Molecular Dynamics Simulations of a DMPC Bilayer Using Nonadditive Interaction Models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.     

The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions

The non-polar component of the potential of mean force of dimerization of alanine dipeptide has been calculated in explicit solvent by free energy perturbation. We observe that the calculated PMF is inconsistent with a non-polar hydration free energy model based solely on the solute surface area. The non-linear behavior of the solute-solvent van der Waals energy is primarily responsible for the non-linear dependence of the potential of mean force with respect to the surface area. The calculated potential of mean force is reproduced by an implicit solvent model based on a solvent continuum model for the solute-solvent van der Waals interaction energy and the surface area for the work of forming the solute cavity.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.     

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.

     

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.     

Electrodynamics of Lipid Membrane Interactions in the Presence of Zwitterionic Buffers

Due to thermal motion and molecular polarizability, electrical interactions in biological systems have a dynamic character. Zwitterions are dipolar molecules that typically are highly polarizable and exhibit both a positive and a negative charge depending on the pH of the solution. We use multilamellar structures of common lipids to identify and quantify the effects of zwitterionic buffers that go beyond the control of pH. We use the fact that the repeat spacing of multilamellar lipid bilayers is a sensitive and accurate indicator of the force balance between membranes. We show that common buffers can in fact charge up neutral membranes. However, this electrostatic effect is not immediately recognized because of the concomitant modification of dispersion (van der Waals) forces. We show that although surface charging can be weak, electrostatic forces are significant even at large distances because of reduced ionic screening and reduced van der Waals attraction. The zwitterionic interactions that we identify are expected to be relevant for interfacial biological processes involving lipid bilayers, and for a wide range of biomaterials, including amino acids, detergents, and pharmaceutical drugs. An appreciation of zwitterionic electrodynamic character can lead to a better understanding of molecular interactions in biological systems and in soft materials in general.     

The Effect of Electrical Deformation Forces on the Electropermeabilization of Erythrocyte Membranes in Low- and High-Conductivity Media

Electrical breakdown of erythrocytes induces hemoglobin release which increases markedly with decreasing conductivity of the pulse medium. This effect presumably results from the transient, conductivity-dependent deformation forces (elongation or compression) on the cell caused by Maxwell stress. The deformation force is exerted on the plasma membrane of the cell, which can be viewed as a transient dipole induced by an applied DC electric field pulse. The induced dipole arises from the free charges that accumulate at the cell interfaces via the Maxwell-Wagner polarization mechanism. The polarization response of erythrocytes to a DC field pulse was estimated from the experimental data obtained by using two complementary frequency-domain techniques. The response is very rapid, due to the highly conductive cytosol. Measurements of the electrorotation and electrodeformation spectra over a wide conductivity range yielded the information and data required for the calculation of the deformation force as a function of frequency and external conductivity and for the calculation of the transient development of the deformation forces during the application of a DC-field pulse. These calculations showed that (i) electric force precedes and accompanies membrane charging (up to the breakdown voltage) and (ii) that under low-conductivity conditions, the electric stretching force contributes significantly to the enlargement of ``electroleaks' in the plasma membrane generated by electric breakdown. Received: 12 December 1997/Revised: 13 March 1998     

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.     

Anisotropic electric properties of purple membrane and their change during the photoreaction cycle

Purple membrane suspension shows two different orientations in electric fields of different frequencies. The orientation at low frequencies (less than or equal to approximately 10 Hz), with the membrane surface perpendicular to the electric field, is due to permanent dipole moment of the membrane and the orientation at high frequencies (greater than or equal to approximately 100 Hz), with the surface parallel to the electric field, is due to induced dipole moment. By quantitative analysis of these orientations, we determined the permanent dipole moment and the polarizability. Both values varied according to the membrane size: the permanent dipole moment ranged from 500 kD to 10 MD and was proportional to the square of the diameter of the membrane. The polarizability ranged from 1 X 10(-13) to 1 X 10(-11)cm3 and was proportional to the third to fourth power of the diameter. Because the permanent dipole moment was proportional to the area of the membrane, we could determine permanent dipole moment per bacteriorhodopsin. By determining the actual membrane size under electron microscopy, we got 98 D/bacteriorhodopsin. We also concluded that the direction of the permanent dipole moment was from the cytoplasmic to the extracellular side. These values, however, were strongly dependent on the ionic strength in the medium, suggesting a screening effect due to counter ions near the membrane surface. We evaluated the screening effect and showed about a four-charge difference between the two sides of the purple membrane. Under illumination, we found that the permanent dipole moment decreased from 98 to 63 D/bacteriorhodopsin. From the best-oriented sample, we also concluded that the angle of retinal against the axis normal to the membrane surface was greater than 68.6 degrees.     

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.     

