Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study.

The lateral diffusion coefficient for mixtures of mobile and immobile particles is obtained from Monte Carlo calculations of random walks by mobile tracers in the presence of immobile obstacles on a triangular lattice. The diffusion coefficient of the mobile species is obtained as a function of the area fractions of mobile and immobile species. The results are applied to diffusion of band 3 in the erythrocyte membrane, and indicate that obstruction of diffusion of mobile band 3 by band 3 and glycophorin attached to the membrane skeleton is not sufficient to explain the observed diffusion coefficient.     

Differences in the response of several cell types to inhibition of surface receptor mobility by local concanavalina binding

Concanavalin A (conA) modulates the lateral mobility of cell surface receptors differently on different cell types. This was demonstrated by using fluorescence photobleaching recovery (FPR) to measure the inhibition of the lateral mobility of conA receptors by localized binding of conA on lymphocytes, fibroblasts, and macrophages. On mouse spleen lymphocytes, binding of conA platelets above a threshold coverage (about 12% of the upper cell-surface area) reduced the diffusion coefficient of mobile TMR-SconA-receptor complexes from 3.0×10^?10 cm²/sec to 0.6× 10^?10 cm²/sec (a 5-fold decrease), and the fraction of mobile receptors was concomitantly reduced from 0.4 to 0.11. Below the threshold occupancy, no effect on either parameter was detected. On 3T3 cells, a qualitatively similar threshold phenomenon was observed: coverage of over 9% of the upper cell surface by conA platelets induced a 3-fold reduction in the diffusion coefficient of TMR-SconA-receptor complexes from 5×10^?10 cm²/sec to 1.7× 10^?10 cm²/sec. However, no effect on the mobile fraction (about 0.4) was observed. In contrast, neither the diffusion coefficient nor the mobile fraction of TMR-SconA-receptor complexes on mouse peritoneal macrophages (both resident and thioglycolate-stimulated) or on the mouse macrophage cell line P388D₁ were affected by the binding of conA platelets in amounts covering over 50% of the upper cell surface (approx. 4.6× 10^?10 cm²/sec and 0.5 for the diffusion coefficient and mobile fraction, respectively). These differences are correlated to the different cytoskeletal functions of the various cell types studied, and are discussed regarding the mechanism of the conA-induced modulation.     

Mobility measurement by analysis of fluorescence photobleaching recovery kinetics.

Fluorescence photobleaching recovery (FPR) denotes a method for measuring two-dimensional lateral mobility of fluorescent particles, for example, the motion of fluorescently labeled molecules in approximately 10 mum2 regions of a single cell surface. A small spot on the fluorescent surface is photobleached by a brief exposure to an intense focused laser beam, and the subsequent recovery of the fluorescence is monitored by the same, but attenuated, laser beam. Recovery occurs by replenishment of intact fluorophore in the bleached spot by lateral transport from the surrounding surface. We present the theoretical basis and some practical guidelines for simple, rigorous analysis of FPR experiments. Information obtainable from FPR experiments includes: (a) identification of transport process type, i.e. the admixture of random diffusion and uniform directed flow; (b) determination of the absolute mobility coefficient, i.e. the diffusion constant and/or flow velocity; and (c) the fraction of total fluorophore which is mobile. To illustrate the experimental method and to verify the theory for diffusion, we describe some model experiments on aqueous solutions of rhodamine 6G.     

Cell-specific constraints to the lateral diffusion of a membrane glycoprotein.

We have previously shown that the lateral diffusion, D, of the class I Major Histocompatibility Complex (MHC) glycoprotein H-2Ld is constrained by its glycosylation, when expressed in mouse L-cells. Removal of one or more of the 3 N-linked oligosaccharides of H-2Ld glycoproteins results in an increase in D. In order to further examine the influence of glycosylation on D, we compared lateral diffusion of H-2Ld expressed in wild-type CHO cells with lateral diffusion of the same molecule expressed in mutant CHO cells with aberrant surface glycosylation. In addition, we compared lateral diffusion of wild-type and unglycosylated H-2Ld antigens in these cells. In contrast to the large effect of glycosylation state on lateral diffusion of H-2Ld in mouse L-cells, there was little effect of glycosylation on lateral diffusion of H-2Ld in any of the CHO cells. This, together with similar results on hamster class I antigens, indicates that the constraints to D of H-2Ld and other class I MHC molecules are different in CHO cells than in L-cells. Measurements of lateral diffusion after treatment of cells with cytochalasin D make it clear that interactions between MHC class I molecules and a cytoskeleton are important in reducing the mobile fraction of diffusing molecules, R, though they cannot be shown to directly affect the diffusion coefficient, D.     

