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Metastable protein-rich microdroplets are produced from liquid-liquid phase separation (LLPS) of protein aqueous solutions. These globules can be intermediates for the formation of other protein-rich phases. Lysozyme aqueous solutions undergo LLPS around 0 °C in the presence of NaCl near physiological conditions. Here, it is shown that insertion of small amounts of 4-(2-hydroxyethyl)-1-piperazineethanesulfonate (HEPES, 0.1 M) as a second additive to lysozyme-NaCl-water solutions near physiological ionic strength (0.2 M) is an essential step for triggering conversion of protein-rich droplets into another phase. Specifically, LLPS induced by cooling reproducibly leads to a rapid and high-yield formation of compact tetragonal crystalline microparticles only in the presence of HEPES. These microcrystals exhibit small size (1-3 μm), narrow size distribution and guest-binding properties. The temperature-concentration phase diagram shows a characteristic topology with LLPS boundary metastable with respect to tetragonal microcrystals, which in turn become less stable than rod-shaped orthorhombic crystals above 40 °C. Interestingly, dynamic light scattering, hydrogen-ion titrations and isothermal titration calorimetry reveal that lysozyme-HEPES interactions were found to be weakly attractive and exothermic. Our findings indicate that additives of salting-in type can represent an important factor controlling the fate of metastable protein-rich microdroplets relevant to drug formulations, femtosecond crystallography, and potential implications in protein-driven cytoplasmic compartmentalization., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Diffusion of a solute can be induced by the concentration gradient of another solute in solution. This transport mechanism is known as cross-diffusion. We have investigated cross-diffusion in a ternary protein-salt-water system. Specifically, we measured the two cross-diffusion coefficients for the lysozyme-NaCl-water system at 25 °C and pH 4.5 as a function of protein and salt concentrations by Rayleigh interferometry. One cross-diffusion coefficient characterizes salt osmotic diffusion induced by a protein concentration gradient, and is related to protein-salt thermodynamic interactions as described by the theories of Donnan membrane equilibrium and protein preferential hydration. The other cross-diffusion coefficient characterizes protein diffusiophoresis induced by a salt concentration gradient, and is described as the difference between a preferential-interaction coefficient and a transport parameter. We first relate our experimental results to the protein net charge and the thermodynamic excess of water near the protein surface. We then extract the Stefan-Maxwell diffusion coefficient describing protein-salt interactions in water. We find that the value of this coefficient is negative, contrary to the friction interpretation of Stefan-Maxwell equations. This result is explained by considering protein hydration. Finally, protein diffusiophoresis is quantitatively examined by considering electrophoretic and hydration effects on protein migration and utilized to accurately estimate lysozyme electrophoretic mobility. To our knowledge, this is the first time that protein diffusiophoresis has been experimentally characterized and a protein-salt Stefan-Maxwell diffusion coefficient reported. This work represents a significant contribution for understanding and modeling the effect of concentration gradients in protein-salt aqueous systems relevant to diffusion-based mass-transfer technologies and transport in living systems.

We have experimentally investigated multicomponent diffusion in a protein-polymer-salt-water quaternary system. Specifically, we have measured the nine multicomponent diffusion coefficients, D(ij), for the lysozyme-poly(ethylene glycol)-NaCl-water system at pH 4.5 and 25 degrees C using precision Rayleigh interferometry. Lysozyme is a model protein for protein-crystallization and enzymology studies. We find that the protein diffusion coefficient, D(11), decreases as polymer concentration increases at a given salt concentration. This behavior can be quantitatively related to the corresponding increase in fluid viscosity only at low polymer concentration. However, at high polymer concentration (250 g/L), protein diffusion is enhanced compared to the corresponding viscosity prediction. We also find that a protein concentration gradient induces salt diffusion from high to low protein concentration. This effect increases in the presence of poly(ethylene glycol). Finally, we have evaluated systematic errors associated with measurements of protein diffusion coefficients by dynamic light scattering. This work overall helps characterize protein diffusion in crowded environments and may provide guidance for further theoretical developments in the field of protein crystallization and protein diffusion in such crowded systems, such as the cytoplasm of living cells.

Understanding protein solubility is important for a rational design of the conditions of protein crystallization. We report measurements of lysozyme solubility in aqueous solutions as a function of NaCl, KCl, and NH4Cl concentrations at 25 degrees C and pH 4.5. Our solubility results are directly compared to preferential-interaction coefficients of these ternary solutions determined in the same experimental conditions by ternary diffusion. This comparison has provided new important insight on the dependence of protein solubility on salt concentration. We remark that the dependence of the preferential-interaction coefficient as a function of salt concentration is substantially shaped by the common-ion effect. This effect plays a crucial role also on the observed behavior of lysozyme solubility. We find that the dependence of solubility on salt type and concentration strongly correlates with the corresponding dependence of the preferential-interaction coefficient. Examination of both preferential-interaction coefficients and second virial coefficients has allowed us to demonstrate that the solubility dependence on salt concentration is substantially affected by the corresponding change of protein chemical potential in the crystalline phase. We propose a simple model for the crystalline phase based on salt partitioning between solution and the hydrated protein crystal. A novel solubility equation is reported that quantitatively explains the observed experimental dependence of protein solubility on salt concentration.

