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PubMed2006

Lateral diffusion and percolation in membranes.

An algorithm based on Voronoi tessellation and percolation theory is presented to study the diffusion of model membrane components (solutes) in the plasma membrane. The membrane is modeled as a two-dimensional space with integral membrane proteins as static obstacles. The Voronoi diagram consists of vertices, which are equidistant from three matrix obstacles, joined by edges. An edge between two vertices is said to be connected if solute particles can pass directly between the two regions. The percolation threshold, pc, determined using this passage criterion is pc approximately equal to 0.53. This is smaller than if the connectivity of edges were assigned randomly, in which case the percolation threshold pr=2/3, where p is the fraction of connected edges. Molecular dynamics simulations show that diffusion is determined by percolation of clusters of edges.

Algorithms↗
PubMed1977

Temporal effects in the estimation of pulmonary diffusing capacity.

Steady state estimates of the pulmonary diffusing capacity for carbon monoxide (DLCO) require measurement of the uptake and the average alveolar partial pressure of carbon monoxide (PACO). The expired alveolar sample obtained by different experimental methods and/or breathing patterns rarely represents the actual PACO. It is widely accepted that nonuniform distribution of ventilation, diffusion and perfusion causes discrepancies in the measurement of diffusing capacity. tan additional source of error in choosing PACO arises in the sampling time chosen by the experimental method. A theoretical study of a ramp-with-pause and a square breathing pattern demonstrates that the sample-time error exists even in the homogeneous lung. The study shows for the homogeneous lung that the correct fractional concentration of alveolar carbon monoxide (FAV) occurs at a time (TAV), one-half of a breathing period after the effective inspiration time (TI) for the two very different breathing patterns. TI is well-defined in relation to any breathing pattern which can be approximated by ramps and pauses. If TAV and the sample time chosen by the experimental method are known, then the measured DLCO can be corrected to the actual diffusing capacity (DL). The theory agrees with experimental results and computer simulations of inhomogeneous lungs from the literature. This agreement suggests that the theory for the homogeneous lung is also relevant to the inhomogeneous lung.

Carbon Monoxide↗
PubMed1984

Bilayer membranes containing the ganglioside GM1: models for electrostatic potentials adjacent to biological membranes.

Although the Gouy-Chapman-Stern theory of the aqueous diffuse double layer describes well the electrostatic potential adjacent to negatively charged phospholipid bilayer membranes, it does not describe adequately the zeta potential of biological membranes: the zeta potential of an erythrocyte is about half the value predicted from the theory by using the known density of negatively charged sialic acid residues. To investigate the factors responsible for this low electrophoretic mobility, we formed membranes from mixtures of the zwitterionic lipid phosphatidylcholine, PC, and the glycolipid galactosyl-N-acetylgalactosaminyl(N-acetylneuraminyl) -galactosylglucosylceramide, GM1. This glycolipid differs from phospholipids in two respects. First, the negative charge on GM1 is located about 1 nm from the surface, which tends to increase the electrophoretic mobility of vesicles. Second, the head group of GM1 contains five sugar groups that exert a hydrodynamic drag, which tends to decrease the mobility of the vesicles. In a decimolar monovalent salt solution, where the Debye length is about 1 nm, the electrophoretic mobility of the PC-GM1 vesicles is about half the mobility of PC-phosphatidylserine or PC-phosphatidylglycerol vesicles of equivalent composition. In addition, conductance measurements with planar bilayer membranes as well as 31P nuclear magnetic resonance and fluorescence measurements with sonicated vesicles indicate that the potential at the surface of PC-GM1 membranes is about half the value measured for PC-phosphatidylserine membranes in a 0.1 M monovalent salt solution.

G(M1) Ganglioside↗
PubMed1999

Identification of spin diffusion pathways in isotopically labeled biomolecules.

One-dimensional NOE experiments applicable to labeled macromolecules are presented which allow the manipulation of specific spin diffusion pathways and thus unambiguously identify clandestine spins through which the direct NOE is mediated. A treatment of spin diffusion using average Liouvillian theory is shown to describe adequately these phenomena. Experiments are carried out on an 15N-labeled sample of human ubiquitin.

