"Three-dimensional hybridization" with polyvalent DNA-gold nanoparticle conjugates

We have determined the minimum number of base pairings necessary to stabilize DNA-Au NP aggregates as a function of salt concentration for particles between 15 and 150 nm in diameter. Significantly, we find that sequences containing a single base pair interaction are capable of effecting hybridization between 150 nm DNA-Au NPs. While traditional DNA hybridization involves two strands interacting in one dimension (1D, Z), we propose that hybridization in the context of an aggregate of polyvalent DNA-Au NP conjugates occurs in three dimensions (many oligonucleotides oriented perpendicular to the X, Y plane engage in base pairing), making nanoparticle assembly possible with three or fewer base pairings per DNA strand. These studies enabled us to compare the stability of duplex DNA free in solution and bound to the nanoparticle surface. We estimate that 4-8, 6-19, or 8-33 additional DNA bases must be added to free duplex DNA to achieve melting temperatures equivalent to hybridized systems formed from 15, 60, or 150 nm DNA-Au NPs, respectively. In addition, we estimate that the equilibrium binding constant (K(eq)) for 15 nm DNA-Au NPs (3 base pairs) is approximately 3 orders of magnitude higher than the K(eq) for the corresponding nanoparticle free system.     

Electrode screening by ionic liquids

In this work we are concerned with the short-range screening provided by the ionic liquid dimethylimidazolium chloride near a charged wall. We study the free energy profiles (or potentials of mean force) for charged and neutral solutes as a function of distance from a charged wall. Four different wall charge densities are used in addition to a wall with zero charge. The highest magnitude of the charge densities is ±1 e nm(-2) which is close to the maximum limit of charge densities accessible in experiments, while the intermediate charges ±0.5 e nm(-2) are in the range of densities typically used in most of the experimental studies. Positively and negatively charged solutes of approximately the size of a BF ion and a Cl(-) ion are used as probes. We find that the ionic liquid provides excellent electrostatic screening at a distance of 1-2 nm. The free energy profiles show minima which are due to layering in the ionic liquid near the electrodes. This indicates that the solute ions tend to displace ionic liquid ions in the layers when approaching the electrode. The important role of non-electrostatic forces is demonstrated by the oscillations in the free energy profiles of uncharged solutes as a function of distance from the wall.     

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.     

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-Hu?ckel 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.     

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.     

Is a small number of charge neutralizations sufficient to bend nucleosome core DNA onto its superhelical ramp?

X-ray diffraction structures of the nucleosome core particle along with a variety of experiments are consistent with the idea that an important source of the free energy holding DNA to the superhelical ramp on the histone octamer surface is obtained from a relatively small amount of electrostatic neutralization of the DNA phosphate charge by positively charged histone groups, especially arginine residues. Here we present a theoretical analysis of a simple model that emphasizes the competition between the high degree of bending of the stiff DNA molecule required for its tight curvature on the histone octamer and the neutralization of the DNA phosphate charge by basic histone residues. Our calculation accounts for the strong influence of condensed counterions on the electrostatic interactions. We find that the minimum amount of free energy required to bend DNA into axial conformity with the superhelical ramp at physiological salt concentration can be provided by a scant 6% neutralization of the phosphate charge, in close correspondence to the stoichiometric neutralization of phosphate charge by the arginine side chain that intrudes into the inward-facing minor groove of each DNA double helical turn.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

Modeling the surface charge evolution of spherical nanoparticles by considering dielectric discontinuity effects at the solid/electrolyte solution interface

It is well known that the electrostatic repulsions between charges on neighboring sites decrease the effective charge at the surface of a charged nanoparticle (NP). However, the situation is more complex close to a dielectric discontinuity, since charged sites are interacting not only with their neighbors but also with their own image charges and the image charges of all neighbors. Titrating site positions, solution ionic concentration, dielectric discontinuity effects, and surface charge variations with pH are investigated here using a grand canonical Monte Carlo method. A Tanford and Kirkwood approach is used to calculate the interaction potentials between the discrete charged sites. Homogeneous, heterogeneous, and patch site distributions are considered to reproduce the various titrating site distributions at the solid/solution interface of spherical NPs. By considering Coulomb, salt, and image charges effects, results show that for different ionic concentrations, modifications of the dielectric constant of NPs having homogeneous and heterogeneous site distributions have little effect on their charging process. Thus, the reaction field, due to the presence of image charges, fully counterbalances the Coulomb interactions. This is not the case for patch distributions, where Coulomb interactions are not completely counterbalanced by the reaction field. Application of the present model to pyrogenic silica is also performed and comparison is made with published experimental data of titration curves at various ionic concentrations.     

