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.     

Topology of gel-phase domains and lipid mixing properties in phase-separated two-component phosphatidylcholine bilayers.

The influence of the lipid mixing properties on the lateral organization in a two-component, two-phase phosphatidylcholine bilayer was investigated using both an experimental (fluorescence recovery after photobleaching (FRAP)) and a simulated (Monte Carlo) approach. With the FRAP technique, we have examined binary mixtures of 1-stearoyl-2-capryl-phosphatidylcholine/1,2-distearoyl-phosphat idylcholine (C18C10PC/DSPC), and 1-stearoyl-2-capryl-phosphatidylcholine/1,2-dipalmitoyl-phospha tid ylcholine (C18C10PC/DPPC). Comparison with the 1,2-dimyristoyl-phosphatidylcholine/1,2-distearoyl-phosphatidylcholine (DMPC/DSPC) previously investigated by FRAP by Vaz and co-workers (Biophys. J., 1989, 56:869-876) shows that the gel phase domains become more effective in restricting the diffusion coefficient when the ideality of the mixture increases (i.e., in the order C18C10PC/DSPC-->C18C10PC/DPPC-->DMPC/DSPC). However, an increased lipid miscibility is accompanied by an increasing compositional dependence: the higher the proportion of the high-temperature melting component, the less efficient the gel phase is in compartmentalizing the diffusion plane, a trend that is best accounted for by a variation of the gel phase domain shape rather than size. Computer-simulated fluorescence recoveries obtained in a matrix obstructed with obstacle aggregates of various fractal dimension demonstrate that: 1) for a given obstacle size and area fraction, the relative diffusion coefficient increases linearly with the obstacle fractal dimension and 2) aggregates with a lower fractal dimension are more efficient in compartmentalizing the diffusion plane. Comparison of the simulated with the experimental mobile fractions strongly suggests that the fractal dimension of the gel phase domains increases with the proportion of high-temperature melting component in DMPC/DSPC and (slightly) in C18C10PC/DPPC.     

Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.     

Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy

We investigate the challenges and limitations that are encountered when studying membrane protein dynamics in vivo by means of fluorescence correlation spectroscopy (FCS). Based on theoretical arguments and computer simulations, we show that, in general, the fluctuating fluorescence has a fractal dimension D(0) >or= 1.5, which is determined by the anomality alpha of the diffusional motion of the labeled particles, i.e., by the growth of their mean square displacement as (Deltax)(2) approximately t(alpha). The fractality enforces an initial power-law behavior of the autocorrelation function and related quantities for small times. Using this information, we show by FCS that Golgi resident membrane proteins move subdiffusively in the endoplasmic reticulum and the Golgi apparatus in vivo. Based on Monte Carlo simulations for FCS on curved surfaces, we can rule out that the observed anomalous diffusion is a result of the complex topology of the membrane. The apparent mobility of particles as determined by FCS, however, is shown to depend crucially on the shape of the membrane and its motion in time. Due to this fact, the hydrodynamic radius of the tracked particles can be easily overestimated by an order of magnitude.     

A laser light scattering study of gellan gels

A study of gellan has been made using the technique of photon correlation spectroscopy. It has been confirmed that gellan gels are largely stationary at a molecular level like other polysaccharide gels and quite unlike the gels of flexible polymers such as polyacrylamide. Solution-gel transitions of deacetylated gellan in 0.025MNaCl have been studied both as a function of concentration and temperature, and the results compared with those of a parallel investigation of agarose. The interstitial spaces within gellan gels have also been studied by measuring the diffusion coefficients of dextran fractions within the gels. Since all gels are nonergodic systems, the theory of dynamic light scattering from such systems is discussed insofar as it affects the present work. It has been shown that the gellan and agarose aqueous systems are fundamentally different, in that agarose does not from a solution at very low concentrations, but splits up into macroscopic gel particles. At very low concentrations, gellan forms a solution in the presence of both gelleing and nongelling ions, the molecules of which shows little change in hydrodynamic diameter with temperature in the range 20–80°C. At higher concentrations where gels are formed, both gellan and agarose exhibit hystersis in their tempertature transitions from gel to solution and solution to gel, the solution being of large molecular aggregates. The transitions are sharp, but in both cases ther is a continous rearrangement in the structural morphology over the entire temperature range on heating, rendering the system more homogeneous prior to dissociation. In the case of gellan, however, there are two distincit phases in these structural changes—this is not true of agarose. The mean mass per unit length of the gellan fibre in the presence of 0.025M NaCl is 19 k daltons/nm at 0.7% concentration and varies with concentration to the power 0.15. The mass per unit length of the agarose fibre is much larger (ca. 110 k Daltons/nm), this difference being consistent with the difference in properties at very low concentrations. © 1994 John Wiley & Sons, Inc.     