Diffusion↗
PubMed2004

Planar vanadium oxide clusters: two-dimensional evaporation and diffusion on Rh(111).

The formation of novel vanadium oxide cluster molecules by oxidative two-dimensional evaporation from vanadium oxide nanostructures is reported on a Rh(111) metal surface. The structure and stability of the planar V6O12 clusters and the physical origin of their 2D evaporation process have been elucidated by high-resolution scanning tunneling microscopy (STM) and ab initio density functional theory calculations. The surface diffusion of the clusters has been followed in elevated-temperature STM experiments, and the diffusion parameters have been extracted, indicating diffusion by hopping of the entire surface stabilized cluster units.

Journal Article↗
PubMed1991

A paradox concerning ion permeation of the delayed rectifier potassium ion channel in squid giant axons.

1. The fully activated current-voltage relation (I-V) of the delayed rectifier potassium ion channel in squid giant axons has a non-linear dependence upon the driving force, V-EK, as I have previously demonstrated, where V is membrane potential and EK is the equilibrium potential for potassium ions. 2. The non-linearity of the I-V relation and its dependence upon external potassium ion concentration are both well described, phenomenologically, by the Goldman-Hodgkin-Katz (GHK) flux equation, as I have also previously demonstrated. As illustrated below, this result can be modelled using the Eyring rate theory of single-file diffusion of ions through a channel in the low-occupancy limit of the theory. 3. The GHK equation analysis and the low-occupancy limit of the Eyring rate theory are both consistent with the independence principle for movement of ions through the channel, which is at odds with tracer flux ratio results from the delayed rectifier, published elsewhere. Those results suggest that the channel is multiply occupied by two, or perhaps three, ions. 4. The resolution of this paradox is provided by a triple-binding site, multiple-occupancy model in which only one vacancy, at most, is allowed in the channel. This model predicts current-voltage relations which are consistent with the data (and with the phenomenological prediction of the GHK flux equation). The model is also consistent, approximately, with the tracer flux ratio results.

Animals↗
PubMed2005

Fourier's law from Schrödinger dynamics.

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are met. By numerically solving the time dependent Schrödinger equation, we verify this prediction. Close to equilibrium we analyze this behavior in terms of heat conduction and compute the respective coefficient directly from the theory.

Journal Article↗
PubMed1978

Paired ions: Dipolar pairs as subset of diffusion pairs.

Previous models for which theories of electrolytic conductance have been developed are reviewed. Discrepancies between theoretically derived values of parameters and parameters characteristic of real physical systems suggested the following revised model. Ions are counted as diffusion pairs if their center-to-center distance r is in the range a </= r </= R, in which a is contact distance and R is the diameter of the Gurney cosphere. A fraction alpha of these pairs diffuse to contact to form nonconducting dipolar pairs; alpha/(1-alpha) = exp(-E(s)/kT), in which E(s) is the difference in energy between a diffusion pair at r = R and a contact pair, k is the Boltzmann constant, and T is the absolute temperature. This model permits separate treatment of long-range and short-range interionic effects. The former (relaxation field and electrophoresis) depend on R and the values of the dielectric constant and viscosity of the pure solvent. The latter (formation of dipolar pairs) is described by E(s), or alternatively by K(s) = exp(-E(s)/kT) in which K(s) is the constant describing the steady state between solvent-separated diffusion pairs and dipolar (contact) pairs. For solutions of the alkali halides, a simple empirical correlation is found between R and the Pauling radii of the cations, and also between E(s) and the sum of the radii of cation and anion.

Journal Article↗
PubMed1983

Large divalent cations and electrostatic potentials adjacent to membranes. A theoretical calculation.

