Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

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.     

Effects of dielectric saturation on planar electric double layers in salt solutions

The effects of dielectric saturation on planar electric double layers in salt solutions are examined by solving the Poisson-Boltzmann equation analytically where the dielectric constant is given as a function of the electric displacement. The activity and the distribution of small ions, the surface potential and the Donnan potential are calculated. The salt exclusion parameter and the Donnan potential decrease while the surface potential increases as a result of the dielectric saturation. The electrostatic entropy is affected considerably by the dielectric saturation while the electrostatic energy is little influenced. Generally, the effects of dielectric saturation on the distribution of small ions and the thermodynamic properties are enhanced by the addition of salt.     

Surface electrostatic effects in oligonucleotide microarrays: control and optimization of binding thermodynamics

We present a theoretical thermodynamic framework for the design of more efficient oligonucleotide microarrays. A general thermodynamic relation is derived to describe the electrostatic surface effects on the binding of the assayed biomolecule to a surface-tethered molecular probe. The relation is applied to analyze how the nucleic acid target, the oligonuleotide probe, and their DNA duplex electrostatic interactions with the surface affect the hybridization on DNA arrays. Taking advantage of a closed form exact solution of the linear Poisson-Boltzmann equation for a charged ion-penetrable sphere in electrolyte solution interacting with a plane wall, we study the effects of the surface and solution conditions. Binding free energy is found as a function of the surface material, dielectric or metal, the surface charge density, linker molecule length, temperature, and added salt content. The charge or electric potential of the dielectric or metal surface, respectively, is shown to dominate the hybridization, especially at low added salt or short linker length. We predict that substantial enhancement of sensitivity, selectivity, and reliability of microarrays can be achieved by control of the surface conditions. As examples, we discuss how to overcome two limitations of current technologies: nonequal sensitivity of the probes with different GC and AT bases content, and poor match/mismatch discrimination. In addition, we suggest the design of microarray conditions where the tested nucleic acid is unfolded, thus making possible the screening of a larger sequence with single nucleotide resolution. These promising findings are discussed and further experimental tests suggested.     

An iterative approach to placing counterions around DNA

An iterative approach, in which the effect of placing counter ions around DNA influences the electrostatic potential that the other subsequently approaching ions feel, has been used to place sodium ions around polynucleotides. The main focus of this report is to study the sequence and structure dependence on the distribution of ions around DNA, particularly that of tightly bound ions. The interesting results of the calculations are that there is significant sequence dependence on the electrostatic potentials in the B form of DNA, whereas relatively less difference in A form. In the case of Z form, the cations bridge the inter-stand phosphates along the minor groove.     

An electrostatic model for the dielectric effects,the adsorption of multivalent ions,and the bending of B-DNA

We have studied electrostatic properties of DNA with a discrete charge model consisting of a cylindrical dielectric core with a radius of 8 Å and a dielectric constant D_i = 4, surrounded by two helical strings of phosphate point charges at 10 Å from the axis, immersed in an aqueous medium with dielectric constant D_w = 78.54. Eliminating the dielectric core makes potentials in the phosphate surface less negative by about 0.5 kT/e. Salt effects are evaluated for the model without a dielectric core, using the shielded Coulomb potential. Smearing the phosphate charges increases their potential by about 2.5 kT/e, due mostly to the self-potential of the smeared charge. Potentials in the center of the minor and major grooves vary less than 0.02 kT/e along their helical path. The potential in the center of the minor groove is from 1.0 to 1.7 kT/e, more negative than in the center of the major groove, depending on dielectric core and salt concentration. So multivalent cations and also larger cationic ligands, such as some antibiotics, are likely to adsorb in the minor groove, in agreement with earlier computations by A. and B. Pullman. Dielectric effects on the surface potential and the local potential variations are found to be relatively small. Bending of DNA is studied by placing a multivalent cation, M^Z+, in the center of the minor or major groove, curving DNA around it for a certain length, and calculating the free energy difference between the bent and the straight configuration. Boltzmann averaged bending angles, 〈β〉, are found to be maximal in 0.03M monovalent salt, for a length of about 50 or 25 Å of curved DNA when an M^Z+ ion is adsorbed in the minor or the major groove, respectively. When the dielectric constant of water is used throughout the calculation, we find maximal bends of 〈β〉 = 11° for M²⁺ and 〈β〉 = 16° for M³⁺ in the minor groove, 〈β〉 = 13° for M³⁺ in the major groove. The absence of bends in DNA adsorbed to mica in the presence of Mg salts supports the role of Mg²⁺ in “ion bridging” between DNA and mica. The treatment of the effective dielectric constant between two points outside a dielectric cylinder in water is appended. © 1998 John Wiley & Sons, Inc. Biopoly 46: 503–516, 1998     

