The so-called extended law of corresponding states, as proposed by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)], involves a mapping of the phase behaviors of systems with short-range attractive interactions. While it has already extensively been applied to various model potentials, here we test its applicability to protein solutions with their complex interactions. We successfully map their experimentally determined metastable gas-liquid binodals, as available in the literature, to the binodals of short-range square-well fluids, as determined by previous as well as new Monte Carlo simulations. This is achieved by representing the binodals as a function of the temperature scaled with the critical temperature (or as a function of the reduced second virial coefficient) and the concentration scaled by the cube of an effective particle diameter, where the scalings take into account the attractive and repulsive contributions to the interaction potential, respectively. The scaled binodals of the protein solutions coincide with simulation data of the adhesive hard-sphere fluid. Furthermore, once the repulsive contributions are taken into account by the effective particle diameter, the temperature dependence of the reduced second virial coefficients follows a master curve that corresponds to a linear temperature dependence of the depth of the square-well potential. We moreover demonstrate that, based on this approach and cloud-point measurements only, second virial coefficients can be estimated, which we show to agree with values determined by light scattering or by Derjaguin-Landau-Verwey-Overbeek (DLVO)-based calculations.

In light chain (LC) diseases, monoclonal immunoglobulin LCs are abundantly produced with the consequence in some cases to form deposits of a fibrillar or amorphous nature affecting various organs, such as heart and kidney. The factors that determine the solubility of any given LC in vivo are still not well understood. We hypothesize that some of the biochemical properties of the LCs that have been shown to correlate with amyloid fibril formation in patients also can be used as predictors for the degree of kidney damage in a patient group that is only biased by protein availability. We performed detailed biochemical and biophysical investigations of light chains extracted and purified from the urine of a group of 20 patients with light chain disease. For all samples that contained a sufficiently high concentration of LC, we quantified the unfolding temperature of the LCs, the monomer-dimer distribution, the digestibility by trypsin and the formation of amyloid fibrils under various conditions of pH and reducing agent. We correlated the results of our biophysical and biochemical experiments with the degree of kidney damage in the patient group and found that most of these parameters do not correlate with kidney damage as defined by clinical parameters. However, the patients with the greatest impairment of kidney function have light chains which display very poor digestibility by trypsin. Most of the LC properties reported before to be predictors of amyloid formation cannot be used to assess the degree of kidney damage. Our finding that poor trypsin digestibility correlates with kidney damage warrants further investigation in order to probe a putative mechanistic link between these factors.

Protein phase behavior and protein-protein interactions can be tuned by additives. We experimentally determined the phase behavior of lysozyme solutions, namely, the cloud-point temperature (CPT), in the presence of two additives, sodium chloride (NaCl) and guanidine hydrochloride (GuHCl). Their concentrations are chosen to maintain the secondary structure, as verified by CD spectroscopy. Our data indicate that the salts affect the CPT through electrostatic screening and salt-specific contributions. At high salt concentrations, the CPT is a linear function of the additive concentration for the salts NaCl and GuHCl as well as for a nonionic additive, glycerol, and a solvent, dimethyl sulfoxide (DMSO). Their molar temperature increments, which rank their specific effects on the CPT (NaCl > 0 > DMSO > glycerol > GuHCl), are found to be essentially independent of the protein concentration. In particular, the specific effects of NaCl and GuHCl in mixtures are found to be additive, indicating the absence of synergies or suppressions between both salts. Thus, molar temperature increments represent a characteristic measure for the specific effects of additives on protein interactions, which is easily accessible in lab experiments and which will help to characterize the effects of additives on protein interactions and phase behavior.

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.

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.