Molecular Diffusion Constants Research Articles

Dynamic range and background filtering in raster image correlation spectroscopy.

Raster-scan image correlation spectroscopy (RICS) enables researchers to measure molecular translational diffusion constants and concentrations from standard confocal laser scanning microscope images and is suitable for measuring a wide range of mobility, especially fast-diffusing molecules. However, as RICS analysis is based on the spatial autocorrelation function of fluorescence images, it is sensitive to the presence of fluorescent structures within the image. In this study, we investigate methods to filter out immobile or slow moving background structures and their impact on RICS results. Both the conventional moving-average subtraction-based method and cross-correlation subtraction-based method are rationalized and quantified. Simulated data and experimental measurements in living cells stress the importance of optimizing the temporal resolution of background filtering for reliable RICS measurements. Finally, the capacity of RICS analysis to separate two species isstudied.

Arbitrary-Region Raster Image Correlation Spectroscopy

Combining imaging with correlation spectroscopy, as in raster image correlation spectroscopy (RICS), makes it possible to extract molecular translational diffusion constants and absolute concentrations, and determine intermolecular interactions from single-channel or multicolor confocal laser-scanning microscopy (CLSM) images. Region-specific RICS analysis remains very challenging because correlations are always calculated in a square region-of-interest (ROI). In this study, we describe a generalized image correlation spectroscopy algorithm that accepts arbitrarily shaped ROIs. We show that an image series can be cleaned up before arbitrary-region RICS (ARICS) analysis. We demonstrate the power of ARICS by simultaneously measuring molecular mobility in the cell membrane and the cytosol. Mobility near dynamic subcellular structures can be investigated with ARICS by generating a dynamic ROI. Finally, we derive diffusion and concentration pseudo-maps using the ARICS method. ARICS is a powerful expansion of image correlation spectroscopy with the potential of becoming the new standard for extracting biophysical parameters from confocal fluorescence images.

The impact of diffusion and mixing in expanding fluid drops on the rate of surface tension change

The dynamics of surface tension change in expanding drops of surfactant solution was studied using drop shape analysis. Experiments explored the dynamics of surface tension change resulting from the flow of surfactant-free water into a surfactant-containing drop. Experiments were conducted for two surfactants, one cationic (cetylpyridinium chloride) and one anionic (sodium octylbenzenesulfonate), both selected because they exhibit rapid adsorption/desorption, allowing for the study of mixing behind the expanding interface. Results were interpreted through the use of a spherical diffusion model designed to simulate drop expansion resulting from influx of surfactant-free water at the core of the drop. Best-fit diffusion constants were found to be consistent with reported molecular diffusion constants for the two surfactants, suggesting that hydraulic mixing within the drop does not play a significant role in the dynamics of surface tension change for the conditions studied. The results of the work have practical implications for applications where interface motion is induced by solute delivery, in that diffusion near the interface is likely to control the dynamics of interfacial tension reduction under many conditions.

Arbitrary-Region Image Correlation Spectroscopy

Combining imaging with correlation spectroscopy (ICS), as in raster image correlation spectroscopy (RICS), makes it possible to extract molecular translational diffusion constants (D), absolute concentrations (c), and intermolecular binding constants from single or multicolor confocal laser-scanning microscopy (CLSM) images. The difficulty with performing quantitative fluctuation imaging in living cells is complications due to aggregates or vesicles moving with the image. Also, current algorithms require square or rectangular regions-of-interest (ROI), which is often problematic in a live-cell context. Here, we describe a new algorithm for performing ICS with an arbitrary ROI. This enables whole-cell and even cell-organelle specific analyses to be performed. We describe the theory behind arbitrary region ICS (ARICS) as well as ways of automatically generating the ROI, given some simple threshold parameters. Automatic ROI generation significantly reduces analysis time, opening the door for medium-throughput automated analysis, and allows threshold-specific analyses. We demonstrate the advantages of ARICS on both simulated data and from measurements in live HeLa and E.coli cells. Arbitrary region ICS has the potential of becoming the new standard for extracting biophysical parameters from confocal fluorescence images.

