Measuring Ultra-Weak Protein Self-Association by Non-ideal Sedimentation Velocity.

Ultra-weak self-association can govern the macroscopic solution behavior of concentrated macromolecular solutions ranging from food products to pharmaceutical formulations and the cytosol. For example, it can promote dynamic assembly of multi-protein signaling complexes, lead to intracellular liquid-liquid phase transitions, and seed crystallization or pathological aggregates. Unfortunately, weak self-association is technically extremely difficult to study, as it requires very high protein concentrations where short intermolecular distances cause strongly correlated particle motion. Additionally, protein samples near their solubility limit in vitro frequently show some degree of polydispersity. Here we exploit the strong mass-dependent separation of assemblies in the centrifugal field to study ultra-weak binding, using a sedimentation velocity technique that allows us to determine particle size distributions while accounting for colloidal hydrodynamic interactions and thermodynamic non-ideality (Chaturvedi, S. K.; et al. Nat. Commun. 2018, 9, 4415; DOI: 10.1038/s41467-018-06902-x ). We show that this approach, applied to self-associating proteins, can reveal a time-average association state for rapidly reversible self-associations from which the free energy of binding can be derived. The method is label-free and allows studying mid-sized proteins at millimolar protein concentrations in a wide range of solution conditions. We examine the performance of this method with hen egg lysozyme as a model system, reproducing its well-known ionic-strength-dependent weak self-association. The application to chicken γS-crystallin reveals weak monomer-dimer self-association with K _D = 24 mM, corresponding to a standard free energy change of approximately -9 kJ/mol, which is a large contribution to the delicate balance of forces ensuring eye lens transparency.