Mean Diffusion Constant Research Articles

Diffusion of dissolved ions from wet silica sol–gel monoliths: Implications for biological encapsulation

Divalent nickel (Ni(2+)), Cu(II)EDTA, methyl orange, and dichromate were used to investigate diffusion from hydrated silica sol-gel monoliths. The objective was to examine diffusion of compounds on a size regime relevant to supporting biological components encapsulated within silica gel prepared in a biologically compatible process space with no post-gelation treatments. With an initial sample set, gels prepared from tetraethoxysilane were explored in a factorial design with Ni(2+) as the tracer, varying water content during hydrolysis, acid catalyst present during hydrolysis, and the final concentration of silica. A second sample set explored diffusion of all four tracers in gels prepared with aqueous silica precursors and a variety of organically modified siloxanes. Excluding six outliers which displayed significant syneresis, the mean diffusion constant (D(gel)) across the entire process space of sample set 1 was 2.42×10(-10) m(2) s(-1); approximately 24% of the diffusion coefficient of Ni(2+) in unconfined aqueous solution. In sample set 2, the tracer size and not gel hydrophobicity was the primary determinant of changes in diffusion rates. A strong linear inverse correlation was found between tracer size and the magnitude of D(gel). Based on correlation with the tracers used in this investigation, the characteristic 1-h diffusion distance for carbonate species relevant to supporting active phototrophic organisms was approximately 1.5mm. These results support the notion that silica sol-gel formulations may be optimized for a given biological entity of interest with manageable impact to the diffusion of small ions and molecules.

Super-Resolution Study of the Dynamics and Spatial Distribution of Ribosomes in Live E. Coli Cells

Little is known about the spatial organization and dynamics of the translational machinery in bacteria. We have examined the distribution and diffusion of ribosomes in live E. coli cells by localizing and tracking single ribosomes labeled by an S2-eYFP construct expressed from the chromosome. Fast reversible photobleaching of eYFP was used to image single ribosome molecules and obtain the time-averaged spatial distribution of ribosomes with ∼30-nm resolution. In medium growth conditions (doubling time 62 minutes) the ribosomes are highly segregated from the nucleoid. In DNA rich regions the concentrations of ribosomes is less than 20% of that in the ribosome-rich regions in the end caps and space between the two nucleoid lobes. This is in reasonable agreement with a Monte Carlo model using realistic parameters for the number of ribosomes and the amount of plectonemic DNA. We have studied dynamics of single ribosomes by using time lapse imaging. The mean diffusion constant is Dribo = 0.04 μm2/s. Halting of transcription with Rifampicin resulted in about 10 fold increase in the diffusion constant and a homogeneous distribution of labels throughout the cytoplasm. The drastic change in dynamics can be explained in part by conversion of polysomes to monomeric ribosomes and 30S subunits in the absence of new mRNA synthesis. Expansion of the nucleoid after rifampicin treatment might be responsible for eliminating ribosome/DNA segregation and may further enhance diffusion. Halting of translation by Chloramphenicol treatment increased the ribosome-DNA segregation as the DNA compacted. The diffusion constant remained the same. Studies of the spatial distribution of different size fluorescent proteins in the presence and absence of drugs suggest that the degree of segregation from DNA is largely size dependent.

Probing Diffusion in Live E. coli using Single-Molecule Tracking

Measurement of protein diffusion in vivo probes the effects of bacterial cytoplasm on protein mobility. We used single-particle tracking (SPT) and fluorescence recovery after photobleaching (FRAP) to study diffusion of the photo-activatable protein Kaede inside live E. coli cells. Photo-activation of the molecule Kaede enables us to study only one or two fluorescent molecules at a time. The non-spherical shape of E. coli led us to separate the tracking data into displacements along the long axis and short axis of the cell. Kaede molecules diffuse rapidly, exploring the entire cell on a timescale of 100 ms. This containment effect resulted in sub-linear increase of the mean-square displacement (MSD) vs time. We used Monte Carlo simulations and the analytical expression for the long-time MSD in a spherocylinder to fit the SPT data. Within a single cell, the tracking data were consistent with homogeneous diffusion. Across a population of cells, the tracking data had a mean diffusion constant of <DSPT> = 7.2 ± 1.9 µm2/s. The value of the MSD at long times as measured by SPT was consistent with the predicted long time MSD based on the cell shape and size. This implies that the molecules explore the entire volume of the cell. The sub-linear increase of MSD with time can be explained completely by the containment of diffusing molecules by the cell. For a few cells, we also performed FRAP on the unactivated state of Kaede, yielding <DFRAP> = 8.5 ± 2.0 µm2/s in agreement with the SPT result for the activated state. Among single cells, DSPT and DFRAP were correlated (r = 0.32).

