Abstract:
Antibodies are a fundamental part of the immune system. They are injected subcutaneously to treat different diseases, such as SARS-CoV-2. The concentration of antibodies of these solutions is elevated, to minimize the number of injections. It is important to study these highly concentrated solutions to avoid unwanted behavior, for example aggregation, phase separation or very high viscosity, which do not permit a painless injection. Phase separation is a type of phase transition that has been studied for many years by various disciplines, such as physics, chemistry, biology and engineering. In recent years it was discovered that phase separation is ubiquitous in cells, and in general in biological organisms. The phase separation of a solution starts at the molecular level, where the particle-particle interactions induce the formation of domains, which then grow with time until, eventually, the system reaches macroscopic phase separation. It has been shown that this process can be slowed down to the point where the growth of the domains is arrested. To obtain this, the molecular diffusion properties of the two phases have to be very different, meaning that the value of the mobility of the particle in one of the two phases has to be much smaller than in the other. By controlling these phenomena, it is possible to tune the morphology of the system to grant, for example, specific mechanical properties to the system. However, the mechanism through which the mobility is reduced is not completely understood.
In this thesis, the diffusion of antibodies is probed while in aqueous solution with polymers. The dynamics is monitored on different time and length scales to identify which type of motion the particles are subjected to. With this, we hope to clarify the connection between the microscopic and macroscopic properties of the solution. To achieve this, we probed the solution during phase separation and in the single-phase state with neutron, light and X-ray scattering techniques.
In the first study the system was probed on a micrometer length scale via light and X-ray scattering. The intensity collected via small angle scattering shows a typical spinodal peak, with which the kinetics of the phase separation can be monitored. For deep quenches, the phase separation is slowed down, reaching an almost complete arrest of the growth within the experimental time frame. The correlation functions collected via X-ray photon correlation spectroscopy during the phase separation show that two relaxation modes are present. Both of them have typical characteristics of ballistic motion as seen for colloidal gels. When measuring the system in the one-phase region via dynamic light scattering, the correlation functions show two decays as well. However, the type of diffusion is different: The fast mode, which we interpret as the diffusion of the monomers, indicates Brownian motion. The slow mode is more difficult to interpret due to the high concentration of the solution. The experimental results during the phase separation are compared with simulated data based on the Cahn-Hilliard equations. Qualitative comparability is obtained only if a strong dependence of the mobility on protein concentration is introduced. The limitations of the model are visible and we speculate that they are due to the lack of visco-elasticity in the model.
In the second study, the diffusion on molecular length scale and below was measured with quasi-elastic neutron spectroscopy. The signal was collected at three different temperatures, i.e. when the solution is 1) in a single phase, 2) in phase separation and 3) in arrested phase separation. In the two latter states, the dense phase, which occupies the majority of the volume and has a higher concentration, is the main contributor to the overall signal. This means that the system can be monitored while the concentration increases, providing an estimate of the change of the diffusion coefficient with protein concentration. The results further validate the results of the first study, as the diffusion coefficient has a strong dependence on protein concentration. A discrepancy between the temperature dependency of the diffusion coefficient we obtain via neutron spin echo and neutron back-scattering is evident. This can be explained considering the different length scales covered by the two methods via a simple model which takes into account the motion of the lobes of the protein. According to this model, while the global diffusion of the protein is strongly affected by the crowding, the single lobes' motion is not hindered to the same extent since their size is smaller.
In the third study, the measurements performed on a molecular length scale, as in the second study, but with the goal of accessing the long-time diffusion and not the short-time as done in the previous study. To access these large time scales ($\gtrsim 500\,$ ns) X-ray photon correlation spectroscopy was employed. To have a sufficient signal the photon density on the sample has to be much larger than the first study, which implies a much higher dose on the sample. Beam effects on the structure and the diffusion of the particles are observed and quantified. Although the dynamics is influenced by X-ray effects, it is possible to see that the correlation is not completely lost, meaning that the decay time is in a time range above seconds. Furthermore, the samples in the arrested state presents $q$ dependent aging. At large $q$, the diffusion does not seem to be dependent on waiting time, which is consistent with the absence of aging seen in the second study on the short-time diffusion. This is a clear difference with the results of the simulations of colloidal system.
In conclusion, we connect the kinetics and dynamics of phase separation with the molecular diffusion of the proteins via the Cahn-Hilliard equation. The model we used describes the kinetics and qualitatively the dynamics of the phase separation. The diffusion on micrometer length scale is of different type in the single phase and in the phase separation region, but, interestingly, it does not show a sharp transition between a classical phase separation and an arrested phase transition. This suggests a smooth transition between the liquid state to the gel state.
X-ray Photon Correlation Spectroscopy
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