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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 in 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 (SAXS). It can be described by Baxter's adhesive hard-sphere model, which implies a single fit parameter from which the normalized second virial coefficient $b_2$ is inferred and found to quantitatively agree with previous results from static light scattering. The $b_2$ 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 $b_2$ follow a universal behaviour. 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., Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://doi.org/10.1063/5.0088601

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 $B_2$ 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 $B_2$. The results for $B_2$ agree quantitatively with those of static light scattering and small-angle X-ray scattering experiments. Furthermore, $B_2$ 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 $B_2$ values.

Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of size determination methods in relation to the range of scattering vectors covered by the data is discussed. Improvements are presented to existing MC methods in which the particle shape is assumed to be known. A discussion of the problems with the ambiguous convergence criteria of the MC methods are given and a convergence criterion is proposed, which also allows the determination of uncertainties on the determined size distributions., Comment: Accepted author manuscript, 7 pages, 7 figures

We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allows a composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is furthermore generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units., Comment: Complete rewrite generalizing the formalism to arbitrary functional sub-units and including a new Feynmann like diagrammatic interpretation

Recently we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each sub-unit has reference points associated with it. These are well defined positions where sub-units can be linked together. In the present paper, we generalize the formalism to the case where each reference point can represent a distribution of potential link positions. We also present a generalized diagrammatic representation of the formalism. Scattering expressions required to model rods, polymers, loops, flat circular disks, rigid spheres and cylinders are derived. and we use them to illustrate the formalism by deriving the generic scattering expression for micelles and bottle brush structures and show how the scattering is affected by different choices of potential link positions., Comment: Paper no. 2 of a series

The possibilities to tune the structure of solid like material resulting from arrested spinodal decomposition is investigated using a system composed of lysozyme, a globular protein, dispersed in a water solution as model system for colloids with short range attraction. It is shown that the resulting arrested spinodal decomposition is driven by the interplay between the early kinetics of the spinodal decomposition and the dynamical arrest. The initial concentration, the quench depth and speed from the fluid state to the arrested state enable to tailor the mesh size of the solid network of the arrested spinodal decomposition., Comment: submitted to Soft Matter