A fluorescence photobleaching study of vesicular stomatitis virus infected BHK cells. Modulation of G protein mobility by M protein

The mobility of vesicular stomatitis virus (VSV) G protein on the surface of infected BHK cells was studied by using the technique of fluorescence photobleaching recovery. The fraction of surface G protein that was mobile in that time scale of the measurement (minutes) was at least 75%, a relatively high value among cell surface proteins so far observed. For studies of the effect of an internal viral protein (M protein) on G protein mobility, cells infected with wild-type VSV were compared with those infected with temperature-sensitive VSV mutants of complementation group III, which contains lesions in the M protein. At the permissive temperature, a pronounced decrease in the mobile fraction of surface G was observed for each of three mutants studied, while mobility of surface G at the nonpermissive temperature was indistinguishable in mutant and wild-type infected cells. A significantly lower mobile fraction of G protein was also observed in SV40 transformed 3T3 cells infected with wild-type VSV, but not in 3T3 or chick embryo fibroblast cells similarly infected. None of the variables tested had a measurable effect on the lateral diffusion coefficient of the mobile G protein. These results are interpreted as modulation of the mobility of a specific cell surface protein by a specific intracellular protein.     

Fibronectin receptor exhibits high lateral mobility in embryonic locomoting cells but is immobile in focal contacts and fibrillar streaks in stationary cells

The dynamic process of embryonic cell motility was investigated by analyzing the lateral mobility of the fibronectin receptor in various locomotory or stationary avian embryonic cells, using the technique of fluorescence recovery after photobleaching. The lateral mobility of fibronectin receptors, labeled by a monoclonal antibody, was defined by the diffusion coefficient and mobile fraction of these receptors. Even though the lateral diffusion coefficient did not vary appreciably (2 X 10(-10) cm2/S less than or equal to D less than or equal to 4 X 10(-10) cm2/S) with the locomotory state and the cell type, the mobile fraction was highly dependent on the degree of cell motility. In locomoting cells, the population of fibronectin receptors, which was uniformly distributed on the cell surface, displayed a high mobile fraction of 66 +/- 19% at 25 degrees C (82 +/- 14% at 37 degrees C). In contrast, in nonmotile cells, the population of receptors was concentrated in focal contacts and fibrillar streaks associated with microfilament bundles and, in these sites, the mobile fraction was small (16 +/- 8%). When cells were in a stage intermediate between highly motile and stationary, the population of fibronectin receptors was distributed both in focal contacts with a small mobile fraction and in a diffuse pattern with a reduced mobile fraction (33 +/- 9%) relative to the diffuse population in highly locomotory cells. The mobile fraction of the fibronectin receptor was found to be temperature dependent in locomoting but not in stationary cells. The mobile fraction could be modulated by affecting the interaction between the receptor and the substratum. The strength of this interaction could be increased by growing cells on a substratum coated with polyclonal antibodies to the receptor. This caused the mobile fraction to decrease. The interaction could be decreased by using a probe, monoclonal antibodies to the receptor known to perturb the adhesion of certain cell types which caused the mobile fraction to increase. From these results, we conclude that in locomoting embryonic cells, most fibronectin receptors can readily diffuse in the plane of the membrane. This degree of lateral mobility may be correlated to the labile adhesions to the substratum presumably required for high motility. In contrast, fibronectin receptors in stationary cells are immobilized in focal contacts and fibrillar streaks which are in close association with both extracellular and cytoskeletal structures; these stable complexes appear to provide firm anchorage to the substratum.     

Lateral diffusion of cholesterol in monolayers.

The surface diffusion coefficient of cholesterol in cholesterol monolayers has been measured as a function of cholesterol surface concentration. Two different radiochemical methods, one integral and the other differential, were developed which gave comparable results. In the integral method two cholesterol monolayers, one of which is radioactive, are isolated on inert hydrophilic supports and then brought into contact. After some time the supports are separated and the radioactivity of the supports is measured. The differential method is an autoradiographic experiment. Two cholesterol monolayers, one of which is radioactive, are separated by means of a thin barrier. Upon removal of the barrier and at later times, an autoradiographic plate is brought to within a fraction of a mm from the aqueous surface and exposed. The plates are developed and analysed. The data show that the cholesterol surface diffusion coefficient in the dilute monolayers is approximately 10(-6)cm2/s and is nearly independent of surface concentration up to a concentration corresponding to an area of 40 A2/molecule. As the monolayer becomes compressed beyond this surface concentration, the diffusion coefficient decreases ubruptly with the deeply decreasing surface tension to about 10(-7) cm2/s, when a fully condensed surface layer of 38 A2/molecule is reached. This diffusion coefficient is of the same order of magnitude as the diffusion coefficients measured in lipid bilayers and in membranes.     