Anisotropic Membrane Diffusion of Human Mesenchymal Stem Cells on Aligned Single-Walled Carbon Nanotube Networks

The diffusion of lipids and proteins in cell membranes is involved in various cellular processes such as cell adhesion and cellular signaling. We report the anisotropic molecular diffusion in the membranes of human mesenchymal stem cells on aligned single-walled carbon nanotube networks. In this study, the cells were first cultured on the surfaces of glass, graphene, and carbon nanotube networks with random or aligned orientations. Then, the molecular diffusion constants of the cell membranes were measured using a fluorescence-recovery-after-photobleaching technique. The cells on graphene exhibited a diffusion constant comparable to that on glass substrate, while those on the rough surface of randomly oriented carbon nanotube networks exhibited a rather low diffusion constant. On the aligned carbon nanotube networks, the molecules in the cell membrane were found to diffuse faster along the direction parallel to the aligned carbon nanotubes than along the direction orthogonal to the nanotubes. These results indicate that the nanoscale properties of nanostructured materials may significantly affect the molecular diffusion in cell membranes and, possibly, related cellular processes.

Modeling and Simulation for Fuel Cell Polymer Electrolyte Membrane

We have established methods to evaluate key properties that are needed to commercialize polyelectrolyte membranes for fuel cell electric vehicles such as water diffusion, gas permeability, and mechanical strength. These methods are based on coarse-graining models. For calculating water diffusion and gas permeability through the membranes, the dissipative particle dynamics–Monte Carlo approach was applied, while mechanical strength of the hydrated membrane was simulated by coarse-grained molecular dynamics. As a result of our systematic search and analysis, we can now grasp the direction necessary to improve water diffusion, gas permeability, and mechanical strength. For water diffusion, a map that reveals the relationship between many kinds of molecular structures and diffusion constants was obtained, in which the direction to enhance the diffusivity by improving membrane structure can be clearly seen. In order to achieve high mechanical strength, the molecular structure should be such that the hydrated membrane contains narrow water channels, but these might decrease the proton conductivity. Therefore, an optimal design of the polymer structure is needed, and the developed models reviewed here make it possible to optimize these molecular structures.

Transient diffraction grating measurements of molecular diffusion in the undergraduate laboratory

Diffusion is a central process in many biological, chemical, and physical systems. We describe an experiment that employs the interference of laser beams to allow the measurement of molecular diffusion on submillimeter length scales. The interference fringes of two intersecting pump beams within a dye solution create a sinusoidal distribution of long-lived molecular excited states. A third probe beam is incident at a wavelength at which the indices of refraction of the ground and excited states are different, so the probe beam diffracts from the spatially periodic excited-state pattern. After the pump beams are switched off, the excited-state periodicity washes out as the system diffuses back to equilibrium. The molecular diffusion constant is obtained from the rate constant of the exponential decay of the diffracted beam. It is also possible to measure the excited-state lifetime.

Host and adsorbate dynamics in silicates with flexible frameworks: Empirical force field simulation of water in silicalite

Molecular dynamics simulations are performed on the pure silica zeolite silicalite (MFI framework code), maintaining via a new force field both framework flexibility and realistic account of electrostatic interactions with adsorbed water. The force field is similar to the well-known "BKS" model [B. W. H. van Beest et al., Phys. Rev. Lett. 64, 1955 (1990)], but with reduced partial atomic charges and reoptimized covalent bond potential wells. The present force field reproduces the monoclinic to orthorhombic transition of silicalite. The force field correctly represents the hydrophobicity of pure silica silicalite, both the adsorption energy, and the molecular diffusion constants of water. Two types of adsorption, specific and weak unspecific, are predicted on the channel walls and at the channel intersection. We discuss molecular diffusion of water in silicalite, deducing a barrier to crossing between the straight and the zigzag channels. Analysis of the thermal motion shows that at room temperature, framework oxygen atoms incurring into the zeolite channels significantly influence the dynamics of adsorbed water.

