Electrostatic Potential of B-DNA: Effect of Interionic Correlations

Modified Poisson-Boltzmann (MPB) equations have been numerically solved to study ionic distributions and mean electrostatic potentials around a macromolecule of arbitrarily complex shape and charge distribution. Results for DNA are compared with those obtained by classical Poisson-Boltzmann (PB) calculations. The comparisons were made for 1:1 and 2:1 electrolytes at ionic strengths up to 1 M. It is found that ion-image charge interactions and interionic correlations, which are neglected by the PB equation, have relatively weak effects on the electrostatic potential at charged groups of the DNA. The PB equation predicts errors in the long-range electrostatic part of the free energy that are only ∼1.5 kJ/mol per nucleotide even in the case of an asymmetrical electrolyte. In contrast, the spatial correlations between ions drastically affect the electrostatic potential at significant separations from the macromolecule leading to a clearly predicted effect of charge overneutralization.     

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr–Lys–Pro–Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson–Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 133–143, 1999     

The ionic atmosphere around A-RNA: Poisson-Boltzmann and molecular dynamics simulations

The distributions of different cations around A-RNA are computed by Poisson-Boltzmann (PB) equation and replica exchange molecular dynamics (MD). Both the nonlinear PB and size-modified PB theories are considered. The number of ions bound to A-RNA, which can be measured experimentally, is well reproduced in all methods. On the other hand, the radial ion distribution profiles show differences between MD and PB. We showed that PB results are sensitive to ion size and functional form of the solvent dielectric region but not the solvent dielectric boundary definition. Size-modified PB agrees with replica exchange molecular dynamics much better than nonlinear PB when the ion sizes are chosen from atomistic simulations. The distribution of ions 14 Å away from the RNA central axis are reasonably well reproduced by size-modified PB for all ion types with a uniform solvent dielectric model and a sharp dielectric boundary between solvent and RNA. However, this model does not agree with MD for shorter distances from the A-RNA. A distance-dependent solvent dielectric function proposed by another research group improves the agreement for sodium and strontium ions, even for shorter distances from the A-RNA. However, Mg²⁺ distributions are still at significant variances for shorter distances.     

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.     

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.     

Effects of viscous solvent on DNA polymer in a fiber

The viscous forces acting on a DNA macromolecule in a fiber are calculated. The DNA polymer is modeled as an infinite rod of elliptical cross section with a grooved surface. The viscous solvent is hydrodynamic water. Appropriate boundary conditions for determining the viscous forces on the acoustic vibrational modes are discussed. The viscous forces acting on each mode are then calculated as functions of both frequency and amount of water in the fiber. The mass loading of the DNA due to water in the grooves is shown to reduce the longitudinal acoustic velocity, which agrees with recent experimental results. The longitudinal modes are determined to be underdamped and correspondingly sharp over a range of frequencies and humidities appropriate to experimental conditions. The torsional and transverse acoustic modes are still strongly overdamped.     

Modeling the electrophoresis of lysozyme. II. Inclusion of ion relaxation.

In this work, boundary element methods are used to model the electrophoretic mobility of lysozyme over the pH range 2-6. The model treats the protein as a rigid body of arbitrary shape and charge distribution derived from the crystal structure. Extending earlier studies, the present work treats the equilibrium electrostatic potential at the level of the full Poisson-Boltzmann (PB) equation and accounts for ion relaxation. This is achieved by solving simultaneously the Poisson, ion transport, and Navier-Stokes equations by an iterative boundary element procedure. Treating the equilibrium electrostatics at the level of the full rather than the linear PB equation, but leaving relaxation out, does improve agreement between experimental and simulated mobilities, including ion relaxation improves it even more. The effects of nonlinear electrostatics and ion relaxation are greatest at low pH, where the net charge on lysozyme is greatest. In the absence of relaxation, a linear dependence of mobility and average polyion surface potential, (lambda zero)s, is observed, and the mobility is well described by the equation [formula: see text] where epsilon 0 is the dielectric constant of the solvent, and eta is the solvent viscosity. This breaks down, however, when ion relaxation is included and the mobility is less than predicted by the above equation. Whether or not ion relaxation is included, the mobility is found to be fairly insensitive to the charge distribution within the lysozyme model or the internal dielectric constant.     