Amino-functionalized cellulose nanoparticles: preparation, characterization, and interactions with living cells

Spherical nanoparticles with sizes from 80 to 200 nm are obtained by self-assembly of highly functionalized 6-deoxy-6-(ω-aminoalkyl)aminocellulosecarbamates. The particles are very stable, nontoxic, and possess primary amino groups that are accessible to further modifications in aqueous suspension. The particles can be labeled with rhodamine B isothiocyanate without changing their size, stability, and shape. The nanoparticles obtained are investigated by means of photo correlation spectroscopy, zeta potential measurements, SEM and fluorescence spectroscopy. Incorporation of the nanoparticles in human foreskin fibroblasts BJ-1-htert and breast carcinoma MCF-7 cells without any transfection reagent is proved by means of confocal laser scanning microscopy.     

Putting thought to paper: a microARCS protease screen

In micro-arrayed compound screening (microARCS), an agarose gel is used as a reaction vessel that maintains humidity and compound location as well as being a handling system for reagent addition. Two or more agarose gels may be used to bring test compounds, targets, and reagents together, relying on the pore size of the gel matrix to regulate diffusion of reactants. It is in the microenvironment of the agarose matrix that all the components of an enzymatic reaction interact and result in inhibitable catalytic activity. In an effort to increase the throughput of microARCS-based screens, reduce the effort involved in manipulating agarose gels, and reduce costs, blotter paper was used rather than a second agarose gel to introduce a substrate to a gel containing a target enzyme. In this assay, the matrix of the blotter paper did not prevent the substrate from diffusing into the enzyme gel. The compound density of the microARCS format, the ease of manipulating sheets of paper for reagent addition, and a scheduled protocol for running multiple gels allowed for a throughput capacity of more than 200,000 tests per hour. A protease assay was developed and run in the microARCS format at a rate of 200,000 tests per hour using blotter paper to introduce the substrate. Picks in the primary screen were retested in the microARCS format at a density of 384 compounds per sheet. IC(50) values were confirmed in a 96-well plate format. The screen identified several small molecule inhibitors of the enzyme. The details of the screening format and the analysis of the hits from the screen are presented.     

Microfluidity mapping using fluorescence correlation spectroscopy: a new way to investigate plasma membrane microorganization of living cells

Diffusion time distribution analysis has been employed to highlight the microfluidity fingerprint of plasma membrane of living cells. Diffusion time measurements were obtained through fluorescence correlation spectroscopy performed at the single cell level, over various eukaryotic cell lines (MCF7, LR73, KB3.1, MESSA and MDCKII). The nonsymmetric profile of the diffusion time distributions established experimentally, is discussed according to Monte Carlo simulations, which reproduce the diffusion of the fluorescent probe in heterogeneous membrane.     

High-sensitivity DNA detection with a laser-excited confocal fluorescence gel scanner

A high-sensitivity, laser-excited confocal fluorescence gel scanner has been developed and applied to the detection of fluorescently labeled DNA. An argon ion laser (1-10 mW at 488 nm) is focused in the gel with a high-numerical aperture microscope objective. The laser-excited fluorescence is gathered by the objective and focused on a confocal spatial filter, followed by a spectral filter and photodetector. The gel is placed on a computer-controlled scan stage, and the scanned image of the gel fluorescence is stored and analyzed in a computer. This scanner has been used to detect DNA separated on sequencing gels, agarose mapping gels and pulsed field gels. Sanger sequencing gels were run on M13mp18 DNA using a fluoresceinated primer. The 400-microns-thick gels, loaded with 30 fmol of DNA fragments in 3-mm lanes, were scanned at 78-microns resolution. The high resolution of our scanner coupled with image processing allows us to read up to approximately 300 bases in four adjacent sequencing lanes. The minimum band size that could be detected and read was approximately 200 microns. This instrument has a limiting detection sensitivity of approximately 10 amol of fluorescein-labeled DNA in a 1 x 3-mm band. In applications to agarose mapping gels, we have exploited the fact that DNA can be prestained with ethidium homodimer, followed by electrophoresis and fluorescence detection to achieve picogram sensitivity. We have also developed methods using both ethidium homodimer and thiazole orange staining which permit two-color detection of DNA in one lane.(ABSTRACT TRUNCATED AT 250 WORDS)     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Exclusion of spheres by agarose gels during agarose gel electrophoresis: dependence on the sphere's radius and the gel's concentration

