Mutual Diffusion Coefficient Dm Research Articles

Use of Debye–Hückel–Henry charge measurements in early antibody development elucidates effects of non-specific association

The diffusion interaction parameter (kD) has been demonstrated to be a high-throughput technique for characterizing interactions between proteins in solution. kD reflects both attractive and repulsive interactions, including long-ranged electrostatic repulsions. Here, we plot the mutual diffusion coefficient (Dm) as a function of the experimentally determined Debye–Hückel–Henry surface charge (ZDHH) for seven human monoclonal antibodies (mAbs) in 15 mM histidine at pH 6. We find that graphs of Dm versus ZDHH intersect at ZDHH, ~ 2.6, independent of protein concentration. The same data plotted as kD versus ZDHH show a transition from net attractive to net repulsive interactions in the same region of the ZDHH intersection point. These data suggest that there is a minimum surface charge necessary on these mAbs needed to overcome attractive interactions.

Rheological Modeling of the Mutual Diffusion and the Interphase Development for an Asymmetrical Bilayer Based on PMMA and PVDF Model Compatible Polymers

The mutual diffusion process and interphase development taking place at an asymmetrical polymer–polymer interface between two compatible model polymers, poly(methyl methacrylate) (PMMA) with varying molecular weights and poly(vinylidene fluoride) (PVDF) in the molten state, were investigated by small-amplitude oscillatory shear measurements. The rheology method, Lodge–McLeish model, and test of the time–temperature superpositon (tTS) principle were employed to probe the thermorheological complexity of this polymer couple. The monomeric friction coefficient of each species in the blend has been examined to vary with composition and temperature and to be close in the present experimental conditions, and the failure of the tTS principle was demonstrated to be subtle. These were attributed to the presence of strong enthalpic interaction between PMMA and PVDF chains that couples the component dynamics. Hence, a quantitative rheological model modified from a primitive Qiu–Bousmina’s model that connected the mobility in the mixed state to the properties of the matrix was proposed to determine the mutual diffusion coefficient (Dm). The modified model takes into account the rheological behavior of the interphase for the first time. In turn, viscoelastic properties and thicknesss of the interphase have been able to be quantified on the basis of the modified model. Effects of the annealing factors like welding time, angular frequency, temperature, and the structural properties as well molecular weight and Flory–Huggins parameter (χ) on the kinetics of diffusion and the interphase thickness and its viscoelastic properties were investigated. On one hand, Dm was observed to decrease with frequency until leveling off at the terimnal zone, to depend on temperature obeying the Arrhenius law, and to be nearly independent of PMMA molar mass, corroborating the prediction of the fast-mode theory. On the other hand, the generated interphase which reached dozens of micrometers was revealed to own a rheological property approaching its equivalent blend. Scanning electron microscopy coupled with energy dispersive X-ray analysis (SEM-EDX) and transmission electron microscopy(TEM) were also carried out and confronted to the rheological results. Comparisons between mathematical modeling of concentration profile based on the Dm obtained from rheology and the experimental ones of SEM-EDX and TEM were conducted. Thus, a better correlation between theory and experimental results in terms of mutual diffusion and the interphase properties was nicely attained. The obtained data are in good agreement with literatures using other spectroscopical methods.

Effects of phase behavior on mutual diffusion at polymer layers interface

Using oscillation mode of rheology and theoretical calculation, we have observed for the first time the crossover of mutual diffusion coefficient, Dm, from high to low temperatures at the multiple layers interface of polymer films. A model which reflects a more realistic terminal state has been proposed to fairly fit the experimental data, by which the mutual diffusion coefficient Dm can be determined. It is substantially found that the diffusion keeps proceeding for the multilayer system at the temperature lower than the critical temperature due to the requirement of a period of time for binodal compositions to reach. Moreover, it is found that the apparent activation energy, Ed, derived from the Arrhenius relation of Dm versus 1/T, increases surprisingly when the welding temperature is below 150 °C, which relates closely to the effects of the phase behavior occurring in the two-phase region of the blend.

Effect of protein–protein interactions on protein aggregation kinetics

The mutual diffusion coefficient Dm of dilute lysozyme solutions is measured by the dynamic light scattering technique. The relation between the osmotic second virial coefficient B22 and the protein mutual diffusion coefficient Dm of dilute solutions is examined experimentally and theoretically. The role of B22 in relation with Dm in protein aggregation kinetics was analyzed based on the effect of the average protein pairwise interactions on the protein aggregation kinetics. The empirical “crystallization window” proposed by George and Wilson [Acta Crystallogr., Sect. D: Biol. Crystallogr. 50, 361 (1994)] can be interpreted from the point view of crystallization kink kinetics.