Ions around DNA: Monte Carlo estimates of distribution with improved electrostatic potentials

Coulomb's law for the electrostatic interactions between ions is modified when discontinuities in dielectric constant (relative permittivity) occur. In a DNA solution such a discontinuity occurs at the interface between the DNA molecular helix and the surrounding water. We take the modified interaction potentials from a previous report [Macromolecules (1986) 19 , 1186–1194] and use them with the Monte Carlo method to find the distribution of univalent and bivalent counterions around the DNA helix in the absence of coions (i.e., no added salt). In comparing the ion distribution with the modified potential to the distribution without, we find that the effects of the modifications to the potentials are considerable. The modifications tend to drive the ions out of the grooves of the helix, especially out of the major groove. This result comes partly from the repulsion exerted on the ions by the low-permittivity helix and partly from the concentration of the field of the phosphates at the surface of the helix, a concentration that is also caused by the discontinuity in permittivity.     

An Iterative Approach to Placing Counterions Around DNA

Abstract

An iterative approach, in which the effect of placing counter ions around DNA influences the electrostatic potential that the other subsequently approaching ions feel, has been used to place sodium ions around polynucleotides. The main focus of this report is to study the sequence and structure dependence on the distribution of ions around DNA, particularly that of tightly bound ions. The interesting results of the calculations are that there is significant sequence dependence on the electrostatic potentials in the B form of DNA, whereas relatively less difference in A form. In the case of Z form, the cations bridge the inter-stand phosphates along the minor groove.     

Biological ion exchanger resins. VII. Counter-ion activity coefficients in solutions of biological polyelectrolytes.

The single ion activity coefficients of K+ and Cl- counter-ions were determined in concentrated polyelectrolyte solutions. The polyelectrolytes investigated included DNA and several proteins. Results indicate that ion gradients of up to 40:1 do not lower the counter-ion activity coefficient below 0.5. Thus, published values of the intracellular activity coefficient of K+ are not incompatible with cellular models utilizing cytoplasmic ion exchange.     

Molecular dynamics simulations of DNA in solutions with different counter-ions

Molecular dynamics simulations of the [d(ATGCAGTCAG]2 fragment of DNA, in water and in the presence of three different counter-ions (Li+, Na+ and Cs+) are reported. Three-dimensional hydration structure and ion distribution have been calculated using spatial distribution functions for a detailed picture of local concentrations of ions and water molecules around DNA. According to the simulations, Cs+ ions bind directly to the bases in the minor groove, Na+ ions bind prevailing to the bases in the minor groove through one water molecule, whereas Li+ ions bind directly to the phosphate oxygens. The different behavior of the counter-ions is explained by specific hydration structures around the DNA and the ions. It is proposed how the observed differences in the ion binding to DNA may explain different conformational behavior of DNA. Calculated self-diffusion coefficients for the ions agree well with the available NMR data.     

Donnan potential and surface potential of a charged membrane.

A model is presented for the electrical potential distribution across a charged biological membrane that is in equilibrium with an electrolyte solution. We assume that a membrane has charged surface layers of thickness d on both surfaces of the membrane, where the fixed charges are distributed at a uniform density N within the layers, and that these charged layers are permeable to electrolyte ions. This model unites two different concepts, that is, the Donnan potential and the surface potential (or the Gouy-Chapman double-layer potential). Namely, the present model leads to the Donnan potential when d much greater than 1/k' (k' is the Debye-Hückel parameter of the surface charge layer) and to the surface potential as d----0, keeping the product Nd constant. The potential distribution depends significantly on the thickness d of the surface charge layer when d less than or approximately equal to 1/k'.     

