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PubMed2004

Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment, and deposition.

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for postdeposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1 ) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further ( epsilont )(1/3) coarsening of average cluster size; and t(-1/2) approach to a saturation size varying as epsilon(-1/2) . Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law [ ( epsilont )(1/2) ] cluster size coarsening through the redistribution allowed by slow detachment. The basic ( epsilont )(1/3) domain growth laws and epsilon(-1/2) saturation in model I are explained by a simple scaling picture involving the time for a particle to detach and diffuse to the next cluster. A second, fuller approach is presented that employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows, through the steady state solution of the corresponding equation for a cluster probability generating function, quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.

Journal Article↗
PubMed1986

Kinetics of sorption of ionizable solutes by plastic infusion bags.

Aqueous solutions of several ionizable substances were stored in plastic infusion bags and the sorption of the substances monitored with time. The substances used were p-nitrophenol, p-toluidine, warfarin sodium [3-(alpha-acetonylbenzyl)-4-hydroxycoumarin sodium salt] and trifluoperazine hydrochloride (10-[3-(4-methyl-1-piperazinyl)propyl]-2-(trifluoromethyl)phenothiazine dihydrochloride). The rate and extent of sorption for each substance varied with pH and was consistent with a preferential uptake of the un-ionized species. The uptake of p-nitrophenol and p-toluidine was adequately described by a diffusion model derived assuming that sorption is rate-controlled by the diffusivity of the solute in the plastic matrix, and that only the un-ionized species was sorbed by the plastic matrix. However, the uptake of warfarin sodium and trifluoperazine hydrochloride was described more accurately by a diffusion model in which the diffusional resistance of the plastic matrix and of an interfacial resistance barrier both contributed to the diffusional resistance encountered in the sorption process. It appeared that the rate of uptake of the un-ionized form of these solutes was diminished due to the influence of interfacial or aqueous diffusional barriers. Solute lipophilicity and degree of ionization appeared to be important factors determining the relative contribution of the respective barriers to the overall diffusional resistance.

Absorption↗
PubMed2001

Generalized empty-interval method applied to a class of one-dimensional stochastic models.

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models that cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called interparticle distribution function (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model that cannot be solved directly by the conventional IPDF method and that can be viewed as a generalization of the voter model and/or as an epidemic model. We also consider the reversible diffusion-coagulation model with input of particles and determine other reaction-diffusion models that can be mapped onto the latter via suitable similarity transformations. Finally we study the problem of the propagation of a wave front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.

Journal Article↗
PubMed2003

Rotational diffusion tensor of nucleic acids from 13C NMR relaxation.

Rotational diffusion properties have been derived for the DNA dodecamer d(CGCGAATTCGCG)(2) from (13)C R(1rho) and R(1) measurements on the C(1'), C(3'), and C(4') carbons in samples uniformly enriched in (13)C. The narrow range of C-H bond vector orientations relative to the DNA axis make the analysis particularly sensitive to small structural deviations. As a result, the R(1rho)/R(1) ratios are found to fit poorly to the crystal structures of this dodecamer, but well to a recent solution NMR structure, determined in liquid crystalline media, even though globally the structures are quite similar. A fit of the R(1rho)/R(1) ratios to the solution structure is optimal for an axially symmetric rotational diffusion model, with a diffusion anisotropy, D(\|)/D(perpendicular), of 2.1+/-0.4, and an overall rotational correlation time, (2D(\|)+4D(perpendicular))(-1), of 3.35 ns at 35 degrees C in D(2)O, in excellent agreement with values obtained from hydrodynamic modeling.

Carbon Isotopes↗
PubMed2006

Dose and airflow dependence of benzyl alcohol disposition on skin.

The penetration of benzyl alcohol (BA) through split-thickness cadaver skin was measured in nonoccluded Franz cells placed in a fume hood. BA, dissolved in a small volume of ethanol and spiked with (14)C radiolabel, was applied to skin at nine doses ranging from 0.9 to 10600 microg/cm(2). The percentage of radioactivity penetrated after 24 h increased gradually with dose, ranging from 19.8 +/- 2.9% at the lowest dose to 29.2 +/- 3.0% at the highest. Less than 4% of the radioactivity was retained in the tissue at 24 h; the remainder was considered to be evaporated. These data and those from a previous study were analyzed in terms of a finite dose diffusion/evaporation model. The analysis showed that the increase in BA absorption with dose was consistent with a threefold increase in BA diffusivity in the stratum corneum, as its concentration increased from tracer levels to saturation. The variable diffusivity model was able to describe the combined observations from the two studies to within an rms error of 4.2% of dose. A method of estimating the diffusion model parameters independently of the experiment was found to yield good agreement with the experimentally-derived values at low and moderate doses.

