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. 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.     

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 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.     

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.     

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.     

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).     

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 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)     

Lateral diffusion of M-13 coat protein in model membranes.

A fluorescent derivative of the M-13 phage coat protein (molecular weight 5260) was reconsituted into oriented multilayers and giant liposomes of dimyristoylphosphatidylcholine. The rate of lateral diffusion of the labeled protein in the fluid phase was measured as a function of temperature and found to be comparable to that of lipid probes. The protein was found to have a nonuniform lateral distribution in the solid phase of both types of model membranes. Cardiolipin (0.5 mol %) included in the multibilayers did not have any substantial effect upon the rate of diffusion.     

Lateral diffusion of lipids and glycophorin in solid phosphatidylcholine bilayers. The role of structural defects

The lateral mobility of the lipid analog N-4-nitrobenzo-2-oxa-1,3 diazole phosphatidylethanolamine and of the integral protein glycophorin in giant dimyristoylphosphatidylcholine vesicles was studied by the photobleaching technique. Above the temperature of the chain-melting transition (Tm = 23 degrees C), the diffusion coefficient, Dp, of the protein [Dp = (4 +/- 2) X 10(-8) cm2/s at 30 degrees C] was within the experimental errors equal to the corresponding values DL of the lipid analog. In the P beta 1 phase the diffusion of lipid and glycophorin was studied as a function of the probe and the protein concentration. (a) At low lipid-probe content (cL less than 5 mmol/mol of total lipid), approximately 20% of the probe diffuses fast (D approximately equal to 10(-8) - 10(-9) cm2/s), while the mobility of the rest is strongly reduced (D less than 10(-10) cm2/s). At a higher concentration (cp approximately 20 mmol), all probe is immobilized (D less than 10(-10) cm2/s). (b) Incorporation of glycophorin up to cp = 0.4 mmol/mol of total lipid leads to a gradual increase of the fraction of mobile lipid probe due to the lateral-phase separation into a pure P beta 1 phase and a fraction of lipid that is fluidized by strong hydrophilic lipid-protein interaction. (c) The diffusion of the glycophorin molecules is characterized by a slow and a fast fraction. The latter increases with increasing protein content, which is again due to the lateral-phase separation caused by the hydrophilic lipid-protein interaction. The results are interpreted in terms of a fast transport along linear defects in the P beta 1 phase, which form quasi-fluid paths for a nearly one dimensional and thus very effective transport. Evidence for this interpretation of the diffusion measurements is provided by freeze-fracture electron microscopy.     

Lateral diffusion of saturated phosphatidylcholines in cholesterol-containing bilayers

A pulsed field gradient NMR was used to study lateral diffusion in the cholesterol-containing oriented bilayers of saturated (dipalmitoyl- and dimyristoyl-) phosphatidylcholines, upon their limiting hydration. Similar dependences of lateral diffusion coefficients on temperature and cholesterol concentration were observed, which agree with phase diagram showing the presence of the regions of disordered and ordered liquid-crystalline phases and a two-phase region. Under the same conditions, the lateral diffusion coefficient of dipalmitoylphosphatidylcholine is lower, which agrees qualitatively with its larger molecular weight. The comparison of data for dipalmitoylphosphatidylcholine with previous results for dipalmitoylsphingomyelin-cholesterol bilayers under the same conditions, in spite of similarity of phase diagrams, shows large (two–three times) differences in the lateral diffusion coefficient and a different profile of its dependence on cholesterol concentration. The comparison of data for dimyristoylphosphatidylcholine with previous results shows that the values of lateral diffusion coefficient and the shape of its dependence on cholesterol concentration coincide at high concentrations (>15 mol%) but differ at lower concentrations The revealed disagreement may be caused by the fact that the measurements were carried out at different water content in the system. At limiting hydration (more than 35% of water), the lateral diffusion coefficient for lipids decreases when cholesterol concentration rises, while at water content about 25% (as a result of equilibrium hydration from vapors) the lateral diffusion coefficient of phosphatidylcholine may be independent of cholesterol concentration. This is the consequence of the denser packing of molecules in the bilayer at reduced water content, an effect that competes with the ordering effect of cholesterol.     

