In situ effective diffusion coefficient profiles in live biofilms using pulsed‐field gradient nuclear magnetic resonance

Diffusive mass transfer in biofilms is characterized by the effective diffusion coefficient. It is well documented that the effective diffusion coefficient can vary by location in a biofilm. The current literature is dominated by effective diffusion coefficient measurements for distinct cell clusters and stratified biofilms showing this spatial variation. Regardless of whether distinct cell clusters or surface‐averaging methods are used, position‐dependent measurements of the effective diffusion coefficient are currently: (1) invasive to the biofilm, (2) performed under unnatural conditions, (3) lethal to cells, and/or (4) spatially restricted to only certain regions of the biofilm. Invasive measurements can lead to inaccurate results and prohibit further (time‐dependent) measurements which are important for the mathematical modeling of biofilms. In this study our goals were to: (1) measure the effective diffusion coefficient for water in live biofilms, (2) monitor how the effective diffusion coefficient changes over time under growth conditions, and (3) correlate the effective diffusion coefficient with depth in the biofilm. We measured in situ two‐dimensional effective diffusion coefficient maps within Shewanella oneidensis MR‐1 biofilms using pulsed‐field gradient nuclear magnetic resonance methods, and used them to calculate surface‐averaged relative effective diffusion coefficient (D_rs) profiles. We found that (1) D_rs decreased from the top of the biofilm to the bottom, (2) D_rs profiles differed for biofilms of different ages, (3) D_rs profiles changed over time and generally decreased with time, (4) all the biofilms showed very similar D_rs profiles near the top of the biofilm, and (5) the D_rs profile near the bottom of the biofilm was different for each biofilm. Practically, our results demonstrate that advanced biofilm models should use a variable effective diffusivity which changes with time and location in the biofilm. Biotechnol. Bioeng. 2010;106: 928–937. © 2010 Wiley Periodicals, Inc.     

A novel computational framework for D(t) from Fluorescence Recovery after Photobleaching data reveals various anomalous diffusion types in live cell membranes

Diffusion of proteins and lipids in lipid membranes plays a pivotal role in almost all aspects of cellular biology, including motility, exo?/endocytosis and signal transduction. For this reason, gaining a detailed understanding of membrane structure and function has long been a major area of cell biology research. To better elucidate this structure‐function relationship, various tools have been developed for diffusion measurements, including Fluorescence Recovery After Photobleaching (FRAP). Because of the complexity of cellular microenvironments, biological diffusion is often correlated over time and described by a time‐dependent diffusion coefficient, D(t) , although the underlying mechanisms are not fully understood. Since D(t) provides important information regarding cellular structures, such as the existence of subresolution barriers to diffusion, many efforts have been made to quantify D(t) by FRAP assuming a single power law, D(t) = Γt ^{α ? 1} where Γ and α are transport coefficient and anomalous exponent. However, straightforward approaches to quantify a general form of D(t) are lacking. In this study, we develop a novel mathematical and computational framework to compute the mean square displacement of diffusing molecules and diffusion coefficient D(t) from each individual time point of confocal FRAP data without the single power law assumption. Additionally, we developed an auxiliary equation for D(t) which can readily distinguish normal diffusion or single power law anomalous diffusion from other types of anomalous diffusion directly from FRAP data. Importantly, by applying this approach to FRAP data from a variety of membrane markers, we demonstrate the single power law anomalous diffusion assumption is not sufficient to describe various types of D(t) of membrane proteins. Lastly, we discuss how our new approaches can be applied to other fluorescence microscopy tools such as Fluorescence Correlation Spectroscopy (FCS) and Single Particle Tracking (SPT).     