We experimentally demonstrated that liquid-liquid phase separation (LLPS) of protein aqueous solutions can be induced by isothermal protein oligomerization. This phenomenon is analogous to LLPS induced by the polymerization of small organic molecules in solution. Specifically, using glutaraldehyde for protein cross-linking, we observed the formation of protein-rich liquid droplets for bovine serum albumin and chicken egg lysozyme at 25 degrees C. These droplets evolved into cross-linked protein microspheres. If the aqueous solutions of the protein monomer do not show LLPS at temperatures lower than the oligomerization temperature, protein-rich droplets are not observed. We experimentally linked the formation of these droplets to the increase of LLPS temperature during protein oligomerization. When macroscopic aggregation competes with LLPS, a rationale choice of pH, polyethylene glycol, and salt concentrations can be used to favor LLPS relative to aggregation. Although glutaraldehyde has been extensively used to cross-link protein molecules, to our knowledge, its use in homogeneous aqueous solutions to induce LLPS has not been previously described. This work contributes to the fundamental understanding of both phase transitions of protein solutions and the morphology of protein condensed phases. It also provides guidance for the development of new methods based on mild experimental conditions for the preparation of protein-based materials.

To investigate the effect of calcium salts on the thermodynamic and transport properties of aqueous solutions of proteins, we report ternary diffusion coefficients for the lysozyme-CaCl2-water ternary system at 25 degrees C and pH 4.5. We have used our ternary diffusion coefficients to calculate preferential-interaction coefficients as a function of salt concentration. This has allowed us to characterize protein-salt thermodynamic interactions. We have observed the presence of large common-ion effects by examining the dependence of the diffusion coefficients on salt concentration. Our results are compared to those previously reported for the lysozyme-MgCl2-water ternary system. We have found that the common-ion effect is essentially the same for both salt cases. On the other hand, by examining the dependence of the preferential-interaction coefficient on salt concentration, we have found that salt preferentially interacts with the protein in the lysozyme-CaCl2-water system, whereas water preferentially interacts with the protein in lysozyme-MgCl2-water system. This is consistent with the known generally larger affinity of Mg2+ for water, as compared to Ca2+, and the different roles that these two divalent metal ions play in biochemical processes. We remark that neglecting the common-ion contribution of the preferential-interaction coefficient can lead to qualitatively inaccurate descriptions of protein-salt aqueous systems, even at high salt concentrations. Indeed, for the lysozyme-CaCl2 system, this approximation would lead to interpretations inconsistent with the known destabilizing effect of calcium ions on proteins.

We report the four diffusion coefficients for the lysozyme-MgCl2-water ternary system at 25 degrees C and pH 4.5. The comparison with previous results for the lysozyme-NaCl-water ternary system is used to examine the effect of salt stoichiometry on the transport properties of lysozyme-salt aqueous mixtures. We find that the two cross-diffusion coefficients are very sensitive to salt stoichiometry. One of the cross-diffusion coefficients is examined in terms of common-ion, excluded-volume, and protein-preferential hydration effects. We use the four ternary diffusion coefficients to extract chemical-potential cross-derivatives and protein-preferential interaction coefficients. These thermodynamic data characterize the protein-salt thermodynamic interactions. We demonstrate the presence of the common-ion effect (Donnan effect) by analyzing the dependence of the preferential-interaction coefficient not only with respect to salt concentration but also with respect to salt stoichiometry. We conclude that the common-ion effect and the protein-preferential hydration are both important for describing the lysozyme-MgCl2 thermodynamic interaction.

We use accurate thermodynamic derivatives extracted from high-precision measurements of the four volume-fixed diffusion coefficients in ternary solutions of lysozyme chloride in aqueous NaCl, NH4Cl, and KCl at pH 4.5 and 25 degrees C to (a) assess the relative contributions of the common-ion and nonideality effects to the protein chemical potential as a function of salt concentration, (b) compare the behavior of the protein chemical potential for the three salts, which we found to be consistent with the Hofmeister series, and (c) discuss our thermodynamic data in relation to the dependence of the protein solubility on salt concentration. The four diffusion coefficients are reported at 0.6 mM lysozyme chloride and 0.25, 0.5, 0.9, 1.2, and 1.5 M KCl and extend into the protein-supersaturated region. The chemical potential cross-derivatives are extracted from diffusion data using the Onsager reciprocal relation and the equality of molal cross-derivatives of solute chemical potentials. They are compared to those calculated previously from diffusion data for lysozyme in aqueous NaCl and NH4Cl. We estimate the effective charge on the diffusing lysozyme cation at the experimental concentrations. Our diffusion measurements on the three salts allowed us to analyze and interpret the four diffusion coefficients for charged proteins in the presence of 1:1 electrolytes. Our results may provide guidance to the understanding of protein crystallization.

Dynamic light scattering (DLS) is extensively used for measuring macromolecule diffusion coefficients. Contrary to classical techniques based on macroscopic concentration gradients, DLS probes microscopic fluctuations in concentration. DLS accuracy and its concordance with macroscopic-gradient techniques remains an outstanding important issue. We measured lysozyme diffusion coefficients in aqueous salt using both DLS and Rayleigh interferometry, a highly accurate macroscopic-gradient technique. The precision of our results is unprecedented. We find that our DLS values were systematically 2% higher than interferometry values. We believe that our interferometric measurements have produced the most accurate diffusion data ever reported for a protein, providing a new standard for quality control of DLS measurements. Furthermore, by interferometry, we have determined the whole diffusion coefficient matrix required for rigorously describing lysozyme-salt coupled diffusion. For the first time, we experimentally demonstrate that DLS does not provide the protein diffusion coefficient but one eigenvalue of the diffusion coefficient matrix.