Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials.

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

Widespread amyloidogenicity potential of multiple myeloma patient-derived immunoglobulin light chains.

BACKGROUND: In a range of human disorders such as multiple myeloma (MM), immunoglobulin light chains (IgLCs) can be produced at very high concentrations. This can lead to pathological aggregation and deposition of IgLCs in different tissues, which in turn leads to severe and potentially fatal organ damage. However, IgLCs can also be highly soluble and non-toxic. It is generally thought that the cause for this differential solubility behaviour is solely found within the IgLC amino acid sequences, and a variety of individual sequence-related biophysical properties (e.g. thermal stability, dimerisation) have been proposed in different studies as major determinants of the aggregation in vivo. Here, we investigate biophysical properties underlying IgLC amyloidogenicity. RESULTS: We introduce a novel and systematic workflow, Thermodynamic and Aggregation Fingerprinting (ThAgg-Fip), for detailed biophysical characterisation, and apply it to nine different MM patient-derived IgLCs. Our set of pathogenic IgLCs spans the entire range of values in those parameters previously proposed to define in vivo amyloidogenicity; however, none actually forms amyloid in patients. Even more surprisingly, we were able to show that all our IgLCs are able to form amyloid fibrils readily in vitro under the influence of proteolytic cleavage by co-purified cathepsins. CONCLUSIONS: We show that (I) in vivo aggregation behaviour is unlikely to be mechanistically linked to any single biophysical or biochemical parameter and (II) amyloidogenic potential is widespread in IgLC sequences and is not confined to those sequences that form amyloid fibrils in patients. Our findings suggest that protein sequence, environmental conditions and presence and action of proteases all determine the ability of light chains to form amyloid fibrils in patients.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions.

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

Protein solutions close to liquid-liquid phase separation exhibit a universal osmotic equation of state and dynamical behavior.

Liquid-liquid phase separation (LLPS) of protein solutions is governed by highly complex protein-protein interactions. Nevertheless, it has been suggested that based on the extended law of corresponding states (ELCS), as proposed for colloids with short-range attractions, one can rationalize not only the thermodynamics, but also the structure and dynamics of such systems. This claim is systematically and comprehensively tested here by static and dynamic light scattering experiments. Spinodal lines, the isothermal osmotic compressibility κT and the relaxation rate of concentration fluctuations Γ are determined for protein solutions in the vicinity of LLPS. All these quantities are found to exhibit a corresponding-states behavior. This means that, for different solution conditions, these quantities are essentially the same if considered at similar reduced temperature or second virial coefficient. For moderately concentrated solutions, the volume fraction ϕ dependence of κT and Γ can be consistently described by Baxter's model of adhesive hard spheres. The off-critical, asymptotic T behavior of κT and Γ close to LLPS is consistent with the scaling laws predicted by mean-field theory. Thus, the present work aims at a comprehensive experimental test of the applicability of the ELCS to structural and dynamical properties of concentrated protein solutions.

Universal effective interactions of globular proteins close to liquid-liquid phase separation: Corresponding-states behavior reflected in the structure factor.

Intermolecular interactions in protein solutions, in general, contain many contributions. If short-range attractions dominate, the state diagram exhibits liquid-liquid phase separation (LLPS) that is metastable with respect to crystallization. In this case, the extended law of corresponding states (ELCS) suggests that thermodynamic properties are insensitive to details of the underlying interaction potential. Using lysozyme solutions, we investigate the applicability of the ELCS to the static structure factor and how far effective colloidal interaction models can help to rationalize the phase behavior and interactions of protein solutions in the vicinity of the LLPS binodal. The (effective) structure factor has been determined by small-angle x-ray scattering. It can be described by Baxter's adhesive hard-sphere model, which implies a single fit parameter from which the normalized second virial coefficient b2 is inferred and found to quantitatively agree with previous results from static light scattering. The b2 values are independent of protein concentration but systematically vary with temperature and solution composition, i.e., salt and additive content. If plotted as a function of temperature normalized by the critical temperature, the values of b2 follow a universal behavior. These findings validate the applicability of the ELCS to globular protein solutions and indicate that the ELCS can also be reflected in the structure factor.

Layering and packing in confined colloidal suspensions.

Confinement modifies the properties of a fluid. The particle density is no longer uniform but depends on the distance from the walls; parallel to the walls, layers with different particle densities form. This affects the particle packing in the layers. We investigated colloidal fluids with volume fractions between 0.19 and 0.32 confined between rough walls. The particle-particle interactions were dominated by hard-sphere interactions but also contained some electrostatic interactions. The particle locations were determined using confocal microscopy and served to calculate the density profile, radial distribution function, anisotropic and generalized structure factors but also to characterize the arrangement of the wall particles leading to the roughness of the walls. The experiments are complemented by molecular dynamics simulations and fundamental-measure theory. While the particle arrangements are mainly controlled by hard-core interactions, electrostatic interactions become more important as the volume fraction decreases. Furthermore, the structure of the rough walls was varied and found to have a significant effect on the fluid structure. An appropriate representation of the rough walls in the simulations is thus crucial to successfully mimic the experiments.

