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PubMed2002

Measurement of the lateral diffusion of human MHC class I molecules on HeLa cells by fluorescence recovery after photobleaching using a phycoerythrin probe.

The mobility of cell surface MHC class I molecules on HeLa cells was measured by fluorescence recovery after photobleaching (FRAP). The probe used for these studies was the phycobiliprotein R-phycoerythrin coupled to Fab fragments of a monoclonal antibody specific for human monomorphic MHC class I molecules. It was found that the recovery curves could be equally well fitted by either a random diffusion model with an immobile component or by an anomalous diffusion model. In the latter case, the anomalous diffusion exponent was consistent with that previously determined by single-particle tracking (SPT) experiments using the same probe (P. R. Smith, I. E. G. Morrison, K. M. Wilson, N. Fernandez, and R. J. Cherry. 1999. Biophys. J. 76:3331-3344). The FRAP experiments, however, yielded a considerably higher value of D(0), the diffusion coefficient for a time interval of 1 s. To determine whether the results were probe dependent, FRAP measurements were also performed with the same monoclonal antibody labeled with Oregon Green. These experiments gave similar results to those obtained with the phycoerythrin probe. FRAP experiments with the lipid probe 5-N-(octadecanoyl) aminofluoroscein (ODAF) bound to HeLa cells gave typical results for lipid diffusion. Overall, our observations and analysis are consistent with anomalous diffusion of MHC class I diffusion on HeLa cells, but quantitative differences between FRAP and SPT data remain to be explained.

Antibodies, Monoclonal↗

PubMed2004

Desorption kinetics of phenanthrene in aquifer material lacks hysteresis.

Desorption experiments were carried out in flow through columns following long-term sorption batch experiments (up to 1010 days at 20 degrees C; Rügner, H.; Kleineidam, S.; Grathwohl, P. Long-term sorption kinetics of phenanthrene in aquifer materials. Environ. Sci. Technol. 1999, 33, 1645-1651) to elucidate sorption/desorption hysteresis phenomena of phenanthrene in aquifer materials. Most of the sorbents employed in this study (homogeneous lithocomponents separated from aquifer sediments or fresh rock fragments) showed highly nonlinear sorption isotherms because of coal particles embedded inside the grains. Because sorption capacities were high, sorption equilibrium was not reached in most of the sorbents during the initial sorptive uptake experiments lasting up to 1010 days. Desorption was studied up to 90 days at 20 degrees C. The temperature was raised after that stepwise from originally 20 to 30, 40, 50, and finally to 70 degrees C for selected samples to estimate activation energies of desorption. A numerical intraparticle pore diffusion model was used to fit sorptive uptake data and subsequently for pure forward prediction of the release rates in the desorption column experiments. Desorption was initially fast followed by extended tailing which in other studies is fitted by using multirate first-order models. Our results demonstrate that the retarded intraparticle pore diffusion model can predict the desorption rates with a single diffusion rate constant obtained independently from the long-term batch sorption experiment. No evidence for hysteresis was found, suggesting that many hysteresis phenomena reported earlier are experimental artifacts resulting from nonequilibrium effects and "nonphysical" models. The different temperature steps allowed one to additionally calculate activation energies of desorption (45-59 kJ mol(-1)), which were in reasonably good agreement with results from earlier studies for a retarded pore diffusion process. In addition, equilibrium sorption isotherms were determined at 20 and 40 degrees C to compare sorption and desorption enthalpies. Both were in good agreement, confirming that desorption was not significantly different from sorption.

Adsorption↗

PubMed2002

Fluorescence evidence that a phase transition causes the induction time in the reduction in dynamic tension during surfactant adsorption to a clean air/water interface and a kinetic-diffusive transport model for the phase-induced induction.