Contribution of asymmetric ligand binding to the apparent permanent dipole moment of DNA

Despite its antiparallel symmetry, DNA often appears to possess a permanent electric dipole moment in transient electro-optical experiments. We propose that this may be due to the asymmetric binding of charged ligands to the DNA. We have used the fluctuating dipole theory of Kirkwood and Shumaker to calculate the contribution of asymmetric ligand binding to the electro-optic orientation function, and Monte Carlo computer simulation to calculate the reversing pulse behavior, as a function of ligand binding density. The results indicate that the effect should be observable even against the background of the sizable induced dipole moment produced by polarization of the counterion atmosphere.     

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.     

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.     

Mapping interaction forces with the atomic force microscope.

Force curves were recorded as the sample was raster-scanned under the tip. This opens new opportunities for imaging with the atomic force microscope: several characteristics of the samples can be measured simultaneously, for example, topography, adhesion forces, elasticity, van der Waals, and electrostatic interactions. The new opportunities are illustrated by images of several characteristics of thin metal films, aggregates of lysozyme, and single molecules of DNA.     

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.     

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.     

Using the atomic force microscope to study the interaction between two solid supported lipid bilayers and the influence of synapsin I

To measure the interaction between two lipid bilayers with an atomic force microscope one solid supported bilayer was formed on a planar surface by spontaneous vesicle fusion. To spontaneously adsorb lipid bilayers also on the atomic force microscope tip, the tips were first coated with gold and a monolayer of mercapto undecanol. Calculations indicate that long-chain hydroxyl terminated alkyl thiols tend to enhance spontaneous vesicle fusion because of an increased van der Waals attraction as compared to short-chain thiols. Interactions measured between dioleoylphosphatidylcholine, dioleoylphosphatidylserine, and dioleoyloxypropyl trimethylammonium chloride showed the electrostatic double-layer force plus a shorter-range repulsion which decayed exponentially with a decay length of 0.7 nm for dioleoylphosphatidylcholine, 1.2 nm for dioleoylphosphatidylserine, and 0.8 nm for dioleoyloxypropyl trimethylammonium chloride. The salt concentration drastically changed the interaction between dioleoyloxypropyl trimethylammonium chloride bilayers. As an example for the influence of proteins on bilayer-bilayer interaction, the influence of the synaptic vesicle-associated, phospholipid binding protein synapsin I was studied. Synapsin I increased membrane stability so that the bilayers could not be penetrated with the tip.     

Transient electric birefringence of T-even bacteriophages. I. T4B in the absence of tryptophan and fiberless T4 particles

Measurements of the electric birefringence of suspensions of T4B in the absence of tryptophan and of fiberless T4 particles show that both kinds of particles are hydrodynamically equivalent. Their rotational diffusion coefficients corrected to 25°C and water viscosity (D_25,w) are 280 ± 9 sec^?1 and 295 ± 10 sec^?1, respectively. These corrected rotational diffusion coefficients are almost independent of buffer concentration and temperature. The sedimentation coefficient (s_20,w) of T4 B is equal to 1023 ± 12 S, a value which is likewise independent of buffer concentration. By analysis of the field strength dependence of the steady-state birefringence and by reversing pulse experiments it could be shown that the orientation in an electric field is largely due to a permanent dipole moment. This dipole moment is somewhat dependent on buffer concentration and amounts to about 24,000 debye for T4B and 95,000 debye for fiberless T4. An approximate calculation shows that the difference in dipole moment may be ascribed to positive charges on the fiber tip (at least ten per fiber), to negative charges along the fiber or (and) positive charges on the fiberless particle at those places where the fibers are attached in normal particles.     

Voltage sensitivity of the fluorescent probe RH421 in a model membrane system.

The voltage sensitivity of the fluorescent styrylpyridinium dye RH421 has been investigated in dimyristoylphosphatidylcholine vesicles by inducing an intramembrane electric field through the binding of the hydrophobic ion tetraphenylborate (TPB). To assess the probability of electrochromic and solvatochromic mechanisms for the dye response, the ground-state dipole moment of the dye in chloroform solution was determined from dielectric constant measurements to be 12 (+/- 1) Debye, and the change in dipole moment upon excitation was calculated from measurements of the Stokes shift in solvents of varying polarity to be 25 (+/- 11) Debye. As well as causing absorbance and fluorescence changes of membrane-bound dye, the TPB-induced electrical field was found to reduce significantly the pKa of the dye. The pH at which experiments are carried out is, thus, an important factor in determining the amplitude of the voltage-induced absorbance and fluorescence changes. The observed absorbance changes induced by the field are inconsistent with a pure electrochromic mechanism. A reorientation/solvatochromic mechanism, whereby the electrical field reorients the dye molecules so that they experience a change in polarity of their lipid environment is likely to make a significant contribution to both the spectral changes and to the field effect on the acid-base properties of the dye.