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PubMed1985

The effect of diffusion on the binding of membrane-bound receptors to coated pits.

We have formulated a kinetic model for the primary steps that occur at the cell membrane during receptor-mediated endocytosis. This model includes the diffusion of receptor molecules, the binding of receptors to coated pits, the loss of coated pits by invagination, and random reinsertion of receptors and coated pits. Using the mechanistic statistical theory of nonequilibrium thermodynamics, we employ this mechanism to calculate the two-dimensional radial distribution of receptors around coated pits at steady state. From this we obtain an equation that describes the effect of receptor diffusion on the rate of binding to coated pits. Our equation does not assume that ligand binding is instantaneous and can be used to assess the effect of diffusion on the binding rate. Using experimental data for low density lipoprotein receptors on fibroblast cells, we conclude that the effect of diffusion on the binding of these receptors to coated pits is no more than 84% diffusion controlled. This corresponds to a dissociation rate constant for receptors on coated pits (k-) that is much less than the rate constant for invagination of the pits (lambda = 3.3 X 10(-3)/s) and a correlation length for the radial distribution function of six times the radius of a coated pit. Although the existing experimental data are compatible with any value of k-, we obtain a lower bound for the value of the binding constant (k+) of 2.3 X 10(-2)(micron)2/s. Comparison of the predicted radial distributions with experiment should provide a clear indication of the effect of diffusion on k+.

Coated Pits, Cell-Membrane↗

PubMed1986

Use of a membrane-bound fluorophore to characterize diffusion boundary layers around human erythrocytes.

A novel method is used to demonstrate the presence of diffusion boundary layers around erythrocytes following rapid mixing in a stopped-flow spectrophotometer and to estimate the apparent dimensions of the diffusion boundary layers. Pink erythrocyte ghosts labeled on their external surfaces with tetramethyl rhodamine isothiocyanate (TRITC) were mixed in a stopped-flow apparatus with 50 mM NaI in Ringer's solutions. I- is an effective collisional quencher of TRITC fluorescence. TRITC fluorescence after flow stopped decreased monoexponentially with time. The concentration of I- at the cell surface as a function of time was estimated from the dependence of TRITC fluorescence on I- concentration in steady-state experiments. The kinetics of the increase in I- concentration at the cell surface was fit to two diffusional models: a planar erythrocyte ghost bounded by planar diffusion boundary layer and a spherical erythrocyte surrounded by a spherical shell diffusion boundary layer. The planar model best fits the experimental data with a diffusion boundary layer 4.68 microns thick. Using the spherical model the experimental data is best fit by a 6.9 microns diffusion boundary layer.

Diffusion↗

PubMed1986

Lateral diffusion of ganglioside GM1 in phospholipid bilayer membranes.

The lateral diffusion coefficient of ganglioside GM1 incorporated into preformed dimyristoylphosphatidylcholine (DMPC) vesicles has been investigated under a variety of conditions using the technique of fluorescence photobleaching recovery. For these studies the fluorescent probe 5-(((2-Carbohydrazino)methyl)thio)acetyl) amino eosin was covalently attached to the periodate-oxidized sialic acid residue of ganglioside GM1. This labeled ganglioside exhibited a behavior similar to that of the intact ganglioside, and was able to bind cholera toxin. The lateral diffusion coefficient of the ganglioside was dependent upon the gel-liquid crystalline transition of DMPC. Above Tm the lateral diffusion coefficient of the ganglioside was 4.7 X 10(-9) cm2 s-1 (with greater than 80% fluorescence recovery). This diffusion coefficient is significantly slower than the one previously observed for phospholipids in DMPC bilayers. The addition of increasing amounts of ganglioside, up to a maximum of 10 mol %, did not have a significant effect on the lateral diffusion coefficient or in the percent recovery. At 30 degrees C, the lateral mobility of ganglioside GM1 was not affected by the presence of 5 mM Ca2+, suggesting that, at least above Tm, Ca2+ does not induce a major perturbation in the lateral organization of the ganglioside molecules. The addition of stoichiometric amounts of cholera toxin to samples containing either 1 or 10 mol % ganglioside GM1 produced only a small decrease in the measured diffusion coefficient. The fluorescence recovery after photobleaching experiments were complemented with excimer formation experiments using pyrene-phosphatidylcholine. Above the transition temperature the presence of 10 mol % ganglioside GMI induced a large decrease in the rate of excimer formation. These results also indicated that the addition of ganglioside GMI to phospholipid bilayer vesicles induces a significant restriction in the lateral mobility parameters of the lipid bilayer and that the presence of Ca2' does not have a further effect in the mobility of the probe molecules.