Transient state isoelectric focusing. Experimental determination of apparent diffusion coefficients in polyacrylamide gels

A photoelectric scanning assembly utilizing uv absorption optics and an on-line digital data acquisition and processing system has been used to follow kinetically zone spreading during the defocusing stage (absence of electric field) of transient state isoelectric focusing (TRANSIF) in polyacrylamide gels. Measurement of the variance (σ²) of a diffusing zone as a function of time yields a linear relationship, the slope of which corresponds to the apparent diffusion coefficient (D) of the protein. A linear relationship is also obtained when the logarithm of the apparent diffusion coefficients (logD) are plotted vs acrylamide concentration (T). This relationship can be used to extrapolate D to zero gel concentration. The apparent diffusion coefficient measured in this way is significantly larger than the true diffusion coefficient. The slope of the plot logD vs T, designated C_R, is expected to be a measure of molecular size related to the retardation coefficient in polyacrylamide gel electrophoresis.     

A molecular-dynamics simulation study of diffusion of a single model carbonic chain on a graphite (001) surface

Molecular-dynamics simulations have been used to study the diffusion of a short single model carbonic chain on the graphite (001) surface. The calculated diffusion coefficient (D) first increases, then decreases with increasing chain length (N). This abnormal behavior is similar to polymer lateral diffusion at the solid–liquid interface. Furthermore, we have studied the relation between the mean-square gyration radius and N. Figure Log–log plot of the self-diffusion coefficient D versus the chain length N. The error bars are the standard deviation measured in three repeated simulations     

QELS-SEF study on poly(lysine) in the extraordinary phase: Effect of electric field strength on the apparent diffusion coefficient

The technique of quasielastic light scattering (QELS) in the presence of a sinusoidal electric field (QELS-SEF) was used to examine the diffusion of poly(lysine) in the extraordinary phase, which is defined by the anomalously small value in the apparent diffusion coefficient (D_app, obtained by QELS methods) as the added salt concentration is lowered below 10 mM. Spectra were obtained for high-molecular-weight poly(lysine) (800,000) in 0.5 mM KCl, using a driving frequency of 90 Hz. It was observed that the linewidth, hence apparent diffusion coefficient (D_SF), increased with electric field strength (E) over the range 6 < E < 30 V/cm. As might be anticipated, the asymptotic limit, D_SF(E = 0), was almost numerically equivalent to D_app at this KCl concentration. As E approached the upper limit value of 31 V/cm, the value of D_SF approached the high salt (500 mM KCl) value of D_app. These observations are discussed in terms of small-ion dispersion effects.     

Solvent effect on the relative quantum yield and fluorescence quenching of a newly synthesized coumarin derivative

We estimated the relative florescence quantum yield (Φ) of 8‐methoxy‐3‐[1‐(4,5‐dicarbomethoxy‐1,2,3‐triazoloacetyl)]coumarin [8MDTC] using a single‐point method with quinine sulfate in 0.1 M of sulfuric acid used as a standard reference. The fluorescence lifetimes, radiative and non‐radiative decay rate constants are calculated. Relative quantum yields were found to be less in the non‐polar solvents, indicating that the solute exhibits less fluorescence in a non‐polar environment. The fluorescence quenching of [8MDTC] by aniline was studied at room temperature by examining the steady state in five different solvents in order to explore various possible quenching mechanisms. The experimental results show a positive deviation in Stern–Volmer plots in all solvents. Ground state complex and sphere of action static quenching models were used to interpret the results. Many quenching rate parameters were calculated using these models. The values of these parameters suggest that the sphere of action static quenching model agrees well with the experimental results. Further, a finite sink approximation model was used to check whether these bimolecular reactions were diffusion limited or not. The values of the distance parameter R′ and the diffusion coefficient D were determined and are compared with the values of the encounter distance R and diffusion coefficient D calculated using the Stokes–Einstein equation. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of temperature on DNA secondary structure in the absence and presence of 0.5 M tetramethylammonium chloride

