Coarse-grained molecular dynamics simulation of cation distribution profiles on negatively charged lipid membranes during phase separation.

Revealing the ion distributions on a charged lipid membrane in aqueous solution under the influence of long-range interactions is essential for understanding the origin of the stability of the bilayer structure and the interaction between biomembranes and various electrolytes. However, the ion distributions and their dynamics associated with the phase separation process of the lipid bilayer membrane are still unclear. We perform coarse-grained molecular dynamics simulations to reveal the Na+ and Cl- distributions on charged phospholipid bilayer membranes during phase separation. During the phase separation, cations closely follow the position of negatively charged lipids on a microsecond timescale and are rapidly redistributed parallel to the lipid bilayer. In the homogenous mixture of zwitterionic and negatively charged lipids, cations weakly follow negatively charged lipids, indicating the strong interaction between cations and negatively charged lipids. We also compare cation concentrations as a function of surface charge density obtained by our simulation with those obtained by a modified Poisson-Boltzmann theory. Including the ion finite size makes the statistical results consistent, suggesting the importance of the ion-ion interactions in aqueous solution. Our simulation results advance our understanding of ion distribution during phase separation.

Reappearance of slow mode in mixtures of polyethylene glycol and poly(sodium methacrylate).

Mixtures of an anionic polyelectrolyte, poly(sodium methacrylate), NaPMA, and a neutral polymer, polyethylene glycol, PEG, were investigated by dynamic and static light scattering techniques at different concentrations and chain-lengths of PEG. The NaPMA standard with a narrow molecular weight distribution was chosen for the study. The so called slow-mode behaviour, characteristic of salt-free NaPMA solutions, vanishes as the simple salt, NaCl in this case, is added in a sufficient amount. However, in NaPMA-NaCl-PEG mixtures, the slow-mode signal is observed again. We assume that the dielectric constant of the mixture with PEG, which is substantially lower than that of pure water, causes the reappearance of the slow-mode signal through reinforced electrostatic interactions between NaPMA polyions. Monte Carlo simulations of a coarse-grained model of the system confirm stronger correlations between NaPMA molecules and thus qualitatively agree with experimental results.

Interactions between charged surfaces mediated by stiff, multivalent zwitterionic polymers.

The interaction between like-charged objects in electrolyte solutions can be heavily altered by the presence of multivalent ions which possess a spatially distributed charge. In this work, we examine the influence of stiff, multivalent zwitterionic polymers on the interaction between charged surfaces using a splitting field theory previously shown to be accurate for the weak to the intermediate to the strong electrostatic coupling regimes. The theory is compared to Monte Carlo simulations and good agreement is found between both approaches. For surface separations shorter than the polymer length, the polymers are mainly oriented parallel to the surfaces, and the surface-surface interaction is repulsive. When the surface separation is comparable to the length of polymers, the polymers have two main orientations. The first corresponds to the polymers adsorbed onto the surface with their centers located near to or in contact with the surface; the second corresponds to polymers which are perpendicular to the charged surfaces, bridging both surfaces and leading to an attractive force between them. Increasing the surface charge density leads to more pronounced attraction via bridging. At surface separations greater than the polymer length, the polymers in the center of the system are still mainly perpendicular to the surfaces, due to "chaining" between zwitterions that enable them to bridge the surfaces at larger separations. This leads to an attractive interaction between the surfaces with a range significantly longer than the length of the polymers.

Electrolyte Solution at Zwitterionic Lipid Layer.

A coarse-grained model of simple monovalent electrolyte solution in contact with a zwitterionic lipid layer in continuum solvent is studied by canonical Monte Carlo computer simulations and extended Poisson-Boltzmann theory. A structure of zwitterionic layer as well as concentration profiles of positively and negatively charged monovalent ions were obtained from simulations and compared to theoretical predictions. A relatively good agreement between the Monte Carlo computer simulations and theory was observed.

Experimental and theoretical study of the silica particle interactions in the presence of multivalent rod-like ions.

The silica particle interactions in the presence of spermidine were systematically investigated both from experimental and theoretical points of view. The hydrodynamic radii and the corresponding polydispersity indices of the colloidal silica particles were determined by dynamic light scattering (DLS) as a function of spermidine concentration. Whereas the effective size of the silica particles increases with increasing spermidine concentration (pointing to the particle aggregation), the polydispersity index first increases reaches a maximum and then further decreases with the increasing spermidine concentration. From the mobility measurements it was concluded that the increase in spermidine concentration causes less negative values of zeta potential, meaning that the adsorption of spermidine leads to the less negative silica surface. Moreover, Monte Carlo (MC) simulations also confirmed that the addition of spermidine reduces the repulsion between silica particles. The MC concentration profiles of spermidine close to the charged silica particle are in a very good agreement with the results obtained by theory. An important motivation for our study is the effectiveness of multivalent ions to coagulate colloidal suspensions; e.g., the multivalent ions are exploited in the water purification process.