First-passage statistics of colloids on fractals: Theory and experimental realization.

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

Interactions in protein solutions close to liquid-liquid phase separation: ethanol reduces attractions via changes of the dielectric solution properties.

Ethanol is a common protein crystallization agent, precipitant, and denaturant, but also alters the dielectric properties of solutions. While ethanol-induced unfolding is largely ascribed to its hydrophobic parts, its effect on protein phase separation and inter-protein interactions remains poorly understood. Here, the effects of ethanol and NaCl on the phase behavior and interactions of protein solutions are studied in terms of the metastable liquid-liquid phase separation (LLPS) and the second virial coefficient B2 using lysozyme solutions. Determination of the phase diagrams shows that the cloud-point temperatures are reduced and raised by the addition of ethanol and salt, respectively. The observed trends can be explained using the extended law of corresponding states as changes of B2. The results for B2 agree quantitatively with those of static light scattering and small-angle X-ray scattering experiments. Furthermore, B2 values calculated based on inter-protein interactions described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential and considering the dielectric solution properties and electrostatic screening due to the ethanol and salt content quantitatively agree with the experimentally observed B2 values.

ArGSLab: a tool for analyzing experimental or simulated particle networks.

Microscopy and particle-based simulations are both powerful techniques to study aggregated particulate matter such as colloidal gels. The data provided by these techniques often contains information on a wide array of length scales, but structural analysis methods typically focus on the local particle arrangement, even though the data also contains information about the particle network on the mesoscopic length scale. In this paper, we present a MATLAB software package for quantifying mesoscopic network structures in colloidal samples. ArGSLab (Arrested and Gelated Structures Laboratory) extracts a network backbone from the input data, which is in turn transformed into a set of nodes and links for graph theory-based analysis. The routines can process both image stacks from microscopy as well as explicit coordinate data, and thus allows quantitative comparison between simulations and experiments. ArGSLab furthermore enables the accurate analysis of microscopy data where, e.g., an extended point spread function prohibits the resolution of individual particles. We demonstrate the resulting output for example datasets from both microscopy and simulation of colloidal gels, in order to showcase the capability of ArGSLab to quantitatively analyze data from various sources. The freely available software package can be used either with a provided graphical user interface or directly as a MATLAB script.

Two-dimensional Brownian motion of anisotropic dimers.

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

The crystallization enthalpy and entropy of protein solutions: microcalorimetry, van't Hoff determination and linearized Poisson-Boltzmann model of tetragonal lysozyme crystals.

During a first-order phase transition, a thermodynamic system releases or absorbs latent heat. Despite their fundamental importance, the heat or enthalpy change occurring during protein crystallization has been directly measured only in a few cases, and the associated entropy change can only be determined indirectly. This work provides an experimental determination and theoretical analysis of the dependence of the molar crystallization enthalpy of lysozyme solutions, ΔHxtal, on the physicochemical solution parameters. Its value is determined directly by isothermal microcalorimetry and indirectly by a van't Hoff analysis of solubility data, which quantitatively agree. This suggests a two-state crystallization process, in which oligomeric intermediates play a minor role. ΔHxtal is found to be negative on the order of few tens of the thermal energy per molecule. It is independent of protein concentration and stirring speed, but weakly depends on salt (NaCl) concentration and solution pH. Assuming that crystals are electrostatically neutral, these trends are explained by a linearized Poisson-Boltzmann theory. In addition, the molar crystallization entropy, ΔSxtal, is analyzed. The dependence of the van't Hoff entropy on salt concentration and pH is captured by the model, complementing the analysis of crystallization thermodynamics.

From normal diffusion to superdiffusion: Photothermal heating of plasmonic core-shell microgels.

The motion of core-shell colloids during laser heating is studied using angle-dependent pump-probe dynamic light scattering. The cores consist of a single spherical gold nanoparticle whose localized surface plasmon resonance has a strong spectral overlap with the wavelength of the pump laser. They are homogeneously encapsulated in thick hydrogel shells composed of either chemically cross-linked poly-N-isopropylacrylamide or poly[2-(2-methoxyethoxy)ethyl methacrylate], both of which exhibit a temperature-dependent volume phase transition. Thus, upon heating beyond the transition temperature, the hydrogel shells shrink. Intensity-time autocorrelation functions are recorded while illuminating the samples with the pump laser and hence heating the gold cores. With increasing laser intensity, the dynamics changes from normal Brownian motion to superdiffusion. Nevertheless, in the high-q limit, the relaxation times can be extracted and used to estimate the temperature increase, which can reach almost 10 K. This causes a significant deswelling of the hydrogel shells, which is also measured.