Changes in the average secondary structures of three different linear DNAs over the premelting region from 5 to 60°C were investigated by measuring their CD spectra and also their torsion elastic constants (〈α〉) by time-resolved fluorescence polarization anisotropy. For one of these DNAs, the HaeII fragment of pBR322, the apparent diffusion coefficients [D_app (k)] at small and large scattering vectors (k) were also measured by dynamic light scattering. With increasing temperature, all three DNAs exhibited typical premelting changes in their CD spectra, and these were accompanied by 1.4- to 1.7-fold decreases in 〈α〉. Also for the 1876 base pair fragment, D_app(k) at large scattering vectors, which is sensitive to the dynamic bending rigidity, decreased by 17%, even though there was no change at small scattering vectors, where D_app(k) = D₀ is the translational diffusion coefficient of the center-of-mass. These observations demonstrate conclusively that the premelting CD changes of these DNAs are associated with a significant change in average secondary structure and mechanical properties, though not in persistence length. In the presence of 0.5 M tetramethylammonium chloride (TMA-Cl) the premelting change in CD is largely suppressed, and the corresponding changes in 〈α〉 and D_app(k) at large scattering vectors are substantially diminished. These observations suggest that TMA-Cl, which binds preferentially to A · T-rich regions and stabilizes those regions (relative to G · C-rich regions) against melting, effectively stabilizes the prevailing low-temperature secondary structure sufficiently that the DNA is effectively trapped in that state over the temperature range observed. © 1998 John Wiley & Sons, Inc. Biopoly 45: 503–515, 1998     

Temperature dependence of the dynamic light scattering of linear phi 29 DNA: implications for spontaneous opening of the double-helix

The apparent diffusion coefficient D_app(K) of a single sample of linear ?29 DNA (M_r = 11.5 × 10⁶) has been measured as a function of K² from 0.21 × 10¹⁰ to 20 × 10¹⁰ cm^?2 at a variety of temperatures from ?0.5 to +70°C. D_app(K) scales closely as T/η at every value of K². All of these data are simulated by a particular Rouse-Zimm model comprised of a constant number of subchains with constant rms subchain extension b = 1057 Å and an apparent subchain diffusion coefficient D_plat that scales at T/η from ?0.5 to +70°C. It is inferred from these results that any temperature dependence of the flexural and torsional rigidities of DNA must be rather weak. A less firm inference is that these rigidities actually increase slightly with temperature, possibly in proportion to T, which is weak T dependence in this context. These findings eliminate the possibility that spontaneous transient opening of the DNA structure has any significant effect on the flexural and torsional rigidities of the DNA filament. A review of the most pertinent available data from other experiments concerning spontaneous transient opening of the DNA is presented. The formaldehyde kinetics data do not unequivocally implicate an open base-pair intermediate and provide only an upper limit to the fraction of open base pairs. An alternative nonopening model with a protonated doorway state is proposed to accommodate the hydrogen-exchange data. It is concluded that there is presently no incontrovertible evidence for a fraction of unstacked open base pairs greater than about 10^?4.     

Modelling Diffusion in Zeolites by Molecular Dynamics Simulations

Abstract

The diffusion of molecules sorbed in zeolites is of growing interest for understanding the mechanisms of chemical processes with regard to selectivity and reactivity [1].

MD simulations give insight into physical systems on the molecular level allowing to study and visualize the motion of molecules even beyond the possibilities of experiments [2,3]. Single system parameters can easily be varied to study their influence, also those parameters that are fixed in reality (e.g., the size of particles). We present a cross section of our recent work to illustrate the capabilities of MD: The self diffusion coefficients (D) of a mixture of methane and xenon in silicalite show remarkable deviations from those of the pure species. This is shown and confirmed by PFG NMR experiments [4].

Simulating ethane in zeolite A the mechanism of diffusion has been studied. The effects of rotation on the diffusion lead to cases where D decreases with growing temperature [5].

The independence of self diffusion on lattice vibrations is proven even for zeolites with windows of guest particle size comparing simulations with rigid and vibrating zeolite lattice [6].     

