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Value and limits of Graham's law for prediction of diffusivities of gases in gas mixtures.

The validity of Graham's law, i.e. the inversely proportional relationship between diffusivity (diffusion coefficient) and the square root of the molecular mass, is tested for test gases and gas mixtures of physiological interest based on recent measurements of diffusivities of gases in gas phase. With gases of medium molecular mass (10 to 30 g/mol) predictions on the basis of Graham's law are reasonably accurate, deviations from experimental values not exceeding 20%. With gases of high and low molecular masses, however, larger discrepancies are encountered. The prediction of diffusion coefficients on the basis of the Chapman-Enskog theory is in most cases more accurate than that based on Graham's law.

Diffusion↗

Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer.

Fluorescence recovery after photobleaching (FRAP) has recently been used to examine the percolation properties of coexisting phases in two-component, two-phase phosphatidylcholine bilayers [Vaz, W. L. C., Melo, E. C. C., & Thompson, T. E. (1989) Biophys. J. 56, 869-876]. We now report the use of FRAP to study two additional problems in similar systems. The first is the effect of solid-phase obstacles on the lateral diffusion in the fluid phase. The second is the question of whether or not, in a single bilayer, solid-phase domains in one monolayer are exactly superimposed on solid domains in the apposing monolayer. To address the first problem, the lateral diffusion of N-(7-nitrobenzoxa-2,3-diazol-4-yl)-1-palmitoyl-2-oleoylphosp hatidylethanolamine (NBD-POPE), a probe soluble only in the fluid phase when solid and fluid phases coexist, has been studied in the mixture N-lignoceroyldihydrogalactosylceramide (LigGalCer)/dipalmitoylphosphatidylcholine (DPPC). Percolation of the fluid phase occurs at a high mass fraction of solid phase. This indicates that the solid domains have a centrosymmetric shape, a characteristic which makes this a good experimental system to test theoretical simulations of diffusion in an archipelago. It is shown that agreement between theory and experiment is poor, a result that had already been observed when the obstacles were integral membrane proteins. We develop an effective-medium model for diffusion in two-phase systems which explains both our results and those obtained with integral proteins. The distinctive feature of the model is the consideration of an annular region around the obstacles where the lipids are more ordered than in the bulk fluid phase. The diffusion coefficient is then calculated by extending the free area model to two-phase systems, taking these annuli into account. The second question, the organization of the solid-phase domains across the lipid bilayer, is examined in the systems LigGalCer/DPPC and dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) by comparing the diffusion of a fluid-phase-soluble, gel-phase-insoluble lipid derivative which spans the two monolayers of a bilayer (NBD-membrane-spanning-phosphatidylethanolamine, NBD-msPE) with that of a probe which is restricted to a single monolayer. In LigGalCer/DPPC, 20:80, the distribution of solid domains in one of the monolayers is independent of the distribution in the apposing monolayer. In contrast, in DMPC/DSPC, 50:50, the solid domains in one monolayer are exactly superimposed upon the solid domains existing in the apposing monolayer.

Diffusion↗

Determination of binary diffusion coefficients of various gas species used in respiratory physiology.

In order to provide data required for quantitative analysis of gas diffusion in lung airways, diffusion of He, CO, O2, CO2 and SF6 in various gases used in respiratory physiology was studied in vitro at 37 degrees C and 25 degrees C. The gases were allowed to mix by diffusion in a closed cylindrical tube (length 2 m, internal diameter 1 cm), one half of which was initially filled with 1% test gas in a second gas and the other half of which was filled with the second gas only. Kinetics of diffusional equilibration was determined by withdrawal of spot samples analyzed by gas chromatography. The binary (mutual) diffusion coefficients (D) computed there from were in most cases in good agreement with values calculated on the basis of the Chapman-Enskog theory.

Diffusion↗

Preparation of solid phantoms with defined scattering and absorption properties for optical tomography.