Diffusion changes in patients with systemic lupus erythematosus

Systemic lupus erythematosus (SLE) is an autoimmune disease in which almost all the organs are involved. Neuropsychiatric SLE is of one of the major concerns in the clinical evaluation of this disease. Routine magnetic resonance imaging (MRI) findings are often nonspecific or negative. In this study, we explored the use of diffusion tensor imaging in assisting with the diagnosis of SLE. Data from 34 SLE patients (age range, 18-73 years) and 29 age-matched volunteers (age range, 29-64 years) were analyzed. MRI was performed on a 1.5-T clinical MR scanner with a quadrature head coil. The average diffusion constant (D(av)) and diffusion anisotropy maps [fractional anisotropy (FA)] were determined on a pixel-by-pixel basis. Regional diffusion measurements were made by region of interest in the genu and splenium of the corpus callosum (CC), anterior and posterior limb of the internal capsule (IC) and frontal lobe and thalamus. The diffusion distribution was fitted to a triple-Gaussian model. The mean of the brain tissue distribution was determined as a mean diffusion constant for the whole brain (BD(av)). Student's t test was used to determine the diffusion difference between SLE patients and control subjects. The SLE patients were separated into two groups according to their MRI results. A P value lower than .05 was considered to be statistically significant. Twenty of the 34 SLE patients with abnormal MRI results showed findings dominated by nonspecific white matter disease. The BD(av) and D(av) values of the frontal lobe, splenium CC and anterior IC were significantly higher in all SLE patients as compared with the control subjects. The SLE patients with normal MRI results also showed higher BD(av) and D(av) values in the frontal lobe, splenium and anterior and posterior limbs of the IC as compared with the control subjects. There was no significant difference in the D(av) values of the thalamus between the SLE patients and the control subjects. The BD(av) value in the SLE patient group was robustly correlated with the D(av) values of the frontal lobe, splenium and thalamus. These correlations were found to be similarly significant for the SLE patients with normal MRI findings. The diffusion anisotropy measurements showed that splenium CC had the highest FA value in both the control subjects and SLE patients. Overall, SLE patients had lower FA values in the genu and splenium CC as compared with the control subjects. In the group of patients with normal MRI findings, the FA values of the genu and splenium CC as well as the anterior IC were also lower than those in the control subjects. Pearson's correlation statistics revealed robust correlations between the measurements of D(av) and FA values in the SLE patient group. Quantitative diffusion imaging and diffusion anisotropy showed early changes in the brains of the SLE patients. Increased BD(av) and D(av) values of the frontal lobe as well as decreased anisotropy in the genu CC and anterior IC may represent preclinical signs of central nervous system involvement of SLE even when the routine MRI findings are negative or nonspecific. Quantitative diffusion analysis may prove to be useful in detecting the initial brain involvement of SLE and may enable monitoring of early disease progression and treatment efficacy.

A Modified Surface Forces Apparatus for Single Molecule Tracking

To unravel molecular motion within confined liquids, we have combined a surface forces apparatus (SFA) with a highly sensitive fluorescence microscope. Details of our setup including important modifactions to enable the tracking of single dye molecules within nanometer thin confined liquid films are presented. The mechanical and optical performance of our setup is discussed in detail. For a load of 20 mN we observed a circular-shaped contact region (d approximately 300 microm), which results in a confining pressure of about 280 kPa. First experiments on liquid films of tetrakis(2-ethylhexoxy)silane (TEHOS) doped with rhodamine B demonstrated the ability to track single dye molecules within the confining gap of a SFA. The mean diffusion constant was independent of the liquid film thickness of approximately 3x10(-8) cm2/s and thus 10 times smaller than the diffusion constant of rhodamine B in bulk TEHOS. This points to the existence of a thin interface layer with slower molecular dynamics and an attractive potential parallel to the solid surface trapping molecules in this interface region.

