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PubMed1974

Restricted diffusion in biophysical systems. Experiment.

The pulsed-gradient spin echo nuclear magnetic resonance (PGSENMR) technique was used to measure restricted diffusion of water in three types of animal tissue: human blood plasma and red cells; rat and rabbit heart; rat and rabbit liver. Characteristic lengths (L) for restriction of diffusion are estimated from dependence on the measuring time. Limitations on the range of observable restrictive lengths (1.5-15 mum) are discussed.The decrease in diffusivity due to 1 mum alumina powder (volume fraction = 0.18) in glycerin/water mixtures agrees with the Wang theory assuming spherical particles and no hydration. The characteristic length (L approximately 4 mum) is larger than the particle size (1 mum) or separation (1.8 mum). Comparison of the diffusivities in tissues at short diffusion times with the Wang theory indicates some bound or trapped water.For packed red blood cells, a restriction (L approximately 2.3 mum) was attributed tothe red cell membrane. A permeability p approximately 0.014 cm/s may be estimated from the decrease in diffusivity. Average values of diffusivity ratio in heart were: 0.36 +/- 0.02 for rat; and 0.26 +/- 0.03 for rabbit; and in liver: 0.25 +/- 0.01 for rat; 0.25 +/- .04 for 10-day old rabbit; and 0.195 +/- 0.03 for 2-yr old rabbit. A restriction (L approximately 2.7 mum) in rat liver probably results from the mitochondria.

Aluminum↗

PubMed1978

Water and hermal diffusivity in a lipid-water smectic phase.

We report the first application of light scattering to measurement of the hydrodynamic relaxation of inhomogeneities in water concentration within a multilamellar, or smectic A, phospholipid water system (dipalmitoyl) phosphatidyl choline). Although the relaxation process in the multilamellar phase is different from the diffusion process in liquid phases, the relaxation rate can be described in terms of a diffusion coefficient. For diffusion parallel to the lamellae, diffusion coefficients ranging from 8 x 10(-7) to 2 x 10(-5) cm2/s were measured over a range of temperature and water concentrations. We describe a model that expresses the diffusion coefficient in terms of the chemical potential for water inside the multilamellar phase and the effective thickness of a "free water zone." The deduced thickness of this free water zone is in good agreement with estimates from X-ray diffraction results. The activation energy for the diffusion process is also deduced from the data, and is found to decrease monotonically with increasing water concentration. We also found the thermal diffusivity to be about 10(-3) cm2/s with only a weak temperature and water concentration dependence. The experimental technique is a new version of forced Rayleigh scattering. The method uses the phase information of the scattered light to improve the ability to detect weak signals. Experimental details are reported.

Diffusion↗

PubMed1979

Diffusion-controlled reactions on spherical surfaces. Application to bacteriophage tail fiber attachment.

We have explored the kinetic implications of a model that may account for the acceleration of tail fiber (F) attachment to baseplates (B) by whiskers (W) on bacteriophage T4. The model assumes that a W-F complex is formed initially, and that the tethered fiber then undergoes rotational diffusion until a B-F encounter takes place. In the absence of whiskers, B-F complexes must form unassisted. Formation of a W-F intermediate will accelerate F attachment to B if (a) the bimolecular rate constant for W-F complex formation is larger than that for direct B-F interaction and (b) subsequent rotational diffusion of the tip of F to B is not much slower than the dissociation of W-F. Condition a was investigated by applying a recent theory of orientational effects on translational diffusion-controlled reactions. This theory suggests that substantial rate enhancement is expected if the reaction half-angle theta 0 is larger for W-F than for B-F complex formation. Condition b was investigated by calculating the mean and the variance of the time required for the diffusion of a molecule (the proximal tip of the fiber) on a spherical surface (whose radius is the distance from the tip to the whisker tethering point) into a circular sink (the baseplate site). The mean time is on the order of the inverse rotational diffusion coefficient, DR, of the fiber, but is sensitive to theta 0. Both conditions are satisfied for plausible choices of parameters. The solution to the diffusion equation we have obtained should have application to other physical situations, such as the rate of quenching of a fluorophore as it diffuses on the surface of a spherical membrane into proximity with a quencher.

Diffusion↗

PubMed1979

Diffusion of ions in myelinated nerve fibers.

