Diffusion and microstructural properties of solutions of charged nanosized proteins: Experiment versus theory

Structure and short-time diffusion of concentrated suspensions consisting of silicone-stabilised PMMA particles: a quantitative analysis taking polydispersity effects into account

We characterise structure and dynamics of concentrated suspensions of silicone-stabilised PMMA particles immersed in index-matching decalin-tetralin mixtures by means of static and quasielastic light scattering experiments. These particles can reproducibly be prepared via a comparatively easy route and are thus promising model systems with hard-sphere interaction. We demonstrate the hard-sphere behaviour of dense suspensions of these systems rigorously taking polydispersity effects into account. Structure factors S(Q) can in the entire range of volume fractions with liquid-like structure quantitatively be modelled using a multi-component Percus-Yevick ansatz regarding the particle size distribution and the form factor assuming a core-shell model with a scattering length density gradient in the PMMA core. Herewith, hydrodynamic functions H(Q) are in the whole accessible Q-range beyond the second maximum of H(Q) quantitatively modelled using a rescaled δγ-approach for all investigated volume fractions. With these data, previously provided characterisation of dilute systems is extended: the excellent agreement of structural and dynamic properties with theoretical predictions for hard spheres demonstrates the suitability of these particles as a model system for hard spheres.

Nanoscale Bending Dynamics in Mixed-Chain Lipid Membranes

Lipids that have two tails of different lengths are found throughout biomembranes in nature, yet the effects of this asymmetry on the membrane properties are not well understood, especially when it comes to the membrane dynamics. Here we study the nanoscale bending fluctuations in model mixed-chain 14:0–18:0 PC (MSPC) and 18:0–14:0 PC (SMPC) lipid bilayers using neutron spin echo (NSE) spectroscopy. We find that despite the partial interdigitation that is known to persist in the fluid phase of these membranes, the collective fluctuations are enhanced on timescales of tens of nanoseconds, and the chain-asymmetric lipid bilayers are softer than an analogous chain-symmetric lipid bilayer with the same average number of carbons in the acyl tails, di-16:0 PC (DPPC). Quantitative comparison of the NSE results suggests that the enhanced bending fluctuations at the nanosecond timescales are consistent with experimental and computational studies that showed the compressibility moduli of chain-asymmetric lipid membranes are 20% to 40% lower than chain-symmetric lipid membranes. These studies add to growing evidence that the partial interdigitation in mixed-chain lipid membranes is highly dynamic in the fluid phase and impacts membrane dynamic processes from the molecular to mesoscopic length scales without significantly changing the bilayer thickness or area per lipid.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Structure and Dynamics of Ribonuclease A during Thermal Unfolding: The Failure of the Zimm Model

Disordered regions as found in intrinsically disordered proteins (IDP) or during protein folding define response time to stimuli and protein folding times. Neutron spin-echo spectroscopy is a powerful tool to directly access the collective motions of the unfolded chain to enlighten the physical origin of basic conformational relaxation. During the thermal unfolding of native ribonuclease A, we examine the structure and dynamics of the disordered state within a two-state transition model using polymer models, including internal friction, to describe the chain dynamics. The presence of four disulfide bonds alters the disordered configuration to a more compact configuration compared to a Gaussian chain that is defined by the additional links, as demonstrated by coarse-grained simulation. The dynamics of the disordered chain is described by Zimm dynamics with internal friction (ZIF) between neighboring amino acids. Relaxation times are dominated by mode-independent internal friction. Internal friction relaxation times show an Arrhenius-like behavior with an activation energy of 33 kJ/mol. The Zimm dynamics is dominated by internal friction and suggest that the characteristic motions correspond to overdamped elastic modes similar to the motions observed for folded proteins but within a pool of disordered configurations spanning the configurational space. For IDP, internal friction dominates while solvent friction and hydrodynamic interactions are smaller corrections.

Binary mixtures of charged colloids: a potential route to synthesize disordered hyperuniform materials

A new route to fabricate large samples of 2D disordered hyperuniform materials via self-assembly of mixtures of charged colloids.

