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.     

Plasmonic and Energy Studies of Ag Nanoparticles in Silica-Titania Hosts

The present work reports an investigation of surface plasmon resonance (SPR) of silver nanoparticles in SiO₂–TiO₂ hosts. The surface plasmon resonance of silver nanoparticles was observed in the wavelength range 300–400 nm. Numerical calculation of SPR of silver nanoparticles with spherical morphology was done on the basis of discrete dipole approximation (DDA) method. The observed fluorescence spectrum fits well with the theoretically calculated one. The luminescence enhancement is attributed to the strong local electric field which increases the exciting and emitting photons coupled to SPR. An effort has been made to study the surface plasmon mediated excitation energy transfer (EET) between two spherical metal nanoparticles. The van der Waals (vdW) energy between plasmonic silver nanoparticles in the present hosts has been estimated.     

Temperature-dependent van der Waals forces

Biological systems can experience a strong van der Waals interaction involving electromagnetic fluctuations at the low frequency limit. In lipid-water mixtures the free energy of this interaction is proportional to temperature, primarily involves an entropy change, and has qualitative features of a “hydrophobic bond.” Protein-protein attraction in dilute solution is due as much to low frequency proton fluctuation (Kirkwood-Shumaker forces) and permanent dipole forces as to high frequency (infrared and UV) van der Waals intreactions. These conclusions are described in terms of numerical calculations via the Lifshitz theory of van der Waals forces.     

Van der Waals locks: loop-n-lock structure of globular proteins

In a globular protein the polypeptide chain returns to itself many times, making numerous chain-to-chain contacts. The stability of these contacts is maintained primarily by van der Waals interactions. In this work we isolated and analysed van der Waals contacts that stabilise spatial structures of nine major folds. We suggest a specific way to identify the tightest contacts of prime importance for the stability of a given crystallized protein and introduce the notion of the van der Waals lock. The loops closed by the van der Waals interactions provide a basically novel view of protein globule organization: the loop-n-lock structure. This opens a new perspective in understanding protein folding as well: the consecutive looping of the polypeptide chain and the locking of the loop ends by tight van der Waals interactions.     

On the Role of Density Fluctuations in the Equation of State of a Simple Fluid

Abstract

We address the wellknown problems intorduced into the theory of fluids by density fluctuations in the form of van der Waals loops and nonclassical critical phenomena. A clean separation of long and short range density fluctuations is achieved by use of cell-constrained models which display well-defined van der Waals loops and classical behaviour around the critical point. For a pure Lennard-Jones fluid with occupancy restricted to 1 or 8 particles per cell, the phase diagram is determined by Monte Carlo simulation. By considering the deviations from the normal simulations without cell constraint, the effects of longer range density fluctuations are exposed. The system size dependence of the van der Waals loops present in all simulations of fluids is analyzed in terms of the GvdW free energy density functional theory, which is formuiated on the basis of the cell concept. The loops are found to gradually disappear either with greater cel occupancy or increasing total particle number in the simulation box.     

Stereochemical complementarity of progesterone, RU486 and cavities between base pairs in partially unwound double stranded DNA assessed by computer modeling and energy calculations

Computer modeling was used to examine the relative fit of progesterone and RU486 in cavities constructed between base pairs in double stranded DNA. Progesterone was capable of forming two stereospecific hydrogen bonds between the carbonyl groups and protonated phosphate groups on adjacent strands. Favorable van der Waals and electrostatic energies were exhibited upon insertion of progesterone into DNA indicating an excellent fit. While RU486 could be accommodated between the base pairs and formed hydrogen bonds, there was a high van der Waals energy in the resulting complex. When the complexes were subjected to energy minimization, the conformation of the DNA was significantly altered in the RU486-DNA complex but not in the progesterone-DNA complex. No mechanistic interpretation of these results is proffered; however, such information may have evolutionary significance and could prove useful in designing new progesterone agonists and antagonists.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

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.     

Free-energy force-field three-dimensional quantitative structure–activity relationship analysis of a set of p38-mitogen activated protein kinase inhibitors

The p38-mitogen-activated protein kinases (p38-MAPKs) belong to a family of serine–threonine kinases activated by pro-inflammatory or stressful stimuli that are known to be involved in several diseases. Their biological importance, related to the release of inflammatory pro-cytokines such as tumor necrosis factor-α (TNF-α) and interleukin-1 (IL-1), has generated many studies aiming at the development of selective inhibitors for the treatment of inflammatory diseases. In this work, we developed receptor-based three dimensional (3D) quantitative structure–activity relationship (QSAR) models for a series of 33 pyridinyl imidazole compounds [Liverton et al. (1999) 42:2180], using a methodology named free-energy force-field (FEFF) [Tokarski and Hopfinger (1997) 37:792], in which scaled intra- and intermolecular energy terms of the Assisted Model Building Energy Refinement (AMBER) force field combined with a hydration-shell solvation model are the independent variables used in the QSAR studies. Multiple temperature molecular-dynamics simulations (MDS) of ligand–protein complexes and genetic-function approximation (GFA) were employed using partial least squares (PLS) as the fitting functions to develop FEFF-3D-QSAR models for the binding process. The best model obtained in the FEFF-3D-QSAR receptor-dependent (RD) method shows the importance of the van der Waals energy change upon binding and the electrostatic energy in the interaction of ligands with the receptor. The QSAR equations described here show good predictability and may be regarded as representatives of the binding process of ligands to p38-MAPK. Additionally, we have compared the top FEFF-3D-QSAR model with receptor independent (RI) 4D-QSAR models developed in a recent study [Romeiro et al. (2005) 19:385]. 1 Q_adjusted ² values obtained for the best models with 3 to 6 terms for the FEFF MDS simulation temperatures after GFA-PLS optimization     