Animals↗

PubMed1987

Diffusion of dihydropyridine calcium channel antagonists in cardiac sarcolemmal lipid multibilayers.

A membrane bilayer pathway model has been proposed for the interaction of dihydropyridine (DHP) calcium channel antagonists with receptors in cardiac sarcolemma (Rhodes, D.G., J.G. Sarmiento, and L.G. Herbette. 1985. Mol. Pharmacol. 27:612-623) involving drug partition into the bilayer with subsequent receptor binding mediated (though probably not rate-limited) by diffusion within the bilayer. Recently, we have characterized the partition step, demonstrating that DHPs reside, on a time-average basis, near the bilayer hydrocarbon core/water interface. Drug distribution about this interface may define a plane of local concentration for lateral diffusion within the membrane. The studies presented herein examine the diffusional dynamics of an active rhodamine-labeled DHP and a fluorescent phospholipid analogue (DiIC16) in pure cardiac sarcolemmal lipid multibilayer preparations as a function of bilayer hydration. At maximal bilayer hydration, the drug diffuses over macroscopic distances within the bilayer at a rate identical to that of DiI (D = 3.8 X 10(-8) cm2/s), demonstrating the overall feasibility of the membrane diffusion model. The diffusion coefficients for both drug and lipid decreased substantially as the bilayers were dehydrated. While identical at maximal hydration, drug diffusion was significantly slower than that of DiIC16 in partially dehydrated bilayers, probably reflecting differences in mass distribution of these probes in the bilayer.

Animals↗

PubMed1989

Mutual diffusion of interacting membrane proteins.

The generalized Stokes-Einstein equation is used, together with the two-dimensional pressure equation, to analyze mutual diffusion in concentrated membrane systems. These equations can be used to investigate the role that both direct and hydrodynamic interactions play in determining diffusive behavior. Here only direct interactions are explicitly incorporated into the theory at high densities; however, both direct and hydrodynamic interactions are analyzed for some dilute solutions. We look at diffusion in the presence of weak attractions, soft repulsions, and hard-core repulsions. It is found that, at low densities, attractions retard mutual diffusion while repulsions enhance it. Mechanistically, attractions tend to tether particles together and oppose the dissipation of gradients or fluctuations in concentration, while repulsions provide a driving force that pushes particles apart. At higher concentrations, changes in the structure of the fluid enhance mutual diffusion even in the presence of attractions. It is shown that the theoretical description of postelectrophoresis relaxation and fluorescence correlation spectroscopy experiments must be modified if interacting systems are studied. The effects of interactions on mutual diffusion coefficients have probably already been seen in postelectrophoresis relaxation experiments.

Diffusion↗

PubMed1989

The spectrin network as a barrier to lateral diffusion in erythrocytes. A percolation analysis.

The spectrin network on the cytoplasmic surface of an erythrocyte can be modeled as a triangular lattice of spectrin tetramers (Tsuji, A., and S. Ohnishi, 1986. Biochemistry. 25:6133-6139). The tetramers act as barriers to protein diffusion, while dissociated dimer pairs, single dimers, and missing tetramers do not. Diffusion in the presence of these barriers is shown to be equivalent to bond percolation on the honeycomb lattice. Monte Carlo calculations for this system then yield the relative diffusion constant of a mobile integral protein as a function of the fraction of spectrin tetramers. At high concentrations of spectrin tetramer, long-range diffusion is blocked, but short-range diffusion is still possible. Monte Carlo calculations yield the average distance over which short-range diffusion can occur, as a function of the fraction of spectrin tetramers. Applications to erythrocyte development and hereditary hemolytic anemia are discussed.

Algorithms↗

PubMed1992

Modulation of lateral transport of membrane components by spatial variations in diffusivity and solubility.

The effect of spatially varying diffusivity and solubility on the efficiency of intramembrane transport is investigated by obtaining solutions to the generalized lateral diffusion equation in which both the diffusion coefficient, D(r), and the partition coefficient, K(r), are functions of position. The mean-time-to-capture by a sink, tc, of particles diffusing in a plane is obtained analytically for the case of a sink surrounded by gradients in D(r) and K(r) with radially symmetrical geometry. It is shown that for particles originating at random locations, tc is shortened dramatically, if in an annular region around the sink, D and K are significantly greater than in the remainder of the plane. Similarly, a viscous boundary layer surrounding a sink is demonstrated to represent a significant barrier for diffusing particles. To investigate more complex geometries, a finite difference numerical integration method is used and is shown to provide comparable results for tc with modest computational power. The same method is used to calculate the tc for particles originating at a source that is joined to the sink by a channel. The increase in the rate with which particles travel from a source to a sink when they are joined by a high diffusivity and/or solubility channel is illustrated by several numerical examples and by graphical representations that show the equilibrium particle density (and hence the effective particle flow) in the presence of different sink, source, and channel combinations. These results are discussed in terms of fluidity domains and other membrane heterogeneities.

