Magnus Ullner

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.

The electrostatic persistence length calculated from Monte Carlo, variational and perturbation methods

Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-Huckel screening length, κ−1. As long as the salt content is low and κ−1 is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with κ−1. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as ξp/κ, in agreement with experiment on flexible polyelectrolytes, where ξp is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the κ−1 dependence becomes ...

A Monte Carlo study of solutions of oppositely charged polyelectrolytes

The formation of complexes appearing in solutions containing oppositely charged polyelectrolytes has been investigated by Monte Carlo simulations using two different models. The polyions are described as flexible chains of 20 connected charged hard spheres immersed in a homogenous dielectric background representing water. The small ions are either explicitly included or their effect described by using a screened Coulomb potential. The simulated solutions contained 10 positively charged polyions with 0, 2, or 5 negatively charged polyions and the respective counterions. Two different linear charge densities were considered, and structure factors, radial distribution functions, and polyion extensions were determined. A redistribution of positively charged polyions involving strong complexes formed between the oppositely charged polyions appeared as the number of negatively charged polyions was increased. The nature of the complexes was found to depend on the linear charge density of the chains. The simplified model involving the screened Coulomb potential gave qualitatively similar results as the model with explicit small ions. Finally, owing to the complex formation, the sampling in configurational space is nontrivial, and the efficiency of different trial moves was examined.

A Monte Carlo study of titrating polyelectrolytes

Monte Carlo simulations have been used to study three different models for linear, titrating polyelectrolytes in a salt‐free environment: (i) a rigid polymer with rigid bonds (rigid rod); (ii) a flexible polymer with rigid bonds; and (iii) a flexible polymer with flexible bonds. The use of a very efficient pivot algorithm has made it possible to simulate very long chains, with up to several thousand titrating groups. The results have been compared to a mean field approximation for a rigid rod and variational results emanating from a Flory type approach. It is found that the rigid rod mean field model gives a qualitatively correct description for the apparent dissociation constant for all three models. At room temperature, the energy contribution to the apparent dissociation constant often dominates over the entropic term, which partly explains the relative success of this approach. In the case of flexible bonds, both the conformational behavior and the behavior of the apparent dissociation constant are well described by a variational ansatz with a quadratic term, largely thanks to the harmonicity of the bonds themselves. The approach is less successful for rigid bonds, which becomes evident for highly charged chains where a harmonic entropy term is incorrect. This can be remedied by replacing it with an expression valid in the strong coupling regime. Empirical scaling expressions have also been found, primarily for the end‐to‐end distance.

Conformational Properties and Apparent Dissociation Constants of Titrating Polyelectrolytes: Monte Carlo Simulation and Scaling Arguments

Titrating polyelectrolytes with up to 2000 monomers are studied by Monte Carlo simulations. The polyelectrolyte, regarded to be a polyacid in a salt‐free solution, is modelled with harmonic bonds between monomers that can be either neutral or negatively charged. The charges are allowed to fluctuate in a grand canonical ensemble and charged monomers interact via a Coulomb potential. Scaling laws expressing the root‐mean‐square end‐to‐end distance and the apparent dissociation constant as functions of the number of monomers and degree of ionization are obtained from a simple Flory approach. Comparisons with the simulation results show that these scaling laws describe a universal behavior for long and highly charged chains.

A Debye–Hückel theory for electrostatic interactions in proteins

The site–site Ornstein–Zernike equation with a simple mean spherical closure is used to study electrostatic interactions of proteins. Using a Debye–Huckel approximation for the correlation functions of the bulk electrolyte and a simple basis expansion for the protein–salt direct correlation functions, we obtain a very simple variational expression for the electrostatic component of the excess chemical potential of a protein in an electrolyte solution. The predictions of the theory are tested on a model of the protein calbindin D9k. Our calculations for calcium binding affinities and protein acidity constants are found to be in excellent agreement with the results of computer simulations.

Monte carlo simulations of parallel charged platelets as an approach to tactoid formation in clay.