The impact of <Emphasis Type="Italic">Trichoderma reesei</Emphasis> Cel7A carbohydrate binding domain mutations on its binding to a cellulose surface: a molecular dynamics free energy study

A critical role of the Family 7 cellobiohydrolase (Cel7A) carbohydrate binding domain (CBD) is to bind to a cellulose surface and increase the enzyme concentration on the surface. Several residues of Trichoderma reesei Cel7A CBD, including Y5, N29, Y31, Y32 and Q34, contribute to cellulose binding, as revealed by early experimental studies. To investigate the interactions between these important residues and cellulose, we applied a thermodynamic integration method to calculate the cellulose–Cel7A CBD binding free energy changes caused by Y5A, N29A, Y31A, Y32A and Q34A mutations. The experimental binding trend was successfully predicted, proving the effectiveness of the complex model. For the two polar residue mutants N29A and Q34A, the changes in the electrostatics are comparable to those of van der Waals, while for three Y to A mutants, the free energy differences mainly come from van der Waals interactions. However, in both cases, the electrostatics dominates the interactions between individual residues and cellulose. The side chains of these residues are rigidified after the complex is formed. The binding free energy changes for the two mutants Y5W and Y31W were also determined, and for these the van der Waals interaction was strengthened but the electrostatics was weakened.     

Calculation of binding affinities of HIV-1 RT and β-secretase inhibitors using the linear interaction energy method with explicit and continuum solvation approaches

The linear interaction energy (LIE) approach has been applied to estimate the binding free energies of representative sets of HIV-1 RT and β-Secretase inhibitors, using both molecular dynamics (MD) and tethered energy minimization sampling protocols with the OPLS-AA potential, using a range of solvation methodologies. Generalized Born (GB), ‘shell’ and periodic boundary condition (PBC) solvation were used, the latter with reaction field (RF) electrostatics. Poisson-Boltzmann (PB) and GB continuum electrostatics schemes were applied to the simulation trajectories for each solvation type to estimate the electrostatic ligand-water interaction energy in both the free and bound states. Reasonable agreement of the LIE predictions was obtained with respect to experimental binding free energy estimates for both systems: for instance, ‘PB’ fits on MD trajectories carried out with PBC solvation and RF electrostatics led to models with standard errors of 1.11 and 1.03 kcal mol⁻¹ and coefficients of determination, r ² of 0.76 and 0.75 for the HIV-1 RT and β-Secretase sets. However, it was also found that results from MD sampling using PBC solvation provided only slightly better fits than from simulations using shell or Born solvation or tethered energy minimization sampling. Figure Evolution of the running averages for compound H11 (binding to HIV-1RT) of the bound state ligand-water and ligand-protein interaction energies. The ligand-water electrostatic terms are twice the corresponding GB and PB electrostatic solvation free energies. The ligand-receptor van der Waals and Coulombic interaction energies are also shown, in addition to the ligand-water van der Waals interaction term. The terms were calculated (without application of a cut-off) from a trajectory sampled under PBC solvation with reaction field electrostatics Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

van der Waals forces influencing adhesion of cells

Adhesion molecules, often thought to be acting by a ‘lock and key’ mechanism, have been thought to control the adhesion of cells. While there is no doubt that a coating of adhesion molecules such as fibronectin on a surface affects cell adhesion, this paper aims to show that such surface contamination is only one factor in the equation. Starting from the baseline idea that van der Waals force is a ubiquitous attraction between all molecules, and thereby must contribute to cell adhesion, it is clear that effects from geometry, elasticity and surface molecules must all add on to the basic cell attractive force. These effects of geometry, elasticity and surface molecules are analysed. The adhesion force measured between macroscopic polymer spheres was found to be strongest when the surfaces were absolutely smooth and clean, with no projecting protruberances. Values of the measured surface energy were then about 35 mJ m⁻², as expected for van der Waals attractions between the non-polar molecules. Surface projections such as abrasion roughness or dust reduced the molecular adhesion substantially. Water cut the measured surface energy to 3.4 mJ m⁻². Surface active molecules lowered the adhesion still further to less than 0.3 mJ m⁻². These observations do not support the lock and key concept.     