Molecular motion in cell membranes: Analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G -protein coupled mu -opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.

Simulations of (An)Isotropic Diffusion on Curved Biological Surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of ∼4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of ∼2 in different ER samples.

Effects of Organelle Shape on Fluorescence Recovery after Photobleaching

The determination of diffusion coefficients from fluorescence recovery data is often complicated by geometric constraints imposed by the complex shapes of intracellular compartments. To address this issue, diffusion of proteins in the lumen of the endoplasmic reticulum (ER) is studied using cell biological and computational methods. Fluorescence recovery after photobleaching (FRAP) experiments are performed in tissue culture cells expressing GFP–KDEL, a soluble, fluorescent protein, in the ER lumen. The three-dimensional (3D) shape of the ER is determined by confocal microscopy and computationally reconstructed. Within these ER geometries diffusion of solutes is simulated using the method of particle strength exchange. The simulations are compared to experimental FRAP curves of GFP–KDEL in the same ER region. Comparisons of simulations in the 3D ER shapes to simulations in open 3D space show that the constraints imposed by the spatial confinement result in two- to fourfold underestimation of the molecular diffusion constant in the ER if the geometry is not taken into account. Using the same molecular diffusion constant in different simulations, the observed speed of fluorescence recovery varies by a factor of 2.5, depending on the particular ER geometry and the location of the bleached area. Organelle shape considerably influences diffusive transport and must be taken into account when relating experimental photobleaching data to molecular diffusion coefficients. This novel methodology combines experimental FRAP curves with high accuracy computer simulations of diffusion in the same ER geometry to determine the molecular diffusion constant of the solute in the particular ER lumen.

Fluctuation Correlation Spectroscopy with a Laser-Scanning Microscope: Exploiting the Hidden Time Structure

Images obtained with a laser-scanning microscope contain a time structure that can be exploited to measure fast dynamics of molecules in solution and in cells. The spatial correlation approach provides a simple algorithm to extract this information. We describe the analysis used to process laser-scanning images of solutions and cells to obtain molecular diffusion constant in the microsecond to second timescale.

NMR spectroscopic characterization of copper(II) and zinc(II) complexes of indomethacin.

Molecular diffusion constants were studied by NMR spectroscopy to provide information about the solution structures of a variety of Cu(II) and Zn(II) monomeric and dimeric complexes of indomethacin (IndoH). These studies showed that monomeric Zn(II)-Indo complexes substantially dimerize in DMF-d7 and DMSO-d6 solutions at room temperature, whereas the Cu(II) and Zn(II) dinuclear complexes remain largely intact in these solutions. There is evidence of an equilibrium between monomers and dimers for the Zn(II) complexes in solution, as shown by a reduced diffusion constant and lower average radius compared to the Cu(II) dimer. Such an equilibrium between monomers and dimers for the Zn(II) complexes is also consistent with previous results obtained from XAFS analysis of DMF solutions of such complexes. The greater lability and lower thermodynamic stability of the Zn(II) dimer complex compared to the Cu(II) analogue, as determined from the NMR experiments, is likely to result in the more ready release of free Indo in the GI tract. This is consistent with the previously observed higher GI toxicities of the Zn-Indo pharmaceutical preparations compared to the Cu(II)-Indo counterparts.

Denitrification and a numerical modelling approach for shallow waters.

