Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.     

Lateral diffusion in an archipelago. Dependence on tracer size.

In a pure fluid-phase lipid, the dependence of the lateral diffusion coefficient on the size of the diffusing particle may be obtained from the Saffman-Delbrück equation or the free-volume model. When diffusion is obstructed by immobile proteins or domains of gel-phase lipids, the obstacles yield an additional contribution to the size dependence. Here this contribution is examined using Monte Carlo calculations. For random point and hexagonal obstacles, the diffusion coefficient depends strongly on the size of the diffusing particle, but for fractal obstacles--cluster-cluster aggregates and multicenter diffusion-limited aggregates--the diffusion coefficient is independent of the size of the diffusing particle. The reason is that fractals have no characteristic length scale, so a tracer sees on average the same obstructions, regardless of its size. The fractal geometry of the excluded area for tracers of various sizes is examined. Percolation thresholds are evaluated for a variety of obstacles to determine how the threshold depends on tracer size and to compare the thresholds for compact and extended obstacles.     

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.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

The concentration dependence of the hemoglobin mutual diffusion coefficient

Laser correlation Spectroscopy was used to measure the mutual diffusion coefficient, D, of human cyanomethemoglobin (Fe⁺⁺⁺:CN) at varying protein concentrations. These measurements were male at 20°C in a 0.1 M phosphate buffer solution at pH 7.0. For low protein concentrations we find D = (6.43 ± 0.26) × 10^?7 cm²/S and that there is a near linear decrease from this value at higher concentrations. The linear relation between the diffusion coefficient and protein concentration allows us to deduce the value of the linear frictional volume fraction coefficient, K_f= 7.75. and to extrapolate to hemoglobin concentrations equivalent to that in the red blood cell where we estimate D = 4.25 × 10^?7 cm²/s Various theoretical predictions of the dependence of the mutual diffusion coefficient on concentration are tested; we find that the generalized Stokes-Einstein relation can be made to fit our high concentration data if we assume a hard-sphere model and if we include a term involving a hydrodynamic interaction integral.     

Lateral pressure dependence of the phospholipid transmembrane diffusion rate in planar-supported lipid bilayers

The dependence of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) flip-flop kinetics on the lateral membrane pressure in a phospholipid bilayer was investigated by sum-frequency vibrational spectroscopy. Planar-supported lipid bilayers were prepared on fused silica supports using the Langmuir-Blodgett/Langmuir-Schaeffer technique, which allows precise control over the lateral surface pressure and packing density of the membrane. The lipid bilayer deposition pressure was varied from 28 to 42 mN/m. The kinetics of lipid flip-flop in these membranes was measured by sum-frequency vibrational spectroscopy at 37°C. An order-of-magnitude difference in the rate constant for lipid translocation (10.9 × 10⁻⁴ s⁻¹ to 1.03 × 10⁻⁴ s⁻¹) was measured for membranes prepared at 28 mN/m and 42 mN/m, respectively. This change in rate results from only a 7.4% change in the packing density of the lipids in the bilayer. From the observed kinetics, the area of activation for native phospholipid flip-flop in a protein-free DPPC planar-supported lipid bilayer was determined to be 73 ± 12 Å²/molecule at 37°C. Significance of the observed activation area and potential future applications of the technique to the study of phospholipid flip-flop are discussed.     

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.     

Cytoplasmic hydrogen ion diffusion coefficient.