We have extended the Gouy-Chapman theory of the electrostatic diffuse double layer by considering the finite size of divalent cations in the aqueous phase adjacent to a charged surface. The divalent cations are modeled as either two point charges connected by an infinitely thin, rigid "rod" or two noninteracting point charges connected by an infinitely thin, flexible "string." We use the extended theory to predict the effects of a cation of length 10 A (1 nm) on the zeta and surface potentials of phospholipid bilayer membranes. The predictions of the rod and string models are similar to one another but differ markedly from the predictions of the Gouy-Chapman theory. Specifically, the extended model predicts that a large divalent cation will have a smaller effect on the potential adjacent to a negatively charged bilayer membrane than a point divalent cation, that the magnitude of this discrepancy will decrease as the Debye length increases, and that a large divalent cation will produce a negative zeta potential on a membrane formed from zwitterionic lipids. These predictions agree qualitatively with the experimental results obtained with the large divalent cation hexamethonium. We discuss the biological relevance of our calculations in the context of the interaction of cationic drugs with receptor sites on cell membranes.

Cations, Divalent↗
PubMed2005

Anisotropic diffusion in nematic liquid crystals and in ferrofluids.

A unified, mean-field kinetic theory approach to the anisotropic translational diffusion observed in liquid crystals and in ferrofluids is proposed. In the dilute regime, unified expressions for the parallel as well as for the perpendicular diffusion coefficient in terms of orientational order parameters are found that apply for liquid crystals as well as for ferrofluids. This result explains the common origin of the anisotropic diffusion found in liquid crystals and in ferrofluids. Differences between the two liquids appear in the semi-dilute regime, where the diffusion coefficients depend on the specific interaction potentials. Explicit expressions for the diffusion coefficients are worked out also in this regime within a mean-field approximation. Comparisons with previous theoretical and experimental results are performed, showing satisfactory agreement to the present results.

Journal Article↗
PubMed1999

A Comparison of Strontium Sorption to Hydrous Aluminum, Iron, and Manganese Oxides.

Strontium sorption to hydrous aluminum (HAO) and manganese (HMO) oxides was studied using macroscopic studies on short- and long-term bases. These studies were compared with previous results for strontium sorption to hydrous ferric oxide (HFO). Sorption to these microporous oxides can be described as a two-step process: a rapid and reversible adsorption reaction to the external surface including the macropores is followed by a slow surface diffusion along the micropore walls of the oxides. Strontium adsorption is a physical type of reaction, where the sorbate retains its hydration sheath. Because the relationship between the amount sorbed and the bulk aqueous concentration was linear (over six orders of magnitude), the range of surface sites can be described with one average type of site. Thermodynamically, this adsorption is an entropy-driven endothermic reaction. Transient studies revealed surface diffusion coefficients ranged from 10(-12) to 10(-11) cm(2)/s; these diffusivities were compared to theoretical diffusivities using site activation theory. Results observed in these studies are consistent with those of HFO where for all the oxides, the energy barrier between sites is approximately equivalent. The long-term studies revealed as much as 90% of the total sites were located on the internal surfaces of the hydrous oxides. Therefore, current transport models must include the contribution from intraparticle diffusion to accurately describe the migration of Sr in the aquatic environments. Copyright 1999 Academic Press.

Journal Article↗
PubMed1981

Time-dependent absorption anisotropy and rotational diffusion of proteins in membranes.

The decay of flash-induced absorption anisotropy, r(t), of a chromophore in a membrane protein is closely correlated with rotational diffusion of the protein in the membrane. We develop a theory of time-dependent absorption anisotropy which is applicable to both linear chromophores and planar chromophores which have two different absorption moments at right angles to one another. The theory treats two types of rotational diffusion of membrane proteins: one is rotation of the whole protein about the normal to the plane of the membrane, and the other is restricted wobbling of the whole or part of the protein molecule. In the former case, r(t) is determined by a rotational diffusion coefficient and an angle between the absorption moment(s) and the normal to the plane of the membrane. Rotation of rigid transmembrane proteins can be described by this treatment. In the latter case, r(t) is characterized by a wobbling diffusion coefficient and the degree of orientational constraint. This treatment may be applicable to independent wobbling of the hydrophilic part of membrane proteins. We further show that, for linear and circularly degenerate chromophores, the effect of the excitation flash intensity on r(t) can be accounted for by a constant scaling factor.

