Indole localization in lipid membranes revealed by molecular simulation

It is commonly known that the amino acid residue tryptophan and its side-chain analogs, e.g., indole, are strongly attracted to the interfacial region of lipid bilayers. Phenylalanine and its side-chain analogs, e.g., benzene, do not localize in the interface but are distributed throughout the lipid bilayer. We use molecular dynamics to investigate the details of indole and benzene localization and orientation within a POPC bilayer and the factors that lead to their different properties. We identify three sites in the bilayer at which indole is localized: 1), a site in the interface near the glycerol moiety; 2), a weakly bound site in the interface near the choline moiety; and 3), a weakly bound site in the center of the bilayer's hydrocarbon core. Benzene is localized in the same three positions, but the most stable position is the hydrocarbon core followed by the site near the glycerol moiety. Transfer of indole from water to the hydrocarbon core shows a classic hydrophobic effect. In contrast, interfacial binding is strongly enthalpy driven. We use several different sets of partial charges to investigate the factors that contribute to indole's and benzene's orientational and spatial distribution. Our simulations show that a number of electrostatic interactions appear to contribute to localization, including hydrogen bonding to the lipid carbonyl groups, cation-pi interactions, interactions between the indole dipole and the lipid bilayer's strong interfacial electric field, and nonspecific electrostatic stabilization due to a mismatch in the variation of the nonpolar forces and local dielectric with position in the bilayer.     

Total internal reflection fluorescence. Measurement of spatial and orientational distributions of fluorophores near planar dielectric interfaces

The fluorescence collected from a fluorophore which is near a planar interface and is excited by a laser beam that is totally internally reflected at the interface depends on the direction of the absorption and emission transition dipole moments of the fluorophore with respect to the interface, on the distance from the fluorophore to the interface, on the angle of incidence and polarization direction of the exciting beam, and on properties of the collection optics. Expressions are derived for the excitation and subsequent emission and collection of fluorescence from a population of fluorophores near a planar interface. Presented is a general model-independent method of obtaining characteristic parameters of the spatial and orientational distribution of the population of fluorophores, from a measure of the fluorescence collected as a function of the polarization and the incidence angle of the totally internally reflected laser beam. The method is illustrated with several simulation calculations.     

Effect of planar dielectric interfaces on fluorescence emission and detection. Evanescent excitation with high-aperture collection.

We consider the effect of planar dielectric interfaces (e.g., solid/liquid) on the fluorescence emission of nearby probes. First, we derive an integral expression for the electric field radiated by an oscillating electric dipole when it is close to a dielectric interface. The electric field depends on the refractive indices of the interface, the orientation of the dipole, the distance from the dipole to the interface, and the position of observation. We numerically calculate the electric field intensity for a dipole on an interface, as a function of observation position. These results are applicable to fluorescent molecules excited by the evanescent field of a totally internally reflected laser beam and thus very close to a solid/liquid interface. Next, we derive an integral expression for the electric field radiated when a second dielectric interface is also close to the fluorescent molecule. We numerically calculate this intensity as observed through the second interface. These results are useful when the fluorescence is collected by a high-aperture microscope objective. Finally, we define and calculate a "dichroic factor," which describes the efficiency of collection, in the two-interface system, of polarized fluorescence. The limit when the first interface is removed is applicable for any high-aperture collection of polarized or unpolarized fluorescence. The limit when the second interface is removed has application in the collection of fluorescence with any aperture from molecules close to a dielectric interface. The results of this paper are required for the interpretation of order parameter measurements on fluorescent probes in supported phospholipid monolayers (Thompson, N.L., H. M. McConnell, and T. P. Burghardt, 1984, Biophys. J., 46:739-747).     

Single molecule fluorescence image patterns linked to dipole orientation and axial position: application to myosin cross-bridges in muscle fibers

Background

Photoactivatable fluorescent probes developed specifically for single molecule detection extend advantages of single molecule imaging to high probe density regions of cells and tissues. They perform in the native biomolecule environment and have been used to detect both probe position and orientation.

