Modeling the depletion effect caused by an addition of polymer to monoclonal antibody solutions

We present a theoretical study of colloidal stability of the model mixtures of monoclonal antibody molecules and non-adsorbing (no polymer-protein attraction) polymers. The antibodies are pictured as an assembly of seven hard spheres assuming a Y-like shape. Polymers present in the mixture are modeled as chain-like molecules having from 32 up to 128 monomers represented as hard spheres. We use Wertheim's thermodynamic perturbation theory to construct the two molecular species and to calculate measurable properties. The calculations are performed in the osmotic ensemble. In view that no direct attractive interaction is present in the model Hamiltonian, we only account for the entropic contribution to the phase equilibrium. We calculate chemical potentials and the equation of state for the model mixture to determine the liquid-liquid part of the phase diagram. We investigate how the critical antibody number density depends on the degree of polymerization and the bead size ratio of the polymer and protein components. The model mixture qualitatively correctly predicts some basic features of real systems. The effects of the model 'protein' geometry, that is the difference in results for the flexible Y-shaped protein versus the rigid spherical one, are also examined.