Kinetics↗
PubMed2002

New model of surface diffusion in reversed-phase liquid chromatography.

A new model of surface diffusion in reversed-phase liquid chromatography (RPLC) was derived by assuming a correlation between surface and molecular diffusion. Analysis of surface diffusion data under different conditions of sample compounds, mobile and stationary phases, and temperature in RPLC systems validates this assumption and shows that surface diffusion should be regarded as a molecular diffusion restricted by the adsorptive interactions between the adsorbate molecule and the stationary phase surface. A surface-restricted molecular diffusion model was proposed as a first approximation for the mechanism of surface diffusion. The model is formulated according to the absolute rate theory. The activation energy of surface diffusion (Es) was quantitatively interpreted assuming that Es consists of the contributions of two processes, a hole-making and a jumping one. The former contribution is nearly equal to the activation energy of molecular diffusion and is correlated with the evaporative energy of the mobile phase solvent. The latter contribution is a fraction of the isosteric heat of adsorption. An appropriate explanation based on this new model of surface diffusion is provided for two contradictory results related to the relationship between retention equilibrium and surface diffusion in RPLC and to the surface diffusion coefficient for weakly retained sample compounds.

Chromatography, Liquid↗
PubMed1998

Analysis of biocide transport limitation in an artificial biofilm system.

An alginate gel bead artificial biofilm system was used to assay biofilm susceptibility to four biocides and to analyse the extent to which each agent penetrated the biofilm. Chlorine, glutaraldehyde, an isothiazolone, and a quaternary ammonium compound were tested on alginate-entrapped Enterobacter aerogenes in gel beads ranging from 1.8 to 6 mm in diameter. Gel-entrapped bacteria were less susceptible to all four antimicrobial agents than were planktonic micro-organisms. The degree of kill measured in artificial biofilm gel beads depended on the size of the gel bead and the cell density at which it was loaded. Disinfection efficacy decreased as gel bead radius or cell density increased. The manifest dependence of biofilm disinfection efficacy on the physical properties of the artificial biofilm (radius and cell density) suggests the impingement of transport limitation of biocide transport into the biofilm. A previously developed theory of biocide reaction and diffusion in biofilm was tested by calculating an appropriate Thiele modulus. In accordance with the theory, the efficacy of all four biocides decreased, albeit noisily, as the Thiele modulus exceeded 1. This result demonstrates that transport limitation can impact antimicrobial performance against biofilms not only of oxidizing biocides but also of nonoxidizing agents.

Biofilms↗
PubMed2004

Detection performance of a diffusive wave phased array.

Diffusive wave phased arrays have been demonstrated to be a sensitive method of detecting inhomogeneities embedded in heavily scattering media. However, the increase in sensitivity is coupled with an increase in noise, so that the optimum performance may not be obtained when the sources are modulated in antiphase. The performance of a range of configurations in the presence of Gaussian noise is investigated by using probabilistic detection theory. A model of diffusive wave propagation through scattering media is used to demonstrate that the phase performance can be improved by controlling the relative phase difference between the two sources. However, the best performance is obtained by using the amplitude response of a single source system. The major benefit of a phased array system is therefore the rejection of common systematic noise.

Artifacts↗
PubMedDate not supplied

The quantitative relations between diffusion-controlled reaction rate and characteristic parameters in enzyme-substrate reactions systems. II. Charged substrates.

The quantitative relationship between the spatial factor and the force-range factor on the one hand and the ionic strength and the charges of reactants on the other has been calculated for non-spherically symmetric reaction systems. New upper limits of combination reactions between enzymes and charged substrates have been obtained. Applying the calculated results to the reactions catalyzed by fumarase and D-glyceraldehyde-3 phosphate dehydrogenase, we have been able to interpret experimental phenomena which could not be accounted for by the conventional theory of the diffusion-controlled reaction. Furthermore, the conditions under which the Bronsted equation is valid in the non-equilibrium steady state reaction system have been discussed.

Binding Sites↗