Agarose gel electrophoresis of spheres (radius = R) has been used to determine the effective radius (PE) of the pores of an agarose gel (percentage of agarose in a gel = A). The value of PE at a given A was taken to be the R of the largest sphere that enters the gel. When log PE is plotted as a function of log A, the results can be represented by: PE = 118A-0.74 for 0.2 less than or equal to A less than or equal to 4.0 (PE in nm). However, the data suggest significant nonlinearity in this plot, the magnitude of the exponent of the PE vs A relationship increasing by about 20% as A increases from 0.2 to 4.0. From these data, PE's as big as 1500 nm and as small as 36 nm can be achieved with agarose gels formed with unmodified, unadulterated agarose and usable for electrophoresis.     

A mathematical model of single target site location by Brownian movement in subcellular compartments

The location of distinct sites is mandatory for many cellular processes. In the subcompartments of the cell nucleus, only very small numbers of diffusing macromolecules and specific target sites of some types may be present. In this case, we are faced with the Brownian movement of individual macromolecules and their "random search" for single/few specific target sites, rather than bulk-averaged diffusion and multiple sites. In this article, I consider the location of a distant central target site, e.g. a globular protein, by individual macromolecules executing unbiased (i.e. drift-free) random walks in a spherical compartment. For this walk-and-capture model, the closed-form analytic solution of the first passage time probability density function (p.d.f.) has been obtained as well as the first and second moment. In the limit of a large ratio of the radii of the spherical diffusion space and central target, well-known relations for the variance and the first two moments for the exponential p.d.f. were found to hold with high accuracy. These calculations reinforce earlier numerical results and Monte Carlo simulations. A major implication derivable from the model is that non-directed random movement is an effective means for locating single sites in submicron-sized compartments, even when the diffusion coefficients are comparatively small and the diffusing species are present in one copy only. These theoretical conclusions are underscored numerically for effective diffusion constants ranging from 0.5 to 10.0 microm(2) s(-1), which have been reported for a couple of nuclear proteins in their physiological environment. Spherical compartments of submicron size are, for example, the Cajal bodies (size: 0.1-1.0 microm), which are present in 1-5 copies in the cell nucleus. Within a small Cajal body of radius 0.1 microm a single diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter a medium-sized protein of radius 2.5 nm within 1 s with a probability near certainty (p=0.98).     

Phase topology and percolation in two-component lipid bilayers: a monte Carlo approach.

Monte Carlo simulations of fluorescence recovery after photobleaching (FRAP) experiments on two-component lipid bilayers systems in the solid-fluid phase coexistence region were carried out to study the geometry and size of fluid domains in these bilayers. The gel phase was simulated by superposable elliptical domains, which were either of predetermined dimensions, increasing in number with increasing gel phase fraction, or of predetermined number, increasing in dimensions with increasing gel phase fraction. The simulations were done from two perspectives: 1) a time-independent analysis of fractional fluorescence recovery as a function of fractional fluid phase in the system; and 2) a time-dependent analysis of fractional fluorescence recovery as a function of time at a given fraction of fluid phase in the system. The time-dependent simulations result in recovery curves that are directly comparable to experimental FRAP curves and provide topological and geometrical models for the coexisting phases that are consistent with the experimental result.     

Coarse-grained modeling of mucus barrier properties

We designed a simple coarse-grained model of the glycocalyx layer, or adhesive mucus layer (AML), covered by mucus gel (luminal mucus layer) using a polymer lattice model and stochastic sampling (replica exchange Monte Carlo) for canonical ensemble simulations. We assumed that mucin MUC16 is responsible for the structural properties of the AML. Other mucins that are much smaller in size and less relevant for layer structure formation were not included. We further assumed that the system was in quasi-equilibrium. For systems with surface coverage and concentrations of model mucins mimicking physiological conditions, we determined the equilibrium distribution of inert nanoparticles within the mucus layers using an efficient replica exchange Monte Carlo sampling procedure. The results show that the two mucus layers penetrate each other only marginally, and the bilayer imposes a strong barrier for nanoparticles, with the AML layer playing a crucial role in the mucus barrier.     