A numerical model (`DiffDeni') has been developed to describe the disappearance of nitrate from the water column of 10–200 cm deep waters. The disappearance is caused by bacterial denitrification in the sediments. The model employs the molecular diffusion constant, an acceleration factor describing eddy diffusion, and three bacterial growth constants, viz. the inoculum size, the maximum growth rate and the half saturation constant for the hyperbolic process. The values of these system-constants were varied over a wide range. The curves obtained were compared with the curves for well-defined situations, viz. in which diffusion takes place without any or with a complete, immediate reaction. These cases have analytical solutions, and were simulated closely by the model `DiffDeni', though this model is based on different assumptions. It is shown that, when the bacterial growth rate is above a critical value, a negative exponential curve describes the nitrate disappearance well. On the other hand, a more complicated negative exponential equation can be used to describe the first phase of this denitrification in which bacterial activity is low and nitrate behaves as a conservative compound. The change-over period from phase 1 (no reaction) to phase 2 (complete, immediate reaction) which may vary between <1 and 50 days cannot be described analytically (mathematically correctly). The influence of temperature on denitrification is assessed and it is shown that both bacterial activity and diffusion may influence the denitrification rate.

Deuterium and Carbon‐13 NMR Study of Molecular Rotational Diffusion in Two Star‐Hydrocarbon Oils

AbstractRelaxation rates of carbon‐13 magnetization of the C9 carbon positions in two poly‐n‐octyl star‐hydrocarbon oils, 9‐n‐octyl‐n‐heptadecane and 9,10‐di‐n‐octyl‐n‐octadecane, and of deuterium magnetization in 9‐n‐octyl‐n‐heptadecane‐9d, and 9,10‐di‐n‐octyl‐n‐octadecane‐9d1, labelled with deuterium at the same carbon position, have been measured over wide ranges of temperature and at two field strengths. In this paper simulation of the observed relaxation rates within the assumptions of the Lipari and Szabo picture of molecular rotational diffusion, and dipolar and quadrupolar relaxation mechanisms, determined molecular rotational diffusion constants, activation energies, and Lipari and Szabo order parameters and correlation times for internal molecular motion at the labelled positions. The appropriate quadrupolar coupling constants could also be determined from the measured data. The effect of the rate of internal molecular isomerization was discussed and it was shown that in general this had to be included in the theoretical picture in order to derive a consistent set of motional parameters that generated all observable relaxation rates of magnetization.

13C-NMR relation study of heparin-disaccharide interactions with tripeptides GRG and GKG.

Heparin is a polydisperse sulphated copolymer consisting mostly of 1-->4 linked glucosamine and uronic acid residues, i.e. 2-deoxy-2-sulphamido-D-glucopyranose 6-sulphate and L-idopyranosyluronic acid 2-sulphate. 13C NMR has been used to study the interactions of heparinase-derived and purified heparin disaccharide with N- and C-terminally-blocked tripeptides GRG and GKG. Titration of the disaccharide with peptide indicates that GRG binds the disaccharide more strongly than does GKG, with interactions in either case being stronger at uronate ring positions. In the presence of GRG, a carboxylate pKa depression suggests electrostatic interactions between the arginine guanidinium group and the uronate carboxylate group. 13C relaxation data have been acquired for all disaccharide and peptide carbons in the presence and absence of GRG and GKG. 13C relaxation rates for the disaccharide are significantly faster in the presence of peptide, especially with GRG. Analysis of these relaxation data has been done in terms of molecular diffusion constants, D [symbol: see text] and D parallel, and an angle alpha between D parallel and a molecular frame defined by the moment of inertia tensor calculated for an internally rigid disaccharide. Disaccharide conformational space in these calculations has been sampled for both uronate half-chair forms (2H1 and 1H2) and over a range of glycosidic bond angles defined by motional order parameters and inter-residue nuclear Overhauser effects (+/- 30 degree from the average). In the absence of peptide, the ratio D [symbol: see text] /D parallel falls between 0.4 and 0.7; therefore molecular diffusion occurs preferentially about D parallel, which runs through both disaccharide rings. In the presence of peptide, D [symbol: see text] /D parallel is decreased, indicating that GRG is oriented along D parallel and proximal to the uronic acid ring. A model for this is shown.

ChemInform Abstract: UV‐Laser Photochemistry: Diffusion‐Controlled Trapping of Cyclic 1,3‐Diradicals by Molecular Oxygen. Conformational Effects on Triplet Lifetimes.