Lateral diffusion of saturated phosphatidylcholines in cholesterol-containing bilayers

Lateral diffusion in oriented bilayers of saturated cholesterol-containing phosphatidylcholines, dipalmitoylphosphatidylcholine and dimyrilstoylphosphatidylcholine upon their limiting hydration has been studied by NMR with impulse gradient of magnetic field. For both systems, similar dependences of the coefficient of lateral diffusion on temperature and cholesterol concentration were observed, which agree with the phase diagram showing the presence of regions of ordered and unordered liquid-crystalline phases and a two-phase region. Under similar conditions, the coefficient of lateral diffusion for dipalmytoylphosphatidylcholine has lower values, which is in qualitative agreement with its greater molecular mass. A comparison of data for dipalmytoylphosphatidylcholine with the results obtained earlier for dipalmytoylsphyngomyelin/cholesterol under the same conditions shows, despite a similarity in phase diagrams, greater (two- to threefold) differences in the values of the coefficient of lateral diffusion and a different mode of dependence of the coefficient on cholesterol concentration. A comparison of data for dimyrilstoylphosphatidylcholine with the results obtained previously shows that the values of the coefficient of lateral diffusion and the mode of its dependence on cholesterol concentration coincide in the region of higher concentrations (more than 15 mole %) and differ in the region of lower concentrations (below 15 mole %). The discrepancies may be explained by different contents of water in the systems during the measurements. At a limiting hydration (more than 35%) of water, the coefficient of lateral diffusion decreases with increasing cholesterol concentration. If the content of water is about 25% (as a result of equilibrium hydration from vapors), the coefficient of lateral diffusion of phosphatidylcholine is probably independent of cholesterol concentration. This results from a denser packing of molecules in the bilayer at a lower water concentration, an effect that competes with the ordering effect of cholesterol.     

The diffusion of an inhibitor in a spherical tumor.

The purpose of this paper is to show the correct mathematical behavior of the solution to a diffusion equation that has previously been used in a modeling situation involving a spherical tumor.     

Permeabilized rat cardiomyocyte response demonstrates intracellular origin of diffusion obstacles

Intracellular diffusion restrictions for ADP and other molecules have been predicted earlier based on experiments on permeabilized fibers or cardiomyocytes. However, it is possible that the effective diffusion distance is larger than the cell dimensions due to clumping of cells and incomplete separation of cells in fiber preparations. The aim of this work was to check whether diffusion restrictions exist inside rat cardiomyocytes or are caused by large effective diffusion distance. For that, we determined the response of oxidative phosphorylation (OxPhos) to exogenous ADP and ATP stimulation in permeabilized rat cardiomyocytes using fluorescence microscopy. The state of OxPhos was monitored via NADH and flavoprotein autofluorescence. By varying the ADP or ATP concentration in flow chamber, we determined that OxPhos has a low affinity in cardiomyocytes. The experiments were repeated in a fluorometer on cardiomyocyte suspensions leading to similar autofluorescence changes induced by ADP as recorded under the microscope. ATP stimulated OxPhos more in a fluorometer than under the microscope, which was attributed to accumulation of ADP in fluorometer chamber. By calculating the flow profile around the cell in the microscope chamber and comparing model solutions to measured data, we demonstrate that intracellular structures impose significant diffusion obstacles in rat cardiomyocytes.     

Overcoming obstacles: the effect of obstacles on locomotor performance and behaviour

Sprinting and jumping ability are key performance measures that have been widely studied in vertebrates. The vast majority of these studies, however, use methodologies that lack an ecological context by failing to consider the complex habitats in which many animals live. Because successfully navigating obstacles within complex habitats is critical for predator escape, running, climbing, and/or jumping performance are each likely to be exposed to selection. In the present study, we quantify how behavioural strategies and locomotor performance change with increasing obstacle height. Obstacle size had a significant influence on behaviour (e.g. obstacle crossing strategy, intermittent locomotion) and performance (e.g. sprint speed, jump distance). Jump frequency and distance increased with obstacle size, suggesting that it likely evolved because it is more efficient (i.e. it reduces the time and distance required to reach a target position). Jump angle, jump velocity, and approach velocity accounted for 58% of the variation in jump distance on the large obstacle, and 33% on the small obstacle. Although these variables have been shown to significantly influence jump distance in static jumps, they do not appear to be influential in running (dynamic) jumps onto a small obstacle. Because selection operates in simple and complex habitats, future studies should consider quantifying additional measures such as jumping or climbing with respect to the evolution of locomotion performance. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.