On the importance of van der Waals interaction in the groove binding of DNA with ligands: restrained molecular dynamics study

Comparison of interaction energy between an oligonucleotide and a DNA-binding ligand in the minor and major groove modes was made by use of restrained molecular dynamics. Distortion in DNA was found for the major groove mode whereas less significant changes for both ligand and DNA were detected for the minor groove binding after molecular dynamics simulation. The conformation of the ligand obtained from the major groove mode resembles that computed with the ligand soaked in water. The van der Waals contact energy was found to be as significant as electrostatic energy and more important for difference in binding energy between these two binding modes. The importance of van der Waals force in groove binding was supported by computations on the complex formed by the repressor peptide fragment from the bacteriophage 434 and its operator oligonucleotide.     

Experimental and Theoretical Volumes of Nucleic Acids

Abstract

Further evidence of the need to incorporate both experimental and theoretical results in estimates of the volumes of molecules is presented. The volumes of a series of alkyllated purines and pyrimidines, with experimentally known volumes, were estimated by van der Waals and Semi-empirical quantum mechanical methods. In all instances, the van der Waals methods failed to reproduce the experimental volumes. The Semi-empircal methods were able to reproduce the experimental volumes consistentally.     

Monte Carlo Study of the Buckingham Exponential-six Fluid

Abstract

In this paper we report the results of extensive Monte Carlo simulations of a pure fluid of Buckingham modified exponential-six molecules. Data are presented for the configurational energy and pressure covering a wide range of temperatures and densities. These data are interpreted using the generalized van der Waals partition function with a novel separation into free volume and mean potential terms. We find, surprisingly, that the Buckingham fluid is described by a simple van der Waals-like equation of state provided that the b parameter is temperature dependent and chosen in a theoretically correct manner.     

Regulation of channel function due to physical energetic coupling with a lipid bilayer

Regulation of membrane protein functions due to hydrophobic coupling with a lipid bilayer has been investigated. An energy formula describing interactions between lipid bilayer and integral ion channels with different structures, which is based on the screened Coulomb interaction approximation, has been developed. Here the interaction energy is represented as being due to charge-based interactions between channel and lipid bilayer. The hydrophobic bilayer thickness channel length mismatch is found to induce channel destabilization exponentially while negative lipid curvature linearly. Experimental parameters related to channel dynamics are consistent with theoretical predictions. To measure comparable energy parameters directly in the system and to elucidate the mechanism at an atomistic level we performed molecular dynamics (MD) simulations of the ion channel forming peptide–lipid complexes. MD simulations indicate that peptides and lipids experience electrostatic and van der Waals interactions for short period of time when found within each other’s proximity. The energies from these two interactions are found to be similar to the energies derived theoretically using the screened Coulomb and the van der Waals interactions between peptides (in ion channel) and lipids (in lipid bilayer) due to mainly their charge properties. The results of in silico MD studies taken together with experimental observable parameters and theoretical energetic predictions suggest that the peptides induce ion channels inside lipid membranes due to peptide–lipid physical interactions. This study provides a new insight helping better understand of the underlying mechanisms of membrane protein functions in cell membrane leading to important biological implications.     

Base-Stacking Interactions in Double-Helical DNA Structures: Experiment Versus Theory

Abstract

Atom-atom potential energy calculations have been undertaken for deriving stacking energies in double-helical structures. A comparison between the energy patterns of A- and B-type double-helical fragments determined by single-crystal X-ray diffraction methods versus idealized uniform models based on fiber diffraction data shows that the van der Waals stacking energy is largely sensitive to local changes in the relative orientation of adjacent base pairs. The sequence-dependent conformational variability observed in the high-resolution structures appears to be a consequence of the equipartitioning of the stacking energy along the double helix. The large energy variations expected for a uniform structure are dampened considerably in the observed structures by means of local changes in conformational features such as helix rotation and roll angles between base pairs.     

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.     

A preliminary analysis of the three-dimensional structure of dimeric di-haem split-Soret cytochrome c from Desulfovibrio desulfuricans ATCC 27774 at 2.5-Å resolution using the MAD phasing method: a novel cytochrome fold with a stacked-haem arrangement

Haem-containing proteins are directly involved in electron transfer as well as in enzymatic functions. The "split-Soret" cytochrome (SSC) was isolated from the sulfate- and nitrate-reducing bacterium Desulfovibrio desulfuricans ATCC 27774 and has no significant nitrate or nitrite reductase activity. The protein received its name due its unusual spectral properties. It is a dimer containing two identical subunits of 26.3 kDa, each with two haem-c groups. A preliminary model for the three-dimensional structure of this cytochrome was derived using the Multiple Wavelength Anomalous Dispersion (MAD) phasing method. This model shows that SSC is indeed a dimer containing four haems at one end of the molecule. In each monomer the two haems have their edges overlapped within van der Waals contacts with an iron-to-iron distance of 9?Å. The polypeptide chain of each monomer supplies the sixth axial ligand to the haems of the other monomer. This work shows that SSC constitutes a new class of cytochrome. The stacking of the two haems in the monomer within van der Waals distances of each other, and also the short (van der Waals) distances between the two monomers in the dimeric molecule are unprecedented in hemoproteins. This particular haem arrangement is an excellent model for the spectral study (undertaken several years ago) of haem-haem interaction using the aggregated haem undecapeptide derived from mammalian cytochrome c.     

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.