Methods and Findings

Fluorescence emission from a single photoactivated probe captured in an oil immersion, high numerical aperture objective, produces a spatial pattern on the detector that is a linear combination of 6 independent and distinct spatial basis patterns with weighting coefficients specifying emission dipole orientation. Basis patterns are tabulated for single photoactivated probes labeling myosin cross-bridges in a permeabilized muscle fiber undergoing total internal reflection illumination. Emitter proximity to the glass/aqueous interface at the coverslip implies the dipole near-field and dipole power normalization are significant affecters of the basis patterns. Other characteristics of the basis patterns are contributed by field polarization rotation with transmission through the microscope optics and refraction by the filter set. Pattern recognition utilized the generalized linear model, maximum likelihood fitting, for Poisson distributed uncertainties. This fitting method is more appropriate for treating low signal level photon counting data than χ² minimization.

Conclusions

Results indicate that emission dipole orientation is measurable from the intensity image except for the ambiguity under dipole inversion. The advantage over an alternative method comparing two measured polarized emission intensities using an analyzing polarizer is that information in the intensity spatial distribution provides more constraints on fitted parameters and a single image provides all the information needed. Axial distance dependence in the emission pattern is also exploited to measure relative probe position near focus. Single molecule images from axial scanning fitted simultaneously boost orientation and axial resolution in simulation.     

Generalized stern models of the electric double layer considering the spatial variation of permittvity and finite size of ions in saturation regime

The interaction between a charged metal implant surface and a surrounding body fluid (electrolyte solution) leads to ion redistribution and thus to formation of an electrical double layer (EDL). The physical properties of the EDL contribute essentially to the formation of the complex implant-biosystem interface. Study of the EDL began in 1879 by Hermann von Helmholtz and still today remains a scientific challenge. The present mini review is focused on introducing the generalized Stern theory of an EDL, which takes into account the orientational ordering of water molecules. To ascertain the plausibility of the generalized Stern models described, we follow the classical model of Stern and introduce two Langevin models for spatial variation of the relative permittivity for point-like and finite sized ions. We attempt to uncover the subtle interplay between water ordering and finite sized ions and their impact on the electric potential near the charged implant surface. Two complementary effects appear to account for the spatial dependency of the relative permittivity near the charged implant surface — the dipole moment vectors of water molecules are predominantly oriented towards the surface and water molecules are depleted due to the accumulation of counterions. At the end the expressions for relative permittivity in both Langevin models were generalized by also taking into account the cavity and reaction field.     

An analysis of the spatial mechanisms responsible for electrosensitivity in rays-modelling results

Mathematical methods have helped to reveal the possible mechanisms of information conversion processes by the Lorenzinian ampullae during spatial detection of the dipole electric field. A stationary voltage distribution in the inhomogeneous media has been calculated by means of numerical methods. The skate body has been represented by a thin disk. If the dipole axis was positioned in the disk plane, potential distortions near the disk were negligibly small. In other cases the electrical field energy absorbed by ampullary groups has been dramatically reduced. It was supposed that body tissues served as the space filter of the electroreceptive system. Based on the result presented here, a new mechanism of the electrolocation was proposed. The ampullary groups were predicted to play the role of arrays which were able to perceive spatial characteristics of the external electric field. The theoretical analysis of ampullary groups circular sensitivity diagrams supported the prediction.     

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin–Poisson–Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin–Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson–Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.     

Influence of the solvent structure on the electrostatic interactions in proteins

The proper estimation of the influence of the many-body dynamic solvent microstructure on a pairwise electrostatic interaction (PEI) at the protein-solvent interface is very important for solving many biophysical problems. In this work, the PEI energy was calculated for a system that models the interface between a protein and an aqueous solvent. The concept of nonlocal electrostatics for interfacial electrochemical systems was used to evaluate the contribution of a solvent orientational polarization, correlated by the network of hydrogen bonds, into the PEI energy in proteins. The analytical expression for this energy was obtained in the form of Coulomb's law with an effective distance-dependent dielectric function. The asymptotic and numerical analysis carried out for this function revealed several features of dielectric heterogeneity at the protein-solvent interface. For charges located in close proximity to this interface, the values of the dielectric function for the short-distance electrostatic interactions were found to be remarkably smaller than those determined by the classical model, in which the solvent was considered as the uniform dielectric medium of high dielectric constant. Our results have shown that taking into consideration the dynamic solvent microstructure remarkably increases the value of the PEI energy at the protein-solvent interface.     