The diffusion of ions towards or away from the inner side of the nodal membrane in preparations, the cut ends of which are placed in various media, was investigated. The ion concentration changes were calculated by numerical solution of the unidimensional electrodiffusion equation under a variety of media compositions, axoplasmic diffusion coefficients, and internal anionic compositions. The potassium and cesium ion diffusion along the axon towards the node was determined experimentally by two different electrophysiological methods. On the basis of comparison between the experimental data and the computational predictions the axoplasmic potassium ion diffusion coefficient was determined to be almost equal to that in free aqueous solution, while that of cesium ion was close to one half of that in aqueous solution. Utilizing the values of diffusion parameters thus determined, we solved the electrodiffusion equation for a number of common experimental procedures. We found that in short fibers, cut 0.1-0.2 cm at each side of the node, the concentration approached values close to the new steady-state values within 5-30 min. In long fibers (over 1 cm long) steady-state concentrations were obtained only after a few hours. Under some conditions the internal concentrations transiently overshot the steady-state values. The diffusion potentials generated in the system were also evaluated. The ion concentration changes and generation of diffusion potential cannot be prevented by using side pools with cation content identical to that of the axoplasm.

Animals↗

PubMed1982

Diffusion of molecules on biological membranes of nonplanar form. A theoretical study.

Lateral mobility of molecules on cell membranes has been recently studied by fluorescence photobleaching recovery (FPR) techniques. The interpretation of these results in terms of diffusion along the membranes is based on the assumption that the surface is planar, although biological membranes may have blebs and microvilli. To study the effect of nonplanarity on the diffusion rate, the diffusion equation along curved surfaces was derived and was solved numerically for a "wavy" surface of the form A cos kx cos ky. Calculations show that for k = 10 pi micrometer-1 and a bleached spot of 1 micrometer in diameter, the time dependence of the intensity of fluorescence in the bleached spot depends on A at A less than 0.5 micrometer, while at higher values of A (a and 2 micrometer) the dependence is weak. If one calculates diffusion coefficients from FPR measurements and assumes that the membrane is planar, the resulting diffusion coefficient is not less than about half of the real one. Because of the tortuous shape of the spot boundary, increasing the microvilli length from 0.5 micrometer to 1 or 2 micrometer does not change the diffusion rates. These considerations are valid for times when the diffusion is dominated by molecules that were initially located close to the spot boundary.

Cell Membrane↗

PubMed1986

Effects of spatial variation in membrane diffusibility and solubility on the lateral transport of membrane components.

There exist many examples of membrane components (e.g. receptors) accumulating in special domains of cell membranes. We analyze how certain variations in lateral diffusibility and solubility of the membrane would increase the efficiency of transport to these regions. A theorem is derived to show that the mean-time-of capture, tc, for particles diffusing to a trap from an annular region surrounding it, is intermediate to the tc values that correspond to the minimum and maximum diffusion coefficients that obtain in this region. An analytical solution for tc as a function of the gradient of diffusivity surrounding a trap is derived for circular geometry. Since local diffusion coefficients can be increased dramatically by reducing the concentration of intra-membrane particles and/or allowing them to form aggregates, such mechanisms could greatly enhance the diffusion-limited transport of particular membrane components to a trap (e.g. coated pit). If the trap is surrounded by an annular region in which the probe particles' partition function is increased, say, by the local segregation of certain phospholipids, tc is shown to vary inversely with the logarithm of the relative partition function. We provide some conjectural examples to illustrate the magnitude of the effects which heterogeneities in diffusibility and solubility may have in biological membranes.

Diffusion↗

PubMed1990

Effects of lateral diffusion on the fluorescence anisotropy in hexagonal lipid phases. I. Theory.

It is shown that fluorescence anisotropy from lipidlike probes in the hexagonal HII phase gives information of (a) orientational order parameters, (b) the wobbling diffusion constant, and (c) the hopping diffusion constant of the probe, DH, equals DL/R2, the lateral diffusion constant over the square of the radius of the hexagonal tubes. Here we consider only lipidlike probes having the absorption transition movement and/or the emission transition moment along the long axis of the molecule. Three models are introduced for analysis of time-resolved data: the "WOBHOP," the "reduced WOBHOP," and the "P2P4HOP" model. The fluorescence anisotropy in response to a very short excitation pulse in each of the three models is a constant plus a number of exponentials. The WOBHOP and reduced WOBHOP models have 3 and 2 exponentials, respectively, and both contain four fitting parameters: r0 (the fundamental anisotropy), (P2) (the second rank orientational order parameter), DW (the wobbling diffusion constant), and DH (the hopping diffusion constant). The P2P4HOP model has eight exponentials and five fitting parameters: the four parameters listed above and (P4) (the fourth rank orientational order parameter). Analysis of fluorescence anisotropy data in the hexagonal HII phase using one of these models allows for obtaining the hopping diffusion constant, and, if the lateral diffusion constant is known, the radius of the hexagonal tubes. Substitution of DH = 0 in each of the three models yields an expression for the fluorescence anisotropy that is used in the literature for lamellar (L alpha or L beta) phases. The fluorescence anisotropy in coexisting L alpha/HII phases is discussed.