Crowding-Controlled Cluster Size in Concentrated Aqueous Protein Solutions: Structure, Self- and Collective Diffusion

We investigate the concentration-controlled formation of clusters in β-lactoglobulin (BLG) protein solutions combining structural and dynamical scattering techniques. The static structure factor from small-angle X-ray scattering as well as de-Gennes narrowing in the nanosecond diffusion function D(q) from neutron spin echo spectroscopy support a picture of cluster formation. Using neutron backscattering spectroscopy, a monotonous increase of the average hydrodynamic cluster radius is monitored over a broad protein concentration range, corresponding to oligomeric structures of BLG ranging from the native dimers up to roughly four dimers. The results suggest that BLG forms compact clusters that are static on the observation time scale of several nanoseconds. The presented analysis provides a general framework to access the structure and dynamics of macromolecular assemblies in solution.

Thermal activation of 'allosteric-like' large-scale motions in a eukaryotic Lactate Dehydrogenase

Conformational changes occurring during the enzymatic turnover are essential for the regulation of protein functionality. Individuating the protein regions involved in these changes and the associated mechanical modes is still a challenge at both experimental and theoretical levels. We present here a detailed investigation of the thermal activation of the functional modes and conformational changes in a eukaryotic Lactate Dehydrogenase enzyme (LDH). Neutron Spin Echo spectroscopy and Molecular Dynamics simulations were used to uncover the characteristic length- and timescales of the LDH nanoscale motions in the apo state. The modes involving the catalytic loop and the mobile region around the binding site are activated at room temperature, and match the allosteric reorganisation of bacterial LDHs. In a temperature window of about 15 degrees, these modes render the protein flexible enough and capable of reorganising the active site toward reactive configurations. On the other hand an excess of thermal excitation leads to the distortion of the protein matrix with a possible anti-catalytic effect. Thus, the temperature activates eukaryotic LDHs via the same conformational changes observed in the allosteric bacterial LDHs. Our investigation provides an extended molecular picture of eukaryotic LDH's conformational landscape that enriches the static view based on crystallographic studies alone.

Influence of temperature and charge effects on thermophoresis of polystyrene beads⋆

We study the thermodiffusion behavior of spherical polystyrene beads with a diameter of 25 nm by infrared thermal diffusion Forced Rayleigh Scattering (IR-TDFRS). Similar beads were used to investigate the radial dependence of the Soret coefficient by different authors. While Duhr and Braun (Proc. Natl. Acad. Sci. U.S.A. 104, 9346 (2007)) observed a quadratic radial dependence Braibanti et al. (Phys. Rev. Lett. 100, 108303 (2008)) found a linear radial dependence of the Soret coefficient. We demonstrated that special care needs to be taken to obtain reliable thermophoretic data, because the measurements are very sensitive to surface properties. The colloidal particles were characterized by transmission electron microscopy and dynamic light scattering (DLS) experiments were performed. We carried out systematic thermophoretic measurements as a function of temperature, buffer and surfactant concentration. The temperature dependence was analyzed using an empirical formula. To describe the Debye length dependence we used a theoretical model by Dhont. The resulting surface charge density is in agreement with previous literature results. Finally, we analyze the dependence of the Soret coefficient on the concentration of the anionic surfactant sodium dodecyl sulfate (SDS), applying an empirical thermodynamic approach accounting for chemical contributions.