Mobility of creatine phosphokinase and beta-enolase in cultured muscle cells.

The diffusion of beta-enolase and creatine phosphokinase in muscle cells has been studied by modulated fringe pattern photobleaching. Beta-enolase is mobile in the sarcoplasm. At 20 degrees C, the diffusion coefficient is 13.5 +/- 2.5 microm2 s(-1) in the cytosol and 56 microm2 s(-1) in aqueous media. As in the case of dextrans of the same hydrodynamic radius, its mobility is hindered by both the crowding of the fluid phase of the cytoplasm and the screening effect due to myofilaments. A fraction of creatine phosphokinase is mobile in the sarcoplasm. Its diffusion coefficient in the cytosol, 4.5 +/- 1 microm2 s(-1), is lower than that of the dextran of equivalent size. The other fraction (20 to 50%) is very slightly mobile, with an apparent diffusion coefficient varying from 0.0035 to 0.043 microm2 s(-1). This low mobility might be attributed to exchange between free and bound creatine phosphokinase. The bound fraction of the endogenous enzyme was localized by immunocytofluorescence on the cultured muscle cells. Our results favor a localization of bound cytosolic creatine phosphokinase on the M-line and a diffuse distribution in all myotubes.     

The membrane skeleton of erythrocytes. A percolation model.

The spectrin network on the cytoplasmic surface of the erythrocyte membrane is modeled as a triangular lattice of spectrin tetramers. This network obstructs lateral diffusion of proteins and provides mechanical reinforcement to the membrane. These effects are treated in a systematic and unified manner in terms of a percolation model. The diffusion coefficient is obtained as a function of the fraction of normal spectrin tetramers for both static and fluctuating barriers. The elasticity of the network is calculated as a function of the fraction of normal spectrin and the ratio of bending to stretching energies. For static barriers, elasticity and lateral diffusion are incompatible: if a network is connected enough to be elastic, it is connected enough to block long-range lateral diffusion. The elasticity and the force required for mechanical breakdown go to zero at the percolation threshold; experimental evidence suggests the existence of a stability threshold at or near the percolation threshold. The model is qualitatively applicable to other cells with membrane skeletons, such as epithelial cells, in which localization of membrane proteins is essential to differentiation.     

Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient.

An understanding of the distance dependence of the lateral diffusion coefficient is useful in comparing the results of diffusion measurements made over different length scales, and in analyzing the kinetics of mobile redox carriers in organelles. A distance-dependent, concentration-dependent diffusion coefficient is defined, and it is evaluated by Monte Carlo calculations of a random walk by mobile point tracers in the presence of immobile obstacles on a triangular lattice, representing the diffusion of a lipid or a small protein in the presence of immobile membrane proteins. This work confirms and extends the milling crowd model of Eisinger, J., J. Flores, and W. P. Petersen (1986. Biophys J. 49:987-1001). Similar calculations for diffusion of mobile particles interacting by a hard-core repulsion yield the distance dependence of the self-diffusion coefficient. An expression for the range of short-range diffusion is obtained, and the distance scales for various diffusion measurements are summarized.     

Inhomogeneous translational diffusion of monoclonal antibodies on phospholipid Langmuir-Blodgett films.

The translational mobility of fluorescent-labeled monoclonal antibodies specifically bound to supported phospholipid bilayers containing hapten-conjugated phospholipids has been measured as a function of the surface concentration of bound antibodies using fluorescence recovery after photobleaching. Fluorescence recovery curves are fit well by a model that assumes the presence of two populations of antibodies with different lateral diffusion coefficients. The larger diffusion coefficient equals 3.5 x 10(-9) cm2/s, the smaller diffusion coefficient ranges from 1.5 x 10(-9) cm2/s to 2.5 x 10(-10) cm2/s, and the fractional fluorescence recovery associated with the smaller coefficient increases from approximately 0 to approximately 0.7 with increasing concentration of bound antibody. These results suggest that complexes of haptenated phospholipids and antibodies in phospholipid Langmuir-Blodgett films form clusters or domains in a concentration-dependent fashion.     

A milling crowd model for local and long-range obstructed lateral diffusion. Mobility of excimeric probes in the membrane of intact erythrocytes.