The apparent cytoplasmic proton diffusion coefficient was measured using pH electrodes and samples of cytoplasm extracted from the giant neuron of a marine invertebrate. By suddenly changing the pH at one surface of the sample and recording the relaxation of pH within the sample, an apparent diffusion coefficient of 1.4 +/- 0.5 x 10(-6) cm2/s (N = 7) was measured in the acidic or neutral range of pH (6.0-7.2). This value is approximately 5x lower than the diffusion coefficient of the mobile pH buffers (approximately 8 x 10(-6) cm2/s) and approximately 68x lower than the diffusion coefficient of the hydronium ion (93 x 10(-6) cm2/s). A mobile pH buffer (approximately 15% of the buffering power) and an immobile buffer (approximately 85% of the buffering power) could quantitatively account for the results at acidic or neutral pH. At alkaline pH (8.2-8.6), the apparent proton diffusion coefficient increased to 4.1 +/- 0.8 x 10(-6) cm2/s (N = 7). This larger diffusion coefficient at alkaline pH could be explained quantitatively by the enhanced buffering power of the mobile amino acids. Under the conditions of these experiments, it is unlikely that hydroxide movement influences the apparent hydrogen ion diffusion coefficient.     

Pulsed field gradient nmr determination of the temperature dependence of the tracer diffusion coefficient of hemoglobin

We have studied the temperature dependence of the tracer diffusion coefficient of carbonmonoxy hemoglobin A (HbA-CO) by means of pulsed-field gradient nmr (PFG-nmr). Measurements were made over the temperature range from 15 to 35°C for samples having concentrations 7.4 and 16.7 g/dL. No significant deviations were found from the predictions of the Stokes-Einstein relation. Thus, this work does not corroborate the recently proposed conformational change in hemoglobin at 22°C. The advantages of PFG-nmr for the study of hemoglobin are discussed.     

Concentration dependence of protein diffusion.

The concentration dependence of protein self-diffusion constants is described by a free volume diffusion theory which accounts for the effects of local protein concentration fluctuations.     

Lateral diffusion of proteins in the periplasm of Escherichia coli.

We have introduced biologically active, fluorescently labeled maltose-binding protein into the periplasmic space of Escherichia coli and measured its lateral diffusion coefficient by the fluorescence photobleaching recovery method. Diffusion of this protein in the periplasm was found to be surprisingly low (lateral diffusion coefficient, 0.9 X 10(-10) cm2 s-1), about 1,000-fold lower than would be expected for diffusion in aqueous medium and almost 100-fold lower than for an equivalent-size protein in the cytoplasm. Galactose-binding protein, myoglobin, and cytochrome c were also introduced into the periplasm and had diffusion coefficients identical to that determined for the maltose-binding protein. For all proteins nearly 100% recovery of fluorescence was obtained after photobleaching, indicating that the periplasm is a single contiguous compartment surrounding the cell. These data have considerable implications for periplasmic structure and for the role of periplasmic proteins in transport and chemotaxis.     

Lateral diffusion in nuclear membranes

Chemical modification of rat liver nuclei with citraconic anhydride selectively removed outer nuclear membrane. This conclusion was based on (a) transmission electron microscopy, (b) lipid analysis, (c) lamin B as an inner membrane-associated marker, and (d) the demonstration of phospholipid lateral mobility on outer membrane-depleted nuclei as a criteria for inner membrane integrity. Addition of urea or N-ethylmaleimide resulted in the additional disruption of inner membrane. Fluorescence photobleaching was used to determine the long range (greater than 4 microns) lateral transport of lectin receptors and a phospholipid analog in both membranes. The diffusion coefficient for wheat germ agglutinin on whole nuclei was 3.9 X 10(-10) cm2/s whereas the diffusion coefficient for wheat germ agglutinin in outer membrane-depleted nuclei was less than or equal to 10(-12) cm2/s. Phospholipid mobilities were the same in whole and outer membrane-depleted nuclei (3.8 X 10(-9) cm2/s). The protein diffusion differences observed between whole and outer membrane-depleted nuclei may be interpreted in the context of two functionally different membrane systems that compose the double bilayer of the nucleus.     

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.     

Calcium diffusion coefficient in rod photoreceptor outer segments.