Ultrafiltration of charge-stabilized dispersions at low salinity

We present a comprehensive study of cross-flow ultrafiltration (UF) of charge-stabilized suspensions, under low-salinity conditions of electrostatically strongly repelling colloidal particles. The axially varying permeate flux, near-membrane concentration-polarization (CP) layer and osmotic pressure profiles are calculated using a macroscopic diffusion-advection boundary layer method, and are compared with filtration experiments on aqueous suspensions of charge-stabilized silica particles. The theoretical description based on the one-component macroion fluid model (OCM) accounts for the strong influence of surface-released counterions on the renormalized colloid charge and suspension osmotic compressibility, and for the influence of the colloidal hydrodynamic interactions and electric double layer repulsion on the concentration-dependent suspension viscosity η, and collective diffusion coefficient Dc. A strong electro-hydrodynamic enhancement of Dc and η, and likewise of the osmotic pressure, is predicted theoretically, as compared with their values for a hard-sphere suspension. We also point to the failure of generalized Stokes-Einstein relations describing reciprocal relations between Dc and η. According to our filtration model, Dc is of dominant influence, giving rise to an only weakly developed CP layer having practically no effect on the permeate flux. This prediction is quantitatively confirmed by our UF measurements of the permeate flux using an aqueous suspension of charged silica spheres as the feed system. The experimentally detected fouling for the largest considered transmembrane pressure values is shown not to be due to filter cake formation by crystallization or vitrification.

Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker-Mazur and pairwise additivity methods

We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.

Observation of small cluster formation in concentrated monoclonal antibody solutions and its implications to solution viscosity

Monoclonal antibodies (mAbs) are a major class of biopharmaceuticals. It is hypothesized that some concentrated mAb solutions exhibit formation of a solution phase consisting of reversibly self-associated aggregates (or reversible clusters), which is speculated to be responsible for their distinct solution properties. Here, we report direct observation of reversible clusters in concentrated solutions of mAbs using neutron spin echo. Specifically, a stable mAb solution is studied across a transition from dispersed monomers in dilute solution to clustered states at more concentrated conditions, where clusters of a preferred size are observed. Once mAb clusters have formed, their size, in contrast to that observed in typical globular protein solutions, is observed to remain nearly constant over a wide range of concentrations. Our results not only conclusively establish a clear relationship between the undesirable high viscosity of some mAb solutions and the formation of reversible clusters with extended open structures, but also directly observe self-assembled mAb protein clusters of preferred small finite size similar to that in micelle formation that dominate the properties of concentrated mAb solutions.

Distinguishing the monomer to cluster phase transition in concentrated lysozyme solutions by studying the temperature dependence of the short-time dynamics

Recent combined experiments by small angle neutron scattering (SANS) and neutron spin echo (NSE) have demonstrated that dynamic clusters can form in concentrated lysozyme solutions when the right combination of a short-ranged attraction and a long-ranged electrostatic repulsion exists. In this paper, we investigate the temperature effect on the dynamic cluster formation and try to pinpoint the transition concentration from a monomeric protein phase to a cluster phase. Interestingly, even at a relatively high concentration (10% mass fraction), despite the significant change in the SANS patterns that are associated with the change of the short-ranged attraction among proteins, the normalized short-time self-diffusion coefficient is not affected between 5 and 40 °C. This is interpreted as a lack of cluster formation in this condition. However, at larger concentrations such as 17.5% and 22.5% mass fraction, we show that the average hydrodynamic radius increases significantly and causes a large decrease of the normalized self-diffusion coefficient as a result of cluster formation when the temperature is changed from 25 to 5 °C.

Short-time rheology and diffusion in suspensions of Yukawa-type colloidal particles

A comprehensive study is presented on the short-time dynamics in suspensions of charged colloidal spheres. The explored parameter space covers the major part of the fluid-state regime, with colloid concentrations extending up to the freezing transition. The particles are assumed to interact directly by a hard-core plus screened Coulomb potential, and indirectly by solvent-mediated hydrodynamic interactions. By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity η(∞), we investigate the accuracy of two fast and easy-to-implement analytical schemes. The first scheme, referred to as the pairwise additive (PA) scheme, uses exact two-body hydrodynamic mobility tensors. It is in good agreement with the ASD simulations of H(q) and η(∞), for smaller volume fractions up to about 10% and 20%, respectively. The second scheme is a hybrid method combining the virtues of the δγ scheme by Beenakker and Mazur with those of the PA scheme. It leads to predictions in good agreement with the simulation data, for all considered concentrations, combining thus precision with computational efficiency. The hybrid method is used to test the accuracy of a generalized Stokes-Einstein (GSE) relation proposed by Kholodenko and Douglas, showing its severe violation in low salinity systems. For hard spheres, however, this GSE relation applies decently well.