Do electrostatic interactions destabilize protein–nucleic acid binding?

The negatively charged phosphates of nucleic acids are often paired with positively charged residues upon binding proteins. It was thus counter-intuitive when previous Poisson-Boltzmann (PB) calculations gave positive energies from electrostatic interactions, meaning that they destabilize protein-nucleic acid binding. Our own PB calculations on protein-protein binding have shown that the sign and the magnitude of the electrostatic component are sensitive to the specification of the dielectric boundary in PB calculations. A popular choice for the boundary between the solute low dielectric and the solvent high dielectric is the molecular surface; an alternative is the van der Waals (vdW) surface. In line with results for protein-protein binding, in this article, we found that PB calculations with the molecular surface gave positive electrostatic interaction energies for two protein-RNA complexes, but the signs are reversed when the vdW surface was used. Therefore, whether destabilizing or stabilizing effects are predicted depends on the choice of the dielectric boundary. The two calculation protocols, however, yielded similar salt effects on the binding affinity. Effects of charge mutations differentiated the two calculation protocols; PB calculations with the vdW surface had smaller deviations overall from experimental data.     

Travel depth, a new shape descriptor for macromolecules: application to ligand binding

Depth is a term frequently applied to the shape and surface of macromolecules, describing for example the grooves in DNA, the shape of an enzyme active site, or the binding site for a small molecule in a protein. Yet depth is a difficult property to define rigorously in a macromolecule, and few computational tools exist to quantify this notion, to visualize it, or analyze the results. We present our notion of travel depth, simply put the physical distance a solvent molecule would have to travel from a surface point to a suitably defined reference surface. To define the reference surface, we use the limiting form of the molecular surface with increasing probe size: the convex hull. We then present a fast, robust approximation algorithm to compute travel depth to every surface point. The travel depth is useful because it works for pockets of any size and complexity. It also works for two interesting special cases. First, it works on the grooves in DNA, which are unbounded in one direction. Second, it works on the case of tunnels, that is pockets that have no "bottom", but go through the entire macromolecule. Our algorithm makes it straightforward to quantify discussions of depth when analyzing structures. High-throughput analysis of macromolecule depth is also enabled by our algorithm. This is demonstrated by analyzing a database of protein-small molecule binding pockets, and the distribution of bound magnesium ions in RNA structures. These analyses show significant, but subtle effects of depth on ligand binding localization and strength.     

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

Allowance for Spatial Dispersion of Dielectric Permittivity in Polyelectrolyte Model of DNA

Abstract

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy difference as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

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.     

The ultrasonic degradation of biological macromolecules under conditions of stable cavitation. II. Degradation of deoxyribonucleic acid

Solutions of T7 bacteriophage or calf thymus DNA arc degraded in solution by ultrasonic fields of low intensity in the presence of vibrating air bubbles but are not degraded at these low intensities when such bubbles are absent. Evidence is presented for the hydrodynamic nature of the observed degradation and theoretical simulation of a plausible degradation mechanism is compared with experimental degradation studies. It is concluded that degradation of such linear macromolecules as DNA may occur as a result of stresses induced in the macromolecule; these stresses are the result of a relative movement of solvent molecules and the macromolecules in the time-independent flow of solvent near the vibrating bubbles.     

The electrostatic field of DNA: the role of the nucleic acid conformation.

Calculations of the electrostatic field of DNA in two very different double helical conformations, A and Z, are reported and compared with the results previously obtained for B-DNA. Striking contrasts between these fields and the associated electrostatic potentials are brought into evidence. One of the major differences is that while the deepest potentials are generally located in the grooves of DNA, the strongest fields are associated with the phosphate groups. The results of screening the nucleic acids by counterions are also presented.     

