Size dependence of protein diffusion very close to membrane surfaces: measurement by total internal reflection with fluorescence correlation spectroscopy

The diffusion coefficients of nine fluorescently labeled antibodies, antibody fragments, and antibody complexes have been measured in solution very close to supported planar membranes by using total internal reflection with fluorescence correlation spectroscopy (TIR-FCS). The hydrodynamic radii (3-24 nm) of the nine antibody types were determined by comparing literature values with bulk diffusion coefficients measured by spot FCS. The diffusion coefficients very near membranes decreased significantly with molecular size, and the size dependence was greater than that predicted to occur in bulk solution. The observation that membrane surfaces slow the local diffusion coefficient of proteins in a size-dependent manner suggests that the primary effect is hydrodynamic as predicted for simple spheres diffusing close to planar walls. The TIR-FCS data are consistent with predictions derived from hydrodynamic theory. This work illustrates one factor that could contribute to previously observed nonideal ligand-receptor kinetics at model and natural cell membranes.     

On the role of solute solvation and excluded-volume interactions in coupled diffusion

Coupled diffusion is observed in multicomponent liquid mixtures in which strong thermodynamic interactions occur. This phenomenon is described by cross terms in the matrix of multicomponent diffusion coefficients. This paper reports a theoretical analysis on the relative role of thermodynamic factors and Onsager cross-coefficients on cross-diffusion coefficients relevant to ternary mixtures containing macromolecules or colloidal particles in the presence of salting-out conditions. A new model based on frictional coefficients between solvated solutes is reported. This model predicts that the Onsager cross-coefficient is negative and contributes significantly to cross-diffusion coefficients even at infinite dilution for solutes with a large difference in size. These predictions are consistent with recent experimental results. The role of preferential solvation and excluded-volume interactions on the thermodynamic factors are also examined. Excluded-volume interactions are introduced through the use of the McMillan-Mayer thermodynamic framework after emphasizing some important aspects of diffusion reference frames and thermodynamic driving forces. Finally, new expressions for cross-diffusion coefficients are proposed.     

Free-volume estimates in heterogeneous polymer systems. I. Diffusion in crystalline ethylene–propylene copolymers

Apparent thermodynamic diffusion coefficients were obtained from carbon tetrachloride, benzene, and n-hexane sorption-desorption kinetics in crystalline and amorphous ethylene-propylene copolymers (with propylene content from 1 to 70 wt. %, and crystallinity from 0% to 77%), in high-density and low-density polyethylene, and in polypropylene. The dependence of the diffusion coefficient vs. concentration curves on crystallinity and propylene content in the copolymers is reported. The diffusion coefficient at zero penetrant concentration increases with decrease in crystallinity. The apparent diffusion activation energies in the temperature interval investigated (25 to 75°C) are independent of temperature and are constant for crystalline copolymers. A modified Fujita-like free-volume theory for diffusion in crystalline polymer systems is introduced, and the theoretical estimates of diffusion coefficients show satisfactory agreement with experiment.     

Diffusion of polarizable colloids in electromagnetic fields

Diffusion of polarizable colloids in electromagnetic fields is considered. Extensive and intensive thermodynamic formulations of magnetic and electric polarization energy is used to establish driving forces that generate diffusion of colloids. Effects of concentration, activity coefficient, and interfacial and polarization energies are formulated in terms of corresponding concentration dependent diffusion coefficients. Magnetic and electric diffusion coefficients are defined and it is shown that the former can be made comparable and even larger than ordinary diffusion coefficients of polarizable colloids. Magnetic diffusion coefficients are derived for mono- and polydisperse colloid mixtures relative to the fluid and then are transformed to the dispersion frame of reference. It is shown that ordinary and magnetic diffusion coefficients of polydisperse colloids can be resolved into four and three basic coefficients, respectively.     

Equilibrium and Transport Properties of Sodium n-Octyl Sulfonate Aqueous Solutions

Measurements of osmotic coefficients, mutual diffusion coefficients, and conductivity were performed on the binary system sodium n-octyl sulfonate (C₈SO₃Na)–water at 25°C both below and above the micellar composition range. The osmotic coefficient data were obtained through vapor-pressure osmometry, while the Taylor dispersion method was used to measure diffusion coefficients. The mass equilibrium model was applied to this self-aggregating system, taking into account the deviation of the activity coefficients from the Debye–Hückel limiting law by using the Guggenheim corrective terms for mixed electrolyte solutions. The expressions derived from the model fit the experimental osmotic and diffusion coefficient data well, when the same values of aggregation number, fraction of condensed counterions, and equilibrium constant are used. Osmotic coefficients were also used to determine the thermodynamic factor required to compute the solute mobility from diffusion data. Conductivity data were used to test two theoretical models, namely, the Onsager–Fuoss and the Mean Spherical Approximation theories. Both models have been found to yield unsatisfactory fits to our experimental data and some arbitrary terms had to be applied to the theoretical expressions to obtain good agreement between experiment and theory.     