Raman spectroscopy as a tool for measuring mutual-diffusion coefficients in hydrogels.

Raman spectroscopy has been exploited to characterize the diffusion properties of solutes in hydrogels. Raman active vibrations were used as intrinsic probes of the solute concentration along gel cylinders. The resulting one-dimensional solute distribution, characterized as a function of both time and space, could be analyzed with a model based on Fick's diffusion law, and the mutual-diffusion coefficient (Dm) was then determined. To illustrate the potential of this approach, we measured the Dm of two polyethylene glycols (PEG) in Ca-alginate gels. In this case, the intensity of the CH stretching band was used to obtain the concentration profiles of PEGs, whereas the OH stretching band of water was used as an internal intensity standard. In addition to providing a straightforward approach to measuring diffusion coefficients, the Raman profile analysis provides information relative to the accessibility of gels to large molecules. As an example, it was found that the PEG penetration in Ca-alginate gels was restricted, a phenomenon that was dependent on PEG size. The Raman technique presented here effectively characterizes transport properties of solutes in gels, and such characterization is required for developing several technical applications of gels, such as their use as materials for controlled release of drugs.

Characterization of Polymer Solutions Containing a Small Amount of Aggregates by Static and Dynamic Light Scattering

Aggregate-containing solutions of poly(n-hexyl isocyanate) (PHIC) and atactic polystyrene of finite concentrations were studied by static and dynamic light scattering. Their static structure factors Ŝ(k) and the intensity autocorrelation functions g(2)(t) exhibited the enhanced low-angle scattering and bimodal relaxation, respectively. From Ŝ(k) and g(2)(t) obtained, the fast- and slow-mode components of the static structure factor (Ŝfast(k) and Ŝslow(k)) and of the first cumulant (Γfast and Γslow) were estimated as functions of the magnitude of the scattering vector k. As verified by a theory based on the dynamic mean-field theory, if the solution contains only a small amount of aggregates with diffusion coefficients much smaller than that of the nonaggregating component, Ŝfast(k) and Γfast give us the osmotic compressibility ∂c/∂Π and mutual diffusion coefficient Dm of aggregate-free solutions, respectively, and Ŝslow(k) and Γslow provide us the radius of gyration 〈S2〉z,A1/2 and hydrodynamic radius RH,A...

Dynamic light scattering evidence of a `fragile' character of protein aqueous solutions

Dynamic light scattering has been used to measure the mutual diffusion coefficient Dm of bovine serum albumin as a function of temperature at different protein concentrations. A deviation from the Arrhenius behaviour is observed, at each protein concentration investigated, corresponding to a characteristic temperature TA, whose value is found to be dependent on the protein concentration itself. In the whole temperature range, the dependence of Dm on T is well represented by a Vogel–Fulcher–Tamman law. The results are discussed in the framework of the so-called strong/fragile classification scheme for glass-forming liquids, connected to the peculiar properties of the water–protein system.

Effects of ionic strength and pH on the diffusion coefficients and conformation of chitosans molecule in solution

The effects of ionic strength and pH on the diffusion coefficients and gross conformation of chitosan molecules in solution were studied. Chitosan with 83% degree of deacetylation (DD) was prepared from red shrimp (Solemocera prominenitis) processing waste. Ten different molecular weight chitosans were prepared by ultrasonic degradation, and their molecular weights were determined by static light scattering. The weight-average molecular weight (Mw) were between 78 to 914 kilo dalton (KDa). Solution of different ionic strengths (I = 0.01, 0.10, and 0.20) but the same pH (2.18) and different pHs (2.37, 3.10, and 4.14) but the same ionic strength (I = 0.05) were prepared to measure their mutual diffusion coefficient (Dm). The diffusion coefficients for standard condition (D20,w) were derived from Dm. Intrinsic viscosities ([η]) were determined by a capillary viscometer in different pH solutions. The Mark–Houwink exponents a and ε were obtained from plots of Log [η] and Log D20,w versus Log Mw, respectively. The results show that diffusion coefficients increased with increasing ionic strength or with increasing pH or with decreasing Mw. Value of ε and a were between 0.503 to 0.571 and ranged from 0.543 to 0.632, respectively. The results indicates that chitosans conformation were in random coil in solutions in the ranges of ionic strength and pH studied. The values of a*, ε* and a**, ε**, Mark–Houwink exponents of smaller and higher than 223 KDa chitosans, respectively, were between 0.752 to 0.988 and 0.585 to 0.777 for smaller Mw chitosans and 0.406 to 0.428 and 0.430 to 0.518 for larger Mw chitosans, respectively. Molecular-weight-induced conformational transition occurred because smaller Mw chitosans was more extended than higher Mw chitosans. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2041–2050, 1999

Solvent and Solute Effects on Hydration and Aggregation Numbers of Triton X-100 Micelles

Quasi-elastic light scattering spectroscopy was used to measure the mutual diffusion coefficient Dm of Triton X-100 micelles, and the probe diffusion coefficient Dp of polystyrene latex spheres diffusing through micelle solutions. The solution ionic strength has a substantial effect on aggregation number N and hydration δ of Triton X-100 micelles, N and δ both increasing with increasing salt concentration. This behavior may be qualitatively described as arising from a salt-induced change in the location of the water/Triton X-100 cloud curve.