The Electrostatic Interaction of a Charged Particle with a Surface: The Effect of Surface Charge Rearrangement

In this paper we investigate the electric interaction between a charged particle and a surface in which the charged ions are capable of moving in response to the electric potential disturbance caused by the approach of the charged particle. Such surfaces include ionic surfactants distributed in air-water interface and charged lipids in bilayer membranes. On the basis of the mean field theory, the free energy of the system, which includes the electrostatic internal energy and the entropy of the mobile ions and surface ions, can be written down. The surface charge-potential relation is then derived by the calculus of variation. When the potential disturbance is small enough, a linear charge regulation model is obtained. The interaction energy associated with a long rod parallel to the interface is studied and an analytical expression is obtained. When a rod approaches an oppositely charged surface, the interaction can change from attraction to repulsion, depending on the ratio of the characteristic regulation length to the Debye length. At low surface charge density, the surface behaves as under the condition of constant charge density and acts as that of constant potential for high enough charge density. Copyright 2001 Academic Press.     

Interaction of nanometric clay platelets

The free energy of interaction between two nanometric clay platelets immersed in an electrolyte solution has been calculated using Monte Carlo simulations as well as direct integration of the configurational integral. Each platelet has been modeled as a collection of charged spheres carrying a unit charge the face of a platelet contains negative charges, and the edge, positive charges. The calculations predict that a configuration of "overlapping coins" is the global free energy minimum at intermediate salt concentrations (10-100 mM). A second weaker minimum, corresponding to the well-known "house of cards" configuration, also appears in this salt interval. At low salt concentrations the electrostatic repulsion dominates, while at intermediate concentrations electrostatic interactions alone can create a net attraction between the platelets. At sufficiently high salt content (>200 mM), the van der Waals interaction takes over and the net interaction becomes attractive at essentially all separations. From the calculated free energy and its derivative, we can derive a yield stress and elasticity modulus in fair agreement with experiment. The roughness of the platelets affects the quantitative behavior of the free energy of interaction but does not alter the results in a qualitative way. From the variation of the free energy of interaction, we would tentatively describe the phase behavior as follows: At low salt, the interaction is strongly repulsive and the dispersion should appear as a solid ("repulsive gel"). With increasing salt concentration, the repulsion is weakened and a liquid phase appears ("sol"). A further increase of the salt content leads a second solid phase ("attractive gel") governed by attractive interactions between the platelets. Finally, at sufficiently high salinity, the clay precipitates due to van der Waals forces.     

Adhesion between a charged particle in an electrolyte solution and a charged substrate: Electrostatic and van der Waals interactions

The equilibrium separation between a charged particle in an electrolyte solution and a substrate with an initially uniform surface charge density is obtained using the classical Derjaguin-Landau-Verwey-Overbeek theory. The electrostatic free energy is obtained by coupling the electric response of the substrate with the electric potential obtained from the solution of the Debye-Hückel equation. The van der Waals free energy is calculated by integrating the 6-12 Lennard-Jones potential. Metallic, dielectric, and semiconducting substrates are considered in turn. At low ionic strength, our results demonstrate a distinct response to the charged particle in each case. For example, in the case of a metallic substrate, the attached state (corresponding to equilibrium separation at short range) is always close to the van der Waals energy minimum. In addition, the application of a surface charge of sign opposite to that of the particle facilitates the transition from the detached state (corresponding to large separation at which the interaction between the particle and the substrate is negligible) to the attached state but scarcely changes the equilibrium separation. In the case of a dielectric substrate, the attached state is located at a distance of around two orders of magnitude larger than that for a metallic substrate and this equilibrium separation decreases as the (opposing) surface charge increases. A semiconducting substrate can behave either like a metal or like a dielectric, depending on the ratio of its Debye length to that of the electrolyte solution.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Adsorption of heterogeneously charged nanoparticles on a variably charged surface by the extended surface complexation approach: charge regulation, chemical heterogeneity, and surface complexation