High electric field dielectric studies of aqueous myoglobin solutions.

High field dielectric measurements of the Piekara factor deltaepsilon/E2 have been carried out for a range of concentrations of horse heart myoglobin in water at 293K. Using the literature value for the dipole moment of myoglobin and the established theory for the classical orientational dipolar non-linear effect predicts a value of deltaepsilon/E2 one order of magnitude greater than that for water. The measured effect, however, was found to be one order of magnitude less than for water. This difference is explained as being most probably due to the existence of antiparallel molecular dipole pairs in the myoglobin solution. The possibility of a positive deltaepsilon due to a field induced conformational change of the myoglobin cannot, however, be ruled out.     

Integral equation theories for predicting water structure around molecules

Water plays a crucial role in the structure and function of proteins and other biological macromolecules; thus, theories of aqueous solvation for these molecules are of great importance. However, water is a complex solvent whose properties are still not completely understood. Statistical mechanical integral equation theories predict the density distribution of water molecules around a solute so that all particles are fully represented and thus potentially both molecular and macroscopic properties are included. Here we discuss how several theoretical tools we have developed have been integrated into an integral equation theory designed for globular macromolecular solutes such as proteins. Our approach predicts the three-dimensional spatial and orientational distribution of water molecules around a solute. Beginning with a three-dimensional Ornstein-Zernike equation, a separation is made between a reference part dependent only on the spatial distribution of solvent and a perturbation part dependent also on the orientational distribution of solvent. The spatial part is treated at a molecular level by a modified hypernetted chain closure whereas the orientational part is treated as a Boltzmann prefactor using a quasi-continuum theory we developed for solvation of simple ions. A potential energy function for water molecules is also needed and the sticky dipole models of water, such as our recently developed soft-sticky dipole (SSD) model, are ideal for the proposed separation. Moreover, SSD water is as good as or better than three point models typically used for simulations of biological macromolecules in structural, dielectric and dynamics properties and yet is seven times faster in Monte Carlo and four times faster in molecular dynamics simulations. Since our integral equation theory accurately predicts results from Monte Carlo simulations for solvation of a variety of test cases from a single water or ion to ice-like clusters and ion pairs, the application of this theory to biological macromolecules is promising.     

Dielectric properties of hemoglobin and myoglobin. II. Dipole moment of sperm whale myoglobin

This paper is concerned with the molecular origin of the dipole moment of sperm whale myoglobin as it can be calculated from the dielectric dispersion at 1 Mcps on the basis of a mechanism of orientational polarization. It was possible to compare the dielectric increment of native myoglobin and its change during the reaction with bromo acetate with dipole moments calculated according to the known coordinates of the charged groups of the molecule. The agreement between the two shows that in myoglobin only the permanent dipole moment due to these charged groups is important, and that contributions from other possible sources remain within the limits of experimental error.     

Single-molecule detection with total internal reflection excitation: comparing signal-to-background and total signals in different geometries.

Excitation of fluorescence with total internal reflection (TIR) excitation yields very low background scattered light and good signal-to-background contrast. The background and its associated noise can be made low enough to detect single fluorescent molecules under ambient conditions. In this paper, different TIR geometries were compared for excitation and detection of single rhodamine 6G (R6G) molecules at air-silica interfaces and single B-phycoerythrin proteins at water-silica interfaces. Through-objective, objective-coverslip, and prism-based TIR geometries were investigated. The signal-to-background ratio (SBR) and the number of photons detected before photobleaching (Nb) were optimum in different geometries. The greatest image contrast was obtained when using prism-TIR (SBR = 11.5), but the largest number of detected signal photoelectrons was obtained by using through-objective TIR for R6G-air-silica ( = 10(4)). The results were discussed in terms of the TIR field enhancements and the modified dipole emission pattern near a dielectric interface. The SBR and total detected photons are important parameters for designing photon-limited experiments.     