Administration, Cutaneous↗
PubMed2002

Tip splittings and phase transitions in the dielectric breakdown model: mapping to the diffusion-limited aggregation model.

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an "effectively" universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to 74 degrees (which corresponds to eta = 4.0+/-0.3).

Journal Article↗
PubMed2004

Analytical approach to localized structures in a simple reaction-diffusion system.

We study from an analytical point of view a simple reaction-diffusion model, which admits stable oscillating localized structures as a consequence of the coexistence between a stable limit cycle and a stable fixed point. Using a generalized matching approach we are able to find approximate analytical expressions for localized oscillating structures in this reaction-diffusion model capturing all the essential ingredients of these breathing particlelike solutions.

Diffusion↗
PubMed2006

Parallel pore and surface diffusion of levulinic acid in basic polymeric adsorbents.

The equilibrium and kinetics of levulinic acid (LA) adsorption on two basic polymeric adsorbents, 335 (highly porous gel) and D315 (macroreticular), were investigated. Experimental adsorption rates in batch stirred vessels under a variety of operating conditions were described successfully by the parallel pore and surface diffusion model taking into account external mass transfer and nonlinear Toth isotherm. The film-pore diffusion model was matched with the rate data and the resulting apparent pore diffusivities were strongly concentration-dependent and approached to a constant value for 335 adsorbent. Thus, the constant value was taken as the accurate pore diffusivity, while the pore diffusivity in D315 was estimated from the particle porosity. The surface diffusivities decreased with increasing initial bulk concentration for both adsorbents. The inverse concentration dependence was correlated reasonably well to the change of isosteric heat of adsorption as amount adsorbed.

Adsorption↗
PubMed1985

Comparison of models describing the sorption of nitroglycerin and diazepam by plastic infusion systems: diffusion and compartment models.

The time course of sorption of diazepam and nitroglycerin from aqueous solutions into plastic materials has been represented by the diffusion and compartmental models for a variety of storage conditions. The diffusion model seemed to be the more satisfactory model in respect to both description and prediction of the drug uptake for all conditions. The compartment model appeared to be useful for describing the drug uptake at earlier times, giving a satisfactory fit to the data and reliable final parameter estimates. However, that model was not able to describe the loss as equilibrium was approached or accurately predict the disappearance profiles for these solutes with alterations in solution volume or infusion bag size. Approximations of the diffusion model gave parameter estimates consistent with those obtained by nonlinear regression using the full equations.

Adsorption↗
PubMed1995

Characterization of a folding intermediate of human carbonic anhydrase II: probing local mobility by electron paramagnetic resonance.

The spin-labeling method was used to investigate human carbonic anhydrase, HCA II, undergoing unfolding induced by guanidine-HCI (Gu-HCI). The spin-probe, N-(2,2,5,5-tetramethyl-1-yloxypyrrolidinyl-3-yl)iodoacetamide, was attached covalently to the single cysteine (position 206) in the enzyme. The electron paramagnetic resonance spectrum of the folded structure showed the characteristic slow motional spectra. When the concentration of the denaturing agent, Gu-HCI, was gradually increased, new spectral components with narrower lines evolved to give complex electron paramagnetic resonance spectra, apparently containing superimposed contributions from several components of different mobility. By a differentiation technique, it was possible to follow the relative increase of the narrow components as a function of Gu-HCI concentration. The amplitude of difference spectra versus Gu-HCI concentration showed two distinct maxima, indicating the existence of a folding intermediate state/structure. The results were found to agree with optical absorption data, which showed similar transitions at the same Gu-HCI concentrations. From line-shape simulations assuming a Brownian diffusion model, the rotational diffusion constants for the spin-label in the folded, folding intermediate, and unfolded structures were determined. The relative abundances of the three conformations in the region 0-4 M Gu-HCI were obtained by least squares fitting of the simulated spectra to the experimental ones. The folding intermediate was found to have a maximum population of 39 +/- 4% at approximately 0.7 M Gu-HCI.

Carbonic Anhydrases↗
PubMed1988

A diffusion-adsorption model for the computation of the amount of hormone around a secreting cell, detected by the reverse hemolytic plaque assay.

