Van der Waals forces. Special characteristics in lipid-water systems and a general method of calculation based on the Lifshitz theory

A practical method for examining and calculating van der Waals forces is derived from Lifshitz'' theory. Rather than treat the total van der Waals energy as a sum of pairwise interactions between atoms, the Lifshitz theory treats component materials as continua in which there are electromagnetic fluctuations at all frequencies over the entire body. It is necessary in principle to use total macroscopic dielectric data from component substances to analyze the permitted fluctuations; in practice it is possible to use only partial information to perform satisfactory calculations. The biologically interesting case of lipid-water systems is considered in detail for illustration. The method gives good agreement with measured van der Waals energy of interaction across a lipid film. It appears that fluctuations at infrared frequencies and microwave frequencies are very important although these are usually ignored in preference to UV contributions. “Retardation effects” are such as to damp out high frequency fluctuation contributions; if interaction specificity is due to UV spectra, this will be revealed only at interactions across <200 angstrom (A). Dependence of van der Waals forces on material electric properties is discussed in terms of illustrative numerical calculations.     

Binding to δ and μ opioid receptors by deltorphin I/II analogues modified at the Phe and Asp/Glu side chains: a report of 32 new analogues and a QSAR study

The synthesis and binding affinities of 32 X³Gly⁴ dual-substitution analogues of the natural opioid heptapeptides deltorphin I and II are reported. A multiple regression QSAR analysis was performed using those results along with literature data for the X³Asp⁴ and Phe³X⁴ side chain analogues. Fitting to a three-term potential well model with hydrophobic and van der Waals attraction terms and a steric repulsion term indicates that the δ and μ receptor sites for binding the residue three side chain are similar, and that the binding interaction is primarily van der Waals and secondarily hydrophobic. Further analysis indicates that both sites are more constrained with respect to side chain length than width or thickness, and the μ site appears to be somewhat larger. A binding model consistent with these findings pictures the native third residues Phe ring laying on a step notched out of the receptor surface, pointing toward the back (riser) of the step, and sandwiched between the receptor and ligand. However, the binding sites for the residue four side chains are quite different on δ and μ receptors. Binding to the δ site appears to involve both electrostatic attraction (probably to a partial positive charge) and van der Waals attraction, but not necessarily hydrogen bonding, and more constraint with respect to side chain length than width or thickness. In contrast, there is no evidence for any kind of binding attraction between the side chain of residue four and the μ site, which acts more as steric repulsion site, as though the space that is a pocket on the δ receptor is filled in on the μ receptor. A regression model based only on steric repulsion by van der Waals bulk and/or the effective bulk of a hydration layer accounts for over 80% of the residue four related variation in μ affinity.

Abstract

Thirty-two new X³Gly⁴ analogues of deltrophin I/II opioid peptides are described. A QSAR study of the X³Gly⁴, X³Asp⁴, and Phe³X⁴ analogue series using a potential well model reveals the roles of hydrophobic, van der Waals, electrostatic, hydrogen bonding and steric interactions in δ and μ receptor binding of X³ and X⁴ side chains.     

Van der Waals Forces Between Plasmonic Nanoparticles

We propose a new approach to calculate van der Waals forces between nanoparticles where the van der Waals energy can be reduced to the energy of localized plasmons in nanoparticles. The general theory is applied to describe the interaction between two metallic nanoparticles and between a nanoparticle and a perfectly conducting plane. Our results could be used to prove experimentally the existence of new, recently predicted type of plasmon oscillation (Klimov and Guzatov, Phys Rev B 75:024303, 2007a; Klimov and Guzatov, Quantum Electron 37:209, 2007b) and to elaborate new control mechanisms for the adherence of nanoparticles between each other or onto surfaces.     

Interrod forces in aqueous gels of tobacco mosaic virus.

The lateral separation of virus rod particles of tobacco mosaic virus has been studied as a function of externally applied osmotic pressure using an osmotic stress technique. The results have been used to test the assumption that lattice equilibrium in such gels results from a balance between repulsive (electrostatic) and attractive (van der Waals and osmotic) forces. Results have been obtained at different ionic strengths (0.001 to 1.0 M) and pH's (5.0 to 7.2) and compared with calculated curves for electrostatic nad van der Waals pressure. Under all conditions studied, interrod spacing decreased with increasing applied pressure, the spacings being smaller at higher ionic strengths. Only small differences were seen when the pH was changed. At ionic strengths near 0.1 M, agreement between theory and experiment is good, but the theory appears to underestimate electrostatic forces at high ionic strengths and to underestimate attractive forces at large interrod spacings (low ionic strengths). It is concluded that an electrostatic-van der Waals force balance can explain stability in tobacco mosaic virus gels near physiological conditions and can provide a good first approximation elsewhere.     