AbstractFrom O2 trapping experiments in solvents of different viscosity it is estimated that the lifetime of the diradical (IIa) falls in the range 100 ±30 ns; diffusion control holds for the trapping of the triplet radicals (IIa) by O2, provided that the molecular diffusion constants and not the macroscopic viscosities are employed in estimating the rate constants.

Dependence of the shape of the plasma fibronectin molecule on solvent composition. Ionic strength and glycerol content.

Fibronectin has been purified to apparent homogeneity according to measurements of molecular weight and diffusion constant from light scattering and sedimentation in the analytical ultracentrifuge. This gives two estimates of molecular weight close to 500,000. (The difference with the gel electrophoretic value of 440,000 may indicate the presence of some material of molecular weight higher than that of the monomer.) The (corrected) diffusion constant is found to decrease with ionic strength, much more rapidly in 30% glycerol than in water. A corresponding change occurs when the glycerol content is varied from 0 to 30% at moderate ionic strength, but at very low ionic strength the diffusion constant does not depend on glycerol content. It is concluded that fibronectin can occur in two extreme conformations: the open form, in 30% glycerol at moderate ionic strength, should correspond to the extended shapes visualized by others by electron microscopy of samples prepared from solutions containing glycerol, while the closed form occurs under more physiological conditions. The Stokes radii of these forms, 14.5 and 9.6 nm, respectively, have been compared with calculated Stokes radii of chains of beads of overall length 140 nm having varying stiffness, simulated by a Monte Carlo procedure. These have a Stokes radius of 14.5 nm when made relatively extended to where the distance between chain ends averages 90 nm, as observed in the electron micrographs. When these chains are made very flexible, the Stokes radius reaches a limit of about 10 nm, apparently a lower limit to which a randomly coiled molecule of this size and volume may collapse in a disordered fashion. These results and electron micrographs obtained at low ionic strength suggest a tangled model of the compact form, rather than the ordered model recently proposed by others. Finally, some speculation is offered in regard to a possible physiological role of a conformation change of fibronectin.

Temperature dependences of micellar molecular weight and radius of nonionic surface active agent in the aqueous solution

The molecular weight and diffusion constant of poly(oxyethylene) dodecyl ether (C 12OE 9·3) micelles with an average of 9.3 oxyethylene group were determined from light-scattering measurements and free boundary experiments over a wide temperature range. It was found that micelles formed by C 12OE 9·3 were monodisperse in the temperature range studied. Plots of the logarithms of micellar molecular weight and micellar radii estimated from the diffusion constants against the temperature have a break point around 45°C. This temperature agrees with a theta point where the second virial coefficient obtained from light-scattering measurements is zero. Although the number of the molecules participating in micelle formation increases with temperature, the size of the micelle remains constant up to the temperature corresponding to the theta point, because the spherical micelle is packed with increasing tightness. The increase in the size and weight beyond that point may be attributed to a departure from spherical shape.

Liquid Chromatography in Helically Coiled Open Tubular Columns

Abstract Limitations on pressure, packing procedures, and extra-column broadening make it unlikely that the use of particles smaller than 2 μm in packed columns for liquid chromatography will be effective. We have therefore investigated the potential of alternative column types, in particular open tubular columns, for LC. When tubes are tightly coiled into helices, the radial mass transfer in the mobile phase is greatly enhanced by radial convection, called secondary flow, originating from centrifugal forces. A criterion is developed for the velocity up to which the classical description of axial dispersion in straight columns, after Golay, can be expected to hold. A correction for curvature effects is given for intermediate and high velocities. In principle, the corrected equations enable one to determine molecular diffusion constants from peak broadening within short times, even for macromolecular solutions. At high velocities a drastic decrease in peak broadening is expected, and this was experimentally confirmed for nonretained solutes. The separation speed increases at least quadratically with velocity such that 103 to 104 plates/sec can easily be obtained at pressures not higher than those presently needed for packed columns. The coating of a stable homogeneous layer of stationary phase onto the column wall has been only partially solved. Experience gained with various types of coating is discussed.