An aqueous soluble surfactant adsorbing from solution onto an initially clean air/water interface often exhibits an induction period in the surface tension relaxation in which, as the adsorption begins, the tension remains near the clean interface value for an extended period of time before decreasing rapidly to the equilibrium value. In this study, using a model nonionic soluble surfactant, C14E6(CH3(CH2)13-(OCH2CH2)6-OH), we present direct fluorescence evidence that this induction is due to a first-order phase transition from a gaseous (G) to a liquid expanded (LE) phase that the assembling monolayer undergoes at constant surface pressure. An open channel flow cell is initially filled with water, and onto its air/water interface is spread an insoluble amphiphilic dye that fluoresces upon irradiation in the LE phase and whose fluorescence is quenched in the G phase. An aqueous solution of C14E(6) is then allowed to flow through the channel. We observe the immediate appearance of bright islands of the LE phase growing in a dark (G) background, confirming the presence of the G/LE phase transition. These islands eventually occupy the entire surface, after which the interface remains uniformly bright. We correlate this phase transition to the induction period by simultaneously measuring the tension of the interface of the open channel, and verifying that as the islands grow the tension remains at the clean value until the bright LE phase occupies the entire surface, whereupon the tension rapidly decreases. We further develop a phase transition surfactant transport model for the induction period in which surfactant diffuses toward and kinetically adsorbs onto the surface, and then rapidly equilibrates between the G and LE phases. For our model surfactant C14E6, we independently measure the surface concentration of the nucleating LE phase, the LE phase surfactant equation of state, the kinetic rate constants for adsorption into the LE phase, and the bulk diffusion coefficient. Using these measurements, we predict induction times for adsorption onto a clean surface without convection. We also measure these induction times in tension relaxation for adsorption onto a pendant bubble using axisymmetric shape analysis, and demonstrate agreement with the simulations with no adjustable constants.

Journal Article↗

PubMed2001

The effect of hydrogen bonding on diffusion across model membranes: consideration of the number of H-bonding groups.

The diffusion of a series of phenols across simple silicone membranes impregnated with either octanol or toluene was studied. These solvents are taken up and saturate the membrane. The presence of the solvents in a solid membrane allows them to interact with any permeant that cross the membrane. This membrane was used to simulate a bio-membrane, e.g. the skin, capable of hydrogen bonding with the permeant. As the number of H-bonding groups was increased the flux across both the octanol and toluene impregnated membranes decreased. However, deconvolution of the data showed that for the octanol impregnated membrane the diffusion coefficient (Dm) decreased significantly with the number of H-bonding groups. This was not the case for the toluene impregnated membrane. Furthermore the spatial configuration of the -OH groups around the aromatic ring had a significant effect on the decrease in Dm. These findings have considerable implications in understanding the absorption of permeants across bio-membranes capable of H-bonding.

Catechols↗

PubMed2003

Ion fluxes in giant excised cardiac membrane patches detected and quantified with ion-selective microelectrodes.

We have used ion-selective electrodes (ISEs) to quantify ion fluxes across giant membrane patches by measuring and simulating ion gradients on both membrane sides. Experimental conditions are selected with low concentrations of the ions detected on the membrane side being monitored. For detection from the cytoplasmic (bath) side, the patch pipette is oscillated laterally in front of an ISE. For detection on the extracellular (pipette) side, ISEs are fabricated from flexible quartz capillary tubing (tip diameters, 2-3 microns), and an ISE is positioned carefully within the patch pipette with the tip at a controlled distance from the mouth of the patch pipette. Transport activity is then manipulated by solution changes on the cytoplasmic side. Ion fluxes can be quantified by simulating the ion gradients with appropriate diffusion models. For extracellular (intrapatch pipette) recordings, ion diffusion coefficients can be determined from the time courses of concentration changes. The sensitivity and utility of the methods are demonstrated with cardiac membrane patches by measuring (a) potassium fluxes via ion channels, valinomycin, and Na/K pumps; (b) calcium fluxes mediated by Na/Ca exchangers; (c) sodium fluxes mediated by gramicidin and Na/K pumps; and (d) proton fluxes mediated by an unknown electrogenic mechanism. The potassium flux-to-current ratio for the Na/K pump is approximately twice that determined for potassium channels and valinomycin, as expected for a 3Na/2K pump stoichiometery (i.e., 2K/charge moved). For valinomycin-mediated potassium currents and gramicidin-mediated sodium currents, the ion fluxes calculated from diffusion models are typically 10-15% smaller than expected from the membrane currents. As presently implemented, the ISE methods allow reliable detection of calcium and proton fluxes equivalent to monovalent cation currents <1 pA in magnitude, and they allow detection of sodium and potassium fluxes equivalent to <5 pA currents. The capability to monitor ion fluxes, independent of membrane currents, should facilitate studies of both electrogenic and electroneutral ion-coupled transporters in giant patches.

Cell Culture Techniques↗

PubMed2005

Sorption kinetics of strontium in porous hydrous ferric oxide aggregates II. Comparison of experimental results and model predictions.