Characterization of Interaction between Cationic Lipid-Oligonucleotide Complexes and Cellular Membrane Lipids Using Confocal Imaging and Fluorescence Correlation Spectroscopy

Complexes formed by cationic liposomes and single-strand oligodeoxynucleotides (CL-ODN) are promising delivery systems for antisense therapy. ODN release from the complexes is an essential step for inhibiting activity of antisense drugs. We applied fluorescence correlation spectroscopy and confocal laser scanning microscopy to monitor CL-ODN complex interaction with membrane lipids leading to ODN release. To model cellular membranes we used giant unilamellar vesicles and investigated the transport of Cy-5-labeled ODNs across DiO-labeled membranes. For the first time, we directly observed that ODN molecules are transferred across the lipid bilayers and are kept inside the giant unilamellar vesicles after release from the carriers. ODN dissociation from the carrier was assessed by comparing diffusion constants of CL-ODN complexes and ODNs before complexation and after release. Freely diffusing Cy-5-labeled ODN (16-nt) has diffusion constant D(ODN) = 1.3 +/- 0.1 x 10(-6) cm2/s. Fluorescence correlation spectroscopy curves for CL-ODN complexes were fitted with two components, which both have significantly slower diffusion in the range of D(CL-ODN) = approximately 1.5 x 10(-8) cm2/s. Released ODN has the mean diffusion constant D = 1.1 +/- 0.2 x 10(-6) cm2/s, which signifies that ODN is dissociated from cationic lipids. In contrast to earlier studies, we report that phosphatidylethanolamine can trigger ODN release from the carrier in the full absence of anionic phosphatidylserine in the target membrane and that phosphatidylethanolamine-mediated release is as extensive as in the case of phosphatidylserine. The presented methodology provides an effective tool for probing a delivery potential of newly created lipid formulations of CL-ODN complexes for optimal design of carriers.

Monitoring brain development with quantitative diffusion tensor imaging

AbstractQuantifying changes that occur during brain maturation may help in diagnosing diseases that affect pediatric patients. By obtaining normative curves that define brain maturation, pathological changes may be easier to recognize. We assessed diffusion changes which are inherently related to the brain structure during maturation and obtained normative curves. MR scans were obtained for 26 pediatric subjects (ages 0 to 11 years) and four adults. The MR images were all normal. Maps of the average diffusion constant (Dav) were calculated for each subject. Changes in Dav were determined with distribution analysis for the entire brain and compared with regions of interest measurements from the periventricular white matter and thalamus. The mean diffusion constant of the whole brain changes quite rapidly as the brain matures. The data suggest that at least two distinct processes are responsible for the change. Quantitative diffusion tensor imaging may provide means of quantifying overall human brain maturation that may be useful in diagnosing pathology.

Free Brownian Motion of Individual Lipid Molecules in Biomembranes

The mobility of phospholipids in free-standing and supported membranes was investigated on the level of individual molecules. For the analysis of trajectories a new statistical treatment was developed that permitted us to clearly distinguish different types of diffusional motion. A freely diffusing subfraction of lipids within supported membranes was identified. Its mobility was characterized by a mean lateral diffusion constant of D(supp) = 4.6 microm(2)/s. In comparison, the mobility of lipids embedded in "free-standing" planar membranes yielded an increase in the mean diffusion constant by a factor of 4.5, D(free) = 20.6 microm(2)/s. This increase is attributed to the ultrathin (<or=1 nm) lubricating water layer between membranes and glass support.