Diffusion↗

PubMed1993

Lipid and water diffusion in bicontinuous cubic phases measured by NMR.

Lipid and water diffusion coefficients in bicontinuous cubic liquid crystalline phases have been determined with the NMR pulsed magnetic field gradient technique. In the monoolein-water system, a discontinuity in the variation of the water diffusion coefficient with water content is observed, which coincides with the two-phase region between the two cubic phases in this system. The degree of water association to the lipid has been determined, considering the obstruction factor for diffusion in the cubic phases. The lipid diffusion coefficient increases with increased unsaturation of the lipid, and decreases when larger amphiphile molecules like cholesterol, gramicidin-A, and lyso-oleoyl-phosphatidylcholine are solubilized in the cubic phase. In a cubic liquid crystal of monoolein (MO), dioleoylphosphatidylcholine (DOPC), and water, the individual lipid diffusion coefficients have been determined simultaneously in the same sample. The diffusion coefficients of MO and DOPC differ by a factor of two, and both decrease with increasing DOPC content. The results are discussed in relation to probe techniques for measurements of lipid diffusion.

Biophysical Phenomena↗

PubMed1997

Estimation of the diffusion-limited rate of microtubule assembly.

Microtubule assembly is a complex process with individual microtubules alternating stochastically between extended periods of assembly and disassembly, a phenomenon known as dynamic instability. Since the discovery of dynamic instability, molecular models of assembly have generally assumed that tubulin incorporation into the microtubule lattice is primarily reaction-limited. Recently this assumption has been challenged and the importance of diffusion in microtubule assembly dynamics asserted on the basis of scaling arguments, with tubulin gradients predicted to extend over length scales exceeding a cell diameter, approximately 50 microns. To assess whether individual microtubules in vivo assemble at diffusion-limited rates and to predict the theoretical upper limit on the assembly rate, a steady-state mean-field model for the concentration of tubulin about a growing microtubule tip was developed. Using published parameter values for microtubule assembly in vivo (growth rate = 7 microns/min, diffusivity = 6 x 10(-12) m2/s, tubulin concentration = 10 microM), the model predicted that the tubulin concentration at the microtubule tip was approximately 89% of the concentration far from the tip, indicating that microtubule self-assembly is not diffusion-limited. Furthermore, the gradients extended less than approximately 50 nm (the equivalent of about two microtubule diameters) from the microtubule tip, a distance much less than a cell diameter. In addition, a general relation was developed to predict the diffusion-limited assembly rate from the diffusivity and bulk tubulin concentration. Using this relation, it was estimated that the maximum theoretical assembly rate is approximately 65 microns/min, above which tubulin can no longer diffuse rapidly enough to support faster growth.

Animals↗

PubMed1997

Diffusion behavior of lipid vesicles in entangled polymer solutions.

Dynamic light scattering was used to follow the tracer diffusion of phospholipid/cholesterol vesicles in aqueous polyacrylamide solutions and compared with the diffusive behavior of polystyrene (PS) latex spheres of comparable diameters. Over the range of the matrix concentration examined (Cp = 0.1-10 mg/ml), the diffusivities of the PS spheres and the large multilamellar vesicles exhibited the Stokes-Einstein (SE) relation, while the diffusivity of the unilamellar vesicles did not follow the increase of the solution's viscosity caused by the presence of the matrix molecules. The difference between the diffusion behaviors of unilamellar vesicles and hard PS spheres of similar size is possibly due to the flexibility of the lipid bilayer of the vesicles. The unilamellar vesicles are capable of changing their shape to move through the entangled polymer solution so that the hindrance to their diffusion due to the presence of the polymer chains is reduced, while the rigid PS spheres have little flexibility and they encounter greater resistance. The multilamellar vesicles are less flexible, thus their diffusion is similar to the hard PS spheres of similar diameter.

Acrylic Resins↗

PubMed1998

Non-steady-state diffusion in a multilayered tissue initiated by manipulation of chemical activity at the boundaries.