Attraction between like-charged surfaces: effect of counterion dimerization.

A force between two equally charged surfaces depends on the composition of intervening solution. While the force is always repulsive for monovalent counterions, multivalent counterions turn the interaction into the attractive one. An example of the attraction between like charged surfaces is the aggregation of colloidal particles mediated by multivalent counterions with spatially separated charges. A model system represents the colloids by equally charged planar surfaces. In our consideration the intervening salt-free solution is composed of rod-like dimmers. Some of dimmers can be disconnected to monovalent ions. This model system was solved using the Monte Carlo (MC) simulations and the Poisson-Boltzmann (PB) theory, which was extended to deal with rigid complex ions. The study was made by varying a range of parameters including the surface charge density and the ratio of the number of monovalent counterions to the number of all counterions. The calculated pressure shows that with increasing surface charge density the lower fraction of dimeric counterions is needed to induce attractive force between surfaces. A good agreement between the MC simulations and the theoretical results was obtained.

Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties.

In this study we derived a model for a multicomponent lipid monolayer in contact with an aqueous solution by means of a generalized classical density functional theory and Monte Carlo simulations. Some of the important biological lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, additional internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler-Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the electric double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the electric double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge density of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concentration in the system.

Debye-Hückel theory for mixtures of rigid rodlike ions and salt.

Like-charged surfaces are able to attract each other if they are embedded in an electrolyte solution of multivalent rodlike ions, even if the rods are long. To reproduce this ability the Poisson-Boltzmann model has recently been extended so as to account for the rodlike structure of the mobile ions. Our model properly accounts for intraionic correlations but still neglects correlations between different rodlike ions. For sufficiently long rods, the model shows excellent agreement with Monte Carlo simulations and exhibits two minima - a depletion and a bridging minimum - in the interaction free energy. In the present work, we generalize the Poisson-Boltzmann model to systems with polydisperse rod lengths and arbitrary charge distributions along the rods, including the presence of salt. On the level of the linearized Debye-Hückel model we derive a general criterion for whether an electrolyte with given distribution of rodlike ions is able to mediate attraction between like-charged surfaces. We numerically analyze two special cases, namely the influence of salt on symmetric and asymmetric mixtures of monodisperse rodlike ions. The symmetric mixture is characterized by the presence of both negatively and positively charged (but otherwise identical) rodlike ions. For the asymmetric mixture, the system contains rodlike ions of only one type. We demonstrate that the addition of salt retains the depletion minimum but tends to eliminate the bridging minimum.

Solubility of lysozyme in polyethylene glycol-electrolyte mixtures: the depletion interaction and ion-specific effects.

The solubility of aqueous solutions of lysozyme in the presence of polyethylene glycol and various alkaline salts was studied experimentally. The protein-electrolyte mixture was titrated with polyethylene glycol, and when precipitation of the protein occurred, a strong increase of the absorbance at 340 nm was observed. The solubility data were obtained as a function of experimental variables such as protein and electrolyte concentrations, electrolyte type, degree of polymerization of polyethylene glycol, and pH of the solution; the last defines the net charge of the lysozyme. The results indicate that the solubility of lysozyme decreases with the addition of polyethylene glycol; the solubility is lower for a polyethylene glycol with a higher degree of polymerization. Further, the logarithm of the protein solubility is a linear function of the polyethylene glycol concentration. The process is reversible and the protein remains in its native form. An increase of the electrolyte (NaCl) concentration decreases the solubility of lysozyme in the presence and absence of polyethylene glycol. The effect can be explained by the screening of the charged amino residues of the protein. The solubility experiments were performed at two different pH values (pH = 4.0 and 6.0), where the lysozyme net charge was +11 and +8, respectively. Ion-specific effects were systematically investigated. Anions such as Br(-), Cl(-), F(-), and H(2)PO(4)(-) (all in combination with Na(+)), when acting as counterions to a protein with positive net charge, exhibit a strong effect on the lysozyme solubility. The differences in protein solubility for chloride solutions with different cations Cs(+), K(+), and Na(+) (coions) were much smaller. The results at pH = 4.0 show that anions decrease the lysozyme solubility in the order F(-) < H(2)PO(4)(-) < Cl(-) < Br(-) (the inverse Hofmeister series), whereas cations follow the direct Hofmeister series (Cs(+) < K(+) < Na(+)) in this situation.

Bridging like-charged macroions through long divalent rodlike ions.

