Molecular hydrophobic attraction and ion-specific effects studied by molecular dynamics

Much is written about "hydrophobic forces" that act between solvated molecules and nonpolar interfaces, but it is not always clear what causes these forces and whether they should be labeled as hydrophobic. Hydrophobic effects roughly fall in two classes, those that are influenced by the addition of salt and those that are not. Bubble adsorption and cavitation effects plague experiments and simulations of interacting extended hydrophobic surfaces and lead to a strong, almost irreversible attraction that has little or no dependence on salt type and concentration. In this paper, we are concerned with hydrophobic interactions between single molecules and extended surfaces and try to elucidate the relation to electrostatic and ion-specific effects. For these nanoscopic hydrophobic forces, bubbles and cavitation effects play only a minor role and even if present cause no equilibration problems. In specific, we study the forced desorption of peptides from nonpolar interfaces by means of molecular dynamics simulations and determine the adsorption potential of mean force. The simulation results for peptides compare well with corresponding AFM experiments. An analysis of the various contributions to the total peptide-surface interactions shows that structural effects of water as well as van der Waals interactions between surface and peptide are important. Hofmeister ion effects are studied by separately determining the effective interaction of various ions with hydrophobic surfaces. An extension of the Poisson-Boltzmann equation that includes the ion-specific potential of mean force yields surface potentials, interfacial tensions, and effective interactions between hydrophobic surfaces. There, we also analyze the energetic contributions to the potential of mean force and find that the most important factor determining ion-specific adsorption at hydrophobic surfaces can best be described as surface-modified ion hydration.     

The combined simulation approach of atomistic and continuum models for the thermodynamics of lysozyme crystals

We have studied the thermodynamic properties of hen egg white lysozyme crystals using a novel simulation method combining atomistic Monte Carlo simulation to calculate van der Waals interactions and the boundary element method to solve the Poisson-Boltzmann equation for the electrostatic interactions. For computational simplicity, we treat the protein as a rigid body, using the crystallographic coordinates of all non-hydrogen atoms of the protein to describe the detailed shape. NVT Monte Carlo simulations are carried out for tetragonal and orthorhombic crystals to obtain the van der Waals energy, incorporating an implicit solvation effect. For crystal phases, an optimally linearized Poisson-Boltzmann equation is used to include the effect of the Donnan equilibrium of the salt ions. The Helmholtz energy is obtained from expanded ensemble Monte Carlo simulations. By using the force field parameters that had previously been tuned for the solution properties, reasonable agreement with experiment is found for the crystallization energy of the tetragonal form. The prediction of the entropy is also reasonable with a slight underestimation suggesting the release of a few water molecules per protein during the crystallization. However, the predictions of the properties of the orthorhombic crystal are poor, probably due to differences in the solvation structure as indicated by experiments, and also as a result of the approximate force field used.     

Finite volume solution of the modified Poisson-Boltzmann equation for two colloidal particles

The double layer forces between spherical colloidal particles, according to the Poisson-Boltzmann (PB) equation, have been accurately calculated in the literature. The classical PB equation takes into account only the electrostatic interactions, which play a significant role in colloid science. However, there are at, and above, biological salt concentrations other non-electrostatic ion specific forces acting that are ignored in such modelling. In this paper, the electrostatic potential profile and the concentration profile of co-ions and counterions near charged surfaces are calculated. These results are obtained by solving the classical PB equation and a modified PB equation in bispherical coordinates, taking into account the van der Waals dispersion interactions between the ions and both surfaces. Once the electrostatic potential is known we calculate the double layer force between two charged spheres. This is the first paper that solves the modified PB equation in bispherical coordinates. It is also the first time that the finite volume method is used to solve the PB equation in bispherical coordinates. This method divides the calculation domain into a certain number of sub-domains, where the physical law of conservation is valid, and can be readily implemented. The finite volume method is implemented for several geometries and when it is applied to solve PB equations presents low computational cost. The proposed method was validated by comparing the numerical results for the classical PB calculations with previous results reported in the literature. New numerical results using the modified PB equation successfully predicted the ion specificity commonly observed experimentally.     

A model for selective ion adsorption including van der Waals interaction

A model for the selective adsorption phenomenon in an isotropic liquid accounting for a van der Waals interaction between the ions and the surface is presented, in the framework of the Poisson-Boltzmann theory. The fundamental equations governing the electric field distribution are exactly solved for low and high potential regimes.     

The van der Waals interaction between protein molecules in an electrolyte solution

In this report we present a general formulation to calculate the van der Waals interaction between two protein molecules in an electrolyte solution using boundary element method of solving linearized Poisson-Boltzmann equation. Our formulation is based upon an inhomogeneous dielectric model of proteins at the residue level. Our results for bovine pancreatic trypsin inhibitor at various relative orientations indicate that the anisotropy of the interaction can be tens of kBT.     