Cheek cell membrane fluidity measured by fluorescence recovery after photobleaching and steady-state fluorescence anisotropy

Membrane fluidity of human cheek cells was determined using fluorescence recovery after photobleaching (FRAP) and steady-state fluorescence anisotropy. The FRAP data showed that the lateral diffusion coefficient (D) and mobile fraction (%R) of lipid in the plasma membrane of control cells were 2.01×10^–9 cm²/ sec and 54.25%, respectively. Trypsin treatment increased D and %R to 6.4×10^–9 cm²/sec and 72.15%. In contrast, the anisotropy (r) for control cells was 0.270 which remained unchanged by trypsin treatment. The results show that diffusion of lipids in the plane of the membrane is restricted by trypsin-sensitive barriers.     

Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D_app(K) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D_app(K) is predicted to reach a limiting plateau value at extermely large values of KL, where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi-plateau with a very gradual slope. Dynamic light-scattering studies have been performed on tobacco mosaic virus from K² = (0.4–20) × 10¹⁰ cm^?2 using 632-8-nm laser radiation. The present data yield D₀ = (4.19 ± 0.10) × 10^?8 cm²/s (corrected to 20,w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D_R = 318s^?1, yield also Δ ≡ D_∥ ? D_⊥ = (1.79 ± 0.38) × 10^?8 cm²/s. The experimental data closely follow the curve of D_app(K) vs K² calcuated for these parameters. The present value of D₀ substantially exceeds all previous dynamic light-scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/D₀ = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D₀ lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D₀ and Δ/D₀ could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.     

Bounding fluid viscosity and translational diffusion in a fluid lipid bilayer

Fluorescence recovery after photobleaching was used to investigate the translational diffusion of a fluorescent derivative of a membrane-spanning lipid in L phase multibilayers of 1-palmitoyl-2-oleoylphosphatidylcholine prepared in water and in glycerol. The translational diffusion coefficient in hydrated bilayers (D _w) ranged between 2 and 5x10^–8 cm²/s and in glycerinated bilayers (D _g) the range was between 3 and 24×10^–10 cm²/s between 10° and 40°C. These results are discussed in terms of models for diffusion in membranes.     

Effects of low temperature on lateral diffusion in plasma membranes on maize (Zea mays L.) root cortex protoplasts: relevance to chilling sensitivity

The effects of temperature on the lateral diffusion of fluorescent phospholipids, sterols and proteins in the plasma membranes of maize root cortex protoplasts were monitored using fluorescence photobleaching recovery (FPR). Diffusion parameters were measured in two cultivars of maize having different chilling tolerance. Hydrodynamic theory predicts that the diffusion coefficient, D, should increase with increasing temperature. In the more chilling-tolerant cultivar, however, D for all three probes was nearly insensitive to temperature. In the more chilling-sensitive cultivar, D was also insensitive to temperature over the range from 12 to 21°C, but D for the lipid probes tended to be higher and more variable at lower temperatures. The proportion of probe molecules free to diffuse in the membrane was less than 1 for all probes, and increased significantly with increasing temperature for the protein probe. These results, taken together, support the concept that the plasma membrane contains domains having differing diffusional characteristics. Temperature effects on membrane diffusion are moderated by the existence of these domains to limit significant changes. The observed tendency for higher diffusion coefficients at low temperatures in the chilling-sensitive cultivar may correlate to morphological changes observed with protoplasts of that cultivar at low temperatures.     

Li+ counterion self-diffusion in ordered DNA

The anisotropic self-diffusion coefficient of ⁷Li⁺ (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li-(B)DNA fibers at relatively high water contents, corresponding to approximate DNA-DNA helix axis distances of 22–35 Å, using the pulsed field gradient hmr spin-echo method. Self-diffusion coefficients parallel (D_∥) and perpendicular (D_?) to the DNA helix axis increase with increasing salt content and with increasing DNA-DNA helix axis distance. The observed anisotropy D_∥/D_? decreases from 1.6 to 1.2 with the DNA-DNA separation increasing from 22 to 35 Å in the salt-free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li⁺ self-diffusion coefficients in the most water-rich system with no added salt (corresponding to an approximate distance of 35 Å between the DNA helix axes) were D_∥ ～ 1.15 × 10^?10 m² s^?1 and D_? ～ 0.98 × 10^?10 m² s^?1, compared to 9.14 × 10^?10 m² s^?1 for the diffusion of Li⁺ in an aqueous solution of LiCl (～ 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self-diffusion coefficient at different effective diffusion times. The self-diffusion coefficient of Li⁺ in the sample with the largest DNA-DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. © 1994 John Wiley & Sons, Inc.     