Diffusion of ionic and nonionic species in multilayered tissues plays an important role in the metabolic processes that take place in these tissues. To create a mathematical model of these diffusion processes, we have chosen as an example hydrogen-bicarbonate ion pair diffusion within the mammalian cornea. This choice was based on the availability of experimental data on this system. The diffusion coefficient of the hydrogen-bicarbonate ion pair in corneal stroma and epithelium is calculated from the observed change in pH in the stroma when conditions at the corneal anterior epithelial surface are changed while the posterior surface is continually bathed with a Ringer's solution in equilibrium with a CO2-gas air mixture. Matching experimental results to a mathematical model of the cornea as a two-layer diffusion system yields, at 37 degrees C, a diffusion coefficient of the hydrogen-bicarbonate ion pair of 2.5 x 10(-6) cm2/s in the stroma and 0.4 x 10(-6) cm2/s in the epithelium. Application of the Nernst-Einstein equation to these data gives the following diffusion coefficients in the two layers: 1) stroma, D(H+) = 11.8 x 10(-6) cm2/s; D(HCO3-) = 1.5 x 10(-6) cm2/s; and 2) epithelium, D(H+) = 1.9 x 10(-6) cm2/s; D(HCO3-) = 0.22 x 10(-6) cm2/s.

Animals↗

PubMed1999

Cyclic AMP diffusion coefficient in frog olfactory cilia.

Cyclic AMP (cAMP) is one of the intracellular messengers that mediate odorant signal transduction in vertebrate olfactory cilia. Therefore, the diffusion coefficient of cAMP in olfactory cilia is an important factor in the transduction of the odorous signal. We have employed the excised cilium preparation from the grass frog (Rana pipiens) to measure the cAMP diffusion coefficient. In this preparation an olfactory cilium is drawn into a patch pipette and a gigaseal is formed at the base of the cilium. Subsequently the cilium is excised, allowing bath cAMP to diffuse into the cilium and activate the cyclic nucleotide-gated channels on the plasma membrane. In order to estimate the cAMP diffusion coefficient, we analyzed the kinetics of the currents elicited by step changes in the bath cAMP concentration in the absence of cAMP hydrolysis. Under such conditions, the kinetics of the cAMP-activated currents has a simple dependence on the diffusion coefficient. From the analysis we have obtained a cAMP diffusion coefficient of 2.7 +/- 0.2. 10(-6) cm2 s-1 for frog olfactory cilia. This value is similar to the expected value in aqueous solution, suggesting that there are no significant diffusional barriers inside olfactory cilia. At cAMP concentrations higher than 5 microM, diffusion slowed considerably, suggesting the presence of buffering by immobile cAMP binding sites. A plausible physiological function of such buffering sites would be to prolong the response of the cell to strong stimuli.

Animals↗

PubMed1999

Anomalous diffusion of major histocompatibility complex class I molecules on HeLa cells determined by single particle tracking.

Single-particle tracking (SPT) was used to determine the mobility characteristics of MHC (major histocompatibility complex) class I molecules at the surface of HeLa cells at 22 degrees C and on different time scales. MHC class I was labeled using the Fab fragment of a monoclonal antibody (W6/32), covalently bound to either R-phycoerythrin or fluorescent microspheres, and the particles were tracked using high-sensitivity fluorescence imaging. Analysis of the data for a fixed time interval suggests a reasonable fit to a random diffusion model. The best fit values of the diffusion coefficient D decreased markedly, however, with increasing time interval, demonstrating the existence of anomalous diffusion. Further analysis of the data shows that the diffusion is anomalous over the complete time range investigated, 4-300 s. Fitting the results obtained with the R-phycoerythrin probe to D = D0talpha-1, where Do is a constant and t is the time, gave D0 = (6.7 +/- 4.5) x 10(-11) cm2 s-1 and alpha = 0.49 +/- 0.16. Experiments with fluorescent microspheres were less reproducible and gave slower anomalous diffusion. The R-phycoerythrin probe is considered more reliable for fluorescent SPT because it is small (11 x 8 nm) and monovalent. The type of motion exhibited by the class I molecules will greatly affect their ability to migrate in the plane of the membrane. Anomalous diffusion, in particular, greatly reduces the distance a class I molecule can travel on the time scale of minutes. The present data are discussed in relation to the possible role of diffusion and clustering in T-cell activation.

Adenosine Triphosphate↗

PubMed2001

The physical basis of diffusion-weighted MRI.

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is the only technique that permits a non-invasive in vivo assessment of water molecular diffusion, which reflects tissue configuration at a microscopic level. Therefore, this technique appears to be particularly useful in monitoring brain abnormalities. However, the quantitative measurement of diffusion is not without problems, which may limit the widespread use of diffusion-weighted MRI. In this report, the phenomenon of diffusion is described, together with its effect on the nuclear magnetic resonance signal. The concepts of diffusion anisotropy and diffusion tensor are also introduced, and the technical and hardware requirements are discussed.