Interfacial interactions of glutamate, water and ions with carbon nanopore evaluated by molecular dynamics simulations

Molecular dynamics simulations were used to assess the transport of glutamate, water and ions (Na(+) and Cl(-)) in a single wall carbon nanopore. The spatial profiles of Na(+) and Cl(-) ions are largely determined by the pore wall charges. Co-ions are repelled whereas the counter-ions are attracted by the pore charges, but this 'rule' breaks down when the water concentration is set to a level significantly below that in the physiological bulk solution. In such cases water is less able to counteract the ion-wall interactions (electrostatic or non-electrostatic), co-ions are layered near the counter-ions attracted by the wall charges and are thus layered as counter-ions. Glutamate is concentrated near the pore wall even at physiological water concentration, and irrespective of whether the pore wall is neutral or charged (positively or negatively), and its peak levels are up to 40 times above mean values. The glutamate is thus always layered as a counter-ion. Layering of water near the wall is independent of charges on the pore wall, but its peak levels near the wall are 'only' 6-8 times above the pore mean values. However, if the mean concentration of water is significantly below the level in the physiological bulk solution, its layering is enhanced, whereas its concentration in the pore center diminishes to very low levels. Reasons for such a 'paradoxical' behavior of molecules (glutamate and water) are that the non-electrostatic interactions are (except at very short distances) attractive, and electrostatic interactions (between the charged atoms of the glutamate or water and the pore wall) are also attractive overall. Repulsive interactions (between equally charged atoms) exist, and they order the molecules near the wall, whereas in the pore center the glutamate (and water) angles are largely randomly distributed, except in the presence of an external electric field. Diffusion of molecules and ions is complex. The translational diffusion is in general both inhomogeneous and anisotropic. Non-electrostatic interactions (ion-wall, glutamate-wall or water-wall) powerfully influence diffusion. In the neutral nanopore the effective axial diffusion constants of glutamate, water and Na(+) and Cl(-) ions are all <10% of their values in the bulk, and the electrostatic interactions can reduce them further. Diffusion of molecules and ions is further reduced if the water concentration in the pore is low. Glutamate(-) is slowed more than water, and ions are reduced the most especially co-ions. In conclusion the interfacial interactions influence the spatial distribution of glutamate, water and ions, and regulate powerfully, in a complex manner and over a very wide range their transport through nanosize pores.     

Electrostatic field of the large fragment of Escherichia coli DNA polymerase I

The electrostatic field of the large fragment of Escherichia coli DNA polymerase I (Klenow fragment) has been calculated by the finite difference procedure on a 2 A grid. The potential field is substantially negative at physiological pH (reflecting the net negative charge at this pH). The largest regions of positive potential are in the deep crevice of the C-terminal domain, which is the proposed binding site for the DNA substrate. Within the crevice, the electrostatic potential has a partly helical form. If the DNA is positioned to fulfil stereochemical requirements, then the positive potential generally follows the major groove and (to a lesser extent) the negative potential is in the minor groove. Such an arrangement could stabilize DNA configurations related by screw symmetry. The histidine residues of the Klenow fragment give the positive field of the groove a sensitivity to relatively small pH changes around neutrality. We suggest that the histidine residues could change their ionization states in response to DNA binding, and that this effect could contribute to the protein-DNA binding energy.     

