Multicomponent Equilibrium Model for the Effects of Charge Regulation on Liquid-liquid Phase Separation of a Globular Eye Lens Protein

We study how charge regulation affects liquid-liquid phase separation of bovine gammaB-crystallin. Our grand-canonical distribution model indicates that hundreds of charging patterns have enough probability to affect protein interactions. We measured times for rotational diffusion via nuclear magnetic resonance, and for translational diffusion to neighbors with quasielastic light scattering. Both times are orders of magnitude faster than time scales for some protonation state changes of titrating residues. Here, we apply chemical equilibrium conditions to a first-order perturbation model for the multicomponent, pattern-dependent free energy. Standard chemical potentials result from our existing dilute solution model. We estimate screened electrostatic, pattern-pair dependent interactions using a linearized Poisson-Boltzmann code that accounts for dielectric heterogeneity and includes all titratable groups. We estimate van der Waals interactions using a simplified protein geometry, and adopt an effective Hamaker coefficient by comparison with the experimental second virial coefficient. This model provides a framework for evaluating how charging pattern probabilities change with increasing concentration, and how they affect liquid-liquid coexistence.