environment on the electric polarizability

In order to test the diffuse ion atmosphere polarization model recently developed by us, the effects of ionic strength, titrating with Mg2+ and Co(NH3)3+6, and coion charge on the electric polarizability of short fragments of DNA are investigated. The results are consistent with the predictions of the theory and show that the diffuse ion atmosphere polarization contributes significantly to the overall orientation of DNA. At low ionic strengths, we attempt to separate the total dipole moment into two components: one that agrees well with the Debye-Hückel ion atmosphere calculations, while the other, presumably due to condensed counterion polarization, appears to be substantially independent of the ionic strength. At higher salt concentrations, however, a simple separation into dipole components is not possible, perhaps due to a significant coupling of ion flows between the diffuse atmosphere and the condensed counterion layer.     

Ion Competition in Condensed DNA Arrays in the Attractive Regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt³⁺ Hexammine, or Co³⁺Hex) and one nonDNA-condensing ion (Mg²⁺) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co³⁺Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg²⁺, the Co³⁺Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg²⁺ and Co³⁺Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co³⁺Hex. It is also observed that only ∼20% DNA charge neutralization by Co³⁺Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.     

Ion Competition in Condensed DNA Arrays in the Attractive Regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt³⁺ Hexammine, or Co³⁺Hex) and one nonDNA-condensing ion (Mg²⁺) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co³⁺Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg²⁺, the Co³⁺Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg²⁺ and Co³⁺Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co³⁺Hex. It is also observed that only ∼20% DNA charge neutralization by Co³⁺Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.     

Studies of base pair sequence effects on DNA solvation based on all-atom molecular dynamics simulations

Detailed analyses of the sequence-dependent solvation and ion atmosphere of DNA are presented based on molecular dynamics (MD) simulations on all the 136 unique tetranucleotide steps obtained by the ABC consortium using the AMBER suite of programs. Significant sequence effects on solvation and ion localization were observed in these simulations. The results were compared to essentially all known experimental data on the subject. Proximity analysis was employed to highlight the sequence dependent differences in solvation and ion localization properties in the grooves of DNA. Comparison of the MD-calculated DNA structure with canonical A- and B-forms supports the idea that the G/C-rich sequences are closer to canonical A- than B-form structures, while the reverse is true for the poly A sequences, with the exception of the alternating ATAT sequence. Analysis of hydration density maps reveals that the flexibility of solute molecule has a significant effect on the nature of observed hydration. Energetic analysis of solute-solvent interactions based on proximity analysis of solvent reveals that the GC or CG base pairs interact more strongly with water molecules in the minor groove of DNA that the AT or TA base pairs, while the interactions of the AT or TA pairs in the major groove are stronger than those of the GC or CG pairs. Computation of solvent-accessible surface area of the nucleotide units in the simulated trajectories reveals that the similarity with results derived from analysis of a database of crystallographic structures is excellent. The MD trajectories tend to follow Manning's counterion condensation theory, presenting a region of condensed counterions within a radius of about 17 A from the DNA surface independent of sequence. The GC and CG pairs tend to associate with cations in the major groove of the DNA structure to a greater extent than the AT and TA pairs. Cation association is more frequent in the minor groove of AT than the GC pairs. In general, the observed water and ion atmosphere around the DNA sequences is the MD simulation is in good agreement with experimental observations.     

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.     

The interaction in vitro of the intermediate filament protein vimentin with naturally occurring RNAs and DNAs

The binding of the intermediate filament protein vimentin to a variety of naturally occurring RNAs and DNAs was studied. The relative capacities of the various nucleic acids to associate with pure [3H]vimentin were determined in competition experiments with 28 S rRNA from Ehrlich ascites tumor cells. The reaction products were analyzed by sucrose gradient centrifugation at low ionic strength and in the presence of EDTA. Under these ionic conditions, vimentin reacted preferentially with single-stranded nucleic acids, particularly with those of high (G + C) content. The vimentin binding potentials of single-stranded RNAs and DNAs were largely comparable. However, when the concentrations of mono- and divalent cations were raised to physiological and higher values, only single-stranded DNA retained its vimentin binding capacity. With increasing KCl concentrations at 0 to 1 mM Mg2+, increasing amounts of vimentin were detected in complexes which sedimented considerably faster than the bulk of the DNA, suggesting cooperative binding of vimentin. The salt optimum of this cooperativity was at 200 mM KCl. Thus, the capability of vimentin to discriminate between single-stranded RNA and DNA under physiological ionic conditions points to specificity of the interaction of vimentin with nucleic acids.     