Short-time diffusion of charge-stabilized colloidal particles: generic features

Analytical theory and Stokesian dynamics simulations are used in conjunction with dynamic light scattering to investigate the role of hydrodynamic interactions in short-time diffusion in suspensions of charge-stabilized colloidal particles. The particles are modeled as solvent-impermeable charged spheres, repelling each otherviaa screened Coulomb potential. Numerical results for self-diffusion and sedimentation coefficients, as well as hydrodynamic and short-time diffusion functions, are compared with experimental data for a wide range of volume fractions. The theoretical predictions for the generic behavior of short-time properties obtained from this model are shown to be in full accord with experimental data. In addition, the effects of microion kinetics, nonzero particle porosity and residual attractive forces on the form of the hydrodynamic function are estimated. This serves to rule out possible causes for the strikingly small hydrodynamic function values determined in certain synchrotron radiation experiments.

Observation of protein domain motions by neutron spectroscopy

High-resolution inelastic neutron scattering, which is available with neutron spin-echo spectroscopy (NSE) is introduced as a tool for the analysis of biomolecule flexibility. Coherent scattering in a range where it is sensitive to length scales of nanometers and covering a time range from picoseconds to several 100 ns makes the motion of larger subdomains within proteins visible. We show that and how the internal domain motion within a protein in solution can be measured. Comparison with displacement patterns from normal mode analysis provides further insight into the nature of the geometry of the motions that lead to the observed dynamic signature. The NSE experiment on alcohol dehydrogenase (ADH) is used as example to illustrate the general principles of the method.

Generic behavior of the hydrodynamic function of charged colloidal suspensions

We discuss the generic behavior of the hydrodynamic function H(q) and diffusion function D(q) characterizing the short-time diffusion in suspensions of charge-stabilized colloidal spheres, by covering the whole fluid regime. Special focus is given to the behavior of these functions at the freezing transition specified by the Hansen-Verlet freezing rule. Results are presented in dependence on scattering wavenumber q, effective particle charge, volume fraction, salt concentration, and particle size, by considering both the low-charge and high-charge branch solutions of static structure factors. The existence of two charge branches leads to the prediction of a re-entrant melting-freezing-melting transition for increasing particle concentration at very low salinity. A universal limiting contour line is derived for the principal peak height value of H(q), independent of particle charge and diameter, and concentration and salinity, which separates the fluid from the fluid-solid coexistence region. This line is only weakly dependent on the value of the structure factor peak height entering the Hansen-Verlet rule. A dynamic freezing criterion is derived in terms of the short-time cage diffusion coefficient, a quantity easily measurable in a scattering experiment. The higher-dimensional parameter scans underlying this study make use of the fast and highly efficient deltagamma-scheme in conjunction with the analytic rescaled mean spherical approximation input for the static structure factor. Our results constitute a comprehensive database useful to researchers performing dynamic scattering experiments on charge-stabilized dispersions.

Neutron spin-echo studies of hemoglobin and myoglobin: multiscale internal dynamics