A new model for lateral diffusion, the milling crowd model (MC), is proposed and is used to derive the dependence of the monomeric and excimeric fluorescence yields of excimeric membrane probes on their concentration. According to the MC model, probes migrate by performing spatial exchanges with a randomly chosen nearest neighbor (lipid or probe). Only nearest neighbor probes, one of which is in the excited state, may form an excimer. The exchange frequency, and hence the local lateral diffusion coefficient, may then be determined from experiment with the aid of computer simulation of the excimer formation kinetics. The same model is also used to study the long-range lateral diffusion coefficient of probes in the presence of obstacles (e.g., membrane proteins). The dependence of the monomeric and excimeric fluorescence yields of 1-pyrene-dodecanoic acid probes on their concentration in the membranes of intact erythrocytes was measured and compared with the prediction of the MC model. The analysis yields an excimer formation rate for nearest neighbor molecules of approximately 1 X 10(7) s-1 and an exchange frequency of approximately greater than 2 X 10(7) s-1, corresponding to a local diffusion coefficient of greater than 3 X 10(-8) cm2 s-1. This value is several times larger than the long-range diffusion coefficient for a similar system measured in fluorescence photobleaching recovery experiments. The difference is explained by the fact that long-range diffusion is obstructed by dispersed membrane proteins and is therefore greatly reduced when compared to free diffusion. The dependence of the diffusion coefficient on the fractional area covered by obstacles and on their size is derived from MC simulations and is compared to those of other theories lateral diffusibility.     

Protein lateral movement in lipid bilayers. Stimulation studies of its dependence upon protein concentration

A number of mechanisms have been proposed to account for the decrease in protein lateral diffusion coefficients in a lipid bilayer membrane, as the concentration of proteins is increased. One such mechanism is the steric hindrance (via, say, a hard-core repulsion) to the lateral movement of a protein due to the proximity of other proteins. Here a model is presented to study this effect alone. It is argued that the model will overestimate the effect being studied. The results of computer simulations show that such a mechanism will decrease the lateral diffusion coefficient by less than a factor of 20 below the zero-concentration limit, even when up to 81.7% of the bilayer surface is composed of integral proteins. This result supports the opinion (Kell, D.B. (1984) Trends Biochem. Sci. 9, 379) that such a mechanism cannot account for a decrease in the lateral diffusion coefficient by two or three orders of magnitude.     

Multidimensional diffusion modes and collision frequencies of cytochrome c with its redox partners

We have determined the modes and rates of cytochrome c diffusion as well as the collision frequencies of cytochrome c with its redox partners at the surface of the isolated, mitochondrial inner membrane over a broad range (0-150 mM) of ionic strengths. Using fluorescence recovery after photobleaching, resonance energy transfer, and direct binding assay, we determined that the diffusion coefficient of cytochrome c is independent of its concentration and quantity bound to the inner membrane, that the distance of cytochrome c from the membrane surface increases with increasing ionic strength, and that there is no significant immobile fraction of cytochrome c on the membrane regardless of ionic strength. The rate of cytochrome c diffusion increases while its mode of diffusion changes progressively from lateral to three-dimensional with increasing ionic strength. At physiological ionic strength (100-150 mM), the diffusion of cytochrome c is three-dimensional with respect to the surface of the inner membrane with a coefficient of 1.0 x 10(-6) cm2/s, and little, if any cytochrome c is bound to the membrane regardless of its concentration. Furthermore, as ionic strength is raised from zero to 150 mM, the cytochrome ckd for the inner membrane increases, its mean occupancy time on the inner membrane to collide with a redox partner (tau) decreases, and its diffusion-based collision frequencies with its redox partners decrease. These data reveal the significance of both diffusion and concentration (affinity) of cytochrome c near the surface of the inner membrane in the control of the collision frequency of cytochrome c with its redox partners.     

Diffusive properties of water in Artemia cysts as determined from quasi-elastic neutron scattering spectra.

Results have been obtained on the quasi-elastic spectra of neutrons scattered from pure water, a 20% agarose gel (hydration four grams H2O per gram of dry solid) and cysts of the brine shrimp Artemia for hydrations between 0.10 and 1.2 grams H2O per gram of dry solids. The spectra were interpreted using a two-component model that included contributions from the covalently bonded protons and the hydration water, and a mobile water fraction. The mobile fraction was described by a jump-diffusion correlation function for the translation motion and a simple diffusive orientational correlation function. The results for the line widths gamma (Q2) for pure water were in good agreement with previous measurements. The agarose results were consistent with NMR measurements that show a slightly reduced translational diffusion for the mobile water fraction. The Artemia results show that the translational diffusion coefficient of the mobile water fraction was greatly reduced from that of pure water. The line width was determined mainly by the rotational motion, which was also substantially reduced from the pure water value as determined from dielectric relaxation studies. The translational and rotational diffusion parameters were consistent with the NMR measurements of diffusion and relaxation. Values for the hydration fraction and the mean square thermal displacement [u2] as determined from the Q-dependence of the line areas were also obtained.     

