Attraction between DNA molecules mediated by multivalent ions

Inter-DNA attraction mediated by divalent counterions

Can nonspecifically bound divalent counterions induce attraction between DNA strands? Here, we present experimental evidence demonstrating attraction between short DNA strands mediated by Mg2+ ions. Solution small angle x-ray scattering data collected as a function of DNA concentration enable model independent extraction of the second virial coefficient. As the [Mg2+] increases, this coefficient turns from positive to negative reflecting the transition from repulsive to attractive inter-DNA interaction. This surprising observation is corroborated by independent light scattering experiments. The dependence of the observed attraction on experimental parameters including DNA length provides valuable clues to its origin.

Electrostatics of DNA Complexes with Cationic Lipid Membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.

Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na+ and Mg2+ play distinctive roles in helix-helix assembly. High [Na+] (>0.3 M) causes a reduced helix-helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix-helix attraction and results in a more compact and ordered helix-helix packing. Mg2+ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.

Computer Simulation of the Ionic Atmosphere around Z-DNA

We describe a coarse-grained model for Z-DNA that mimics the DNA shape with a relatively small number of repulsive interaction sites. In addition, negative charges are placed at the phosphate positions. The ionic atmosphere around this grooved Z-DNA model is then investigated with Monte Carlo simulation. Cylindrically averaged concentration profiles as well as the spatial distribution of ions have been calculated. The results are compared to those for other DNA models differing in the repulsive core. This allows the examination of the effect of the DNA shape in the ionic distribution. It is seen that the penetrability of the ions to the DNA groove plays an important role in the ionic distribution. The results are also compared with those reported for B-DNA. In both conformers the ions are structured in alternating layers of positive and negative charge. In Z-DNA the layers are more or less concentric to the molecular axis. Besides, no coions enter into the single groove of this conformer. On the contrary, the alternating layers of B-DNA are also structured along the axial coordinate with some coions penetrating into the major groove. In both cases we have found five preferred locations of the counterions and two for the coions. The concentration of counterions reaches its absolute maximum at the narrow Z-DNA groove and at the minor groove of B-DNA, the value of the maximum being higher in the Z conformer.

Computer simulation study of molecular recognition in model DNA microarrays

DNA microarrays have been widely adopted by the scientific community for a variety of applications. To improve the performance of microarrays there is a need for a fundamental understanding of the interplay between the various factors that affect microarray sensitivity and specificity. We use lattice Monte Carlo simulations to study the thermodynamics and kinetics of hybridization of single-stranded target genes in solution with complementary probe DNA molecules immobilized on a microarray surface. The target molecules in our system contain 48 segments and the probes tethered on a hard surface contain 8-24 segments. The segments on the probe and target are distinct and each segment represents a sequence of nucleotides ( approximately 11 nucleotides). Each probe segment interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how the probe length, temperature, or hybridization energy, and the stretch along the target that the probe segments complement, affect the extent of hybridization. For systems containing single probe and single target molecules, we observe that as the probe length increases, the probability of binding all probe segments to the target decreases, implying that the specificity decreases. We observe that probes 12-16 segments ( approximately 132-176 nucleotides) long gave the highest specificity and sensitivity. This agrees with the experimental results obtained by another research group, who found an optimal probe length of 150 nucleotides. As the hybridization energy increases, the longer probes are able to bind all their segments to the target, thus improving their specificity. The hybridization kinetics reveals that the segments at the ends of the probe are most likely to start the hybridization. The segments toward the center of the probe remain bound to the target for a longer time than the segments at the ends of the probe.

Effect of confinement on the interaction between two like-charged rods

Monte Carlo simulations were employed to study two charged rods confined between two unlike charged plates, all immersed in a model electrolyte. Recently, it was shown that two rods immersed in a multivalent counterion solution may show attraction [Phys. Rev. Lett. 78, 2477 (1997)10.1103/PhysRevLett.78.2477]. Here we show for a monovalent electrolyte that rod-rod attraction and repulsion can switch sign depending on confinement and ionic size. We also propose a simple self-assembling mechanism which may be helpful to understand the DNA-lipid bilayers complexation.

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.