Dynamic light scattering from a semiflexible polymer at very low concentrations

Dynamic light scattering measurements on semiflexible poly(γ-benzyl-α,L-glutamate) have been performed at very low concentrations, near the limit for reliable multiangle detection, in N,N-dimethylformamide. By several methods of data analysis, the mutual diffusion coefficient Dm is initially level or slightly decreasing with polymer concentration. It then increases substantially, as expected in a good solvent. Static light scattering measurements offer no thermodynamic explanation for the initially level or decreasing behavior, which is apparently a manifestation of the decrease in lateral mobility as the rods become entangled in semidilute solutions. The coefficient C describing the dependence of the first cumulant of the electric field autocorrelation function upon squared scattering vector decreases with concentration, even in the most dilute regime measured. The reliability of persistence lengths estimated for this polymer by dynamic light scattering is considered.

Diffusion of TiO2 probe particles through a poly(ethylene oxide) melt

AbstractQuasi‐elastic light scattering (QELS) spectroscopy was for the first time used to measure the mutual diffusion coefficient Dm of titanium dioxide (TiO2) particles of 0,37 μm and 0,31 μm diameters in a poly(ethylene oxide) melt (weight‐average mol. wt. 7 500) between 85 °C and 160 °C. Dm exhibits a strong dependence on the temperature. The effective shear imposed by diffusing particles on the polymer melt was estimated through a comparison of the viscosity obtained by a cone‐and‐plate viscometer with the microviscosity calculated from the diffusion coefficients and hydrodynamic radii of the particles through the Stokes‐Einstein equation. The rate of shear found was ≥ 104 · s−1.

Diffusion in concentrated micellar and hard sphere solutions

We present experimental results of quasi-elastic light scattering for different charged micellar solutions. The characteristic concentration dependence of the mutual diffusion coefficient Dm at large volume fraction arises from the many-body hydrodynamic interactions. These interactions are introduced through the quasi-empirical screened Navier-Stokes equation. The effective pair mobility tensor has been calculated for terms up to r -7 (r is the inter-particle distance) with the formalism of Mazur and van Saarloos. The tensor is not « screened » in the sense that its long distance behaviour is as an inverse power of r, rather than exponential. A single « screening » constant K is proposed which is volume fraction dependent with only one adjustable parameter. The evolution of Dm with the micellar concentration has been well reproduced by the same value of K at various ionic strengths. At large volume fraction Φ the hydrodynamic interactions are essentially dominated by uncharged hard-sphere repulsions. This observation is confirmed by the fit of the dynamics of concentrated hard-sphere solutions. The behaviour of the self and mutual diffusion coefficients is described by using the same « screening » constant. This can be written as Ka ≃ Φ where a is the particle radius, which is in agreement with the results previously derived by Adelman.

Photon and fluorescence correlation spectroscopy and light scattering of eye-lens proteins at moderate concentrations

The bovine eye-lens protein, alpha L-crystallin, has been studied with photon correlation spectroscopy to obtain the mutual diffusion coefficient, Dm, with fluorescence correlation spectroscopy to determine the tracer diffusion coefficient, DT, and with light scattering to get the isothermal osmotic compressibility (delta pi/delta c) P,T. The concentration dependence of Dm, DT, and (delta pi/delta c) P,T up to a volume fraction phi of the protein of 2.5 x 10(-2) has been interpreted on the basis of four different interaction potentials: (a) an extended hard-sphere potential; (b) a shielded Coulomb potential; (c) a shielded Coulomb interaction where the effect of counterions is included; (d) a simple mixed potential. The three parameters Dm, DT, and (delta pi/delta c) P,T have also been combined in the generalized Stokes-Einstein equation, Dm = [(delta pi/delta c)P,T . (1--phi) . (DT)]/(kappa B . T). Our results indicate that, in the case that photon correlation spectroscopy gives the mutual diffusion coefficient Dm, the applicability of the Stokes-Einstein equation can be questioned; or that, when one assumes the Stokes-Einstein equation to be valid, there is significant discrepancy between the result of photon correlation spectroscopy and Dm.