Like-charged macroions in aqueous electrolyte solution can attract each other because of the presence of inter- and/or intramolecular correlations. Poisson-Boltzmann theory is able to predict attractive interactions if the spatially extended structure (which reflects the presence of intramolecular correlations) of the mobile ions in the electrolyte is accounted for. We demonstrate this for the case of divalent, mobile ions where each ion consists of two individual charges separated by a fixed distance. Variational theory applied to this symmetric 2:2 electrolyte of rodlike ions leads to an integro-differential equation, valid for arbitrary rod length. Numerical solutions reveal the existence of a critical rod length above which electrostatic attraction starts to emerge. This electrostatic attraction is distinct from nonelectrostatic depletion forces. Analysis of the orientational distribution functions suggests a bridging mechanism of the rodlike ions to hold the two macroions together. For sufficiently large rod length, we also observe "overcharging", that is, an over-compensation of the macroion charges by the diffuse layer of mobile rodlike ions. Our results emphasize the importance of the often rodlike internal structure that condensing agents such as polyamines, peptides, or polymer segments exhibit. The results were compared with Monte Carlo simulations.

Potential of mean force between charged colloids: effect of dielectric discontinuities.

The potential of mean force between two spherical and like-charged macroions in a salt-free aqueous solution has been determined using an extended primitive model and canonical Monte Carlo simulations. The systems considered covered the range from a purely repulsive to a purely attractive potential of mean force as the electrostatic coupling was increased. The macroions were modeled as spherical dielectric cavities, and the polarization surface charge densities occurring at the dielectric discontinuities were expanded in spherical harmonics. The surface polarization gave rise to (i) an attenuation of the counterion accumulation at the macroion surfaces at all cases considered, (ii) an enhanced repulsive potential of mean force in the weak to intermediate electrostatic coupling regime, and (iii) a less attractive at short separation and an enhanced attractive potential of mean force at longer macroion-macroion separation in the strong electrostatic coupling regime.

Recycling of uranyl from contaminated water.

Many separation processes are related to the behavior of ions close to charged surfaces. In this work, we examine uranyl ions, which can be considered as rod-like molecular ions with a spatially distributed charge, embedded in a system of like charged surfaces. The analysis of the system is based on an approximate field theory which is accurate from the weak to the strong electrostatic coupling regimes. The numerical results show that close to the charged surface the ions are oriented parallel to the surface, whereas at distances greater than half of the ion length, they are randomly oriented. Due to the restriction of the orientational degrees of freedom, the density of ions at the charged surface decreases to zero. For large surface charge densities, the force between like charged surfaces becomes attractive, as a result of charge correlations. The theoretical results are in good agreement with Monte Carlo simulation results.

Thermodynamics of the lysozyme--salt interaction from calorimetric titrations.

It is well-known that the addition of salts influences the properties of proteins in solution. The essential nature of this phenomenon is far from being fully understood, partly due to the absence of the relevant thermodynamic information. To help fill this gap, in this work isothermal titration calorimetry (ITC) was employed to study the ion-lysozyme association in aqueous buffer solutions at pH = 4.0. ITC curves measured for NaCl, NaBr, NaI, NaNO3, NaSCN, KCl, CaCl2, and BaCl2 salts at three different temperatures were described by a model assuming two sets of independent binding sites on the lysozyme. The resulting thermodynamic parameters of binding of anions (counterions) to the first class of sites (N approximately 7) indicate that the binding constant (K approximately 102 M-1) increases in the order Cl- < Br- < I- < NO3- < SCN-. The anion-lysozyme association is entropy driven, accompanied by a small favorable enthalpy contribution and a positive change in heat capacity. It seems that the entropy and heat capacity increase is due to the water released upon binding, while the net exothermic effect originates from the anion-NH3+ pair formation. Moreover, the results reveal that the nature of the cation has little effect on the thermodynamics of the anion-lysozyme association under the given experimental conditions. Taken together, it seems that the observed thermodynamics of association is a result of a combination of both electrostatic and short-range interactions. The anion ordering reflects the strength of water mediated interactions between anions and lysozyme.

Osmotic Pressure, Small-Angle X-Ray, and Dynamic Light Scattering Studies of Human Serum Albumin in Aqueous Solutions.

Osmotic pressure measurements of human serum albumin (HSA) dissolved in water and in 0.01, 0.1, and 1.0 M phosphate buffer are reported as a function of the protein concentration. Two different forms of the protein were studied: defatted HSA (HSA1) and HSA with fatty acids (HSA2). The measured values of the osmotic coefficient were well below 1, indicating large deviations from ideality even for dilute protein solutions. The measured values increased with increasing HSA concentration and the increase was a function of pH. For higher concentrations of added phosphate buffer, the pH of solution had less influence on the measured osmotic pressure. The osmotic pressure of HSA1 in water was found to be considerably lower than that of the HSA2 modification. This effect was ascribed to formation of dimers in the HSA1 solution. The osmotic measurements were complemented by the small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) studies of dilute HSA solutions in water. The SAXS and DLS data confirmed the dimerization of HSA1 molecules under these conditions. Detailed analysis of the SAXS data suggested a parallel orientation of two protein molecules in a dimer. Copyright 2001 Academic Press.