In a previous paper, we introduced the Donnan diffusion model to describe cation diffusion into microporous solids with variably charged surfaces, such as hydrous ferric oxides (HFO). Here, we present experiments investigating slow diffusion and sorption of strontium by HFO aggregates with well-characterized porosity. Adsorption of protons and strontium at the HFO surface was evaluated by acid-base titration and batch adsorption experiments with dispersed HFO. The experimental data were fitted with a 1-pK basic Stern model including surface ion pair formation of Na(+) and NO(3)(-) and charge distribution for Sr surface complexes. Sorption-diffusion experiments were conducted in flow-through columns at controlled flow rates and at two different pH values, pH 4 and 7. Wet HFO aggregates, which were synthesized using a freezing and thawing method, were packed into chromatographic columns, pre-equilibrated to reach a constant pH, and then Sr breakthrough curves for adsorption and desorption of Sr were recorded. Strong retardation of Sr indicated that diffusion was sufficiently fast in a fraction of pores, so that sorption sites in these pores were rapidly accessible. Based on the analysis of NaNO(3) breakthrough curves, this rapidly accessible pore fraction was estimated to be 37% of the total aggregate pore volume at pH 4.0 and 72% at pH 7.0, respectively. Taking this into account, the Donnan diffusion model gave a good description of the experimental Sr breakthrough curves. Cation exclusion was correctly predicted at pH 4.0. At pH 7, the strong tailing of Sr breakthrough curves due to Sr diffusion into the smallest pores was very well simulated. The Donnan diffusion model proved adequate for pore sizes between approximately 2 and 5 nm, depending on pH and ionic strength. This category of pores was dominant in the HFO aggregates used in this work.

Journal Article↗

PubMedDate not supplied

A model for diffusion controlled bioavailability of crude oil components.

Crude oil is a complex mixture of several different structural classes of compounds including alkanes, aromatics, heterocyclic polar compounds, and asphaltenes. The rate and extent of microbial degradation of crude oil depends on the interaction between the physical and biochemical properties of the biodegradable compounds and their interactions with the non-biodegradable fraction. In this study we have systematically altered the concentration of non-biodegradable material in the crude oil and analyzed its impact on transport of the biodegradable components of crude oil to the microorganisms. We have also developed a mathematical model that explains and accounts for the dependence of biodegradation of crude oil through a putative bioavailability parameter. Experimental results indicate that as the asphaltene concentration in oil increases, the maximum oxygen uptake in respirometers decreases. The mathematically fitted bioavailability parameter of degradable components of oil also decreases as the asphaltene concentration increases.

Algorithms↗

PubMed2006

Phenomenological model of diffuse global and regional atrophy using finite-element methods.

The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition artefacts is also presented. Cross-sectional and longitudinal sets of simulated data are shown and a visual classification protocol has been used by experts to rate real and simulated scans according to their degree of atrophy. Results confirm the potential of the proposed methodology.

Alzheimer Disease↗

PubMed2000

Modeling of diffusion and concurrent metabolism in cutaneous tissue.

Clearance by cutaneous metabolism can shield the body from penetration of environmental and therapeutic xenobiotics. Here we report on a physical model to relate Fickian diffusion and concurrent Michaelis-Menten metabolism of drugs in the viable epidermis of human skin. For this purpose, we numerically generated substrate concentration profiles within the metabolizing tissue and the resulting donor-to-receiver substrate fluxes through the tissue for various mass transport and metabolism parameters. To validate the model, permeation and concurrent metabolism of a peptidomimetic compound, L -Ala-4-methoxy-2-naphthylamide (Ala-MNA), across both stripped human skin and HaCaT cell culture sheets were compared to numerical simulations. Parameter estimates for those calculations were extracted from independent experiments. Experimental data and numerical predictions were in excellent agreement. Also, numerical fits and independently validated parameters correlated closely, indicating the principal validity of the physical model. Numerical simulations and theoretical derivations illustrate the kinetic impact of the factors involved, i.e. the diffusion coefficient D, substrate donor concentration C(S,D), substrate partition coefficient P, tissue thickness L and maximum metabolic rate V(max), on drug permeation, with L having the strongest effect. In the steady state, the coefficient 2 alpha, i.e. the dimensionless ratio of the residence time term (L(2)/D) of a substrate in the tissue to the metabolic half-life term (C(S,D)P/2 V(max)), allows to estimate concentration gradients within the tissue and the extent of metabolism. High 2 alpha values represent practically complete metabolic cleavage upon penetration. Epidermis ( approximately 40 microm thick) of stripped human skin and HaCaT sheets ( approximately 10 microm) had 2 alpha values of 43 and 2.7, respectively, indicating that intact Ala-MNA could only permeate HaCaT sheets, but not skin. Independent permeation experiments confirmed this outcome. This physical model may be applicable to other metabolizing tissues as well.