Multiexponential decay autocorrelation function in dynamic light scattering in near-critical ternary liquid mixture

The dynamic structure factor of a ternary liquid mixture is calculated from the theory of thermodynamic fluctuations with the help of linearized hydrodynamic equations. The theoretical model allows evaluating and classifying the transport properties near a critical solution point of a ternary mixture. In the vicinity of the critical solution point, experimental dynamic light scattering measurements reveal two hydrodynamic relaxation modes with well-separated characteristic relaxation times. From the autocorrelation functions, we can determine two effective diffusivities D(1) and D(2). As theoretically predicted by a model developed in this work, one of these two modes can be associated with thermal diffusion and the other with mass diffusion. In the special case of an incompressible liquid mixture limit, D(1) and D(2) are decoupled, becoming thermodiffusion coefficient D(T) and mutual mass diffusion coefficient D(ij). A possible physical meaning of D(1) and D(2) for a ternary mixture is discussed.     

On the mutual diffusion properties of ethanol-water mixtures

The structural organization, the number of hydrogen bonds (H bond), and the self- and mutual diffusion coefficients of ethanol-water mixtures were studied by molecular dynamics simulation. It was found that both the numbers of H bonds per water and per ethanol decrease as the mole fraction of ethanol increases. The composition dependences and the relationships between the self- and the mutual diffusion coefficients were further discussed. The self-diffusion coefficient of water has a large drop as the concentration of ethanol increases from 0 to 0.3 and then it nearly keeps constant, while that of ethanol has a minimum around ethanol mole fraction of 0.5. The mutual diffusion coefficient could be divided into two parts, the kinematic factor and the thermodynamic factor. Both the kinematic and thermodynamic factors for ethanol-water mixtures were calculated. It was found that the change trend of mutual diffusion coefficients with the composition is mainly dependent on the thermodynamic factors.     

Light scattering measurement and theoretical interpretation of mutual diffusion coefficients in binary liquid mixtures

Mutual diffusion coefficients for eleven binary systems of simple organic liquids have been measured by laser light scattering. By separating the mutual diffusion coefficient into a kinetic diffusion coefficient and a thermodynamic factor, we have been able to analyze the dynamical information contained in the kinetic coefficient in terms of a simple hard sphere theory of molecular motion. The hard sphere model of the kinetic diffusion coefficient is shown to be accurate for ideal and moderately nonideal solutions, and for both spherical and very nonspherical molecules. Only for extremely nonideal solutions were we unable to interpret diffusion coefficient data by our methods of analysis.     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.     

Diffusion of sodium dodecyl sulfate micelles in agarose gels

The gradient diffusion of ionic sodium dodecyl sulfate micelles in agarose gel was investigated at moderate concentrations above the CMC. Of particular interest were the effects of micelle, gel, and sodium chloride concentration on the micelle diffusivity. Holographic interferometry was used to measure the gradient diffusion coefficient at three sodium chloride concentrations (0, 0.03, 0.10 M), three gel concentrations (0, 1, 2 wt%), and several surfactant concentrations. Time-resolved fluorescence quenching was used to measure aggregation numbers both in solution and gel. The micelle diffusivity increased linearly with surfactant concentration at the two larger sodium chloride concentrations and all gel concentrations. In general, the strength of this effect increased with decreasing sodium chloride concentration and increased with gel concentration. This behavior is evidence of decreasing micelle-micelle electrostatic interactions with increasing sodium chloride concentrations, and increasing excluded volume effects and hydrodynamic screening with increasing gel concentration, respectively. The only exception was at 0.1M sodium chloride and 2 wt% agarose, which showed a slight reduction in the slope compared to 1 wt% agarose. It was found that the concentration effect is quite strong for charged solutes: at a NaCl concentration of 0.03 M in a 2% agarose gel, in a solution with 3% SDS micelles by volume, the micelle diffusion coefficient is doubled relative to its value in the same gel at infinite dilution. The extrapolated, infinite-dilution diffusion coefficients and the rate at which the micelle diffusivity increased with surfactant concentration were compared with predictions of previously published theories in which the micelles are treated as charged, colloidal spheres and the gel as a Brinkman medium. The experimental data and theoretical predictions were in good agreement.     

用于聚合物溶液扩散系数计算的活度系数模型比较

用40个聚合物溶液体系的实验数据,对三个有代表性的活度系数模型用于计算联系自扩散系数和互扩散系数的热力学因子的精度进行了比较,结果表明三个模型的精度相近,误差一般在20％左右。,因而本工作揭示了聚合物溶注保由自扩散系数计算与扩散系数的一个潜在问题。即由于活度系数模型计算热力学因子误差较大所带来的较大不确定性。     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.     