Correlation between the pulse rates of atmospherics and temperature variations of the atmosphere

The pulse rates of atmospherics at 10 and 28 kHz have been compared with the variations of outside air temperature up to a height of 7 km. In the 10 kHz band the pulse rate showed a strong statistically significant correlation with air temperature for all heights up to 7 km, the maximum correlation coefficient beingr=0.78 at a level of significanceP0.001. In the 28 kHz band the correlation is weaker: up to a height of 3 km the correlation coefficient ranges from 0.17 to 0.3 (P 0.001 and 0.02, respectively) and above 3 kmr ranges from 0.15 to 0.17 (P 0.02 and 0.05, respectively).As the outdoor absolute humidity depends mainly on the air temperature, it is now clear why previous investigations showed strong correlations between the difference (S) of the atmospherics pulse rates at 10 and 28 kHz, the absolute humidity (AH) outdoors and the diffusion time (T _D ) of ions in gelatin films, measured in a fully air-conditioned working-room.     

Insulin adsorption into porous charged membranes: Effect of the electrostatic interaction

Insulin adsorption into a series of porous charged membranes was investigated by batch adsorption experiments, and the experimental results were analyzed by the homogeneous diffusion model. The membranes used in this study were prepared by pore‐surface modification of porous poly(acrylonitrile) (PAN) membranes by grafting with weak acidic and basic functional groups. The amount of insulin adsorbed into the membrane was determined from the material balance of insulin. The insulin partition coefficient K between the membrane and solution was estimated from the equilibrium adsorption amount, and the effective diffusion coefficient D was estimated by matching the model with the experimental data as a fitting parameter. The dependence of K and D on the charge properties of the insulin and membrane is observed and discussed. The partition coefficient K increased when the insulin and the membrane carried opposite charges, on the other hand, the effective diffusion coefficient D was reduced. These results indicate that the electrostatic interaction between the insulin and the membranes played an important role in the insulin adsorption. © 2009 American Institute of Chemical Engineers Biotechnol. Prog. 2009     

Diffusion of DNA at very low concentrations

The diffusion behavior of DNA samples of molecular weights between 1 × 10⁶ and 25 × 10⁶ Daltons was investigated under standard conditions at mean concentrations c? between 0.0009 and 0.017 g/dl. Special techniques described previously were used and supplemented. The sensitivity required was accomplished by multiple passage through the sample cells (effective path length of 10–45 cm) and application of the Gouy interference method. The maximum DNA refraction index difference has been determined more precisely from Gouy interference fringes by applying a systematic variation procedure and a linear-plot criterion. Convection was prevented by a temperature constancy better than 0.002°C/day, vibrationless operation, and by application of a slight density gradient of heavy water, which also improved the boundary-forming procedure. The corresponding optical HDO gradient was compensated. The concentration dependence of the DNA diffusion coefficient average D_A was found to be positive and very small at extremely low concentrations, that is, below c? = 0.008 g/dl, for the sample of highest molecular weight investigated. With beginning penetration of different DNA molecules, D_A increases markedly. The diffusion constant averages of our polydisperse samples will be corrected for monodisperse subfractions in a following paper. The resulting molecular weights M from diffusion and sedimentation constants (D⁰, s⁰) together with data from literature are the basis of new s⁰–M, D⁰ ? M, and [η]–M relations for monodisperse DNA samples.     