Cell Membrane↗

PubMed1992

Analysis of lateral diffusion from a spherical cell surface to a tubular projection.

Cell surfaces are often heterogeneous with respect to the lateral distribution and mobility of membrane components. Because lateral mobility is related to membrane structure, measurement of a particular component's local diffusion coefficient within a distinct surface region provides useful information about the formation and maintenance of that region. Many structurally interesting cell surface features can be described as narrow tubular projections from the body of the cell. In a companion paper, we consider the thin "tethers" that can be mechanically drawn from the red blood cell membrane, and we measure the transport of fluorescent integral proteins from the surface of the cell body onto the tether. In this paper we present an analysis to describe the surface diffusion of membrane particles from a spherical shell onto a thin cylindrical process. Provision is made for different rates of diffusion within the two morphologically distinct regions. The relative role of each region in controlling the diffusive flux between regions is determined primarily by a single dimensionless parameter. This parameter incorporates the ratio of the two diffusion coefficients as well as the dimensions of each region. The analysis can be applied to a fluorescence photobleaching experiment in which the extended process is bleached. If the dimensions of the spherical cell body and the cylindrical extension are known, then the diffusion coefficients of both regions can be determined from the experimental fluorescence recovery curve.

Cell Membrane↗

PubMed1995

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves.

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.

Animals↗

PubMed1995

Cyclic GMP diffusion coefficient in rod photoreceptor outer segments.

Cyclic GMP (cGMP) is the intracellular messenger that mediates phototransduction in retinal rods. As photoisomerizations of rhodopsin molecules are local events, the longitudinal diffusion of cGMP in the rod outer segment should be a contributing factor to the response of the cell to light. We have employed the truncated rod outer segment preparation from bullfrog (Rana catesbeiana) and tiger salamander (Ambystoma tigrinum) to measure the cGMP diffusion coefficient. In this preparation, the distal portion of a rod outer segment was drawn into a suction pipette for measuring membrane current, and the rest of the cell was then sheared off with a glass probe, allowing bath cGMP to diffuse into the outer segment and activate the cGMP-gated channels on the surface membrane. Addition and removal of bath cGMP were fast enough to produce effectively step changes in cGMP concentration at the open end of the outer segment. When cGMP hydrolysis is inhibited by isobutylmethylxanthine (IBMX), the equation for the diffusion of cGMP inside the truncated rod outer segment has a simple analytical solution, which we have used to analyze the rise and decay kinetics of the cGMP-elicited currents. From these measurements we have obtained a cGMP diffusion coefficient of approximately 70 x 10(-8) cm2 s-1 for bullfrog rods and approximately 60 x 10(-8) cm2 s-1 for tiger salamander rods. These values are six to seven times lower than the expected value in aqueous solution. The estimated diffusion coefficient is the same at high (20-1000 microM) and low (5-10 microM) concentrations of cGMP, suggesting no significant effect from buffering over these concentration ranges.

1-Methyl-3-isobutylxanthine↗

PubMed1995

Monte Carlo simulation of diffusion and reaction in two-dimensional cell structures.

Diffusion and reaction processes control the dynamics of many different biological systems. For example, tissue respiration can be limited by the delivery of oxygen to the cells and to the mitochondria. In this case, oxygen is small and travels quickly compared with the mitochondria, which can be considered as immobile reactive traps in the cell cytoplasm. A Monte Carlo theoretical investigation quantifying the interplay of diffusion, reaction, and structure on the reaction rate constant is reported here for diffusible particles in two-dimensional, reactive traps. The placement of traps in overlapping, nonoverlapping, and clustered spatial arrangements can have a large effect on the rate constant when the process is diffusion limited. However, under reaction-limited conditions the structure has little effect on the rate constant. For the same trap fractions and reactivities, nonoverlapping traps have the highest rate constants, overlapping traps yield intermediate rate constants, and clustered traps have the lowest rate constants. An increase in the particle diffusivity in the traps can increase the rate constant by reducing the time required by the particles to reach reactive sites. Various diffusive, reactive, and structural conditions are evaluated here, exemplifying the versatility of the Monte Carlo technique.