We have developed diffusely scattering solid phantoms with optical (scattering) properties amenable to theoretical calculations. Monodisperse quartz glass spheres were used as scatterers embedded in polyester resin. An infrared dye was added to simulate absorption by biological tissue. Solid phantoms were tested for their macroscopic homogeneity. Several phantoms were built with well-defined spatial variations in their transport scattering and absorption coefficients to be used for optical tomography. Scattering, transport scattering, and absorption coefficients of solid, homogeneous phantoms and of aqueous suspensions of monodisperse quartz glass spheres were derived from measurements of time-integrated collimated transmittance and time-resolved diffuse transmittance. For aqueous suspensions of monodisperse quartz glass spheres at known number density scattering and transport scattering coefficients calculated by Mie theory are in quantitative agreement with experimentally derived values. In addition, diffuse reflectance and diffuse transmittance of aqueous suspensions at various number densities were measured and found to be in excellent agreement with results of Monte Carlo calculations using theoretical values for the scattering coefficients and anisotropy parameters.

Humans↗

Spatial signaling in the development and function of neural connections.

In the vertebrate central nervous system, afferent axons find their appropriate target structures under the influence of local environmental cues. In many target regions, appropriate patterns of activity in the afferents are also required to establish normal mappings between the source cells and the target region. Specific mappings arise in these targets because temporal contiguity in firing is somehow transformed into spatial contiguity of synaptic contacts. In this article, we propose a theory that utilizes the covariance of a transient diffusive signal produced at active synapses with the firing of presynaptic axon terminals to account for many of these activity-dependent features of vertebrate neuroanatomy. Computer simulations of the growth of axons within a three-dimensional volume of neural tissue reveal the generality of the proposed mechanism in accounting for the self-organization of a broad range of diverse neuroanatomical structures, including those in the cerebral cortex. The proposed mechanism is consistent with detailed anatomical and physiological data, and direct experimental tests of predictions of the theory are suggested.

Animals↗

Effect of initial conditions on the speed of reaction-diffusion fronts.

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed.

Journal Article↗

Effect of helicity on the effective diffusivity for incompressible random flows.

The advection of a passive scalar by a quenched (frozen) incompressible velocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second-order self-consistent perturbation theory, in the absence of helicity, perfectly predicts the effective diffusivity of a tracer particle in such a field. In the presence of helicity in the flow, simulations reveal an unexpectedly strong enhancement of the effective diffusivity which is highly nonperturbative and most visible when the bare molecular diffusivity of the particle is small. We develop and analyze a series of approximation schemes which indicate that this enhancement of the diffusivity is due to a second order effect, whereby the helical component of the field, which does not directly renormalize the effective diffusivity, enhances the strength of the nonhelical part of the flow, which in turn renormalizes the molecular diffusivity. We show that this renormalization is most important at a low bare molecular diffusivity, in agreement with numerical simulations.

Journal Article↗

A theoretical description of non-steady-state diffusion of hydrophobic ions across lipid vesicle membranes including effects of ion-ion interactions in the aqueous phase.

A theoretical model of hydrophobic ion diffusion across vesicular membranes is presented, which is based upon activated rate theory. The model is applicable to the sudden addition of hydrophobic ions to a vesicle suspension, for example in a stopped-flow experiment. The time course of diffusion is calculated by numerical integration of differential rate equations for the ion concentrations and electrical potential differences across the membrane. The model utilizes the three-capacitor model of the membrane and an extended Debye-Hückel theory, taking into account non-neutrality on each side of the membrane. At low ionic strengths good agreement is found between the infinite time diffusion potential and the equilibrium Nernst potential. At large excess of inert electrolyte discrepancies are found, but under such conditions the membrane potential is negligible due to screening.

Cell Membrane↗

Measurement of restricted rotational diffusion of fluorescent lipids in supported planar phospholipid monolayers using angle-dependent polarized fluorescence photobleaching recovery.

