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.

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.

The rheological properties of a medium can be inferred from the Brownian motion of colloidal tracer particles using the microrheology procedure. The tracer motion can be characterized by the mean-squared displacement (MSD). It can be calculated from the intermediate scattering function determined by Differential Dynamic Microscopy (DDM). Here we show that DDM together with the empirical Cox–Merz rule is particularly suited to measure the steady-shear viscosity, i.e. the viscosity towards zero frequency, due to its ability to provide reliable information on long time and length scales and hence small frequencies. This method, η-DDM, is tested and illustrated using three different systems: Newtonian fluids (glycerol–water mixtures), colloidal suspensions (protein samples) and a viscoelastic polymer solution (aqueous poly(ethylene oxide) solution). These tests show that common lab equipment, namely a bright-field optical microscope, can be used as a convenient and reliable microliter viscometer. Because η-DDM requires much smaller sample volumes than classical rheometry, only a few microliters, it is particularly useful for biological and soft matter systems.

Dynamics of colloids in random energy landscapes.

Cosolvents modulate not only the stability of proteins, but also protein–protein interactions and protein phase behaviour.