Cells, Cultured↗

PubMed2002

Distributed modeling of diffusive solute transport in peritoneal dialysis.

The diffusive transport between blood and an ex-tissue medium (dialysis fluid) is evaluated using a mathematical model that takes into account the (quasicontinuous) distribution of capillaries within the tissue at various distances from the tissue surface, and includes diffusive-convective transport through the capillary wall and lymphatic absorption from the tissue. General formulas for solute penetration depth, lambda, and for the diffusive mass transport coefficient for the transport between blood and dialysis fluid, K(BD), are provided in terms of local transport coefficients for capillary wall, tissue, and lymphatic absorption. For pure diffusive transport between blood and dialysis fluid and thick tissue layers (i.e., if the solute penetration depth is much lower than the tissue thickness) these formulas yield previously known expressions. It is shown that apparent tissue layers, with widths lambdaTBL and lambdaT, respectively, may be defined according to the values of local transport parameters in such a way that K(BD) is equal to the solute clearance K(TBL) from the tissue by blood and lymph for a layer with width lambdaTBL or to the solute clearance K(T) from blood to dialysate by diffusion through the tissue layer with width lambdaT. For tissue layers with width much higher than the penetration depth: lambdaT approximately = lambdaTBL approximately = lambda. These characteristic width lengths depend on the transport parameters (and thus on the size) of solutes. Effective blood flow, which may be related to the exchange of the solute between blood and dialysate, is defined using an analogy to the extraction/absorption coefficients for blood-tissue exchange. Various approximations for the distributed model formula for diffusive mass transport coefficient (K(BD)) are possible. The appropriate range for their application is obtained from the general formula.

Animals↗

PubMed1990

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.

Adsorption↗

PubMed2006

Traveling waves and spread rates for a West Nile virus model.

A reaction-diffusion model for the spatial spread of West Nile virus is developed and analysed. Infection dynamics are based on a modified version of a model for cross infection between birds and mosquitoes (Wonham et al., 2004, An epidemiological model for West-Nile virus: Invasion analysis and control application. Proc. R. Soc. Lond. B 271), and diffusion terms describe movement of birds and mosquitoes. Working with a simplified version of the model, the cooperative nature of cross-infection dynamics is utilized to prove the existence of traveling waves and to calculate the spatial spread rate of infection. Comparison theorem results are used to show that the spread rate of the simplified model may provide an upper bound for the spread rate of a more realistic and complex version of the model.

Algorithms↗

PubMed2006

Microscopic model of diffusion limited aggregation and electrodeposition in the presence of leveling molecules.

We present a cellular automata approach for microscopic modeling of the effect of unbinding in diffusion limited aggregation. The automata represent active particles, which are able to change their internal state and affect their neighbors. The geometry resembles electrochemical deposition-"ions" diffuse at random from the top of a container until encountering an aggregate in contact with the bottom, to which they stick. This model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules that unbind atoms from the aggregate transforms the deposit to a 100% dense one (in three dimensions). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called leveler molecules which are used in electrochemical deposition.

Journal Article↗

PubMed1998

Aggregation During Precipitation from Solution. A Pore Diffusion-Reaction Model for Calcium Oxalate Monohydrate.

We have studied the precipitation of calcium oxalate monohydrate (COM) from supersaturated saline solutions both as an in vitro model of the formation of human kidney stones and more generally as a model of particle-size enlargement during precipitation from solution. In any precipitation system there are two mechanisms for size enlargement: growth, by which is meant the deposition of ionic or molecular species on crystal surfaces, and aggregation, the process by which crystals collide, adhere to each other, and form new, stable particles. In this paper we report batch precipitation experiments conducted at constant initial supersaturation and varying ratios of calcium to oxalate ions. By comparison with a simple diffusion-reaction model we are able to draw substantial inferences on the processes that control aggregation. We conclude that at constant temperature and agitation, the aggregation rate constant depends only on the cementing rate, which in turn depends on the solution composition and an appropriately formulated Thiele modulus only. Thus, for the first time, it is possible to propose and evaluate a physico-chemical model for the kinetics of aggregation during precipitation from solution. Copyright 1998 Academic Press.

Journal Article↗

PubMed2006

Removal of ammonium ion from aqueous solution using natural Turkish clinoptilolite.

