Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA

Effects of dielectric inhomogeneity on electrostatic twist rigidity of a helical biomolecule in Debye-Hückel regime

The electrostatic interactions play a crucial role in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Hückel regime using the analytical Green function that is calculated in the paper. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as a DNA and an actin filament. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters, and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.

Water-mediated ordering of nanoparticles in an electric field

Interfacial polar molecules feature a strongly anisotropic response to applied electric field, favoring dipole orientations parallel to the interface. In water, in particular, this effect combines with generic orientational preferences induced by spatial asymmetry of water hydrogen bonding under confined geometry, which may give rise to a Janus interface. The two effects manifest themselves in considerable dependence of water polarization on both the field direction relative to the interface and the polarity (sign) of the field. Using molecular simulations, we demonstrate strong field-induced orientational forces acting on apolar surfaces through water mediation. At a field strength comparable to electric fields around a DNA polyion, the torques we predict to act on an adjacent nanoparticle are sufficient to overcome thermal fluctuations. These torques can align a particle with surface as small as 1 nm2. The mechanism can support electrically controlled ordering of suspended nanoparticles as a means of tuning their properties and can find application in electro-nanomechanical devices.

Molecular dynamics studies of ion distributions for DNA duplexes and DNA clusters: salt effects and connection to DNA melting

We present extensive molecular dynamics simulations of the ion distributions for DNA duplexes and DNA clusters using the Amber force field with implicit water. The distribution of ions and the electrostatic energy of ions around an isolated DNA duplex and clusters of DNA duplexes in different salt (NaCl) concentrations over the range 0.2-1.0 mol/L are determined on the basis of the simulation results. Using the electrostatic energy profile, we determine a local net charge fraction phi, which is found to increase with increasing of salt concentration. For DNA clusters containing two DNA duplexes (DNA pair) or four DNA duplexes, phi increases as the distance between the duplexes decreases. Combining this result with experimental results for the dependence of the DNA melting temperature on bulk salt concentration, we conclude that for a pair of DNA duplexes the melting temperature increases by 5-10 K for interaxis separations of 25-40 A. For a cluster of four DNA duplexes, an even larger melting temperature increase should occur. We argue that this melting temperature increase in dense DNA clusters is responsible for the cooperative melting mechanism in DNA-linked nanoparticle aggregates and DNA-linked polymer aggregates.

Computational and analytical modeling of cationic lipid-DNA complexes

We present a theoretical study of the physical properties of cationic lipid-DNA (CL-DNA) complexes--a promising synthetically based nonviral carrier of DNA for gene therapy. The study is based on a coarse-grained molecular model, which is used in Monte Carlo simulations of mesoscopically large systems over timescales long enough to address experimental reality. In the present work, we focus on the statistical-mechanical behavior of lamellar complexes, which in Monte Carlo simulations self-assemble spontaneously from a disordered random initial state. We measure the DNA-interaxial spacing, d(DNA), and the local cationic area charge density, sigma(M), for a wide range of values of the parameter (c) representing the fraction of cationic lipids. For weakly charged complexes (low values of (c)), we find that d(DNA) has a linear dependence on (c)(-1), which is in excellent agreement with x-ray diffraction experimental data. We also observe, in qualitative agreement with previous Poisson-Boltzmann calculations of the system, large fluctuations in the local area charge density with a pronounced minimum of sigma(M) halfway between adjacent DNA molecules. For highly-charged complexes (large (c)), we find moderate charge density fluctuations and observe deviations from linear dependence of d(DNA) on (c)(-1). This last result, together with other findings such as the decrease in the effective stretching modulus of the complex and the increased rate at which pores are formed in the complex membranes, are indicative of the gradual loss of mechanical stability of the complex, which occurs when (c) becomes large. We suggest that this may be the origin of the recently observed enhanced transfection efficiency of lamellar CL-DNA complexes at high charge densities, because the completion of the transfection process requires the disassembly of the complex and the release of the DNA into the cytoplasm. Some of the structural properties of the system are also predicted by a continuum free energy minimization. The analysis, which semiquantitatively agrees with the computational results, shows that that mesoscale physical behavior of CL-DNA complexes is governed by interplay among electrostatic, elastic, and mixing free energies.

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.

Attraction between DNA molecules mediated by multivalent ions

The effective force between two parallel DNA molecules is calculated as a function of their mutual separation for different valencies of counterion and salt ions and different salt concentrations. Computer simulations of the primitive model are used and the shape of the DNA molecules is accurately modeled using different geometrical shapes. We find that multivalent ions induce a significant attraction between the DNA molecules whose strength can be tuned by the averaged valency of the ions. The physical origin of the attraction is traced back either to electrostatics or to entropic contributions. For multivalent counterions and monovalent salt ions, we find a salt-enhanced repulsion effect: the force is first attractive but gets repulsive with increasing salt concentration. Furthermore, we show that the multivalent-ion-induced attraction does not necessarily correlate with DNA overcharging.