Novel homodimer model of the β-adrenergic receptor in complex with free fatty acids and cholesterol: first-principles calculation studies

We propose a theoretical novel homodimer model of the β- adrenergic receptor (βAR) in complex with a heterogeneous mixture of free fatty acids (FFAs) and cholesterol based on first-principles calculations. We used the density-functional-based tight binding with dispersion (DFTB-D) method, which accurately evaluates van der Waals interactions between FFAs and amino acid residues in the receptor. The calculations suggest that a stable homodimer of bAR can form a complex with FFAs and cholesterol by extensive van der Waals interactions in the cell membrane, and that the heterogeneous composition of the FFAs is important for the stability of the homodimer complex. The stable van der Waals interactions propagate from one of the bAR to the other through the cholesterol and FFAs in the homodimer complex. The energy propagation in the complex has the potential to enhance molecular signaling in adipocytes, because the stability of the complex can influence anti-adiposity effects after oral treatment of the FFA components.     

Long range intermolecular forces between macroscopic bodies: macroscopic and microscopic approaches.

Van der Waals energies of interaction are calculated by two methods, the macroscopic method of Lifshitz and the microscopic method of London-Casimir and Polder-Hamaker for the case of two semi-infinite slabs separated by a thin film. When retardation effects may be neglected, the London-Hamaker approach yields values of dispersion interactions which almost coincide with those of the Lifshitz approach, the magnitude of the former values being larger by approximately 10–25%, which is attributed to the effect of the molecular environment in condensed media. At 50–100 Å film thicknesses where retardation effects are small, dispersion terms are generally the major part of van der Waals forces in the Lifshitz formulation. Hence, for 50–100 Å film thicknesses the Hamaker approach, which only includes dispersion interactions is generally adequate. By accounting for retardation effects, which significantly reduce the magnitude of dispersion interactions at several hundred Å, there is a reasonable agreement between the values obtained by the macroscopic and microscopic approaches. When polar substances are present and for film thicknesses of several hundred Å, where dispersion interactions are significantly reduced, the major contribution to van der Waals forces may arise from orientation and induction terms. For such cases the Hamaker approach may lead to critical underestimates of the calculated magnitude of van der Waals forces. An ad hoc way to overcome this difficulty which is applicable to any geometry is proposed. This study presents a simple procedure for the determination of free energies of interaction between macroscopic bodies of various shapes. The procedure, which is applicable when the molecules of bodies and surrounding medium are isotropic, yields results which closely approximate those obtained with the Lifshitz theory.     

The structures of solvated methylmercury(II) chlolade,bromide and iodide in pyridine solution; Implications for aqueous solution

The structures of solvated methylmercury(II) halides in pyridine solution were determined by a large angle X-ray scattering technique. Near-linear CH₃HgX (X = Cl, Br and I) species solvated by two weakly-coordinated pyridine molecules are indirectly interpreted. Additional mercury-pyridine interactions, through van der Waals forces, are found at the sum of the van der Waals radii. The HgX bond distances in the methylmercury(II) halides are found to be 2.325(8), 2.480(3) and 2.649(3) Å for chloride, bromide and iodide, respectively. The HgC bond distances are assumed to be ∼2.08 Å. This interaction is indicated in the radial distribution functions. The bond distance between mercury and the two solvating pyridine molecules is ∼2.8 Å, e.g., 2.84(2) Å in methylmercury(II) bromide. The additional mercury interactions with roughly two pyridine molecules at the sum of van der Waals radii are revealed at around 3.15 Å. Comparison between Raman stretching vibrations and the solvated structures of methylmercury(II) complexes found in various solvents indicates a lower limit in solvent donor property for the formation of solvate bonds to mercury for the methylmercury(II) halides.     