Effect of long-range hydrodynamic and direct intermacromolecular forces on translational diffusion

Within the framework of recently formulated microscopic theories of macromolecular diffusion it is shown that hydrodynamic forces act always to diminish the influence of direct forces, but never to reverse the sign of the correction term due to direct forces alone. Although the correction term D(k) to the intrinsic diffusion coefficient may vary with scattering vector |k|, it is shown that a reversal in sigh of the correction term with increasing |k|, if it occurs, must be associated with an amplitude of less than 10% of the correction term at |k| = 0. At |k| = 0 direct repulsive forces are predicted to always increase the apparent diffusion constant, even after accounting for hydrodynamic interactions. Although experiments on polylysine (1 mg/ml) at salt concentrations above 0.01 M are in qualitative accord with the theory, below 10^?3 M salt the apparent diffusion coefficient is reduced by a factor of about 20, concomitant with a much reduced intensity of scattered light. The strong contradiction of the theory implied by this observation is attributed to a dramatic rise in Stokes friction arising from long-range interionic forces in the low-salt solutions.     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Influence of neutral cyclodextrin concentration on plate numbers in capillary electrophoresis

A quantitative theory of plate number N in capillary electrophoresis was developed for buffers containing neutral cyclodextrins (CDs) capable of forming inclusion complexes. In the theory, N was modeled by longitudinal diffusion, injection extent, width of the detection window, and the detector time constant. The apparent mobility was modeled as a weighted sum of the mobilities of the free-solution analyte and the inclusion complex. The apparent diffusion coefficient was modeled as a similarly weighted sum. Both the apparent mobility and diffusion coefficient were corrected by functions that compensated for increases of buffer temperature caused by Joule heat. The experimental N's and apparent mobilities of neutral thiourea and of the anions, dansyl D- and L-leucine, dansyl D- and L-aspartic acid, benzoate, and 4-nitrophenolate, were determined in buffers containing from 0 to 15 mM beta-CD. The binding constants, and mobilities and diffusion coefficients of the free-solution analyte and inclusion complex, were calculated as regression coefficients by fitting theory to these determinations. The regression coefficients were shown to have physicochemical meaning, as assessed by literature values, independent measurements, and theoretical predictions. The assessment showed the Nernst-Einstein equation does not relate mobilities and diffusion coefficients at the electrolyte concentration used. The interdependence of mobilities, diffusion coefficients, binding constants, and other dispersion sources was interpreted to evaluate the factors affecting the variation of N with CD concentration. From the interpretation, an approximate equation for N in low-concentration CD buffers was derived. The equation depends on free-solution and inclusion-complex mobilities and diffusion coefficients, the binding constant, the potential difference over the effective capillary length, and the number of plates in a CD-free buffer.     

Measurement of the hydrodynamic radii of PEE-G dendrons by diffusion spectroscopy on a benchtop NMR spectrometer

Benchtop nuclear magnetic resonance (NMR) spectroscopy is a useful tool for the rapid determination of the self-diffusion coefficient and the hydrodynamic radius of dendrons. The self-diffusion coefficients of the first four generations of poly ethoxy ethyl glycinamide (PEE-G) dendrons are measured by diffusion-ordered spectroscopy (DOSY) on a benchtop NMR equipped with diffusion gradient coils. The hydrodynamic radii of the dendrons are calculated via the Stokes–Einstein equation. The effects of solvent and pH are determined with the hydrodynamic radius increasing with generation and decreasing upon neutralization of an acidic solution. These measurements provide valuable information for biological and pharmaceutical applications of dendrons.     

The concentration dependence of micelle aggregation and the shape of micelles of sodium dodecyl sulfate and hexadecyltrimethylammonium bromide

The recently reported data by Corti and Degiorgio for the diffusion coefficients and micelle molecular weights of two surfactants were used for correlating the concentration dependence of hydrodynamic and thermodynamic properties of micellar particles.     

良溶剂中环形高分子单链的结构与动力学性质的模拟研究

本文采用多粒子碰撞动力学与分子动力学耦合的模拟方法研究了环形高分子单链在良溶剂中的静态与动态性质,并与线形分子进行了对比.研究发现,环形高分子链内粒子之间的平均距离小于线形链,即粒子排列得更加紧密;相应的均方回转半径也小于线形链,线形链与环形链的均方回转半径的比值为1.77;同时,环形链扩散的速度也比线形链快,两者比值为1.10.模拟结果揭示了扩散行为是排斥体积作用和流体力学相互作用耦合的结果,在扩散过程中,流体力学相互作用消减了排斥体积作用对扩散行为的贡献.此外,通过对有和没有流体力学相互作用的多粒子碰撞动力学得到的结果作对比,研究了流体力学相互作用对高分子静态和动态行为的影响,结果表明,流体力学相互作用使高分子链在极稀溶液中的扩散速度变快.     

Sorption and diffusion of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) blend membranes

The diffusion and sorption of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) (NBR/EVA) blend membranes has been studied. The influence of blend composition, cross-linking systems, temperature and size of penetrants on the transport behaviour has been analysed. It was observed that as the EVA content increases in the blends, the solvent uptake decreases. An increase in the penetrant size also decreases the solvent uptake. The diffusion experiments were carried out in the temperature range 23–75 °C. As temperature increases the equilibrium uptake also increases. The transport coefficients namely diffusion coefficient, sorption coefficient and permeation coefficient have been calculated. The sorption data has been used to estimate the activation energies for permeation and diffusion. The van’t Hoff relationship was used to determine the thermodynamic parameters. The affine and phantom models for chemical cross-links were used to predict the nature of cross-links. Models for permeability were used and the theoretical values compared with the experimental results.     

Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.