Electrolyte distribution around two like-charged rods: Their effective attractive interaction and angular dependent charge reversal

A simple model for two like-charged parallel rods immersed in an electrolyte solution is considered. We derived the three point extension (TPE) of the hypernetted chain/mean spherical approximation (TPE-HNC/MSA) and Poisson-Boltzmann (TPE-PB) integral equations. We numerically solve these equations and compare them to our results of Monte Carlo (MC) simulations. The effective interaction force, F(T), the charge distribution profiles, rho(el)(x,y), and the angular dependent integrated charge function, P(theta), are calculated for this system. The analysis of F(T) is carried out in terms of the electrostatic and entropic (depletion) contributions, F(E) and F(C). We studied several cases of monovalent and divalent electrolytes, for which the ionic size and concentration are varied. We find good qualitative agreement between TPE-HNC/MSA and MC in all the cases studied. The rod-rod force is found to be attractive when immersed in large size, monovalent or divalent electrolytes. In general, the TPE-PB has poor agreement with the MC. For large monovalent and divalent electrolytes, we find angular dependent charge reversal charge inversion and polarizability. We discuss the intimate relationship between this angular dependent charge reversal and rod-rod attraction.

Nonlinear elasticity of single collapsed polyelectrolytes

Nonlinear elastic responses of short and stiff polyelectrolytes are investigated by dynamic simulations on a single-molecule level. When a polyelectrolyte condensate undergoes a mechanical unfolding, two types of force-extension curves--i.e., a force plateau and a stick-release pattern--are observed depending on the strength of the electrostatic interaction. We provide a physical interpretation of such force-extension behavior in terms of intramolecular structures of the condensates. We also describe charge distributions of counterions condensed onto a polyelectrolyte, which clarify formation of one-dimensional strongly correlated liquid at large Coulomb coupling regime. These findings may provide significant insights into the relationship between a molecular elasticity and a molecular mechanism of like-charge attractions observed in a wide range of charged biopolymer systems.

Direct observation of azimuthal correlations between DNA in hydrated aggregates

This study revisits the classical x-ray diffraction patterns from hydrated, noncrystalline fibers originally used to establish the helical structure of DNA. We argue that changes in these diffraction patterns with DNA packing density reveal strong azimuthally dependent interactions between adjacent molecules up to approximately 40 A interaxial or approximately 20 A surface-to-surface separations. These interactions appear to force significant torsional "straightening" of DNA and strong azimuthal alignment of nearest neighbor molecules. The results are in good agreement with the predictions of recent theoretical models relating DNA-DNA interactions to the helical symmetry of their surface charge patterns.

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polyelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are pointlike, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also show that if the attractive interactions between the rods become frustrated as the bundle grows, finite-size bundles can be obtained with pointlike counterions.

Statistical mechanics of columnar DNA assemblies

Many physical systems can be mapped onto solved or "solvable" models of magnetism. In this work, we have mapped the statistical mechanics of columnar phases of ideally helical rigid DNA--subject to the earlier found unusual, frustrated pair potential (A.A. Kornyshev, S. Leikin, J. Chem. Phys. 107, 3656 (1997))--onto an exotic, unknown variant of the XY model on a fixed or restructurable lattice. Here, the role of the "spin" is played by the azimuthal orientation of the molecules. We have solved this model using a Hartree-Fock approximation, ground-state calculations, and finite-temperature Monte Carlo simulations. We have found peculiar spin order transitions, which may also be accompanied by positional restructuring, from hexagonal to rhombohedric lattices. Some of these have been experimentally observed in dense columnar aggregates. Note that DNA columnar phases are of great interest in biophysical research, not only because they are a useful in vitro tool for the study of DNA condensation, but also since these structures have been detected in living matter. Within the approximations made, our study provides insight into the statistical mechanics of these systems.

Absence of charge inversion on rodlike polyelectrolytes with excess divalent counterions

Filamentous viruses such as fd and M13 are highly charged rodlike polyelectrolytes. In this study, we employ fd virus to test the recent prediction of charge inversion [Nguyen, Rouzina, and Shklovskii, J. Chem. Phys. 112, 2562 (2000)]. Light scattering measurements show bundle formation and resolubilization of fd viruses when MgCl(2) was added from 0 to 600 mM. The effective charge of fd was studied by measuring their electrophoretic mobility using a filament tracking method uniquely suited for the system. Monte Carlo simulations were performed under canonical ensemble to predict the charge distribution around the rodlike virus. Charge inversion, which has been suggested theoretically to accompany with bundle resolubilization, was not observed in either experiments or simulations. A modified analysis of force balance is called upon to account for these new findings.