A study on ion exchange kinetics and equilibrium isotherms of ammonium ion on natural Turkish clinoptilolite (zeolite) was conducted using a batch experiment technique. The effects of relevant parameters, such as temperature, contact time and initial ammonium (NH(4)(+)) concentration were examined, respectively. The pseudo first-order, pseudo second-order kinetic models and intraparticle diffusion model were used to describe the kinetic data. The pseudo second-order kinetic model provided excellent kinetic data fitting (R(2)>0.990) and intraparticle diffusion effects ammonium uptake. The Langmuir and Freundlich models were applied to describe the equilibrium isotherms for ammonium uptake and the Langmuir model agrees very well with experimental data. Thermodynamic parameters such as change in free energy (DeltaG(0)), enthalpy (DeltaH(0)) and entropy (DeltaS(0)) were also determined. An examination of the thermodynamic parameters shows that the exchange of ammonium ion by clinoptilolite is a process occurring spontaneously and physical in nature at ambient conditions (25 degrees C). The process is also found to be exothermic. The results indicate that there is a significant potential for the natural Turkish clinoptilolite as an adsorbent material for ammonium removal from aqueous solutions.

Kinetics↗

PubMed1996

Development of an atmospheric 222Rn concentration model using a hydrodynamic meteorological model: II. Three-dimensional research-purpose model.

This paper describes a new type of three-dimensional numerical model for 222Rn transport in an atmospheric boundary layer. The model is a combination of a prognostic hydrodynamic meteorological model including a turbulence closure model and an atmospheric diffusion model for 222Rn. The first part provides the second part with the meteorological conditions needed for calculations of the 222Rn transport and diffusion. The model is capable of giving consideration to horizontal source distribution, complex terrain, and non-uniform and non-steady atmosphere. The model's results were compared with 222Rn field measurements in a mountain-valley area and represented qualitatively a typical diurnal variation of the 222Rn concentration in nocturnal drainage flows. The model was also applied to the transport of 222Rn in a seacoast area. These results indicated that the model could be effective as a research tool for numerical analysis of 222Rn behavior under various atmospheric conditions.

Air Pollutants, Radioactive↗

PubMed1976

A unified mathematical model for diffusion from drug-polymer composite tablets.

The derivation and experimental verification of a unified mathematical model for the estimation of drug release rate from drug-polymer composite tablets are presented. Cylindrical coordinates are utilized in the solution of the diffusion equation for a three-dimensional system. The model is applicable to tablets that range from the shape of a flat disk (radius greater than thickness) to that of a cylindrical rod (radius less than thickness). The general solution for the fraction of drug released at a time t is (see article). This approach to a three-dimensional system, utilizing cylindrical coordinates, presents a comprehensive method for the estimation of drug release rates from sustained release tablets with drug distributed homogeneously throughout a polymer matrix. The calculated and experimental drug diffusion rate of pyrimethamine from pyrimethamine-silicone rubber composite tablets that range in shape from that of a disk to a cylinder, and of hydrocortisone from EVA, polycaprolactone, and PVA terpolymer, are compared.

Caprolactam↗

PubMed1994

A new model of diffuse brain injury in rats. Part I: Pathophysiology and biomechanics.

This report describes the development of an experimental head injury model capable of producing diffuse brain injury in the rodent. A total of 161 anesthetized adult rats were injured utilizing a simple weight-drop device consisting of a segmented brass weight free-falling through a Plexiglas guide tube. Skull fracture was prevented by cementing a small stainless-steel disc on the calvaria. Two groups of rats were tested: Group 1, consisting of 54 rats, to establish fracture threshold; and Group 2, consisting of 107 animals, to determine the primary cause of death at severe injury levels. Data from Group 1 animals showed that a 450-gm weight falling from a 2-m height (0.9 kg-m) resulted in a mortality rate of 44% with a low incidence (12.5%) of skull fracture. Impact was followed by apnea, convulsions, and moderate hypertension. The surviving rats developed decortication flexion deformity of the forelimbs, with behavioral depression and loss of muscle tone. Data from Group 2 animals suggested that the cause of death was due to central respiratory depression; the mortality rate decreased markedly in animals mechanically ventilated during the impact. Analysis of mathematical models showed that this mass-height combination resulted in a brain acceleration of 900 G and a brain compression gradient of 0.28 mm. It is concluded that this simple model is capable of producing a graded brain injury in the rodent without a massive hypertensive surge or excessive brain-stem damage.

Animals↗