Neutron spin-echo spectroscopy was used to study structural fluctuations that occur in hemoglobin (Hb) and myoglobin (Mb) in solution. Using neutron spin-echo data up to a very high momentum transfer q ( approximately 0.62 A(-)(1)), we characterized the internal dynamics of these proteins at the levels of dynamic pair correlation function and self-correlation function in the time range of several picoseconds to a few nanoseconds. In the same protein solution, data transition from pair correlation motion to self-correlation motion as the momentum transfer q increases. At low q, coherent scattering dominates; at high q, observations are largely due to incoherent scattering. The low q data were interpreted in terms of an effective diffusion coefficient; on the other hand, the high q data were interpreted in terms of mean square displacements. Comparison of data from the two homologous proteins collected at different temperatures and protein concentrations was used to assess the contributions made by translational and rotational diffusion and internal modes of motion to the data. The temperature dependence of decay times can be attributed to changes in the viscosity and temperature of the solvent, as predicted by the Stokes-Einstein relationship. This is true for contributions from both diffusive and internal modes of motion, indicating an intimate relationship between the internal dynamics of the proteins and the viscosity of the solvent. Viscosity change associated with protein concentration can account for changes in diffusion observed at different concentrations, but is apparently not the only factor involved in the changes in internal dynamics observed with change in protein concentration. Data collected at high q indicate that internal modes in Mb are generally faster than those in Hb, perhaps due to the greater surface-to-volume ratio of Mb and the fact that surface groups tend to exhibit faster motion than buried groups. Comparison of data from Hb and data from Mb at low q indicates an unexpectedly rapid motion of Hb alphabeta dimers relative to one another. Dynamic motion of subunits is increasingly perceived as important to the allosteric behavior of Hb. Our data demonstrate that this motion is highly sensitive to protein concentration, temperature, and solvent viscosity, indicating that great care needs to be exercised in interpreting its effect on protein function.

Collective thermal diffusion of silica colloids studied by nonlinear optics

We investigate the collective thermal diffusion of silica charged spheres in Sulpho-Rhodamine B/water solution at different concentrations by measuring time-dependent thermal and Soret lensings. We show a significant concentration-dependence of the thermal diffusion coefficient D(T), not previously reported. Moreover, the results clearly show that both mass diffusion and Soret coefficient are collective quantities being strongly dependent on the particles' packing fraction. Our Z-scan setup allows us to investigate the dynamics of the system at low wave vector, which addresses the influence of the interparticle interactions on the thermal diffusion of the colloids.

Linear and nonlinear magneto-optics of ferritin

Measurements of Rayleigh light scattering and Cotton-Mouton (CM) effect are carried out at room temperature for 100 mM NaCl solutions of apoferritin/ferritin loaded with 0, 90, 100, 500, 700, and 1500 Fe atoms/molecule. Because of the spherical shape, ferritin macromolecule should not manifest magnetic anisotropy; however, in solution it shows the induced magnetic birefringence (CM effect) and changes in intensity of the scattered light components. The newly obtained data support the previously reported conclusions indicating that the deformation of linear optical polarizability induced in the ferritin by a magnetic field and the orientation of the induced magnetic dipole moment by this field are the main sources of the magneto-optical phenomena observed. Nevertheless, it is also found that the orientation of the permanent magnetic dipole moment contributes to both effects. The magnetic field induced changes in the light scattering and the CM effect theoretically depend on the linear magneto-optical polarizability, chi, on the nonlinear magneto-optical polarizability, eta, and square of the permanent magnetic dipole moment value of the macromolecule, mu(2). On the basis of the theory describing both effects as well as the experimental data, the values of the anisotropy of linear magneto-optical polarizabilities components, the values of the linear optical polarizability and its anisotropy, nonlinear magneto-optical polarizability and its anisotropy, are estimated. Also the magnetic dipole moment of the ferritin macromolecule is found. Interestingly, not all iron atoms in the ferritin are indicated to be in the superparamagnetic state, some of them occur in the diamagnetic form.

Direct observation of correlated interdomain motion in alcohol dehydrogenase

Interdomain motions in proteins are essential to enable or promote biochemical function. Neutron spin-echo spectroscopy is used to directly observe the domain dynamics of the protein alcohol dehydrogenase. The collective motion of domains as revealed by their coherent form factor relates to the cleft opening dynamics between the binding and the catalytic domains enabling binding and release of the functional important cofactor. The cleft opening mode hardens as a result of an overall stiffening of the domain complex due to the binding of the cofactor.