Traveling band formation in feedback-driven colloids.

Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.

Glassy dynamics in asymmetric binary mixtures of hard spheres.

We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.

Binary colloidal glasses: linear viscoelasticity and its link to the microscopic structure and dynamics.

We study the relation between the microscopic structure and dynamics and the macroscopic rheological response of glass-forming colloidal suspensions, namely binary colloidal hard-sphere mixtures with large size asymmetry (1 : 5) that span a large range of mixture compositions close to the glass transition. The dynamical shear moduli are measured by oscillatory rheology and the structure and dynamics on the single-particle level by confocal microscopy. The data are compared with Brownian Dynamics simulations and predictions from mode-coupling theory based on the Percus-Yevick approximation. Experiments, simulations and theory consistently observe a strong decrease of the intermediate-frequency mechanical moduli combined with faster dynamics at intermediate mixing ratios and hence a non-monotonic dependence of these parameters but a localization of the large particles which decreases monotonically as the fraction of small particles is increased. We find that the Generalized-Stokes Einstein relation applied to the mean square displacements of the two components leads to a reasonable estimate of the shear moduli of the mixtures and hence links the rheological response to the particle dynamics which in turn reflects the microscopic structure.

Different scenarios of dynamic coupling in glassy colloidal mixtures.

Colloidal mixtures represent a versatile model system to study transport in complex environments. They allow for a systematic variation of the control parameters, namely size ratio, total volume fraction and composition. We study the effects of these parameters on the dynamics of dense suspensions using molecular dynamics simulations and differential dynamic microscopy experiments. We investigate the motion of small particles through the matrix of large particles as well as the motion of large particles. A particular focus is on the coupling of the collective dynamics of small and large particles and on the different mechanisms leading to this coupling. For large size ratios, of about 1 : 5, and an increasing fraction of small particles, the dynamics of the two species become increasingly coupled and reflect the structure of the large particles. This is attributed to the dominant effect of the large particles on the motion of the small particles, which is mediated by the increasing crowding of the small particles. Furthermore, for moderate size ratios of about 1 : 3 and sufficiently high fractions of small particles, mixed cages are formed and hence the dynamics are also strongly coupled. Again, the coupling becomes weaker as the fraction of small particles is decreased. In this case, however, the collective intermediate scattering function of the small particles shows a logarithmic decay corresponding to a broad range of relaxation times.

Structure of colloidal gels at intermediate concentrations: the role of competing interactions.

Colloidal gels formed by colloid-polymer mixtures with an intermediate volume fraction (ϕc ≈ 0.4) are investigated by confocal microscopy. In addition, we have performed Monte Carlo simulations based on a simple effective pair potential that includes a short-range attractive contribution representing depletion interactions, and a longer-range repulsive contribution describing the electrostatic interactions due to the presence of residual charges. Despite neglecting non-equilibrium effects, experiments and simulations yield similar gel structures, characterised by, e.g., the pair, angular and bond distribution functions. We find that the structure hardly depends on the strength of the attraction if the electrostatic contribution is fixed, but changes significantly if the electrostatic screening is changed. This delicate balance between attractions and repulsions, which we quantify by the second virial coefficient, also determines the location of the gelation boundary.

Second Virial Coefficient As Determined from Protein Phase Behavior.

We quantitatively link the macroscopic phase behavior of protein solutions to protein-protein interactions based on a coarse-grained colloidal approach. We exploit the extended law of corresponding states and apply the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in order to infer the second virial coefficient b2, an integral measure of the interaction potential, from the phase behavior, namely, cloud-point temperature (CPT) measurements under conditions favoring protein crystallization. This determination of b2 yields values that quantitatively agree with the results of static light scattering (SLS) experiments. The strength of the attractions is quantified in terms of an effective Hamaker constant, which accounts for van der Waals attractions as well as non-DLVO forces, such as hydration and hydrophobic interactions. Our approach based on simple lab experiments to determine the CPT in combination with the DLVO theory is expected to facilitate further biophysical research on protein-protein interactions in complex solution environments.

Colloids exposed to random potential energy landscapes: From particle number density to particle-potential and particle-particle interactions.

Colloidal particles were exposed to a random potential energy landscape that has been created optically via a speckle pattern. The mean particle density as well as the potential roughness, i.e., the disorder strength, were varied. The local probability density of the particles as well as its main characteristics were determined. For the first time, the disorder-averaged pair density correlation function g((1))(r) and an analogue of the Edwards-Anderson order parameter g((2))(r), which quantifies the correlation of the mean local density among disorder realisations, were measured experimentally and shown to be consistent with replica liquid state theory results.

Time- and ensemble-averages in evolving systems: the case of Brownian particles in random potentials.

Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general.