Effect of spatial inhomogeneity in dielectric permittivity on DNA double layer formation

In solutions of tetramethylammonium (TMA+) DNA (double stranded) without added low-molecular-weight salt, the counterion radial density is calculated using the cylindrical Poisson-Boltzmann equation with a distance-dependent quasimacroscopic dielectric permittivity. Comparisons with small-angle neutron scattering data indicate that any inhomogeneity in dielectric permittivity is confined to one or two solvent layers from the DNA surface. At least for TMA+, which may be too large to penetrate the grooves of DNA to any significant extent, dielectric inhomogeneity modeled in this way has no detectable effect on the radial distribution.     

The contribution of transient counterion imbalances to DNA bending fluctuations

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it. The second class of fluctuations is characterized by movement of some counterions from one side of the DNA to the other. The root-mean-square fluctuation for each class is calculated from counterion condensation theory. The amplitude of the root-mean-square fluctuation depends on the ionic strength as well as the length of the segment considered and is of the order 5-10%. Both classes of fluctuation result in transient bends toward the side of greater counterion density. The bending amplitudes are approximately 15% of the total root-mean-square bends associated with the persistence length of DNA. We are thus led to suggest that asymmetric fluctuations of counterion density contribute modestly but significantly toward the aggregate of thermalized solvent fluctuations that cause bending deformations of DNA free in solution. The calculations support the idea that counterions may exert some modulating influence on the fine structure of DNA.     

A molecular dynamics simulation study of polyamine– and sodium–DNA. Interplay between polyamine binding and DNA structure

Four different molecular dynamics (MD) simulations have been performed for infinitely long ordered DNA molecules with different counterions, namely the two natural polyamines spermidine(3+) (Spd³⁺) and putrescine(2+) (Put²⁺), the synthetic polyamine diaminopropane(2+) (DAP²⁺), and the simple monovalent cation Na⁺. All systems comprised a periodical hexagonal cell with three identical DNA decamers, 15 water molecules per nucleotide, and counterions balancing the DNA charge. The simulation setup mimics the DNA state in oriented DNA fibers, previously studied using NMR and other experimental methods. In this paper the interplay between polyamine binding and local DNA structure is analyzed by investigating how and if the minor groove width of DNA depends on the presence and dynamics of the counterions. The results of the MD simulations reveal principal differences in the polyamine–DNA interactions between the natural [spermine(4+), Spd³⁺, Put²⁺] and the synthetic (DAP²⁺) polyamines.Abbreviations DAP diaminopropane - DDD Drew–Dickerson dodecamer - MD molecular dynamics - Put putrescine - RDF radial distribution function - Spd spermidine - Spm spermine     

Azimuthal frustration and bundling in columnar DNA aggregates

The interaction between two stiff parallel DNA molecules is discussed using linear Debye-Hückel screening theory with and without inclusion of the dielectric discontinuity at the DNA surface, taking into account the helical symmetry of DNA. The pair potential furthermore includes the amount and distribution of counterions adsorbed on the DNA surface. The interaction does not only depend on the interaxial separation of two DNA molecules, but also on their azimuthal orientation. The optimal mutual azimuthal angle is a function of the DNA-DNA interaxial separation, which leads to azimuthal frustrations in an aggregate. On the basis of the pair potential, the positional and orientational order in columnar B-DNA assemblies in solution is investigated. Phase diagrams are calculated using lattice sums supplemented with the entropic contributions of the counterions in solution. A variety of positionally and azimuthally ordered phases and bundling transitions is predicted, which strongly depend on the counterion adsorption patterns.     

Structure, stability, and thermodynamics of lamellar DNA-lipid complexes.

We develop a statistical thermodynamic model for the phase evolution of DNA-cationic lipid complexes in aqueous solution, as a function of the ratios of charged to neutral lipid and charged lipid to DNA. The complexes consist of parallel strands of DNA intercalated in the water layers of lamellar stacks of mixed lipid bilayers, as determined by recent synchrotron x-ray measurements. Elastic deformations of the DNA and the lipid bilayers are neglected, but DNA-induced spatial inhomogeneities in the bilayer charge densities are included. The relevant nonlinear Poisson-Boltzmann equation is solved numerically, including self-consistent treatment of the boundary conditions at the polarized membrane surfaces. For a wide range of lipid compositions, the phase evolution is characterized by three regions of lipid to DNA charge ratio, rho: 1) for low rho, the complexes coexist with excess DNA, and the DNA-DNA spacing in the complex, d, is constant; 2) for intermediate rho, including the isoelectric point rho = 1, all of the lipid and DNA in solution is incorporated into the complex, whose inter-DNA distance d increases linearly with rho; and 3) for high rho, the complexes coexist with excess liposomes (whose lipid composition is different from that in the complex), and their spacing d is nearly, but not completely, independent of rho. These results can be understood in terms of a simple charging model that reflects the competition between counterion entropy and inter-DNA (rho < 1) and interbilayer (rho > 1) repulsions. Finally, our approach and conclusions are compared with theoretical work by others, and with relevant experiments.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

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.     