Determination of the concentration dependence of polyelectrolyte diffusion coefficients by application of the Boltzmann gradient method

The concentration dependence of a polyelectrolyte diffusion coefficient in aqueous low salt solution (KCl, 1 mM) is determined from a single dynamic gradient experiment. The Boltzmann method is applied to calculate the diffusion coefficient. A special diffusion cell is constructed that minimizes aberrations in the optical detection of the polyion concentration profile. Bovine serum albumin (BSA) is chosen as a model polyion. To get information about the diffusion process down to very small polyion concentrations, the BSA molecule is fluorescently labeled. The fluorescence intensity is used as a measure of the polyion concentration. The change of the polyion net charge caused by labeling is discussed. The cell is illuminated by an LED, and the fluorescence intensity profile is detected by a CCD camera. Experiments at 5 and 17 degrees C show that the diffusion coefficient of labeled BSA remains constant in the very low polyion concentration range below a threshold of about 1.5 g/l. This is in contradiction to the linear concentration dependence of polyion diffusion coefficients at very low concentrations often postulated in the literature without reference to direct experimental evidence. Our finding is confirmed by dynamic light scattering experiments published recently. An explanation for this behavior based on a modified Donnan osmotic compressibility approach is given.

Neutron spin echo studies on ferritin: free-particle diffusion and interacting solutions

The dynamics of proteins are often studied by means of quasielastic neutron scattering (QENS), for example by time-of-flight methods. The spatial dimensions (10-20 nm) present in protein solutions are accessible by neutron scattering. In this article, a systematic study of diffusive dynamics of ferritin and apoferritin (=ferritin without iron core) is presented. Apoferritin consists of a spherical shell built of 24 protein units and carries net negative charge at pH 5. We have studied diffusive dynamics of ferritin solutions by neutron spin echo (NSE). We pay attention to an important feature of this technique compared to other QENS methods, which being the usage of a broad wavelength band. Using a more sophisticated fit function than usually used in NSE, we find as expected in low concentrated systems that the diffusion coefficient approaches the free-particle value of apoferritin and coincides with the diameter of the apoferritin shell (12.2 nm). In interacting solutions, the NSE results reveal that the dynamic picture of this complex liquid is dominated by slowing down of the dynamics. In low-salt solutions, a structure factor peak appears due to ordering of the ferritin molecules on the length scale of several intermolecular distances. We discuss the usage of different NSE fit functions for interacting solutions near the structure factor peak. Comparison of the dependence of elastic and dynamic data on the scattering vector value shows the influence of indirect interactions on the dynamic picture, irrespective of the way of data analysis, which being necessary due to the broad wavelength spectrum.

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.

Collective diffusion coefficient of proteins with hydrodynamic, electrostatic, and adhesive interactions

A theory is presented for lambdaC, the coefficient of the first-order correction in the density of the collective diffusion coefficient, for protein spheres interacting by electrostatic and adhesive forces. An extensive numerical analysis of the Stokesian hydrodynamics of two moving spheres is given so as to gauge the precise impact of lubrication forces. An effective stickiness is introduced and a simple formula for lambdaC in terms of this variable is put forward. A precise though more elaborate approximation for lambdaC is also developed. These and numerically exact expressions for lambdaC are compared with experimental data on lysozyme at pH 4.5 and a range of ionic strengths between 0.05M and 2M.

Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.

Salt concentration and particle density dependence of electrophoretic mobilities of spherical colloids in aqueous suspension

Using laser Doppler velocimetry in the superheterodyne mode, we conducted a systematic study of the electrophoretic mobility of dispersions of small silica spheres (a=18 nm) suspended in water at different salinities and particle concentrations. The concentration of NaCl was varied from 40 microM up to 16 mM, while the particle concentrations were varied between 4.2x10(18) and 2.1x10(20) m-3. We find a decrease of mobility with increasing salt concentrations and an increase with increased particle number densities. The latter observation is not backed by the standard cell model of electrophoresis with Shilov-Zharkikh boundary conditions. Rather, if the experimental data are interpreted within that model, an unexpected change of the zeta potential at constant added salt concentration results. Interestingly, all experimental data collapse onto a single master curve, if plotted versus the ratio C* of particle counterions to added salt ions. We obtain a logarithmic increase of mobility for C*<1 and a plateau for C*>1. This may indicate a change of the Stern layer structure not yet included in the theoretical model.

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.