Algorithms↗

PubMed1996

Molecular diffusion into horse spleen ferritin: a nitroxide radical spin probe study.

Electron paramagnetic resonance spectroscopy and gel permeation chromatography were employed to study the molecular diffusion of a number of small nitroxide spin probes (approximately 7-9 A diameter) into the central cavity of the iron-storage protein ferritin. Charge and polarity of these radicals play a critical role in the diffusion process. The negatively charged radical 4-carboxy-2,2,6,6-tetramethylpiperidine-N-oxyl (4-carboxy-TEMPO) does not penetrate the cavity whereas the positively charged 4-amino-TEMPO and 3-(aminomethyl)-proxyl radical and polar 4-hydroxy-TEMPO radical do. Unlike the others, the apolar TEMPO radical does not enter the cavity but instead binds to ferritin, presumably at a hydrophobic region of the protein. The kinetic data indicate that diffusion is not purely passive, the driving force coming not only from the concentration gradient between the inside and outside of the protein but also from charge interactions between the diffusant and the protein. A model for diffusion is derived that describes the observed kinetics. First-order half-lives for diffusion into the protein of 21-26 min are observed, suggesting that reductant molecules with diameters considerably larger than approximately 9 A would probably enter the protein cavity too slowly to mobilize iron efficiently by direct interaction with the mineral core.

Animals↗

PubMed1996

Pulsed field gradient-spin echo NMR studies of water diffusion in a phospholipid model membrane.

Water diffusion in the lamellar phase of egg phosphatidylcholine (egg PC)-water was studied by 1H NMR using the pulsed field gradient-spin echo method. The curvature of diffusion plots obtained with egg PC-water mixtures indicates that water diffusion is highly anisotropic with respect to lipid lamellae. This was confirmed by measurements made on macroscopically aligned egg PC-water as a function of orientation that categorically establish DII/DI >> .1, where the respective subscripts refer to parallel and perpendicular to the lipid bilayer. A smooth, monotonic dependence on water concentration was observed for water diffusion in aligned egg PC-water, varying at 25 degrees C from DII = 1.2 x 10(-10) m2 s 1 at n = 4.9 mol water/lipid to DII = 4.0 x 10(-10) m2 s-1 at n = 18.6 mol water/lipid. The diffusion is approximately a factor of 10 slower than in pure water because of water binding and restriction to translational motion within the aqueous layer. No evidence for a sudden drop in water diffusion coefficient at a specific water content, as previously reported with egg PC-water mixtures (Lange and Gary Bobo. 1974. J. Gen. Physiol 63:690-706), was detected. A morphological reorganization of lamellar domains, which in random orientational distribution comprise lipid-water mixtures, is the likely explanation. The study of aligned lipid-water systems is manifestly preferable.

Diffusion↗

PubMed1996

Interactions of spermidine and methylspermidine with DNA studied by nuclear magnetic resonance self-diffusion measurements.

The NMR pulsed field gradient self-diffusion method has been used to study the self-diffusion of the polyamine spermidine and the polyamine analog methylspermidine (completely N-methylated spermidine). The self-diffusion coefficient, D, was measured in solutions of calf thymus DNA prepared from nucleosome core particles (with an average length of 120 base pairs) as a function of the concentration ratio of polyamine to DNA phosphate. A study of the self-diffusion quotient, D/Do (where Do is the diffusion coefficient for free polyamine, not associated with DNA), in additions of spermidine and methyl-spermidine to solutions of NaDNA/NaCl, gave almost identical results with complete association of polyamine to DNA in the initial part of the titrations, indicating similar affinities for DNA. A large influence on the measured self-diffusion coefficients was detected for methylspermidine in NaDNA solutions with different concentrations of NaCl, which shows a considerable salt effect on the polyamine-DNA association. No notable differences in D/Do for methylspermidine were observed in competitive titrations of solutions of Li- and NaDNA, indicating that sodium and lithium ions behave similarly in their interactions with DNA. In titration experiments of methylspermidine into MgDNA solution, the results showed that the polyamine association is less effective than in the case of NaDNA, because of competition from magnesium binding to DNA. Comparisons with calculations based on the electrostatic Poisson-Boltzmann cell model were performed. It is suggested that the interaction is primarily of electrostatic nature, with no binding to specific sites on the DNA molecule.

Animals↗

PubMed1997

Barriers to diffusion of plasma membrane proteins form early during guinea pig spermiogenesis.