Interpenetrating network formation in agarose–sodium gellan gel composites

Aqueous cold-set gels from mixtures of agarose and sodium gellan have been characterised structurally and mechanically using optical and electron microscopy, turbidity measurements, differential scanning calorimetry, mechanical spectroscopy and compression testing. Consistent with expectations for charged–uncharged polymer combinations at low ionic strength there is no liquid–liquid demixing in sols prior to gelation, and although transmission electron microscopy reveals heterogeneities in gel microstructures at the higher polymer concentrations, these are small in extent, and are unlikely to arise from normal segregative demixing. Overall, ‘molecularly’ interpenetrating networks (IPNs) are indicated, in which the gellan and agarose architectures pass through one another on a distance scale comparable to their pore sizes. At concentrations greater than 2% w/w gellan, where gellan is the first gelling species, and when the agarose concentration is greater than 0.5% w/w, the composite modulus falls below that expected for the agarose alone. At 0.5% w/w agarose, on the other hand, modulus contributions from the components are much closer to additive. These findings are reflected in the results of large deformation compression testing where breaking stresses show similar trends.     

Determination of hematocrit based on diffusion of an inert molecular probe from agarose gels into whole blood

Whole blood hematocrit was determined by an approach which depends on the diffusion of an inert probe, to which red blood cells are impermeable, from a small agarose gel into a stirred, much larger blood sample. Blood cells influence the diffusion rate of the probe by, on the average, physically blocking a fraction of the gel surface. The blocking effect increases with the hematocrit. Cyanocobalamin (B-12) was found to be a suitable probe because it did not penetrate, bind to, or lyse blood cells and was not bound by plasma solutes. The loss of B-12 from gels in contact with blood was monitored by determination of the absorbance change at 540 nm of gels which had been quickly rinsed. The visible spectrum of B-12 in agarose gels was identical to the spectrum in water. Beer's Law was obeyed in 1-mm thick agarose gels over a concentration range of 0.1-0.8 mM. Based on the results from 48 blood samples covering the hematocrit range 25-69, a least-squares line was generated with a slope, -3.46 X 10(-3) delta A/hematocrit unit, a Y intercept of 0.295, and a correlation coefficient of 0.971. The precision of the technique was +/- 9.7%. The assay was insensitive to mean corpuscular volume and sample volume as long as the latter was 50-fold larger than the gel volume. The diffusion coefficient for B-12 in 1% agarose gels was found to be 1.4 +/- 0.2 X 10(-6) cm2 sec-1.     

Erythrocyte orientational and cell volume effects on NMR <Emphasis Type="Italic">q</Emphasis>-space analysis: simulations of restricted diffusion

Pulsed field-gradient spin echo nuclear magnetic resonance spectroscopy of water diffusing in erythrocytes leads to diffusion interference and diffraction effects, which are visualised in q-space plots of signal intensity versus the magnitude of the spatial wave-number vector q. Interpretation of the features of these q-space plots has been aided by Monte Carlo random walk simulations of diffusion in lattices of virtual erythrocytes. Here, the effect of varying the orientation of the cells with respect to the direction in which diffusion is measured, on the appearance of q-space plots, was investigated, together with the effect of changing the cell volume. We show that these changes are reflected in the appearance of the plots in a way that is diagnostic of the microscopic geometry of the sample.     

Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.     

Stability of hydrogels used in cell encapsulation: An in vitro comparison of alginate and agarose

The present studies were undertaken to evaluate the in vitro gel stability of the hydrogels alginate and agarose. Gel strength (of alginate and agarose) and protein diffusion (of alginate only) were shown to correlate with gel stability and to be useful techniques to monitor gel stability over time. The gel strengths of alginate and agarose were followed for a 90-day period using gel strength as a measure of gel stability. The gel strength of agarose diminished in the presence of cells because the cells likely interfered with the hydrogen bond formation required for agarose gelation. In the presence of cells, the gel strength of agarose decreased by an average of 25% from time 0 to 60 days, thereafter maintaining that value to 90 days. The gel strength of calcium- or barium-crosslinked alginate decreased over 90 days, with an equilibrium gel strength being achieved after 30 days. The presence of cells did not further decrease alginate gel strength. The gel strengths of calcium- and barium-crosslinked alginates were similar at 60 days-350 +/- 20 g and 300 +/- 60 g, respectively-indicating equivalence in their stability. The stability of calcium-crosslinked sodium alginate gels over a 60-day time period was monitored by diffusion of proteins ranging in molecular weight from 14.5 to 155 kD. From these diffusion measurements, the average pore size of the calcium-crosslinked alginate gels was estimated, using a semi-empirical model, to increase from approximately 176 to 289 A over a period of 60 days. (c) 1996 John Wiley & Sons, Inc.