The free energy of interaction between parallel charged platelets with divalent counterions has been calculated using Monte Carlo simulations to investigate the electrostatic effects on aggregation. The platelets are primarily intended to represent clay particles. With divalent counterions, the free energy for two platelets or two tactoids (clusters of parallel platelets) shows a minimum at a short separation due to the attraction caused by ion-ion correlations. In a salt-free system, the free energy of interaction has a long-range repulsive tail beyond the minimum. The repulsion increases for tactoids with larger aggregation numbers, whereas the depth of the free-energy minimum is gradually reduced. For large enough aggregation numbers, the repulsion is dominating and the minimum is no longer a global free-energy minimum. This is an effect of the depletion of counterions free in solution (outside tactoids) as counterions and platelets aggregate into tactoids and the resulting redistribution of counterions in the system changes the effective interactions between platelets and tactoids. The difference in tactoid-tactoid interactions as a function of aggregation number can be removed by adding enough salt to mask the depletion. Adding salt also reduces the repulsive tail of the free energy of interaction and enhances the minimum. No dependence on the aggregation number suggests that an isodesmic model with a monotonically decaying distribution of aggregation numbers can be used to describe a clay system. This may help to explain the experimental observations of low average numbers of platelets in tactoids, although factors not included in the simulation model may also play an important role.

Interaction and aggregation of charged platelets in electrolyte solutions: a coarse-graining approach.

A coarse-graining approach has been developed to replace the effect of explicit ions with an effective pair potential between charged sites in anisotropic colloidal particles by optimizing a potential of mean force against the results of simulations of two such colloidal particles with all ions in a cell model. More specifically, effective pair potentials were obtained for charged platelets in electrolyte solutions by simulating two rotating parallel platelets with ions at the primitive model level, enclosed in a cylindrical cell. One-component bulk simulations of many platelets interacting via the effective pair potentials are in excellent agreement with the corresponding bulk simulations with all mobile charges present. The bulk simulations were mainly used to study the effects of platelet size, flexibility, and surface charge density on platelet aggregation in an aqueous 2:1 electrolyte, but systems in a 1:1 electrolyte were also investigated.

Structure of a cyclic peptide with a catalytic triad, determined by computer simulation and NMR spectroscopy.

SummaryWe report the design of a cyclic, eight-residue peptide that possesses the catalytic triad residues of the serine proteases. A manually built model has been relaxed by 0.3 ns of molecular dynamics simulation at room temperature, during which no major changes occurred in the peptide. The molecule has been synthesised and purified. Two-dimensional NMR spectroscopy provided 35 distance and 7 torsion angle constraints, which were used to determine the three-dimensional structure. The experimental conformation agrees with the predicted one at the β-turn, but deviates in the arrangement of the disulphide bridge that closes the backbone to a ring. A 1.2 ns simulation at 600 K provided extended sampling of conformation space. The disulphide bridge reoriented into the experimental arrangement, producing a minimum backbone rmsd from the experimental conformation of 0.8 Å. At a later stage in the simulation, a transition at Ser3 produced more pronounced high-temperature behaviour. The peptide hydrolyses p-nitrophenyl acetate about nine times faster than free histidine.

The persistence length of adsorbed dendronized polymers

The persistence length of cationic dendronized polymers adsorbed onto oppositely charged substrates was studied by atomic force microscopy (AFM) and quantitative image analysis. One can find that a decrease in the ionic strength leads to an increase of the persistence length, but the nature of the substrate and of the generation of the side dendrons influence the persistence length substantially. The strongest effects as the ionic strength is being changed are observed for the fourth generation polymer adsorbed on mica, which is a hydrophilic and highly charged substrate. However, the observed dependence on the ionic strength is much weaker than the one predicted by the Odijk, Skolnik, and Fixman (OSF) theory for semi-flexible chains. Low-generation polymers show a variation with the ionic strength that resembles the one observed for simple and flexible polyelectrolytes in solution. For high-generation polymers, this dependence is weaker. Similar dependencies are found for silica and gold substrates. The observed behavior is probably caused by different extents of screening of the charged groups, which is modified by the polymer generation, and to a lesser extent, the nature of the substrate. For highly ordered pyrolytic graphite (HOPG), which is a hydrophobic and weakly charged substrate, the electrostatic contribution to the persistence length is much smaller. In the latter case, we suspect that specific interactions between the polymer and the substrate also play an important role.