DNA minor groove electrostatic potential: influence of sequence-specific transitions of the torsion angle gamma and deoxyribose conformations

The structural adjustments of the sugar-phosphate DNA backbone (switching of the γ angle (O5′–C5′–C4′–C3′) from canonical to alternative conformations and/or C2′-endo → C3′-endo transition of deoxyribose) lead to the sequence-specific changes in accessible surface area of both polar and non-polar atoms of the grooves and the polar/hydrophobic profile of the latter ones. The distribution of the minor groove electrostatic potential is likely to be changing as a result of such conformational rearrangements in sugar-phosphate DNA backbone. Our analysis of the crystal structures of the short free DNA fragments and calculation of their electrostatic potentials allowed us to determine: (1) the number of classical and alternative γ angle conformations in the free B-DNA; (2) changes in the minor groove electrostatic potential, depending on the conformation of the sugar-phosphate DNA backbone; (3) the effect of the DNA sequence on the minor groove electrostatic potential. We have demonstrated that the structural adjustments of the DNA double helix (the conformations of the sugar-phosphate backbone and the minor groove dimensions) induce changes in the distribution of the minor groove electrostatic potential and are sequence-specific. Therefore, these features of the minor groove sizes and distribution of minor groove electrostatic potential can be used as a signal for recognition of the target DNA sequence by protein in the implementation of the indirect readout mechanism.     

Molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer with NaCl

Molecular dynamics simulations are performed on two hydrated dipalmitoylphosphatidylcholine bilayer systems: one with pure water and one with added NaCl. Due to the rugged nature of the membrane/electrolyte interface, ion binding to the membrane surface is characterized by the loss of ion hydration. Using this structural characterization, binding of Na(+) and Cl(-) ions to the membrane is observed, although the binding of Cl(-) is seen to be slightly weaker than that of Na(+). Dehydration is seen to occur to a different extent for each type of ion. In addition, the excess binding of Na(+) gives rise to a net positive surface charge density just outside the bilayer. The positive density produces a positive electrostatic potential in this region, whereas the system without salt shows an electrostatic potential of zero.     

Interpreting protein/DNA interactions: distinguishing specific from non-specific and electrostatic from non-electrostatic components

We discuss the effectiveness of existing methods for understanding the forces driving the formation of specific protein-DNA complexes. Theoretical approaches using the Poisson-Boltzmann (PB) equation to analyse interactions between these highly charged macromolecules to form known structures are contrasted with an empirical approach that analyses the effects of salt on the stability of these complexes and assumes that release of counter-ions associated with the free DNA plays the dominant role in their formation. According to this counter-ion condensation (CC) concept, the salt-dependent part of the Gibbs energy of binding, which is defined as the electrostatic component, is fully entropic and its dependence on the salt concentration represents the number of ionic contacts present in the complex. It is shown that although this electrostatic component provides the majority of the Gibbs energy of complex formation and does not depend on the DNA sequence, the salt-independent part of the Gibbs energy--usually regarded as non-electrostatic--is sequence specific. The CC approach thus has considerable practical value for studying protein/DNA complexes, while practical applications of PB analysis have yet to demonstrate their merit.     

Dielectric saturation of the aqueous boundary layers adjacent to charged bilayer membranes

Summary The surface charge density resulting from the adsorption of hydrophobic anions of dipicrylamine onto dioleyl-lecithin bilayer membranes has been measured directly using a high field pulse method. The surface charge density increases linearly with adsorbate concentration in the water until electrostatic repulsion of impinging hydrophobic ions by those already adsorbed becomes appreciable. Then Gouy-Chapman theory predicts that surface charge density will increase sublinearly, with the power [z ⁺/(z ⁺+2)] of the adsorbate concentration, wherez ⁺ is the cation valence of the indifferent electrolyte screening the negatively charged membrane surface. The predicted 1/3 and 1/2 power laws for univalent and divalent cations, respectively, have been observed in these experiments using Na⁺, Mg⁺⁺, and Ba⁺⁺ ions. Gouy-Chapman theory predicts further that the change from linear to sublinear dependence takes place at a surface charge density governed by the static dielectric constant of water and the concentration of indifferent electrolyte. Quantitative agreement with experiment is obtained at electrolyte concentrations of 10^–4 m and 10^–3 m, but can be maintained at higher concentrations only if the aqueous dielectric constant is decreased. A transition field model is proposed in which the Gouy-Chapman theory is modified to take account of dielectric saturation of water in the intense electric fields adjacent to charged membrane surfaces.     