Algorithms↗

PubMed2000

Diffusion in Pseudomonas aeruginosa biofilms: a pulsed field gradient NMR study.

A Pseudomonas aeruginosa biofilm is studied with pulsed field gradient echo nuclear magnetic resonance. Although not all spectral components are assigned yet, the experimental results show that a biofilm consists of components with very different diffusion coefficients. The various biofilm components that give motionally narrowed 1H NMR signals, can be grouped into five classes with diffusion coefficients, ranging from 2 x 10(-9) to 1 x 10(-13) m2 s-1. Investigation of the diffusion behavior of water in the biofilm shows three fractions with different diffusion coefficients. Besides the highly mobile bulk water at least two other fractions with much lower diffusion coefficients are detected. It is shown that one of the fractions with the low diffusion coefficient probably arises from intracellular water. Also for another component of the biofilm, glycerol, three fractions with diffusion coefficients that differ more than a factor ten are detected. Also a group of signals exists which result from practically immobile components.

Alginates↗

PubMed1999

Diffusion-controlled drug delivery systems: calculation of the required composition to achieve desired release profiles.

The aim of this study was to investigate the effect of the composition of diffusion-controlled release devices (type and amount of plasticizer, type of polymer) on the drug diffusivity and the resulting release kinetics in a quantitative way. Diltiazem hydrochloride and theophylline were investigated in ethyl cellulose (EC) and Eudragit((R)) RS 100, plasticized with various amounts of acetyltributyl citrate (ATBC), acetyltriethyl citrate (ATEC), dibutyl phthalate (DBP), dibutyl sebacate (DBS), diethyl phthalate (DEP), and tributyl citrate (TBC). Thin drug-containing films (monolithic solutions) were used to determine the diffusion coefficients experimentally. The effect of the type and amount of plasticizer on the drug diffusivity was found to be significant, whereas the chain length of the polymer only played a minor rule in the investigated systems. Interestingly, a quantitative relationship between the diffusion coefficient of the drug and the plasticizer level could be established. Based on these results, the release kinetics of diffusion-controlled drug delivery systems could be predicted. In this study, the release patterns from microparticles were calculated and the significant effect of the composition of the device on the resulting release rate was simulated. The latter could be effectively modified by varying the type and amount of plasticizer. Independent experiments verified the theoretical predictions. The practical benefit of the presented method is to calculate the required composition of diffusion-controlled drug delivery systems (monolithic solutions) to achieve desired release profiles.

Cellulose↗

PubMed2001

Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity.

Matrix diffusion is an important transport process in geologic materials of low hydraulic conductivity. For predicting the fate and transport of contaminants, a detailed understanding of the diffusion processes in natural porous media is essential. In this study, diffusive tracer transport (iodide) was investigated in a variety of geologically different limestone and sandstone rocks. Porosity, structural and mineralogical composition, hydraulic conductivity, and other rock properties were determined. The effective diffusion coefficients were measured using the time-lag method. The results of the diffusion experiments indicate that there is a close relationship between total porosity and the effective diffusion coefficient of a rock (analogous to Archie's Law). Consequently, the tortousity factor can be expressed as a function of total porosity. The relationship fits best for thicker samples (> 1.0 cm) with high porosities (> 20%), because of the reduced influence of heterogeneity in larger samples. In general, these correlations appear to be a simple way to determine tortuosity and the effective diffusion coefficient from easy to determine rock porosity values.

Diffusion↗

PubMed2003

Effect of silica sand on activation energy for diffusion of sodium ions in montmorillonite and silica sand mixture.

The effect of silica sand on the diffusion of sodium ions in mixtures of montmorillonite and silica sand was studied by measuring the apparent diffusion coefficients, activation energies for diffusion, and the basal spacing of the mixed samples. These diffusion experiments suggest that the apparent diffusion coefficients of sodium ions in the mixed samples were almost the same as those of pure montmorillonite samples having the same partial dry densities of montmorillonite. The activation energy dependence for diffusion of sodium ions on the partial dry density was different between the mixed samples and the pure montmorillonite samples. The activation energy increased by adding silica sand at the partial dry density of 1.0 Mg m(-3), and decreased by adding silica sand at the partial dry densities higher than 1.2 Mg m(-3). A change in the XRD profile was observed after adding silica sand at the partial dry density of 1.6 Mg m(-3). Here, a three-water-layer hydrate state of montmorillonite was found in the mixed sample whereas only a two-water-layer hydrate state was observed in the pure montmorillonite sample. These experimental results suggest that silica sand changed the montmorillonite microstructure in the mixed samples, which then altered the sodium-ion diffusion process.

Bentonite↗