A theory describing the shapes of polarized fluorescence photobleaching recovery (PFPR) curves for a population of fluorophores undergoing restricted rotational diffusion in two-dimensional systems such as planar membranes has been developed. In this model, restricted rotational diffusion of the fluorophores is described by using reflective boundary conditions, in which the fluorophores are assumed to diffuse freely but only within an angular space of width 2 omega. The magnitude and apparent rate of the PFPR postbleach fluorescence curves are a function of both omega and the angle between the bleaching and observation beam polarizations psi. It is shown that estimates of the degree of rotational restriction omega may be obtained from changes in the psi-dependent postbleach fluorescence intensities. Using angle-dependent PFPR, slow rotational reorientations of the fluorescent lipid analogue 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine in distearoylphosphatidylcholine Langmuir-Blodgett monolayers deposited on octadecyltrichlorosilane-treated fused quartz were measured. As theoretically predicted for a rotationally restricted fluorophore population, both the initial F psi (0) and final F psi (infinity) postbleach fluorescence intensities varied as a function of psi, and no measurable change in the postbleach fluorescence intensities was observed for psi = 45 degrees. Using the theory for restricted rotational motion, the psi-dependent variations of the final fluorescence intensities F psi (infinity) obtained at two bleaching intensities gave an average apparent omega approximately 52 degrees. However, to adequately fit the F psi (0) data, inclusion of the theoretical effects of rapid (faster than the duration of the photobleaching pulse) fluorophore dynamics was also required. Best fits of the F psi (0) and F psi (infinity) data were obtained when the fluorophores were assumed to rapidly wobble within a cone of semiangle delta approximately 30 degrees-50 degrees while slowly rotating within an angular space defined by semiangle omega approximately 35 degrees-60 degrees. Subsequent analysis of the time- and psi-dependent changes in the post-bleach fluorescence curves F psi (t) gave apparent diffusion coefficients ranging from D approximately 10(-3) s-1 to 4 x 10(-2) s-1.

Carbocyanines↗

Food materials adhesion: a review.

This article reviews the various theories of adhesion mechanism and, more specifically, studies concerning foodstuffs adhesion to industrial equipment and packaging surfaces. Adhesion is governed by mechanical interlocking, wetting, electrostatic and chemical forces, and diffusion. Direct conclusions about the validity of one of these theories were seldom made in the empirical studies reviewed. The different food adhesion determination methods were detailed: direct observations, evaluations (weighting, UV absorbance, and adhesive loss), adhesion strength measurements, and indirect measurements via the wetting theory (tilted plane method, contact angle, and surface tension). The importance of proteins, product rheological properties, solid surface rugosity, and wetting phenomena in many adhesion cases is highlighted. Conclusions were made that fundamental mechanisms of food-contact surfaces interactions still need to be investigated to improve understanding in the science of food materials.

Adhesiveness↗

Cytoplasmic viscosity near the cell plasma membrane: translational diffusion of a small fluorescent solute measured by total internal reflection-fluorescence photobleaching recovery.

Total internal reflection-fluorescence recovery after photobleaching (TIR-FRAP) was applied to measure solute translational diffusion in the aqueous phase of membrane-adjacent cytoplasm. TIR fluorescence excitation in aqueous solutions and fluorescently labeled cells was produced by laser illumination at a subcritical angle utilizing a quartz prism; microsecond-resolution FRAP was accomplished by acousto-optic modulators and electronic photomultiplier gating. A mathematical model was developed to determine solute diffusion coefficient from the time course of photobleaching recovery, bleach time, bleach intensity, and evanescent field penetration depth; the model included irreversible and reversible photobleaching processes, with triplet state diffusion. The validity and accuracy of TIR-FRAP measurements were first examined in aqueous fluorophore solutions. Diffusion coefficients for fluorescein isothiocyanate-dextrans (10-2000 kDa) determined by TIR-FRAP (recovery t1/2 0.5-2.2 ms) agreed with values measured by conventional spot photobleaching. Model predictions for the dependence of recovery curve shape on solution viscosity, bleach time, and bleach depth were validated experimentally using aqueous fluorescein solutions. To study solute diffusion in cytosol, MDCK epithelial cells were fluorescently labeled with the small solute 2',7'-bis-2-carboxyethyl-5-carboxyfluorescein-acetoxymethyl-ester (BCECF). A reversible photobleaching process (t1/2 approximately 0.5 ms) was identified that involved triplet-state relaxation and could be eliminated by triplet-state quenching with 100% oxygen. TIR-FRAP t1/2 values for irreversible BCECF bleaching, representing BCECF translational diffusion in the evanescent field, were in the range 2.2-4.8 ms (0.2-1 ms bleach times), yielding a BCECF diffusion coefficient 6-10-fold less than that in water. These results establish the theory and the first experimental application of TIR-FRAP to measure aqueous-phase solute diffusion, and indicate slowed translational diffusion of a small solute in membrane-adjacent cytosol.

Animals↗

Neuroepithelial (colloid) cysts. Pathogenesis and unusual features.

