Monte Carlo Simulation Study of DNA Polyelectrolyte Properties in the Presence of Multivalent Polyamine Ions

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.

Competition between compaction of single chains and bundling of multiple chains in giant DNA molecules

It has been established that in a dilute solution individual giant DNA molecules undergo a large discrete transition between an elongated coil state and a folded compact state. On the other hand, in concentrated solutions, DNA molecules assemble into various characteristic states, including multichain aggregate, liquid crystalline, ionic crystal, etc. In this study, we compared single-chain and multiple-chain events by observing individual chains using fluorescence microscopy. We used spermidine, SPD(3+), as a condensing agent for giant DNA. When the concentration of DNA is below 1 microM in base-pair units, individual DNA molecules exhibit a transition from an elongated state to a compact state. When the concentration of DNA is increased to 10 microM, a thick fiberlike assembly of multiple chains appears. AFM measurements of this thick fiber revealed that more than tens of DNA molecules form a bundle structure with parallel ordering of the chains. The transition between single-chain compaction and bundle formation with multiple-chain assemblies was reproduced by a theoretical calculation.

Mechanism of mesoporous silica formation. A time-resolved NMR and TEM study of silica-block copolymer aggregation

The dynamics of the synthesis of a mesoporous silica material SBA-15 is followed using time-resolved in situ 1H NMR and transmission electron microscopy (TEM). Block copolymer-silica particles of two-dimensional hexagonal symmetry evolve from an initially micellar solution. The synthesis was carried out with the block copolymer Pluronic P123 (EO20-PO70-EO20) at 35 degrees C and using tetramethyl orthosilicate as the silica precursor. By using TEM, we can image different stages during the evolution of the synthesis. Flocs of spherical micelles held together by the polymerizing silica are observed prior to precipitation. With time, the structure of these flocs evolves and the transition from spherical to cylindrical hexagonally packed micelles can be monitored. The signal from the methyl protons of the PO part was recorded with 1H NMR. One observes a continuous increase in the signal width but with distinct changes in the spectral characteristics occurring in narrow time intervals. The spectral changes can be attributed to structural changes of the self-assembled aggregates. The 1H NMR and TEM studies reveal the same mechanism of formation. It is concluded that the aggregation is caused by a micelle-micelle attraction induced by oligomeric/polymeric silica that adsorbs to the EO palisade layer of the micelles and has the ability to bridge to another micelle. This adsorption also favors the formation of cylindrical aggregates relative to spherical micelles. The sequence of NMR and TEM observations can then be interpreted as the following sequence of events: (i) silicate adsorption on globular micelles possibly accompanied with some aggregate growth, (ii) the association of these globular micelles into flocs, (iii) the precipitation of these flocs, and (iv) micelle-micelle coalescence generating (semi)infinite cylinders that form the two-dimensional hexagonal packing.

Adsorption of monovalent and multivalent cations and anions on DNA molecules

Adsorption of monovalent and multivalent cations and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modeled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modeled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major-groove cationic charge is independent of the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salts. Simulations for larger ion radii, which mimic the effect of ion hydration, indicate an increased adsorbtion of cations in the major groove.

Nonmonotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient B2 of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the "primitive model." The salt and counterions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that B2 first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that linear and nonlinear Poisson Boltzmann theories fail for large ionic strength. The observed nonmonotonicity of B2 is compared with experiments. Implications for protein crystallization are discussed.

Osmotic pressure of charged colloidal suspensions: a unified approach to linearized Poisson-Boltzmann theory

We study theoretically the equation of state of a fluid suspension of charged objects (e.g., colloids, polyelectrolytes, clay platelets, etc.) dialyzed against an electrolyte solution using the cell model and linear Poisson-Boltzmann (PB) theory. From the volume derivative of the grand potential functional of linear theory we obtain two expressions for the osmotic pressure in terms of the potential or ion profiles, neither of which coincides with the expression known from nonlinear PB theory, namely, the density of microions at the cell boundary. We show that the range of validity of linearization depends strongly on the linearization point and prove that expansion about the self-consistently determined average potential is optimal in several respects. For instance, screening inside the suspension is automatically described by the actual ionic strength, resulting in the correct asymptotics at high colloid concentration. Together with the analytical solution of the linear PB equation for cell models of arbitrary dimension and electrolyte composition, explicit and very general formulas for the osmotic pressure ensue. A comparison with nonlinear PB theory is provided. Our analysis also shows that whether or not linear theory predicts a phase separation depends crucially on the precise definition of the pressure, showing that depending on the choice, an artificial phase separation in systems as important as DNA in physiological salt solution may result.

