Simulation of Gilbert theory for self-association in sedimentation velocity experiments: a guide to evaluate best fitting models

There is a long tradition in the Biophysics community of using simulations as a means to understand macromolecular behavior in various physicochemical methods. This allows a rigorous means to interpret observations in terms of fundamental principles, including chemical equilibrium, reaction kinetics, transport processes and thermodynamics. Here we simulate data for the Gilbert Theory for self-association, a fundamental analytical ultracentrifuge (AUC) technique to understand the shape of sedimentation velocity reaction boundaries that involve reversible monomer–Nmer interactions. Simulating monomer–dimer through monomer–hexamer systems as a function of concentration about the equilibrium constant allows a visual means to differentiate reaction stoichiometry by determining end points and inflection positions. Including intermediates (eg A₁-A₂-A₃-A₄-A₅-A₆) in the simulations reveals the smoothing of the reaction boundary and the removal of sharp inflections between monomers and polymers. The addition of cooperativity restores sharp boundaries or peaks to the observation and allows more discrimination in the selection of possible fitting models. Thermodynamic nonideality adds additional features when applied across wide ranges of concentration that might be appropriate for high-concentration therapeutic monoclonal antibody (mAb) solutions. This presentation serves as a tutorial for using modern AUC analysis software like SEDANAL for selecting potential fitting models.