Direct measurements of forces between phosphatidylcholine and phosphatidylethanolamine bilayers in aqueous electrolyte solutions

We report direct measurements of the full interbilayer force laws (force vs. distance) between bilayers of various phosphatidylcholines and phosphatidylethanolamine in aqueous solutions. Bilayers were first deposited on molecularly smooth (mica) surfaces and the interbilayer forces then measured at a resolution of 1 A. Three types of forces were identified: attractive van der Waals forces, repulsive electrostatic (double-layer) forces, and (at short range) repulsive steric hydration forces. Double-layer forces, which arise from ion binding, were insignificant in monovalent salt solutions, e.g., NaCl up to 1 M, but were already present in solutions containing millimolar levels of CaCl2 and MgCl2, giving rise to forces in excellent agreement with theory. Ca2+ binds more strongly than Mg2+, and both bind less to lecithin bilayers in the fluid state (T greater than Tc). The plane of charge coincides with the location of the negative phosphate groups, while the effective plane of origin of the van der Waals force is 4-5 A farther out. In water, the adhesion energies are in the range 0.10-0.15 erg/cm2 for lecithins and approximately 0.8 erg/cm2 for phosphatidylethanolamine. The adhesion energies vary on addition of salt due to changes in the repulsive double-layer and hydration forces rather than to a change in the attractive van der Waals force. The short-range repulsive forces which balance the van der Waals force at separations of 10-30 A are due to a combination of hydration and steric repulsions, the latter arising from thermal motions of head groups and thickness fluctuations of fluid bilayers (above Tc). It is also concluded that bilayer fusion is not simply related to the interbilayer force law.     

Many-atom van der Waals interactions lead to direction-sensitive interactions of covalent bonds

Strict physical theory and numerical calculations show that a specific coupling of many-atom van der Waals interactions with covalent bonding can significantly (half as much) increase the strength of attractive dispersion interactions when the direction of interaction coincides with the direction of the covalent bond, and decrease this strength when the direction of interaction is perpendicular to the direction of the covalent bond. The energy effect is comparable to that caused by the replacement of atoms (e.g. N by C or O) in conventional pairwise van der Waals interactions. Analysis of protein structures shows that they bear an imprint of this effect. This means that many-atom van der Waals interactions cannot be ignored in refinement of protein structures, in simulations of their folding, and in prediction of their binding affinities.     

Numerical Analysis of the Adhesive Forces in Nano-Scale Structure

Nanohairs, which can be found on the epidermis of Tokay gecko＇s toes, contribute to the adhesion by means of van der Waals force, capillary force, etc. This structure has inspired many researchers to fabricate the attachable nano-scale structures. However, the efficiency of artificial nano-scale structures is not reliable sufficiently. Moreover, the mechanical parameters related to the nano-hair attachment are not yet revealed qualitatively. The mechanical parameters which have influence on the ability of adhesive nano-hairs were investigated through numerical simulation in which only van der Waals force was considered. For the numerical analysis, finite element method was utilized and van der Waals force, assumed as 12-6 Lennard-Jones potential, was implemented as the body force term in the finite element formulation.     

Morphology of modified regenerated model cellulose II surfaces studied by atomic force microscopy: effect of carboxymethylation and heat treatment

Model cellulose II surfaces with different surface charge have been prepared from carboxymethylated wood pulp. AFM tapping-mode imaging in air showed that the introduction of charged groups into the film does not appreciably change the surface morphology. However, after a mild heat treatment (heating at 105 degrees C for 6 h), an irreversible surface structure change, from near spherical-type aggregates to a fibrillar structure, was observed. This might be attributed to the formation of strong hydrogen bonds in the crystalline region of the films while the amorphous regions shrank upon drying. The suitability of these charged cellulose films for surface forces studies was also investigated. At pH below the pK(a) of the carboxyl groups present in the film, the interaction force could be fit by a van der Waals force interaction. At higher pH, the interaction was of a purely electrostatic nature with no van der Waals component observable due to the swelling of the surfaces.     

Swelling of phospholipids by monovalent salt

Critical to biological processes such as membrane fusion and secretion, ion-lipid interactions at the membrane-water interface still raise many unanswered questions. Using reconstituted phosphatidylcholine membranes, we confirm here that multilamellar vesicles swell in salt solutions, a direct indication that salt modifies the interactions between neighboring membranes. By varying sample histories, and by comparing with data from ion carrier-containing bilayers, we eliminate the possibility that swelling is an equilibration artifact. Although both attractive and repulsive forces could be modified by salt, we show experimentally that swelling is driven primarily by weakening of the van der Waals attraction. To isolate the effect of salt on van der Waals interactions, we focus on high salt concentrations at which any possible electrostatic interactions are screened. By analysis of X-ray diffraction data, we show that salt does not alter membrane structure or bending rigidity, eliminating the possibility that repulsive fluctuation forces change with salt. By measuring changes in interbilayer separation with applied osmotic stress, we have determined, using the standard paradigm for bilayer interactions, that 1 M concentrations of KBr or KCl decrease the van der Waals strength by 50%. By weakening van der Waals attractions, salt increases energy barriers to membrane contact, possibly affecting cellular communication and biological signaling.     