Near-Infrared Super Resolution Imaging with Metallic Nanoshell Particle Chain Array

We propose a near-infrared super resolution near field imaging system with an array of metallic nanoshell particle chain. The imaging array can plasmonically transfer the near field components of dipole sources and the super resolution images can be reconstructed in the output plane. By decreasing the metallic nanoshell’s thickness of the fixed size nanoparticle, the plasmon resonance wavelength of the isolate nanoshell particle is red-shifted to the near-infrared region. The operation wavelength of the imaging array is correspondingly red-shifted to the near-infrared region. In this paper, we study the incoherent and coherent super resolution imaging. The field intensity distributions at the different planes of imaging process are calculated using the finite element method. The simulation results demonstrate that the array has super resolution imaging capability at near-infrared wavelengths in the incoherent and coherent manners. The results also show that the image formation highly depends on the source coherence. In the same structural parameters, the reconstructed images under the illumination of incoherent light source reach to the higher image quality and spatial resolution than the images under the illumination of coherent light source of in phase. By reasonably designing parameters of the imaging array, the approximate spatial resolutions of λ/13 in incoherent case and λ/10 in coherent case are obtained at the near-infrared wavelength of 764 nm. Furthermore, the image–array distance and the chains’ spacing also affect the image reconstruction.     

A Monte Carlo Simulation Study of Orientational Domain Clusters in the Planar Quadrupole Model

Abstract

We have carried out a series of Monte Carlo simulations of the planar quadrupole model, using the Distributed Array Processor. A very large system size, 16 384 molecules, was employed, and special attention was given to orientational domain clustering near the order—disorder transition. Very slow fluctuations of the orientational order parameter, possibly associated with switching from one orientational domain to another, are observed. Close to the phase transition, domain clusters become extremely ramified, with highly irregular borders. On heating through the transition, the low-temperature dominant domain disappears, essentially by becoming a fractal object. The associated Hausdorff dimension decreases from D = 2 to D = 1.6 as this occurs. Although our results are consistent with a continuous, rather than a first-order, phase transition, effects of finite system size and long time scales prevent us from drawing a definite conclusion on this point.     

A theoretical study of the dielectric constant of protein

The dielectric properties of a protein molecule were investigated by calculating a 'local dielectric constant' with the aid of normal mode analysis. This local dielectric constant was calculated from the electronic polarization of atoms and the orientational polarization of local dipoles. The former was obtained from atomic polarizations of the whole atoms in a protein molecule. The latter was determined from the fluctuation-dissipation theorem. The degree of dipole fluctuation was calculated from the positional fluctuation of each atom obtained by the normal mode analysis. Assuming a minimum volume for a continuum model, the resulting local dielectric constants ranged from 1 to 20 inside the protein.     

Evaluation of the influence of the internal aqueous solvent structure on electrostatic interactions at the protein-solvent interface by nonlocal continuum electrostatic approach

The dielectric properties of the polar solvent on the protein-solvent interface at small intercharge distances are still poorly explored. To deconvolute this problem and to evaluate the pair-wise electrostatic interaction (PEI) energies of the point charges located at the protein-solvent interface we used a nonlocal (NL) electrostatic approach along with a static NL dielectric response function of water. The influence of the aqueous solvent microstructure (determined by a strong nonelectrostatic correlation effect between water dipoles within the orientational Debye polarization mode) on electrostatic interactions at the interface was studied in our work. It was shown that the PEI energies can be significantly higher than the energies evaluated by the classical (local) consideration, treating water molecules as belonging to the bulk solvent with a high dielectric constant. Our analysis points to the existence of a rather extended, effective low-dielectric interfacial water shell on the protein surface. The main dielectric properties of this shell (effective thickness together with distance- and orientation-dependent dielectric permittivity function) were evaluated. The dramatic role of this shell was demonstrated when estimating the protein association rate constants.     

A Simple Force-Motion Relation for Migrating Cells Revealed by Multipole Analysis of Traction Stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.     

A Simple Force-Motion Relation for Migrating Cells Revealed by Multipole Analysis of Traction Stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.     

Electromagnetic wave in a relativistic magnetized plasma

Results are presented from a theoretical investigation of the dispersion properties of a relativistic plasma in which an electromagnetic wave propagates along an external magnetic field. The dielectric tensor in integral form is simplified by separating its imaginary and real parts. A dispersion relation for an electromagnetic wave is obtained that makes it possible to analyze the dispersion and collisionless damping of electromagnetic perturbations over a broad parameter range for both nonrelativistic and ultrarelativistic plasmas.