Investigation of the electric potential near the DNA-solvent interface: conclusions about the stability of B-DNA

In the present paper DNA is treated as a crystal with symmetry corresponding to a double-helix surface charge density, due to the phosphate groups, immersed in a weak electrolyte. The surrounding solvent is treated via the nonlinear Poisson-Boltzmann equation and the boundary conditions of electrostatics are exactly fulfilled on the DNA-solvent interface. Analytical solutions for the electric potentials and fields inside and outside DNA are obtained. The results give the possibility for a map of the surface potential of DNA to be created. They also show that the electric field inside DNA may decay in two different ways if we change the chemical content of the surrounding solvent. According to this we can draw conclusions about the stability of DNA with respect to the internal and changeable parameters of the system such as chemical content of the aqueous solvent. The position of the condensed counterions around DNA in the Manning cloud can be determined.

Structure-based computational database screening, in vitro assay, and NMR assessment of compounds that target TAR RNA

There has been little prior effort to discover new drugs on the basis of a unique RNA structure. Binding of the viral transactivator Tat to the 5' bulge of the transactivation response (TAR) element is necessary for HIV-1 replication, so TAR RNA is a superb target. A computational approach was developed to screen a large chemical library for binding to a three-dimensional RNA structure. Scoring function development, flexible ligand docking, and limited target flexibility were essential. From the ranked list of compounds predicted to bind TAR, 43 were assayed for inhibition of the Tat-TAR interaction via electrophoretic mobility shift assays. Eleven compounds (between 0.1 and 1 microM) inhibited the Tat-TAR interaction, and some inhibited Tat transactivation in cells. NMR spectra verified specific binding to the 5' bulge and no interaction with other regions of TAR.

Effective interaction between helical biomolecules

The effective interaction between two parallel strands of helical biomolecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than 6 A it can be both attractive and repulsive. Furthermore, we report a nonmonotonic behavior of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the biomolecules is suitably renormalized.

Electrostatic interaction between long, rigid helical macromolecules at all interaxial angles

We derive formulas for the electrostatic interaction between two long, rigid macromolecules that may have arbitrary surface charge patterns and cross at an arbitrary interaxial angle. We calculate the dependence of the interaction energy on the interaxial angle, on the separation, and on the precise alignment of the charge pattern on one molecule with respect to the other. We focus in particular on molecules with helical charge patterns. We report an exact, explicit expression for the energy of interaction between net-neutral helices in a nonpolar medium as well as an approximate result for charged helices immersed in an electrolyte solution. The latter result becomes exact in the asymptotic limit of large separations. Molecular chirality of helices manifests itself in a torque that tends to twist helices in a certain direction out of parallel alignment and that has a nontrivial behavior at small interaxial angles. We illustrate the theory with the calculation of the torque between layers of idealized, DNA-like double helices in cholesteric aggregates. We propose a mechanism of the observed cholesteric-to-columnar phase transition and suggest an explanation for the observed macroscopic (0.4-5 microm) pitch of the cholesteric phase of B-DNA.

The phase behavior of cationic lipid-DNA complexes

We present a theoretical analysis of the phase behavior of solutions containing DNA, cationic lipids, and nonionic (helper) lipids. Our model allows for five possible structures, treated as incompressible macroscopic phases: two lipid-DNA composite (lipoplex) phases, namely, the lamellar (L(alpha)(C)) and hexagonal (H(II)(C)) complexes; two binary (cationic/neutral) lipid phases, that is, the bilayer (L(alpha)) and inverse-hexagonal (H(II)) structures, and uncomplexed DNA. The free energy of the four lipid-containing phases is expressed as a sum of composition-dependent electrostatic, elastic, and mixing terms. The electrostatic free energies of all phases are calculated based on Poisson-Boltzmann theory. The phase diagram of the system is evaluated by minimizing the total free energy of the three-component mixture with respect to all the compositional degrees of freedom. We show that the phase behavior, in particular the preferred lipid-DNA complex geometry, is governed by a subtle interplay between the electrostatic, elastic, and mixing terms, which depend, in turn, on the lipid composition and lipid/DNA ratio. Detailed calculations are presented for three prototypical systems, exhibiting markedly different phase behaviors. The simplest mixture corresponds to a rigid planar membrane as the lipid source, in which case, only lamellar complexes appear in solution. When the membranes are "soft" (i.e., low bending modulus) the system exhibits the formation of both lamellar and hexagonal complexes, sometimes coexisting with each other, and with pure lipid or DNA phases. The last system corresponds to a lipid mixture involving helper lipids with strong propensity toward the inverse-hexagonal phase. Here, again, the phase diagram is rather complex, revealing a multitude of phase transitions and coexistences. Lamellar and hexagonal complexes appear, sometimes together, in different regions of the phase diagram.