Measuring electrostatic, van der Waals, and hydration forces in electrolyte solutions with an atomic force microscope

In atomic force microscopy, the tip experiences electrostatic, van der Waals, and hydration forces when imaging in electrolyte solution above a charged surface. To study the electrostatic interaction force vs distance, curves were recorded at different salt concentrations and pH values. This was done with tips bearing surface charges of different sign and magnitude (silicon nitride, Al₂O₃, glass, and diamond) on negatively charged surfaces (mica and glass). In addition to the van der Waals attraction, neutral and negatively charged tips experienced a repulsive force. This repulsive force depended on the salt concentration. It decayed exponentially with distance having a decay length similar to the Debye length. Typical forces were about 0.1 nN strong. With positively charged tips, purely attractive forces were observed. Comparing these results with calculations showed the electrostatic origin of this force.

In the presence of high concentrations (> 3 M) of divalent cations, where the electrostatic force can be completely ignored, another repulsive force was observed with silicon nitride tips on mica. This force decayed roughly exponentially with a decay length of 3 nm and was ~0.07-nN strong. This repulsion is attributed to the hydration force.

     

Adhesion of the positively charged bacterium Stenotrophomonas (Xanthomonas) maltophilia 70401 to glass and Teflon.

Medical implants are often colonized by bacteria which may cause severe infections. The initial step in the colonization, the adhesion of bacteria to the artificial solid surface, is governed mainly by long-range van der Waals and electrostatic interactions between the solid surface and the bacterial cell. While van der Waals forces are generally attractive, the usually negative charge of bacteria and solid surfaces leads to electrostatic repulsion. We report here on the adhesion of a clinical isolate, Stenotrophomonas maltophilia 70401, which is, at physiological pH, positively charged. S. maltophilia has an electrophoretic mobility of +0.3 x 10(-8) m2 V-1 s-1 at pH 7 and an overall surface isoelectric point at pH 11. The positive charge probably originates from proteins located in the outer membrane. For this bacterium, both long-range forces involved in adhesion are attractive. Consequently, adhesion of S. maltophilia to negatively charged surfaces such as glass and Teflon is much favored compared with the negatively charged bacterium Pseudomonas putida mt2. While adhesion of negatively charged bacteria is impeded in media of low ionic strength because of a thick negatively charged diffuse layer, adhesion of S. maltophilia was particularly favored in dilute medium. The adhesion efficiencies of S. maltophilia at various ionic strengths could be explained in terms of calculated long-range interaction energies between S. maltophilia and glass or Teflon.     

A statistical mechanical treatment of fatty acyl chain order in phospholipid bilayers and correlation with experimental data. A. Theory

A theoretical model has been developed in order to describe the organization of acyl chains in phospholipid bilayers. Since the model is intended to reproduce highly quantitative experimental results such as the deuterium magnetic resonance (NMR) data and to supplement the experimental information, all the rotameric degrees of freedom, the excluded volume interactions and the van der Waals interactions have been considered. The model is a direct extension of a generalized van der Waals theory of nematic liquid crystals to flexible molecules. In this picture, the anisotropy of the short-range repulsive forces which are treated by a hard core potential is introduced as the dominant factor governing intrinsic order among the chains. The anisotropy of the attractive forces, which are approximated by a molecular field, plays a somewhat secondary role. The dependence of the energy of interaction on the relative chain conformations is approximated by two order parameters reflecting respectively the ‘average shape’ of the molecules and the ‘average shape’ in a ‘mean orientation’. The influence of the interactions in the polar region on the lateral chain area is accounted for by an effective lateral pressure. In certain aspects the model has features in common with the Mar?elja theory.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Molecular mechanical perspective on halogen bonding