On possible microscopic origins of the swelling of neutral lipid bilayers induced by simple salts

It was recently suggested that the swelling of neutral multilipid bilayers upon addition of a salt can be simply explained only by the electrolyte screening of the van der Waals attractions, while assuming that the hydration force and the repulsion due to thermal undulations of membranes are unaffected by the salt. While we agree that the screening of the van der Waals interactions plays a role, we suggest that the increase in the hydration force upon addition of a salt has also to be taken into account. In a statistical model, which accounts for the membrane undulations, parameters could be found to explain the multibilayer swelling even when the van der Waals attraction is considered unaffected by the electrolyte screening. These results point out that the decrease by a factor of three of the Hamaker constant upon addition of a salt, suggested recently to be responsible for the swelling of neutral multilipid bilayers, is perhaps too large, and a smaller decrease in Hamaker constant, coupled with the above mentioned effects might explain the swelling.     

Nanoscale electrostatic actuators in liquid electrolytes

Equilibrium and energy analyses were performed for an electrostatic actuator consisting of two plane parallel electrodes, operated using DC voltages, separated by a liquid electrolyte. One electrode is fixed, and the other electrode is connected to a spring and is free to move. The mechanical equilibrium includes the spring force, the van der Waals force, and the electrochemical force as given by the solution of the linearized Poisson-Boltzmann equation. The electrode separation is determined as a function of the applied potential, the natural (i.e., zeta) potential, the Debeye length, the initial electrode separation, the spring constant, and the Hamaker constant. The actuator exhibits the classical "pull-in" instability. The natural potential increases the critical applied potential but does not significantly affect the critical separation. For zero natural potential, the spring constant does not affect the critical separation. Ratios of the maximum spring energy, the maximum van der Waals energy, and the maximum electrochemical energy were plotted as functions of the Hamaker constant and the initial electrode separation.     

Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution

Monte Carlo simulations are used to establish the potential of mean force between two globular proteins in an aqueous electrolyte solution. This potential includes nonelectrostatic contributions arising from dispersion forces first, between the globular proteins, and second, between ions in solution and between each ion and the globular protein. These latter contributions are missing from standard models. The potential of mean force, obtained from simulation, is fitted to an analytic equation. Using our analytic potential of mean force and Barker-Henderson perturbation theory, we obtain phase diagrams for lysozyme solutions that include stable and metastable fluid-fluid and solid-fluid phases when the electrolyte is 0.2 M NaSCN or NaI or NaCl. The nature of the electrolyte has a significant effect on the phase diagram.     

Ion-specific thermodynamic properties of colloids and proteins

Franz Hofmeister established in 1888 that different salt solutions with the same ionic charges have different efficiencies in precipitating proteins from whole egg white. We will discuss how this can be understood from the modified Poisson–Boltzmann equation that accounts for ion specificity via the ion-surface non-electrostatic potential of mean force (NE-PMF) from molecular dynamics simulations. Using this approach, it is at least in principle possible to capture the important physics of the system due to the inclusion of ion-surface van der Waals forces, short range hydration, image potential and different solvent-mediated forces. The method has been proved to be efficient and suitable for describing phenomena where the water structure close to the interface plays an essential role. As an illustrative example, we demonstrate why the double layer force between two gold electrodes coated with hydrophobic self-assembled monolayers in different electrolytes can be highly ion specific. Important thermodynamic properties related to protein aggregation, essential in biotechnology and pharmaceutical industries, can be obtained from the method shown here.     

Neutron scattering from a deformed “vander Waals chain”-quasi Gaussian approximation

We calculate the neutron scattering form of an affinely deformed van der Waals chain, i.e., a labeled chain embedded in a network, whose deformation behavior can be described by an effective van der Waals equation in an effective Gaussian approximation. This provides microscopic information about the deformation behavior of van der Waals networks and complements the macroscopic information given by stress-strain relations.dedicated to Prof H.-G. Kilian on occasion of his 66th birthday     

Finite extensibility and orientational effects in rubbers. A physical interpretation of the ‘van der Waals equation’ for the elastic force

We propose a physical interpretation of the so-called van der Waals equation of state for rubbers, which gives a relation between the force and the deformation. On a phenomenological basis this equation takes the finite extensibility and a non-defined interaction into account. Here the fininte extensibility is discussed for the dilute case (no entanglements) and the highly entangled limit. The intramolecular interactions are described by orientational effects. The resulting equation of state for the force shows the same features as the van der Waals equation.Dedicated to Prof. H.-G. Kilian on the occasion of his 60th birthday.     