Water and ion binding around RNA and DNA (C,G) oligomers

The dynamics, hydration, and ion-binding features of two duplexes, the A(r(CG)(12)) and the B(d(CG)(12)), in a neutralizing aqueous environment with 0.25 M added KCl have been investigated by molecular dynamics (MD) simulations. The regular repeats of the same C=G base-pair motif have been exploited as a statistical alternative to long MD simulations in order to extend the sampling of the conformational space. The trajectories demonstrate the larger flexibility of DNA compared to RNA helices. This flexibility results in less well defined hydration patterns around the DNA than around the RNA backbone atoms. Yet, 22 hydration sites are clearly characterized around both nucleic acid structures. With additional results from MD simulations, the following hydration scale for C=G pairs can be deduced: A-DNA相似文献   

The superstructure of chromatin and its condensation mechanism

Synchroton radiation X-ray scattering experiments have been performed on chicken erythrocyte chromatin fibres over a wide range of ionic conditions and on various states of the fibres (i.e. "native" in solution, in gels and in whole nuclei; chromatin depleted of the H1 (H5) histones and chromatin with bound ethidium bromide). A correlation between the results obtained with the various chromatin preparations provides evidence for a model according to which at low ionic strength the chromatin fibre already possesses a helical superstructure, with a diameter comparable to that of condensed chromatin, held together by the H1(H5) histone. The most significant structural modification undergone upon an increase of the ionic strength is a reduction of the helix pitch, this leads to condensation in a manner similar to the folding of an accordion. The details of this process depend on whether monovalent or divalent cations are used to raise the ionic strength, the latter producing a much higher degree of condensation. Measurements of the relative increase of the mass per unit length indicate that the most condensed state is a helical structure with a pitch around 3.0-4.0 nm. In this paper we give a detailed presentation of the experimental evidence obtained from static and time-resolved scattering experiments, which led to this model.     

DNA structure: what's in charge?

DNA structure is well known to be sensitive to hydration and ionic strength. Recent theoretical predictions and experimental observations have raised the idea of the intrusion of monovalent cations into the minor groove spine of hydration in B-form DNA. To investigate this further, extensions and further analysis of molecular dynamics (MD) simulations on d(CGCCGAATTCGCG), d(ATAGGCAAAAAATAGGCAAAAATGG) and d(G(5)-(GA(4)T(4)C)(2)-C(5)), including counterions and water, have been performed. To examine the effective of minor groove ions on structure, we analyzed the MD snapshots from a 15 ns trajectory on d(CGCGAATTCGCG) as two subsets: those exhibiting a minor groove water spine and those with groove-bound ions. The results indicate that Na(+) at the ApT step of the minor groove of d(CGCCGAATTCGCG) makes only small local changes in the DNA structure, and these changes are well within the thermal fluctuations calculated from the MD. To examine the effect of ions on the differential stability of a B-form helix, further analysis was performed on two longer oligonucleotides, which exhibit A-tract-induced axis bending localized around the CpG step in the major groove. Plots of axis bending and proximity of ions to the bending locus were generated as a function of time and revealed a strong linear correlation, supporting the idea that mobile cations play a key role in local helix deformations of DNA and indicating ion proximity just precedes the bending event. To address the issue of "what's in charge?" of DNA structure more generally, the relative free energy of A and B-form d(CGCGAATTCGCG) structures from MD simulations under various environmental circumstances were estimated using the free energy component method. The results indicate that the dominant effects on conformational stability come from the electrostatic free energy, but not exclusively from groove bound ions per se, but from a balance of competing factors in the electrostatic free energy, including phosphate repulsions internal to the DNA, the electrostatic component of hydration (i.e. solvent polarization), and electrostatic effects of the counterion atmosphere. In summary, free energy calculations indicate that the electrostatic component is dominant, MD shows temporal proximity of mobile counterions to be correlated with A-track-induced bending, and thus the mobile ion component of electrostatics is a significant contributor. However, the MD structure of the dodecamer d(CGCGAATTCGCG) is not highly sensitive to whether there is a sodium ion in the minor groove.