Calcium (Ca(2+)) modulates several of the enzymatic pathways that mediate phototransduction in the outer segments of vertebrate rod photoreceptors. Ca(2+) enters the rod outer segment through cationic channels kept open by cyclic GMP (cGMP) and is pumped out by a Na(+)/Ca(2+),K(+) exchanger. Light initiates a biochemical cascade, which leads to closure of the cGMP-gated channels, and a concomitant decline in the concentration of Ca(2+). This decline mediates the recovery from stimulation by light and underlies the adaptation of the cell to background light. The speed with which the decline in the Ca(2+) concentration propagates through the rod outer segment depends on the Ca(2+) diffusion coefficient. We have used the fluorescent Ca(2+) indicator fluo-3 and confocal microscopy to measure the profile of the Ca(2+) concentration after stimulation of the rod photoreceptor by light. From these measurements, we have obtained a value of 15 +/- 1 microm(2)s(-1) for the radial Ca(2+) diffusion coefficient. This value is consistent with the effect of a low-affinity, immobile buffer reported to be present in the rod outer segment (L.Lagnado, L. Cervetto, and P.A. McNaughton, 1992, J. Physiol. 455:111-142) and with a buffering capacity of approximately 20 for rods in darkness(S. Nikonov, N. Engheta, and E.N. Pugh, Jr., 1998, J. Gen. Physiol. 111:7-37). This value suggests that diffusion provides a significant delay for the radial propagation of the decline in the concentration of Ca(2+). Also, because of baffling by the disks, the longitudinal Ca(2+) diffusion coefficient will be in the order of 2 microm(2)s(-1), which is much smaller than the longitudinal cGMP diffusion coefficient (30-60 microm(2)s(-1); ). Therefore, the longitudinal decline of Ca(2+) lags behind the longitudinal spread of excitation by cGMP.     

Lateral diffusion in inhomogeneous membranes. Model membranes containing cholesterol.

The problem of lateral diffusion in inhomogeneous membranes is illustrated by a theoretical calculation of the lateral diffusion of a fluorescent lipid probe in binary mixtures of phosphatidylcholine and cholesterol under conditions of temperature and composition such that this lipid mixture consists of alternating parallel domains of fluid and solid lipid, having separations that are small compared with the distance scale employed in photobleaching experiments. The theoretical calculations clearly illustrate how inhomogeneities in membrane composition affecting the lateral motion of membrane components on a small (10-100 nm) distance scale can give complex diffusive responses in experiments such as fluorescence photobleaching that employ comparatively macroscopic distances (10-100 micrometers) for the measurement of diffusive recovery. The theoretical calculations exhibit the unusual dependence of the apparent lateral diffusion coefficient of a fluorescent lipid probe on lipid composition in binary mixtures of cholesterol and phosphatidylcholines as reported by Rubenstein et al. (1979, Proc. Natl. Acad. Sci. U.S.A., 76:15-18).     

Effective diffusion coefficient of sucrose in calcium alginate gel.

The effective diffusion coefficient of sucrose in 5% calcium alginate gel containing 41.6 g.d.c. l-1. Saccharomyces cerevisiae was investigated. Both free and immobilized S. cerevisiae in 0.175 cm and 0.3 cm diameter particles were used and the reactions were achieved in a medium containing 100 g l-1 sucrose and 0.05 M CaCl2. With the assumption that the microorganisms did not grow or die in this medium, the results were analyzed according to Michaelis-Menten kinetics and the values of the parameters were determined as: Vm = 0.256 g ml-1 gel h-1, Km0 = 0.097 g ml-1, Km1 = 0.125 g ml-1, and Km2 = 0.165 g ml-1. Using these values, effectiveness factors were calculated as eta 1 = 0.89 and eta 2 = 0.76, and effective diffusion coefficients for sucrose in calcium alginate gel were determined as De1 = 4.1 X 10(-6) cm2 s-1 and De2 = 4.0 X 10(-6) cm2 s-1, for the particle size involved.     

Calculating the diffusion coefficient in the eye lens

An experimental investigation of the appearance of a cataract under intensive irradiation is carried out. On the basis of the results obtained a model is proposed of calculating the diffusion coefficient which can model the crystalline lens, its individual peculiarities being taken into account.     

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.     

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.(ABSTRACT TRUNCATED AT 250 WORDS)