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.     

The switch of the binding behaviours between Xe and π system induced by the change of oxidation state of Cu ion

Abstract

The interaction between a xenon atom and aromatic π electron system is generally of van der Waals force with a specifically weak strength. In this work, we suggest the introduction of Cu ion will highly affect the binding behaviour between the xenon and π systems. Once Cu²⁺ ion locates above the benzene ring, the binding is surprisingly strengthened to 11.98 kcal mol^?1 at CCSD(T)/CBS level, which is significantly stronger than average strength of the H-bonds in Watson-Crick guanine-cytosine base pair. If the Cu²⁺ is reduced to Cu⁺, the interaction of interest returns to the weak van der Waals interaction again. This phenomenon indicates the oxidation state shift of Cu ion could regulate the binding strength of Xe with π systems, which would be important for their potential biological functions. This study may provide a plausible understanding of the recent experimental observations of xenon anaesthesia.     

A free energy analysis of nucleic acid base stacking in aqueous solution.

This paper reports a theoretical study of the free energy contributions to nucleic acid base stacking in aqueous solution. Electrostatic interactions are treated by using the finite difference Poisson-Boltzmann method and nonpolar effects are treated with explicit calculation of van der Waals interactions and/or free energy-surface area relationships. Although for some pairs of bases there is a favorable Coulombic interaction in the stacked conformation, generally the net effect of electrostatic interactions is to oppose stacking. This result is caused by the loss of favorable base-solvent electrostatic interactions, that accompany the partial removal of polar atoms from water in the stacked conformation. Nonpolar interactions, involving the hydrophobic effect and enhancement of van der Waals interactions caused by close-packing, drive stacking. The calculations qualitatively reproduce the experimental dependence of stacking free energy on purine-pyrimidine composition.     

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.     

Molecular Dynamics Simulation of Model Lipid Membranes: Structural Effects of Impurities

Abstract

The gel to fluid phase transition or ordered to disordered phase transition observed in biological membranes are simulated by using constant energy Molecular Dynamics. The surface part of the membrane is modelled as a two-dimensional matrix formed by the head groups of the phospholipid molecules. Head molecules which are modelled as three spheres fused with three force centers, interact with each other via van der Waals and Coulomb type interactions. The -so called- impurity or foreign molecule embedded in the surface represents the protein type molecule which is present in biological membranes and control its activity. It is modelled as a pentagon having one force centers in each corner. It also interacts with the surface molecules again via van der Waals and Coulomb type interactions. The surface density is kept constant in the simulations of the systems with or without impurity. Structural and orientational changes due to impurity were observed and proved by monitoring two-dimensional order parameter. It has been shown that melting of the surface or breakage of the ordering of the surface molecules becomes easier and ordered to disordered phase transition temperature was lowered by 100 K if the impurity is present.     

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 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.     

Theoretical study for volume changes associated with the helix-coil transition of peptides.

We calculate the partial molar volumes and their changes associated with the coil(extended)-to-helix transition of two types of peptide, glycine-oligomer and glutamic acid-oligomer, in aqueous solutions by using the Kirkwood-Buff solution theory coupled with the three-dimensional reference interaction site model (3D-RISM) theory. The volume changes associated with the transition are small and positive. The volume is analyzed by decomposing it into five contributions following the procedure proposed by Chalikian and Breslauer: the ideal volume, the van der Waals volume, the void volume, the thermal volume, and the interaction volume. The ideal volumes and the van der Waals volumes do not change appreciably upon the transition. In the both cases of glycine-peptide and glutamic acid-peptide, the changes in the void volumes are positive, while those in the thermal volumes are negative, and tend to balance those in the void volumes. The change in the interaction volume of glycine-peptide does not significantly contribute, while that of glutamic acid-peptide makes a negative contribution.     

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.     

Poisson–Boltzmann model analysis of binding mRNA cap analogues to the translation initiation factor eIF4E

The electrostatic free energy of binding of two analogues of the 5′-mRNA cap, differing in size and electric charge, to the wild type and mutated eukaryotic initiation factor eIF4E was computed using the finite difference solutions to the Poisson–Boltzmann equation. Two definitions of the solute–solvent dielectric boundary were used: van der Waals model, solvent exclusion (SE) model. The computed electrostatic energies were supplemented by estimations of the non polar and entropic contributions. A comparison with experimental data for the investigated systems was done. It appears that the SE model with additional contribution fits experimental findings better than the van der Waals model does.     

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.     

Effect of branching in 4-alkylpyrazoles on liver alcohol dehydrogenase inhibition: A shape analysis study

Shape analysis methodology is applied to the study of 4-alkylpyrazoles which are known inhibitors of liver alcohol dehydrogenase. Elongation of the alkyl chain increases the inhibitory power, whereas branching of the chain diminishes the activity. These two counterpoised effects are studied simultaneously in a selected set of 4-alkylpyrazoles. A systematic conformational analysis followed by topological characterization of the van der Waals surfaces of all the local minima restricts the conformational space to potential bioactive structures. The analysis of the interrelation between the molecular electrostatic potential and van der Waals surfaces provides certain shape codes characteristic of each 4-alkylpyrazole. In both topological analyses van der Waals surfaces and molecular electrostatic potential van der Waals surface interrelations) graphical representations and analytical methods were used. A good correlation between the shape codes and the inhibitory activity is found for the linear derivatives. For branched pyrazoles, a tendency in their inhibitory power is predicted. Isopentylpyrazole is suggested to have the same inhibitory profile as 4-butylpyrazole, the linear derivative with one less carbon atom.     