Light scattering and viscosity study of heat aggregation of insulin

Aggregation behavior and hydrodynamic parameters of insulin have been determined from static and dynamic light scattering experiments and intrinsic viscosity measurements carried out at pH 4.0, 7.5, and 9.0 in the temperature range 20–40°C in aqueous solutions. The protein aggregated extensively at elevated temperatures in the acidic solutions. Intermolecular interactions were found to be attractive and to increase with temperature. The measured intrinsic viscosity [η], diffusion coefficient D₀, molecular weight M, and radius of gyration R_g exhibited the universal behavior: M[η] = (2.4 ± 02) × 10⁻²⁷ (R_e,η/R_e,D)³(D_0η/T)⁻³ and (D₀√n)₋₁ ≃ (√6 πη₀ζβ/k_BT) [1 + 0.201)(v/β³)√n], where n is the number of segments in the polypeptide. The effective hydrodynamic radii deduced from [η], (R_e, η) and the same deduced from D₀, (R_e,D) showed a constant ratio, (R_e,η/R_e,D = 1.1 ± 0.1). R_e,D/R_g = ξ was found to be (0.76 ± 0.07). From the known solvent viscosity η₀, the segment length β was deduced to be (10 ± 1) Å. The excluded volume was deduced to be (5 Å)³ regardless of pH. The Flory-Huggins interaction parameter was found to be χ = 0.45 ± 0.04, independent of pH and temperature. © 1998 John Wiley & Sons, Inc. Biopoly 45: 1–8, 1998     

Chain length and pressure dependence of lipid translational diffusion

The translational diffusion of pyrene, pyrene butyric acid and pyrene decanoic acid has been determined in phosphatidylcholine bilayers of different chain length and under pressure up to 200 bars. In the liquid crystalline phase and at a given temperature the diffusion decreases with increasing chain length. At a constant reduced temperature, T _red (about 10 K above the transition temperature), long chain lipids exhibit the fastest diffusion which is in disagreement with hydrodynamic models but favours free volume models for diffusion in lipid bilayers. The volume of activation, V _act, calculated from the decrease of the diffusion coefficient with pressure, ln D/P, depends on lipid chain length. V _act decreases with decreasing lipid chain length at a given temperature, T=65°C, and increases at the reduced temperature. These results are again in agreement with the dependence of the diffusion on lipid chain length and therefore with the free volume model.Abbreviations DLPC Dilauroylphosphatidylcholine - DMPC Dimyristoylphosphatidylcholine - DPPC Dipalmitoylphosphatidylcholine - DSPC Distearoylphosphatidylcholine - LUV Large unilamellar vesicles - SUV Small unilamellar vesicles - Tris Tris(hydroxymethyl)aminomethan     

Intensity-fluctuation spectroscopy and tRNA conformation. II. Changes of size and shape of tRNA in the melting process

We have measured the translational (D^T) and rotational (D^R) diffusion coefficients of bulk tRNA from baker's yeast during the thermal unfolding process by means of photon-correlation spectroscopy. It should be noted that our estimate of the rotational diffusion coefficient represented, for the first time, measurements on a small macromolecule in solution by the photoelectron time-of-arrival technique with a delay-time resolution of 1 nsec. The melting curves expressed in terms of δD^T vs temperature were consistent with the literature data in revealing the melting steps and their dependence on NaCl concentration. Additionally, it was possible to prove the existence of an intermediate, more compact structure during the initial steps of the thermal unfolding process. We found that the temperature ranges over which this intermediate structure appears depend strongly on salt concentration. By utilizing both translational and rotational diffusion coefficients and Perrin's equations for ellipsoids of revolution, we have computed the values of the equivalent length and width of tRNA molecules in solution at four different temperatures for NaCl concentrations of 0.2, 0.5, and 1M. The approximate model of ellipsoids of revolution also permits us to obtain an estimate of the radius of gyration, which is in very good agreement with literature data measured by means of small-angle x-ray scattering. Furthermore, we have measured the shape and size changes of tRNA with varying NaCl concentrations at room temperatures (25°C). The molecule becomes smaller and more spherical when NaCl concentration increases. As a result of partial melting at 70°C, the macromolecule is surprisingly elongated with an approximate axial ratio of 8:1 and has dimensions of about 180/22Å. Such information on conformational changes by a simultaneous determination of rotational and translational diffusion coefficients illustrates the potential of this approach, not available by other methods.