The reverse hemolytic plaque assay enables the detection of secretion products from individual cells in cultures by visualizing the plaques formed after complement-mediated hemolysis around the secreting cells. However, the precise quantitation of the amount of secretion remains problematic. In this study we propose a computation model for estimating the spreading of the secreted molecules, based on the underlying processes of diffusion and antigen adsorption by immobilized antibodies. The translational diffusion coefficient of rat prolactin at 37 degrees C, determined by laser light scattering, was 9.89 x 10(-7) cm2/s. The time-dependent concentration distribution around a constantly secreting cell in a flat quasi infinite layer, was derived from the diffusion equation, using an analytical approach based on Laplace transformation. The relations between plaque size, incubation time and secretion level were expressed as a function of the threshold concentration of secretion product that can be detected and the effective diffusion coefficient, taking antigen adsorption into account. We obtained very good agreement between observed and predicted results for plaque formation by dispersed prolactin secreting cells of 14-day-old female rat pituitaries. This study confirms the validity of the assumptions underlying the reverse hemolytic plaque assay, provided that the cell density is low, the incubation time is moderately long and the concentration of specific antiserum is sufficiently high.

Adsorption↗
PubMed1999

Nondestructive Monitoring of Sucrose Diffusion in Oil-in-Water Emulsions by Ultrasonic Velocity Profiling.

The diffusion of sucrose through an optically opaque oil-in-water emulsion was monitored nondestructively by measuring the ultrasonic velocity as a function of height. Initially, a corn oil-in-water emulsion (0, 5, 10, 15, or 20 wt% oil) stabilized by Tween 20 (1 wt%) and xanthan (1 wt%) was placed in a measurement cell at 30 degrees C. A 20 wt% sucrose solution containing the same concentration of Tween 20 and xanthan as the aqueous phase in the emulsion was placed on top of the emulsion. The ultrasonic velocity of this two-layer system was measured as a function of sample height and time and then converted into sucrose and oil concentration-distance profiles using empirical calibration curves. The translational diffusion coefficient of the sucrose in the upper and lower layers was determined by fitting the experimental data to a Fickian diffusion model. The measured diffusion coefficients of the sucrose molecules decreased as the droplet concentration in the emulsion increased, indicating retardation of the sugar molecule movement. Ultrasonic profiling was also used to monitor the compression of the emulsion due to movement of water molecules into the upper layer. Copyright 1999 Academic Press.

Journal Article↗
PubMed1990

Fluid flow rates in human peritumoural oedema.

Five patients with various types of brain tumours were infused with x-ray contrast material in a schedule designed to maintain a constant plasma concentration of tracer over a period of 3 hours. CT scans from an equatorial section of the tumour were taken at frequent intervals the first hour; then at 2 and 3 hours, and when possible up to 14 hours. Two different mathematical models-1. simple diffusion, and 2. transport by bulk flow plus diffusion were used to analyze the changes in tracer amount along profiles placed radially from the tumour center into the oedematous white matter. We found that the simple diffusion model could not account for the spread of contrast material in 3 cases. Adding bulk flow transport gave a very good fit to the measurements, also for the late scans. This model gave bulk flow rates of 0.0005 to 0.005 ml cm-2 min-1 for the extratumoural tissue close to the tumour, and values from 0.25 to 0.55 for the extracellular space in this region. We conclude that the peritumoural tissue is "perfused" by oedema fluid at relatively high flow rates and that this flow transports tracer and other components of plasma into the extracellular space.

Body Fluids↗
PubMed2006

Mode transitions in a model reaction-diffusion system driven by domain growth and noise.

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction-diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.

Animals↗
PubMed1976

Measurement of the translational mobility of concanavalin A in glycerol-saline solutions and on the cell surface by fluorescence recovery after photobleaching.

The fluorescence recovery kinetics of succinyl-fluorescein Concanavalin A (S-F-ConA) in glycerol-physiological saline solutions of high viscosity and when bound to the surface of mouse fibroblasts were measured following brief photobleaching using a laser excited fluorescence microscope. In the high viscosity solutions, the recovery kinetics, interpreted on the basis of a simple diffusion model, yielded a diffusion coefficient in close agreement with the values predicted by the Stokes-Einstein equation. Recovery kinetics for S-F-ConA bound to the surface of mouse 3T3 and SV3T3 cells cultured in vitro yielded diffusion coefficients in the range of 5-10-10(-11) cm2/s, values considerably lower than those reported previously for membrane proteins. These measurements indicated that a considerable fraction of the S-F-ConA molecules bound to the cell surface are immobilized. These results are discussed in relation to current concepts of lateral motion of protein components within natural membranes.