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.     

Spermine as a porcine pancreatic elastase activator: spectroscopic and molecular simulation studies

Abstract

The aim of this study was to investigate the spermine effect on the thermal denaturation, conformation and activity of elastase at three temperatures of 303, 313 and 323?K in the Tris buffer, at pH 8.5, using UV–vis spectrophotometry, spectrofluorometry and circular dichroism as well as molecular docking and molecular simulation. The increased absorption of elastase in the presence of spermine suggested a change in the environment of tryptophan. It was found that under the influence of spermine, the emission intensity of elastase extremely was reduced, and the use of the Stern-Volmer equation showed that some static quenching had occurred. The thermodynamic parameters values (enthalpy and entropy) and the molecular docking technique also revealed that van der Waals forces or hydrogen bonding interactions played an important role in the binding process. The spermine–elastase complex formation led to increasing the value of the catalytic constant (k_cat). So it could be considered as an activator. Slight changes were observed in the second structure of elastase (1.06% increase for the α-helix and 0.048% decrease the β-sheet) and the thermal stability effect. Molecular docking results also demonstrated that spermine could bind to porcine pancreatic elastase, and van der Waals forces or hydrogen bonding interactions played the major role in the binding process. Overall, our results showed that spermine could induce structural alterations in elastase, acting as a partial stabilizer and an activator for the enzyme.

Communicated by Ramaswamy H. Sarma     

Molecular dynamic simulation and DFT study on the Drug-DNA interaction; Crocetin as an anti-cancer and DNA nanostructure model

In this research, the interaction of Crocetin as an anti-cancer drug and a Dickerson DNA has been investigated. 25 ns molecular dynamic simulations of Crocetin and DNA composed of 12 base pairs and a sequence of d(CGCGAATTCGCG)₂ were done in water. Three definite parts of the B-DNA were considered in analyzing the best interactive site from the thermodynamic point of view. Binding energy analysis showed that van der Waals interaction is the most important part related to the reciprocal O and H atoms of the Crocetin and DNA. Stabilizing interactions, obtained by ΔG calculations, showed that maximum and minimum interactions are related to the S1 and S3 regions, respectively. This means that the most probable van der Waals interaction site of the Dickerson B-DNA and Crocetin is located in the minor groove of DNA. Two sharp peaks at 2.55 and 1.75 Å in radial distribution functions of the PO?HO and NH?OC parts are related to new hydrogen bonds between the Crocetin and DNA in the complex which can be considered as the driving force of the anti-cancer mechanism of the Crocetin. Average values of 0.3 au and zero for the electron densities of the H?O bonds for DNA and complex, obtained by Quantum theory of atoms in molecules (QTAIM), means that the origin of DNA instability after complexation may be related to the H-bond denaturation by Crocetin. Finally, the evaluation of the dispersion interactions using the dispersion functional, -148.76 kcal.mol^?1, confirmed the importance of the dispersion interaction in drug-DNA complex.     

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.     

Dynamics and Binding Modes of Free cdk2 and its Two Complexes with Inhibitors Studied by Computer Simulations

Abstract

This article presents a molecular dynamics (MD) study of the cdk2 enzyme and its two complexes with the inhibitors isopentenyladenine and roscovitine using the Cornell et al. force field from the AMBER software package. The results show that inserting an inhibitor into the enzyme active site does not considerably change enzyme structure but it seemingly changes the distribution of internal motions. The inhibitor causes differences in the domain motions in free cdk2 and in its complexes. It was found out that repulsion of roscovitine N9 substituent causes conformational change on Lys 33 side chain. Isopentenyladenine forms with Lys 33 side chain terminal amino group a hydrogen bond. It implies that the cavity, where N9 substituent of roscovitine is buried, can adopt larger substituent due to Lys 33 side chain flexibility. The composition of electrostatic and van der Waals interactions between the inhibitor and the enzyme were also calculated along both cdk2/inhibitor MD trajectories together with MM-PB/GBSA analysis. These results show that isopentenyladenine-like inhibitors could be more effective after modifications leading to an increase in their van der Waals contact with the enzyme. We suggest that a way leading to better inhibitors occupying isopentenyladenine binding mode could be: to keep N9 and N7 purine positions free, to keep 3,3-dimethylallylamino group at C6 position, and to add, e.g., benzylamino group at C2 position. The results support the idea that the isopentenyladenine binding mode can be used for cdk2 inhibitors design and that all possibilities to improve this binding mode were not uncovered yet.