Transient alterations in the lateral mobility of erythrocyte membrane components during Sendai virus-mediated fusion.

Destabilization of the target membrane structure by fusion-promoting viral glycoproteins is assumed to be an essential part of the fusion mechanism. To explore this possibility, we employed fluorescence photobleaching recovery to investigate changes in the lateral mobility of native membrane constituents in human red blood cells (RBCs) during the course of Sendai virus-mediated fusion. The mobile fraction of RBC membrane proteins labeled with 5-(4,6-dichloro-5-triazin-2-yl)aminofluorescein increased significantly in the course of fusion, relaxing back to the original values upon completion of the fusion process. A different effect was observed on the lateral mobility of a fluorescent lipid probe, N-(7-nitro-2,1,3-benzoxadiazol-4-yl)phosphatidylethanolamine, incorporated initially into the external monolayer. In this case, the lateral diffusion coefficient (rather than the mobile fraction) increased during fusion; this increase was permanent in the absence of Mg-ATP and transient in its presence. An active viral fusion protein was required to mediate the effects on both protein and lipid mobility. These effects, which take place on the same time scale as that of the fusion process, suggest that the organization of the RBC membrane is perturbed during fusion and that the observed changes may be related to the fusion mechanism.     

Effect of tertiary amine local anesthetics on G protein-coupled receptor lateral diffusion and actin cytoskeletal reorganization

Although widely used clinically, the mechanism underlying the action of local anesthetics remains elusive. Direct interaction of anesthetics with membrane proteins and modulation of membrane physical properties by anesthetics are plausible mechanisms proposed, although a combination of these two mechanisms cannot be ruled out. In this context, the role of G protein-coupled receptors (GPCRs) in local anesthetic action is a relatively new area of research. We show here that representative tertiary amine local anesthetics induce a reduction in two-dimensional diffusion coefficient of the serotonin_1A receptor, an important neurotransmitter GPCR. The corresponding change in mobile fraction is varied, with tetracaine exhibiting the maximum reduction in mobile fraction, whereas the change in mobile fraction for other local anesthetics was not appreciable. These results are supported by quantitation of cellular F-actin, using a confocal microscopic approach previously developed by us, which showed that a pronounced increase in F-actin level was induced by tetracaine. These results provide a novel perspective on the action of local anesthetics in terms of GPCR lateral diffusion and actin cytoskeleton reorganization.     

Lateral diffusion in biological membranes. A normal-mode analysis of diffusion on a spherical surface.

A new approach is described for the analysis of lateral diffusion in biological membranes. It is shown that a suitably defined first moment of the concentration distribution on a spherical surface decays as a single exponential with a relaxation rate proportional to the diffusion coefficient and inversely proportional to the square of the radius of the sphere. The approach is illustrated with an example of fluorescence redistribution after photobleaching of membrane proteins in a spectrin-deficient spherocytic mouse erythrocyte membrane.     

Lateral diffusion in an archipelago. The effect of mobile obstacles.

Lateral diffusion of mobile proteins and lipids (tracers) in a membrane is hindered by the presence of proteins (obstacles) in the membrane. If the obstacles are immobile, their effect may be described by percolation theory, which states that the long-range diffusion constant of the tracers goes to zero when the area fraction of obstacles is greater than the percolation threshold. If the obstacles are themselves mobile, the diffusion constant of the tracers depends on the area fraction of obstacles and the relative jump rate of tracers and obstacles. This paper presents Monte Carlo calculations of diffusion constants on square and triangular lattices as a function of the concentration of obstacles and the relative jump rate. The diffusion constant for particles of various sizes is also obtained. Calculated values of the concentration-dependent diffusion constant are compared with observed values for gramicidin and bacteriorhodopsin. The effect of the proteins as inert obstacles is significant, but other factors, such as protein-protein interactions and perturbation of lipid viscosity by proteins, are of comparable importance. Potential applications include the diffusion of proteins at high concentrations (such as rhodopsin in rod outer segments), the modulation of diffusion by release of membrane proteins from cytoskeletal attachment, and the diffusion of mobile redox carriers in mitochondria, chloroplasts, and endoplasmic reticulum.