Binding Sites↗
PubMed1984

Denervation disperses acetylcholine receptor clusters at the neuromuscular junction in Xenopus cultures.

The effect of denervation on acetylcholine receptor (AChR) cluster distribution on cultured Xenopus muscle cells has been examined in order to study the role of intact nerve in the maintenance of clusters at the nerve-muscle junction during development. AChRs on the muscle cell were labeled with tetramethyl rhodamine-conjugated alpha-bungarotoxin and sequential changes in AChR cluster distribution were examined with a fluorescence microscope using an image intensifier. Denervation was carried out by exposing the nerve cell body to a focused laser light of a high intensity. After this procedure the neurites originating from the cell quickly disintegrated and large AChR clusters associated with nerve divided into smaller clusters. Individual clusters subsequently decreased in size and finally disappeared. In about 30% of the cases new AChR clusters appeared at the extrajunctional region after denervation. These observations indicate that intact nerves are necessary for the maintenance of receptor localization at the nerve-muscle junction and that nerve-induced accumulation is seemingly reversible during the early period of synapse formation. We tested the idea that receptor clusters were lost due to diffusion of receptors in the muscle membrane after denervation. However, the rate of receptor cluster dispersal after denervation was much slower than that predicted by the diffusion model, suggesting that diffusion of receptors is not a rate-limiting step. Furthermore, we found that receptor clusters at the junction stabilize during days in culture. Thus, 80-90% of receptor clusters at the nerve-muscle junction disappeared at 7 hr after denervation in 1-day cocultures, while about 50% of receptor clusters remained after denervation in 3-day cocultures.

Animals↗
PubMed2005

Equilibrium studies for trimethoprim adsorption on montmorillonite KSF.

In this study, the adsorption of trimethoprim (TMP) on montmorillonite KSF was studied under different conditions (pH, ionic strength, temperature). The results indicate that a pH value of 5.04 is optimum value for the adsorption of TMP on KSF. The adsorption kinetics was interpreted using pseudo-first-order kinetic model, pseudo-second-order kinetic model and intraparticle diffusion model. The pseudo-second-order model provides the best correlation with the experimental data of KSF adsorption. The adsorption data could be fitted with Freundlich, Langmuir and Dubinin-Radushkevich equation to find the characteristic parameters of each model. It was found that linear form of Langmuir isotherm seems to produce a better model than linear form of Freundlich equation. From the Langmuir and Freundlich equation, the adsorption capacity values raised as the solution temperature decreased. From DR isotherm, it was also determined that the type of adsorption can be considered as ion-exchange mechanism. Determination of the thermodynamic parameters DeltaH(0), DeltaS(0) and DeltaG(0) showed that adsorption was spontaneous and exothermic in nature. It was also added that adsorption of TMP by KSF may involve physical adsorption.

Adsorption↗
PubMed2005

Adsorption of residue oil from palm oil mill effluent using powder and flake chitosan: equilibrium and kinetic studies.

The adsorption of residue oil from palm oil mill effluent (POME) using chitosan powder and flake has been investigated. POME contains about 2g/l of residue oil, which has to be treated efficiently before it can be discharged. Experiments were carried out as a function of different initial concentrations of residue oil, weight dosage, contact time and pH of chitosan in powder and flake form to obtain the optimum conditions for the adsorption of residue oil from POME. The powder form of chitosan exhibited a greater rate compared to the flake type. The results obtained showed that chitosan powder, at a dosage of 0.5g/l, 15min of contact time and a pH value of 5.0, presented the most suitable conditions for the adsorption of residue oil from POME. The adsorption process performed almost 99% of residue oil removal from POME. Equilibrium studies have been carried out to determine the capacity of chitosan for the adsorption of residue oil from POME using the optimum conditions from the flocculation at different initial concentrations of residue oil. Langmuir and Freundlich adsorption models were applied to describe the experimental isotherms and isotherm constants. Equilibrium data fitted very well with the Freundlich model. The pseudo first- and second-order kinetic models and intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The experimental data fitted well with the second-order kinetic model, which indicates that the chemical sorption is the rate-limiting step, i.e. chemisorption between residue oil and chitosan. The significant uptake of residue oil on chitosan was further proved by BET surface area analysis and SEM micrographs.

Adsorption↗