Comparison of the Poisson-Boltzmann Model and the Donnan Equilibrium of a Polyelectrolyte in Salt Solution

A sequence of charged parallel flat plates immersed in a salt solution is used to model the swelling behavior of a polyelectrolyte. The solution of the nonlinear Poisson-Boltzmann equation gives rise to an analytical expression of the plate distance as a function of swelling pressure (p), plate charge density (varsigma), and salt concentration (n). The exact treatment of the system also yields the connection between polyelectrolyte concentration nP, p, varsigma, and n. A formula for the electric potential difference between polyelectrolyte and salt solutions is derived. On the other hand, the relation between nP, p, and n is known from the Donnan equilibrium. It is shown that the Donnan potential, UD(nP, n), and swelling pressure, pD(nP, n), are always larger than the equivalent quantities in the Poisson-Boltzmann theory (UPB(varsigma, nP, n) and pPB(varsigma, nP, n), respectively). The transition from the Poisson-Boltzmann theory to the Donnan model is achieved by the limiting process varsigma --> 0 which reveals the intrinsic linkage between the two theories. pD(nP, n) = limvarsigma-->0 pPB(varsigma, nP, n) and UD(nP, n) = limvarsigma-->0 UPB(varsigma, nP, n). Copyright 1999 Academic Press.

Electrostatic potentials of DNA. Comparative analysis of promoter and nonpromoter nucleotide sequences

Distribution of electrostatic potential of DNA fragments was evaluated. A method for calculation of electrostatic potential distribution based on Coulomb's law is proposed for long DNA fragments (approximately 1000 nucleotide pairs). For short DNA sequences, this technique provides a good correlation with the results obtained using Poisson-Boltzmann equation thus justifying its application in comparative studies for long DNA fragments. Calculation was performed for several DNA fragments from E. coli and bacteriophage T7 genomes containing promoter and nonpromoter regions. The results obtained indicate that coding regions are characterized by more homogeneous distribution of electrostatic potential whereas local inhomogeneity of DNA electrostatic profile is typical for promoter regions. The possible role of electrostatic interactions in RNA polymerase-promoter recognition is discussed.

Electrostatic interaction between helical macromolecules in dense aggregates: an impetus for DNA poly- and meso-morphism

DNA exhibits a surprising multiplicity of structures when it is packed into dense aggregates. It undergoes various polymorphous transitions (e.g., from the B to A form) and mesomorphous transformations (from hexagonal to orthorhombic or monoclinic packing, changes in the mutual alignment of nearest neighbors, etc). In this report we show that such phenomena may have their origin in the specific helical symmetry of the charge distribution on DNA surface. Electrostatic interaction between neighboring DNA molecules exhibits strong dependence on the patterns of molecular surface groups and adsorbed counter-ions. As a result, it is affected by such structural parameters as the helical pitch, groove width, the number of base pairs per helical turn, etc. We derive expressions which relate the energy of electrostatic interaction with these parameters and with the packing variables characterizing the axial and azimuthal alignment between neighboring macromolecules. We show, in particular, that the structural changes upon the B-to-A transition reduce the electrostatic energy by approximately kcal/mol per base pair, at a random adsorption of counter ions. Ion binding into the narrow groove weakens or inverts this effect, stabilizing B-DNA, as it is presumably the case in Li+-DNA assemblies. The packing symmetry and molecular alignment in DNA aggregates are shown to be affected by the patterns of ion binding.

Symmetry laws for interaction between helical macromolecules

The power of symmetry laws is applied in many scientific areas from elementary particle physics to structural biology. The structures of many biological helices, including DNA, were resolved with the use of pertinent symmetry constraints. It was not recognized, however, that similar constraints determine cardinal features of helix-helix interactions vital for many recognition and assembly reactions in living cells. We now formulate such symmetry-determined interaction laws and apply them to explain DNA "over-winding" from 10.5 base pairs per turn in solution to 10 in hydrated fibers, counterion specificity in DNA condensation, and forces observed over the last 15 A of separation between DNA, collagen, and four-stranded guanosine helices.

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.