Structure effect on water diffusion and hygroscopic stress in polyimide films

AbstractA bending‐beam technique has been used to in situ monitor the diffusion of water in various polyimide films. The polyimides studied are pyromellitic dianhydride‐4.4′‐oxydianiline (PMDA–ODA), pyromellitic dianhydride‐p‐phenylenediamine (PMDA–PDA), and 3,3′,4,4′‐benzophenone tetracarboxylic dianhydride‐p‐phenylenediamine (BPDA–PDA), and their blends and random copolymers. The diffusion of water in these films obeys Fick's law. In PMDA–ODA, the mean diffusion constant is 5.2 ± 0.4 × 10−9 (cm2/s) for thicknesses ranging from 6.7 to 27.3 μm. In PMDA–PDA, it is 2.0 ± 0.4 × 10−9 (cm2/s) for thicknesses ranging from 7.3 to 20.0 μm, and in BPDA–PDA, 0.27 ± 0.02 × 10−9 (cm2/s) for thicknesses ranging from 4.8 to 21.0 μm. In the blends and random copolymer with 50 wt % PMDA–ODA and 50 wt % PMDA–PDA, the diffusion constants are slightly smaller than those in the pure PMDA–ODA, but much larger than in the pure PMDA–PDA. On the contrary, in those with 50 wt % BPDA–PDA and 50 wt % PMDA–PDA, the diffusion constants are much smaller than those in the pure PMDA–PDA, but slightly larger than in the pure BPDA–PDA. These diffusion constants are primarily affected by the chemical structure of the imide molecule. The morphology, such as crystallinity, of the films has played a secondary factor. Hygroscopic stresses due to water uptake in all the studied films increase as the film thickness increases. It can be attributed to that the film orientation decreases with the increase of thickness.

Structural properties of liquid alkali-metal-lead alloys: NaPb, KPb, RbPb, and CsPb.

The structural properties of liquid equiatomic alkali-metal--lead alloys APb, with A=Na, K, Rb, and Cs, have been studied with neutron diffraction. The experimental data are reduced to the neutron-weighted total structure factors S(Q) and radial distribution functions n(r). In all the systems studied, S(Q) is characterized by a first sharp diffraction peak (FSDP) at Q\ensuremath{\sim}1 A\r{} $^{\mathrm{\ensuremath{-}}1}$ and n(r) by structure in the first coordination shell at r=3--4 A\r{}, both features indicating the presence of polyatomic structural units. Two types of structural models have been fitted to the experimental data, both based on consideration of such units: the random packing of structural units model, and the reference interaction site model. The structures of the units are derived from powder-diffraction measurements made with the same instrument on solid polycrystalline samples. Allowing for a slight expansion of the units on melting and using physically reasonable values for the adjustable parameters, both models give satisfactory agreement with the experimental data and are used to give the partial structure factors and pair distribution functions. Inelastic-scattering measurements have been made on one system, liquid KPb, using a spectrometer at the same source. These yield a value for the mean diffusion constant, D=1.2\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{cm}}^{2}$/sec, and a smoothly varying inelastic scattering spectrum with no indication of excitations of a molecular character. The FSDP remains well defined when the inelastic scattering is integrated over small energy transfers, indicating a lifetime of ${10}^{\mathrm{\ensuremath{-}}13}$ sec or longer for the intermediate-range order responsible for this peak.

Chemical Vapor Transport of ZnTe by the Closed-Tube Method and Its Thermodynamic Analysis

The transport and growth rates in the ZnTe–I2 system by the closed-tube method are experimentally investigated as a function of the charged iodine concentration in the range ∼2×10-3 mg/cm3 to ∼2×10 -1 mg/cm3. The thermodynamic calculations are described here in detail so as to clarify the transport mechanism in this system. The two reactions, i.e. the dissociative sublimation and the complicated disproportionations corresponding to low and high iodine concentrations respectively, play an important role in the transport process of ZnTe. The experimentally-determined transport rate can be described quantitatively over the whole range of iodine concentration by using the two different values, ∼0.038 cm2/s and ∼0.015 cm2/s, as the mean diffusion constant in the low and high regions of iodine concentration respectively.