Adsorption of ions onto polymer surfaces and its influence on zeta potential and adhesion phenomena

 The adhesion behavior that governs many technologically and biologically relevant polymer properties can be investigated by zeta potential measurements with varied electrolyte concentration or pH. In a previous work [1] it was found that the difference of the adsorption free energies of Cl^- and K⁺ ions correlates with the adhesion force caused by van der Waals interactions, and that the decrease of adhesion strength by adsorption layers can be elucidated by zeta potential measurements. In order to confirm these interrelations, zeta potential measurements were combined with atomic force microscopy (AFM) measurements. Force–distance curves between poly(ether ether ketone) and fluorpolymers, respectively, and the Si₃N₄ tip of the AFM device in different electrolyte solutions were measured and analysed. The adsorption free energy of anions calculated from the Stern model correlates with their ability to prevent the adhesion between the polymer surface and the Si₃N₄ tip of the AFM device. These results demonstrate the influence of adsorption phenomena on the adhesion behavior of solids. The results obtained by AFM confirm the thesis that the electrical double layer of solid polymers in electrolyte solutions is governed by ion adsorption probably due to van der Waals interactions and that therefore van der Waals forces can be detected by zeta potential measurements. Received: 18 November 1997 Accepted: 19 January 1998     

聚苯乙烯在石墨表面吸附的分子动力学模拟

采用分子动力学(MD)模拟方法研究了单链聚苯乙烯(PS)在石墨表面的吸附. 模拟结果表明, 吸附后PS在平行于石墨表面的方向可视为准二维椭圆结构, 并且在此方向上的均方回转半径值(R2∥)与其所含单体数目(N)具有指数关系R2∥-N2v, 指数2v约等于1.04; 最后指出PS吸附过程的主要驱动力为PS链段与表面之间的范德华作用力.     

Specific ion adsorption and surface forces in colloid science

Mean-field theories that include nonelectrostatic interactions acting on ions near interfaces have been found to accommodate many experimentally observed ion specific effects. However, it is clear that this approach does not fully account for the liquid molecular structure and hydration effects. This is now improved by using parametrized ionic potentials deduced from recent nonprimitive model molecular dynamics (MD) simulations in a generalized Poisson-Boltzmann equation. We investigate how ion distributions and double layer forces depend on the choice of background salt. There is a strong ion specific double layer force set up due to unequal ion specific short-range potentials acting between ions and surfaces.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.     

Phase behavior of aqueous solutions containing dipolar proteins from second-order perturbation theory

Due to the interplay of Coulombic repulsion and attractive dipolar and van der Waals interactions, solutions of globular proteins display a rich variety of phase behavior featuring fluid-fluid and fluid-solid transitions that strongly depend on solution pH and salt concentration. Using a simple model for charge, dispersion and dipole-related contributions to the interprotein potential, we calculate phase diagrams for protein solutions within the framework of second-order perturbation theory. For each phase, we determine the Helmholtz energy as the sum of a hard-sphere reference term and a perturbation term that reflects both the electrostatic and dispersion interactions. Dipolar effects can induce fluid-fluid phase separation or crystallization even in the absence of any significant dispersion attraction. Because dissolved electrolytes screen the charge-charge repulsion more strongly than the dipolar attraction, the ionic strength dependence of the potential of mean force can feature a minimum at intermediate ionic strengths offering an explanation for the observed nonmonotonic dependence of the phase behavior on salt concentration. Inclusion of correlations between charge-dipole and dipole-dipole interactions is essential for a reliable calculation of phase diagrams for systems containing charged dipolar proteins and colloids.     

Study on osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions

To investigate the osmotic pressure of non-ionic and ionic surfactant solutions in the micellar and microemulsion regions, a potential of mean force including hard-core repulsion, van der Waals attraction and electric double layer repulsion is proposed to describe the interactions between micelles and between microemulsions. Both van der Waals attraction and electric double layer repulsion are represented using Yukawa tails. The explicit analytical expression of osmotic pressure derived from the first-order mean spherical approximation is implemented by accounting for the Donnan membrane effect. The proposed theory has been applied to micelle solutions of the non-ionic surfactant, n-dodecyl hexaoxyethylene monoether, the cationic surfactant, cetylpyridinium chloride, the anionic surfactant, sodium dodecyl sulfate, and spherical oil-in-water microemulsion system. Successful comparison is made between the proposed theory and the experimental osmotic pressure data for the studied surfactant solutions. Theoretical results show that the long-range electric double layer repulsion dramatically influences the osmotic pressure of both cationic and anionic surfactant solutions in the micellar region. The regressed model parameters such as effective micelle diameter, the mean aggregation number and effective micellar charge are in good agreement with those from static light scattering studies in the literature.     

A supersonic beam ion cyclotron resonance instrument for the study of van der Waals cluster ions

For the study of ionized van der Waals cluster ions an instrument is presented, which consists of a supersonic beam cluster source coupled to an ICR spectrometer with external ion source. The neutral van der Waals clusters are generated by supersonic expansion and ionized by electron impact in the external source. The cluster ions are extracted at right angle to the neutral cluster beam and fly collision-free parallel to the magnetic field direction into the differentially pumped ICR cell. For the ion transfer, an improved lens system is presented. The cluster ion transfer lens system is capable of focusing ions with energies of a few eV perpendicular to the magnetic field direction through the differential pumping orifice. The ions are injected into the ICR cell with a trap barrier pulse, ion accumulation is possible. With this system the first ICR spectra of small cluster ions of carbon dioxide are obtained.