Spermine: an "invisible" component in the crystals of B-DNA. A grand canonical Monte Carlo and molecular dynamics simulation study

The association of spermine(4+) (Spm(4+)), Mg(2+) and monovalent (M(+)) ions with DNA in crystal form, have been studied using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) computer simulations. GCMC calculations were used to calculate the distribution of Spm(4+), Mg(2+), and M(+) between the equilibrating solvent and the DNA crystal under conditions mimicking the crystal-growing protocols reported in a number of recent X-ray diffraction studies of DNA oligomers. The GCMC simulations show that the composition of ions neutralizing the negative charge of DNA can vary in a broad range. The GCMC simulations were used to provide appropriate conditions for subsequent 6 ns constant pressure and temperature MD simulations of DNA in a typical crystalline environment consisting of three DNA double helix decamers in a periodic hexagonal cell, containing 1200 water molecules, eight Spm(4+), 32 Na(+) and four Cl(-) ions. Based on the simulation results, it seems possible to give an explanation why spermine molecules are usually not detected in X-ray studies in spite of their high concentration in the preparatory samples used as the crystallizing agent. It appears that this flexible polyamine molecule has several binding modes, interacting in fairly irregular manner with different sites on DNA and showing no regular ordering in the DNA crystals. Ions of Na(+) and Spm(4+) compete with each other and with water molecules in binding to bases in the minor groove and they influence the structure of the DNA hydration shell in different ways.

Competitive binding of Mg2+, Ca2+, Na+, and K+ ions to DNA in oriented DNA fibers: experimental and Monte Carlo simulation results

Competitive binding of the most common cations of the cytoplasm (K(+), Na(+), Ca(2+), and Mg(2+)) with DNA was studied by equilibrating oriented DNA fibers with ethanol/water solutions (65 and 52% v/v EtOH) containing different combinations and concentrations of the counterions. The affinity of DNA for the cations decreases in the order Ca > Mg >> Na approximately K. The degree of Ca(2+) and/or Mg(2+) binding to DNA displays maximum changes just at physiological concentrations of salts (60-200 mM) and does not depend significantly on the ethanol concentration or on the kind of univalent cation (Na(+) or K(+)). Ca(2+) is more tightly bound to DNA and is replaced by the monovalent cations to a lesser extent than is Mg(2+). Similarly, Ca(2+) is a better competitor for binding to DNA than Mg(2+): the ion exchange equilibrium constant for a 1:1 mixture of Ca(2+) and Mg(2+) ions, K(c)(Ca)(Mg), changes from K(c)(Ca)(Mg) approximately 2 in 65% EtOH (in 3-30 mM NaCl and/or KCl) to K(c)(Ca)(Mg) approximately 1.2-1.4 in 52% EtOH (in 300 mM NaCl and/or KCl). DNA does not exhibit selectivity for Na(+) or K(+) in ethanol/water solutions either in the absence or in the presence of Ca(2+) and/or Mg(2+). The ion exchange experimental data are compared with results of grand canonical Monte Carlo (GCMC) simulations of systems of parallel and hexagonally ordered, uniformly and discretely charged polyions with the density and spatial distribution of the charged groups modeling B DNA. A quantitative agreement with experimental data on divalent-monovalent competition has been obtained for discretely charged models of the DNA polyion (for the uniformly charged cylinder model, coincidence with experiment is qualitative). The GCMC method gives also a qualitative description of experimental results for DNA binding competitions of counterions of the same charge (Ca(2+) with Mg(2+) or K(+) with Na(+)).