The structure of DAPI bound to DNA

The structure of the DNA fluorochrome 4'-6-diamidine-2-phenyl indole (DAPI) bound to the synthetic B-DNA oligonucleotide C-G-C-G-A-A-T-T-C-G-C-G has been solved by single crystal x-ray diffraction methods, at a resolution of 2.4 A. The structure is nearly isomorphous with that of the native DNA molecule alone. With one DAPI and 25 waters per DNA double helix, the residual error is 21.5% for the 2428 reflections above the 2-sigma level. DAPI inserts itself edgewise into the narrow minor groove, displacing the ordered spine of hydration. DAPI and a single water molecule together span the four AT base pairs at the center of the duplex. The indole nitrogen forms a bifurcated hydrogen bond with the thymine O2 atoms of the two central base pairs, as with netropsin and Hoechst 33258. The preference of all three of these drugs for AT regions of B-DNA is a consequence of three factors: (1) The intrinsically narrower minor groove in AT regions than in GC regions of B-DNA, leading to a snug fit of the flat aromatic drug rings between the walls of the groove. (2) The more negative electrostatic potential within the minor groove in AT regions, attributable in part to the absence of electropositive-NH2 groups along the floor of the groove, and (3) The steric advantage of the absence of those same guanine-NH2 groups, thus permitting the drug molecule to sink deeper into the groove. Groove width and electrostatic factors are regional, and define the relative receptiveness of a section of DNA since they operate over several contiguous base pairs. The steric factor is local, varying from one base pair to the next, and hence is the means of fine-tuning sequence specificity.     

Interfacial interactions of glutamate, water and ions with carbon nanopore evaluated by molecular dynamics simulations

Molecular dynamics simulations were used to assess the transport of glutamate, water and ions (Na⁺ and Cl⁻) in a single wall carbon nanopore. The spatial profiles of Na⁺ and Cl⁻ ions are largely determined by the pore wall charges. Co-ions are repelled whereas the counter-ions are attracted by the pore charges, but this ‘rule’ breaks down when the water concentration is set to a level significantly below that in the physiological bulk solution. In such cases water is less able to counteract the ion-wall interactions (electrostatic or non-electrostatic), co-ions are layered near the counter-ions attracted by the wall charges and are thus layered as counter-ions. Glutamate is concentrated near the pore wall even at physiological water concentration, and irrespective of whether the pore wall is neutral or charged (positively or negatively), and its peak levels are up to 40 times above mean values. The glutamate is thus always layered as a counter-ion. Layering of water near the wall is independent of charges on the pore wall, but its peak levels near the wall are ‘only’ 6-8 times above the pore mean values. However, if the mean concentration of water is significantly below the level in the physiological bulk solution, its layering is enhanced, whereas its concentration in the pore center diminishes to very low levels. Reasons for such a ‘paradoxical’ behavior of molecules (glutamate and water) are that the non-electrostatic interactions are (except at very short distances) attractive, and electrostatic interactions (between the charged atoms of the glutamate or water and the pore wall) are also attractive overall. Repulsive interactions (between equally charged atoms) exist, and they order the molecules near the wall, whereas in the pore center the glutamate (and water) angles are largely randomly distributed, except in the presence of an external electric field. Diffusion of molecules and ions is complex. The translational diffusion is in general both inhomogeneous and anisotropic. Non-electrostatic interactions (ion-wall, glutamate-wall or water-wall) powerfully influence diffusion. In the neutral nanopore the effective axial diffusion constants of glutamate, water and Na⁺ and Cl⁻ ions are all < 10% of their values in the bulk, and the electrostatic interactions can reduce them further. Diffusion of molecules and ions is further reduced if the water concentration in the pore is low. Glutamate⁻ is slowed more than water, and ions are reduced the most especially co-ions. In conclusion the interfacial interactions influence the spatial distribution of glutamate, water and ions, and regulate powerfully, in a complex manner and over a very wide range their transport through nanosize pores.