The nature and strength of halogen bonding in halo molecule-Lewis base complexes were studied in terms of molecular mechanics using our recently developed positive extra-point (PEP) approach, in which the σ-hole on the halogen atom is represented by an extra point of positive charge. The contributions of the σ-hole (i.e., positively charged extra point) and the halogen atom to the strength of this noncovalent interaction were clarified using the atomic parameter contribution to the molecular interaction (APCtMI) approach. The molecular mechanical results revealed that the halogen bond is electrostatic and van der Waals in nature, and its strength depends on three types of interaction: (1) the attractive electrostatic interaction between the σ-hole and the Lewis base, (2) the repulsive electrostatic interaction between the negative halogen atom and the Lewis base, and (3) the repulsive/attractive van der Waals interactions between the halogen atom and the Lewis base. The strength of the halogen bond increases with increasing σ-hole size (i.e., magnitude of the extra-point charge) and increasing halogen atom size. The van der Waals interaction's contribution to the halogen bond strength is most favorable in chloro complexes, whereas the electrostatic interaction is dominant in iodo complexes. The idea that the chloromethane molecule can form a halogen bond with a Lewis base was revisited in terms of quantum mechanics and molecular mechanics. Although chloromethane does produce a positive region along the C-Cl axis, basis set superposition error corrected second-order M?ller-Plesset calculations showed that chloromethane-Lewis base complexes are unstable, producing halogen-Lewis base contacts longer than the sum of the van der Waals radii of the halogen and O/N atoms. Molecular mechanics using the APCtMI approach showed that electrostatic interactions between chloromethane and a Lewis base are unfavorable owing to the high negative charge on the chlorine atom, which overcomes the corresponding favorable van der Waals interactions.     

Molecular dynamics simulations of carbon nanotube oscillators deformed by encapsulated copper nanowires

Pure carbon nanotube (CNT) oscillators are compared to the corresponding CNT oscillators encapsulating copper nanowires (Cu@CNTs) by molecular dynamics simulations. The classical oscillation theory provides a fairly good estimate of the mass dependence of the operating frequency when the CNT surface is not deformed by the Cu nanowire. The structural deformations of the CNT induced by the encapsulated copper nanowire have a greater effect on the oscillation frequency than the mass of the copper nanowire. The excess forces of the Cu@CNT oscillator are slightly higher than those of the CNT oscillator and the excess van der Waals forces induced by the inter-wall interactions are 17 times higher than the excess forces induced by the Cu nanowire–CNT interactions.     

A Minimal or Concise Set of Definition of Life is Not Useful

The binding of ciprofloxacin to lysozyme in the presence of three Ag nano-particles of varying sizes was for the first time investigated by multispectroscopic and isothermal titration calorimetry techniques at pH 7.4. The results indicated that ciprofloxacin quenched the fluorescence intensity of lysozyme through a static mechanism but in the presence of size-II Ag nano-particles, there were two kinds of interaction behaviors. The interaction between ciprofloxacin and lysozyme occurred via a second type of binding site, whereas in the presence of the Ag nano-particles, some changes occurred. The secondary structure of lysozyme–ciprofloxacin in the presence of Ag nano-particles was determined by circular dichroism. The thermodynamic parameters of the interaction between ciprofloxacin and lysozyme in the presence of Ag nano-particles were measured according to the van’t Hoff equation. The enthalpy (ΔH^○) and entropy (ΔS^○) changes were calculated to be ?49.7 (kJ?mol^?1) and ?20.1 (J?mol^?1?K^?1), respectively, which indicated that the interaction of ciprofloxacin with lysozyme was driven mainly by van der Waals forces and hydrogen bonding. In the presence of the three different-sized Ag nano-particles, the enthalpic and the entropic changes were both negative which indicated that hydrogen bonding with van der Waals forces played major roles in the binding between ciprofloxacin and lysozyme. Recent developments in nano-materials offer new pathways for controlling the protein behavior through surface interactions. These data indicate that the recent research on nano-particle/protein interactions will emphasize the importance of such interactions in biological systems with applications including the diagnosis and treatment of human diseases.     

CH/π interactions in the crystal structure of class I MHC antigens and their complexes with peptides

The crystal structure of class I major histocompatibility complex antigens (MHC) bound to their specific ligand peptides were analyzed, in the context of the CH/π interaction, with use of a computer program CHPI. A number of short CH/C_sp² distances have been shown at the boundary of the heavy chain and β2 microglobulin. These interactions are conserved between species, human versus murine. A number of contacts shorter than the conventional van der Waals distance have been disclosed between CH hydrogens and aromatic side-chain groups in the MHC/peptide complexes. The CH/π interaction has been suggested to contribute to the specificity in the complex formation of class I MHC.