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.     

Monte Carlo calculations of ion distributions surrounding the oligonucleotide d(ATATATATAT)2 in the B, A, and wrinkled D conformations.

We calculated the uni-univalent ion distributions around the oligonucleotide d(AT)5.d(AT)5 in the A, B and wrinkled D conformation using the Metropolis Monte Carlo method. All atoms were included in the oligonucleotide model with partial charges and hard sphere radii assigned to each atom. The univalent counter- and coions were modeled as hard spheres with radius 0.3 nm. The solvent was assigned a dielectric constant of 80, corresponding to a temperature of 298K. The counterion distribution surrounding each of the conformers and the distribution surrounding an impenetrable cylinder, were calculated for four salt concentrations. We found significant counterion density in the major groove of the A DNA while fewer counterions occupied the grooves of B DNA. In the wrinkled D DNA, where groove occupancy is sterically hindered, the ion distributions were identical to the distributions surrounding the impenetrable, cylindrical model. This suggests that excluded volume effects significantly influence the details of the ion distributions near the oligomer, while the detailed charge distributions of the oligomer affects the ion distributions only minimally. Although substantial variation in counterion density was observed near the oligomers of differing conformations, the total number of counterions located within a cylinder surrounding the oligomer bounded radially by 2.4 nm was independent of the conformation of the oligomer. Therefore, for this model system, the local univalent counterion distributions are extremely sensitive to the geometry of the oligonucleotide whereas the extent of neutralization of the oligoanion is insensitive to the conformation of the oligomer.     

DNA cholesteric pitch as a function of density and ionic strength

The nature of chiral interactions among chiral biopolymers, such as DNA, protein alpha-helices, and rodlike virus particles, remains elusive. In particular, a satisfactory model connecting molecular chiral interactions and the pitch of the resulting chiral mesophases is lacking. We report the measurement of short-fragment (146-bp) DNA cholesteric spherulite pitch as a function of osmotic pressure, average DNA interaxial spacing, and salt concentration. We determined cholesteric pitch and interaxial spacing by polarizing optical microscopy and x-ray scattering, respectively, from which the twist-angle between DNA molecules can be calculated. Surprisingly, we found that decreasing ionic strength resulted in weaker chiral interactions between DNA chains, as evidenced by the decrease in the twist-angle, and consequent increase in the cholesteric pitch, for a fixed interaxial spacing. We propose that this behavior can be explained by increased smearing-out of the helical charge pattern along DNA as the Debye screening length is increased.     

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.     

Folding of the Tetrahymena ribozyme by polyamines: importance of counterion valence and size

Polyamines are abundant metabolites that directly influence gene expression. Although the role of polyamines in DNA condensation is well known, their role in RNA folding is less understood. Non-denaturing gel electrophoresis was used to monitor the equilibrium folding transitions of the Tetrahymena ribozyme in the presence of polyamines. All of the polyamines tested induce near-native structures that readily convert to the native conformation in Mg(2+). The stability of the folded structure increases with the charge of the polyamine and decreases with the size of the polyamine. When the counterion excluded volume becomes large, the transition to the native state does not go to completion even under favorable folding conditions. Brownian dynamics simulations of a model polyelectrolyte suggest that the kinetics of counterion-mediated collapse and the dimensions of the collapsed RNA chains depend on the structure of the counterion. The results are consistent with delocalized condensation of polyamines around the RNA. However, the effective charge of the counterions is lowered by their excluded volume. The stability of the folded RNA is enhanced when the spacing between amino groups matches the distance between adjacent phosphate groups. These results show how changes in intracellular polyamine concentrations could alter RNA folding pathways.     

Molecular dynamics simulation study of oriented polyamine- and Na-DNA: sequence specific interactions and effects on DNA structure

