Dynamics of liquid-liquid phase separation in protein solutions probed by coherent X-ray scattering

Understanding the fundamental process of liquid--liquid phase separation (LLPS) in biological systems is relevant to a range of diverse areas such as protein crystallization, bio-materials, self-organization of the biological cells, protein condensation-related diseases, and industrial food processing. LLPS is a complex process involving domain evolution of the new phases, microscopic dynamics of density fluctuation, the thermal fluctuation of domain interfaces, and global diffusive motion. This dynamics is strongly intertwined with the kinetics of structural evolution in the early stage of spinodal decomposition (SD) of LLPS. While both the kinetics of domain evolution and the microscopic dynamics are essential for the formation and properties of the various condensates, research so far has mainly focused on the domain growth kinetics. Meanwhile, the dynamics remain largely unknown due to the experimental difficulty in measuring slow dynamics on a micrometer length scale. X-ray photon correlation spectroscopy (XPCS) is a key technique that enables measurements at the corresponding scales. Moreover, it can simultaneously provide both information on the evolution of the structure as well as the dynamics. Nevertheless, until recently, such experiments were not carried out due to the radiation damage problem. This thesis pursues two objectives. One is the study of the microscopic dynamics of LLPS in protein solutions probed by XPCS. The other is to advance the field of XPCS itself: from conducting an experiment on biological samples to interpreting data related to non-equilibrium dynamics. To achieve them, we first investigated the dynamics of the LLPS on the model system of BSA-$\textrm{YCl}_3$ by XPCS with the simultaneous study of growth kinetics by ultra-small angle X-ray scattering (USAXS). Then, to support the experimental results and extend some of the conclusions from phase separation of BSA-$\textrm{YCl}_3$ system to LLPS phenomena in general, Cahn-Hilliard (CH) simulations were performed. In the first part of the results section, it is demonstrated that in the early stage of SD, the kinetics relaxation of BSA-$\textrm{YCl}_3$ is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics is well-described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage, followed by a power-law increase with fluctuations. However, some unresolved issues remain. The classical analysis of XPCS data is insufficient to judge the presence of gelation in the studied sample. Additionally, the experimental results show rich side features in the two-time correlation map (TTC). The physics behind these features might be crucial for understanding the non-equilibrium dynamics; however, only the component along the diagonal is usually in focus, while the side features cannot be easily interpreted via classical analysis or simulation methods. In the next chapter, we propose a Reverse-Engineering (RE) approach based on particle-based heuristic simulations that allows to predict and understand the kinetics and dynamics of systems undergoing non-equilibrium processes. This also addresses the issues that remained open in the previous section. For the microscopic length scale, the typical TTC for LLPS contains three characteristic features: "modulations" along the diagonal, a "square" feature, and "tails". It is demonstrated that the RE approach could go beyond CH theory and build the connection between these features in the TTC and the key parameters, such as relaxation time, concentration distribution, the size distribution of domains, viscosity, and mobility. Furthermore, using the RE approach, it is shown that the degree of visibility of a "square" feature is related to gelation. Based on this new result, as well as previous experimental confirmations, we can confirm the presence of gelation in the BSA-$\textrm{YCl}_3$ system at the investigated time scales identifying a nearby glass transition. All of the results described so far are obtained during measurements near the end of the capillary. In the third results part, it is shown that the dynamics in the middle of the capillary is different. The corresponding changes in TTCs result in the appearance of a special "wing" feature. Based on the measurements supported by the simulations, it is demonstrated that the "wing" feature might result from the flow retraction caused by the volume change upon temperature jump. The shape of this feature is shown to contain information about the flow rates before and after the retraction. The state of the system at the time that the wing feature appears corresponds to a steady state with the minimum influence of flow. These effects of flow on dynamics do not influence the static structure factor. Finally, new insights gained on the conditions to carry out bio-XPCS experiments are combined with the previous knowledge in this area to derive a sequence of steps for conducting an XPCS experiment on proteins. This optimized procedure is presented in the conclusions along with a summary of findings on the relationship between dynamics and features on TTCs. In this thesis, we developed a comprehensive understanding of the procedure and data analysis of XPCS experiments on the protein systems, as well as microscopic dynamics and its interplay with the kinetics of LLPS. The results of this work and the established frameworks are relevant also for various soft-matter systems and phenomena essential for understanding the fundamentals of materials synthesis, processing, and phase transformation.Die Dissertation ist gesperrt bis zum 21. Juli 2023

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400 nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels

Interplay between Kinetics and Dynamics of Liquid–Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy

Microscopic dynamics of complex fluids in the early stage of spinodal decomposition (SD) is strongly intertwined with the kinetics of structural evolution, which makes a quantitative characterization challenging. In this work, we use X-ray photon correlation spectroscopy to study the dynamics and kinetics of a protein solution undergoing liquid–liquid phase separation (LLPS). We demonstrate that in the early stage of SD, the kinetics relaxation is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics can be well described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage followed by a power-law increase with fluctuations. These experimental results are further supported by simulations based on the Cahn–Hilliard equation. The established framework is applicable to other condensed matter and biological systems undergoing phase transitions and may also inspire further theoretical work