The second order concentration corrections to the mutual diffusion coefficient of Brownian macroparticles

From the initial time dependence of the dynamic structure factor S(k,t), we obtain a general form, valid through second order in the concentration, for the mutual diffusion coefficient Dm. All effects of direct and hydrodynamic interactions (other than dynamic friction) are taken into account, including the three-point ’’0seen’’ hydrodynamic tensor Tijl, whose analytic form is obtained here for the first time. The concept of the reference frame correction is re-examined. The usual factor (1−φ) for transition from the fundamental hydrodynamic frame to the volume-fixed frame is argued to be a low-concentration approximation. The general form for Dm is evaluated for a model system of hard spheres. With the use of the auxiliary assumption (relaxed herein) that all hydrodynamic interaction tensors satisfy ∇ ⋅ t = 0, use of our new general method [J. Stat. Phys. 28, 673 (1982)] for reducing N-particle cluster integrals to (N−1)-dimensional integrals shows Dm = D0 (1−0.875φ−19.53φ2).

The wave vector dependence of diffusion coefficients in photon correlation spectroscopy of protein solutions

The mutual diffusion coefficient Dm was measured by means of photon correlation spectroscopy (PCS) for bovine serum albumin (BSA) at pH 4.7 and ionic strength I≃0.12 M. The BSA concentrations ranged from 1.00 to 10.7 g/dℓ and the magnitude of the scattering wave vector K varied from 3.21×104 to 3.51×105 cm−1. It was found that Dm=D0[1−(0.0166±0.0009)C], where D0=(5.92±0.04)×10−7 cm2/s corrected to water at 20 °C and the C measured in units of g/dℓ. The quantity Cn/K3, where Cn is the concentration in number of solute particles per cm3, ranged from 2 to 27 000, but this had no influence on the measured values of Dm. This work does not support the idea that the small size of K−1 or the small number of molecules contained in the volume K−3 affects the magnitudes of diffusion coefficients determined by PCS for proteins at moderate ionic strengths.

Contribution of nonhydrodynamic interactions to the concentration dependence of the friction factor of the mutual diffusion coefficient

The mutual diffusion coefficient Dm of a Brownian particle may be expressed as the ratio of a thermodynamic factor K and a friction factor fm, K and fm both being dependent on the macroparticle concentration. The contribution to fm of direct (e.g., hard sphere, electrostatic) interactions is here estimated to first order in the macroparticle concentration. In contrast to our earlier calculation [J. Chem. Phys. 67, 4690 (1977)] in which the direct interaction contribution Δfm to the Stokes’ Law drag coefficient was obtained from a fluctuation–dissipation equation. Δfm is here obtained directly from a mechanical argument based on the equations of motion of the macroparticles in solution. ΔfD is explicitly evaluated for the case of particles which interact through a weak Gaussian potential.

Experimental evidence that mutual and tracer diffusion coefficients for hemoglobin are not equal

Photon correlation spectroscopy (PCS) has been used to measure the mutual diffusion coefficient Dm for unliganded hemoglobin in the concentration range 0.86 to 15.7 g/dl. The result corrected to water at 20 °C is Dm=Do[1−(0.0057±.0003)c] where Do= (6.75±0.05) ×10−7 cm2/s and c is in units of g/dl. It is shown that Dm can be used with the phenomenological theory of diffusion to predict the tracer diffusion coefficient Dt and that the predictions agree with the results of diaphragm cell measurements [Keller, et al., J. Phys. Chem., 75, 379 (1971)]. In contrast to this, diaphragm cell measurements of Dm do not agree with PCS measurements, with open capillary and free diffusion experiments [Kitchen, et al., J. Polymer Sci. Sym. No. 55, 39 (1976)], or with ultrafiltration measurements [Probstein, et al., J. Phys. Chem. 83, 1228 (1979)]. The evidence indicates that Dm≠Dt for hemoglobin, and that diaphragm cell measurements of Dm are not reliable for proteins. (AIP)

Diffusion in protein solutions at high concentrations: A study by quasielastic light scattering spectroscopy

Quasielastic light scattering spectroscopy was used to study the mutual diffusion coefficient Dm of bovine serum albumin over the pH range 4.3–7.6 for concentrations ranging as high as 334 g/l. Using literature measurements of the tracer diffusion coefficient DT and the osmotic compressibility (∂π/∂c)P,T, we find that Dm depends on concentration and pH as predicted by the generalized Stokes–Einstein relation Dm=DT(∂π/∂c)P,T (1−φ)/KBT, φ being the volume fraction of solute and KB being Boltzmann’s constant. Our data show that Dm and DT depend quite differently on solute concentration; DT can be a factor of 3 smaller than Dm at protein concentrations exceeding 200 g/l.