Molecular dynamics (MD) computer simulations have been carried out on four systems that correspond to an infinite array of parallel ordered B-DNA, mimicking the state in oriented DNA fibers and also being relevant for crystals of B-DNA oligonucleotides. The systems were all comprised of a periodical hexagonal cell with three identical DNA decamers, 15 water molecules per nucleotide, and counterions balancing the DNA charges. The sequence of the double helical DNA decamer was d(5'-ATGCAGTCAG)xd(5'-TGACTGCATC). The counterions were the two natural polyamines spermidine(3+) (Spd(3+)) and putrescine(2+) (Put(2+)), the synthetic polyamine diaminopropane(2+) (DAP(2+)), and the simple monovalent cation Na(+). This work compares the specific structures of the polyamine- and Na-DNA systems and how they are affected by counterion interactions. It also describes sequence-specific hydration and interaction of the cations with DNA. The local DNA structure is dependent on the nature of the counterion. Even the very similar polyamines, Put(2+) and DAP(2+), show clear differences in binding to DNA and in effect on hydration and local structure. Generally, the polyamines disorder the hydration of the DNA around their binding sites whereas Na(+) being bound to DNA attracts and organizes water in its vicinity. Cation binding at the selected sites in the minor and in the major groove is compared for the different polyamines and Na(+). We conclude that the synthetic polyamine (DAP(2+)) binds specifically to several structural and sequence-specific motifs on B-DNA, unlike the natural polyamines, Spd(3+) and Put(2+). This specificity of DAP(2+) compared to the more dynamic behavior of Spd(3+) and Put(2+) may explain why the latter polyamines are naturally occurring in cells.     

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.     

Nanomechanical behaviors of microcantilever-based single-stranded DNA chips induced by counterion osmotic effects

Experiments show that deflections of microcantilever-DNA chip can be induced by many factors, such as grafting density, hybridization efficiency, concentration, length and sequence of DNA molecules, buffer salt concentration, time, and temperature variation. However, there are few theoretical works on microcantilever-DNA chips. The present paper is aimed to study the influence of counterion effects of single-stranded DNA (ssDNA) polyelectrolyte solution on the nanomechanical behaviors of microcantilever-based ssDNA chips during packing process. First, the effect of osmotic pressure induced by ingress of counterions into DNA brush structures is studied with Hagan’s model for a cylindrical polyelectrolyte brush system on the basis of Poisson-Boltzmann distribution hypothesis. Second, Zhang’s two-variable method for a laminated cantilever is used to formulate a four-layer energy model for ssDNA chips with weak interactions. Third, the influence of grafting density, ssDNA chain length, and salt concentration on packing deflection is investigated using the principle of minimum energy. The predictive tendency is qualitatively similar to those observed in some related ssDNA chip experiments. The difference between the four-layer model and the simplified two-layer model for ssDNA chips is also discussed.     

Similarities and differences in interaction of K+ and Na+ with condensed ordered DNA. A molecular dynamics computer simulation study

Four 20 ns molecular dynamics simulations have been performed with two counterions, K⁺ or Na⁺, at two water contents, 15 or 20 H₂O per nucleotide. A hexagonal simulation cell comprised of three identical DNA decamers [d(5′-ATGCAGTCAG) × d(5′-TGACTGCATC)] with periodic boundary condition along the DNA helix was used. The simulation setup mimics the DNA state in oriented DNA fibers or in crystals of DNA oligomers. Variation of counterion nature and water content do not alter averaged DNA structure. K⁺ and Na⁺ binding to DNA are different. K⁺ binds to the electronegative sites of DNA bases in the major and the minor grooves, while Na⁺ interacts preferentially with the phosphate groups. Increase of water causes a shift of both K⁺ and Na⁺ from the first hydration shell of O1P/O2P and of the DNA bases in the minor groove with lesser influence for the cation binding to the bases in the major groove. Mobility of both water and cations in the K–DNA systems is faster than in the Na–DNA systems: Na⁺ organizes and immobilizes water structure around itself and near DNA while for K⁺ water is less organized and more dynamic.     

Thermodynamics of cation-induced DNA condensation.

An estimation of the various free energy contributions to DNA collapse into toroidal particles is made, considering DNA bending and segment mobility, electrostatic repulsions between DNA chains, and attractive forces resulting from correlated counterion fluctuations. It is shown that the process of DNA condensation becomes spontaneous in the presence of divalent cations in methanol, and in the presence of tri- or tetravalent cations in water media. This is a consequence of the large decrease in the electrostatic repulsion between charged DNA segments, allowing the attractive force resulting from correlated fluctuations of bound counterions to become dominant. Our calculations indicate that short DNA fragments would condense into multimolecular particles in order to maximize the attractive force due to counterion fluctuations.     

Magnetic resonance distinction between site bound and atmospherically bound paramagnetic counterions in polyelectrolyte solutions.

A combination of the water protons NMR chemical shifts, longitudinal and transversal relaxation rates and of the paramagnetic counterion EPR signal is shown to provide a clear distinction between site binding, atmospheric trapping and free counterions in solutions of polyelectrolyte TMA salts with increasing concentrations of the divalent counterions Co++ and Mn++. Site binding is defined by the loss of water in the counterion first hydration shell while atmospheric binding results in a change in the counterion correlation time as compared to a free ion.     

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.     

Evaluation of the counterion condensation theory of polyelectrolytes.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.