Investigation of conformational changes of DNA molecule caused by gamma-irradiation in water-ethanol solutions

The intrinsic viscosity, optical anisotropy and spectral properties of DNA molecule gamma-irradiated with the doses of 10, 20 and 30 Gy in water-ethanol solutions with ethanol concentrations 0-6 mol/l are investigated in the work. Specific volume of DNA at all doses used shows a complex non-monotone dependence on the ethanol content with a peculiarity at the alcohol concentration corresponding to the destruction of water structure in the mixed solvent (so-called, critical concentration, 3.5 mol/l). Ethanol presence at the concentrations below the critical one protects macromolecule from the radiation action. At the alcohol concentrations larger the critical an inversion of the dose dependence of the DNA specific volume is observed. At that the equilibrium rigidity and secondary structure of macromolecule do not change noticeably. The results obtained indicate a significant role of the solvent structure in radiation damage of DNA molecule.     

Structure of collapsed persistent macromolecule: Toroid vs. spherical globule

We studied theoretically the behavior of a collapsed persistent macromolecule in poor solvent as a model of collapse transition of single double-stranded DNA chain, and constructed the diagram of states in the variables with contour length of a macromolecule and quality of the solvent. We found that the state of toroidal globule exists as an intermediate state between the states of elongated coil state and the spherical globule. Our theoretical result suggests that a single linear macromolecule with a high degree of polymerization can form a toroidal globule. However, the range in which the toroidal structure is stable decreases as the macromolecule length increases. Experimental observation with transmission electron microscopy has been performed to study the globular structure of single DNA chain (bacteriophage T4 DNA, λ-DNA) collapsed by hexammine cobalt (III) at different concentrations. We found that an extremely long chain of T4 DNA (166 kbp), with a contour length of 56 μm, actually forms a toroidal globule, and that isotropic spherical globule appears at higher hexammine cobalt concentration. © 1997 John Wiley & Sons, Inc.     

Local effects in hydrophobicity. Electrostatic interactions in the restructuring of highly polar solvent around less polar solute

Two simplifying assumptions are frequently used in the biophysical chemistry of aqueous solutions: (i) a dielectric mediates the interactions of polar and ionic molecules in aqueous phases and (ii) the dielectric constant of this medium is high and uniform up to molecular surfaces. Because of their great utility in rationalizing simple electrostatic and dielectric effects in such polar systems, it is important to examine whether these assumptions also lead to deductions that are locally consistent with the solvent restructuring observed in hydrophobic phenomena. In this paper, using a model polar fluid system, these macroscopic assumptions are applied to the rigorous, microscopic nonlinear integral equation for Wki, the potential of mean force between two adjacent polar molecules. In systems of high dielectric constant, linearization of Boltzmann exponentials and approximation of three-molecule potentials of mean force by superposition of two-molecule potentials permit reduction to a linear integral equation for Wki. It is shown that the strictly local electrostatic contributions to Wki exert an effect that is qualitatively similar to the global screening effect of a dielectric medium. Through the relation between Wki and configurational probabilities, it is further found that reducing the polarity of a molecule in a polar fluid shifts local pair probability density from energetically unfavorable to energetically favorable two-molecule configurations. This general effect, which clearly promotes local structure, would augment more specific hydrophobic mechanisms in aqueous systems. Thus, the assumptions upon which the highly successful Debye-Hückel and Onsager models are supported lead also to deductions about local structure that are consistent with hydrophobic structure enhancement.     

Brownian dynamics simulations of ion atmospheres around polyalanine and B-DNA: effects of biomolecular dielectric

We have extended an earlier Brownian dynamics simulation algorithm for simulating the structural dynamics of ions around biomolecules to accommodate dielectric inhomogeneity. The electrostatic environment of a biomolecule immersed in water was obtained by numerically solving the Poisson equation with the biomolecule treated as a low dielectric region and the solvent treated as a high dielectric region. Instead of using the mean-field type approximations of ion interactions as in the Poisson-Boltzmann model, the ions were treated explicitly by allowing them to evolve dynamically under the electrostatic field of the biomolecule. This model thus accounts for ion-ion correlations and the finite-size effects of the ions. For a 13-residue alpha-helical polyalanine and a 12-base-pair bp B-form DNA, we found that the choice of the dielectric constant of the biomolecule has much larger effects on the mean ionic structure around the biomolecule than on the fluctuational and dynamical properties of the ions surrounding the biomolecule.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.