A brief history of the theories of pathogenesis of the origin of neuroepithelial cysts is presented. An origin more diffuse than the paraphysis seems most likely in our opinion, and we attempt to substantiate this theory with several of the cases from our series. One posterior third ventricular neuroepithelial cyst and one in the fourth ventricle are demonstrated roentgenographically. Also included in our series are a case showing suprasellar calcification on plain skull roentgenograms, not previously reported in neuroepithelial cysts, and a case with a cyst measuring 9 cm, the largest neuroepithelial cyst yet reported.

Adult↗

Towards an international theory of nursing.

During the latter half of the 20th century, the development of numerous nursing theories has enriched nursing scholarship and education worldwide, a movement initially led by North American scholars. Recently, nurses outside of North America have begun to reformulate these theories in order to make them relevant in other contexts. This study summarizes those movements in developing an international theory of nursing and suggests future directions for such a theory.

Attitude to Health↗

Kinetic equations for diffusion in the presence of entropic barriers.

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Journal Article↗

Hypoxia and atherosclerosis: re-evaluation of an old hypothesis.

It was hypothesized over 40 years ago that a decrease in the oxygenation of the vascular wall might somehow be involved in atherogenesis. Recent studies concerning the mechanism of oxygenation indicate that diffusion through plasma is of major importance, meaning that a moderate, prolonged hypoxia could be induced by small decreases in the oxygen diffusivity. Combining all of this leads to a comprehensive theory of atherosclerotic change, indicating how aging, smoking, diabetes, hypercholesterolemia and hypertension are correlated with the disease, and suggesting methods of prevention (or reversal).

Arteriosclerosis↗

Partitioning and diffusion of proteins and linear polymers in polyacrylamide gels.

The equilibrium partition coefficient (K) and diffusion coefficient (Dgel) of two proteins and two linear polymers were measured as a function of polymer content of a 2.7% cross-linked polyacrylamide (PA) gel. The gel concentration, expressed as a volume percentage of PA in the gel (phi), varied between 0 and 14%. The measurements were made by fluorescence spectroscopy; fluorescent dyes were covalently attached to the macromolecules. The dependence of K on phi for the proteins agrees with a model of the gel network as randomly placed, impenetrable rods. The diffusion data are interpreted in terms of an effective medium theory for the mobility of a sphere in a Brinkman fluid. Using values of the Brinkman parameter in the literature, the effective medium model with no adjustable parameters fits the diffusion data for the proteins very well but underpredicts Dgel for the linear polymers. The gel effect on partitioning is significantly greater than that on diffusion. The permeability (KDgel) of bovine serum albumin decreased by 10(3) over the range phi = 0 --> 8%, and the ratio of permeabilities for ribonuclease compared to BSA increased from 2 to 30.

Acrylic Resins↗

Computer-aided stochastic modeling of the radiolysis of liquid water.

A computer-aided stochastic model of the radiolysis of liquid water has been developed. It is based on Monte Carlo simulation of charged-particle tracks, a random-flight method to simulate diffusion of species and the Debye-Smoluchowski theory of reactions between radicals. The model takes into account the formation of ionizations, excitations and subexcitation electrons at the physical stage. The corresponding initial yields at approximately 1 fs were found to be G(ion) = 4.37, G(exc) = 2.81 and G(e-sub) = 4.38. The energy spectrum of subexcitation electrons has been calculated. Autoionizations and dissociations of excited molecules, hole migration, electron thermalization, geminate recombination and the cage effect are considered at the physico-chemical stage. The mean thermalization distance of subexcitation electrons is 24.5 nm. The initial yields of e(aq)-, H+, OH, H, H2 and O are 4.89, 4.86, 5.96, 1.10, 0.15 and 0.15, respectively. The reactions between radicals and products as well as their diffusion are simulated at the chemical stage. The decay kinetics of the most important radicals is reported together with the time evolution of the most important reactions. The yields of the reactive radicals, e(aq)-, H+, OH, H and OH-, at 1 ps are 4.84, 4.85, 5.87, 1.09 and 0.0, respectively. The respective steady-state yields at 10 micros are 2.70, 3.58, 2.89, 1.17 and 0.79. The yields of molecular products, H2O2 and H2, are 0.73 and 0.47 at 10 micros. The concentration-dependent yields of e(aq)-, OH and H2O2 are calculated in three different aqueous solutions. The predictions of the model agree fairly well with experimental data.

Chemical Phenomena↗

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Journal Article↗