The plasma membrane of the mature guinea pig sperm is segregated into at least four domains of different composition. Previous studies have shown that some proteins localized within these domains are free to diffuse laterally, suggesting that barriers to protein diffusion are responsible for maintaining the nonuniform distribution of at least some surface proteins in mature sperm. The different membrane domains appear sequentially during sperm morphogenesis in the testis and during later passage through the epididymis. To determine when diffusion barriers become functional during sperm development, we examined the diffusion of two proteins that are expressed on the cell surface of developing spermatids and become segregated to different plasma membrane domains during the course of spermiogenesis. Both proteins exhibited rapid lateral diffusion throughout spermiogenesis, even after they become localized to specific regions of the surface membrane. These results suggest that barriers to membrane diffusion form concomitantly with membrane domains during spermiogenesis.

ADAM Proteins↗

PubMed1998

Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching with an unmodified confocal laser scanning microscope (confocal FRAP) was used to determine the diffusion properties of network forming biological macromolecules such as aggrecan. The technique was validated using fluorescein isothiocyanate (FITC)-labeled dextrans and proteins (molecular mass 4-2000 kDa) at 25 degrees C and with fluorescent microspheres (207 nm diameter) over a temperature range of 5-50 degrees C. Lateral diffusion coefficients (D) were independent of the focus position, and the degree and extent of bleach. The free diffusion coefficient (Do) of FITC-aggrecan determined by confocal FRAP was 4.25 +/- 0.6 x 10(-8) cm2 s-1, which is compatible with dynamic laser light scattering measurements. It appeared to be independent of concentration below 2.0 mg/ml, but at higher concentrations (2-20 mg/ml) the self-diffusion coefficient followed the function D = Do(e)(-Bc). The concentration at which the self-diffusion coefficient began to fall corresponded to the concentration predicted for domain overlap. Multimolecular aggregates of aggrecan ( approximately 30 monomers) had a much lower free diffusion coefficient (Do = 6.6 +/- 1.0 x 10(-9) cm2 s-1) but showed a decrease in mobility with concentration of a form similar to that of the monomer. The method provides a technique for investigating the macromolecular organization in glycan-rich networks at concentrations close to those found physiologically.

Aggrecans↗

PubMed2003

Hypertension and neuronal degeneration in excised rat spinal cord studied by high-b value q-space diffusion magnetic resonance imaging.

Hypertension is one of the major risk factors of stroke and vascular dementia (VaD). We used stroke prone spontaneous hypertensive rats (SPSHRs) as a model for neuronal degeneration frequently occurring in humans with vascular disease. Recently, high b value q-space diffusion-weighted imaging (DWI) was shown to be very sensitive to the pathophysiological state of the white matter. We studied the spinal cords of SPSHR rats ex vivo after the appearance of motor impairments using diffusion anisotropy and q-space diffusion imaging (measured at a high b value of up to 1 x 10(5) s/mm(2)). The diffusion anisotropy images computed from low b value data set (b(max) approximately 2500 s/mm(2)) showed a small but statistically significant decrease (approximately 12%, P < 0.05) in the diffusion anisotropy in the spinal cords of the SPSHR group as compared to control rats. However, more significant changes were found in the high b value q-space diffusion images. The q-space displacement values in the white matter of the SPSHR group were found to be higher by more than 70% (P < 0.002) than that of the control group. These observations concurred with electron microscopy (EM) that showed significant demyelination in the spinal cords of the SPSHR group. These results seem to indicate that high b value q-space DWI might be a sensitive method for following demyelination and axonal loss associated with vascular insults.

Animals↗

PubMed1986

External diffusion in solid-phase immunoassays.

Calculations are presented describing the influence of external diffusion in the kinetics of solid-phase immunoassays. The analysis is concerned with systems where one reactant is immobilized at the surface of a sphere of arbitrary radius. The solution for a plane surface is found as a limiting case. The factors determining whether the reaction is diffusion or reaction controlled are found to be sphere radius, surface concentration of binding sites, forward reaction rate and diffusion constant of reacting species. Means of determining whether the reaction is diffusion or reaction controlled from observable quantities are described. When applied to heterogeneous antibody-antigen binding it is found that normally the binding to cell-size spheres is not limited by external diffusion. However, when applied to solid-phase assays with high surface concentrations of binding sites immobilized at plane surfaces or macroscopic spheres the binding is found to be diffusion limited. The importance of a mass transfer analysis in this case is also discussed.

Antigen-Antibody Complex↗