Adsorption of randomly branched polyelectrolytes, "hairy" particles and internally structured macromolecules, collectively denoted as heterogeneously charged nanoparticles, on charged surfaces is important in many technological and natural processes. In this paper, we will focus on (1) the charge regulation of both the nanoparticle and the surface and (2) the surface complexation between the particle functional groups and the surface sites and will theoretically study the adsorption using the extended surface complexation approach. The model explicitly considers the electrochemical potential of a nanoparticle with an average (smeared-out) structure and charge both in bulk solution and on the surface to obtain the equilibrium adsorption. The chemical heterogeneity of the particle is described by a distribution of the protonation constant. Detailed analysis of the chemical potential of the adsorbed nanoparticle reveals that the pH and salt dependence of the adsorption can be largely explained by the balance between an energy gain resulting from the particle and surface charge regulation and the surface complexation and an energy loss from the unfavorable interparticle electrostatic repulsion close to the surface. This conclusion is also supported by the strong impacts that the chemical heterogeneity of the particle functional groups, the magnitude of the surface complexation, the number of the functional groups, and the size of the particle have on the adsorption.     

Effect of thermodiffusion on pH‐regulated surface charge properties of nanoparticle

Surface properties of nanoparticle are of high importance in the field of biotechnology, drug delivery and micro/nanofabrication. In this article, we developed a comprehensive theoretical model and subsequently solved that numerically to study the effect of thermodiffusion of ions on surface charge properties of nanoparticle. The theoretical study has been done considering silica nanoparticle for two aqueous solutions NaCl and KCl. The effect of solution pH in conjunction with nanoparticle temperature on surface charge density has been obtained for different salt concentrations (1, 10 and 100 mM) and nanoparticle size (diameter of 2 and 100 nm). It is observed from the results that with increasing temperature of the nanoparticle, the negative surface charge density gets higher due to increasing thermodiffusion effect. It is also found out that the magnitude of surface charge density is higher for KCl solution than NaCl solution under same condition which is attributed mostly due to less thermodiffusion of counterions for KCl than NaCl. Present study also shows that magnitude of surface charge density decreases with increasing nanoparticle size until it reaches a limiting value (called critical size) above which the effect of nanoparticle size on surface charge density is insignificant.     

表面电荷对聚乙二醇修饰金纳米粒子生物行为的影响

利用硫-金键将末端修饰甲氧基、氨基或羧基的巯基化聚乙二醇(Thiolated polyethylene glycol,HS-PEG)分子分别组装到金纳米粒子表面, 合成了3种带有不同表面电荷的聚乙二醇修饰金纳米粒子(PEGylated gold nanoparticles,PEG-Au NP).细胞共培养和小鼠尾静脉注射实验结果表明,表面电荷能够显著影响PEG-Au NP的生物行为.细胞对PEG-Au NP的吞噬量遵循正电荷＞电中性＞负电荷的规律.尾静脉注射的PEG-Au NP能够随小鼠的血液循环由全器官分布逐渐向肝脾转移.表面带负电荷的PEG-Au NP较难被小鼠肝脾清除,带但正电荷的PEG-Au NP能够引起小鼠免疫系统较强的响应.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

Electrostatic interactions of charged dipolar proteins in reverse micelles

The electrostatic interactions in a reverse micelle containing a small-ionized protein are studied by Monte Carlo simulation. The electrostatic contribution to the potential of mean force of the protein in the reverse micelle is determined for a neutral protein, a uniformly charged protein, and a uniformly charged protein with a dipole moment. The effect of addition of a simple electrolyte is studied. While symmetrically distributed micellar charge exerts no force on enclosed ionic species, the protein is driven to the micellar wall due to interactions with simple ions. Protein binding to the inner wall of the micelle can be regulated by added salt. The presence of a dipole drives the protein further to the wall. These effects are studied for several proteins characterized by different charges and dipole moments. For a weakly charged protein with a strong dipole moment the contribution of dipolar interaction to the free energy can represent a major driving force for protein solubilization in the microemulsion.     

Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n_max ∼ σ^4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ² when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ^2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m_c ∼ bσ^1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004